Probabilistic Transmission System Planning E-Book

Wenyuan Li

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Veröffentlichungsjahr: 2011

Beschreibung

The book is composed of 12 chapters and three appendices, and can be divided into four parts. The first part includes Chapters 2 to 7, which discuss the concepts, models, methods and data in probabilistic transmission planning. The second part, Chapters 8 to 11, addresses four essential issues in probabilistic transmission planning applications using actual utility systems as examples. Chapter 12, as the third part, focuses on a special issue, i.e. how to deal with uncertainty of data in probabilistic transmission planning. The fourth part consists of three appendices, which provide the basic knowledge in mathematics for probabilistic planning.

Leseprobe

Table of Contents

Cover

Series page

Title page

Copyright page

Dedicated

PREFACE AND ACKNOWLEDGMENTS

1 INTRODUCTION

1.1 OVERVIEW OF TRANSMISSION PLANNING

1.2 NECESSITY OF PROBABILISTIC TRANSMISSION PLANNING

1.3 OUTLINE OF THE BOOK

2 BASIC CONCEPTS OF PROBABILISTIC PLANNING

2.1 INTRODUCTION

2.2 PROBABILISTIC PLANNING CRITERIA

2.3 PROCEDURE OF PROBABILISTIC PLANNING

2.4 OTHER ASPECTS IN PROBABILISTIC PLANNING

2.5 CONCLUSIONS

3 LOAD MODELING

3.1 INTRODUCTION

3.2 LOAD FORECAST

3.3 LOAD CLUSTERING

3.4 UNCERTAINTY AND CORRELATION OF BUS LOADS

3.5 VOLTAGE- AND FREQUENCY-DEPENDENT BUS LOADS

3.6 CONCLUSIONS

4 SYSTEM ANALYSIS TECHNIQUES

4.1 INTRODUCTION

4.2 POWER FLOW

4.3 PROBABILISTIC POWER FLOW

4.4 OPTIMAL POWER FLOW (OPF)

4.5 PROBABILISTIC SEARCH OPTIMIZATION ALGORITHMS

4.6 CONTINGENCY ANALYSIS AND RANKING

4.7 VOLTAGE STABILITY EVALUATION

4.8 TRANSIENT STABILITY SOLUTION

4.9 CONCLUSIONS

5 PROBABILISTIC RELIABILITY EVALUATION

5.1 INTRODUCTION

5.2 RELIABILITY INDICES

5.3 RELIABILITY WORTH ASSESSMENT

5.4 SUBSTATION ADEQUACY EVALUATION

5.5 COMPOSITE SYSTEM ADEQUACY EVALUATION

5.6 PROBABILISTIC VOLTAGE STABILITY ASSESSMENT

5.7 PROBABILISTIC TRANSIENT STABILITY ASSESSMENT

5.8 CONCLUSIONS

6 ECONOMIC ANALYSIS METHODS

6.1 INTRODUCTION

6.2 COST COMPONENTS OF PROJECTS

6.3 TIME VALUE OF MONEY AND PRESENT VALUE METHOD

6.4 DEPRECIATION

6.5 ECONOMIC ASSESSMENT OF INVESTMENT PROJECTS

6.6 ECONOMIC ASSESSMENT OF EQUIPMENT REPLACEMENT

6.7 UNCERTAINTY ANALYSIS IN ECONOMIC ASSESSMENT

6.8 CONCLUSIONS

7 DATA IN PROBABILISTIC TRANSMISSION PLANNING

7.1 INTRODUCTION

7.2 DATA FOR POWER SYSTEM ANALYSIS

7.3 RELIABILITY DATA IN PROBABILISTIC PLANNING

7.4 OTHER DATA

7.5 CONCLUSIONS

8 FUZZY TECHNIQUES FOR DATA UNCERTAINTY

8.1 INTRODUCTION

8.2 FUZZY MODELS OF SYSTEM COMPONENT OUTAGES

8.3 MIXED FUZZY AND PROBABILISTIC MODELS FOR LOADS

8.4 COMBINED PROBABILISTIC AND FUZZY TECHNIQUES

8.5 EXAMPLE 1: CASE STUDY NOT CONSIDERING WEATHER EFFECTS

8.6 EXAMPLE 2: CASE STUDY CONSIDERING WEATHER EFFECTS

8.7 CONCLUSIONS

9 NETWORK REINFORCEMENT PLANNING

9.1 INTRODUCTION

9.2 PROBABILISTIC PLANNING OF BULK POWER SUPPLY SYSTEM

9.3 PROBABILISTIC PLANNING OF TRANSMISSION LOOP NETWORK

9.4 CONCLUSIONS

10 RETIREMENT PLANNING OF NETWORK COMPONENTS

10.1 INTRODUCTION

10.2 RETIREMENT TIMING OF AN AGED AC CABLE

10.3 REPLACEMENT STRATEGY OF AN HVDC CABLE

10.4 CONCLUSIONS

11 SUBSTATION PLANNING

11.1 INTRODUCTION

11.2 PROBABILISTIC PLANNING OF SUBSTATION CONFIGURATION

11.3 TRANSFORMER SPARE PLANNING

11.4 CONCLUSIONS

12 SINGLE-CIRCUIT SUPPLY SYSTEM PLANNING

12.1 INTRODUCTION

12.2 RELIABILITY PERFORMANCE OF SINGLE-CIRCUIT SUPPLY SYSTEMS

12.3 PLANNING METHOD OF SINGLE-CIRCUIT SUPPLY SYSTEMS

12.4 APPLICATION TO ACTUAL UTILITY SYSTEM

12.5 CONCLUSIONS

APPENDIX A: ELEMENTS OF PROBABILITY THEORY AND STATISTICS

A.1 PROBABILITY OPERATION RULES

A.2 FOUR IMPORTANT PROBABILITY DISTRIBUTIONS

A.3 MEASURES OF PROBABILITY DISTRIBUTION

A.4 PARAMETER ESTIMATION

A.5 MONTE CARLO SIMULATION

APPENDIX B: ELEMENTS OF FUZZY MATHEMATICS

B.1 FUZZY SETS

B.2 FUZZY NUMBERS

B.3 TWO TYPICAL FUZZY NUMBERS IN ENGINEERING APPLICATIONS

B.4 FUZZY RELATIONS

APPENDIX C: ELEMENTS OF RELIABILITY EVALUATION

C.1 BASIC CONCEPTS

C.2 CRISP RELIABILITY EVALUATION

C.3 FUZZY RELIABILITY EVALUATION

REFERENCES

Index

IEEE Press Series on Power Engineering

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Technical Reviewers

Roy Billinton

Lalit Goel

Murty Bhavaraju

Wenpeng Luan

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Dedicated to Jun and my family

PREFACE AND ACKNOWLEDGMENTS

Transmission system planning is one of the most essential activities in the electric power industry. Billions of dollars are invested in electric utility systems through planning activities every year. In the past and at present, transmission system planning is basically dominated by deterministic criteria and methods. However, there are a considerable number of uncertain factors in transmission systems, and therefore probabilistic methods will provide planning solutions closer to reality. Fragmentary papers for probabilistic transmission planning have been published so far, but there has not been a book to systematically discuss the subject. The intent of this book is to fill the gap. It is important to appreciate that the purpose of introducing probabilistic models and techniques into transmission planning is not to replace but to enhance the existing deterministic criteria.

The book originated from my deep interest and involvement in this area. My technical reports and papers formed core portions of the book, although general knowledge had to be included to ensure its systematization. All basic aspects in transmission planning are covered, including load forecast and load modeling, conventional and special system analysis techniques, reliability evaluation, economic assessment, and data preparation and uncertainties, as well as various actual planning issues. The probabilistic concept is a main thread throughout the book and touches each chapter. It should be emphasized that probabilistic transmission planning is far beyond reliability evaluation, although the latter is one of most important procedures toward this direction. I have followed such a principle for book structure: any new contents associated with the subject are illustrated in detail, whereas for a topic for which readers can find more information in other sources, an outline that is necessary for the book to stand alone is provided.

Materials in both theory and actual applications are offered. The examples in the applications are all based on real projects that have been implemented. I believe that the book will meet the needs of practicing engineers, researchers, professors, and graduates in the power system field.

I am indebted to many friends and colleagues. My special thankfulness goes to Roy Billinton, Paul Choudhury, Ebrahim Vaahedi, and Wijarn Wangdee for their continuous support and encouragement in my daily work. The papers that I coauthored with them are parts of the materials used in the book. Some data and results in a few examples are based on Wijarn Wangdee’s reports.

Drs. Roy Billinton, Lalit Goel, Murty Bhavaraju, and Wenpeng Luan reviewed the book proposal/manuscript and provided many helpful suggestions. I would also thank all the individuals whose publications are listed in the References at the end of the book.

I am grateful for the cooperation and assistance received from the IEEE Press and John Wiley & Sons, especially Mary Mann and Melissa Yanuzzi.

Finally, I would like to thank my wife, Jun Sun, for her sacrifices and patience in the quite long time period during which I worked on the book.

WENYUAN LI

Vancouver, Canada

February 2011

1

INTRODUCTION

1.1 OVERVIEW OF TRANSMISSION PLANNING

1.1.1 Basic Tasks in Transmission Planning

The fundamental objective of transmission planning is to develop the system as economically as possible and maintain an acceptable reliability level. The system development is generally associated with determination of a reinforcement alternative and its implementation time. A decision on retirement or replacement of aging system equipment is also an important task in planning.

There are many drivers for the development of a transmission system, and these mainly include

Load growthNew-generation sourcesEquipment agingCommercial opportunitiesChanges in export to and import from neighbor systemsVariations in supply reliability requirements of customersAccess of new loads or independent power producers (IPPs)New wheeling requirements

Most transmission development projects are driven by the first three factors: load growth, new-generation sources, and equipment aging. Traditionally, a utility company was vertically organized. Generation, transmission, and distribution were owned and therefore planned by a single company. Generation and transmission have been unbundled in most countries since the deregulation of the power industry in the 1990s. In the deregulated environment, generation and transmission assets generally belong to different owners and thus are operated, planned, and managed separately by different companies. This book focuses on probabilistic planning of transmission systems, and the information on generation sources is treated as a known input.

Transmission planning can be divided into three stages in terms of timespan: long-term planning, medium-term planning, and short-term planning. Long-term planning is associated with a long period, such as 20–30 years. It often focuses on a high-level view of system development. The problems discussed in long-term planning are preliminary and may need significant changes or even redefinitions in subsequent planning stages because of very uncertain input data and information used. Medium-term planning can refer to a timeframe between 10 and 20 years. In this stage, preliminary considerations in long-term planning are modified according to actual information obtained in previous years, and study results are utilized to guide short-term projects. Short-term planning deals with the issues that have to be resolved within 10 years. Concrete alternatives must be investigated in depth and compared. Planning studies at this stage should lead to a capital plan for planning projects.

Transmission planning includes different tasks, such as

Determination of voltage levelNetwork enhancementSubstation configurationReactive resource planningLoad or independent power producer (IPP) connection planningEquipment planning (spare, retirement, or replacement)Selection of new technologies [light high-voltage direct current (HVDC), flexible AC transmission system (FACTS), superconductive technology, wide-area measurement system (WAMS)-based technology]Special protection system scheme versus network reinforcement

A transmission planning project may be associated with one or more of the tasks listed above, and each task requires technical, economic, environmental, social, and political assessments. The technical assessment alone covers multiple considerations in space and time dimensions and requires numerous studies, which include load forecast, power flow calculation, contingency analysis, optimal power flow calculation, voltage and transient stability analysis, short-circuit analysis, and reliability evaluation. Essentially, the studies are operation simulations of future situations in many years. The purpose of the studies is to select and compare planning alternatives. It is necessary to identify which system situations can occur in the future and in which manner the transmission system can operate for each situation. The combinations of system states and operation manners will reach an astronomical figure. It is impractical to simulate all the cases. Obviously, some simplification is necessary in system modeling and selection of system states.

Transmission planning is an extremely complicated problem and is always broken into subproblems in system modeling. Coordination among subproblems is needed. The judgment of planning engineers and preselected feasible alternatives play an important role in coordination. Many optimization modeling approaches for transmission planning have been developed in the past. These approaches are merely techniques for solving one or more special subproblems. It is important to recognize that it is impossible to make a decision for a system reinforcement scheme based only on the result from a single optimization model. In fact, many constraints and considerations in environmental, social, and political aspects cannot be quantitatively modeled.

The load levels, network topologies, generation patterns, availability of system components, equipment ratings in different seasons, possible switching actions, and protection and control measures must be considered in selection of system states. There are two methods for the selection: deterministic and probabilistic. The traditional deterministic method has been used for many years. In this method, selection of system states relies on the judgment of planning engineers, and a planning decision depends only on consequences of selected system states. The probabilistic method is relatively new and has not been widely used yet in the planning practice of most utilities, although some efforts have been devoted to this area. A fundamental idea in the latter method is to stochastically select system states in terms of their probabilities of occurrence. Both probabilities and consequences of simulated system states are combined to create the results for a planning decision.

1.1.2 Traditional Planning Criteria

In order to ensure reliability and economy in system development, conventional transmission planning criteria have been established at a country, regional organization, or company level. The famous NERC (North American Electric Reliability Corporation) reliability standard [1] is a good example. It includes the following sections:

BAL—resource and demand balancingCIP—critical infrastructure protectionCOM—communicationsEOP—emergency preparedness and operationsFAC—facilities design, connections, and maintenanceINT—interchange scheduling and coordinationIRO—interconnection reliability operations (and coordination)MOD—modeling, data, and analysisNUC—nuclearPER—personnel performance, training, and qualificationsPRC—protection and controlTOP—transmission operationTPL—transmission planningVAR—voltage and reactive power

It can be seen that this standard covers a wide range of areas and is beyond transmission planning. However, it is important to appreciate that the criteria for transmission planning are not only limited within the TPL section but should also be associated with the sections of BAL, FAC, MOD, PRC, TOP, TPL, and VAR.

The contents of conventional transmission planning criteria should at least include, but not be limited to, the following aspects [1–3]:

1. Deterministic Security Principle. This basically refers to the N − 1 principle. The N− 1 criterion means that a transmission system must have a sufficient number of elements to ensure that the outage or fault disturbance of a single element in any system condition does not result in any system problem, including overloading, under- or overvoltage, disconnection of other components, unplanned load curtailment, transient instability, and voltage instability. The NERC criteria also include performance requirements for planning conditions associated with two or more element outages. However, only very few important multielement outage conditions can be assessed in actual practice since the number of such conditions is too large.

2. Voltage Levels. The voltage level is often chosen as the one in the existing system as long as it can provide required power transfer capability without incurring unreasonable losses. Where existing voltages do not provide the required capability at a reasonable cost, a new voltage level may be established on the basis of technical and economic analyses.

3. Equipment Ratings. Equipment ratings (including normal and emergency ratings) are essential inputs in planning and are generally specified in manufacturer designs or industry standards. The equipment in a transmission system includes transmission lines, underground or submarine cables, transformers, instrument transformers, shunt and series capacitors, shunt and series reactors, circuit breakers, switches, static VAR compensators (SVCs), static synchronous compensators (STATCOMs), HVDC devices, bus conductors, and protection relays.

4. System Operating Limits. In addition to equipment ratings, system operating limits are also essential inputs in planning and include limits on voltage, frequency, thermal capacity, transient stability, voltage stability, and small-signal stability. The limits are divided into two categories for pre- and postcontingencies, and are expressed in different measure units, such as megawatts (MW), megavolt-amperes reactive (MVAR), amperes, hertz, volts, or a permissible percentage. The violation of a system operating limit may cause a consequence of instability, system split, or/and cascading outages.

5. Transfer Capability. Transfer capability is the amount of electric power that can be moved on a cut-plane between two areas under a specified system condition. A cutplane is often a group of transmission lines. This is associated with two terms: total transfer capability (TTC) and available transfer capability (ATC) [4]. The latter can be determined by

where TRM (transmission reliability margin) is the transfer capability margin required to ensure system security under a reasonable range of uncertainties and possible system conditions, CBM (capacity benefit margin) is the transfer capability reserved to ensure the access to generation from interconnected areas to meet generation reliability requirements, and ETC (existing transmission commitment) is the transfer capability scheduled for transmission services. Obviously, determination of TTC and ATC is associated with not only thermal but also stability limits.

6. Connection Requirements. As transmission system open access becomes a reality with deregulation in the power industry, various interconnections to a transmission system have greatly increased. These include the connections of generation, transmission, and end-user facilities. The term generation facilities refers to not only generators of generation companies but also regular IPPs and renewable sources. The connection projects require considerable feasibility, system impact, and facility studies, which have naturally become parts of transmission planning activities. The connection requirements are not only related to technical studies but also heavily associated with regulatory policies and business models.

7. Protection and Control. In some cases of transmission planning, a protection and control scheme can ensure system security while avoiding addition of primary equipment, resulting in a considerable saving of capital investment. In addition to traditional equipment protection and control schemes, the special protection system (SPS) and wide-area measurement system (WAMS) play a greater role in system security. The SPS, which is sometimes called a remedial action scheme (RAS), includes different schemes such as undervoltage load shedding, underfrequency load shedding, auto-VAR control, generation rejection, line tripping, and transient overvoltage control [5]. All the SPS schemes must meet reliability requirements and design principles. The WAMS, which can be also called a wide-area control system since its function is not limited to measurement, has been rapidly developed and applied in recent years. However, the reliability criteria for WAMS have not been well established so far.

8. Data and Models. All planning studies require adequate and accurate data and models, including those for static and dynamic simulations in both internal and external representations. The data and models for loads, generation sources, and customer connections need the coordination between transmission companies and their customers. The requirements of data management, including validation, database, and historical data analysis, are essential to transmission planning.

9. Economic Analysis Criteria. Generally, more than one system alternative meet the technical planning criteria, and therefore economic analyses are conducted to select the least total cost alternative. The total cost includes capital and operating costs. In traditional planning, unreliability cost is not a component of economic analysis. The cost analysis must be carried out in a planning period of many years. Because of the unpredictability of economic parameters for the future, it is often necessary to perform sensitivity studies to examine the effects of parameter variations.

1.2 NECESSITY OF PROBABILISTIC TRANSMISSION PLANNING

The purpose of probabilistic planning is to add one more dimension enhancing the transmission planning process rather than to replace the traditional criteria summarized in Section 1.1.2. The majority of the traditional criteria will continue to be used in probabilistic planning with the exception of the following new ideas:

The N − 1 principle is no longer a unique security criterion. In addition to single contingencies, multicomponent outages (as many as possible) have to be considered.Not only the consequences but also the occurrence probabilities of outage events must be simulated.Uncertainties in network configurations, load forecast, generation patterns, and other parameters should be represented as possible using probabilistic or/and fuzzy modeling methods.On top of the traditional studies (power flow, optimal power flow, contingency analysis, and stability assessment), the probabilistic techniques (probabilistic power flow, probabilistic contingency analysis, and probabilistic stability assessments) should be conducted. In articular, probabilistic system reliability evaluation is performed and becomes a key step.Unreliability cost assessment is a crucial part of overall economic analysis and plays an important role in planning decisions. Introduction of the unreliability cost, which depends on various probabilistic factors, establishes a probabilistic feature in economic analysis. The uncertain factors in economic parameters can also be considered.

There are numerous reasons for doing probabilistic transmission planning [6–8]:

1. One major weakness of deterministic criteria is the fact that the probabilistic nature of outage data and system parameters is overlooked. For instance, an outage event, even if extremely undesirable, is of little consequence if it is so unlikely that it can be ignored. A planning alternative based on such an event will lead to overinvestment. Conversely, if selected outage events are not very severe but have relatively high probabilities of occurrence, an option based only on the effects of such events will still result in a high-risk outcome. Probabilistic planning can recognize not only the severity but also the likelihood of occurrence of events.

2. The deterministic criterion is based on the worst-case study. The “worst case” may be missed. For example, system peak load is generally used as one of the worst conditions. However, some serious system problems may not necessarily occur at peak load. Also, even if a system withstands the “worst case,” the system is still not risk-free. It is worthy to identify the risk level associated with the N − 1 criterion. This is one of the tasks in probabilistic transmission planning.

3. Major outages are usually associated with multiple component failures or cascading events in real life. This suggests that the N − 1 criterion is insufficient to preserve a reasonable level of system reliability. However, on the other hand, it is almost impossible for any utility to justify the N − 2 or N − 3 principle for all outage events in transmission planning. A better alternative is to bring risk management into planning practice and keep system risk within an acceptable level.

There is no conflict between deterministic and probabilistic planning criteria. A complete system planning process includes societal, environmental, technical, and economic assessments. Probabilistic economic assessment and reliability evaluation are suggested to add as a part of the whole process. Figure 1.1 gives a conceptual example in which seven candidates for planning alternatives are assumed at the beginning. Two of them are excluded on the basis of environmental, societal, or political considerations. Deterministic technical criteria including the N − 1 principle are applied to the remaining five alternatives. Two more alternatives are eliminated from the candidate list because of their inability to meet the deterministic technical criteria. Then probabilistic reliability evaluation and probabilistic economic analysis are performed to select the best scenario. Both the N − 1 principle and probabilistic reliability criteria are satisfied. Other probabilistic techniques can also be applied to system analyses even in the domain of deterministic criteria.

Figure 1.1. System planning process.

Although the majority of the traditional criteria are still effective in probabilistic planning, introduction of the probability-related ideas (particularly the concept of unreliability cost) will significantly change the planning process and the philosophy in decisionmaking. Probabilistic transmission planning brings the missed (overlooked) factors in the traditional planning into studies and will definitely lead to a more reasonable decision in the sense of a tradeoff between reliability and economy.

1.3 OUTLINE OF THE BOOK

The book can be divided into four parts. The first part includes Chapters 2–7, which discuss the concepts, models, methods, and data that are used in probabilistic transmission planning. Chapter 8, as the second part, focuses on a special issue—how to deal with the uncertainty of data in probabilistic planning using fuzzy techniques. The third part, Chapters 9–12, addresses four essential issues in probabilistic transmission planning using actual utility systems as examples. The fourth part consists of three appendixes, which provide the basic knowledge in mathematics for probabilistic planning.

Chapter 2 presents the basic concepts of probabilistic transmission planning emphasizing the criteria and general procedure.

Chapter 3 addresses load modeling issues in both time and space perspectives. Load growth is a major driver in transmission planning. Various practical load forecast methods are discussed. Other aspects of load modeling include load clustering, uncertainty, and correlation of bus loads, as well as voltage and frequency characteristics of loads.

Chapter 4 focuses on system analysis techniques. The traditional analysis methods, which are still required in probabilistic transmission planning, are briefly summarized. These include power flow, optimal power flow, contingency analysis, and voltage and transient stability assessments. Probabilistic power flow, probabilistic optimization techniques, and risk-index-based contingency ranking are presented as new analysis methods.

Chapter 5 illustrates transmission reliability evaluation. This is a key step toward probabilistic transmission planning. Reliability indices and reliability worth assessment are explained. In the adequacy perspective, reliability evaluation methods for composite generation–transmission systems and substation configurations are discussed. In the security perspective, probabilistic voltage and transient stability assessments are proposed as new techniques. This chapter only provides a summary of the topic; more details can be found in the author’s previous book, Risk Assessment of Power Systems, in the same IEEE Press Series on Power Engineering.

Chapter 6 discusses the methods for economic analysis, which is another key in probabilistic transmission planning. Three cost components for planning projects are outlined. Following the basic concepts on time value of money and depreciation methods, the economic assessment techniques for project investment and equipment replacement are presented in detail. A probabilistic method for the uncertainty of economic parameters is also proposed. Compared to books on engineering economics, a major feature is that the unreliability cost is incorporated in the proposed techniques.

Chapter 7 addresses data issues in probabilistic transmission planning. The data for system analysis include equipment parameters, ratings, system operation limits, and load coincidence factors. Preparing reliability data is an important step toward probabilistic planning. Both equipment outage indices and delivery point indices, which are based on outage statistics, are discussed with typical examples. Other data required in planning are also outlined.

Chapter 8 proposes a solution to data uncertainty in probabilistic transmission planning using combined fuzzy and probabilistic techniques. The uncertainty includes both randomness and fuzziness of loads and outage parameters, particularly for the data associated with weather conditions. Two examples for reliability assessment are provided to demonstrate applications of the techniques presented. Similar ideas can be extended to the uncertainty of other data and other system analyses.

Chapters 9–12 are devoted to practical applications that are day-to-day topics in transmission planning. The special concept, method, and procedure for each topic are developed, and actual planning examples from real utility transmission systems are provided. In particular, the results in the applications have been implemented in the utility’s decisionmaking.

Chapter 9 discusses transmission network reinforcement planning. This is a task that transmission planners have to deal with every day. Two applications are developed using probabilistic planning methods. One is the reinforcement of a bulk power supply system; the other is the comparison among planning alternatives for a regional transmission network.

Chapter 10 copes with retirement planning of system components. The retirement timing of a system component is a challenge facing planners as a transmission system ages. New probabilistic planning methods are presented for two applications: (1) the retirement of an AC cable and (2) the replacement strategy of a DC cable.

Chapter 11 discusses substation planning. There are two types of problems in substation planning. One is selection of substation configuration; the other is determination of the number and timing of spare equipment shared by substations. Probabilistic approaches to both problems are established and demonstrated using actual utility application examples.

Chapter 12 is committed to the probabilistic planning method for radial single-circuit supply systems. This is a challenging issue that cannot be resolved using the traditional N − 1 planning criterion. The method presented is based on historical outage indices and probabilistic economic analysis with predictive reliability evaluation. A utility example is provided.

There are three appendixes. Appendix A provides the basic concepts in probability theory and statistics, whereas Appendix B presents the elements in fuzzy mathematics. Appendix C gives the fundamentals in reliability evaluation, including both crisp and fuzzy reliability assessment methods.

Transmission planning covers a very wide range of topics. The book does not pretend to include all known and available materials in this area. The intent is to focus on the basic aspects and most important applications in probabilistic transmission planning.

2

BASIC CONCEPTS OF PROBABILISTIC PLANNING

2.1 INTRODUCTION

The most distinguishing feature of probabilistic planning is a combination of probabilistic reliability evaluation and economic analysis into the planning process. In traditional deterministic planning, system reliability is considered through some simple rules such as the N − 1 principle, whereas in probabilistic planning, system reliability is quantitatively assessed and expressed using one or more indices that represent system risks. Two essential tasks of probabilistic planning are (1) establishment of probabilistic planning criteria through reliability indices and (2) combination of quantitative reliability evaluation with probabilistic economic analysis to form a basic procedure. It is important to appreciate that the objective of introducing probabilistic planning is to enhance but not to replace traditional planning. The new procedure must be designed in such a way that both deterministic and probabilistic criteria are coordinated in a unified process.

Probabilistic planning also requires other power system analysis and assessment techniques in addition to reliability evaluation and economic analysis. These include probabilistic methods in load forecast and load modeling, power flow and probabilistic power flow, traditional and probabilistic contingency analyses, and optimal power flow and probabilistic search-based optimization methods, as well as conventional and probabilistic voltage and transient stability assessments. Another important task is preparation and management of various data required by probabilistic planning activities as well as treatment of data uncertainties. All of these will be discussed in Chapters 3–8.

This chapter focuses on the basic concepts of probabilistic transmission planning. The probabilistic criteria are presented in Section 2.2. The general procedure of probabilistic planning is illustrated in Section 2.3, and other relevant aspects are briefly outlined in Section 2.4.

2.2 PROBABILISTIC PLANNING CRITERIA

Although probabilistic planning criteria are not as straightforward as the deterministic N − 1 criterion, different approaches can be developed to establish probabilistic criteria [7–9]. Four possible approaches are presented in this section. Which one is used depends on the utility business model and the project to which the criterion is applied. For instance, different approaches can be used for bulk networks and regional systems, or for transmission-line addition and substation enhancement.

2.2.1 Probabilistic Cost Criteria

Reliability is one of multiple factors considered in probabilistic transmission planning. System unreliability can be expressed using unreliability costs so that system reliability and economic effects can be assessed on a unified monetary basis. There are two methods for incorporating the unreliability cost: the total cost method and the benefit/cost ratio method.

1. Total Cost Method. The basic idea is that the best alternative in system planning should achieve the minimum total cost:

The calculation of investment cost is a routine economic analysis activity in transmission planning. The operation cost includes OMA (operation, maintenance, and administration) expenditures, network losses, financial charges, and other ongoing costs. The unreliability cost is obtained using the EENS index (expected energy not supplied, in MWh/year) times the unit interruption cost (UIC, $/kWh), which will be discussed in Chapter 5.

2. Benefit/Cost Ratio Method. The capital investment of a planning alternative is the cost, whereas the reduction in operation and unreliability costs is the benefit due to the alternative. The benefit/cost ratios for all preselected alternatives are calculated and compared. In other words, the alternatives can be ranked using their benefit/cost ratios. A project may be associated with multistage investments and a planning timeframe (such as 5–20 years) is always considered. All three cost components should be estimated on an annual basis to create their cash flows on the timeframe first, and then a present value method is applied to calculate the benefit/cost ratios. The BCR method will be discussed in further detail in Chapter 6.

2.2.2 Specified Reliability Index Target

Many utilities have used reliability indices to measure the system performance and made an investment decision based on the metrics. One or more reliability indices can be specified as a target reliability level. For example, the target of an outage duration index such as the T-SAIDI (system average interruption duration index) or an outage frequency index such as the T-SAIFI (system average interruption frequency index) (where the T prefix denotes transmission) can be specified with a tolerant variance range. If the evaluated result exceeds the specified range, an enhancement is required. The definitions of transmission system reliability evaluation indices and historical performance-based indices will be discussed in Chapters 5 and 7, respectively.

The essence of this approach is to use a reliability index as a target. It is well known, for instance, that the LOLE (loss of load expectation) index of one day per 10 years has been used as a target index in generation planning for many years. Unfortunately, it is not easy to set an appropriate index target for transmission system reliability. Historical statistics can help in determination of an index target. On the other hand, caution should be taken regarding the coherent uncertainty and inaccuracy in historical records when this approach is used.

2.2.3 Relative Comparison

In most cases, the purpose of transmission planning is to compare different alternatives (including the doing nothing option). One major index or multiple indices (such as the EENS, probability, frequency, and duration indices) can be used in the comparison.

Performing a relative comparison is often better than using an absolute index target because

Not only reliability indices but also economic and other aspects can be compared.Historical statistics and input data used in probabilistic reliability evaluation are always fraught with uncertainties.The historical system performance may not represent the future performance that a planning projects targets.There are computational errors in modeling and calculation methods, and errors can be offset in a relative comparison.

2.2.4 Incremental Reliability Index

If it is difficult to use unreliability cost in some cases, an incremental reliability index (IRI) can be applied. The IRI is defined as the reliability improvement due to per M$ (million dollars) of investment, which can be expressed as follows:

The cost is the total cost for investment and operation (in M$) required for a reinforcement option. The RIB and RIA respectively are the reliability indices before and after the reinforcement. Conceptually, any appropriate reliability index (such as the EENS, probability, frequency, or duration index) can be used. In most cases, the EENS is suggested if it can be quantified since this index is a combination of outage frequency, duration, and severity, and carries more information than does any other single index.

The IRI can be used to rank projects or compare alternatives for a project. The disadvantage of the IRI approach is the fact that the “doing nothing” option cannot be included.

2.3 PROCEDURE OF PROBABILISTIC PLANNING

There are different ways to perform probabilistic transmission planning [7–9]. Figure 2.1 shows a general process that includes the criteria mentioned above. It also indicates how to combine the deterministic N − 1 principle with the probabilistic criteria.

Figure 2.1. Procedure of probabilistic transmission planning.

The basic procedure of probabilistic transmission planning includes the following four major steps:

1. If the single-contingency criterion is a mandate, select the planning alternatives that meet the N − 1 principle. Otherwise, if the N − 1 principle is not considered as the strict criterion, select all feasible alternatives. In either case, system analysis using the traditional assessment techniques (power flow, optimal power flow, contingency analysis, and stability studies) is needed. These techniques will be summarized in Chapter 4.

2. Conduct probabilistic reliability evaluation and unreliability cost evaluation for the selected alternatives over a planning timeframe (such as 5–20 years) using a reliability assessment tool for transmission systems.

3. Calculate the cash flows and present values of investment, operation, and unreliability costs for the selected alternatives in the planning time period.

4. Select an appropriate criterion described in Section 2.2 and conduct an overall probabilistic economic analysis.

It can be seen that probabilistic reliability evaluation and economic analysis are two key steps, which are briefly discussed in Sections 2.3.1 and 2.3.2 and will be detailed in Chapters 5 and 6.

2.3.1 Probabilistic Reliability Evaluation

There are two fundamental methods for probabilistic reliability evaluation [6,10,11] of transmission systems: Monte Carlo simulation and state enumeration. The difference between the two methods is associated with how to select system states, whereas the system analysis in assessing the consequences of selected outage states is the same. The probabilistic reliability assessment of composite generation–transmission systems using the Monte Carlo method is summarized as follows:

1. A multistep load model is created that eliminates the chronology and aggregates load states using hourly load records during one year. The uncertainty of load at each step can be modeled using a probability distribution if necessary. Annualized indices are calculated first by using only a single load level and are expressed on the one-year basis. All the load-level steps are considered successively, and the resulting indices for each load level that are weighted by the probability for that load level are summed up to obtain annual indices.

2. The system states at a particular load level are selected using Monte Carlo simulation techniques. This includes the following:

a. Generally, generating unit states are modeled using multistate random variables. If generating units do not create different impacts on selected transmission planning alternatives, the generating units can be assumed to be 100% reliable.

b. Transmission component states are modeled using two-state (up and down) random variables. For some special transmission components such as HVDC lines, a multistate random variable can be applied. Weather-related transmission-line forced outage frequencies and repair times can be determined using the method of recognizing regional weather effects. Transmission-line common-cause outages are simulated by separate random numbers.

c. Bus load uncertainty and correlation are modeled using a correlative normal distribution random vector. A correlation sampling technique for the normal distribution vector is used to select bus load states.

3. System analyses are performed for each selected system state. In many cases, this requires power flow and contingency analysis studies to identify possible system problems. In some cases, transient and voltage stability studies may also be required.

4. An optimal power flow (OPF) model is used to reschedule generations and reactive sources, eliminate limit violations (line overloading and/or bus voltage violations), and avoid any load curtailment if possible or minimize the total load curtailment or interruption cost if unavoidable.

5. The reliability indices are calculated on the basis of the probabilities and consequences of all sampled system states.

If the state enumeration method is used, step 2 is carried out differently and all other steps basically remain the same. The reliability evaluation for substation configurations follows a simpler procedure since it is essentially a problem of connectivity between sources and load points, and no power-flow-based model is required. The probabilistic reliability evaluation will be discussed in more detail in Chapter 5.

2.3.2 Probabilistic Economic Analysis

There are three cost components in probabilistic economic analysis [6,10]: investment, operation, and unreliability costs.

Investment analysis is a fundamental part of the economic assessment in a planning process. The cash flow of annual investment cost can be created using the capital return factor (CRF) method and actual capital estimates. The parameters associated with economic analysis of capital investment (such as the useful life of a project, discount rate, and capital estimates) are usually given by deterministic numbers. However, a probabilistic method can be applied to capture the uncertainty of the parameters. For instance, a discrete probability distribution of discount rate can be obtained from historical statistics and considered in the calculation model. The concepts and methods used in the economic analysis will be illustrated in Chapter 6.

The cash flows of operation and unreliability costs are calculated through year-by-year evaluations. In addition to fixed cost components, the operation cost in a transmission system is also related to evaluation of network losses, simulation of system production costs, and estimation of energy prices on the power market. This is associated with considerable uncertainty factors, including load forecasts, generation patterns, maintenance schedules, and power market behaviors. In some cases, on the other hand, the planning alternatives selected may involve only limited modifications of network configuration and have basically the same or close operation cost. In such a situation, the operation cost may not have to be included in the total cost for comparison. This is case-dependent.

As mentioned earlier, the unreliability cost equals to the product of EENS and a unit interruption cost. Obviously, this cost component is a random number that depends on various probabilistic factors in a transmission system, particularly on random outage events. The EENS can be calculated by a probabilistic reliability evaluation method, whereas the unit interruption cost (UIC) can be estimated using one of the following four techniques. The first one is based on customer damage functions (CDFs) that can be obtained from customer surveys. A CDF provides the relationship curve between the average unit interruption cost and duration of power outage. The second one is based on a gross domestic product divided by a total electric energy consumption, which gives a dollar value per kilowatt-hour (kWh) reflecting the average economic damage cost due 1 kWh of energy loss. The third one is based on the relationship between capital investment projects and system EENS indices. The fourth one is based on the lost revenue to the utility due to power outages. This last technique would typically represent the lowest level of UIC. Utilities can select an appropriate technique that best aligns with their business objectives. The details of unreliability cost assessment will be given in Chapter 5.

2.4 OTHER ASPECTS IN PROBABILISTIC PLANNING

Probabilistic planning involves a wide range of study activities, including traditional deterministic analyses and new probabilistic assessments. The traditional analysis techniques used in transmission planning, including power flow, contingency analysis, optimal power flow, transient stability, and voltage stability, will continue to be important while new probabilistic assessment methods are introduced.

Load forecast and generation conditions are two crucial prerequisites of transmission planning. Load forecast has been performed using probabilistic methods even in the conventional planning practice because of the inherent uncertainty in predicting future loads. However, applications of new methods (such as neural network and fuzzy clustering) provide vehicles to improve accuracy in long-term load forecasting. Load forecast and other load modeling issues will be discussed in Chapter 3. Generation conditions, including types of generators, locations, capacities and availability in the future, are the outcome of generation planning, which is a complex task by itself. Detailed discussion of generation planning is beyond the scope of the book. An integrated planning of generation and transmission may be necessary in some cases.

Obviously, probabilistic methods are not limited to reliability evaluation and economic analysis. Probabilistic power flow and probabilistic contingency analysis are often useful tools in probabilistic transmission planning studies. In the optimization analysis for system planning, probabilistic search optimization techniques can provide solutions to some special problems. Probabilistic transient stability and voltage stability assessments should also be considered when necessary. Essentially, these are extensions of conventional transient and voltage stability analyses in order to incorporate probabilistic modeling of various uncertain factors. The basic procedure includes three main aspects: (1) a probabilistic method is used to select random factors for dynamic system states, (2) a stability analysis technique is used to conduct stability simulations of stochastically selected system states, and (3) a probabilistic index or its distribution is created to represent system instability risk. Generally, probabilistic stability assessments provide a deeper and broader insight into system dynamic behavior and instability risk. The additional probabilistic techniques will also be presented in Chapters 4 and 5.

Another crucial aspect is the data preparation for probabilistic transmission planning. This includes not only the regular data for conventional system analyses but also the data for probabilistic assessments. The data required in probabilistic planning will be discussed in detail in Chapter 7. Reliability data are obtained from historical statistical records, and a computerized database is required to collect, store, and manage outage data. Maintaining a high quality of data is a key for successful probabilistic planning.

There are two types of uncertainty in input data and modeling: randomness and fuzziness. Randomness is characterized by probability, whereas fuzziness is characterized by fuzzy variables. Dealing with the two uncertainties is an important issue in probabilistic transmission planning. This will be addressed in Chapter 8.

2.5 CONCLUSIONS

This chapter described the basic concepts of probabilistic transmission planning. The first step toward probabilistic planning is to establish and understand its criteria and procedure. The four probabilistic planning criteria have been discussed. Utilities may select one or more criteria in actual applications to suit their business requirements. A probabilistic planning flowchart is presented to illustrate the details of planning procedure and the coordination between probabilistic and deterministic N − 1 criteria.

The most important tasks in probabilistic planning are quantified probabilistic reliability evaluation and probabilistic economic analysis. The basic ideas of the two tasks have been discussed. Besides, probabilistic studies in other aspects are also required depending on the particular cases and problems under study. These include probabilistic load forecast and load modeling, probabilistic power flow and contingency analysis, and probabilistic transient and voltage stability assessments. It is essential to recognize that the deterministic N − 1 criteria must be used to select initial alternatives for probabilistic planning and the conventional system analysis techniques including power flow, contingency analysis, optimal power flow, and stability simulations are still important tools in the integrated planning process. Probabilistic planning methods are designed to complement and enhance traditional transmission planning.

This chapter provided only a high-level description of the subject. Detailed discussions of each topic will be developed in subsequent chapters.

3

LOAD MODELING

3.1 INTRODUCTION

Power system loads have two basic attributes: spatiotemporal characteristics and voltage/frequency dependence. Modeling the two attributes is the first fundamental task in probabilistic transmission planning. Spatiotemporal characteristics refer not only to the feature of variation with time and space but also to the uncertainty and correlation in variation. Spatiotemporal characteristics of power loads can be modeled using a probabilistic or fuzzy variable. The term refers to the fact that a bus load changes with voltage and frequency. This dependence is deterministic at a specific timepoint and a specific bus location. On the other hand, these two attributes are related to each other because voltage and frequency also change with time and space.