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Smart grid reliability assessment under variable weather conditions
h [electronic resource] /
by Arif Islam.
[Tampa, Fla] :
b University of South Florida,
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Dissertation (Ph.D.)--University of South Florida, 2010.
Includes bibliographical references.
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ABSTRACT: SMART GRID RELIABILITY ASESSMENT UNDER VARIABLE WEATHER CONDITIONS Arif Islam ABSTRACT The needs of contemporary electric utility customers and expectations regarding energy supply require dramatic changes in the way energy is transmitted and delivered. A smart grid is a concept by which the existing and aging electrical grid infrastructure is being upgraded with integration of multiple applications and technologies; such as two way power transfer, two way communication, renewable distributed generation, automated sensors, automated & advanced controls, central control, forecasting system and microgrids. This enables the grid to be more secure, reliable, efficient, self-healing, while reducing greenhouse gases. In addition, it will provide new products & services and fully optimize asset utilization. Also, integration of these innovative technologies to establish a smart grid poses new challenges. There will be need for new tools to assess and predict reliability issues. The goal of this research is both to demonstrate these new electrical system tools and to monitor and analyze the relationship of weather and electrical infrastructure interruptions. This goal will be accomplished by modeling weather and distribution system reliability issues, by developing forecasting tools and finally developing mathematical models for system availability with smart grid functionality. Expected results include the ability to predict and determine the number of interruptions in a defined region; a novel method for calculating a smart grid system's availability; a novel method for normalizing reliability indices; and to determine manpower needs, inventory needs, and fast restoration strategies. The reliability of modern power distribution systems is dependent on many variables such as load capacity, renewable distributed generation, customer base, maintenance, age, and type of equipment. This research effort attempts to study these areas and in the process, has developed novel models and methods to calculate and predict the reliability of a smart grid distribution system. A smart grid system, along with variable weather conditions, poses new challenges to existing grid systems in terms of reliability, grid hardening, and security. The modern grid is comprised of various distributed generation systems. New methods are required to understand and calculate availability of a smart grid system. One such effort is demonstrated in this research. The method that was developed for modeling smart grid dynamic reconfigurations under variable weather conditions combines three modeling techniques: Markov modeling, Boolean Logic Driven Markov Process (BDMP) and the modeling of variable weather condition. This approach has advantages over conventional models because it allows complex dynamic models to be defined, while maintaining its easy readability.
Advisor: Alex Domijan, Ph.D.
Power Distribution System
Reconfiguration for Restoration
x Electrical Engineering
t USF Electronic Theses and Dissertations.
Smart Grid Reliability A ssessment Under Variable Weather Conditions by Arif Islam A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Electrical Engineering College of Engineering University of South Florida Major Professor: Alex ander Domijan, Jr., Ph.D Huseyin Arslan, Ph.D Thomas L. Crisman, Ph.D James R. Mihelcic, Ph.D Stephen E. Saddow, Ph.D Date of Approval: March 26, 2009 Keywords: Power Distribution System, Relia bility Analysis, Reliability Improvement, Microgrid, Reconfiguration for Restoration Copyright 2010, Arif Islam
DEDICATION To my parents Sarwat Pe rveen and Sarwat Islam Brothers Humayun and Asif, Sisters Darakhshan, Kehkashan and Shehla To my wife Yasmeen And to my Lovely daughters Anam & Sanya
ACKNOWLEDGMENT It has been wonderful experience working with my s upervisor Dr. Alex Domijan. We have been together for many years; su ccessfully winning many competitive projects with me being the co-principle investigator. It is this joint effort and constant motivation of Dr. Domijan that today I am able to work towards Ph.D degree. I would like to thank my committee members, Dr. Huseyin Arsla n, Dr. Thomas L. Crisman, Dr. James R. Mihelcic, and Dr. Stephen E. Saddow for thei r generous advice and interest. I would like to pass on my special thanks to Dr. Alek sandar Damnjanovic for his continuous support and direction for helping me complete my research work. I would also like to thank the academic and administrative staff in the Department of Electrical Engineering and the Deans offi ce, where I am a regular with requests to manage various projects. I want to thank the wonderful researchers and professors at the Power Center for Utility Explorations (PCUE). I would like to thank my siblings, who have given me every opportunity to work on my goals of gaining knowledge. I would like to give the hear tiest thanks to my parents who have made countless sacrifices, and show n endless support to make me a successful man. None of this was possible without their endless suppor t. I would like to thank my friends for all their support and advice. Finally I would like to thank my unc onditional supporter and endless motivator; my wife Yasmeen. She is my biggest critic; wanting me to be the be st in my professional and personal life. Yasmeen is always there to motivate me during times of difficulty, when I have spent endless hours designing a nd developing various novel ideas with no view of the end results.
TABLE OF CONTENTS LIST OF TABLES .............................................................................................................vi LIST OF FIGURES ..........................................................................................................vii LIST OF ACRONYMS AND ABBREVIATIONS ..........................................................xi ABSTRACT ......................................................................................................................xii CHAPTER 1: INTRODUCTION .......................................................................................1 1.1 Background of the Study ........................................................................................1 1.2 Objective and Scope of the Research ......................................................................6 1.3 Main Contributions .................................................................................................7 1.4 Outline of Dissertation ............................................................................................8 1.5 Publications Related to this Research .....................................................................9 CHAPTER 2: SMART GRID: A MODERN POWER SYSTEMS .................................11 2.1 The Need to Overhaul Aging Grid Systems .........................................................11 2.2 Modern Power Systems and Smart Grids .............................................................13 2.3 Expectations from Modern Power Systems and Smart Grid ................................17 2.4 Smart Grids Main Methodologie s, Strategies, and Processes.............................18 2.4.1 Advanced Metering Infrastructure (AMI) ...................................................18 2.4.2 Home Area Network and New Products and Services ................................19 2.4.3 Distributed Generation .................................................................................20 2.4.4 Plug-in Hybrid Electric Vehicles (PHEV)...................................................20 2.4.5 Transmission/Substation Automation ..........................................................21 i
2.4.6 Distribution System Enhancements .............................................................21 2.4.7 Central Control Center .................................................................................23 2.4.8 Cyber Security .............................................................................................24 2.4.9 Integration ....................................................................................................25 2.4.10 Integration of Transmission/Substation Intelligence .................................29 CHAPTER 3: SMARTGRID RELI ABILITY AND AVAILABILITY ...........................31 3.1 Introduction to Smart Grid Power Qu ality, Reliability and Availability ..............31 3.1.1 Relationship of Power Quality Reliability, and Availability ......................32 3.2 Power System Reliability, Availability Metrics, and Indices ...............................34 3.2.1 Reliability .....................................................................................................34 3.2.2 Availability ..................................................................................................36 3.2.3 Reliability Indices ........................................................................................36 3.3 Interruption Causes and Modeling ........................................................................37 3.3.1 Equipment Failure ........................................................................................37 18.104.22.168 Transformers .......................................................................................38 22.214.171.124 Underground Cables ...........................................................................40 126.96.36.199 Overhead Lines ...................................................................................41 188.8.131.52 Circuit Breakers ..................................................................................42 3.3.2 Weather Conditions .....................................................................................42 184.108.40.206 Wind ....................................................................................................44 220.127.116.11 Ice Storms ...........................................................................................47 18.104.22.168 Heat Storms .........................................................................................49 22.214.171.124 Rain .....................................................................................................49 ii
126.96.36.199 Lightning Strikes .................................................................................52 188.8.131.52 Temperature ........................................................................................55 3.4 Optimization of Component Modeling .................................................................57 3.4.1 Area Under Study ........................................................................................58 3.4.2 Data Analysis and Processing ......................................................................61 3.4.3 Combined Effects of Modeled Parameters ..................................................65 3.4.4 Design and Risk Assessment for a Predictor ...............................................70 CHAPTER 4: SMART GRID RELIABILITY PARAMETERS AND INDICES ...........77 4.1 Probability Distribution Functions ........................................................................77 4.1.1 Normal Distribution Function ......................................................................79 4.1.2 Exponential Distribution Function ...............................................................79 4.2 Component Reliability Parameters ......................................................................80 4.3 Component Reliability Data .................................................................................81 4.3.1 Overhead and Underground Lines ...............................................................81 4.3.2 Power Transformers .....................................................................................82 4.3.3 Power Generators .........................................................................................82 4.4 Smart Grid Reliability Indices ..............................................................................82 CHAPTER 5: NORMALIZATION OF RELIABILITY INDICES .................................85 5.1 Performance and Reliability Indices.....................................................................85 5.2 Baseline Comparison and Other Methods ............................................................86 5.3 Assumptions and Statistical Tools ........................................................................89 5.4 A Novel Method ...................................................................................................91 5.5 Effectiveness of Results ......................................................................................101 iii
5.6 Assessment and Limitations ...............................................................................105 CHAPTER 6: MODELING METHODS FOR SMART GRIDS ..................................109 6.1 System Modeling and Analysis ..........................................................................110 6.1.1 Markov Modeling of Smart Grid ...............................................................111 6.1.2 Modeling of the Smart Grid with a Boolean Logic Driven Markov Process (BDMP) ...............................................................................................................114 6.1.3 Markov Modeling of Smart Grid Under Variable Weather Condition ......117 7. SMART GRID MODELING AND ANALYSIS ......................................................120 7.1 System with Distributed Generator (DG) ...........................................................121 7.1.1 System with no DG and no Influence of Weather.....................................122 7.1.2 System with no DG and with Normal Weather Conditions .......................124 7.1.3 System with DG and No Influence of Weather .........................................124 7.1.4 System with DG and Alternative Weat her Conditions, Normal and Stormy Weather ...............................................................................................................126 7.2 System with Photovoltaic (PV) and Energy Storage System .............................130 7.2.1 System with no PV and Battery .................................................................132 7.2.2 System with PV and Energy Storage System and no Influence of Weather .............................................................................................................................132 7.2.3 System with PV and Energy Storage System, and Alternative Weather Conditions, Normal and Stormy Weather ...........................................................135 7.3. System with Wind Generato r and Energy Storage System ...............................140 7.3.1 System with no Wind Generator and Energy Storage System (Battery) ...142 7.3.2 System with Wind Generator and no Influence of Weather ......................142 iv
7.3.3 System with Wind Generator and En ergy Storage System, and Alternative Weather Conditions Normal and Stormy Weather .............................................145 CHAPTER 8: DISCUSSION, CONCLUSIONS, AND RECOMMENDATIONS FOR FURTHER RESEARCH ..........................................................................................151 8.1 Discussions and Conclusions ..............................................................................151 8.2 Recommendations for Future Work ....................................................................157 REFERENCES ...............................................................................................................159 APPENDICES ................................................................................................................165 APPENDIX A: DEFINITIONS AND FORMULAE .....................................................166 ABOUT THE AUTHOR ................................................................................................172 v
vi LIST OF TABLES Table 3.1. Weather, Lightning and Interrupt ion (N) Codes and their Expl anations used for Combined Predictor Model ...............................................................60 Table 3.2. P-values by Predictor and by MA  ............................................................67 Table 5.1. Location and Scale Factors ............................................................................101 Table 5.2. Overall Improvements in rho .........................................................................103 Table 5.3. Correlation Magnitude Characterizations......................................................103
LIST OF FIGURES Figure 2.1. Trends for 55 Utilities Providi ng Data Between 2000-2005 (IEEE 2006)  ..................................................................................................................12 Figure 2.2. Smart Grid Technologies and Benefits ...........................................................13 Figure 2.3. Illustrating Renewable SEED S with PHEV Load/Station Center ..................16 Figure 2.4. Top Level View of Inter operability: Smart Grid Systems .............................26 Figure 2.5. Smart Grid Coordination Acro ss Generation, Transmission, and Distribution .....................................................................................................29 Figure 3.1. Availability, Power Quality and Reliability Shown as Subsets of Each Other......................................................................................................34 Figure 3.2. Variation of Average N due to Transformer Failures Versus Maximum Temperature ............................................................................................39 Figure 3 3. Distribution of Interrupt ions by Identifiable Causes......................................43 Figure 3.4. Variation of Mean of N Versus Wind in Dataset being Analyzed .........45 Figure 3.5. Variation of N Versus Wind...........................................................................46 Figure 3.6. Mean of 2 minutes wind speed vs average number of interruptions......47 Figure 3.7. Monthly Mean Distribution of Rain for year 2000 .................................50 Figure 3.8. Monthly Mean Distribution of Rain for Year 2001 ................................50 Figure 3.9. Monthly Mean Distribution of Rain for Year 2002 ................................51 Figure 3.10. Monthly Mean Distribution of Rain for Year 2003 ..............................51 vii
Figure 3.11. Monthly Distribution of LS for year 2000 ............................................53 Figure 3.12. Monthly Distribution of LS for year 2001 ............................................53 Figure 3.13. Monthly Distribution of LS for Year 2002 ...........................................54 Figure 3.14. Monthly Distribution of LS for Year 2003 ...........................................54 Figure 3.15. Variation of Mean N Vers us Average Temperature .............................56 Figure 3.16. Location of Weather Data Recorder.............................................................59 Figure 3.17. Sample List of Key Data(raw) for Modeling a Combined Predictor...........63 Figure 3.18. R2 Values of Modeled Versus Raw Weather Data by MA and by Weather Parameter ..................................................................................66 Figure 3.19. R2 Values of Modeled Vers us Raw Weather Data by MA ..................66 Figure 3.20. Percentage of Occurrences of Average Temperature for Combined Datasets ...................................................................................................68 Figure 3.21. R2 Values of Five Regions...........................................................................71 Figure 3.22. Predictor Value vs Actual N for multiple MAs............................................72 Figure 3.23. Actual and Predicted Numbers of Interruptions...........................................73 Figure 3.24. Neural Network Function Approximation....................................................74 Figure 5.1. Mean of N by Month and Year.......................................................................87 Figure 5.2. Mean of LS by Month and Year.....................................................................87 Figure 5.3. Mean of Rain by Month and Year..................................................................88 Figure 5.4. Confidence Interval s as a Function of n and ...............................................91 Figure 5.5. Probability Plot of 2MMaxS Data..................................................................95 Figure 5.6. Histogram of 2003 Sta ndardized 2MMaxS Data...........................................97 Figure 5.7. Histogram of 2003 2MMaxS Data Standa rdized with 2002 Location viii
and Scale Factors............................................................................................97 Figure 5.8. Histogram of Rain.........................................................................................98 Figure 5.9. Histogram of LS............................................................................................98 Figure 5.10. Pre and Post Adjustment by MA for 4 Years Daily N with 95% Confidence Intervals.....................................................................................101 Figure 5.11. Pre and Post Adjustment by MA for 4 Years Daily CI with 95% Confidence Intervals.....................................................................................102 Figure 5.12. Pre and Post Adjustment by MA for 4 Years Daily CMI with 95% Confidence Intervals.....................................................................................102 Figure 5.13. Pre and Post Adjustment by MA for SAIFI for 46 months with 95% Confidence Intervals.....................................................................................104 Figure 6.1. BDMP with one Trigger ...............................................................................116 Figure 6.2. Standby System ............................................................................................116 Figure 6.3. BDMP Representation of the System in Figure 6.2 .....................................116 Figure 6.4. Markov model representation of the system in Figure 6.2 State Space Diagram ......................................................................................................117 Figure 6.5. Single Unit State Space Diagram .................................................................118 Figure 7.1. Smart Grid Single Line Diagram ..................................................................120 Figure 7.2. System with Distribution Ge nerator (DG) Single Line Diagram .................122 Figure 7.3. State Space Diagram for Sy stem with no DG no Weather Conditions ........123 Figure 7.4. State Space Diagram for Sy stem with DG No Weather Conditions ............125 Figure 7.5. State Space Diagram for Syst em with DG and Alternative Weather Conditions, Normal, and Stormy Weather ....................................................128 ix
Figure 7.6. System with PV and Energy Stor age System (B), Single Line Diagram .....132 Figure 7.7. State Space Diagram for System with PV and Energy Storage System No Weather Conditions ......................................................................................133 Figure 7.8. State Space Diagram for System with PV and Energy Storage System and Alternative Weather Conditions, Normal, and Stormy Weather ...........137 Figure 7.9. System with Wind Generator (Wg) a nd Energy Storage System (B), Single Line Diagram .....................................................................................142 Figure 7.10. State Space Diagram for System with Wg and Energy Storage System no Weather Conditions .................................................................................143 Figure 7.11. State Space Diagram for System with PV and Energy Storage System and Alternative Weather Conditions, Normal, and Stormy Weather ...........147 x
xi LIST OF ACRONYMS AND ABBREVIATIONS AESSadvance energy storage system AMI-advanced metering infrastructure AMR-automated meter reading AMS-advanced metering system ASOS-Automated Surface Observation Stations BDMPBoolean Logic Driven Markov Process CA-Control Area CAIDI-Customer Average Interruption Duration Index CBL-customer baseline load CHP-combined heat and power CIP-critical infrastructure protection CI Confidence Interval CPP-critical peak pricing CPUC-California Public Utilities Commission CMI Customer Minutes Interrupted EPRIElectric Power Research Corporation EPDIRAC Electric Power Di stribution Risk Assessment Calc ulator (A patent product of USF) MAManagement Area (geographic region) NNumber of interruption SAIFI-Systems Average Inte rruption Frequency Index SAIDISystem Average In terruption Duration Index SEEDSSustainable Electrical Energy Delivery System NISTNational Institute of Standards and Technology
SMART GRID RELIABILITY ASESSMENT UNDER VARIABLE WEATHER CONDITIONS Arif Islam ABSTRACT The needs of contemporary electric utility cu stomers and expectations regarding energy supply require dramatic changes in the way energy is transmitted and delivered. A smart grid is a concept by which the existing and agi ng electrical grid infr astructure is being upgraded with integration of multiple appli cations and technologies; such as two way power transfer, two way communication, rene wable distributed generation, automated sensors, automated & advanced controls, central control, forecasting system and microgrids. This enables the grid to be more secure, reliable, efficient, self-healing, while reducing greenhouse gases. In addition, it will provide new products & services and fully optimize asset utilization. Also, integration of these innovative technol ogies to establish a smart grid poses new challenges. There will be need for new tools to assess and predict reliability issues. The goal of this research is both to demonstrate these new electrical system tools and to monitor and analyze the relationship of weat her and electrical infrastructu re interruptions. This goal will be accomplished by modeling weather and distribution system reliability issues, by developing forecasting tools and finally developing mathematical models for system xii
xiii availability with smart grid functionality. E xpected results include the ability to predict and determine the number of interruptions in a defined region; a novel method for calculating a smart grid systems availability; a novel method for normalizing reliability indices; and to determine manpower needs, inventory needs, a nd fast restoration strategies. The reliability of modern power distribut ion systems is dependent on many variables such as load capacity, renewable distributed generation, customer base maintenance, age, and type of equipment. This research effort attempts to study these areas and in the process, has developed novel models and met hods to calculate and predict the reliability of a smart grid distribution system. A smart grid system, along with variable weather conditions, poses new challenges to existing grid systems in terms of reliability, grid hardening, and security. The modern grid is comprised of various distributed generation systems. New methods are required to understand and calculate availa bility of a smart grid system. One such effort is demonstrated in this research. The method that was developed for modeling smart grid dynamic reconfigurations under va riable weather conditi ons combines three modeling techniques: Markov modeling, Boolean Logic Driven Markov Process (BDMP) and the modeling of variable weather condi tion. This approach has advantages over conventional models because it allows complex dynamic models to be defined, while maintaining its easy readability.
1 CHAPTER 1: INTRODUCTION 1.1 Background of the Study A smart grid modernizes electrical tr ansmission and distribution networks to provide customers with dual-dire ction electricity that is secu re, reliable, distributed and has reduced emissions. Smart grids use tw o-way communications, advanced controls, modern sensors, and micro-grids in conjunction with central st ation generation and distributed networking servers/co mputers to improve efficienc y, reliability and safety of power delivery as well as prudent use of energy. Smart Grid is also referred to as Smart Power Grid, Smart Electric Gri d, Intelligrid, and FutureGrid. Electrical power systems include a ne twork of power plants, power lines, substations, distribution lines and consumers. The next generation of power system smart grid will be achieved when a variety of important technolog ies, including smart meters, electronic sensors, electroni c controls, renewable energy sources and energy storage elements are incorporated into one system that will afford automatically correct power supply variability; distribute clean generation an d storage; and maintain system reliability at all times under all conditions. The benefit of a smart grid is that it provides an instantaneously, accurate flow of information, eliminating cumbersome layers of tedious manual decision-making by system operators. Instead, a smart grid automates the complex network of devices that control flow of electricity to work together faster, more
2 efficiently and with a level of precision that is not possible using manually operated systems. The effects of weather, from heat wa ves to hurricanes, on the electrical infrastructure are expected to escalate worl d-wide. Associated power interruptions create economic hardships of several bi llion dollars annually on the state and its citizens, while also posing a significant threat to public safety. The economic impact and threat to public safety will surely escalate as the population in creases, resulting in a steadily increasing demand on electrical infrastructure. Consequently, electrical infrastructure is fragile; as each adverse weather system passes over the st ate, supplying energy and restoring service becomes more difficult. Electrica l infrastructure is considered to be the most complex system ever developed by mankind, and it will take decades to update. An energy plan that incorporates a diversified portfolio of generation sources, from central-station to renewable and distributed, will not become r eality if electrical infrastructure is not appropriately developed in c onjunction with energy supply. Smart grid will allow the current electr icity system to incorporate better renewable energy sources such as wind and so lar power. The benefits of a smart grid include increased efficiency of th e current electrical infrastructure reduced greenhouse gas emissions, and reduced consumer costs. Successfully incorporating renewable electricity sources into existing power transmission and distribution systems requires wide-area deployment of smart grid technology. The goal of a smart grid system will be to optimize supply and delivery of electrical en ergy, minimize losses, self heal, enable maximum use of renewable energy resour ces and substantially increase energy efficiency.
3 It will also improve penetration of renewable distributed gene ration into the grid system since it has a faster response to inte rmittent power and keeps electricity supply in absolute balance with consumer demand at a ll times. As a result, far less storage capacity will be required to keep the power system from failing. In addition, a smart grid can protect users when renewable sources are not operating at optimal generation. It also will enable each transmission and distribution line to carry much more electricity without risk of overloads and blackouts during high generation periods. Finally, a smart grid will enable consumers to control the cost and qual ity of their electricity service better with absolute convenience. Smart grid engineering is divided into planning and design stages. The planning stage is to identify system needs and limitations, propose projects, resolve issues and obtain project approvals. Th e design stage takes a projec t from concept to final realization. Smart grid tec hnologies are expected to ch ange fundamental design and operating requirements of the electric power system. The primary engineering tools for Smart grid analysis and design are power flow and fault-current st udies. A power flow analysis computes steady stat e voltages and currents of th e systems, ensuring that the system will meet criteria of equipment loading, voltage drops and system losses. While power flow modeling can predic t electrical properties of the smart grid, reliability modeling predicts the systems availability and interruption. Reiterating, a smart grid will allow current power electrical systems to incorporate better rene wable energy sources such as wind and solar power, back-up di stribution generators and energy storage systems.
4 Dependability of the smart grid is one of the most important areas of reliability theory application. Random failures are certai n to occur from time to time, especially when weather extremes or other causes pres ent hazards that the power system was not designed to withstand. Reliability methods provi de important analytical tools that can be used to evaluate and compare smart grid de sign and performance. Each component has its unique characteristic. Models should be as simple as possible, but they need to represent all features critical to system reliability. Re liability parameters vary from component to component or from situation to situation. Co mponent reliability data are one of the most important parameters of smart grid reliability assessment. Smart grid reliability information is based on historical utility data and manufacturer test data, as well as technical conferences and peer reviewed literature such as IEEE, International Journal of Power and Energy Systems and Cigre .Electrica l equipment reliability data usually are obtained from surveys of individual industria l equipment failure re ports. Collection of reliability data are a continual process; data is constantly updated. Reliability of power distribution systems is dependent on many variables such as load capacity, customer base and maintenance, as well as age and type of equipment. However, the variable most often responsible for degraded reliability is weather, and common weather conditions often are overlooked in re liability analyses. These conditions include, but are not limited t o, rain, wind, temperature, lightning, humidity, barometric pressure, snow and ice. During an interruption, customers within a community are able to intentionally island, thus reconfiguring total loads to only critical loads wh ile meeting critical loads by managing renewable energy sources and the en ergy storage system. One objective of this
5 study is to evaluate reliability improvement associated with this optimal structure of the power system. Enhancement in reliability wi ll be quantified in terms of proposed new reliability indices that are pertinent to co mmercial-residential communities that contain renewable energy systems along wi th energy storage systems. Common weather does not incl ude catastrophic events such as hurricanes or tornados which exceed reasonable design or operational limits of the electric power system , and for which there are methods in place, or being studied, to define major reliability events, including weather events, and excluding the consequent interruptions from the calculation of relia bility indices [2, 3, 4]. Much of the focus of modeling the e ffects of weather on power distribution systems has remained fixated on extreme w eather conditions [5, 6, 7]. A body of work including weather as a factor in the analysis of specific fault causes also exists [8-13]. However, models that use the combined eff ects of common weather conditions to predict the total number of daily or by-shift in terruptions are presen tly not available. There is a need for methods that can pr edict daily or by shift power distribution system interruptions based on common weat her conditions, and for interruption risk assessment based on immediate weather cond itions. A related method of normalizing reliability indices for common weather conditions also is needed to improve reliability assessments of power distribution systems. Dynamic reconfigurations of the smart grid and variable weather conditions create difficulties in reliability modeling and analysis. To overcome these obstacle, a method combining three modeling techniques has been developed. The techniques include: Markov modeling, Boolean Logic Driven Markov Process (BDMP) and Modeling of
6 variable weather conditions. This mode ling approach enjoys advantages over conventional models because it allows complex dynamic models to be defined while remaining easily readable. 1.2 Objective and Scope of the Research Reliability analysis is stochastic a nd predictive in natu re. The goal of a distribution system reliability tool must be to provide consistent, accurate comparisons between competing design options. In this effo rt, conduct unique research to find out the effects of smart grid infrastructure and variab le weather conditions ov er the reliability of a smart grid. A mathematical concept/tool w ould be utilized to scientifically obtain results and develop conclusions and recommendations for future work. The research has importance because, at present, worldwid e investments are taking place both to modernize grids and to bring smart grid t echnologies to grids hoping that there will be improvement in reliability in te rms of failures of the system. The main objective of this research is to develop models and methods for smart grid reliability assessment under variab le weather conditions Applying different reliability modeling techniques and approaches to solve the present obstacles for smart grid reliability modeling and calculations: Based on common weather conditions, a theo retical model can be used for the prediction of power distribution interrupti ons and for interruption risk assessment based on immediate weather conditions. Using daily and hourly weather data, these models will be used to predict the number of daily or by shift interruptions and to normalize the reliability indices for weather.
7 The method for normalizing reliability indices for common weather conditions has been developed. Power companies are constantly striving to improve their reliability performance and one method commonly used to identify changes in performance is a comparison of present pe rformance with past performance. Such methods are often not accurate due to changing weather conditions which can skew the figures used for comparison. The present method diminishes the impact of common weather conditions and makes comparisons that allow for a more accurate determination of reliability performance. Model dynamic reconfigurations of th e smart grid under variable weather condition combining modeling technique s: Markov modeling, Boolean Logic Driven Markov Process (BDMP) and Mode ling of variable weather condition. 1.3 Main Contributions The main contributions made by this research are the development and application of original mode ls and methods for reliability assessments of smart grids under variable weather conditions: Method for modeling smart grid dynamic rec onfigurations under variable weather conditions combining the aforementione d three modeling techniques( Markov modeling, Boolean Logic Driven Markov Process (BDMP) and the modeling of variable weather conditions). Developed a method of predicting power distribution interruptions in a given region based on common weather cond itions and assessing the risk of interruptions on immediate weather conditions. Using daily and hourly weather data, the method predicts the number of daily or by shift interruptions.
8 Developed is the method for normalizing reliability indices for common weather conditions. The methods commonly used ar e based on changes and comparison of present and past performance. The deve loped method diminishes the impact of variable weather conditions and makes comparisons that allow for a more accurate determination of reliability performance. The predictor method that will reduce th e downtime of power interruptions by proper distribution of the service work force is developed. The model offers an economical tool with negligible maintena nce costs to utilitie s, and improves its Systems Average Interruption Frequency Index (SAIFI) while increasing its power transmission. The research improves reliability assessments by using hourly (or half-hourly) weather data, and reorganizing the in terruption data that are reported by substations into datasets that are geographically centered on ASOSs. 1.4 Outline of Dissertation This dissertation is divided into eight chapters. Chapte r 1 is the introduction and explanation of the study objecti ve. Chapter 2 is an introduct ion to the smart grid. This chapter introduces the important technologies being brought to electricity grid infrastructure to improve efficiency and reliability. Since modernization of the electrical grid is taking plac e as this document is writte n, the studies don e over such a novel system are still unique. Chapter 3 documents in detail the research effort to model various weather parameters affecting the reliability of mode rn distributed systems. It provides the design of the models on which the predic tor will predic t the number of interruptions (N) in an area. It starts with the modeling of effects of individual weather
9 parameters, then slowly builds the combined effect model. Chapter 4 introduces typical tools used in smart grid reliability eval uation: Probability Distribution Functions, Component Reliability Parameters, Component Reliability Data, and Smart Grid Reliability Indices. Chapter 5 develops and documents a novel method to normalize reliability indices for common weather c onditions. Chapter 6 is a brief introduction modeling methods of smart grid and the mode ling techniques used in this research. Chapter 7 is a practical application of the proposed method on different smart grid configurations including: syst em with a distribution generato r, system with a photovoltaic source and energy storage, system with wind generator and energy storage under variable weather conditions. Chapter 8 draws conclusions and proposes future research efforts. 1.5 Publications Related to this Research The following section provides a list of publications submitted, published and presentations made related to the topic of research: Electric Power Distribution System Relia bility Modeling and Risk Assessment, A. Islam, A. Domijan Jr., W.S. W ilcox, IEEE Transactions on Power Delivery, 2010 Statistical Normalization of Relia bility Indices for Common Weather Conditions, A. Islam, A. Domijan, W. S. Wilcox, IEEE Transactions on Power Systems, 2010 Reliability Evaluation Method for a Dynami c Smart Grid System, A. Islam, A. Domijan, Jr., A. Damnjanovic, Internationa l Journal of Power & Energy Systems, 2010
10 Smart Grid Reliability Assessment, A. Islam, A. Damnjanovic, A. Domijan, Jr., PES conference, International Associ ation of Science and Technology for Development (IASTED), 2010 Price Responsive customer screening using load curve with inverted price tier, A. Domijan Jr., A. Islam., M. Islam, A. Miranda, A. Omole, H. Algarra, TECO load research and forecasting team, In ternational Journal of Power & Energy Systems, 2010 Weather & Reliability, A. Islam, A. Domijan, Jr., 2007 PES General Meeting, IEEE Power Engineering Society. Modeling the Effect of Weather Parameters on Power Distribution Interruptions, A. Domijan, Jr., A. Isla m, W.S. Wilcox, R.K. Matavalam, J.R. Diaz, L. Davis, and J. D'Agostini, presented & published(ISBN 0-88986-449-7) at the 7th IASTED Int. Conf. Power and Energy Systems, Clearwater Beach, Fl, USA, Nov. 2004 Panelist for Electricity Grid Infrastr ucture ResearchCurrent and Future Developments at 2007 IEEE PES conference Tampa FL USA Paper presentation at 2007 IEEE PES conference Tampa FL USA Chaired a session SESSION 11 Power System Control And Operations, Chairs: A. Islam (USA) and M. Palorant a (Finland) at 7th IASTED Int. Conf. Power and Energy Systems, Clearwate r Beach, l, USA, Nov. 2004 Posters at UF & USF
11 CHAPTER 2: SMART GRID: MODERN POWER SYSTEMS In order to meet contemporary needs of c onsumers, changes have to be made in production, distribution, and consum ption of electricity. The util ity industry is one of the largest industrial sect ors in the field of technology. In the United Sates, it has a combined asset exceeding trillions of dollars. There are more than 3,273 utilities in the United States, providing electricity to over 131 million customers . The primary goal of these utilities is to provide reliable and effi cient electricity to consumers. Even with the highest quality of utility services, direct and indirect losses attributed to power interruptions are tremendous. 2.1 The Need to Overhaul Aging Grid Systems The national cost of power interruptions is approximately 80 billion dollars annually . In the last 40 years, hundreds of blackouts have occurred in the United States, with the majority occurring in the la st 15 years. The main cause of such massive failures is attributed to the use of ar chaic mechanical systems, which cannot accommodate modern heavy demands for power. Moreover, by improving the efficiency of the grid by a mere 5%, emissions can be reduced by an amount that equates to taking 53 million cars off the road . Reliability indices such as System Average Interruption Frequency Index (SAIFI), System Averag e Interruption Duration Index(SAIDI) and Cumulative Average Interruption Duration Inde x(CAIDI) have all increased in the last decade. SAIDI has increased by more than 20% for the 55 utilities that data were made available to from the department of energy, as shown in figure 2.1.
Figure 2.1. Trends for 55 Utilities Providing Data Between 2000-2005 (IEEE 2006)  In order to respond to increasing demand for electricity and harmful effects of greenhouse gases, the current grid system n eeds to be upgraded. Funding is crucial in implementing such large scale changes in the grid system. The power industry is very significant in the United States economy. It is one of the largest and most capitalintensive sectors in the U.S. economy, 60% of which is invest ed in power plants, 30% in distribution facilities, and 10% in transmission facilities. In order to maintain Americas global competitiveness, electric power needs to be reliable. In the past 4 or 5 decades, no significant changes occurred in overall infrastructure of the transmission and distri bution system of electr icity. Recently, the US government started developing various program s. The goals of these programs are to provide everyone access to abundant, affordable, clean, efficient, and reliable electric power anytime and anywhere. 12
2.2 Modern Power Systems and Smart Grids Smart grid is a modern electrical tran smission and distribution network system that provides customers secure and reliable elec tricity. The advantages of smart grids are: two-way communications, advanced controls, mode rn sensors, micro-grids, and central station generation, which improve the efficiency reliability, and safety of power delivery. Smart grid is also referred to as "Smart Po wer Grid," "Smart Electri c Grid," "Intelligrid," "FutureGrid," and FRIENDS (Flexible Reliab le Intelligent Energy Delivery System). Figure 2.2. Smart Grid Technologies and Benefits The smart grid is an integration of many technologies that modernize the electrical grid infrastructure. Major ar eas and technologies are Advanced Metering 13
14 Infrastructure, distributed re newable generation, predictive a nd central control (diagnostic center), demand side management and bi-dir ectional flow of energy. Modernization of power systems can be achieved by integration of renewable and othe r distributed energy generation systems. This results in adva nced sensors, communication and control technologies, monitoring, diagnostic a nd automation capabilities, and two-way communication between the utility and electric loads. Benefits of such implementations are that these technologies provide improved grid reliability & efficiency, increased security and power quality, reduce restora tion time, new products and services to customers, optimization of asset utilization, and improved energy security. In a situation where there is an outage at the feeder level, the full capability of the grid can be utilized by integration of Distribute d Generation (DG) in a smart grid, Demand Response, VAR control, and Distribution Auto mation. Other key benefits include achieving increased customer reliability under system continge ncies and outage conditions without additional feeder construction, and demonstrating th e opportunity to revolutionize distribution systems globally through the in tegration of technologies. The distribution system is expected to be flexible and responsive to syst em contingencies, such as peak loading due to weather, loss of generation capacity, e quipment failures, and natural disasters. Utilities have excess power generating cap abilities during off-peak hours when consumers are utilizing less energy. Two sites were developed in St. Petersburg, Florida to test the modern storage systems with live connectivity to the grid and power generation via solar panels. The site is called SEEDS (Sustainable Electric Energy Delivery Systems). The renewable SEEDS project uses excess energy to charge a 5KW Advanced Energy Storage System (AESS). AESS is a battery system with modern communication
15 features and grants users cont rol over the rate of charging a nd discharging, which allows storage of energy for future use. It is expect ed that car users would charge their PHEV at off peak times for the grid. This would require additional informational flow to electric consumers about OFF and ON peak demand times and duration. The Renewable SEEDS project has soluti ons for these issues. The Renewable SEEDS site(s) can act as modern power stations to charge PHEV anytime. The site uses the excess off peak energy to charge alrea dy installed 5 KW AESS. In addition, during peak daytime hours, there is a 2KW solar panel (possible expansion to 5KW) which charges the battery. The excess energy will then be stored for future use for PHEVs. The results of SEEDS demonstrated that the p eak load shaving is possible by storing the intermittent renewable energy into AESS and de livering it at the peak power requirement, which is typically in the afternoon for the summ er and early morning in the winters in the south Florida region.
Figure 2.3. Illustrating Renewable SEED S with PHEV Load/Station Center With introduction of distributed generati ons and two way power flow; complexity of the systems involved increases enormousl y. Methods to assess reliability and have some kind of predictive system are necessa ry. The smart grid has the capability to respond to these issues. The unpredictabili ty of the system can be improved by implementing a predictive system across the elec trical distribution sy stem. Smart grid can improve reliability, predict interrupti ons, reduce down times, maximize resource management, and assist in self-healing of th e network. Submitted in this document is a novel model (patent of USF) th at implements this system. Effects of weather (e.g. rain, heat waves, hurricanes) on the electrical infrastructure are expected to escalate globally. Power interruptions are economic 16
17 hardships that cost several bi llion dollars annually. The current electrical infrastructure does not have the capacity to control the effects of power interruptions. 2.3 Expectations from Modern Power Systems and Smart Grid Despite the large amount of time spent in selecting various te chnologies for smart grids, the main goal of providing wealth to customers and investors should not be neglected. Continuous updates and feedback from customers are necessary. The main point is that the utility indus try is full of experts who know instruments and products, but the consumer angle is often lost. Understand ing customers needs and requirements is important to appreciate efforts put into implementing a complex system such as the smart grid. An important challenge for the utility i ndustry is to endure declining growth. The utility industry is high in capital investmen t; thus, opportunities for grid electrification need to be maximized. With advent of mode rn PHEVs (Plug in Hybrid Electric Vehicle), opportunities are present to deve lop interfacing and b illing systems that charge PHEV at every home in the country. Another interesting opportunity is to develop modern/smart appliances for modern grid system. Expectations from smart grid are to: Provide new products, services, and markets. Optimize asset utilization and operate efficiently. Predict and respond to system disturbances (self-heal) Be rugged against man-made and natural disasters. Address modern customer expectations. Involve active participation from the customer.
18 Make available bi-directiona l, reliable, and environmentally friendly power for needs of the 21st century (nano/digital economy). Involve all generation, transmission, distribution, and storage options. The challenges associated with these expectations are: One of the main results expected from smart grid implementation is the fulfillment of modern day customer needs, which is to maximize stakeholders wealth. Focus was initially not on customers due to hardware and technology concerns in initial stages of system implementation. Trend of declining growth, maximizes opportunities of grid electrifications. Develop modern/smart appliances for modern grid system: the last mile solutions 2.4 Smart Grids Main Methodologie s, Strategies, and Processes Smart grid is an integration of mu ltiple technologies, methodologies, and processes, layered and combined together to provide efficien t, reliable, secure power and user friendly interface to consumers. Smart grid technologies can be divided into major areas: Advanced Metering Infrastructure, Home Area Network, Distributed Generation, Plug-in Hybrid Electric Vehicles, Tran smission/Substation Distribution System Enhancements, Central Control Center, and Cyber Security. Following section provides an overview of these technologies. 2.4.1 Advanced Metering Infrastructure (AMI) The overall objective of Advanced Meteri ng Initiative is to provide a foundational communication platform that is robust, reliable, and secure. This platform can then be utilized to provide full 2-wa y communications to field devices including meters, devices
19 in customers homes, distribution system asse ts, and other applications . Deployment of AMI in service territory focuses on colle cting and providing data for every meter in the service area. AMI deployment includes f oundational meter deployment and aspects to fully test the inclusion of in-home devices AMI will create a base platform through a replicable model that demonstrates and quan tifies benefits of smart grid deployment. With AMI in place, there will be quantifiabl e results of its impact on consumer energy usage and conservation. Included are: new rate and pricing opti ons, utility system reliability and power quality, optimization of asset utilization and operating efficiencies, system disturbances and the ability for se lf-healing, and resilience against physical and cyber attacks. Installation of AMI is the firs t step required to enable other aspects of smart grids to be fulfilled. 2.4.2 Home Area Network and New Products and Services The Home Area Network (HAN) provides cust omers with tools, technologies, and billing rates in the conservation effort of energy consumption [19, 20]. Until now, energy is consumed before the customer knows what the total monthly ch arges are. Advance notice of expected energy consumption and possible cost empowers customers to make informed decisions and actions regarding their energy usage at own home. Various demand side management concepts are attempte d to harness the benefits of smart grid technology . This will drive significant ec onomic benefits to all customers through decreased energy bills. A parallel effort is ongoing to develop home appliances and other items that can easily communicate with AMI meters. This would enable control of such appliances from remote locations, and al ong with the help of advance communication setups, consumers will have better control over energy expenditure.
20 2.4.3 Distributed Generation The past decade has seen an enormous increase in the num ber of distributed generation resources. Most of these resource s work in isolation and have no or very limited connectivity with the electric grid. With advent of smart grid technologies, these distributed resources can be brought onto the grid, thus reduc ing capital investment to build more power plants and avoiding creati on of more green house ga ses. Integration of distributed generation technology onto the grid [22, 23] will enable renewable generation to interact with the electric grid, specifically for power ge neration, power quality, reliability, and customer interaction. This also helps quantif y environmental benefits of renewable energy generators. Re newable generation will create and support more jobs in the green technology field. This area analyzes the following: Advanced grid planning and operations n eeded for large-scale integration of distributed renewable systems in to the distribution system. Impact of high-penetration renewable ge neration such as photovoltaics on the utility grid. Voltage regulation issues caused by the in terconnection of various penetration levels of renewable generati on on the distribution system. Energy storage (batteries) and controls systems. 2.4.4 Plug-in Hybrid Electric Vehicles (PHEV) PHEV provides tremendous benefits in reducing carbon emissions, since power plants are relatively more efficient than individual cars working on mechanical engines. Technologies are ready for implementations wherein the consum er can charge the electric vehicle at home. Various efforts are ongoing to establish stations for charging
21 such vehicles . The SEEDS project (described earlier in this chapter) is one such projects where the PHEV vehicle can be ch arged at higher speed if it is capable of accepting a higher rate of current. This reduc es charging time. Implementation of PHEV technology provides another means of servi ce from the utility to its consumers. 2.4.5 Transmission/Substation Automation Implementation of the Smart Grid Reliability System will provide better utilization and reliability of the overall electric grid, w ith reduction of greenhouse gas emissions and an increase in system capacity. By installing field monitoring instrumentation devices to gather real-tim e telemetry information , the following benefits can be provided: Reduce duration of customer service in terruptions through accurate outage detection and feeder automation. Prevent future outages by performing predictive reliability analysis. Reduce system losses, thereby reduci ng energy use and carbon emissions. Increase agility to manage grid load across Transmission and Generation, and more effectively optimize system capacity. Support integration of local storage, distributed ge neration, and hybrid electric vehicles. Effectively dispatch power generation resources based on optimal combination of cost, emissions, fuel, and other future environmental constraints. 2.4.6 Distribution System Enhancements The system will benefit from the comm unications infrastructure of AMI [5 enhancing power] and also by inclusion of self-healing automation and remote
22 monitoring of the distribution components. These improvements will enhance daily operations of grids including reliability of el ectric services. This is accomplished through the following installations: Automated Feeder Switches (AFS), which ha ve capability to work in coordination with the feeder breaker to detect faul ts on the distribution system, isolate the faulted section, and restore servi ce to unaffected line sections. Two-Way Capacitor Controls on feeders to work in coordination with existing Distribution Management System (DMS ) to optimize reactive power of the system. This will reduce energy losses on the distribution system. Today, most grids utilize a one-way radio system to issue control commands to pole-top capacitor banks. Confirmation cannot be ma de if the control has been executed. This often requires multiple control comm ands being issued to a capacitor bank. This causes delays in achieving the desi red level of reactiv e power. Implementing the two-way communications will provide confirmation of control commands that are executed. Monitoring equipment on automatic Thr ow-over switches to communicate status to operators in Distribution Control Center. This will identify any switches that have not operated properly so a field technician can be dispatched quicker to restore service. Voltage and current sensors on distributi on feeders that can provide real-time inputs to enhance power-flow analysis performed by DM S and to provide inputs to predictive models. This will improve operation network analysis functions,
23 utilized for performing switching on the di stribution system to prevent overloaded equipment conditions as we ll as optimizing voltage. Remote fault indicators at strategic loca tions on distribution feeders that can be used in conjunction with fault locating cap abilities of DMS to detect the location of faults in the distribution system. This will enable faster restoration for sustained interruptions and assist in investigation of momentary interruptions. 2.4.7 Central Control Center The intent of the Smart Grid Reliability System is to design and deploy an advanced Central Controls center, which includes an investment in a modernized Energy Management System and Intelligent Electr onic Devices (IEDs) to achieve maximum value from smart grid telemetry [27,28]. This system creates a predictive overall view of generation, transmission, distribution, and customer device data to improve grid performance, increase reliability, and redu ce outage restoration times. In addition to driving efficiencies, it will provide the capability to mode l impacts of hybrid electric vehicles and distributed renewables such as wind and rooftop solar. Prudent investments in measurement devices and system analytics will support regulatory requirements, drive increased system reliability, and meet critical cyber security mandate s. Implementation of the enterprise wide Smart Grid Central Controls Center includes: Develop an Enterprise Wide Smart Grid Central Controls Cent er to incorporate data from Customer, Distribution, Tran smission, and Generation systems for a more comprehensive visualization of grid functions.
24 Develop advanced applications and analytics to provide a predictive overall view of data to improve grid performance, increase reliability, and reduce outage restoration times. Manage reliability and risk profile of energy delivery across the enterprise. Better utilization and reliability to the overall electric grid, reduction in greenhouse gas emissions, and increased system capacity are the anticipated benefits of the Smart Grid Reliability System. By instal ling field monitoring instrumentation devices to gather real-time telemetry information, the system will be able to provide the following benefits: Reduce duration of customer service in terruptions through accurate outage detection and feeder automation. Ability to prevent future outages by performing predictive reliability analyses. Reduce system losses, thereby reduci ng energy use and carbon emissions. Increase agility to manage grid load across Transmission and Generation, which more effectively optimizes system capacity. Support integration of local storage, distributed ge neration, and hybrid electric vehicles. Effective dispatch of power genera tion resources based on the optimal combination of cost, emissions, fuel, and other future environmental constraints. 2.4.8 Cyber Security Cyber security is a critical component in implementation of smart grids because grids that have been working in isola tion will become connected to modern communication systems, including wireless networks. This makes the system prone to
25 cyber attacks . Cyber security is a vast research area in itself; the topic will not be discussed further because it is not the focus of this research. 2.4.9 Integration One of the biggest challenges faced by the power engineering community is how to integrate all these technologies so that interoperability is established as per expectations . One of the biggest efforts in interopera bility has been done by the team of EPRI/NIST (Electric Power Research In stitute/National Institute of Standards and Technology). Interoperability Framework is emerging as a norm for key devices and systems . This clearly defines interface points among business domains, systems, and smart grid components. The following is a subset of a high level view based on EPRI/NIST suggested standards.(figure 2.4). A similar effort is also promoted by GridWise Architectural Council Interoperability Framework.
Figure 2.4. Top Level View of Inter operability: Smart Grid Systems In figure 2.4, the transmission level upgrad es required for the existing grid to transform into a smart grid are: Phasor M easurement Units (PMU), digital disturbance recorders, Intelligen t Electronic Devices(IED) and mi croprocessor based protection. At 26
27 the distribution level, automated feeder sw itches, remote fault indicators, two-way protections systems with AMI are the sele ct few items required. At the load side (customer), smart (AMI) meters with Ho me Area Network(HAN), renewable resources with DSM options are a few of the technologies needed in the implementation of a smart grid. The benefits of smart gr id technology can be achieved if interoperability has been established in proper way. For example, AMI da ta will be used as follows to provide services in day-day operation: Since meters are on an AMI network, the re sponse to any failure can be in micro or milliseconds. If power is lost due to failure, AMI meter can send a signal to the Outage Management System (OMS). Af ter analysis, the OMS can decipher whether a repair service is required or if the fault will be cleared on its own (e.g. Failure of some load item like a refrigerator, TV etc.). To take care of such failure, there would not be any need for a call from the customer, and an automatic service routine will be trigge red on receiving the signal from the AMI meter. Another scenario is when a customer calls because of an electricity outage in the house. The Distribution and outage manage ment system will automatically know (from the AMI meter at customer premis es) whether energy is available at the customers doorsteps or not. Hence, many such failures can be resolved immediately rather than waiting for a serv ice engineer to make a visit to the customer location. This will enable customers to easily acquire information regarding the nature of the ma lfunctions of their electricity.
28 Similarly, if a repair has been recently completed, the AMI meter can verify automatically whether the service is restored or not. Furthermore, the AMI meter working in a network can confirm immediately whether power has failed in the region. This region can also be identified with help of Geographic information sy stem (GIS) linked to AMI meters. Customer loading data will be improved dramatically through hourly usage data from AMI. Present day customer loads are determined by algorithms that have been present for many years. It is also determined by an estimated peak load for a customer based on the monthly reading. Load profiles are estimations based on customer type, season, and day. Using (est imated) diversity factors, data are aggregated to estimate transformer loading
2.4.10 Integration of Transmission/Substation Intelligence Figure 2.5 Smart Grid Coordination Across Gene ration, Transmission, and Distribution Many power plants have already gain ed knowledge regarding the use of technology in monitoring critical equipment, while proactively performing preventative maintenance in order to extend asset life a nd improve reliability. This existing experience with central control tools, and proven su ccess allow leverage for central control applications to improve Transmission and Di stributions Grids st rengths [32 35]. In figure 2.5, the smart grid coordination picture is depicted. This concept would enable transmission and substation intelligence to operate in such a fashion that the auto load 29
30 management, feeder control, monitoring of e quipment remotely and self healing concepts can be implemented. This integration of multiple technologie s to establish a smart grid poses new challenges as well [36-38]. There will be need of new tools to assess and predict reliability issues. The goal of this research is the development of new electrical system tools to monitor and analyze the relationshi p of weather and elect rical infrastructure interruptions. The goal will be accomplished by modeling weather & distribution system reliability issues, developing forecasting tools and by developing mathematical models for the availability of the system with sm art grid functionality. The expected results include the ability to predict and determin e the number of interruptions in a defined region; a novel method for cal culating smart grid systems availability; a novel method for normalizing reliability indices; and to determine manpower needs, inventory needs, and fast restoration strategies. In the following chapter, we will address the modeling of weather and distribution system reliability, and the formation of a novel predictor will be displayed
31 CHAPTER 3: SMARTGRID RELI ABILITY AND AVAILABILITY Electric grid infrastructure requires robust and intelligent systems that can respond dynamically to address natural or manmade faults and interruptions. The effects of weather (e.g. strong winds, rain, lightning, cold fronts, snow, etc.) on the electrical infrastructure are expected to increase in the near future. The resulting power interruptions produce economic ha rdships costing more than 80 billion dollars annually. Since the electrical infrastructure is frag ile, every adverse weather system that passes over it presents a threat to the reliability of the power system. In case of a disruption due to weather, it is very difficult to supply energy and restore the system, especially if transmission and distribution li nes are affected. These issues lead to innovation and to the next generation of power systems that must be flexible, reliable, and intelligent. Envisioned in these advances is a revolutionary way of sensing, intelligence gathering, and corrective actions. The goal of this endeavor is to provide near uninterruptible service during severe weather events, and the abil ity to monitor the critical electrical infrastructure in real time. 3.1 Introduction to Smart Grid Power Qu ality, Reliability and Availability The reliability of power di stribution systems is dependent on many variables such as load capacity, customer base, maintenance, age, a nd type of equipment. Nonetheless, the variable most often cited for lowering th e reliability of the system is weather.
32 Contrarily, the prevailing weather conditions ar e often overlooked in reliability analyses. These conditions include, but are not limited to: rain, wind, temperature, lightning density, humidity, barometric pressure, snow, and ice. In order to analyze power system reliab ility with the aspects listed above, it is necessary to have stringent well-defined measurement and comparison methods. This practice is referred to as metr ics . The standards are bei ng adopted; hence, it is wise to address the commonly used defini tions for the metrics and indices. 3.1.1 Relationship of Power Quality, Reliability, and Availability Power quality is a general term; it has various definitions depending on the context in which it is used. For customers, if the load is negative ly affected, there are power quality issues. For utilities, non-comp liance of any parameters such as harmonics can be a power quality issue [ 39]. One of the definitions of power quality is: the absence of deviation from pure sinusoidal voltage. Th is definition makes all reliability issues (including customer interrupti ons) a part of power quality . There are equal numbers of groups which identify power quality and power reliability issues as a subset of each other. The important point from the industry perspective is that the el ectric utilities gets penalized on reliability issues and thus thei r view is to have all aspects(including power quality) as part of reliability study. Customer interruption is if the voltage reaches zero (power not available for certain duration). This is a deviation from a pure sinusoid thus, a power quality issue. In general, it is agreed that power quality is a subset of power reliability; however, the demarcation of boundaries between the two is not so welldefined Interruptions that exist for more than a few minutes are called sustained interruptions and are regarded as a reliability issue. Whereas, interruptions that exists for
33 less than few minutes are known as momentary interruptions, a nd are classified as power quality issues. The reasons are:  Momentary interruptions happen during intentional operating practices. Momentary interruptions do not generate large numbers of outages/ customer complaints. Difficult to measure However, in the modern age, all kind s of interruptions, including momentary interruptions, count as important customer issues and thus, are considered a reliability issue. The third classification is Availability. Availability is defined as the percentage of time a voltage source remains un-interrupted Since availability is defined in terms of interruptions (un-interr uptions), it is considered a subset of reliability. For our purposes, power quality, reliability, and availability are shown in figure 3.1 as a Venn diagram. Availability is a subset of power quality and power quality in turn is a subset of power reliability. In summary, power quality deals with deviation from a pure sinusoidal voltage and/or current waveform. Reliabi lity addresses all kinds of interruptions and availability deals with the probabi lity of being in an interrupted state.
Figure 3.1. Availability, Power Quality and Reli ability Shown as Subsets of Each Other 3.2 Power System Reliability, Avai lability Metrics, and Indices In this section, important definitions and statistical/aggregation formulaes that are required to fully understand power system reliability and availability, will be explained. 3.2.1 Reliability Electric power distribution reliability pr imarily relates to equipment outages and customer interruptions. Under normal operati ng conditions, all equipment is energized 34
35 (except backup/standby) and the electricity is availabl e to all connected customers. Scheduled and unscheduled events create disruptions to normal operations causing outages and interruptions. Some of the key parameters defi nitions are given below : Contingency: An unexpected event, such as a fault or an open circuit; an unscheduled event. Open Circuit: A point in a circuit that in terrupts load current without causing fault current to flow. False tripping of a circuit breaker is an example. Fault: May be defined as a short circuit. It is the breakdown of di electric insulation of the system. If it clears on its own, it is termed as a self-clearing fault. If the fault is cleared by de-energizing and re-energizing the circuit, it is called as temporary fault. If the fault requires manual intervention for re pair, it is termed as a permanent fault. Outage: When a piece of equipment is de-energized either by scheduled or unscheduled event, it is termed as an ou tage. Un-scheduled outages happen due to contingencies. Momentary Interruptions: When a customer is de-energized for less than a few minutes, it is termed a momentary interrup tion. Most of these happen due to closing of automated switches. Momentary Interruptions Event: If multiple momentary events happen during a short duration of time (several minutes), it is counted as one momentary event. Sustained Interruption: A sustained inte rruption occurs when customer is deenergized for more than few minutes. Thes e situations arise from faults and open circuits. Maximum duration of momentary interrupti on varies from utility to utility. Most
36 utilities follow the guidelines set up by th e Public Service Commissions (PSC) in their individual service area states. Generally, it is considered less than 1 minute. IEEE 1366 standards  identify any in terruptions for less than 5 minutes as momentary. This is done to make sure that an automated switch can take care of the fault (if possible), and that the interruption is listed as momentar y. However, most of the automated equipment cannot take care of faults in less than a minut e. Because of this, the reliability indices calculations are more accurate and promot e the use of automation in the industry. 3.2.2 Availability Availability is the probability of someth ing to be energized. It is calculated in percentage or per unit. The complement of availability is un-a vailability. The annual interruption time can be estimated by compar ing the percent availability between 90% and 99.9999999%. By comparing the number of nin es in the % availability, an estimate to the annual interruption time(AIT) can be given. For example, if the availability is 90% (1 nine), the AIT is 36.5 days. At 99% (2 ni nes), AIT drops to 3.7 days, while at 99.9%(3 nines) it drops even further to 8.8hrs. Follo wing this trend (AIT dropping by a factor of 10 with every additional nine), an ava ilability of 99.9999999% have an AIT of 1.9 cycles (60HZ) or 31.67 ms. This being said, if a customer faces 9 hours of outages in a year, the un-availability is = 9/8760 hours which is 0.1%; th e availability is 1000.1 = 99.9%. 3.2.3 Reliability Indices Appendix A provides a list of definitions and formulae for calculations of various short-term and long-term reliab ility indices. The mathematical formulations of various
37 indices are provided with other parameters . Further discussions regarding the calculations of various reliability indices are done in chapter 4 and 5. 3.3 Interruption Causes and Modeling As discussed earlier that the reliability of power dist ribution systems is dependent on many variables such as load capacity, customer base, maintenance, age and type of equipment. Ironically, the variable most respon sible for decreasing reliability is weather, which is often overlooked in reliability analysis. Reiterating that the weather and envi ronmental conditions to be addressed includes, but are not limited to, rain, wind, temperature, lightning density, humidity, barometric pressure, snow, and ice. The mode ls are developed to al low broad application, since these conditions do not occur simultane ously at any one place, and the range of combinations is great. Using the data collected, statistical and deterministic simulations of the models are done by employing existing so ftware; the results will be used to refine the models. In order to validate the models, pow er interruptions will be predicted in areas that can be easily monitored. The following section explains each important cause of power interruption and their respective models are explained. 3.3.1 Equipment Failure Distribution networks have various kinds of equipment installed to make sure that the electricity supplied is safe and secure. When first installed these equipment have a greater chance of failure due to manufacturing defects, inco rrect installation, and damage due to shipping and handling. Equipment already in place (in circuit) for some time, may fail due to extreme electrical conditions su ch as continuous overload, high voltage, and variable weather conditions (including lightning). Furtherm ore, the equipment may also
38 fail due to changes in the chemical composition, aging, and mechanical wear . We will try to address some of these issues and discuss certain models for equipment failures. The rate of equipment failure needs to be modeled for electric utilities to plan, engineer, and operate a system at the highest levels of reliabi lity for the lowest possible price . Some utilities however, have a problem with the type of equipment being used . Most utilities perform regular equipment inspections and have tacit knowledge that relates inspection data to th e risk of equipment failure. One of the methods used to improve the accuracy of the system is by using equipment inspection data to assign relative condition rankings. These rankings are then mapped to a failure rate function based on worst-case units, average units, and best-case units . 184.108.40.206 Transformers The transformer is a key component fo r any distribution network. Reliability issues of transformers can happen in tw o related ways; overloa d and failure . Transformer forms a sort of bottleneck in th e earlier distribution network. If there is a major failure in the transforme r then there can be power in terruptions to thousands of customers. In order to handle such situations other transformers ar e tasked with taking over the entire load or with sharing the inte rrupted load. If no spare transformer capacity is available, a decision is made to overload ot her in-service transformers, resulting in the deterioration of longevity for those transf ormers. This process compromises either improving the current reliability, or increasi ng the probability of future transformer failure. Understanding transformer ratings a nd thermal aging is critical in making the right decision during such a situatio n of reliability risk management.
Transformer ratings depend on the expect ed life of the winding insulation at a specified temperature. Standard transforme r ratings are designed at a 30C ambient temperature while average winding temperat ure rises from 55C or 65C with an additional hot spot rise of 10C or 15C. Often, the life of the transformer is defined as the time required until it deteriorates to 50% of its mechanical strength. This occurs due to a breakdown of insulation because of excess heat . Temperature rise is a key factor for tr ansformer failure. The temperature rise can be either due to the lo ad or due to harsh weather conditions Thus, it is of high interest to look at the impact of the rise in ambient temp erature, and number of power interruptions due to transformer failure. 65 75 85 95 0 10 20 Mean of Max. Temperature (F) Mean of N Y= 202.803 5.09380X + 0.0328080 X**2 S = 2.62145 R-Sq = 42.0 % R-Sq(adj) = 41.8 %Regression Plot of N Vs. Max. Temp Figure 3.2. Variation of Average N due to Transformer Failures Versus Maximum Temperature  The monthly averages (means) of the maximu m temperatures and the monthly means of the total number of interrupt ions due to transformer failu res, for 4 years (1998-2001) of data collected from the South Florida region is shown in figure 3.2. With these 39
conditions, the total number of monthly data points is approximately 567. The legend for figure 3.2 is as follows: PI Prediction Interval limits Regression 95% CI 95% PI CI Confidence Interval limits In the figure 3.2, the two peaks on each side of the graph maybe due to the overloading of transformer at these te mperatures. It appears that around 750F to 800F, the temperatures are in the comfort zone of the human body and thus the need of excess power is not there. There will not be an in crease in transformer failure interruptions because it is an optimal operating te mperature. After Approximately 800F however, the curve increases in an exponentia l way (right-skewed). This i ndicates that the effects of higher temperatures not only cause more inte rruptions, but also are more predominant than those of lower temperatures are; these e ffects are expected in Florida, whose climate is tropical and sunny throughout the year. If we average th e data points , a clear pattern is observed between the variables by suppressing the disturbances/noise in the data set. The important point that should be observed is that as the number of data points decreases, the plot becomes smoot her with the increase of the R2 value. In the variables given in the equation af ter the regression analysis(next to the plots), R2 represents the proportion of variability in the Y variable accounted for by the X variable. Given the maximum temperature of a day, it is therefore possible to predict the total number of interruptions from a transformer for any management area (MA). 220.127.116.11 Underground Cables Underground cables provide better rugge dness and are more effective against many above ground reliability issues. The tradeoffs are long downtimes in case of 40
41 failures and high cost. Major issues with underground cables are electrochemical and water treeing. When the moisture penetrates in presence of an electric field, the dielectric strength of the cable insulation is reduced; this is called treeing [ 39]. Known as treeing, the moisture permeates the extruded dielectrics of the insulation such as cross-linked polythene (XLPE) or ethylene propylene rubber (EPR); th e breakdown patterns resemble a tree . This in turn reduces the voltage withstand capability of the cable. With time, the insulation strength degrades so much that the voltage transients, such as lightning or switching, causes dielectric br eakdown. With an increase in temperature, the moisture absorption also increases; there is a strong co rrelation between ther mal aging and treeing . Water treeing in XLPE cables is a costly reliability issue for utilities. Manufacturers of cables have developed jacket ed and tree retardant cables (TR-XLPE). Cable jackets prevent moisture to seep in. The tree retardant reduces the development of a tree inside the cable after the moisture s eeps in. Treeing is attributed to impurities and imperfections, which enter during the manufact uring process of cables. Quality control over manufacturing and testing of cables before installation largely improves reliability. 18.104.22.168 Overhead Lines Overhead lines reliability issues are mostly caused by external factors such as vegetation, animals, and variable weather, wh ich will all be discussed in detail in the following sections. Bare conducto rs fair better in terms of temperatures and high current capacity. In any case, higher currents do affect reliability and can cause sagging, annealing, and breakdown if a fault current is not cleared fast enough . Overhead lines are installed on poles. Earlier poles we re of wood but recently, the new norm is to
42 replace wood poles with conc rete poles whenever required. This improves physical ruggedness of the infrastructure under extrem e weather conditions. The major reliability issue with poles is its capability to with stand high wind speed. The effects of wind on overhead infrastructure (e.g., poles, lines, pole mounted equipments) are also discussed in the following section. 22.214.171.124 Circuit Breakers Circuit breakers have many components which increase the complexity of the equipment. With so many parts, the failure of circuit breakers can take place in many ways. Failure can be internal ly related to its own functioning. The two major reasons for circuit breakers failures are: (a) open when it should not, and (b) failed in service (cannot operate). These two failure modes constitute 74% of the reasons why failures in circuit breakers occur . 3.3.2 Weather Conditions The reliability of electric power system has remained a challenge for years. The goal is to provide near uninterruptible serv ice during variable weat her events . But due to the ever increasing demand and high ex pectations from customers, sometimes, power outages are simply unavoidable. Mo st power outages are caused by weatherrelated events . Interruption may be defi ned as a loss of service to one or more customers. As stated before, interrupti ons may be caused due to many factors like equipment failures, animals, weather conditio ns (Common), severe weather conditions (extreme wind, tornados, hurricanes, swingi ng, galloping and Aeolian vibration, lightning storms, ice storms, heat storms, earthquakes ,f ire, etc), trees, human factors, and other causes. Extreme weather is rare, but creates multiple faults on the grid that take a longer
lead time to restore power back to the custom ers. The next section talks about the effects of both extreme and common weather conditions. According to figure 3.3, the distribution of identified causes of interruptions for the area being studied shows that weather contributes approximately 10% to the total number of breakdowns/faults (N). However, this document will demonstrate that as much as 50% of the variation from the mean(N) can be accounted for by weather, especially in distribution networks. Figure 3 3. Distribution of Interru ptions by Identifiable Causes The regression models were developed using both raw weather data and weather data that was modeled to refl ect their known effects on N. R2 was chosen as the statistic of interest because the R2 value of the regression result is the percentage of variance of the mean that is accounted for by the equation. 43
44 The following work also shows the anal ysis of, and modeling for, the power distribution system response to variable weather conditions. Included are the average temperature (T), two minute maximum sustained wind speed (S), daily total rainfall (R), and total daily number of lightning strikes (LS). The results show that the modeled equations return a consistently higher R2 value compared to equations that rely on raw weather data. Consequently, accounting for a larger percentage of the variance from the mean number of interruptions experienced daily. 126.96.36.199 Wind As we see changes in the climate, ma ny things are affected including the local weather, which has also shown extremities at many times. Wind plays havoc in the infrastructure if it reaches higher speeds. The study of wind flow is critical to power engineering. System designed wind flow studies are an important part of power engineering. They are used in system desi gn, maintenance planning, and as an alternative source of energy. It is a known fact that the power of wind is directly proportional to the cube of the wind speed, it should not be su rprising then that the electric power interruptions also show similar thir d order relationship to the wind speed. Extreme winds can be linear or circular (t ornadoes). There are four factors which attribute to the severity of windstorms; a function of sustained wind speed, gust speed, wind direction, and the length of the storm. Severity is dependent on the vegetation and climate as well . A Hurricane is the name of a counter-clockwise rotating storm with wind speeds in excess of 74mph. Hurricanes cause damages to distribution system in many ways. Oftentimes it is caused by uproo ting trees that fall and damage overhead distribution systems. Electric poles may also be blown away, or knocked down with high-
speed winds. Other effects of winds are sw inging, galloping, and Aeolian vibration. Wind speed beyond a certain point has a huge imp act on the number of interruptions. Figure 3.4 shows the relationship between wind speed and the mean number of interruptions in the region. The available data from the presen t weather recorder diminishes beyond 32MPH. . Figure 3.4. Variation of Mean of N Versus Wind in Dataset being Analyzed  The cubic relationship between wind speed and the mean number of interruptions allows the modeling of the e ffect of wind on the total num ber of interruptions as: 45 3 (3.1) 2 3123 avgNYBSBSBS where S is a two-minute maximum sustained gust. There is a very good correlation betw een wind and the total number of interruptions (N) . No significant pattern emerged when the plot was drawn between the daily 2 min. maximum wind gu st (TMMG) speeds (mph) and N.
Figure 3.5. Variation of N Versus Wind For a given value of the TMMG speed, there are different levels of N. Shown in figure 3.5, the plots of the averages of differe nt levels of N occur at each of the speeds of TMMG. From this graph, until wind speed reaches 40mph, there is a visible pattern, beyond that, no emerging pattern is visible. A pattern might have emerged if the TMMG speed levels(greater than 40mph) have happe ned at least 30 times during the 4 years of 1998-2001. Other lower speed levels accounted for for 98.5% of the total data set. Similar to figure 3.5, it can be observed from figure 3.6 that the correlation obtained through this process is very high, R2 = 99.3% and reveals the ex istence of strong cubic relationship between N and TMMG. 46
30 20 10 4 3 2 1 Mean of 2minutes Wind guest speed (mph) Mean of N S = 0.0900810 R-Sq = 99.3 % R-Sq(adj) = 99.2 % 0.0065040 X**2 + 0.0002598 X**3 Y = 0.613754 + 0.0647258 X Regression Plot of N Vs. Wind Figure 3.6. Mean of 2 minutes wind speed vs. average number of interruptions From figures 3.5 and 3.6 after 20mph it can be observed that the total average number of interruptions increases exponentia lly. Accordingly, power distribution poles and overhead equipment, are designed in such a way that there will not be any disruption arising from wind gusts in excess of 20 mph. At present the latest norm is to design system to withstand Category 3 hurricane (in the regions where wind speeds are high). Most of the infrastructure is old and can only withstand 90MPH winds gusts. Beyond this point the electric grid infrastructure faces extreme damages and restoration time runs into days and months. 188.8.131.52 Ice Storms Ice storms occur when super cooled ra in freezes on contact with conductors and tree branches, forming ice layers. This happens when the ground temperature is below freezing and a winter warm front passes th rough that area. Ice buildup increases the surface area facing the wind a nd hence loads excess weight on the conductor and the poles, causing them to either gallop or brea k. Additionally, tree branches with ice buildup 47
48 can break and affect the overhead distributi on network. Ice loading can be computed as follows : Wi = 1.244xTx(D + T) [3.2] Wi = Ice load (lb/ft) T = Radial thickness of ice (in) D = Conductor diameter (in) Typical assumption for ice density is 57-lb/ft  Wind loading is calculated by wind pressure multiplied by the conductor diameter, plus ice thickness: Ww = V x ( D + 2T) (3.3) 4800 Ww = Wind load (lb/ft) V = wind speed (mi/hr) The ice load and the wind load may or may not be in the same direction, regardless, the total conductor load is computed as a vector sum of the two values: W = (Wc + Wi + Ww) (42) W = Total conductor load (lb/ft) Wc = Bare conductor weight (lb/ft) Overhead distribution system s are designed to take care of expected icing and wind conditions.
49 184.108.40.206 Heat Storms Extended periods of exceedingly hot weather create their own issues for distribution networks; such s ituations are termed heat storms. High ambient temperature creates two types of issues: 1.) The equipment cannot dissip ate as much heat to the surrounding air, 2.) The demand fo r electricity increases trem endously with the extensive use of air conditioning. 220.127.116.11 Rain The primary weather parameters contribut ing to N in the area under study are wind, temperature, rain, and lightning. In the earlier discussion in this chapter the correlation between wind, temperature and N ha s been shown. Studies that include other parameters such as humidity have shown consid erably less correlation with N. If we plot four years of rain (RAIN) data with re spect to the time in months, many general conclusions can be drawn. The plots are show n below (figures 3.7 3.10). The Rain data is in inches (in):
Figure 3.7. Monthly Mean Distributi on of Rain for year 2000  Figure 3.8. Monthly Mean Distributi on of Rain for Year 2001  50
Figure 3.9. Monthly Mean Distributi on of Rain for Year 2002  Figure 3.10. Monthly Mean Distributi on of Rain for Year 2003  There is a piecewise relationship be tween the rain and the number of interruptions, N in a region. Rain does not only affect this relationshi p directly, but also 51
through vegetation and other eff ects like rusting and the insula tion failures of equipment. Once the rain is in excess and the vegetation gets saturated; there is a good chance of a tree limb falling on the distribut ion network if proper tree trimming has not been done .Further the soil weakens with continuous rain and causes er osion which further escalates tree falling. Using all of thes e facts and modeling the rain as a piecewise linear function against the total number of interruptions in a region; the following equations are developed with three segments: 10"1"0 R Rainandelsewhere (3.5) 21"2"0 R Rainandelsewhere (3.6) (3.7) 32"0 RRainandelsewhere In developing the model, the complete dataset was re-arranged to follow the above equation. The above definitions compri se the entire dataset, and the regression analyses were done using the fo llowing model equation for rain: (3.8) 312312avgNYCRCRCR 18.104.22.168 Lightning Strikes A lightning strike occurs when the vo ltage generated between the cloud and the ground exceeds the dielectric strength of the air. Distribution syst ems are affected by lightning strikes in specific localized areas. Gi ven below is the statistical analysis of lightning strikes (LS) in th e region under study. Figures 3.15-18 show the monthly distribution of lightning strikes for the period between the years 2000-2003. 52
Figure 3.11. Monthly Distribu tion of LS for year 2000  Figure 3.12. Monthly Distributi on of LS for year 2001  53
Figure 3.13. Monthly Distribu tion of LS for Year 2002  Figure 3.14. Monthly Distributi on of LS for Year 2003  54
Based on figures 3.11-3.14, there is a year-to-year vari ation in monthly averages. The information would be misleading if the reliability reports were not adjusted for seasonal weather patterns. In addition, weathe r patterns change from year-to-year, and the number of interruptions either increase/dec rease accordingly. Consequently, the preferred model needs to incorporate adjustments of the indices in both directions (making it a bilateral analysis). Further analysis over nor malization of reliability indices is done in chapter 5. In Florida, lightning tends to occur in storm cells that may be localized and only pass over a sparsely populated area . Of course, it ma y also affect a heavily populated area where the majority of power lines are buried, thus LS can have a random, though important, effect on N. Generally accompanie d with LS are the combined effects of strong winds and rain. Since there was sparse evidence for a narrow time-frame model of the effects of lightning, a linear predictor m odel was used instead. The model of lightning is given by: 55 S41 avgNYDL (3.9) where LS is the daily total number of lightning strikes. 22.214.171.124 Temperature Previously discussed in section 3.3. 1.1-Transformers, ar e the effects of temperature. This section will model the effects of temperature. The increase of N at low and at high temperatures can be attributed to the increase in power demand due to the heating/cooling requirements of customers .
Average TempMean of N 90 80 70 60 50 40 20 18 16 14 12 10 8 S 1.56052 R-Sq69.7% R-Sq(adj)68.2%Fitted Line PlotMean1 = 78.79 2.076 ByVar1 + 0.01523 ByVar1**2 Figure 3.15. Variation of Mean N Versus Average Temperature  Expressed as a regression equation, the relationship in figure 3.15 is: 278.792.0760.01523avgNT T (3.10) where Navg is the mean number of interruptions and T is the average temperature. Taking the derivative of (3.10) and equating it to zero, we see that at T=68.15 F, which is where the minimum number of interruptions occur. Using integer values, 68 is considered the optimal temperature (OT). Since the demand for power varies with temperature, the effect of ambient temperature movement away from the optim um temperature (OT=68) was modeled. In the model, two parameters are defined, heat ing degrees (HD) and cooling degrees (CD). These parameters are available in the ASOS da ta; however, they are fixed with an OT of 65, so it is desirable to r ecalculate using the local condi tions. HD is defined as the 56
number of degrees below the OT existing on a pa rticular day, while CD is defined as the number of degrees above the OT. Since the relationship between th e average temperature and N is quadratic, this model will ha ve second order terms for HD and CD. The model equation for average temperature follows: 57 2 (3.11) 2 11234NYAHDAHDACDACD where A1, A2, A3 and A4 are the coefficients a nd are not equal to zero. 3.4 Optimization of Component Modeling Earlier research work focused on mode ling the effects of extreme weather conditions on power distribution systems, and on sp ecific weather parameters causing specific faults in the distribution system. A theoretical model based on variable weather conditions is used to predict power distribution interruptions, while immediate weather conditions are used to analy ze interruption risk assessment. Analyzing daily and hourly weather data, these models can normalize the reliability indices for weather and predict the number of daily or by shift interruptions. Aside from the obvious culprits for inte rruptions (i.e. lightning, ground or line-toline faults caused by vegetation and/or wind) the effects of comm on weather conditions on power reliability events have rarely been addressed. When exposed to natural wetting, such as humidity or rain, tests performed on c ontaminated insulators have shown that the electrical characteristics of the insulators are altered . Lower barometric pressure causes coronal effects to be more pronounced which in turn can affect flashover rates . In addition, other environmental phenomenon may also c ontribute to power reliability events in ways that are not considered.
58 Common weather excludes catastrophic even ts such as hurricanes or tornados, which exceed reasonable design or operati onal limits of the electric power system . For extreme weather, there are methods being studied and ones already in place to define major reliability events, such as the afor ementioned, while excluding the consequent interruptions from the calculation of reliabil ity indices [2,3,4]. Since extreme weather physically damages entire power distribution sy stems, it also receive s the most publicity which in turn takes up much of the focus on modeling the effects of weather [5,6,7]. There is also a body of work that includes weat her as a factor in the analysis of specific fault causes [8,9,10]. However, there are no avai lable models that consider the effects of common weather conditions, in order to pred ict the total number of daily or by-shift interruptions. Reiterating that the weather and envi ronmental conditions to be addressed include, but are not limited to, rain, wind, temperature, lightning density, humidity, barometric pressure, snow, and ice. The models are developed to allo w broad application, since these conditions do not occur simultane ously at any one place, and the range of combinations is great. Using the data collected, statistical and deterministic simulations of the models are done by employing existing so ftware; the results will be used to refine the models. In order to validate the models, pow er interruptions will be predicted in areas that can be easily monitored. 3.4.1 Area Under Study One of the largest utilities in Florida ha s been providing reliability and lightning data to support this research. In addition, weather data from the National Climatic Data Center (NCDC) is available to academic ins titutions or governmental bodies. This data is
reported by 886 automated surface observation stations (ASOSs) located at airports around the country . As many as 15 Management Areas (MA), each providing thousands (for daily) or tens of thousands (for hourly) of li nes of data, can be combined with weather data to create the files used for statistical or neural network analysis. This is a unique study of power dist ribution networks, never befo re done on this scale. Figure 3.16. Location of Weather Data Recorder In figure 3.16 the critical automated surface observation stations (ASOSs) are identified. As can be seen, some of the county regions area is quite far away from where the observatories are and hence the data doe s not depict exact weather conditions for 59
60 remote locations from the airport. To re duce such error, the utility companies are installing their own automa ted weather recorders. The parameters being used to develop th e combined predictor and risk analysis model is listed in table 3.1. The list contains weather parameters such as wind, rain, temperature and dew deposition. The lightning parameter and the outages or interruption parameters data is provided by the utility providing services to the region of study. The data provided for research is listed in terms of the utility system. All these data are then processed in order to bring to a common scale and timeline. Table 3.1. Weather, Lightning and Interrupti on (N) Codes and their Explanations Used for Combined Predictor Model Call Sign Call sign for the reporting airport Date Date MaxTemp Maximum temperature for that day MinTemp Minimum temperature for that day AvgTemp Average temperature for the day DepNorm Departure from normal AvgDew Average dew point AvgWet Average rainfall for that day HeatDays Days cooler than some specified temperature when customers are likely to use heaters CoolDays Days warmer than some specified temperature when customers are likely to use AC's SigWeath Weather station identifiers Rain Amount of rain in inches for that day AvgStPR Average atmospheric pressure for that day AvgSeaPR Average sea pressure for that day ResWdS Average resultant wind speed for that day ResWdD Average resultant wi nd direction for that day AvgWdS Average wind speed for that day 5SMaxS Maximum sustained wind speed for 5 seconds for that day 5SMaxD The direction of the maximum sustained wind speed for 5 seconds for that day 2MMaxS Maximum sustained wind sp eed for 2 minutes for that day
61 Table 3.2. (Continued) 2MMaxD The direction of the maximum sustained wind speed for 2 minutes for that day Lightning Strikes Total number of lightning strikes that day Without Exclusions Total number of outages for that day With Exclusions Total number of outages minus the total number of outages caused by allowable exceptions for that day Weather.With Exclusions Total numbe r of weather outages for that day Weather.Exclusions Only Total number of directly corre lated weather related outages minus the number of directly correlated weather related outages caused by allowable exceptions for that day Outages.(Blank) Total outages caused by unknown reasons for that day Outages.Accident Total number of outag es caused by accidents for that day Outages.Animal Total number of outages caused by animals for that day Outages.Corrosion/Decay Total outages caused by corrosion and decay for that day Outages.Dummy CFR Total number of dummy tickets for that day Outages.Equipment Failure Total number of outages caused by equipment failures for that day Outages.Improper Process Total number of outages caused by improper process for that day Outages.Other Total number of outages caused by other reasons for that day Outages.Request Outages caused by customer request Outages.Transmission Total number of transmission outages for that day Outages.Unknown Total number of outages cau sed by unknown reasons for that day Outages.Vegetation Total number of outag es caused by vegetation for that day Outages.Weather Total number of outag es caused by weather for that day 3.4.2 Data Analysis and Processing This study did not only develop novel comb ined theoretical models regarding the effects of common weather (while incorporating existing, rele vant ones), but also applied them by solving the problem of predicting the daily number of interruptions. Real-time interruption risk assessment capabilities was also developed. As mentioned earlier, the data comes from the National Data Center (NCD C), and from one of the largest utilities in the United States. The weather data can be downloaded online a nd includes both daily
62 summaries and hourly, or even half-hourly, reporting. Additionally, the utilities are installing their own weather stat ions at service centers that are centrally located in their various management areas, providing an additional source of weather data. The interruption data used to generate the models includes all interruptions described by all cause codes for an entire da y. On the other hand, the weather data was relatively inaccurate because daily maximums and averages collected from point sources were not usually central to the area being studied. In order to model the data more precisely, the period in which th e weather data is collected needs to be decreased from daily to hourly, and by improving the lo cation of the point weather source. Expanding to include weather variab les not generally occu rring in Florida, a better model can be generated. Using statisti cal methods and neural network theory while translating NCDC and SG interruption data into the proper format, models will be simulated and modified as needed. It has been shown previously that there is significant correlation between wind, temperature, rain, and N Using both raw weather da ta and pre-existing models, regression models were developed to reflect their ef fects on N. The regressions showed that by comparing R2 values, the effects of weather parameters are related and have a severe effect on N, if more than one of these parameters are at their extreme limit. These modeled equations improve the variability by up to 20% from the mean of N, compared to when raw data is used to form the mathematical models. Given below in figure 3.17 are the excerpts of the data of various variables being used in developing the combined model of the predictor. Multiple sets of data are saved for comparison and analysis. Such as when comparing the variability between N and raw
weather data with the variabi lity of N with modeled data. Further analyses were done to compare the variability after simulati ng using neural network software. Figure 3.17. Sample List of Key Data(ra w) for Modeling a Combined Predictor The development of the theoretical models began with the preexisting models and then expanded to include other variables to form a combined model. We have used 63
64 statistical and neural network software to simulate the models and modify them as needed. This additional data from other re gions has broadened the range of weather conditions for which the models may then be validated. The daily summary data used in this study has been able to create files with 40 columns and 14000 rows for computer analys is. The amount of data that requires archiving and correlating has increased tremendously, with the inclusion of hourly reporting and the use of interruption data from additional sources. The creation of a database that can manage that amount of in formation was the first priority. Additionally, the weather data that is downloaded from the NCDC is in ASCII format that is not readily importable to the analysis software. To a dvance the project, addi tional software was configured to handle the NCDC data, the weather data provided by the utility weather stations and any other data that is required that is not pr operly formatted. This document is not proposing to reinvent the wheel; the inte nt is to incorporate existing models to aid the ones being developed. For example, lo ad prediction utilizing the temperature, humidity to find a human comfort zone (hea ting/AC), is a proven technology. Another example is that the probability of flashover due to ice buildup has been studied extensively  and may also be of use. In order to validate these models, sign ificantly accurate predictions of the number or frequency of interruptions must be produced. These predictions will be through simulations using actual weather and interrupt ion data and will be probabilistic rather than deterministic, providing a means of risk assessment rather than a fixed value for the number of interruptions that can be expected This provides a real capability to determine
risk. The R2 value of the predictions will be a stat istic of interest for daily and by shift predictions, while narrower periods would include hourly risk probability assessments. 3.4.3 Combined Effects of Modeled Parameters The equations of the models defined in sections 3.3.3, 3.3.5, 3.3.6, and 3.3.8 were combined to give a composite model of the ef fect of weather on N. The results from the aforementioned equations along with the combin ed equation, were compared with that which does not model the weather parameters. The combined equation for the raw weather data is as follows: (3.12) 5NYATBRCSDLS The combined equation for the modeled data is as follows: (3.13) 22 61234 23 12312 3112 3 NYAHDAHDACDACD BSBSBSCRCR CRDLS Regression analyses were performed on each of the five MAs individually using (3.1),(3.8),(3.9),(3.11),(3.12) and (3.13). Chosen as the statistic of interest, the R2 value of the regression equation, called the multiple coefficient of determination, describes the proportion of the total variation accounted fo r by the predictor variables . Because our datasets had three years of daily data, the result of the additional seven new variables (degrees of freedom) caused us to negate the adjusted R2 (penalizing a model for having too many degrees of freedom). 65 The regression analysis done on the weather and N data w ith the raw data, (3.12), showed R2 values ranging from 36.9% to 43.3% for different MAs. The regression analysis on weather and N data with the modeled equation, (3 .13), showed values ranging between 45.2% and 50.1% for different MAs. Similar results occurred when applying
the regression to individual weather parame ters. The results are shown below in figures 3.18 and 3.19. Figure 3.18. R2 Values of Modeled Versus Raw Weather Data by MA and by Weather Parameter  Figure 3.19. R2 Values of Modeled Versus Raw Weather Data by MA  66
67 To determine whether the a ssociation between the response and the predictor(s) in the modeled equation are statistically significant, it is necessary to set an level and compare the p-value for each predictor against the level. The usually accepted level is 0.050, and if the p-value is la rger than this, the predictor is considered statistically insignificant. Table 3.2 below lists the p-values for each predictor by MA. Table 3.3. P-values by Predictor and by MA  1 2 3 4 5 Constant 0.000 0.010 0.183 0.000 0.000 HD 0.719 0.000 0.795 0.003 0.003 HD2 0.633 0.000 0.141 0.013 0.039 CD 0.545 0.230 0.869 0.153 0.910 CD2 0.003 0.105 0.035 0.210 0.003 R1 0.001 0.000 0.000 0.000 0.000 R2 0.000 0.000 0.000 0.000 0.000 R3 0.000 0.000 0.000 0.140 0.000 S 0.000 0.083 0.459 0.000 0.004 S2 0.000 0.057 0.079 0.000 0.008 S3 0.003 0.210 0.000 0.002 0.075 LS 0.000 0.000 0.000 0.000 0.000 Figures 3.21 and 3.22 show that the modeled equations retu rn a consistently higher R2 value than equations that rely only on raw weather data. This consequently accounts for a larger percentage of the vari ance from the mean num ber of interruptions experienced on a daily basis. It is not surp rising to note that alt hough lightning seems to have a dominant role in Florida, there is no single weather parameter that can be labeled as the primary cause. It is apparent that ther e are some combinatoria l effects, since the R2 value of the combined equation is not the sum of the R2 values of its components. For example, lightning rarely occurs unaccompan ied by wind and rain, but high winds and rain do occur quite often without lightning, so the role of lightning may be overstated by
the fact that it has the largest R2 value (figure 3.18) of all th e weather parameters. Also, it appears from the R2 values for average temperatures, that it does not play a significant role in N. Figure 3.20 below shows a histogram of the temperatures that occurred over the study period. The area under study had a relatively narrow range of commonly occurring temperatures, with 95% of the av erage temperatures recorded ranging from 60 to 86 degrees, a 27-degree spread, which may not be true for regions ou tside of Florida. AvgTempPercent 84 78 72 66 60 54 48 9 8 7 6 5 4 3 2 1 0 Histogram of AvgTemp Figure 3.20. Percentage of Occurrences of Average Temperature for Combined Datasets  68 Some explanations for large p-values ar e uncommon occurrences of that variable in the dataset, or very small coefficients. In addition, when variables have large p-values, their contribution to the R2 value is marginal. Although HD and HD2 rates model predictors as rejections 4/10 times in Tabl e 3.2., figure 3.20 shows that there may not have been enough days below the OT to consider them significant. CD, on the other hand, does not seem to be significant in a ny of the MAs. This is partly due to the
69 dominance of the second order CD2 term in the heavily skewed figure 3.20. The two times that CD2 is rejected, neither HD or HD2 is rejected, supporting the belief that the actual distribution of heating and cooling days among the MAs is very different than figure 3.20 suggests. Because South Florida has a climate that is unique and different from the majority of the rest of the country, none of these temp erature variables should be rejected from a study until it can be shown that they are indeed insignificant. In only one instance, a rain variable come close to rejection while the wind variables are, for the most part, acceptable. It must again be noted that lightning in South Florida is very significant and that different regions of the country woul d have different p-values for different predictors. HD and HD2 would likely be more significant in Chicago than in Miami, and the wind variables would probably dominate in regions that are incorporating wind farms such as the Midwest. Disregarding the possible combinatorial e ffects of the weather parameters, or the occasionally large p-values, the consistent improvement of the R2 values (whether in isolation or in combination) shows that th e modeled equations are valid. Furthermore, it is speculated that the developm ent of new models for the impact of weather conditions on N will provide for better correlations. Another us eful study would be to attempt to reveal some of the combinatorial effects by de signing a non-linear closed loop (using neural networks). Combining linear modeling (as demonstrated in this document) with nonlinear modeling (as suggested for further study) a final model may be constructed. With the high demand for power along with scarce resources, the weather impact on total number of interruptions will be a major point of focus for study in the future.
70 3.4.4 Design and Risk Assessment for a Predictor Using three years of daily interruption and weather data, the models presented in  were developed. The analysis was perf ormed with statistical and neural network software which led to the development of the models. The data set used included weather and interruption from six management areas (MAs). for approximately 5400 exemplars. A multivariable regression analysis was conducted with the total number of daily interruptions as the target value and the re gressors were the total daily rainfall, the maximum two minute sustained wind gust speed and the total daily number of lightning strikes respectively. The other analyses were for function approximation using a one hidden layer back propagation neural network. For both analyses, the same data was used for training to develop a regres sion equations and to train the neural network. Another set of data called test data we re applied to both the regres sion equation and the trained network. The R2 was then calculated using the actu al number of interruptions as the target value and the predicte d number of interruptions by th e earlier two methods as the regressors. The results showed that the trained neural network results were consistently better (in terms of a higher R2 value). This demonstrates that th ere are hidden effects that were not accounted for in the regression equation with the raw data. In the next step the multivariable regression analyses was done using the modified dataset. Around 19 variables were used utiliz ing all the individual models developed to do regression analyses with the target value being the actual number of interruptions. The same variables and corresponding dataset wa s used to train the neural network
breadboard. The results from this analyses we re that for both the multivariable regression equation and for the trained neural network where the R2 values were higher. Figure 3.21 shows R2 values for the five MAs. The comparison in this figure is done between the statistical analyses using the raw data and the regression analyses done by simulations using the modeled data. The re sults are that the si mulation done with the modeled data shows consistent higher R2 values as compared to the R2 values coming out of the analysis with the raw data. Figure 3.21. R2 Values of Five Regions By including barometric pressure as anot her weather variable, and the recent daily interruption data that reflects the weather trend (system variable), it increases the R2 values by an average of 50%. 71
A part of this study was also done by simulating a neural network model using weather data from more than 10 manage ment areas. Although the study took time and recording data at many points became cumbersome ; the results were very interesting. It was seen that as we increase the geogra phic area and try to pr edict the number of interruptions for the whole region, the accuracy of the system decreases (as expected). The accuracy of the system improved by increasing the number of rows of data and by reducing the duration of the data collected. The figur e 3.22 shows a snapshot of one week of 2008 of actual and the pr edicted values from six MAs. 0 5 10 15 20 25 30 35 CE CE GS GS GS SD SD ND ND WG WG WG WD WDGeographic Region N Predicted N Actual Figure 3.22. Predictor Value vs Actual N for multiple MAs Another snapshot is given in the form of a histogram in figure 3.23. Given on the left hand side is the actual number of interrupt ions (N) and on the right is the predicted 72
number of interruptions. This pattern was similar for all the simulations and the histogram shows results of 4 years of combined dataset with multiple MAs. 706050 40 302010 0 9 8 7 6 5 4 3 2 1 0 N Actual Percent 70605040302010 0 10 5 0 N Predicted Percent Figure 3.23. Actual and Predic ted Numbers of Interruptions 73
The statistical distribution is similar except that the predictor is predicting a lower number of smaller values as compared to a lower value of actual number of interruptions. This pattern changes if we have a larger dataset to test. Thus, there is remarkable improvement as we keep on adding data to the predictor. A Positive effect on this particular simulation was that the R2 value returned was 61.3%, which was much higher than what we were getting as in earlier results. This further shows that the size of the data set is extremely important in achieving better results. Furthering the research, the analyses were done using neur al network function approximation. An interesting study was conc luded showing that although the predicted value for any given time may not be complete ly accurate, but a risk assessment calculator can be developed on that basis. Figure 3.24. Neural Netw ork Function Approximation Many histogram charts were developed by finding for each value of interruptions predicted, what the actual numbe r of prediction at that instance were. To better explain; 74
75 in figure 3.24 a histogram is shown for the days when the predic tor predicted nine interruptions. The bar of the histogram displa ys the number of actual interruptions (N) in terms of percentage. On the right side, the cumulative probability is listed based on the actual interruption of the possibility of having up to N interruptions. From the cumulative distribution chart, it can be seen that if the predictor predicts 9 (nine) interruptions then with more than 92% confidence level, one can state that the number of interruptions wont be more than 14. This predictor will be a strong tool in the smart grid configuration of modern grid st ructure. The positive speculations for smart grid are that there will be a predictive and se lf-healing capability in the grid. Applications like this unique predictor can provide this. Furthermore, risk assessment is a strong tool that can be used by the management to ach ieve maximum efficiency when planning the amount of long and short-term manpower and equi pment inventory. This effort is a patent property of the University of South Florida, Tampa, USA. The predictor Electric Power Distribution Interruption Risk Assessment Calculator (EPDIRAC) has a USF patent and related software has USF copyrights. Another unique aspect of this study was to develop methods for benchmarking the dependability of the utilities power delivery service. By normalizing the reliability indices with respect to weather, fair comparisons between the past and present performance of a utility, or between the perfor mances of different utilities, can then be made. Problems that interfere with fair assessments of a systems reliability, beyond the control of the system operator include: The variability of reliability (and by extension reliability indices) from system to system or from year to year within a system . Thus developing models for the normalization of relia bility indices for weather is a necessity.
76 A thorough literature search has turn ed up only one methodology for normalizing reliability indices for weather, and that me thodology relies on a single weather variable: lightning [51, 52]. Although this methodology is well considered, its application is limited to areas where lightning is the domin ant weather variable. In chapter 4, we provide insight to the basic c oncepts being utilized in this study. A novel method for the normalization of reliability indices is suggested in ch apter 5 of this document.
77 CHAPTER 4: SMART GRID RELIABILITY PARAMETERS AND INDICES A smart grid consists of variety of pow er components such as transformers, generators, and overhead lines. The reliability of the smart grid is one of the most important areas of reliability theory application. Random failures are certain to occur from time to time, especially when extremes in weather or other causes present hazards that the power system was not designed to withstand. During these extreme conditions, it is not acceptable that the power system be permitted to collapse and cease operating. Reliability methods also provide important analytical tools th at can be used to evaluate and compare smart grid design, breaker s, underground cables, and so on. Each component has its unique characteristics. Fr om a reliability point of view, component models are critical to the syst em reliability. The models should be as simple as possible, but they need to represent all the features, critical, to the system reliability. In this chapter, we will introduce typical reliability parameters, and how they can be modeled . 4.1 Probability Distribution Functions Reliability parameters vary from compone nt to component or from situation to situation. For example, expect ed repair time is the averag e repair time of the component considering many failures. After each individual failure, the actual repair time may be lower or higher than the expected value. B ecause the actual repair time varies, it is
referred to as a random variable. Random variables are represented by probability distribution functions [54,55]. Probability distribution func tions transfer a large amount of data to an equation described by few parameters. An associated function to the probability distribution function is the density function, f(x), which represents a particular value at which a random variable, t, will be. fprobability density function (4.1) 1,0 tfwhere (4.2) 1 dttfThe integral of the probab ility density function is cumulative distribution function which reflects the probability that f(t) will be equal to or less than t. ; where F = cumulative distribution function (4.3) txtftFt A function that combines both the probability density function and the cumulative distribution function is the hazard function, th The hazard function is equal to the probability of failure for a component which has not already failed. The density function is the probability of a compone nt failure, and the cumulativ e distribution function is the probability that it has already failed. The hazar d rate can be mathematically expressed as : tF tf th 1 (4.4) Several distribution functions are often us ed in practical engineering reliability problem calculations. They are divided into : Discrete Distribution Functions The Discrete Uniform Distribution 78
The Binomial Distribution Continues Distribution Functions Normal Distribution Lognormal Distribution Exponential Distribution Gama Distribution Weibull Distribution Uniform Distribution Raleigh Distribution Presented here are Probability Distribution Functions that are most often used in smart grid reliability evaluation. 4.1.1 Normal Distribution Function It is characterized by two parameters: Expected Value and Variance The formula corresponding to the norma l distribution function is: t tf 2 exp 2 12; t (4.5) 4.1.2 Exponential Distribution Function The exponential distribution function is the most wide ly used function in the calculation of reliability in engineering. It is characterized by a constant hazard function, which represents electrical components duri ng their lifetime. Anot her advantage of the exponential distribution function is that is represented by a si ngle parameter, the expected 79
value The exponential distribution function is the probability of a component surviving a time t with a constant failure rate. The form ula is: t e tf; (4.6) 0 t4.2 Component Reliability Parameters Smart grid components can be describe d by a set of reliab ility parameters. Sophisticated models use many such reliab ility parameters. All of the reliability parameters are important, but component failu re rates have historically received the highest attention. This is because failure rates have unique characteristics and are essential for all types of reliability analyses For our research, the simplified reliability models are used based on component failure rates and component repair time. The Mean Time to Failure (MTTF). The parameter that is characterizing the failure process. It is the time to failure, fo r designated lifetime, T. It is the time elapsed from zero to the first failure of the component. The T is a ra ndom variable and it is not possible to predict exactly when the unit will fail. However, we can compute the expected value or the mean value : dtttfmMTTFT0; (4.7) Where: t is the time Tf is derivative of the failure distribution Mean Time To Repair (MTTR). A repair process can be described the same way as the failure process in terms of a failure di stribution and failure density function. MTTR represents the expected time that will take a failure to be repaired (measured from the 80
time that the failure occurs). MTTR is typi cally used for each component, but separate values can be used for different failure modes. It is not possible to predict time of repair, so we will compute the mean time to repair: dtttgrMTTR0; (4.8) Where: t is the time g is derivative of the repair distribution 4.3 Component Reliability Data Electrical reliability data is a very important parameter of the smart grid reliability assessment. It is based on histor ical utility data, manufacturer test data, professional organizations such as IEEE, a nd other technical conf erences and journal proceedings . 4.3.1 Overhead and Underground Lines Primarily we are focusing on overhead dist ribution lines that have voltage ratings between 5kV and 35 kV. Overhead lines are di rectly exposed to va riations of weather conditions, vegetation, and animals thus, higher rate of failures are expected. At the same time the overhead lines failure is relatively easy to locate so the repair time is shortened. The reliability of underground lines and e quipment is higher than the overhead lines, primarily because they are sheltered from vegetation and weather. However, the faults are difficult to locate so the repair time is longer. 81
82 4.3.2 Power Transformers Accurate reliability data on power tran sformers is necessary for evaluating the smart grid reliability. Failure rates depend on th e age, size, and type of the transformer ( liquid or dry type) voltage rating, indoor or outdoor, etc . The mean time to repair of power transformers is very variable. 4.3.3 Power Generators The generator reliability data is cate gorized in two major groups: continuously applied and emergency or standby generator units. 4.4 Smart Grid Reliability Indices Standards like, IEEE Guide for Electric Power Distribution Reliability Indices (IEEE 1366) were developed to summarize reli ability indices (see Appendix A). Also, the standards outline the methodologies for calculatin g these indices, and indicate the factors that affect the calculation of them. The sta ndards define a long in terruption as an event where the voltage at the customer's connecti on drops to zero and does not re-establish automatically. If the interruptions time is in excess of three minutes then the interruption is referred as a long interruption. An interr uption less than three mi nutes is called a short interruption. These definitions vary from utility to utility and are not accepted as general definitions. Additionally to th is, the term "sustained inte rruption" refers to a longer interruption, ranging from th ree seconds in IEEE 1159 to two minutes in IEEE 1250 . As mentioned previously, ma ny different reliability indi ces have been proposed and are being used. They can be divided into four main categories: Indices that measure the freque ncy of sustained interruptions. Indices that measure the durati on of sustained interruptions.
Indices that measure the freque ncy of momentary interruptions. Indices that measure the freque ncy and depth of voltage sags. The first two categories have been cons idered "reliability" issues, while the last two have been considered "pow er quality" issues. Although there are historical reasons to make the dis tinction between reliability and power quality, for todays loads the sust ained interruptions and momentary interruptions are treated the same. The main reliability indices used for sustained interruptions (outages in excess of five minutes while excluding major event days) are : System average interruption frequency index (SAIFI), System average interruption duration index (SAIDI), and Customer average interrupti on duration index (CAIDI). SAIFI describes how often an average custom er will experience a sustained interruption (greater than five minut es). It is defend as: TN CI SAIFI (4.1) where CI is the number of customers interrupted and is the total number of customers served for the area. TNSAIDI is defined as the total duration of an interruption for an average customer over a specific period. The index is defined as: TN CMI SAIDI (4.2) 83
where CMI is the customer minutes interrupted. In terms of load-based indices, the average system interruption frequency i ndex (ASIFI) is often used to measure performance in areas with few consumers and concentrated loads. ASIFI is defined as: T iL L ASIFI (4.3) where, ASIFI is the ratio of total connected kVA of load interrupted and the total connected kV A served. SAIDI and SA IFI are two of the most common reliability indices used in the industry. Component reliability data is a very important parameter of the smart grid reliability assessment. In our research, we will use reliability information based on historical utility data, manufacturer test da ta, professional organizations such as IEEE and other technical conference s and journal proceedings .Ele ctrical equipment reliability data is usually obtained from surveys of i ndividual industrial equipment failure reports. Collection of reliability data is a continuous process and it is constantly updated. The smart grid reliability indices descri bed above are used to quantify sustained interruptions. Short duration out ages for some customers, such as hospitals and large industrial customers, can result in complex systems shutting down. These customers usually have a backup generation or other m eans of addressing short-duration outages. In particular, it is these types of outages would benefit from the presence of distributed generation and energy storage. Therefore, a reliability index must not only quantify enhanced reliability for sustained interruptions, but must also quantify enhanced reliability for short-duration outages. 84
85 CHAPTER 5: NORMALIZATION OF RELIABILITY INDICES Power companies are constantly striving to improve their reliability performance. The comparison of present performance from past performance is one method that companies use to identify changes in performance. Because of seasonal changes in the weather, these comparisons are often made between the present month and the same month in the previous year. However, because of weather patterns that can shift from year to year, it is difficult to separate the baseline performance from the overall performance. A method of normalizing reliabilit y indices is needed so that engineers can evaluate a systems performance without guessing at the usually highly significant role of weather conditions. 5.1 Performance and Reliability Indices There is already a method being used in Florida, (where the power system under study is located), that can adjust the reliabi lity indices for extreme and catastrophic events the exclusion. The Florida Public Servic e Commission (PSC) allows the exclusion of certain interruptions from the calculation of reliability indices including, but not limited to, those directly caused byplanned in terruptions, a storm named by the National Hurricane Center, a tornado recorded by the National Weather Service, ice on lines, a planned load management event, an elec tric generation disturbance, an electric transmission system disturbance, or an ex treme weather or fire event causing activation
86 of the county emergency operati on center . In terruptions not included in the above definition can be excluded by petition . Another method of normalizing reliability indices has been suggested in . This method is based on the fact that in many areas of Florida, lightning plays a key role in the increase of the number of interruptions (N), and the subsequent increase in other reliability indices. However, there are no met hods described that will allow a utility to normalize their reliability indices for the effects of common weat her conditions that include rain and wind. Such a method would be useful in areas where lightning does not play as significant a role and during times of the year when lightning is not as common. In addition, modeling the effect s of wind, rain, temperature, and lightning on the number of daily interruptions described in  has shown that rain and wind will also contribute significantly to degraded reliability. 5.2 Baseline Comparison and Other Methods Figures (5.1-5.3) show the mean values of total daily rainfall (Rain), number of lightning strikes (LS) and N by month and year for one of the management areas (MAs). A recognizable general pattern can be identifi ed, that of a summer p eak in interruptions with a winter falloff, but that it varies from year to year in its specifics. Sometimes the cause of that variation in N can be seen in the weather charts, such as the 2003 N pattern in months 4-9 coinciding with the 2003 pattern of LS, or the 2001 N pattern in months 510 corresponding to the 2001 patte rn in the Rain figures.
87 12 1110 987654321 2000Figure 5.1. Mean of N by Month and Year Mean of LS 121110 987654321 30 20 10 0 121110 987654321 30 20 10 0 2000 2001 2002 2003Panel variable: Year Figure 5.2. Mean of LS by Month and Year Mean of N 2001 24 18 12 6 0 12 1110 987654321 2002 24 18 12 6 0 2003Panel variable: Year Mean of N Mean of LS
Mean of Rain 12 11 10 987654321 0.4 0.3 0.2 0.1 0.0 1211 10 987654321 2000 200188 0.4 0.3 0.2 0.1 0.0 2002 2003Panel variable: Year Mean of Rain Figure 5.3. Mean of Rain by Month and Year However, these patterns are difficult to s ee, are open to debate and provide little useful information. Further, there are other sp ikes in the figures in which the cause cannot be determined by averages, but may still be due to a single unseasonable event. The one inarguable conclusion that can be drawn from th ese figures is that re liability indices are subject to shifting seasonal w eather variations. Because of th e year-to-year variations in monthly averages, reliability re ports that do not adjust for va riations in seasonal weather patterns would be likely to re sult in misleading conclusions. The method described in this document finds statistical outliers in both common weather and interruption data, and uses these outliers to identify days where co mmon weather conditions interfere with the evaluation of baseline performance. The reliability indices are then adjusted for use during comparative studies. Because it is equally likely that the pres ent year could have milder weather and consequently fewer interruptions, this method provides a bilateral anal ysis with the result that the monthly interruption count, and the associated measures and indices, are equally
as likely to be adjusted up or down. This me thod simply seeks to even the field so that reliability engineers may focus on other reasons for any shift, up or down, in the reliability indices without the guesswork invol ved in evaluating the effects of weather. 5.3 Assumptions and Statistical Tools The primary assumption that this method relies upon is that, barring any unusual differences in the operational or environmental conditions that a system experiences, the daily reliability measures should have a high correlation from year to year. Although there are many reasons that the daily measures may not correlate from year to year, such as improved maintenance, incr eased under-grounding of overhead conductors, or a majority of equipment reaching the end of their service lives; weather is certainly a significant factor. The second assumption this method employs is that accounting for the variance caused by any of the above factors, or any othe rs that are not mentioned, will increase the correlation. It is contended in this docu ment that, no matter where in the range the unadjusted correlation lies, if the method desc ribed consistently and positively improves that correlation by adjusting the N, associated customers interrupted (CI) and customer minutes interrupted (CMI) counts, then some portion of th e effects of common weather have been accounted for. The interpretation of a zero correlation improvement would be that weather patterns did not change. The statistic of interest for the eval uation of the method proposed in this document is the Pearson correlation coef ficient (rho) as given in (5.1). 1 1 n X XYY i nss xy (5.1) 89
Where: X = sample mean for the first variable sx = standard deviation for the first variable Y = sample mean for the second variable sy = standard deviation for the second variable n = number of paired data points The correlation coefficient measures th e strength of the linear relationship between two data sets, has a range of -1 to 1, and is neutral to the means of the variables being correlated. Another statistic that is often reported for correlations is the p-value. The p-value is a measure of the strength of the correlati on; however, confidence intervals have been reported since they provide a measure of the accuracy of the correlation as well as the strength. The confidence intervals for the corr elations in this document were calculated by first using the Fisher z-transform. The tran sformed correlation (z) is a standard normal distribution. (1) 0.5ln (1) z (5.2) The confidence limits of z are found by a pplying the inverse standard normal distribution function, which does not have a closed form and must be computed numerically: 100% 200 3 confidence NORMSINV zz n (5.3) 90
The confidence limits for z (z ) are then transformed b ack to confidence limits for as shown in (5.4). 2 (1 2 (1 z e CL z e) ) (5.4) Figure 5.4 shows a family of curves for the confidence intervals for n paired data points between 5 and 1500 with a of 0.1, 0.5 and 0.9. n 1000 800 600 400 200 0 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.1 0.5 0.9 Rho Figure 5.4. Confidence Interv als as a Function of n and It is apparent from fi gure 5.4 that the confidence intervals have inverse characteristics, though non-linear ly proportional to both the numb er of paired data points and the magnitude of the correlation. 5.4 A Novel Method As was shown in figures 5.1, 5.2, and 5.3, there are seasonal w eather patterns that can be seen in the monthly averages, and sin ce this method is intended to find outliers in common weather conditions, comparisons must be made between relatively small samples. Outliers found using an entire yea rs worth of data would represent extreme weather conditions and would be clustered in the summer and fall months offering little 91
92 or no opportunity to normalize the reliability indices year-round. Monthly sampling was chosen because it is a period of time after wh ich comparative reliability studies are often done. It is also a relatively small sample to capture outliers that woul d otherwise be lost. However, in Florida, occasionally, there are months where the number of days reporting non-exclusionary interruptions is much less than 30. A ugust and September of 2004 are such months, reporting less than eigh t days each month due to back-to-back hurricanes. These months were not included in the analysis and would not have benefited from normalization at any rate. Therefore, the total number of m onths normalized from 2001 through 2004 is 46. For these reasons, monthly sampling provi des the most accurate comparison of one years common weather c onditions to another years common weather conditions. Since 1981, there has been a program to bu ild Automated Surface Observation Stations (ASOSs) at airports throughout the US. These stations were primarily intended as a weather data source for aviato rs, but have since turned out to be the best source of historical surface weather data in the US. Since 1996, the National Climatic Data Center (NCDC) has been making ASOS data available as an online download. This data includes daily and hourly summaries in ASCII format from every ASOS in the country. Five years of daily summary ASOS da ta (2000-2004) was collected from the NCDC for weather stations lo cated within or near nine MAs in the area of study. The value for wind was chosen to be the 2minute maximum sustained gust (2MMaxS) and for Rain, total daily accumulation. One of the largest utilities in Florida pr ovided N and LS data from their records for the MAs of interest. Because this method is designed to normalize reliability indices
93 for common weather conditions, the N data was segmented to exclude interruptions that were either administrative in nature (tickets wr itten in error, no loss of service (NLS), etc) or that were deemed exclusionary by the PSC as described in the introduction. Further, many of these exclusionary interruptions were due to extreme weather conditions, such as hurricanes, that require the exclusion of the en tire days interruptions. In the latter case, the weather for that day in th at MA was also excluded from the calculation of the weather outlier limits. In terms of bilateral analysis, weather and interruption data was compiled for five years for nine MAs, and four separate studi es were performed for each MA. An example of a study performed is 2001 versus 2002 with 2002 being the year that is to be adjusted. In this case, 2001 was initially used as a refe rence year, providing the outlier thresholds that the 2002 weather was compared against, and then the analysis was reversed with 2002 as the reference year a nd 2001 as the target year. Weather outliers were identifie d as those days in the target years that had weather values above the reference outlier limits. All outliers were tabulated, and those days that had interruptions greater than the N outlier th reshold for the month, that also occurred on the same days as one or more weather outliers, were defined as intersections. The determination of how much the 2002 N would have to be adjusted was made daily, by subtracting the 2002 inte rruptions that were found to be related to a weather outlier (defined by the 2001 ou tlier limits), and adding the 2001 interruptions that were found to be related to a weat her outlier (defined by the 2002 outlier limits). In this manner a bilateral analysis was achieved that allowed for the possi bility that the 2002 weather was much milder than the 2001 weat her and that the 2002 N would subsequently
have to be increased in order to perform a comparative reliability study that was not skewed by variable weather patterns. This study compared four daily values: N, 2MMaxS, Rain, and LS. The following discussions of the shapes of the data sets a nd the distributions they most closely resemble provide the rationale for the choice of thresh olds beyond which we determine that a data point is an outlier. Histograms and probability plots of the actual data will be used to show the fit of the data to the distribution chosen to model it. The following figures and plots are repr esentative of all the ASOSs and MAs. Interruptions (N): It is well known that interruption data (N) follows the lognormal probability distribution and have been verified using probability plots of the data provided. The data must first be transforme d by taking its natural log. The transformed data will follow a normal distribution, so to determine the threshold above which the target data will be compared to the weathe r outliers, the mean, plus some number of standard deviations of the transformed ta rget data, the following equation was used: Threshold= A (5.5) Where is the mean of the transformed target data, is the standard deviation of the transformed target data, and A is the numb er of standard deviations wanted. This transformation and the associated threshold calculations are pe rformed on the target data. The wind data defined by the 2MMaxS is most closely modeled by the Largest Extreme Value, or the Gumbel (maximum case) probability distribution. A probability plot of the 2MMaxS data is shown in figure 5. 5. It should be noted that the 2MMaxS data is limited to integer values, thus it cannot be made to fit as well as a randomly generated 94
Gumbel distribution, although the fit is quite good for a naturally oc curring data set as can be seen by the Anderson-Darling value of 2.22. Percent 4540353025201510 99 98 95 90 80 70 50 30 10 1 0.01 Loc <0.010 16.95 Scale3.408 N358 AD2.220 P-Value Largest Extreme Value 95% CI Figure 5.5. Probability Plot of 2MMaxS Data The procedure used to find the outlier th reshold is as follows. The location and scale parameters of the 2MMaxS data, and respectively, must first be estimated from the reference data. The equations for estimating these parameters are as follows. 6 =0.5572 and s X (5.6) Where X and are the sample mean and standard deviation of the reference data respectively. sFor this distribution, unlike the norma l or lognormal distributions, there is a closed form percent point function. The pe rcent point function is the inverse of the cumulative probability function in that it calcu lates the probability that a member of the data set is greater than or equal to x for a given x. The percent point function is given in (5.7). 1 GpLnLn p (5.7) 95
Where p is the percentage under the curv e expressed as a fraction of one. A 0.9 percentage, meaning that 90% of the data wi ll be under the curve at that percent point, can be calculated as a 2.25037 pe rcent point (G (p)). This is a fixed value, independent of the location and scale parameters. To apply this function to the target data, the target data must first be standardized using the location and scale parameters, and of the reference data However, it is not necessary to transform the reference data, merely calculating the location and scale parameters of the reference data. The location and scale parameters of the reference data can then be used to standardize the ta rget data using the following equation. x Gx (5.8) Following this standardization, approxima tely the top 10% of the data, depending on fit, will be greater than or equal to 2.25037. By us ing the location and scale parameters of the reference data to standard ize the target data, shifts in the range of values, which may occur due to annual variations in weather patterns, will be transferred to the standardized data. Th en the outlier threshold will be 2.25037. Figures 5.6 and 5.7 illustrate how the data will shift using the prior years parameters. 96
G(2MMaxS)Frequency 126.96.36.199.20.0 -1.2 -2.4 250 200 150 100 50 0 Figure 5.6. Histogram of 2003 Standardized 2MMaxS Data G(2MMaxS)Frequency 10.0 7.5 5.0 2.5 0.0 -2.5 -5.0 250 200 150 100 50 0 Figure 5.7. Histogram of 2003 2MMaxS Data Standardized with 2002 Location and Scale Factors Although this seems more complicated th an the lognormal tran sformation, it is actually simpler because the pe rcent point function is in closed form, and the outlier threshold is fixed. The Rain and LS data did not fit any of the standard distributions because a large percentage of the data was zeros. The re mainder of the data had, as a general 97
characteristic, a heavy grouping of data poi nts at the lower values with individual extreme values spread across a large range. RainFrequency 8.47.26.04.8 188.8.131.52 0.0 2000 1500 1000 500 0 y Fre q uenc Rain Figure 5.8. Histogram of Rain 2000 1500 1000 500 0y Frequenc Fre q uenc y 700600500400 300 200100 0 LS LS Figure 5.9. Histogram of LS Figures 5.8 and 5.9 show the distribution of the data. Because of the large Y scale, there are many individual data points on the X scale that canno t be shown, but an idea of the shape of the data can be developed by observing that the X scale is limited by the 98
largest value in the datasets. Because of the fact that no di stribution could be found to fit the data, Tchebysheffs Theorem was used to estimate the outlier limits. Tchebysheffs Theorem  states that for a certain number, K, of sta ndard deviations, a certain minimum percentage of data points will always fall within plus or minus the mean plus K standard deviations regardless of the dist ribution. The following equation gives that percentage and can be solved for any number K, with K not limited to integer values. 1 Percentage1 2 K (5.9) Although this equation defines the maximu m number of standard deviations required for a specific percentage of the data to be under the curve, the actual number of standard deviations must be determined empirically. The choice of outlier thresholds for the variables in this method cannot be determined definitively, but must be approached heuristically. A theoretical basis combined with an empirical application provi des the choices with optimal results. An outlier threshold that is generally accepted is the mean plus three standard deviations of a normal distribution which puts approximately 99.77% of the normally distributed data under the curve. This provided a basis for the choices for the thresholds for the Rain and LS reference data. The Rain and LS distributio ns in Figures 5.8 and 5.9 suggest that even at that level, the most damaging days will still be captured. Add itionally, there are many months with very little or no Rain or LS, in which case the location and scale factors applied to the target data would both be zero, effectively making any day with Rain and/or LS an outlier. Direct experimentation showed that the optimal thresholds were nearly the same as the normal mean plus three standard deviations. 99
100 Wind has a cubic relationship with the numbe r of interruptions [ 47],  and after approximately a 25 mph 2MMaxS the effect is magnified substantially. The use of the 99.77% standard for a 2MMaxS outlier w ould set the threshold at over 35 mph, effectively eliminating many possibly extrem e damaging wind values. Furthermore, the weather data is taken at a point source a nd the interruption data is taken from an area source. As such, the 2MMaxS was considered an indicator of the wi nd conditions for that day rather than a definitive value. The threshol d was chosen so that lower values could be captured. The threshold for the interruption data, N, was chosen to be the mean plus 0.8 standard deviations of the log transformed ta rget data. Since the lo cation and scale factors of the N data apply to the ta rget data, it was determined th at the upper 20% of the N data should be available for comparison with th e weather outliers that are defined by the location and scale factors of the reference data. The purpose of this is to allow for those days that have a high number of interruptions whose causes are not related to the weather. Further, a high threshold would limit the effectiveness of the method by denying the ability to cross-correct (when several days in the same month have both positive and negative adjustments, thereby canceling). Table 5.1 shows the location and scale fact ors (or percentage point) chosen and the percent of the data that is under the curve when the location and scale factors are applied to the data from which they are derived.
Table 5.1. Location and Scale Factors Rain Wind LS N Location and Scale +5.15 G(p)=2.00 +5.15 +0.8 Percent Under Curve 99.67 86.23 99.11 79.82 5.5 Effectiveness of Results Five years (2000-2004) of bot h interruption and weather da ta were collected with the first year having its measures adjusted (2001). For the four years when measures were adjusted (2001-2004), there were approximate ly 1,350 (allowing for missing data) paired data points available for correlation in each MA for each measure. Figures 5.10, 5.11, and 5.12 and Table 5.2 show the correlation improvements for each daily measure. For maximum clarity, the data has been sorted from the lowest post-adjustment value to the highest. -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 WDWBBRNDSDCEGSPMWG Upper Post Adj Lower Upper Pre Adj Lower Figure 5.10. Pre and Post Adjustment by MA for 4 Years Daily N with 95% Confidence Intervals 101
-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 WDWBSDNDPMBRGSWGCE Upper Post Adj Lower Upper Pre Adj Lower Figure 5.11. Pre and Post Adjustment by MA for 4 Years Daily CI with 95% Confidence Intervals -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 NDWDWBSDPMGSCEWGBR Upper Post Adj Lower Upper Pre Adj Lower Figure 5.12. Pre and Post Adjustment by MA for 4 Years Daily CMI with 95% Confidence Intervals 102
103 Table 5.2. Overall Improvements in rho n 1350 Avg. 95% Confidence Interval 0.048 N Cl CMI Maximum 0.567 0.380 0.566 Average 0.457 0.301 0.385 Minimum 0.303 0.205 0.133 It can be seen from figures 5.10, 5.11, and 5.12 and Table 5.2 that in each case, the adjustments performed by the proposed method resulted in a medium to strong improvement in the linear relationship between the two years daily measures. It can also be seen that for most of the trials, there was either little, none, or negative linear relationship between the two years for CI. A discussion of correlation coefficients requires some way to characterize their absolute or in the case of comparisons, relative magnitudes. A general rule of thumb for magn itude characterizations is shown in Table 5.3. Table 5.3. Correlation Magnitude Characterizations 0.0-0.1 0.1-0.3 0.3-0.5 0.5-0.7 0.7-0.9 Clinically Small Moderate Large Very Trivial Large It can be seen by applying these character izations to the correlation improvements shown in figures.5.10, 5.11, and 5.12 and Tabl e 5.2 that the improvements in the adjusted measures range from small to large with a mode rate average. It can also be seen that the correlations of the unadjusted measures is small or for the most part, clinically trivial. It is reasonable to assume, based on these results, that the use of the adjusted measures to
calculate the reliability indices N, SAIFI, SAIDI and CAIDI should result in a stronger linear relationship between one years reliability indices and the next year. However, because the reliability indice s are calculated monthly, the number of months in this dataset for each MA is only 46, and referring back to figure 5.4, it can be seen that for moderate to large (using the =0.5 curve) correlations the number of paired data points needed to attain a confidence in terval of 0.10 is approximately 850. While confidence intervals for an n of 46 would be approximately 0.45 for the adjusted indices and 0.55 for the unadjusted indices. figure 5. 13 shows the correlati ons and confidence intervals for Monthly SAIFI. -0.2 0 0.2 0.4 0.6 0.8 1 WDWBSDNDPMBRGSWGCE Upper Post Adj Lower Upper Pre Adj Lower Figure 5.13. Pre and Post Adjustment by MA for SAIFI for 46 Months with 95% Confidence Intervals It can be seen that, although ther e is a consistent improvement in such large confidence intervals overlap not only each other, but also the correlations themselves, so that the correlations cannot be used for comparison. As n goes down, the confidence intervals increase rapidly, so this type of analysis can produce erroneous results if 104
105 performed with a smaller n than is required to attain confidence intervals that do not overlap. 5.6 Assessment and Limitations The limitations of this method can be attr ibuted to the bilate ral nature of the analysis and of the data required. Because th is method compares one year to another by finding outliers in the monthly data, the averaging of many years weather and interruption data would obscu re the very outliers that this method depends on, so comparing a multi-year average could not be done by averaging the raw data. In addition, a multi-year analysis of reliability trending could not be done because each year is normalized to only the previous years raw data rather than its own normalized data. However, both of these types of analysis coul d be done by establishing a baseline year for normalization and averaging or trending th e following years normalized reliability indices. The weather data used is generated by ASOSs located at airports around the country. Although ASOSs are the most prevalent type of weather station available publicly, there are other types available. Howe ver, not every locale will have an available weather station and only the ASOSs have the ra nge of data used in this analysis. This limitation can be overcome by installing dedicated weather stations in the area of interest. If a recording of a single months behavior of a power system and the operational and environmental conditions were taken, and was repeated endlessl y without any change in the operational or environmental conditions, then the behavior of the system for any month would have a one-to-one correlation to the first mont hs behavior. As changes in the operational or environmental conditions were introduced, that correlation would be
106 reduced. However, by accounting for some of those changes and adjusting the later behavior of the system, the corr elation with the first, or ba seline, month would be brought closer to the initial one-to-one. The proposed method has been shown to consistently and positively improve the correlations between the presen t years reliability measures and the previous years reliability measures. Since the adjustments were done solely on the basis of daily weather values, accepting the logic in the above argumen t, it can be concluded that at least some part of the effects of weather on the reliab ility measures N, CI and CMI have been accounted for, and that the measures have been normalized for weather. Because the reliability measures have been normalized for common weather conditions, and reliability indices are calculated from these measures, it can be concluded that the reliability indices have been normalized as well. Several aspects of the future work fo cus on the refinement of the accuracy by which interruptions are captured for adjust ment. It is expected that many of the interruptions that have been captured for the analysis that has been presented, are not associated with the weather. This could be due in part to the fact that the daily weather values represent maximums and totals in part of the fact that some of the interruptions captured are due to causes that are not sensitiv e to the weather. It can be concluded from this that the adjustments may be significantly lower than what is needed to account for all of the variations in the weather. The interruption data used for the analysis presented in this document includes all interruption causes. In all proba bility, however, not all interruption causes are sensitive to weather, and some, such as animal activity, may have negative correlations. For this
107 reason, this method will be applied to the same datasets as used here, except the data will be segmented by an interruption cause. The results of adjusting reliability measures by cause codes and then combining for a total adjustment are expected to provide normalization that is more accurate. As a secondary benefit, the ability to identifying those causes that are most sensitive to the weather will be available. Temperature data was not used in this analysis, although it has been shown to have a definable relation to the number of interruptions . The inclusion of additional weather variables, such as snow and ice, will have to be performed when data from a utility where these conditions occur becomes available. Because the weather data used was collect ed by ASOSs that were constructed for the FAA, the data is not always centrally located within an MA, thereby reducing its accuracy. SG has been installing dedicated weat her stations in locati ons central to their MAs. When sufficient historical data has b een collected, trials of this method will be performed using that data. The use of SGs weather data will improve the geographical reference of the weather data. Although the results shown above are encouraging, further research needs to be done to determine the optimal outlier thresh olds, additional variab les that should be included, and to verify that the model pr oduces consistent results through repeated simulations using different da ta sets. A method of normaliz ing the reliability indices between systems will be developed employing the models used above. Additional variables will be determined that will address the variations in the climate that different systems experience.
108 In the following chapters, we would try to calculate the availability of the system configured with smart grid technologies including renewable distributed generation. This is a unique situation because smart grid app lications are taking place as we write this document. Research of such kind has never b een explored due to current implementation of changes to the existing grid.
109 CHAPTER 6: MODELING METHODS FOR SMART GRIDS The smart grid technologies are expected to change the fundamental design and operating requirements of the electric dist ribution system. A number of topics to understand and analyze this issue have been identified. They can be grouped in the following categories : The need for current analysis tools to e volve and address a ne w, more interactive distribution system of the future. Change and upgrade to distribution engineering tools to simplify their use and more efficiently handle distributed a nd renewable-generation-related issues. Develop new analytical methods and related tools to determine the effects of high-penetration distributed generation on capacity limits. Develop cost and benefit evaluation tools that better define the relationship of distributed resources to power sy stem operations and dispatching. Identify and document modeling and specification requirements for smart grid interconnection equipment. The primary engineering tools are power flow and fault-current studies. A power flow computes steady state vol tages and current of the syst ems ensuring that the system will meet important criteria such as equipmen t loading, voltage drops and system losses. While the power flow modeling can predict the electrical properties of smart grid,
110 reliability modeling is predicting the availability and interruption of such a system. In general, smart grid engineeri ng tasks can be divided into pl anning and design stages . The planning function is to identify system needs and limitations, to propose projects, to resolve the issue, and to gain approval for projects. The de sign function takes a project from concept to realization in a safe, e fficient and cost-effective manner. Primary planning functions are: Load flow Reliability assessment Distribution impacts screening Installation database management Assessment of grid-level impacts Reliability assessment is an ever evolving issue of increasing importance. Planning function that enables re liability modeling are : Design new system to meet reliability target Identify reliability problems on existing systems Design system that can offer different levels of reliability In this chapter we introduce modeling t echniques and methods for analysis of smart grid reliability. 6.1 System Modeling and Analysis Reliability of the power system has been of great interest sinc e the early days of the establishment of the power system structure. There ar e many reliability techniques used in power system analysis. With the in troduction of smart grid technologies to the power systems, the previously developed techniques and models, cannot be used for
111 reliability analysis, because of the new dyna mics. To analyze smart grid new methods need to be developed. The base methods that we will be using for the development of the new method will be introduced here. 6.1.1 Markov Modeling of Smart Grid Markov modeling is a method based on the system states and transitions between these states. Two assumptions are made for Markov models: The system is memory less, which means that the future probability of events is only a function of the existing state, disregarding what has happen prior the system entering this current state. The system probability between the states is constant. The probabilities are not a function of time. Markov modeling can be either discrete or continuous. The discrete Markov modeling is called the Discrete Markov Ch ain, while the continuous is called a Continuous Markov Process . In this resear ch we are modeling smart grid reliability with a Continuous Markov Process. A Markov Process is described by the set of states and transition characteristics between these states. The state transitions in a Markov Process occur continuously. Instead of state probabilities, Markov Proce sses use state transition rates. This is very suitable in the application of sm art grid reliability, because the failure rates of the smart grid components are equivalent to the state tr ansition rates. In order to be able to use Markov modeling, the failures of the smart gr id components equipment are assumed to be exponentially distributed, so the failure ra tes are constant. Also the other values such as: switching rate and repair rate are within exponential distributions. The failure rates,
the switching rates and the repair rates are a reciprocal of the Mean Time to Fail (MTTF), Mean Time to Switch (MTTS) and Mean Time to Repair (MTTR). MTTF 1 ; failure rate MTTS 1 ; switch rate MTTR 1 ; repair rate (6.1) Markov modeling can be used in a general form that is applicable to any size and complexity. The state probabilities or state transition rates can be computed using matrix differential equations, which can then be constructed using the following rule . tp dt tdpi i = (inflow to state i )-(outflow from state i ) (6.2) ij jpjsatefromistatetotransition ofrate ) ( ij ipjsatetoistatefrom transitionofrate ) (Where = probability of system state i at time t. Equation (6.2) can be written in matrix form: tpi Tpp (6.3) The solution of this vector differential equation is: Ate0ptp (6.4) where a vector of initial conditions of a ll states. The exponential equation (6.4) absolutely and uniformly converges in a finite time interval . Common practice is to 0p112
assume that the state where all components are UP with a unity probability while the others have zero probability 1 2 2! ... !2k kk Atk tA I t AAtIe (6.5) In our case, we are interested in the final value of the state probabilities. In this case, derivatives of the equation (6.3) will be zer o, so we will have a system of algebraic equations: Tp0 (6.6) Determinant of is zero, which means that the equations are not linearly independent. However, we can discard one of the equations and substitute the equation T1pn 1i i (6.7) Since we know that the sum of the state pr obabilities is a cert ainty . We can write the transition matrix in the form: nn nn nttt t ... ............ ...tt t...tt T21 2 2221 1n 1211 (6.8) The off-diagonal elements of are the failure rate and repair rates that represent the transitions between the states of the system. The diagonal elements represent the transitions out of the states with a negative sign. If we substitute equation (6.7) for the nth -row of the matrix, we will get a new equation for the transition matrix : T T113
............ ...2 ............ t...tt T1 111 1n 12 11 nnt ttn n n (6.9) We can write the new steady-state equation as: b 1 0 ... 0 p p ... p 1...11 t...tt ............ t...ttn 1n 1 1n 21n11n 1n 12 11 n (6.10) where the right hand side b is no longer ze ro. The final solution of the steady state condition is: bTp-1 n (6.11) which will give a probability of every state in the system. 6.1.2 Modeling of the Smart Grid with a Boolean Logic Driven Markov Process (BDMP) Smart grid will allow current electrical grid to better incorporate renewable energy sources such as wind and solar pow er, back-up distribution generators and advanced energy storage systems. Reliability modeling of smart grid raises difficulties due to dynamic reconfigurations of the syst em. The problem can be modeled using Monte Carlo simulations, but obtaining good precisions is very time consuming when the system is large and dynamic [66, 67, 68]. To solv e the modeling problems, we will use new formalism which combines the Boolean logic of Fault tree technique and Markov Process [69, 70, 71]. This modeling approach has advantages over conventional models because it allows complex dynamic models to be defi ned and still remain easily readable. 114
115 The purpose of BDMPs is to provide a ne w graphic representation of fault trees, augmented only by a new kind of link, represented by dotted arrows. This will enable us to combine conventional fault trees and Mar kov processes in a completely new way. The BDMPs drastically reduce combinatorial problems in operational applications. From a mathematical point of view, a BDMP is a way of defining a global Markov process which is interacting in a given manner. The definition of BDMP is: It is basically a Markov process with two modes, the components that are required and the components that is in standby. The modes can be different in some cases. Obviously, the system can have only one mode. At any time the choice of the mode of one Markov process depends on the value of the Boolean function of the other processes. A BDMP consists of a: multi-top coherent fault tree, a set of triggers, and a set of triggered Markov processes. A trigger is re presented graphically with a dotted line in figure 6.1. The first element of a trigger is called its origin, and the second element is called target. Two triggers must have the same target. This means that it is necessary to create an additional gate G1 in figure 6.1, w hose function is only to define the origin of the trigger. The basic events in the figure 6.1 are e1, e2, e3, and e4. There is only one trigger from G1 to G2 .
G2pe1G1e2 e3e4 Figure 6.1. BDMP with one Trigger In figures 6.2, 6.3, and 6.4 the BDMP is presented along with a Markov model. L T Figure 6.2. Standby System ANDL T Figure 6.3. BDMP Representation of the System in Figure 6.2 116
117 T L L L T LLLT LT LT ation of th Figure 6.4. Markov Model Represent e System in Figure 6.2 State Space s roach can be applied to a single unit 73, 74]. Diagram 6.1.3 Markov Modeling of Smart Grid Under Variable Weather Condition The failure rates of the smart grid components located in relatively fixed environments can be considered to be a constant during the useful life period. For transmission lines and other outdoor component s, the environment is not a constant and can have a considerable effect upon their failur e rates. These two states have a fluctuating environment covering normal and stormy weat her with assumed exponential distribution functions. With these assumptions, the Markov app with a two state failure e nvironment [72, To use this approach we have to define: = normal weather failure and repair rates S S = stormy weather fail ure and repair rates S m 1 where S is expected duration of stormy weather N where N is expected duration of normal weather n 1
118 The state space diagram for the Markov m odel with one component and variable weather conditions is shown in Figure 6.5 State 0 Normal Weather System in Operation State 2 Normal Weather System Failed State 1 Stormy Weather System in Operation State 3 eather System Failed Stormy W m n m n s s Figure 6.5. Single Unit State Space Diagram Differential equations for this diagram in matrix forms are: m nm mm nn tPtPtPtP tP tPS S 0 0 03210 ' 1 0 m tPS S 03 (6.25) The steady sate probabilities can be f ound from the matrixefined (6.26) tP' 2 d in (6.25). 1 0 0 03210 32 0 3 1 0 21 0 PPPP mPPnP PPmnP PmPPnS S
For this system: 119 P( Syst d r le The BDMP modeling approach offers dvantages over conventional models because it allows complex dynamic models to be defined under variable weather conditions. em Operating) = 10PP availability P( System Failed) =32PP unavailability Implementation of smart grid technologi es into the power system creates a completely new structure, the smart grid. Evaluations and analysis of smart grid reliability with dynamic reconfiguration and variable weather conditions with existing analytical tools and methods is presently not possible, so the new modeling tools and techniques must be devel oped. The goal can be achieve d by formulating a new metho which combines techniques used for analysis of dynamic systems and techniques used fo analysis of the power system with variab le weather conditions. We developed a new method called the Variable Weather Boolean L ogic Driven Markov Process or Variab Weather BDMP. This innovation combines two modeling techniques: Markov modeling and modeling of variable weather conditi ons a
7. SMART GRID MODELING AND ANALYSIS The smart grid can offer substantial benef its through the integr ation of different technologies such as, renewable energy, storag e batteries, power and co ntrol electronics. S2System 2 S1System 1 S B PvL TPoint of Supply Pv B S Single R esidential C onsum er System 1st-Consum er K th-Consum er Load L TPoint of Supply Critical LoadL1 T1 T2 L2 STS Point of SupplyT LB Industrial Load D GW G Figure 7.1. Smart Grid Single Line Diagram A smart grid brings better operation of a power system in terms of power losses and reliability. In this section, we will anal yze the smart grid show n in Figure 7.1, under 120
121 variable weather conditions. We will use methods described in Chapter 6 (Boolean Logic Driven Markov Process (BDMP) under variab le weather condition), in our case of normal weather and stormy weather. In the main smart grid system, we have several subsystems: System with Distribution Generator, System with Battery Storage and Photovoltaic, System with Wind Generator a nd Battery Storage, and Static Transfer Switch. The reliability of all subsystems will be analyzed separately. The systems will be analyzed in many ways, such as: with no infl uence of weather, no smart grid elements, with smart grid elements and normal weather, and with the smart grid elements and stormy weather. As for the reliability indices, we will consider availability and unavailability of the power suppl y to the particular consumer industrial, commercial or residential. 7.1 System with Distributed Generator (DG) Distributed Generators (DG) can have an influence on the systems reliability. There are many technologies used for DG, including renewable energy (wind powered induction generators, photovoltaic, small hydro), gas turbine driven synchronous generators, fuel cells and others. The system we considered consists of: L Overhead transmissions line TPower Transformer DGDistribution Generator Load Here we are focusing on the most common applications for example, backup generation, used in hospitals shopping centers, etc. The basic connection is shown in
Figure 7.2. The Distribution Generator remains offline during normal operation, and is started if the utility supply is interrupt ed in order to feed the critical load. Figure 7.2. System with Distribution Generator (DG) Single Line Diagram 7.1.1. System with no DG and no Influence of Weather Parameter values for a Markov Model of a system with no DG and no weather conditions: hr yr L/0000517.0/5.0 hr MTTRyr L4 /25.0 hr yr T/00000388.0/34.0 hr MTTRyr T60 /0167.0 122
The state space diagram is shown in Figure 7.3 1 1 0 L L LT LT LT LT T L L T T T 2 3 0 0 0 Figure 7.3. State Space Diagram for Sy stem with no DG no Weather Conditions Differential equations for this diagram in matrix form are: tP tP tP tP tP tP tP tPTL L T L LT T T LT L T L TL 3 2 1 0 ' 3 2 1 00 0 0 0 (7.1) The steady sate probabilities can be found by solving equation (7.2): tP tP tP tP E E3 2 1 026666.0 0000571.058812.30 25.0 51666.0 058812.3 016666.00 0250038.0 0000571.0 1 1 1 1 0 0 0 1 (7.2) 8.09314.4 551226.7 0002282.0 9996953.03 2 1 0E E P P P P (7.3) For this system: P( Availability of Power Supply) = = 0.9999684 0PP(Unavailability of Power Supply)=321PPP =0.000316 123
7.1.2 System with no DG and with Normal Weather Conditions Parameter values for Markov Models of system with DG and normal weather conditions: hr Eyr L/05561.8/75.0 hr MTTRyr L4 /25.0 hr yr T/00000388.0/34.0 hr MTTRyr T60 /0167.0 The system has the same structure as th e system with no weat her conditions. The Markov state space diagram of the system is th e same, and so is the transition matrix. The solution for the steady state probabilities are: 8.0297.9 000142886.0 000335545.0 999652147.03 2 1 0E P P P P (7.4) For this system: P( Availability of Power Supply) = = 0.99952147 0PP(Unavailability of Power Supply)=321PPP =0.000478524 7.1.3 System with DG and No Influence of Weather Parameter values for Markov Model of a system with DG and no weather conditions: hr yr L/0000517.0/5.0 hr MTTRyr L4 /25.0 hr yr T/00000388.0/34.0 124
hr MTTRyr T60 /0167.0 hr yr G/00000228.0/2.0 hrMTTRyrG8 /125.0 Using BDMP, described in Chapter 6, th e state space diagram, Figure 7.4 is: L L 3 2 1 LT 1 0 L L T T T T 0 0 T T 4 5 1 1 1 G G G GLTG LTG LTG LTG LTG Figure 7.4. State Space Diagram for Sy stem with DG No Weather Conditions Differential equations for this diagram in matrix forms are: tP tP tP tP tP tP tP tP tP tP tP tPTG T G T TG G G GTL L T L LT T T GLT L T L TL 5 4 3 2 1 0 5 4 3 2 1 00 0 0 0 0 0 0 0 00 0 00 0 00 0 (7.5) 125
The steady sate probabilities can be found by solving equation (7.5) : 1167.9 0855.4 07305.5 0023228.0 0002278.0 9974487.05 4 3 2 1 0E E E P P P P P P (7.6) For this system: P( Availability of Power Supply) =3210PPPP = 0.999999958 P(Unavailability of Power Supply)=54PP =4.165E-08 7.1.4 System with DG and Alternative Weather Conditions, Normal and Stormy Weather Parameter values for a Markov Model of the system with DG alternative weather conditions are: Normal Weather Conditions hrEyr L/055616.8/75.0 hrMTTRyr L4 /25.0 hrEyr T/058812.3/34.0 hr MTTRyr T60 /0167.0 hrEyr G/0528.2/2.0 hrMTTRyrG8 /125.0 hrN 200 Normal Weather Duration 005.0 1 N n 126
Stormy Weather Conditions 127 hr yr L/000108447.0/95.0' hrMTTRyr L4 /25.0' hrEyr T/052785.6/55.0' hr MTTRyr T60 /0167.0' hrEyr G/0528.2/2.0' hrMTTRyrG8 /125.0' hrS 20 Stormy Weather Duration 05.0 1 S m Using the methods described in Chapter 6, the state space diagram, Figure 7.5 is developed.
Norm al W eather G G T T G G L L T T T L L T 4 0LTG 5 0LTG 0 1 LT 3 1LTG 2 1LTGLTG 1 1 LTStorm y W eatherLTGLTGLTGLTGLTGNorm al W eatherNorm al W eatherNorm al W eatherNorm al W eatherNorm al W eather 0 1 1 1 2 1 3 1 4 0 5 0 L L T G T T L L T G G T T GStorm y W eather Storm y W eather Stormy W eather Storm y W eather Storm y W eather n m m n m n m n m n m n Figure 7.5. State Space Diagram for Sy stem with DG and Alternative Weather Conditions, Normal, and Stormy Weather Differential equations for this diagram in matrix forms are: 2 1 'DIm InD tPtP (7.7) 128
Where and are matrices: 1D2D n n n n n n DTG T G T TG G G GTL L T L LT T T GLT L T L TL000 00 0 0 0 00 0 00 0 0001 (7.7) m m m m m m DTG T G T TG G G GTL L T L LT T T GLT L T L TL''''000 '''00'0 '0'''''0 00'''0' 00'0'''' 000''''2 (7.8) The steady sate probabilities can be found by solving equation (7.7): 1027.1 0706.1 0794.3 000941.0 000361.0 998698.0 1011.1 0888.5 0711.6 001788.0 000335. 0 997877.0 ' ' '5 4 3 2 1 0 5 4 3 2 1 0E E E E E E P P P P P P P P P P P P (7.9) 129
For the system: Normal Weather P( Availability of Power Supply) =3210PPPP = 0.999999941 P(Unavailability of Power Supply)=54PP =5.894E-08 Stormy Weather P(Availability of Power Supply) =3210'''' PPPP = 0.999999894 P(Unavailability of Power Supply)=54'' PP =1.06055E-07 7.2 System with Photovoltaic (P V) and Energy Storage System Photovoltaic systems (PV) deliver available renewable resources to a larger energy market. It improves the economics of transmission and the distribution of electrical energy. Todays ch allenge is that the signifi cant deployment of PV energy requires modernization of the electrical energy distribution grid to a new generation smart grid. The distribution PV systems operate interactively with available solar resources, varying conditions on the grid, and other local resources, includi ng load control and future generation and storage resources. However, the solar energy has drawbacks since it does not provide a constant supply of energy. There are days where the sun just doesnt come out. When connected to a battery storag e system, the energy can be stored and used as needed. The cycle of charging and disc harging will repeat itself daily, and the consumer will only have to pay for the initial installation of the system, after that, the energy is literally free. 130
131 By storing energy, utilities can eliminate the need for a peaking generator that will only be used when demand is at its highest, and whose capacity will never be realized. In addition, by turning on extra generators, they overshoot the market demand. Consumers who live in remote areas that are not conn ected to a distribution system can rely on renewable energy to supply them. The most obvious uses of an Energy Storage System are for better efficiency of the smart grid and for capital gain. Perhaps their biggest advantage is the ability to regulate all the energy that is being produced By practically eliminating losses through storage and then releasing the required amount during peak times, the system can use all the energy effectively. For this study we ar e considering individual residential consumers with the following structure, Figure 7.6: L Overhead transmissions line TPower Transformer PvPhotovoltaic BBattery (Energy Storage System) S Residential Consumer
Figure 7.6. System with PV and Energy St orage System (B), Single Line Diagram 7.2.1 System with no PV and Battery The system will consist only of a Line and Transformer. The analysis and the results are the same as for the system with th e DG that we analyzed in sections 7.1.1 and 7.12. 7.2.2 System with PV and Energy Storage System and no Influence of Weather Parameter values for a Markov Model for a system with PV and Energy Storage System and no weather conditions are: hr yr L/0000517.0/5.0 hrMTTRyr L4 /25.0 hr yr T/00000388.0/34.0 hr MTTRyr T60 /0167.0 132
hr yr Pv/00000228.0/02.0 hrMTTRyr Pv4 /25.0 hr yr B/0000114.0/1.0 hr MTTRyr B5.2 /4.0 Using BDMP, described in Chapter 6, th e state space diagram, figure 7.7, is: T B B L L B B 1 1LTBPvLTBPv 1 2 LTBPv 0 3 LT 1 0 LTBPv 0 5 LTBPv 1 4 T L L T T L T B L PV PV PV 7 0LTGPvLTGPv 0 8 LTGPv 1 9 LTGPv 0 6 LTGPv 0 10 B PV PV T L L T T PV B B PV PV Figure 7.7. State Space Diagram for System with PV and Energy Storage System No Weather Conditions 133
Differential equations for this diagram in matrix forms are: T PV Pv T B PVBTB B L B BPVT L T L BPVL B L B LTB T T BLT L T L TL tP tP tP tP tP tP tP tP tP tP tP 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 0 00 0 0 0 0 0 00 0 0 0 00 0 0 0 0 0 0 0 0' 10 9 8 7 6 5 4 3 2 1 0 tP tP tP tP tP tP tP tP tP tP tP LBTPV B L T L BPV T LPV TPV PV PV PV BTPV T PV PV B 10 9 8 7 6 5 4 3 2 1 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (7.10) The steady sate probabilities can be found by solving equation (7.10): 16 42064.5 12 84608.4 13 06725.6 14 93737.5 09 49848.6 1077231.1 0730575.5 08 63922.6 002322832.0 000227728.0 997448836.010 9 8 7 6 5 4 3 2 1 0E E E E E E E E P P P P P P P P P P P (7.11) 134
For this system: P (Availability of Power Supply) =94210PPPPP = 0.9999999269 P (Unavailability of Power Supply)=1087653PPPPPP =7.3000685E-08 7.2.3 System with PV and Energy Stor age System, and Alternative Weather Conditions, Normal and Stormy Weather Parameter values for a Markov Model of a system with PV and Energy Storage System and alternative weather conditions are: Normal Weather Conditions hrEyr L/055616.8/75.0 hrMTTRyr L4 /25.0 hrEyr T/058812.3/34.0 hr MTTRyr T60 /0167.0 hr yr Pv/00000228.0/08.0 hrMTTRyr Pv4 /25.0 hr yr B/0000114.0/1.0 hr MTTRyr B5.2 /4.0 Normal Weather Duration hrN 200 005.0 1 N n Stormy Weather Conditions hr yr L/000108447.0/95.0' hrMTTRyr L6 /1666.0' 135
136 hrEyr T/052785.6/55.0' hr MTTRyr T60 /0167.0' hr yr Pv/00001415.0/1.0' hrMTTRyr Pv6 /1666.0' hr yr B/0000114.0/1.0' hrMTTRyr B4 /25.0' hrS 20 Stormy Weather Duration 05.0 1 S m Differential equations for this diagram in matrix forms are: 2 1 'DIm InD tPtP (7.12) Using methods described in Chapter 6, th e state space diagram, figure 7.8, is:
n m n m n m n m m n 0 10 1 9 0 8 0 7 0 6 7 0LTGPvLTGPv 0 8 LTGPv 1 9 LTGPv 0 6 LTGPv 0 10 B PV PV T L L T T PV B B PV PV LTGPv LTGPv LTGPv LTGPv LTGPv B T PV L PV T L PV Normal Weather Stormy Weather Stormy WeatherNormal WeatherNormal Weather Stormy WeatherNormal Weather Stormy WeatherNormal Weather Stormy Weather L L B B B B TStormy WeatherNormal Weather Stormy WeatherNormal Weather Stormy WeatherNormal Weather Stormy WeatherNormal Weather Stormy WeatherNormal Weather PV L PV T L L PV L T T B T LT LTBPv LTBPv LTBPv LTBPv LTBPv T B B L L B B n m n m n m n m n m m n 0 5 1 4 0 3 1 2 1 1 1 0Stormy Weather 1 1LTBPvLTBPv 1 2 LTBPv 0 3 LT 1 0 LTBPv 0 5 LTBPv 1 4 T L L T T L T B L PV PV PV Normal Weather T Figure 7.8. State Space Diagram for System with PV and Energy Storage System and Alternative Weather Conditions, Normal, and Stormy Weather 137
In equation (7.12), and are matrices: 1D2D T PV Pv T B PVBTB B L B BPVT L T L BPVL B L B LTB T T BLT L T L TL D 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 0 00 0 0 0 0 0 00 0 0 0 00 0 0 0 0 0 0 0 01 LB TPV B L T L BPV T LPV TPV PV PV PV B TPV T PV PV B 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (7.13) 138
T PV Pv T B PVBTB B L B BPVT L T L BPVL B L B LTB T T BLT L T L TL D 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 '0 ''''' 0 0 0 ''''0 '0 0'''' 0 0 0 ''''0' 0 0 0'''' 0 0 0 '''2 LB TPV B L T L BPV T LPV TPV PV PV PV B TPV T PV PV B ''''' ' 0 ' 0 0 0 0'' 0 0 0 0 0'' ' 0 0 .''' 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (7.14) The steady sate probabilities can be found by solving equation (7.12): Normal Weather Stormy Weather 15 25232.3 11 90739.2 12 42928.2 13 56202.3 097466.9 1065821.2 07 95793.7 08 64353.6 00232257.0 000341553.0 997335004.010 9 8 7 6 5 4 3 2 1 0E E E E E E E E P P P P P P P P P P P (7.15) 14 92133.2 10 67302.1 11 18033.1 12 01785.2 08 95751.2 09 24487.1 06 44214.2 07 72014.1 003750572.0 000647821.0 995598961.0 ' ' ' ' ' '10 9 8 7 6 5 4 3 2 1 0E E E E E E E E P P P P P P P P P P P 139
For the system: Normal Weather P( Availability of Power Supply) =94210PPPPP = 0.999999924 P(Unavailability of Power Supply)=1087653PPPPPP =7.645E-08 Stormy Weather P( Availability of Power Supply) =94210''''' PPPPP = 0.999999792 P(Unavailability of Power Supply)=1087653'''''' PPPPPP =2.028E-07 7.3. System with Wind Generator and Energy Storage System 140 Wind power is currently supplying a noticeable amount of electricity around the world. In some countries, about 20% of electrical loads are supplied from the wind generations. Wind generated power is an importa nt part of the smart grid. Some question whether wind power, being a variable resour ce (meaning it generates electricity when the wind is blowing, not on demand) can be relied upon as part of a sy stem that provides reliable electricity to cons umers without interruption. Wind generated power today with the smart grid technologies can readily be accommodated into power electric system operations reliably and economically. As the speed of the wind changes, so does the electrical output from a wind turbine. The En ergy Storage System, batteries are needed to store power and smooth out fluctuations in the power supply. In the future, through advances in technologies such as batteri es and compressed air, energy storage may become cost-effective. The prospect of plug-in hybrid electric vehicles holds great promise because the expense of their batteries would be covered by their fuel cost savings and they could provide many megawatts of storage for the overall electrical power system. When wind isn't blowing, reliable el ectrical service is maintained by turning up
141 the output of other power source to the smart grid system. Wind behaves similar to load in that it is "variable," meaning its output rises and falls within hourly and daily time periods; and it is "non-dispat chable," meaning its output can be controlled only to a limited extent. Wind turbine system reliability is a critic al factor in the success of a wind energy project. A wind turbines reliability is depende nt largely on the particular machine model, how well it is designed, and the quality of manufacture. Reliability also varies with the operating environment, as it is the machin es reaction to the wind environment that determines the loading imposed on the compone nts. The variety of potential component failures gearbox bearings, ge nerator bearings and windings power electronics, gearbox torque arms, pitch drive electronics indi cate that the operati ng conditions and load conditions for a large wind turbin e and not completely understood. For this study, we are considering in dividual industrial consumers supplied by Wind Generations and Energy Storage System with the following structure, figure 7.9: L Overhead transmissions line TPower Transformer WgWind Generator BBattery (Energy Storage System) Industrial Consumer
Figure 7.9. System with Wind Generator (W g) and Energy Storage System (B), Single Line Diagram 7.3.1 System with no Wind Generator and Energy Storage System (Battery) The system will consist only of a Line and Transformer. The analysis and the results will be the same as for the system w ith the DG, we analyzed in 7.1.1 and 7.12. 7.3.2 System with Wind Generator and no Influence of Weather Parameter values for Markov Model for system with Wind Generator and Energy Storage System and no weather conditions: hr yr L/0000517.0/5.0 hr MTTRyr L4 /25.0 142
hr yr T/00000388.0/34.0 hr MTTRyr T60 /0167.0 hr yr G/000005707.0/05.0 hrMTTRyr Pv5 /2.0 hr yr B/0000114.0/1.0 hr MTTRyr B5.2 /4.0 Using BDMP, described in Chapter 6, th e state space diagram, figure 7.10, is: T B B L L B B 1 1LTBWgLTBWg 1 2 LTBWg 0 3 LT 1 0 LTBWg 0 5 LTBWg 1 4 T L L T T L T B L PV PV PV 7 0LTGWgLTGWg 0 8 LTGWg 1 9 LTGWg 0 6 LTGWg 0 10 B PV PV T L L T T PV B B PV PV Figure 7.10. State Space Diagram for System with Wg and Energy Storage System no Weather Conditions Differential equations for this diagram in matrix forms are: 143
T Wg Wg T B WgBTB B L B BWgT L T L BWgL B L B LTB T T BLT L T L TL tP tP tP tP tP tP tP tP tP tP tP 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0' 10 9 8 7 6 5 4 3 2 1 0 tP tP tP tP tP tP tP tP tP tP tP LB TWg B L T L BWg T LWg TWg Wg Wg Wg B TWg T Wg Wg B 10 9 8 7 6 5 4 3 2 1 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (7.16) The steady sate probabilities can be found by solving equation (7.16): 15506012.1 11 86524.1 12 89769.1 13 85559.1 094987.6 10 79345.1 07 53508. 6 08 64458.6 08 64458.6 000227736.0 997446872.010 9 8 7 6 5 4 3 2 1 0E E E E E E E E P P P P P P P P P P P (7.17) For this system: P( Availability of Power Supply) =94210PPPPP = P(Unavailability of Power Supply)=1087653PPPPPP = 7.31259E-08 144
7.3.3 System with Wind Generator and Energy Storage System, and Alternative Weather Conditions Normal and Stormy Weather Parameter values for Markov Model of system with Wind Generator and Energy Storage System and alternative weather conditions are: 145 Normal Weather Conditions hrEyr L/055616.8/75.0 hrMTTRyr L4 /25.0 hrEyr T/058812.3/34.0 hr MTTRyr T60 /0167.0 hr yr Wg/00001027.0/09.0 hrMTTRyr Wg7 /142.0 hr yr B/0000114.0/1.0 hr MTTRyr B5.2 /4.0 Normal Weather Duration hrN 200 005.0 1 N n
146 Stormy Weather Conditions hr yr L/000108447.0/95.0' hrMTTRyr L4 /25.0' hrEyr T/052785.6/55.0' hr MTTRyr T60 /0167.0 hr yr Wg/0000228.0/2.0' hr MTTRyr Wg10 /1.0' hr yr B/0000114.0/1.0 hr MTTRyr B5.2 /4.0 hrS 20 Stormy Weather Duration 05.0 1 S m Differential equations for this diagram in matrix forms are: 2 1 'DIm InD tPtP (7.18) Using methods described in Chapter 6, the stat e space diagram, figure 7.11, is given next.
LTBWg LTBWg LTBWg LTBWgLTBWg LTBWg LTBWgNormal Weather Stormy WeatherNormal Weather Stormy WeatherNormal Weather Stormy WeatherNormal Weather Stormy WeatherNormal Weather Stormy Weather T B B B B L LStormy WeatherNormal Weather Stormy WeatherNormal Weather Stormy WeatherNormal WeatherNormal Weather Stormy Weather Stormy WeatherNormal Weather PV L T PV L PV T B PV PV B B PV T T L L T PV PV B 10 0 6 0 9 1 8 0 0 7 6 0 7 0 8 0 9 1 10 0 n m m n m n m n m nLTBWg LTBWg LTBWg LTBWg LTBWg LTBWg LTBWg LTBWg LTBWg LTBWg LTBWg LTBWg TNormal Weather PV PV PV L B T L T T L L T 4 1 5 0 0 1 LT 3 0 2 1LTBWg 1 1Stormy Weather 0 1 1 1 2 1 3 0 4 1 5 0 n m m n m n m n m n m n B B L L B B T LT T B T T L PV L L T PV L PV Figure 7.11. State Space Diagram for System with PV and Energy Storage System and Alternative Weather Conditions, Normal, and Stormy Weather 147
In the equation (7.18), and are matrices: 1D2D T Wg Wg T B WgBTB B L B BWgT L T L BWgL B L B LTB T T BLT L T L TL D 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 01 L B T Wg B L T L B Wg T L Wg T Wg Wg Wg Wg B T Wg T Wg Wg B 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (7.19) T Wg Wg T B WgBTB B L B BWgT L T L BWgL B L B LTB T T BLT L T L TL D 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 '''' 0 0 0 ''' 0 ' 0 0 ''' 0 0 0 ' ''' 0 0 0 0 '''' 0 0 0 ' ''2 LB TWg B L T L BWg T LWg TWg Wg Wg Wg B TWg T Wg Wg B '''' ' 0 ' 0 0 0 0'' 0 0 0 0 0'' ' 0 0 '''' 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (7.20) 148
The steady sate probabilities can be found by solving equation (7.18): Normal Weather Stormy Weather 15 38644.5 11 59902.9 12 80131.4 130146.7 09 74754.9 10 75101.2 06 33462.1 08667.6 002330592.0 000341586.0 997326411.010 9 8 7 6 5 4 3 2 1 0E E E E E E E E P P P P P P P P P P P (7.21) 14 25527.8 107936.8 11 95184.3 127635.6 08 95825.2 09 28244.1 06 85113.3 07 72676.1 003764514.0 000647952.0 995583479.0 ' ' ' ' ' '10 9 8 7 6 5 4 3 2 1 0E E E E E E E E P P P P P P P P P P PFor the system: Normal Weather P( Availability of Power Supply) =94210PPPPP = 0.999999923 P(Unavailability of Power Supply)=108763PPPPP =7.66981E-08 Stormy Weather P( Availability of Power Supply) =94210''''' PPPPP = 0.999999796 P(Unavailability of Power Supply)=108763''''' PPPPP =2.03587E-07 Reliability of the smart grid under norm al and stormy weather conditions is analyzed with a new developed method, VW -BDMP (figure 7.1). The analyzed smart grid consists of several subsystems: System with Distribution Generator, System with Battery Storage and Photovoltaic, System with Wind Generator and Battery Storage. The reliability of all subsystems is analyzed sepa rately. The subsystems will be analyzed with no influence of weather, with no smart grid elements, with smart grid elements and normal weather, and with the smart grid elements and stormy weather. For reliability, 149
150 indices considered are availabi lity and unavailability of the power supply to the particular consumer--industrial, commercial or residentia l. The results show improvement of the reliability indices with the smart grid tec hnologies and also show the influence of the weather. The weather expected has a negativ e influence on the reliability of the smart grid.
151 CHAPTER 8: DISCUSSION, CONCL USIONS, AND RECOMMENDATIONS FOR FURTHER RESEARCH Smart grid engineering is divided into two stages, planni ng, and design. The planning stage is for identifying system n eeds and limitations, to propose projects, to resolve issues, and to obtain approvals for pr ojects. The design stag e takes a project from concept to the final realization. Smart gr id technologies are expected to change fundamental design and operating requirement s of the electric power system. The primary engineering tools for smart grid an alysis and design are power flow and faultcurrent studies. Power flow computes stea dy state voltages and currents of systems ensuring that the system will meet criteria of equipment loading, voltage drops, and system losses. Although power flow modeling can predict electrical properties of the smart grid, reliability modeling predicts the availability and interruptions of such a system. A Smart grid will allow current power electrical systems to incorporate better renewable energy sources such as wind and so lar power, back-up distribution generators and energy storage systems. 8.1 Discussions and Conclusions Reliability of the smart grid is one of the most important areas of reliability theory application. Random failures ar e certain to occur from time to time, especially when elements of weather or other causes pres ent hazards that the power system was not
152 designed to withstand. Failures also happen due to poor maintenance, aging, improper processes and multiple other explanations Reliability methods provide important analytical tools that can be used to evaluate and compare smart grid design and performance since each component has a uni que characteristic. Models should be as simple as possible, but they need to represen t all features that ar e critical to systems reliability. Reliability parameters vary from component to component or from situation to situation. Component reliability data are one of the most important parameters of the smart grid reliability assessment. This research used reliable information based on historical utility data, manufacturer test data documents and references from professional organizations, and other technical confer ences and journal proceedings. Electrical equipment reliability data are usually obtai ned from surveys of individual industrial equipment failure reports. Collec tion of reliability data is a continuous process since it is constantly updated. The smart grid reliability indices are used to quantify sustained interruptions. Short duration outages for some customers, such as hospitals and large industrial customers, can result in complex systems shutting down. In many cases, these customers have installed backup generation or other m eans of addressing short-duration outages. In particular, it is these types of outages that would benefit from the presence of distributed generation and energy storage. Therefore, a reliability index shoul d not only quantify enhanced reliability for sustained interrupt ions, but also for short-duration outages. Earlier research work focused on mode ling the effects of extreme weather conditions on power distribution systems, and on sp ecific weather parameters causing specific faults in the distribution system. Various methods are there to study extreme
153 weather conditions such as tornadoes and hu rricanes. There are also individual models for interruption causes such as equipment fa ilure. A study of interruptions as a function of common weather has not been done in depth thus far. This study bridges that gap. This type of research was not earlier possible for multiple reasons; the weather recording system has improved recently, the communi cation network has improved, only lately have smart grid applications and technologies been introduced to the old grid network. These data are required to conduct such research, and was not available earlier. This study has shown that there is a hidden weather component in most of the causes of interruptions. These interrupti ons and weather conditions are studied probabilistically and a novel, predictive method has b een developed on that basis. A theoretical model based on va riable weather conditions is used to predict power distribution interruptions, wh ile immediate weather conditions are used to analyze interruption risk assessment This study creates a better understand ing of the relationship between common weather conditions and the number of interruptions, which in turn will open a completely new spectrum of research on reliability of power distribution systems. This study did not only develop a novel combined theoretical model regarding the effects of common weather (while incorporating existing, releva nt ones), but applied them by solving the problem of predicting the daily number of interruptions. Furthermore, risk assessment is a strong tool that can be used by manageme nt to achieve maximum efficiency when planning the amount of long and short-term manpower and equipment inventory. This predictor is a patent property of the Univer sity of South Florida, Tampa, Fl USA.
154 Variability of reliability (and reliabil ity indices) from system to system or from year to year within a system (due to ci rcumstances beyond the control of the system operator), are recognized as a problem that inte rferes with a fair assessment of a systems reliability. The development of a method fo r normalization of reliability indices for weather is a recognized need and th is research suggests a solution. Dynamic reconfigurations of the smart grid and variable weather conditions create difficulties in reliability modeling and analysis. To overcome these obstacles, a unique method was developed, which combines th ree modeling techniques: Markov modeling, Boolean Logic Driven Markov Process (BDM P) and Modeling of a variable weather condition. This modeling approach has adva ntages over conventional models because it allows complex dynamic models to be defi ned and still remain easily readable. Markov modeling is a method based on syst em states and the transition between these states. It can be either discrete or continuous. Disc rete Markov modeling is called Discrete Markov Chain, while continuous is called continuous Markov Processes. This research modeled smart grid reliability w ith a continuous Markov Process. Instead of state probabilities, Markov Processes use state transition rates. This is very suitable in application of smart grid reli ability, because failure rates of smart grid components are equivalent to state transition rates. To use Markov modeling, the failures of smart grid components equipment are assumed to be e xponentially distributed, so the failure rates are constant. Also other values such as th e switching rate and the repair rate use exponential distributions. Failure rates, the switch ing rates and the repair rates are reciprocals of the Mean Time to Fail (MTTF ), Mean Time to Switch (MTTS) and Mean Time to Repair (MTTR).
155 The purpose of BDMPs is to provide a ne w graphic representation of fault trees, augmented only by a new kind of link, which is represented by dotted arrows. This enables combined conventional fault trees and Markov processes in a completely new way. BDMPs dramatically reduce combinator ial problems in operational applications. From a mathematical point of view, a BDMP is made of a multi-top coherent fault tree, a set of triggers and a set of triggered Markov processes. Systems were analyzed with a distribu tion generator, a system with a photovoltaic source and energy storage, and a system with a wind generator and energy storage. The systems were all analyzed with no outside influence of weather and any smart grid elements; with smart grid elements and normal weather; and smart grid elements and stormy weather. To view reliability of a smar t grid system, availability and unavailability of power supply to the particular consumer, industrial, commercial or residential was studied. The expected results were obtained. The highest unavailability of the system is with no smart grid elements including an infl uence of weather, follo wing the system with no smart grid elements and no weather. The system, with the smart grid elements and normal weather, has the smallest unavailability, followed by the system with the smart grid and the stormy weather. While availability is in reverse order, the highest availability is the system with smart grid elements a nd normal weather, followed by the system with the smart grid elements and stormy weather. In addition, there is a noticeable improvement of availability/unavailability of systems with smart grid elements.
156 The main contributions as discussed earlier can be su mmarized into a list given below: A Method for modeling smart grid dynamic reconfigurations under variable weather condition combining the three modeling techniques (Markov modeling, Boolean Logic Driven Markov Process (B DMP) and the modeling of variable weather conditions). Developed a method of predicting power distribution interruptions in a given region based on common weather conditions while assessing the risk of interruptions on immediate weather conditions. Using daily and hourly weather data, the method predicts the number of daily or by-sh ift interruptions. A method was developed for normalizing the reliability indices for common weather conditions. The methods comm only used are based on changes and comparisons of present and past performance. The developed method diminishes the impact of variable weather conditions and makes comparisons that allow for more accurate determination of reliability performance. Developed the predictor method that will reduce downtime of power interruptions by proper distribution of the service work force. The model offers an economical tool with negligible maintenance cost s to utilities and improves its Systems Average Interruption Frequency Index (SAIFI), while increasing its power transmission. The goal of this research was to find a new method that can be used for modeling the dynamics of the smart grid with variab le weather conditions. It is achieved by a combination of the techniques mentioned ear lier. To show and prove the models,
157 simplified smart grid configurations were used. While the present research goal is achieved with the new proposed method on the small-scale system, recommendations for future research are to develop an algorithm and software for the large-scale system using this developed method. 8.2 Recommendations for Future WorkSmart grid applications and technologie s are still being implemented to the transmission and distribution grid systems. Relia bility studies of such systems are still in their infancy stage. There are many new things being done on the grid, which is expected to improve its efficiency and reliability. There will be many new things to understand and incorporate in the reliability study. In such situations, a c ontinuous in-depth reliability study is required. It is exp ected that with the expect ed improvement in system performance, research in the reliability fiel d has to keep pace to provide novel methods and tools to understand the modern grid. A smart grid consists of a variety of power components such as transformers, generators, overhead lines, renewable energy resources, energy storage elements and a micro-grid. A smart grid will allow current electricity grids to incorporate better renewable energy sources such as wind and so lar power, back-up distribution generators and advanced energy storage systems. Smart gr id technologies are expected to change the fundamental design and operating requirement s of the electric power system. To understand and analyze smart grid impacts on power system operations and design, several issues have been identified: Current reliability analysis and modeli ng tools must evolve to address the futures more interactive power system and to simplify engineering tools to
158 more efficiently handle the smart grid technologies related issues. New reliability and other analytical methods/tools are needed to determine effects of penetration of smart grid technologies on opera tion of the power system, as well as the resultant effect s on power system quality, reliability, and availability. Modern reliability tools can help in defining strength of grid to absorb more amount of renewable resour ces that can be installe d strategically to serve larger number of customers Novel software programs could be devel oped on the basis of this research to bring in like minded customers to use more amount of renewable energy resources that would help make our world far better place to live.
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APPENDIX A: DEFINITIONS AND FORMULAE The following are the definitions and formulae defined by IEEE (40) for reliability studies. Note: reprinted with permission from IEEE Std. 1366-2003 IEEE Guide for Electric Power Reliability Indices 2003 IEEE]*, by IEEE. The IEEE disclaims any responsib ility or liability resulting from the placement and use in the described manner 4. Reliability Indices 4.1 Basic factors These basic factors specify the data needed to calculate the indices. i denotes an interruption event ir Restoration Time for each Interruption Event CI Customers Interrupted CMI Customer Minutes Interrupted E Event T Total IMt Number of Momentary y Interruptions IMg Number of Momentary g Interruption Events Nr Number of Interrupted Customers N Number of Interrupted Customers for each Momentary Interruptions event during the Reporting Periods NT Total Number of Customers Served for the Areas LV Connected LVA load Interrupted for each Interruption Event LT Total Connected LVA Load Served CN Total Number of Customers who have Experienced a Sustained Interruption during the reporting period CNT Total Number of Customers who have Experienced more than Sustained Interruptions and Momentar y Interruption Events during the Reporting Period From IEEE Std. 1366-2003 IEEE Guide for Electric Power Reliabi lity Indices 2003 IEEE*, by IEEE. All rights reserved. 166
Appendix A (continued) Number of Interruptions Experience d by an Individual Customer in the Reporting Period TMED Major Event day Identifi cation threshold value 4.2 Sustained In terruption Indices 4.2.1 System average interruption frequency index (SAIFI) The system average interruption frequenc y index indicates how often the average customer experiences a sustained interr uption over a predefined period of time. Mathematically, this is given in Equation (1) SAIFI = Serve d Customers o f Number Total dInterrupte Customers of Total (1) To calculate the index, use equation (2) below: SAIFI = T T i N CI N N (2) 4.2.2 System average interru ption duration index (SAIDI) This index indicates the total duration of in terruption for the average customer during a predefined period of time. It is commonly m easured in customer minutes or customer hours of interruption. Mathematically this is given in Equation (3). SAIDI = Serve d Customers o f Number Total Durationon Interrupti Customer (3) To calculate the index, use Equation (4) SAIDI = T T NYNNiiCMI (4) From IEEE Std. 1366-2003 IEEE Guide for Electric Power Reliabili ty Indices 2003 IEEE*, by IEEE. All rights reserved. 167
Appendix A (continued) 4.2.3 Customer average interruption during index (CAIDI) CAIDI represents the average time required to restore service. Mathematically, this is given in Equation (5) CAIDI = dInterrupte Customers ofNumber Total Duration ons Interrupti Customer (5) To calculate this index, use Equation (6) CAIDI = SAIFI SAIDI i iiN NY (6) 4.2.4 Customer total average in terruption durati on index (CTAIDI) This index represents the total average time in the reporting period that customers who actually experienced an interruption were wit hout power. This index is hybrid of CAIDI and is similarly calculated except that thos e customers with multiple interruptions are counted only once. Mathematically, this is given in Equation (7) CTAIDI = dInterrupte Customers ofNumber Total Durationon Interrupti Customer (7) To calculate the index, use Equation (8) CTAIDI = CNiiNT (8) Note Is tallying Total Number of Custom ers Interrupted, each individual customer should only be counted once regardless of times interrupted during the reporting period. This applies to 4.2.4 and 4.2.5. From IEEE Std. 1366-2003 IEEE Guide for Electric Power Reliabi lity Indices 2003 IEEE*, by IEEE. All rights reserved. 168
Appendix A (continued) 4.2.5 Customer average interruption frequency index (CAIFI) This index gives the average frequency of sustained interruptions for those customers experiencing sustained interruptions. The cu stomer is counted on ce regardless of the number of times interrupted for this calculati on. Mathematically, this is given in Equation (9) CAIFI = dInterrupte Customers ofNumber Total dInterrupte Customers ofNumber Total (9) To calculate the index, use Equation (10) CAIFI = CN Ni (10) 4.2.6 Average service availability index (ASAI) The average service availability index repr esents the fraction of time (often in percentage) that a customer has received power during the define d reporting period. Mathematically, this is given in Equation (11) ASAI = Deman d Service Hours Customer tyAvailabili Service Hours Customer (11) To calculate the index, use Equation (12) ASAI = hours/yr) of(Number hours/yr) of(Numner XN Nr XNT ii T (12) NoteThere are 8760 hours in a non-leap year, 8784 hours in a leap year. 4.2.7 Customers experiencing multiple interruptions (CEMIn) This index indicates the ration of individual customers experiencing more than n sustained interruptions to the total number of customers served. From IEEE Std. 1366-2003 IEEE Guide for Electric Power Reliabi lity Indices 2003 IEEE*, by IEEE. All rights reserved. 169
Appendix A (continued) Mathematically, this is given in equation (13) CEMIn= Served Customers ofNumber Total ons interrupti sustained than more experience that Customers ofNumber Total n (13) To calculate the index, use Equation (14) CEMIn = T nkN CN)( (14) Note This index is often used in a series of calculations with n incremented from a value of one to the highe st value of interest. 4.3 Load based indices 4.3.1. Average system interruption frequency index (ASIFI) The calculation of this index is based on load rather than customers affected. ASIFI is sometimes used to measure distribution perfor mance in areas that serve relatively few customers having relatively large concentrations of load, predominantly industrial/commercial customers. Theoretica lly, in a system with homogeneous load distribution, ASIFI would be the same as SAIFI. Mathematically, this is given in Equation (15) ASIFI = Serve d kVA Connecte d Total dInterrupte Load ofkVA Connected Total (15) To calculate the index use Equation (16) ASIFI = T iL L (16) 4.3.2 Average system interruption duration index (ASIDI) The calculation of this index is based on load rather than customers affected. Its use, limitations, and philosophy are stated in the ASIF I definition in 4.3.1. Mathematically, From IEEE Std. 1366-2003 IEEE Guide for Electric Power Reliabi lity Indices 2003 IEEE*, by IEEE. All rights reserved. 170
Appendix A (continued) this is given in Equation (17). ASIDI= ServedkVA Connected Tital dInterrupte Load ofDuration kVA Connected (17) To calculate the index, use Equation (18). ASIDI = T LYLii (18) 4.4 Other indices (momentary) 4.4.1 Monetary average interr uption frequency index (MAIFI) This index indicates the average frequency of momentary interruptions. Mathematically, this is given an Equation (19). MAIFI = Serve d Customers o f Number Total onInterrupti Momentary Customer ofNumber Total (19) To calculate this index, use Equation (20) MAIFI = T N miiNIM (20) From IEEE Std. 1366-2003 IEEE Guide for Electric Power Reliabi lity Indices 2003 IEEE*, by IEEE. All rights reserved. 171
172 ABOUT THE AUTHOR Arif Islam received his B.Tech. degree in Electronics Engineering from A.M.U., India in 1994 and his M.S. degree in electrical and com puter engineering from the University of Florida, Gainesville. He jo ined Siemens in 1994 and has worked in the industry for more than a decade executing ma ny multi-million dollar projects. He enjoys research and produces time bound results utilizing his knowledge, experience and management tools. He is now at the University of South Florida as the Deputy Director of the Power Center for Utility Explorations (PCUE) and the Power & Energy Applied Research Laboratory. His fields of interest include smart grid, power reliability, power electronics, motor and drive systems, unders tanding natural and man-made hazards, and the evaluation of alternative re sources of energy. He has be en successful in receiving on average, 7 million dollars of project grants fr om the industry as well as from federal and state agencies. Currently he is the CoPrinci ple Investigator for more than eight major projects in the smart grid area.