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Multiobjective Economic Load Dispatch Studies in 2-D and 3-D Space by Particle Swarm Optimization Technique

  • N. K. JainEmail author
  • Uma Nangia
  • Jyoti Jain
Original Contribution
  • 4 Downloads

Abstract

In this paper, three important objectives of power systems—cost of generation (FC), system transmission losses (FL) and environmental emissions (FE)—have been considered. The multiobjective economic load dispatch problem has been formulated using weighting method. The noninferior set for IEEE 5 bus, IEEE 14 bus and IEEE 30 bus systems has been generated using particle swarm optimization technique. The noninferior set obtained has been displayed in 3-D space considering all the three objectives and in 2-D space all the combinations of two objectives, viz. for FC & FL, FC & FE and FL & FE for IEEE 5 bus, IEEE 14 bus and IEEE 30 bus systems. The target point or best compromise solution has been obtained by maximizing the minimum relative attainments of all the objectives.

Keywords

Optimization Maximization of minimum relative attainment Noninferior set Ideal point Target point 

Abbreviations

F

Objective function to be optimized

FC

Cost of generation, measured in $/h

FL

Transmission losses, measured in MW

FE

Cost of environmental emission, measured in kg/h

ai, bi, ci

Cost coefficients of ith generator

di, ei, fi

Emission coefficients of ith generator

Pi

Active power generation of the ith generator

Pimax

Maximum power generation limit of ith generator

Pimin

Minimum power generation limit of ith generator

PD

Total power demand

Q

Penalty factor

NG

Total number of generators in the system

Bij, Boi, Boo

Loss coefficients

P

Number of particles in the swarm

\(v_{ij}^{k}\)

Velocity of jth particle of ith generator at kth iteration

W

Inertia weight factor

Cp, Cg

Acceleration coefficients

rp, rg

Random numbers between 0 and 1

\(\it \it x_{ij}^{k}\)

Current position of jth particle of ith generator at kth iteration

\(x_{{{\text{pbest}}ij}}^{k}\)

Personal best position of jth particle of ith generator at kth iteration

\(x_{{{\text{gbest}}i}}^{k}\)

Global best position of swarm for ith generator till kth iteration

IT

Maximum number of iterations

k

Current iteration

W1

Weight attached to cost of generation

W2

Weight attached to transmission losses

W3

Weight attached to environmental emissions

FCmax

Maximum value of cost of generation

FCmin

Minimum value of cost of generation

FLmax

Maximum value of transmission losses

FLmin

Minimum value of transmission losses

FEmax

Maximum value of environmental emission

FEmin

Minimum value of environmental emission

Kount

Function evaluation

τC

Minimum relative attainment for cost of generation

τL

Minimum relative attainment for transmission losses

τE

Minimum relative attainment for environmental emission

Notes

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Copyright information

© The Institution of Engineers (India) 2019

Authors and Affiliations

  1. 1.Electrical Engineering DepartmentDelhi Technological UniversityDelhiIndia

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