GENETIC ALGORITHM IN ECONOMIC LOAD DISPATCH : A REVIEW

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International Journal of Advanced Engineering Science and Technological Research (IJAESTR) ISSN: 2321-1202, www.aestjournal.org @2016 All rights reserved

54

GENETIC ALGORITHM IN ECONOMIC LOAD DISPATCH : A REVIEW

1

DURGESH KUMAR ,

²

VINAY SHARMA

1,2Assistant.Professor.,SWAMI VIVEKANAND SUBHARTI UNIVERSITY Email: ¹[email protected],²[email protected]

ABSTRACT:. In the conventional method like Lagagarge multiplier, Linear programming , and dynamic programming , convergence parameters and incompetency when number of generating units are increased , have been witnessed which not only influenced the efficiency but also cost increased rapidly.

To overcome the following , Genetic algorithm in Economic load dispatch has been implemented which is free from premature convergence and derivation free .ELD approach is basically the scheduling of the generators , connected in parallel , to minimize the fuel cost of the generator units subjected to equality constraints of power balance as per the minimum and maximum operating limits of the generating units. This method of using Genetic Algorithm in Economic load dispatch proposes an effective approach by which the fuel cost has been reduced up to some extent keeping the transmission losses as minimum as it may be possible

Keywords: Economic load dispatch, Optimum load flow, Genetic Algorithm

I. INTRODUCTION:

Electrical power system are designed to meet the continuous variation of power demand . Instability occurs mostly due to unbalancing between active and reactive powers. Earlier, methods which have been incorporated , require the incremental cost curves to be monotonically increasing or linear. These methods also suffer from the problem of local minimum and premature convergence.[4]

Genetic algorithm in Economic load dispatch is free from the problem of the local minimum. ELD aims at allocating the load demand to the committed generating units in such a way that the minimum cost is obtained . Consequently, objective is to minimize the total cost of supply load demand .Equality and inequality constraints are to be considered while approaching to the phenomenon of minimum fuel cost for optimal power flow .[10]

In this paper , with the help of Genetic algorithm to solve ELD problem with power balance equations as the inequality constraints . Here the method has been applied

on 3 generators units to find optimal allocation of generation on each generating unit.

2.OBJECTIVE FUNCTION:

Minimize C

T

= i

^Ng

F

i

(P

gi

) …….(a)

Where:

C

T

= Total generation cost F

i

(P

gi

)= Cost Function

P

gi

= Power output of unit (i) Ng= Number of generator units .

( )

……….(b)

( )[7]

3. CONSTRAINTS:

a). INEQUALITY CONSTRAINTS:

These are the units operational constraints, each generating unit have minimum power

P

^min and maximum power

P

^maxgeneration limit , as the maximum active power generation is limited thermal consideration and minimum generator is limited by flame instability of boiler.[7]

These limits can be designed as a pair of inequality constraints.

…….(c) Where i= 1 to

b)EQUALITY CONSTRAINTS:

According to this total power demand plus losses are always equal to the total power generated.

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International Journal of Advanced Engineering Science and Technological Research (IJAESTR) ISSN: 2321-1202, www.aestjournal.org @2016 All rights reserved

55 ………(d)

PL=losses

PD= Net power demand

Where as transmission losses are given by

……..(e)

P^T= Associate matrix of P B= Ng Coefficient Matrix

B_O= Ng dimensional column vector

4.GENETIC ALGORITHM:

4.1 INTRODUCTION:

The basic principles of GA were first proposed by Holland . . A Genetic Algorithm (GA) is a search technique used in computing to find exact or approximate solutions to optimization and search problems. Genetic algorithms are categorized as global search heuristics.[6]

Genetic algorithms are a particular class of Evolutionary Algorithms (EA) that use techniques inspired by evolutionary biology such as inheritance, mutation, selection, and crossover. Genetic Algorithms (GA‟s) are based on analogy, and are adaptive heuristic search algorithm based on, evolutionary ideas of natural selection and genetics. As such, they GA‟s represent an intelligent exploitation of the random search used, to solve search and optimization problems. The basic techniques of the GA are designed to simulate processes in natural systems necessary for evolution, especially those follow the principles first laid down by Charles Darwin of, "Survival Of The Fittest".

Since in nature, competition among individuals for scanty resources, results in the fittest individuals dominating over the weaker ones.

Genetic Algorithms are better than conventional algorithms in that they are more robust. They do not break easily, even if the inputs are changed slightly, or in the presence of reasonable noise. Also, in searching a large

state-space, multi-modal state-space, or n-dimensional surface, a genetic algorithm may offer significant benefits over more typical search of optimization techniques such as linear programming, heuristic, depth-first, breath first, and praxis.[7]

GA is a method for deriving from one population of “chromosomes” (e.g., strings of ones and zeroes, or bits) a new population. This is achieved by employing “natural selection” together with the genetics inspired operators of recombination (crossover), mutation, and inversion. Each chromosome consists of genes (e.g. bits), and each gene is an instance of a particular allele (e.g, 0 or 1). The selection operator chooses those chromosomes in the population that will be allowed to reproduce, and on average those chromosomes that have a higher fitness factor (defined bellow), produce more offspring than the less fit ones.

Crossover swaps subparts of two chromosomes, roughly imitating biological recombination between two single chromosome (“haploid”) organisms; mutation randomly changes the allele values of some locations (locus) in the chromosome; and inversion reverses the order of a contiguous section of chromosome.[6]

4.2 PROPERTIES OF GA:

 Generally good at finding acceptable solutions to a problem reasonably quickly

 Free of mathematical derivatives

 No gradient information is required

 Free of restrictions on the structure of the evaluation function

 Fairly simple to develop

4.2 GENERAL GENETIC ALGORITHM:

The general GA is as follows:

STEP1: CREATE A RANDOM INITIAL STATE An initial population is created from a random selection of solutions .this is unlike the situation for symbolic AI

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International Journal of Advanced Engineering Science and Technological Research (IJAESTR) ISSN: 2321-1202, www.aestjournal.org @2016 All rights reserved

56

system, where the initial state in a problem is already given.

STEP2: EVALUATE FITNESS

A value for fitness is assigned to each solution depending on how close it actually is solving the problem. These solutions are not to be confused with answers of the problem; think of them as possible characteristics that the system would imply in order to reach the answer.

STEP3: REPRODUE (AND CHILDREN MUTATE) Those chromosomes with a higher fitness value are more likely to reproduce offspring .The offspring is a product of the father and mother, whose composition consists of a combination of genes from the two. This process is known as crossing over.

STEP 4: NEXT GENERATION

If the new generation contains solution that produces an output that is a close enough or equal to the desired answer then the problem has been solved. If this is not the case ,then the new generation will go through the same process as their parents did. This will continue until a solution is reached.

4.3 GA VERSUS TREDITIONAL METHODS OF OPTIMIZATION:[13]

Genetic algorithms are based on the principles of natural genetics and natural selection. The basic elements of natural genetics: reproduction, crossover, mutation are used in the genetic search procedure. Genetic Algorithms differ from the traditional methods of optimization in the following respect:

1.) A population of points (trial design vectors) is used for starting the procedure insteadof a single design point. If the number of design variables is n, usually the size of thepopulation is taken as 2n to 4n. Since several points are used as candidate solutions,Genetic Algorithms are less likely to get trapped at a local optimum.

2.) Genetic Algorithms use only the values of objective function. The derivatives are notused in search procedures.

3.) In GAs the design variables are represented as strings of binary variables thatcorrespond to the chromosomes in natural genetics. For continuous design variables, the string length can be varied to achieve any desired resolution.

4.) The objective function value corresponding to design vector plays the role of fitnessin natural genetics.

5.) In every new generation, a new set of strings is produced by using randomized parentsselection and crossover from the old generation (old set of strings)..

5. ELD WITH LOSS USING GENETIC ALGORITHM:

Different GA techniques are available to solve the optimization problem. In this procedure , we apply binary coded GA .Putting the generating units within the constraints may not be required . Actually these values , automatically remain within the constraints. The sequential steps of solving the given problems are as follow.

Step1:First , initial strings are generated randomly as per the complexity , string length is selected. We select the string length to be 10 for this paper.

Step2: Here the spring which had selected , converted in to a acceptable range by the equation

Actual_ Value(i)= P_min + (( P_max—

P_min) ×P_m(i)))2

^L-1) L= Length of string

P_min= Minimum value of Generating unit P_max= Maximum value of Generating unit Step3: Now equality constraints are checkebythe equation

.

∑

Step4: Fitness evaluation of each chromosome is done according to the cost function.From equation (b)

( )

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International Journal of Advanced Engineering Science and Technological Research (IJAESTR) ISSN: 2321-1202, www.aestjournal.org @2016 All rights reserved

57

Cost function is figured out and those lowest cost function are considered and rest are eliminated for further stages.

Step5: New chromosome are taken for the cross over operation,.

Step6: As soon as crossover period is over, new offsprings are taken for the mutation operation.

Step7: Fitness of new offspringsare calculated and they are filtered in the ascending order .The highest value represents lower fitness and lowest value represents higher fitness. So lowest cost function value are selected for the next stage.

Step8: This process continues upto the maximum iterartions and result are obtained.

6.FLOW CHART :

Following steps of solving the ELD problem can be understood from the flow chart.

7.RESULT AND ANALYSIS:

7.1 INPUT DATA:

Here we have taken three equation by which help we will reach to a solution using Genetic algorithm and give us the minimum cost as required in our paper. The equation are as follow:

F1=0.00156P

1

2

+7.92P

1

+561 Rs/Hr F2=0.00194P

2

+7.85P

2

+310 Rs/Hr F3=0.00482P

3

2

+7.97P

3

+78 Rs/Hr

According to the constraints considered in this work among inequality constraints only active power constraints are constraints are considered. There operating limit of maximum and minimum power are also different. The unit operating ranges are:

100 MW ≤ P1 ≤ 600 MW 100 MW ≤ P2 ≤ 400 MW 50 MW ≤ P3 ≤ 200 MW

The transmission line losses can be calculated by knowing the loss coefficient. The Bmn loss

coefficient matrix is given by Bmn=

0.000075 0.000005 0.0000075 0.001940 0.000015 0.0000100 0.004820 0.000100 0.0000450

Start

Generation of the spring for the cost function Conversion of the string into

maxima and minima of cost function

∑

Calculation of equality constraints by the equation

Evaluation of the fitness function as per the cost

function

Selection of chromosome for crossover

Extraction of new values for the mutation operation

Filtering of best cost function or minimum cost

function

Check the convergence

yes

Stop Yes

NO

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Now these equation with the help of Matlab are performed and the output is obtained in the form of the graphs where cost and number of iteration are shown

7.2 Table showing the distribution of the load among different units.

S.NO Power laod demand in (MW)

P₁

(MW)

P₂

(MW)

P₃

(MW)

1 450 203.1 189.8 57.7

2 700 321.45 287.63 94.29

3 800 369.5 326.07 108.6

7.3 Table showing the respected cost,Losses and timings during different loads.

S.NO Loss in (MW)

Ft Rs/Hr

Time in sec s

1.

1.36 4664.2 13.58

2.

3.38 6868.82 10.06

3.

4.44 7779.37 7.45

7.4 OUTPUT FOR 450MW LAOD :Here in this as we know that as soon as the load is distributed among the different generating units, The cost is varied as per the distribution of the load.Here on the 450MW we can see that for the large number of iterations the value of the cost is declining rapidly.

7.5 OUTPUT FOR 700MW LAOD :Now the load has been increased and due to which the value of the cost willincrese

7.8 OUTPUT FOR 800MW LAOD :Here we see that as soon as load is increasing the execution time is decreasing and losses are increasing .Time reduction at large load plays a vital role as far load scheduling at different load is concerned.

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8.CONCLUSION: In this paper , the value of fuel cost has been reduced and the time which is required for the load to be carried has been distributed among different generating units with minimum lossess. Other optimization techniques has also been effective for the calculation of the economic load dispatch but they were facing the problem of premature convergence and local minimum which doesn’t yield the desirable result and caused a losses to the system, 9.REFRENCES:

1.Power System Analysis by HasanSaeed

2.Sunil kumarsingh ,LobzangPhunchok , “ Genetic algorithm a noble approach for the Economic load dispatch”National conference on emerging trends in engineering &Technologhy.(VNCET-30 March 2012),International journal of engineering research and applications. (IJERA)ISBN:2248-9622

3.C.L. Chiang, Improved genetic algorithm for power economic dispatch of units with valve-point effects and multiple fuels, IEEE Trans. Power Syst. 20 (4) (2005), pp.

1690–1699..

4.IEEE Committee Report, Present practices in the economic operation of power systems, IEEE Trans. Power Appa. Syst., PAS-90 (1971) 1768–1775.

5.B.H. Chowdhury and S. Rahman, A review of recent advances in economic dispatch, IEEE Trans. Power Syst, 5 (4) (1990), pp. 1248–1259.

6.Genetic algorithm solution of economic dispatch with valve point loading, IEEE Trans. Power Syst., 8 (August (3)) (1993), pp. 1325–1332

7.Aoki K. and Satoh T., “ Economic dispatch with network security constraints using parametric quadratic programming”, IEEE Transactions

8. P. Attaviriyanupap, H. Kita, E. Tanaka and J. Hasegawa, A hybrid EP and SQP for dynamic economic dispatch with nonsmooth fuel cost function, IEEE Trans. Power Syst., 17 (May (2)) (2002), pp. 411–416.

9. Walters David C. and Sheble Gerald B., “Genetic algorithm solution of economic dispatch ”, IEEE Transactions on Power Systems, Vol. 8, No. 3, August 1993.

10.Chiang C.L, “Genetic based algorithm for power

economic load dispatch”, IET

Gener.Transm.Distrib,1,(2),pp.261-269,2007

11.Mori Hiroyuki and Horiguchi Takuya, “Genetic algorithm based approach to economic load dispatching”, IEEE Transactions on power system, Vol.1,pp.145- 150,1993.

12.H. Happ, “Optimal power dispatch-A comprehensive survey”, IEEE Trans. Power Apparat.Syst.,vol. PAS-90, pp. 841-854, 1977

13.P. Aravindhababu and K.R. Nayar, Economic dispatch based on optimal lambda using radial basis function network, Elect. Power Energy Syst,. 24 (2002), pp. 551–

556.

14.D.C. Walters and G.B. Sheble, Genetic algorithm solution of economic dispatch with valve point loading, IEEE Trans. Power Syst., 8 (August (3)) (1993), pp. 1325–

1332