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E-raamat: Probabilistic Transmission System Planning

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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.

Arvustused

"Principle engineer at a Canadian electric company, Li uses his technical reports and papers as a foundation for a comprehensive guide to planning a system to transmit electricity from its generation source to the sub-transmission stations where it enters the distribution system." (Book News, 1 August 2011)  

Preface and Acknowledgments xxi
1 Introduction
1(10)
1.1 Overview of Transmission Planning
1(5)
1.1.1 Basic Tasks in Transmission Planning
1(2)
1.1.2 Traditional Planning Criteria
3(3)
1.2 Necessity of Probabilistic Transmission Planning
6(2)
1.3 Outline of the Book
8(3)
2 BASIC CONCEPTS OF PROBABILISTIC PLANNING
11(10)
2.1 Introduction
11(1)
2.2 Probabilistic Planning Criteria
12(2)
2.2.1 Probabilistic Cost Criteria
12(1)
2.2.2 Specified Reliability Index Target
13(1)
2.2.3 Relative Comparison
13(1)
2.2.4 Incremental Reliability Index
13(1)
2.3 Procedure of Probabilistic Planning
14(3)
2.3.1 Probabilistic Reliability Evaluation
14(3)
2.3.2 Probabilistic Economic Analysis
17(1)
2.4 Other Aspects in Probabilistic Planning
17(1)
2.5 Conclusions
18(3)
3 Load Modeling
21(28)
3.1 Introduction
21(1)
3.2 Load Forecast
22(15)
3.2.1 Multivariate Linear Regression
22(1)
3.2.1.1 Regression Equation
22(1)
3.2.1.2 Statistical Test of Regression Model
23(2)
3.2.1.3 Regression Forecast
25(1)
3.2.2 Nonlinear Regression
26(1)
3.2.2.1 Nonlinear Regression Models
26(1)
3.2.2.2 Parameter Estimation of Models
27(1)
3.2.3 Probabilistic Time Series
28(1)
3.2.3.1 Conversion to a Stationary Time Series
29(1)
3.2.3.2 Model Identification
30(1)
3.2.3.3 Estimating Coefficients of Models
31(1)
3.2.3.4 Load Forecast Equation
32(1)
3.2.3.5 A Posteriori Test of Load Forecast Accuracy
33(1)
3.2.4 Neural Network Forecast
34(1)
3.2.4.1 Feedforward Backpropagation Neural Network (FFBPNN)
34(2)
3.2.4.2 Learning Process of FFBPNN
36(1)
3.2.4.3 Load Prediction
37(1)
3.3 Load Clustering
37(5)
3.3.1 Multistep Load Model
37(3)
3.3.2 Load Curve Grouping
40(2)
3.4 Uncertainty and Correlation of Bus Loads
42(2)
3.5 Voltage- and Frequency-Dependent Bus Loads
44(2)
3.5.1 Bus Load Model for Static Analysis
45(1)
3.5.1.1 Polynomial Bus Load Model
45(1)
3.5.1.2 Exponential Bus Load Model
45(1)
3.5.2 Bus Load Model for Dynamic Analysis
46(1)
3.6 Conclusions
46(3)
4 System Analysis Techniques
49(36)
4.1 Introduction
49(1)
4.2 Power Flow
50(3)
4.2.1 Newton-Raphson Method
50(1)
4.2.2 Fast Decoupled Method
51(1)
4.2.3 DC Power Flow
52(1)
4.3 Probabilistic Power Flow
53(4)
4.3.1 Point Estimation Method
54(1)
4.3.2 Monte Carlo Method
55(2)
4.4 Optimal Power Flow (OPF)
57(7)
4.4.1 OPF Model
58(2)
4.4.2 Interior Point Method (IPM)
60(1)
4.4.2.1 Optimality and Feasibility Conditions
60(2)
4.4.2.2 Procedure of IPM
62(2)
4.5 Probabilistic Search Optimization Algorithms
64(8)
4.5.1 Genetic Algorithm (GA)
64(1)
4.5.1.1 Fitness Function
65(1)
4.5.1.2 Selection
65(1)
4.5.1.3 Recombination
66(1)
4.5.1.4 Mutation
67(1)
4.5.1.5 Reinsertion
67(1)
4.5.1.6 Procedure of Genetic Algorithm
68(1)
4.5.2 Particle Swarm Optimization (PSO)
69(1)
4.5.2.1 Inertia Weight Approach
70(1)
4.5.2.2 Constriction Factor Approach
70(1)
4.5.2.3 Procedure of PSO
71(1)
4.6 Contingency Analysis and Ranking
72(4)
4.6.1 Contingency Analysis Methods
72(1)
4.6.1.1 AC Power-Flow-Based Method
72(1)
4.6.1.2 DC Power-Flow-Based Method
73(2)
4.6.2 Contingency Ranking
75(1)
4.6.2.1 Ranking Based on Performance Index
75(1)
4.6.2.2 Ranking Based on Probabilistic Risk Index
75(1)
4.7 Voltage Stability Evaluation
76(4)
4.7.1 Continuation Power Flow Technique
76(1)
4.7.1.1 Prediction Step
77(1)
4.7.1.2 Correction Step
78(1)
4.7.1.3 Identification of Voltage Collapse Point
78(1)
4.7.2 Reduced Jacobian Matrix Analysis
78(2)
4.8 Transient Stability Solution
80(3)
4.8.1 Transient Stability Equations
80(1)
4.8.2 Simultaneous Solution Technique
81(1)
4.8.3 Alternate Solution Technique
82(1)
4.9 Conclusions
83(2)
5 Probabilistic Reliability Evaluation
85(38)
5.1 Introduction
85(1)
5.2 Reliability Indices
86(4)
5.2.1 Adequacy Indices
86(2)
5.2.2 Reliability Worth Indices
88(1)
5.2.3 Security Indices
89(1)
5.3 Reliability Worth Assessment
90(3)
5.3.1 Methods of Estimating Unit Interruption Cost
90(1)
5.3.2 Customer Damage Functions (CDFs)
91(1)
5.3.2.1 Customer Survey Approach
91(1)
5.3.2.2 Establishment of CDF
91(1)
5.3.3 Application of Reliability Worth Assessment
92(1)
5.4 Substation Adequacy Evaluation
93(6)
5.4.1 Outage Modes of Components
94(1)
5.4.2 State Enumeration Technique
95(1)
5.4.3 Labeled Bus Set Approach
96(1)
5.4.4 Procedure of Adequacy Evaluation
97(2)
5.5 Composite System Adequacy Evaluation
99(8)
5.5.1 Probabilistic Load Models
100(1)
5.5.1.1 Load Curve Models
100(1)
5.5.1.2 Load Uncertainty Model
100(1)
5.5.1.3 Load Correlation Model
101(1)
5.5.2 Component Outage Models
101(1)
5.5.2.1 Basic Two-State Model
101(1)
5.5.2.2 Multistate Model
101(1)
5.5.3 Selection of System Outage States
102(1)
5.5.3.1 Nonsequential Sampling
102(1)
5.5.3.2 Sequential Sampling
103(1)
5.5.4 System Analysis
103(1)
5.5.5 Minimum Load Curtailment Model
104(1)
5.5.6 Procedure of Adequacy Evaluation
105(2)
5.6 Probabilistic Voltage Stability Assessment
107(7)
5.6.1 Optimization Model of Recognizing Power Flow Insolvability
108(2)
5.6.2 Method for Identifying Voltage Instability
110(1)
5.6.3 Determination of Contingency System States
111(1)
5.6.3.1 Selection of Precontingency System States
111(1)
5.6.3.2 Selection of Contingencies
112(1)
5.6.4 Assessing Average Voltage Instability Risk
113(1)
5.7 Probabilistic Transient Stability Assessment
114(6)
5.7.1 Selection of Prefault System States
114(1)
5.7.2 Fault Probability Models
115(1)
5.7.2.1 Probability of Fault Occurrence
115(1)
5.7.2.2 Probability of Fault Location
115(1)
5.7.2.3 Probability of Fault Type
115(1)
5.7.2.4 Probability of Unsuccessful Automatic Reclosure
116(1)
5.7.2.5 Probability of Fault Clearing Time
116(1)
5.7.3 Selection of Fault Events
117(1)
5.7.4 Transient Stability Simulation
117(1)
5.7.5 Assessing Average Transient Instability Risk
118(2)
5.8 Conclusions
120(3)
6 Economic Analysis Methods
123(26)
6.1 Introduction
123(1)
6.2 Cost Components of Projects
124(1)
6.2.1 Capital Investment Cost
124(1)
6.2.2 Operation Cost
124(1)
6.2.3 Unreliability Cost
125(1)
6.3 Time Value of Money and Present Value Method
125(6)
6.3.1 Discount Rate
125(1)
6.3.2 Conversion between Present and Future Values
126(1)
6.3.3 Cash Flow and Its Present Value
127(1)
6.3.4 Formulas for a Cash Flow with Equal Annual Values
128(1)
6.3.4.1 Present Value Factor
129(1)
6.3.4.2 End Value Factor
129(1)
6.3.4.3 Capital Return Factor
129(1)
6.3.4.4 Sinking Fund Factor
130(1)
6.3.4.5 Relationships between the Factors
130(1)
6.4 Depreciation
131(6)
6.4.1 Concept of Depreciation
131(1)
6.4.2 Straight-Line Method
132(1)
6.4.3 Accelerating Methods
133(1)
6.4.3.1 Declining Balance Method
133(1)
6.4.3.2 Total Year Number Method
134(1)
6.4.4 Annuity Method
135(1)
6.4.5 Numerical Example of Depreciation
135(2)
6.5 Economic Assessment of Investment Projects
137(5)
6.5.1 Total Cost Method
137(2)
6.5.2 Benefit/Cost Analysis
139(1)
6.5.2.1 Net Benefit Present Value Method
139(1)
6.5.2.2 Benefit/Cost Ratio Method
139(1)
6.5.3 Internal Rate of Return Method
140(1)
6.5.4 Length of Cash Flows
141(1)
6.6 Economic Assessment of Equipment Replacement
142(2)
6.6.1 Replacement Delay Analysis
142(1)
6.6.2 Estimating Economic Life
143(1)
6.7 Uncertainty Analysis in Economic Assessment
144(3)
6.7.1 Sensitivity Analysis
145(1)
6.7.2 Probabilistic Analysis
145(2)
6.8 Conclusions
147(2)
7 Data In Probabilistic Transmission Planning
149(32)
7.1 Introduction
149(1)
7.2 Data for Power System Analysis
150(13)
7.2.1 Equipment Parameters
150(1)
7.2.1.1 Parameters of Overhead Line
150(2)
7.2.1.2 Parameters of Cable
152(1)
7.2.1.3 Parameters of Transformer
153(2)
7.2.1.4 Parameters of Synchronous Generator
155(1)
7.2.1.5 Parameters of Other Equipment
155(1)
7.2.2 Equipment Ratings
155(2)
7.2.2.1 Current Carrying Capacity of Overhead Line
157(1)
7.2.2.2 Current Carrying Capacity of Cable
158(1)
7.2.2.3 Loading Capacity of Transformer
159(2)
7.2.3 System Operation Limits
161(1)
7.2.4 Bus Load Coincidence Factors
161(2)
7.3 Reliability Data in Probabilistic Planning
163(13)
7.3.1 General Concepts of Reliability Data
163(1)
7.3.2 Equipment Outage Indices
164(1)
7.3.2.1 Outage Duration (OD)
165(1)
7.3.2.2 Outage Frequency (OF)
166(1)
7.3.2.3 Unavailability (U)
167(1)
7.2.3.4 Calculating Equipment Outage Indices
167(2)
7.2.3.5 Examples of Equipment Outage Indices
169(2)
7.3.3 Delivery Point Indices
171(1)
7.3.3.1 Definitions of Delivery Point Indices
172(3)
7.3.3.2 Examples of Delivery Point Indices
175(1)
7.4 Other Data
176(2)
7.4.1 Data of Generation Sources
176(1)
7.4.2 Data for Interconnections
177(1)
7.4.3 Data for Economic Analysis
177(1)
7.5 Conclusions
178(3)
8 Fuzzy Techniques For Data Uncertainty
181(34)
8.1 Introduction
181(1)
8.2 Fuzzy Models of System Component Outages
182(8)
8.2.1 Basic Fuzzy Models
183(1)
8.2.1.1 Fuzzy Model for Repair Time
183(2)
8.2.1.2 Fuzzy Model for Outage Rate
185(1)
8.2.1.3 Fuzzy Model for Unavailability
186(1)
8.2.2 Weather-Related Fuzzy Models
186(1)
8.2.2.1 Exposure to One Weather Condition
186(1)
8.2.2.2 Exposure to Two Weather Conditions
187(1)
8.2.2.3 Exposure to Multiple Weather Conditions
188(2)
8.3 Mixed Fuzzy and Probabilistic Models for Loads
190(2)
8.3.1 Fuzzy Model for Peak Load
190(1)
8.3.2 Probabilistic Model for Load Curve
190(2)
8.4 Combined Probabilistic and Fuzzy Techniques
192(4)
8.4.1 Probabilistic Representation for Region-Divided Weather States
192(1)
8.4.2 Hybrid Reliability Assessment Method
193(1)
8.4.2.1 Evaluating Membership Functions of Reliability Indices
193(3)
8.4.2.2 Defuzzification of Membership Functions
196(1)
8.5 Example 1: Case Study Not Considering Weather Effects
196(6)
8.5.1 Case Description
196(2)
8.5.2 Membership Functions of Reliability Indices
198(4)
8.6 Example 2: Case Study Considering Weather Effects
202(10)
8.6.1 Case Description
202(2)
8.6.2 Membership Functions of Reliability Indices
204(7)
8.6.3 Comparisons between Fuzzy and Traditional Models
211(1)
8.7 Conclusions
212(3)
9 Network Reinforcement Planning
215(22)
9.1 Introduction
215(1)
9.2 Probabilistic Planning of Bulk Power Supply System
216(9)
9.2.1 Description of Problem
216(1)
9.2.2 Economic Comparison between Two Options
217(1)
9.2.3 Reliability Evaluation Method
217(2)
9.2.4 Reliability Comparison between Two Options
219(1)
9.2.4.1 Data Preparation
219(1)
9.2.4.2 EENS (Expected Energy Not Supplied) Indices
220(1)
9.2.5 Effect of the Existing HVDC Subsystem
221(1)
9.2.5.1 Comparison between Cases with and without the Existing HVDC
221(1)
9.2.5.2 Effect of Replacing a Reactor of the Existing HVDC
222(1)
9.2.5.3 Comparison between the 230-kV AC Line and Existing HVDC
223(1)
9.2.6 Summary
224(1)
9.3 Probabilistic Planning of Transmission Loop Network
225(9)
9.3.1 Description of Problem
225(1)
9.3.2 Planning Options
225(2)
9.3.3 Planning Method
227(1)
9.3.3.1 Basic Procedure
227(1)
9.3.3.2 Evaluating Unreliability Cost
227(1)
9.3.3.3 Evaluating Energy Loss Cost
228(1)
9.3.3.4 Evaluating Annual Investment Cost
229(1)
9.3.3.5 Calculating Present Values of Costs
229(1)
9.3.4 Study Results
229(1)
9.3.4.1 Unreliability Costs
229(1)
9.3.4.2 Energy Loss Costs
230(1)
9.3.4.3 Cash Flows of Annual Investments
231(1)
9.3.4.4 Benefit/Cost Analysis
232(2)
9.3.5 Summary
234(1)
9.4 Conclusions
234(3)
10 Retirement Planning Of Network Components
237(22)
10.1 Introduction
237(1)
10.2 Retirement Timing of an Aged AC Cable
238(9)
10.2.1 Description of Problem
239(1)
10.2.2 Methodology in Retirement Planning
239(1)
10.2.2.1 Basic Procedure
239(1)
10.2.2.2 Evaluating Parameters in the Weibull Model
240(1)
10.2.2.3 Evaluating Unavailability of System Components
241(1)
10.2.2.4 Evaluating Expected Damage Cost Caused by End-of-Life Failure
241(2)
10.2.2.5 Economic Analysis Approach
243(1)
10.2.3 Application to Retirement of the Aged AC Cable
244(1)
10.2.3.1 α and β in the Weibull Model
244(1)
10.2.3.2 Unavailability Due to End-of-Life Failure
244(1)
10.2.3.3 Expected Damage Costs
245(1)
10.2.3.4 Economic Comparison
246(1)
10.2.4 Summary
247(1)
10.3 Replacement Strategy of an HVDC Cable
247(10)
10.3.1 Description of Problem
247(2)
10.3.2 Methodology in Replacement Strategy
249(1)
10.3.2.1 Basic Procedure
249(1)
10.3.2.2 Evaluating Capacity State Probability of HVDC Subsystem
250(1)
10.3.2.3 Evaluating Reliability of Overall System
250(1)
10.3.2.4 Benefit/Cost Analysis of Replacement Strategies
251(1)
10.3.3 Application to Replacement of the Damaged HVDC Cable
251(1)
10.3.3.1 Study Conditions
251(1)
10.3.3.2 Capacity Probability Distributions of HVDC Subsystem
252(2)
10.3.3.3 EENS Indices of Supply System
254(1)
10.3.3.4 Strategy Analysis of Three Replacement Options
255(2)
10.3.4 Summary
257(1)
10.4 Conclusions
257(2)
11 Substation Planning
259(24)
11.1 Introduction
259(1)
11.2 Probabilistic Planning of Substation Configuration
260(12)
11.2.1 Description of Problem
260(1)
11.2.2 Planning Method
261(1)
11.2.2.1 Simplified Minimum Cutset Technique for Reliability Evaluation
261(4)
11.2.2.2 Economic Analysis Approach
265(1)
11.2.3 Comparison between the Two Configurations
266(1)
11.2.3.1 Study Conditions and Data
266(1)
11.2.3.2 Reliability Results
267(3)
11.2.3.3 Economic Comparison
270(1)
11.2.3.4 Other Considerations
271(1)
11.2.4 Summary
272(1)
11.3 Transformer Spare Planning
272(8)
11.3.1 Description of Problem
272(1)
11.3.2 Method of Probabilistic Spare Planning
273(1)
11.3.2.1 Basic Procedure
273(1)
11.3.2.2 Reliability Evaluation Technique for a Transformer Group
274(1)
11.3.2.3 Reliability Criterion
275(1)
11.3.3 Actual Example
276(1)
11.3.3.1 Case Description
276(1)
11.3.3.2 Fixed Turn Ratio Transformer Group
276(2)
11.3.3.3 On-Load Tap Changer (OLTC) Transformer Group
278(1)
11.3.3.4 Combined Fixed Turn Ratio and OLTC Transformer Group
278(2)
11.3.4 Summary
280(1)
11.4 Conclusions
280(3)
12 Single-Circuit Supply System Planning
283(26)
12.1 Introduction
283(2)
12.2 Reliability Performance of Single-Circuit Supply Systems
285(3)
12.2.1 Delivery Point Reliability Indices
285(1)
12.2.2 Contributions of Different Components to Reliability Indices
286(2)
12.3 Planning Method of Single-Circuit Supply Systems
288(10)
12.3.1 Basic and Weighted Reliability Indices
288(1)
12.3.1.1 Basic Reliability Indices
289(3)
12.3.1.2 Weighted Reliability Index
292(1)
12.3.2 Unit Incremental Reliability Value Approach
293(1)
12.3.2.1 Annual Capital Investment
293(1)
12.3.2.2 Unit Incremental Reliability Value
293(1)
12.3.3 Benefit/Cost Ratio Approach
294(1)
12.3.3.1 Expected Damage Cost
294(1)
12.3.3.2 Benefit/Cost Ratio
295(1)
12.3.4 Procedure of Single-Circuit Supply System Planning
296(2)
12.4 Application to Actual Utility System
298(9)
12.4.1 Short List Based on Weighted Reliability Index
298(3)
12.4.2 Financial Justification of Reinforcement
301(1)
12.4.3 Ranking Priority of Single-Circuit Systems
302(5)
12.5 Conclusions
307(2)
APPENDIX A ELEMENTS OF PROBABILITY THEORY AND STATISTICS
309(12)
A.1 Probability Operation Rules
309(1)
A.1.1 Intersection
309(1)
A.1.2 Union
310(1)
A.1.3 Conditional Probability
310(1)
A.2 Four Important Probability Distributions
310(3)
A.2.1 Binomial Distribution
310(1)
A.2.2 Exponential Distribution
311(1)
A.2.3 Normal Distribution
311(1)
A.2.4 Weibull Distribution
312(1)
A.3 Measures of Probability Distribution
313(1)
A.3.1 Mathematical Expectation
313(1)
A.3.2 Variance and Standard Deviation
313(1)
A.3.3 Covariance and Correlation Coefficient
314(1)
A.4 Parameter Estimation
314(2)
A.4.1 Maximum Likelihood Estimation
314(1)
A.4.2 Mean, Variance, and Covariance of Samples
315(1)
A.4.3 Interval Estimation
315(1)
A.5 Monte Carlo Simulation
316(5)
A.5.1 Basic Concept
316(1)
A.5.2 Random-Number Generator
317(1)
A.5.3 Inverse Transform Method
317(1)
A.5.4 Three Important Random Variates
318(1)
A.5.4.1 Exponential Distribution Random Variate
318(1)
A.5.4.2 Normal Distribution Random Variate
318(1)
A.5.4.3 Weibull Distribution Random Variate
319(2)
APPENDIX B ELEMENTS OF FUZZY MATHEMATICS
321(8)
B.1 Fuzzy Sets
321(2)
B.1.1 Definition of Fuzzy Set
321(1)
B.1.2 Operations of Fuzzy Sets
322(1)
B.2 Fuzzy Numbers
323(2)
B.2.1 Definition of Fuzzy Number
323(1)
B.2.2 Arithmetic Operation Rules of Fuzzy Numbers
323(1)
B.2.2.1 Addition
323(1)
B.2.2.2 Subtraction
323(1)
B.2.2.3 Multiplication
323(1)
B.2.2.4 Division
324(1)
B.2.2.5 Maximum and Minimum Operations
324(1)
B.2.3 Functional Operation of Fuzzy Numbers
324(1)
B.3 Two Typical Fuzzy Numbers in Engineering Applications
325(1)
B.3.1 Triangular Fuzzy Number
325(1)
B.3.2 Trapezoidal Fuzzy Number
325(1)
B.4 Fuzzy Relations
326(3)
B.4.1 Basic Concepts
326(1)
B.4.1.1 Reflexivity
327(1)
B.4.1.2 Symmetry
327(1)
B.4.1.3 Resemblance
327(1)
B.4.1.4 Transitivity
327(1)
B.4.1.5 Equivalence
327(1)
B.4.2 Operations of Fuzzy Matrices
327(2)
APPENDIX C ELEMENTS OF RELIABILITY EVALUATION
329(12)
C.1 Basic Concepts
329(2)
C.1.1 Reliability Functions
329(1)
C.1.2 Model of Repairable Component
330(1)
C.2 Crisp Reliability Evaluation
331(4)
C.2.1 Series and Parallel Networks
331(1)
C.2.1.1 Series Network
331(1)
C.2.1.2 Parallel Network
332(1)
C.2.2 Minimum Cutsets
333(1)
C.2.3 Markov Equations
333(2)
C.3 Fuzzy Reliability Evaluation
335(6)
C.3.1 Series and Parallel Networks Using Fuzzy Numbers
335(1)
C.3.2 Minimum Cutset Approach Using Fuzzy Numbers
336(2)
C.3.3 Fuzzy Markov Models
338(1)
C.3.3.1 Approach Based on Analytical Expressions
338(1)
C.3.3.2 Approach Based on Numerical Computations
339(2)
References 341(8)
Index 349
Award-winning author Wenyuan Li is well known and highly respected in the field of electrical power engineering. He serves as Principle Engineer at BC Hydro and is a fellow of IEEE and EIC, serving on the editorial board of several international journals.He has published five books and numerous academic papers on power systems.
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