A New Method for Composite System Annualized Reliability Indices Based on Genetic Algorithms

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A New Method for Composite System Annualized
Reliability Indices Based on Genetic Algorithms
By

• Nader Samaan, Student,IEEE
• Dr. C. Singh, Fellow, IEEE
• Department of Electrical Engineering
• Texas AM University
• College Station, TX 77843, USA

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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.

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Power System Reliability Functional Zones
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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)

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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

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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.

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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.

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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.

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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.

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Initialization
GA generates random binary chromosomes each of
them represents a system state
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State Array Construction
Sampled State
States PropltPthreshold
Yes
Ignore this state, get a new sampled state
No
Previously Saved?
Get its data , get a new sampled state
Yes
No
Call state evaluation module save states data in
state array
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Evaluation Function

• The suitable choice for the evaluation function
  can add the required intelligence to GA state
  sampling

EPNSj LCj . PSj
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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 .
  fitnessj A . evalj 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.

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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 lt pm
flip that bit from 1 to zero or zero to one in
case of binary representation.
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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.

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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.

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DC Based Maximization Model
The variables vector that will be calculated by
the linear programming solver is Xip , PGj ,
?k
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Assessment of Composite System Adequacy Indices
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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.
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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
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Load Importance Effect on Buses Indices
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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

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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.

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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

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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.

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Questions?