optimal placement of capacitor using fuzzy logic and genetic algorithm in distribution system copy

8/8/2019 Optimal Placement of Capacitor Using Fuzzy Logic and Genetic Algorithm in Distribution System Copy

1/29

OPTIMAL CAPACITOR PLACEMENT IN A

DISTRIBUTION SYSTEM

Gaurav Ranjan


2/29

Capacitors have been very commonly employed to providereactive power compensation to distribution systems.

Capacitors are used to minimize the power and energylosses and to enhance the voltage profile.

We represent an optimization method which uses fuzzyand genetic algorithm for capacitor placement.


3/29

Fuzzy reasoning finds the sensitive nodes.

Three membership functions are defined for real power loss,reactive power loss and voltage deviation, respectively.

A high power loss section of the feeder is given a lowmembership value, while a low power loss section of the feeder

is given a high membership value.

The voltage deviation can be similarly defined, a bus with high

voltage deviation is given a low membership values.


4/29

The alpha-cut operation of a fuzzy set is used to obtain thecandidate location for capacitor installation.

The genetic algorithm determines the capacitor size and type forinstallation.

In genetic algorithm application, the fitness function for each stringof the population is defined as the objective function of the systemmodel, which is composed of the peak power losses and cost of

capacitors added.


5/29


6/29

Power System Capacitor is an assembly

of dielectric Materials and Metal-electrodes in a container (casing), with

terminals brought out, that is intended to

introduce capacitance into an electric

power circuit.


7/29

POWER CAPACITOR IN SERVICE


8/29

The power capacitor can be considered to be a

VAR-GEN (reactive power Source), since it actuallysupplies needed-magnetizing current requirements

for inductive loads.

The fundamental function of power capacitor is toprovide needed reactive power compensation.


9/29

Power factor correction

Feeder-Loss Reduction

Release of System capacity

Voltage- Stabilization/Regulation

Efficient Power Utilization

Power Quality Enhancement

Power Harmonic Filtering


10/29

The Capacitor Location or Placement for low voltage

systems determines capacitor type, size, location and

control schemes.

Optimal capacitor placement is generally a hard

combinatorial .optimization problem that can be

formulated as a nonlinear/Search Minimization problem.


11/29

Almost all the methods to solve capacitor placement problems are

based on the historical data of the load models and associated cost

of the energy and the cost of capacitor banks.

Cost for Power savings and Losses (Power losses/Energy losses


12/29

Historical Data and Load models are uncertain and may

change in reality.

To account for such load model and load pattern/cycles

uncertainties Soft-Computing AI Based algorithms using fuzzy

sets/Neural networks/Genetic Algorithm can be utilized.


13/29

In general, capacitor placement problemscan be solved in two steps:

1.Use of load flow model and find the V,P,Qat all the buses and also the feeder losses

2.Minimize the cost function-Jo-min -subject to constraints, like practical limitsof voltage and capacitor size!


14/29


15/29

Zadeh (1965) introduced Fuzzy Sets where he

replaced the characteristic function with membership

Membership is a generalization of characteristic

function and gives a degree of membership

Successful applications in control theoretic settings

(appliances, gearbox)

Fuzzy Sets


16/29

The fuzzy relation R between Sets X and Y is

a fuzzy set in the Cartesian product XY

mR: X Y [0,1] gives the degree to which x

and y are related to each other in R.


17/29

Different views

Foundation for reasoning based on uncertain

statements Foundation for reasoning based on uncertain

statements where fuzzy set theoretic tools are used

(original Zadeh)

As a multi valued logic with operations chosen in a

special way that has some fuzzy interpretation


18/29

If x in A then y in B is a relation R between

A and B

Two model types

Implicative: (x in Ay in B) is an upper bound

Conjunctive: (x in A ^ y in B) is a lower bound


19/29

F

uzzy sets can be said to model inherentvagueness

Bob is "tall" -vagueness in the meaning

of "tall", not in Bob's height


20/29


21/29

21

Genetic Algorithms (GA) OVERVIEW

yA class of probabilistic optimization algorithms

y Inspired by the biological evolution process

y Uses concepts ofNatural Selection and GeneticInheritance (Darwin 1859)

y Originally developed by John Holland (1975)

y Genetic Algorithms follow the idea ofSURVIVAL OF

THE FITTEST- Better and better solutions evolvefrom previous generations until a near optimalsolution is obtained.


22/29

22

GA overview (cont)y

Particularly well suited for hard problems wherelittle is known about the underlying search spaceWidely-used in business, science and engineering

y Based on Darwinians principle of evolution


23/29

Selection : This operator selects chromosomes in thepopulation for reproduction.The fitter the chromosome,the more times it is likely to be selected to reproduce.

Crossover : This operator randomly chooses a locus andexchanges the subsequences before and after that locus

between two chromosomes to create two offspring.Mutation :This operator randomly flips some of the bitsin a chromosome.


24/29

Alternate solutions are too slow or overly complicated

Need an exploratory tool to examine new approaches

Problem is similar to one that has already beensuccessfully solved by using a GA

Want to hybridize with an existing solution

Benefits of the GA technology meet key problem

requirements


25/29

Multiple solutions can be obtained without extra effort.

GAs are implicitly parallel and can be implemented onparallel machines.

GAs are quite successful in locating the regions containingoptimal solution(s), if not the optimum solution itself.

GAs can solve problems involving large time domain.


26/29

GAs work with a population of candidate solutions and not asingle point.

GAs work with coding of parameters instead of parametersthemselves.

GAs do not require any domain knowledge (gradientinformation etc.) and just use the payoff information.

GAs are stochastic methods, i.e., use probabilistic transitionrules and not deterministic ones.

Applies to a variety of problems and not works in a restricteddomain.


27/29

1.Optimize the cost using GA in MATLAB

2.SOLVING LOAD-FLOW using MATLAB


28/29

GENETIC ALGORITHMS


29/29

optimal placement of capacitor using fuzzy logic and genetic algorithm in distribution system copy

Documents