Power System Reliability Analysis with RES Dr. Naran M. Pindoriya Assistant Professor, EE Department Indian Institute of Technology Gandhinagar

Transcription

1 Power System Reliability Analysis with RES Dr. Naran M. Pindoriya Assistant Professor, EE Department Indian Institute of Technology Gandhinagar 25/05/11 1

2 Talk outline v v v v Introduction to Reliability Power system Reliability MCS-SVM Model for Composite Reliability Assessment Power System Reliability Analysis with Renewable Energy Sources 25/05/11 2

3 What is Reliability? Basic Steps in System Reliability Analysis Objective of the analysis Component /system modeling Performance function Reliability Evaluation Introduction to Reliability 25/05/11 3

4 What is Reliability? Ability of a system to perform its intended function Within a specified period of time Under stated condition Relate to the absence of failures, that due to random phenomenon (e.g., Random failures, Uncertainties ) Define numerically as average or mean value Can be treated as a parametric quantity Can be traded off with other parameters such as cost How to model uncertainty? 25/05/11 4

5 How to model Uncertainty? Probability of failure Chance that a component will fail Probabilistic value with no unit May be difficult to interpret Frequency of failure (failure rate) In terms of number of failure within specified time Easier to predict from history Express in per hour, per day, per year How to quantify reliability? 25/05/11 5

6 Example : Transmission Lines G 100 MW 100 MW Load 100 MW G 100 MW Load 100 MW System A System B Given that each transmission lines has the following level of reliability System Failure Probability Which system is more reliable? Which system is more cost-effective? Cost (million Rs) A B /05/11 6

7 Cost-Benefit Analysis High reliability achieved with high cost Is it worthwhile to have high reliability? Source: 25/05/11 7

8 System Reliability Analysis Objective: Interest to know the time-to-failure distribution of a component/system Helps to predict the failure probability at any point in time λ = failure rate q Basic Steps: Up Down q Component/ System Modeling μ = repair rate Describe state of each components in the system Ex: a generator has two states (either up or down) In terms of probability distribution Ex: a generator fails with probability of failure = /05/11 8

9 System Reliability Analysis Cont d q Performance Function Need to define intended function. Ex: Minimization of load curtailment q Reliability Evaluation Each component described by random variables Gen. states Output (MW) Probability System states constructed from possible combinations of component states 25/05/11 9

10 Objective of Reliability Analysis Levels of Reliability Analysis Power System Reliability Indexes and Criterion Deterministic Probabilistic Power system Reliability 25/05/11 10

11 Uncertainties in Power Systems Generation Generating units with failure and repair rates Generating capacity associated with probability Transmission line capacity Transmission line with failure and repair rates Transmission line capacity associated with probability System load Vary with time Construct load distribution from history 25/05/11 11

12 Objective Reliability is a measure of the ability of the power system to deliver electricity to all points of utilization within accepted standards and in the amount desired, for the period of time intended, under the operating conditions intended. RELIABILITY Analyzed either on deterministic or probabilistic basis Adequacy SECURITY Adequacy : relates to the existence of sufficient facilities within the system to satisfy the consumer load demand at all times; taking into account scheduled/ unscheduled outages assessed using the power flow (AC/DC) solutions Security : ability of the electric systems to respond to sudden disturbances arising within that system, such as electric short circuits assessed using dynamic calculation 25/05/11 12

13 Areas of Power System Reliability Analysis Generating capacity reliability Concern with generation adequacy All generators and loads are connected to a single bus Composite system reliability Concern with generation and transmission capability adequacy LEVEL Distribution system reliability Local network connected to end-users Interest to find out the reliability level at load point 25/05/11 13

14 Composite Power System Reliability Basic intention:- to determine some probabilistic measure of the undesirable events in power systems No State Selection Load Curtailment Yes Unit and System Models Operating Strategies Evaluation Success State Failure State Classification of system states in the whole state space Success States Failed States Reliability Indices Calculation State Space 25/05/11 14

15 Power Systems Reliability Indexes Deterministic indexes Do not take into account the uncertainties that affect reliability Simple calculation and require less data Percentage reserve Reserve margin as the largest unit online Probabilistic indexes Reflect uncertainties in the system Loss of load probability (LOLP) Probability that generation will not meet demand in a year Loss of load frequency (LOLF) How often does the system fail in a year Expected energy not supplied (EENS) 25/05/11 15

16 Power Systems Reliability Criterion Deterministic criteria N-m contingency analysis System with N components should be able to serve peak load when loss m components Sometimes called security analysis Probabilistic criteria Loss of load expectation, for example, 1 day in 10 years 25/05/11 16

17 Monte Carlo Simulation (MCS): Introduction SVM and LSSVM classifier Tool MCS-LSSVM Model for Reliability Assessment Simulation results for different case studies MCS-SVM Model for Composite Reliability Assessment 25/05/11 17

18 Reliability Evaluation: Methods Classical Approaches demands strict mathematical analysis use some device to circumvent the problem of straightforward enumeration such as State space pruning, Variance reduction technique Simulation Select system states based on their respective sampling mechanism (e.g., sequential or random sampling) Monte Carlo Simulation (MCS) AI based algorithm used in ü State selection as an alternative to MCS (for ex. PSO, GA, etc ) ü Pattern classification techniques for state evaluation as an aid to MCS 25/05/11 18

19 Simulation Methods: Remarks (1) The most significant difference between MCS and AI based search algorithm lies in their sampling mechanism. system states are sampled based on their occurrence probability, and both success and failure states sampled contribute to the estimation of reliability indices. ability to model complex systems in more detail and accuracy than is possible in analytical methods; can not only calculate the expected value of reliability indices but also their distributions MCS Method: Some Remarks Even though the state is a repeated sample, is still count for index calculation when MCS is used to deal with highly reliable systems, its efficiency may become low since a large number of system states need to be sampled and evaluated. (e.g. quite time-consuming) 25/05/11 19

20 Simulation Methods: Remarks (2) AI based Search Method: Some Remarks Unlike MCS, AI based search method is rather problem-dependent, where system states with higher failure probabilities have higher chances to be selected and evaluated. the failure probability of system state is used to guide the search. Also, unlike MCS, in AI based search method only the failure states are useful in estimating reliability indices. 25/05/11 20

21 MCS for Composite Reliability Evaluation MCS: the non-sequential and the sequential MCS the non-sequential approach samples the system states randomly, while in sequential approach the system states preserve the Computational chronological characteristics steps for the of non-sequential the system MCS 1. Select a state of the power system, by random sampling the states of all components and the load levels. 2. Characterize (or classify) the selected state, x, (success or failure) through test function f(x), by performing the adequacy analysis, which usually involves optimal power flow (OPF) analysis. 3. Update the estimate, E(f ) 4. If the stopping criterion is satisfied, stop; otherwise return to step 1. 25/05/11 21

22 IEEE-RTS-79 Test System BUS 17 Unit 21 (1 155 MW) Unit 22 (1 400 MW) BUS 16 BUS 15 BUS 18 Unit 15~19 (5 12 MW) Unit 20 (1 155 MW) BUS 24 BUS 14 BUS 19 BUS 11 BUS 21 BUS 22 BUS 20 BUS 23 BUS 12 Unit 12~14 (3 197MW) BUS 13 (slack bus) BUS 3 BUS 9 BUS 10 BUS 6 cable BUS 4 BUS 5 BUS 1 BUS 2 Unit 1~2 (2 20 MW) Unit 3~4 (2 76 MW) Unit 23 (1 400 MW) cable Synch. Cond. Unit 5~6 (2 20 MW) Unit 7~8 (2 76 MW) Unit 24~29 (6 50 MW) Unit 9~11 (3 100 MW) Unit 30~31 (2 155 MW) Unit 32 (1 350 MW) 230 kv 138 kv BUS 8 BUS 7 Ø 24 buses (10 generation buses and 17 load buses), 38 Ckts, 32 generating units, Total installed capacity: 3405 MW and peak load: 2850MW Ø Ø Ø Two well defined areas: Ø Ø 138 kv (dominated by load) 230 kv (dominated by generation, 2721 MW) Ckts are, fully available at all times Load buses are considered to the fully correlated with the total system load 25/05/11 22

23 Load Profile of IEEE RTS Load (pu) Hours Load Prob. Load Prob. Load Prob. Case 1: Fixed peak load = 2850 MW Case 2: Multiple load levels Case 3: Time varying load /05/11 23

24 MCS-LSSVM: Flowchart Input/output training data set obtained by MCS procedure Testing patterns obtained by random states sampling (MCS computation-step 1) Identify most relevant input variables Extract the training patterns through K- means clustering LSSVM classifier modeling and supervised training (10-fold cross validation) Once LSSVM is trained Power system state space pre-classification by the trained LSSVM model instead of OPF Classifier accuracy assessment and calculate reliability indices by analyzing only failure states classified by LSSVM # Naran M. Pindoriya, Panida Jirutitijaroen, Dipti Srinivasan, and Chanan Singh, Composite reliability evaluation using MCS and least squares support vector classifier, IEEE Transactions on Power Systems, Feb (Accepted and available for early access). 25/05/11 24

25 Introduction to SVM SVM provides an approach to the two-category (operating or failed) classification problem with clear connections to the underlying statistical learning theory Let, the problem of separating the set of training vectors (N data points) belongs to two separate classes: { ( 1, 1 ),..., N (, N )}, n OO, { 1,1 } D = x y x y x y with a hyperplane: H : y = w Ox b = 0 w (weight vector) and b (bias) are the parameters that control the function. the is b / the w perpendicular distance to the origin. Linear separation Optimization problem: 1 T Min w w, s. t. yi ( w Ox b) O1 w, b 2 LR augmented optimization function 25/05/11 25

26 Non-linear SVM: If the surface separating the two classes is not linear, the data points can be transformed to another high dimensional feature space where the problem is linearly separable Let, the transformation be then φ ᅲ the lagrangian function in the high dimensional feature space is: L ( ) 1 = Oα Oα α y y φ φ i 2 ij k ( xi, x j ) ( x ) ( x ) D i i j i j i j Mapping the input space to the feature space, where linear classification is possible 25/05/11 26

27 LSSVM In contrast to the standard SVM, the LSSVM uses a least squares cost function and involves equality constraints instead of inequalities in the problem formulation. As a result, the solution is obtained by solving a set of linear equations instead of QP and hence, LSSVM can reduce the computational complexity. Kernel functions 25/05/11 27

28 Input Data Projection Input data projection (Case 2) Input data projection (Case 3) 1800 Success state Failure state 2500 Success state Failure state Generation Reserve (MW) Generation Reserve (MW) Unavailable Generation Capacity (MW) Unavailable Generation Capacity (MW) 25/05/11 28

29 Case 1 (Fixed peak load = 2850 MW) Training patterns are generated by Algorithm MCS runs until coefficient of variation (β) converge to 10% No. of total samples = 873 No. of success states = 783 No. of failure states = 90 LOLP = , EPNS = MW Execution time for MCS= Sec LOLP/Coefficient of variation LOLP Coeff. of variation EPNS EPNS(MW) SVM training data patterns Inputs : [ unavlbe_gen, res_gen ] Training samples = 270 [failure state (1): success states(2)] Obtained using K-means clustering algo Number of iterations

30 Case-1 : Simulation results Case 1 (Fixed peak load) LSSVM Classifier Performance (Case 1) MCS (benchmark) MCS-LSSVM Linear kernel RBF kernel # success states # failure states Sensitivity (%) NA Specificity (%) NA g-mean (%) NA Composite Reliability Indices Comparison (Case 1) Esti. index LOLP Error (%) EPNS (MW) Esti. index Error (%) Total Comp. time (sec) MCS (benchmark) # Naran M. Pindoriya, Panida Jirutitijaroen, Dipti Srinivasan, and Chanan Singh, Composite reliability evaluation using MCS and least squares support vector classifier, IEEE Transactions on Power Systems, Feb (Accepted and available for early access). MCS- LSSVM Linear kernel RBF kernel

31 Case 2 (Multiple load levels) LOLP EPNS(MW) Coefficient of variation No. of samples No. of samples Training patterns are generated by MCS Algorithm runs until coefficient of variation (β) converge to 0.15 No. of total samples = 3701 Execution time for MCS= Sec

32 Case 2 (Multiple load levels) 1800 INPUT DATA PROJECTION 1800 INPUT DATA PROJECTION Generation reserve (MW) Generation reserve (MW) Unavailable generation capacity (MW) Unavailable generation capacity (MW) No. of success states = 3603 No. of failure states = 98 LOLP = EPNS = MW SVM training data patterns Inputs : [ unavlbe_gen, res_gen] Training samples = 294 [failure state (1): success states(2)] Obtained using K-means clustering algo.

33 Case 2 (Multiple load levels) LSSVM Classifier Performance (Case 2) MCS (benchmark) MCS-LSSVM Linear kernel RBF kernel # success states # failure states Sensitivity (%) NA Composite Reliability Indices Comparison (Case 2) Specificity (%) NA g-mean (%) NA Esti. index LOLP Error (%) EPNS (MW) Esti. index Error (%) Comp. time (sec) MCS (benchmark) MCS- LSSVM Linear kernel RBF kernel /05/11 33

34 Case 3 (Time varying load) 3 x LOLP EPNS(MW) Coefficient of variation ( β ) No. of samples No. of samples Training patterns are generated by MCS Algorithm runs until coefficient of variation (β) converge to 0.2 No. of total samples = Execution time for MCS= Sec

35 Case 3 (Time varying load) 2500 INPUT DATA PROJECTION success state failure state TRAINING SAMPLES Generation reserve (MW) Generation reserve (MW) Unavailable generation capacity (MW) Unavailable generation capacity (MW) No. of success states = No. of failure states = 25 LOLP = EPNS = MW SVM training data patterns Inputs : unavlbe_gen, res_gen [ ] Training samples = 175 [failure state (1): success states(6)] Obtained using K-means clustering algo.

36 Case 3 (Time varying load) INPUT DATA PROJECTION (TESTING SET) 2500 MCS (Benchmark) Testing samples through MCS until it reaches (β = 0.05) = 2,97,139 Execution time for MCS= Sec. Success states = 2,96,739 and Failure states = 400 LOLP = , EPNS = MW Generation reserve (MW) MCS-LSSVM Unavailable generation capacity (MW) LOLP EPNS (MW) Kernel type # Success states # Failure stats Sensitivity (%) Specificity (%) g-mean Esti. index Error (%) Esti. index Error (%) LSSVM+ OPF time (sec) [A] Lin. kernel RBF kernel Poly. kernel Total (MCS for tra. patt. =350.8+A)

37 Case 3 (Time varying load) # Naran M. Pindoriya, Panida Jirutitijaroen, Dipti Srinivasan, and Chanan Singh, Composite reliability evaluation using MCS and least squares support vector classifier, IEEE Transactions on Power Systems, Feb (Accepted and available for early access). LSSVM Classifier Performance Linear kernel MCS-LSSVM RBF kernel Polynomial kernel # success states # failure states Sensitivity (%) NA Specificity (%) NA g-mean (%) NA Esti. index LOLP Error (%) EPNS (MW) Esti. index Error (%) Com. time (sec) [A] Total [MCS for tra. patt. (=350.8) +A] MCS (benchmark) NA MCS (benchmark) MCS- LSSVM Lin. kernel RBF kernel Poly. kernel Composite Reliability Indices Comparison

38 Concluding Remarks LSSVM classifier takes the equality constraints in place of the inequality counterparts with SVM, and the solution follows from solving a set of linear equations, instead of quadratic optimization problem for SVM. Because the LSSVM is fast and effective nonlinear classifier in compare to ANN classifiers, it has used to preclassify the entire system operating states into success or failure, so then only failure states are fully evaluated for adequacy analysis to calculate composite reliability indices. MCS LSSVM allows to avoid the adequacy analysis of success states (which are usually much greater than the number of failure states in power systems) and hence it provides significant reductions in the computational cost required while evaluating composite reliability. 25/05/11 38

39 Case Studies ERCOT System with wind energy Augmented IEEE RTS with PV generation Power System Reliability Analysis with Renewable energy sources 25/05/11 39

40 Objective Reliability analysis of power system including RES, with an emphasis of bus loads and intermittent behavior of RES such as wind and solar power q ERCOT System with wind energy Zhen Shu and Panida Jirutitijaroen, Latin Hypercube Sampling Techniques for Power Systems Reliability Analysis With Renewable Energy Sources, IEEE Transactions on Power Systems, Jan (Accepted and available for early access). 25/05/11 40

41 q Augmented IEEE RTS with PV generation Weekly load and PV curves in IEEE RTS case PV power generated from MIT Weather Station in 2009, Available: Zhen Shu and Panida Jirutitijaroen, Latin Hypercube Sampling Techniques for Power Systems Reliability Analysis With Renewable Energy Sources, IEEE Transactions on Power Systems, Jan (Accepted and available for early access). 25/05/11 41

42 Thank you for your attention!!! Questions??? 25/05/11 42