International Journal of Engineering Trends and Technology (IJETT) – Volume 12 Number 4 - Jun 2014
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1.Assistant Professor,
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2.Assistant Professor & Head of Dept.
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Computer Science & Engineering, RTMNU Nagpur
Priyadarshini Indira Gandhi College of engineering, Nagpur
Abstract— This paper presents an efficient and reliable Dynamic particle swarm optimization (Dynamic PSO) algorithm based technique for solving the emission and economic dispatch (E&ED) problems. The harmful ecological effects by the emission of particulate and gaseous pollutants from fossil fuel power plants can be reduced by proper load allocation among the various generating units of the plants. But this load allocation may lead to increase in the operating cost of the generating units. So, it is necessary to find out a solution which gives a balanced result between emission and cost. In this paper, Dynamic particle swarm optimization solution to E&ED problem is presented.
The results are obtained for a test system with six generating units. The performance of the Dynamic PSO is compared with simple particle swarm optimization method, real coded genetic algorithm and hybrid genetic algorithm. The results clearly show that the proposed method gives global optimum solution compared to the other methods.
The rest of paper is organized as follow: Section II represent problem formulation, Section III represents the overview of dynamic particle swarm optimization algorithm.
II.
PROBLEM FORMULATION
The objective of ED problem is to simultaneously minimize the total generation cost ( FT ) and to meet the load demand of a power system over some appropriate period while satisfying various constraints,
The objective function is,
Index Terms— Economic dispatch (ED ), Economic Load Dispatch
(ELD), Dynamic Particle Swarm Optimization, PSO.
I.
I NTRODUCTION
Where P
Gi
: Power generation of unit i, Fi (PGi) : Generation cost function for PGi and Ai , Bi , Ci : Cost coefficients of ith generator. There are two constraints considered in the problem, i.e. the generation capacity of each generator and the power balance of the entire power system.
A. Constraint 1: Generation capacity constraint
For normal system operations, real power output of each generator is restricted by lower and can be expressed as follows,
Economic Dispatch (ED) problem is one of the fundamental issues in power system operation. In essence, it is an optimization problem and its main objective is to reduce the total generation cost of units, while satisfying constraints. [1] Previous efforts on solving ED problems have employed various mathematical programming methods and optimization techniques excluding losses. In traditional economic dispatch, the operating cost is reduced by proper allocation of the amount of power to be generated by different generating units. However the optimum economic dispatch may not be the best: n terms of the environmental criteria. Recently many countries throughout the world have concentrated on the reduction of the amount of pollutants from fossil fuel power generating units. Apart from particulate pollutants, there are three gaseous pollutants namely carbon di-oxide, sulphur oxides and nitrogen oxides emitted from fossil fuel power plants. These gaseous pollutants cause harmful effects to the human beings and the environment. So, during the load allocation process, the cost economy should not be the only objective, but the emission economy must also be taken into account.
In this paper we present the dynamic particle swarm optimization algorithm which gives solution to this problem.
The experiment is conducted for test system with six generating units. The performance of dynamic PSO is compared with simple PSO. The results clearly show that the proposed method gives global optimum solution compared to the other methods.
Where, are the minimum and maximum power generated by generator i, respectively .
B. Constraint 2: Power balance constraint
The total power generation must cover the total demand PD and the real power loss in transmission lines PL . This relation can be expressed as,
Here a reduction is applied to model transmission losses as a function of the generators output through Kron’s loss coefficients . The Kron’s loss formula can be expressed as follows :
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International Journal of Engineering Trends and Technology (IJETT) – Volume 12 Number 4 - Jun 2014
Where B ij,
B oi ,
B oo are the transmission network power loss Bcoefficients, which are assumed to be constant, and reasonable accuracy can be achieved when the actual operating conditions are close to the base case where the B-coefficients were derived.
In the summary, the objective of environmental/ economic power dispatch optimization is to minimize FT subject to the constraints (2) and (3).
III.DYNAMIC PARTICLE SWARM OPTIMIZATION
While searching for food, the birds are either scattered or go together before they locate the place where they can find the food. While the birds are searching for food from one place to another, there is always a bird that can smell the food very well, that is, the bird is perceptible of the place where the food can be found, having the better food resource information. Because they are transmitting the information, especially the good information at any time while searching the food from one place to another, conducted by the good information, the birds will eventually flock to the place where food can be found. As far as particle swam optimization algorithm is concerned, solution swam is compared to the bird swarm, the birds’ moving from one place to another is equal to the development of the solution swarm, good information is equal to the most optimist solution, and the food resource is equal to the most optimist solution during the whole course
Particle swarm optimization is a global optimization algorithm for dealing with problems in which a best solution can be represented as a point or surface in an n-dimensional space.
Hypothesis are plotted in this space and seeded with an initial velocity, as well as communication channel between the particles. Particles then move through the solution space and are evaluated according to some fitness function after each timestamp. Over time particles are accelerated towards those particles within their grouping which have better fitness values.
In dynamic PSO there is variation with swarm size and variation in topology.
The dynamic particle swarm optimization concept consists of, at each time step, changing the velocity of (accelerating) each particle toward its pbest and lbest (for lbest version).
Acceleration is weighted by random term, with separate random numbers being generated for acceleration towards pbest and lbest locations. After finding the best values, the particle updates its velocity and positions with following equations.
V[id]=v[ id]+c1*r(id)*(pbest[id ]-x[ id])+c2*r*(id)(gbest[id]-x[ id])------ (a) x[ id] = x[ id]+v[ id]------------------------(b) where, v[id ] is particle velocity x[ id] is the current particle r(id ) is random number between (0,1) c1 and c2 are learning factors usually c1=c2=2
The pseudo code of the procedure is as follows,
For each particle
Initialize Function value
END
Calculate average fitness value
Do
For each particle
If fitness value is less than average
Consider the particle
Calculate fitness value.
If the fitness value is better than the best
Fitness value (pbest) in history
Set current value as the new pbest.
END
Choose the particle with the best fitness value of all
the particles as the gbest
For each particle
Calculate particle velocity according to equation (a)
Update particle position according equation (b)
END
While maximum iterations or minimum error criteria is not attained
IV.DYNAMIC PSO ALGORITHM TO SOLVE ELD
PROBLEM
The power outputs from each generator are taken as the particles of the Dynamic PSO. Then the Dynamic PSO algorithm for dispatch problem is as follows.
Stepl: The particles are randomly generated between the maximum and minimum operating limits of the generators.
Step2: Initialized the function value for each particle. The particle velocities are generated
Step3: Objective function values of the particles are evaluated:
Penalties are given for violation of demand constraint (2).These values is set the pbest value of the particles.
Step4: The best value among all the pbest values
(gbest) is identified.
Step5: New velocities for the particles are calculated using(a).
Step6The positions are each particle are updated using (b)
Step7: New objective function values are calculated for pbest. If the stopping criteria is met, the positions of better than the previous pbest, the new value is set to particles represent the optimal solution. Otherwise the procedure is repeated from step4.
V.EXPERIMENTAL WORK
In order to show the effectiveness of the Dynamic PSO, the optimization results for a six unit test system [2] are presented here. For implementation of Dynamic PSO, population size of
40 and maximum number of iterations of 1000 are taken. All the
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International Journal of Engineering Trends and Technology (IJETT) – Volume 12 Number 4 - Jun 2014 related programs are written in MATLAB software package. To compare the performance of PSO with other algorithms, the results were taken from [2] and [6].
The results for pure economic dispatch for a demand of100 MW are presented in
Table I,and the results for pure emission dispatch for a demand of 700 MW are presented in Table 2.From the results it is clear that PSO gives global optimum solution with less computation time ,than the other techniques .It is also observed that the losses are also minimum. Table 3 presents dispatch results for economic and emission dispatch.
Method PL a
MW Fuel
Cost(FC),$/hr
Conventional
Method
Real Coded
GA
26,570
23.124
Hybrid GA 23.124
Dynamic
PSO
18.591
1677991.5
1671208.2
1671208.2
1663068.1
495.348
489.559
489.559
481.074
0.25
14.61
1.21
1.03
Table I Pure economic dispatch results for 700 MW
Method PL a
MW Fuel
Cost(FC),$/hr
Emission
Release(EC),
Kg/hr
Execution
Time
Sec
Conventional
Method
Real Coded
GA
20,240
17.366
Hybrid GA 17.366
1726402.5
1718388.0
1718388.0
Emission
Release(EC),
Kg/hr
495.348
489.559
489.559
Execution
Time
Sec
0.26
14.61
1.21
Dynamic
PSO
16.548 1715940.0 481.074 1.03
Table II Pure emission dispatch results for 700 MW
Dispatch Economic
Dispatch
Emission Dispatch
P
1
MW
P
2
MW
P
3
MW
30.712
18.681
P
4
MW
P
P
5
L
MW
P
6
MW
MW
P
D
MW
130.568
134.288
206.088
198.252
18.591
700
Fuel Cost(FC),$/hr 1663068.1
Emission
Release(EC) Kg/hr
481.074
VI.
CONCLUSION
80.3178
83.4732
111.0704
116.6904
157.919
167.0772
16.548
700
1715940.00
434.480
In this paper Dynamic Particle swarm optimization algorithm for economic and emission dispatch is proposed. The solution algorithm has been tested for a test system with six generating units. The results obtained are compared with the results of conventional method, RGA and HGA .From the outcome of the results it is shown that the proposed algorithm provides global optimum solution .
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