1 A New Method for Composite System Annualized Reliability Indices Based on Genetic Algorithms Nader Samaan, Student,IEEE Dr. C. Singh, Fellow, IEEE Department of Electrical Engineering Texas A&M University College Station, TX 77843, USA By

2 Outline Introduction to Power System Reliability and GA Classification of Existing Methods. Genetic Algorithm Approach for the Proposed Method. Chromosome representation and States Array construction. Algorithmic Structure. State evaluation module. Calculating Adequacy Annualized Indices. Application to the RBTS Advantage over conventional methods. Conclusions & Work in Progress.

3 Power System Reliability Functional Zones

4 Indices Calculated at Each Zone Generation Capacity Reliability Evaluation LOLP, LOLE, LOLF, EENS Composite system Reliability Annualized indices, Annual indices For the whole system and each bus LOLP, LOLE, LOLF,EENS Distribution System Customer load point indices,Failure Rate, EENS, ECOST System indices :Average interruption frequency index, Customer average interruption duration Contribution to Customer Failure ( 12% 5% 83%) Composite failure (global effect) Distribution failure(localized effect)

5 Classification of the Methods Used in Reliability Assessment of Composite System Analytical Methods: Contingency enumeration approach Simulation methods: Monte Carlo Method Random Sampling, Sequential Sampling Hybrid methods : Monte Carlo simulation for states sampling and then the use of linearized flow equation to evaluate sampled states

6 Limitations of Conventional Methods Analytical Methods:- Difficulty to trace the numerous number of system states. Therefore the aim of methods based on analytical techniques is to prune the huge state space. This can be achieved by state ranking or state evaluation until a certain level of component outages is reached. Monte Carlo Methods:- Simulation time increases as system components are more reliable. As statistically based approach all sampled states need to be evaluated and may be more than once.

7 GA Construction A genetic algorithm is a simulation of evolution where the rule of survival of the fittest is applied to a population of individuals. The basic genetic algorithm is as follows : 1. Create an initial population 2. Evaluate all of the individuals 3. Select a new population from the old population based on the fitness of the individuals. 4.Apply some genetic operators (mutation & crossover) to members of the population to create new solutions.

8 GA Approach The proposed method can be divided into two main parts. First GA searches intelligently for failure states through its fitness function using the linear programming module to determine if a load curtailment is needed for each sampled state. Sampled state data are then saved in state array. After the search process stops The second step begins by using all of the saved state data to calculate the annualized indices for the whole system and at each load bus.

9 Chromosome Representation Single line diagram of the RBTS test system. Each power generation unit and transmission line is assumed to have two states, up and down.

10 Initialization GA generates random binary chromosomes each of them represents a system state

11 State Array Construction States Prop<P threshold Sampled State Call state evaluation module save states data in state array Previously Saved? Get its data, get a new sampled state Ignore this state, get a new sampled state Yes No Yes

12 Evaluation Function The suitable choice for the evaluation function can add the required intelligence to GA state sampling EPNS j = LC j. PS j

13 Evolution of New Generation The fitness of any chromosome “j” is calculated by linearly scaling its evaluation function value.. Scaling has the advantage of maintaining a reasonable difference between fitness values of different chromosomes. It also enhances the effectiveness of search by preventing an earlier super-chromosome from dominating other chromosomes which decreases the probability of obtaining new more powerful chromosomes. fitness j = A. eval j + C All chromosomes in the current generation are evaluated The termination criterion is not satisfied then produce a new generation to scan more system states. Old population passes through,selection, crossover operator and mutation operator to produce a new population.

14 GA operators One point crossover, uniform flip mutation Tournament selection: A set of chromosomes is randomly chosen. The chromosome that has the best fitness value, the highest in the proposed algorithm, is chosen for reproduction. Binary tournament is used in which the chosen set consists of two chromosomes. The probability of choosing any chromosome in the selected set is proportional to its fitness value relative to the whole population fitness value. Mutation: get a random number r if r < p m flip that bit from 1 to zero or zero to one in case of binary representation.

15 The Aim of GA –The main idea of the proposed method is that at each generation more failure states are scanned especially those with higher probabilities i.e. have higher fitness. –Each of them will be saved in the state array. If dealing with an ordinary optimization problem the purpose is to obtain the maximum value of the fitness function and the decoded value for its chromosome.

16 States Evaluation State evaluation is a very important stage in composite power system reliability assessment. Through this stage the current system state to be evaluated is judged if it is a failure or success state. If it is a failure state the amount of load curtailment for the whole system and the share of each load bus in this amount will be determined. For the same optimal solution it is possible to have many scenarios of load curtailment at each bus. A load curtailment philosophy should be used. Importance of load is taken into consideration as a load curtailment philosophy. Each load is divided into three parts Weights are given for each part in the objective according to the relative importance for each bus in comparison with the remaining buses. Weights are also adjusted so that the first part of each load is the least important and the third part is the most important.

17 DC Based Maximization Model The variables vector that will be calculated by the linear programming solver is { X ip, PG j,  k }

18 Assessment of Composite System Adequacy Indices

19 Case Study-RBTS System The proposed algorithm has been implemented through C++ The total number of states that GA has sampled and has saved in the states array is 2198 states from which 1449 states result in load curtailment i.e. 66% of saved states are failure states. It can be seen that GA truncated the huge states space of the 20 components in the system which is larger than 1 million into a very small fraction of it.

20 Best Chromosome Two different fitness function gives two different best chromosomes, The first has the highest failure probability the second has the highest risk index

21 Load Importance Effect on Buses Indices

22 Advantages of GA Over Monte Carlo Simulation GA provides an intelligent search method. Through its fitness function it can be guided to acquire any part of the state space hunting more dominant events. Sampled states are evaluated once which is not the case in Monte Carlo simulation. In case of very reliable systems, Monte Carlo simulation needs much more time to converge, which is not the case with GA as it depends on fitness value comparison Obtained states array can be analyzed to acquire valuable information about system states Parallel operation of GA Sampling can provide computational time reduction

23 Conclusions& Research in Progress An innovative method for composite power system reliability evaluation is presented Guided by its fitness function and reproduction mechanism GA acts as an intelligent search tool to search for failure states that result in load curtailment States sampled by GA are saved with all their related data in the states array which is used to calculate the annualized adequacy indices for system and load points. A linear programming model was used to evaluate each state taking into consideration loads importance. Accuracy and advantages of the proposed method over Monte Carlo methods has been shown.

24 Taking load Curve into consideration and representation of multi-state components Using clustering techniques the 8760 load values can be represented by certain number of point, each with a certain probability. Load value is represented in the chromosome State #5  101 Multi state components will be represented using two or more genes

25 Parallel Operation of GA Sampling Checking if a certain state was saved previously, becomes a burden on the computational effort in case of large system. GA sampling can be preformed on different machines on the same time saving only a small portion of the state space on each machine. Each portion is not overlapping with other portions.

26 Questions?