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Mine blast algorithm for environmental economic load dispatch with valve loading effect

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Abstract

Economic load dispatch (ELD) is the process of allocating the required load between the available generation units such that the cost of operation is minimized. The ELD problem is formulated as a nonlinear constrained optimization problem with both equality and inequality constraints. The dual-objective combined economic emission dispatch (CEED) problem is considering the environmental impacts that accumulated from emission of gaseous pollutants of fossil-fueled power plants. In this paper, an implementation of mine blast algorithm (MBA) to solve ELD and CEED problems in power systems is discussed. Results obtained by the proposed MBA are compared with other optimization algorithms for various power systems. The results introduced in this paper show that the proposed MBA outlasts other techniques in terms of total cost and computational time.

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Abbreviations

ELD:

Economic load dispatch

CEED:

Combined economic emission dispatch

MBA:

Mine blast algorithm

ED:

Economic dispatch

EA:

Evolutionary algorithm

PSO:

Particle swarm optimization

CS:

Cuckoo search

FA:

Firefly algorithm

GSA:

Gravitational search algorithm

ABC:

Artificial bee colony

FPA:

Flower pollination algorithm

SFL:

Shuffled frog leaping

BFO:

Bacteria foraging optimization

MABC:

Modified artificial bee colony

MODE:

Multi-objective differential evolution

NSGA-II:

Nondominated sorting genetic algorithm-II

PDE:

Pareto differential evolution

SPEA-2:

Strength Pareto evolutionary algorithm 2

ABC_PSO:

ABC and PSO

EMOCA:

Enhanced multi-objective cultural algorithm

DEC-SQP:

Differential evolution combination with sequential quadratic programming

NN-EPSO:

Neural network with efficient particle swarm optimization

EP-EPSO:

Evolutionary programming based efficient particle swarm optimization

CPU:

Computational time

NA:

Not available

PV:

Photovoltaic

F t :

The total fuel cost of generation in $

F i (P i ):

The fuel cost function of ith generator in $

γ i , β i , α i :

The cost coefficients of ith generator in $/MW2, $/MW and $, respectively

P i :

The real power generation of ith generator in MW

d :

The number of generators connected in the network

P D :

The total load of the system in MW

P L :

The transmission losses of the system in MW

P i , P j :

The real power injections at ith and jth buses, respectively

B ij , B 0i , B 00 :

The loss coefficients of transmission loss formula

\( P_{i}^{\hbox{min} } ,P_{i}^{\hbox{max} } \) :

The minimum and maximum values of real power allowed at generator i

e i, f i :

The coefficients of ith generator due to valve point effect in $ and MW−1, respectively

F :

The optimal cost of total generation and emission

F i (P i ), E i (P i ):

The total fuel cost and total emission of generators, respectively

a, b, c :

The emission coefficients of generators in kg/MW2, kg/MW and kg, respectively

η i , δ i :

The emission coefficients of ith generator in ton and MW−1, respectively

h :

The price penalty factor value in $/kg

X o :

The generated first shot point

LB:

The lower bounds of the problem

UB:

The upper bounds of the problem

rand:

The uniformly distributed random number between 0 and 1

N d :

The search space dimension equal to the number of independent variables

θ :

The angle of the shrapnel pieces which is calculated using θ = 360/N S

N S :

The number of shrapnel pieces

N pop :

The number of initial population

\( X_{e(n + 1)}^{f} \) :

The location of exploding mine bomb collided by shrapnel

\( d_{n + 1}^{f} \) :

The distance of the thrown shrapnel pieces in each iteration

\( m_{n + 1}^{f} \) :

The direction of the thrown shrapnel pieces in each iteration

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Authors and Affiliations

  1. Electric Power and Machine Department, Faculty of Engineering, Zagazig University, Zagazig, Egypt

    E. S. Ali & S. M. Abd Elazim

Authors
  1. E. S. Ali
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  2. S. M. Abd Elazim
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Correspondence to E. S. Ali.

Appendix

Appendix

See Tables 4, 5 and the transmission line losses coefficient.

Table 4 Ten-unit generator characteristics
Full size table
Table 5 Generator cost coefficients for the 13 generating unit system
Full size table

The transmission line losses coefficient of ten-unit system.

$$ B_{ij} = 0.0001 \times \left[ {\begin{array}{*{20}c} {0.49} & {0.14} & {0.15} & {0.15} & {0.16} & {0.17} & {0.17} & {0.18} & {0.19} & {0.20} \\ {0.14} & {0.45} & {0.16} & {0.16} & {0.17} & {0.15} & {0.15} & {0.16} & {0.18} & {0.18} \\ {0.15} & {0.16} & {0.39} & {0.10} & {0.12} & {0.12} & {0.14} & {0.14} & {0.16} & {0.16} \\ {0.15} & {0.16} & {0.10} & {0.40} & {0.14} & {0.10} & {0.11} & {0.12} & {0.14} & {0.15} \\ {0.16} & {0.17} & {0.12} & {0.14} & {0.35} & {0.11} & {0.13} & {0.13} & {0.15} & {0.16} \\ {0.17} & {0.15} & {0.12} & {0.10} & {0.11} & {0.36} & {0.12} & {0.12} & {0.14} & {0.15} \\ {0.17} & {0.15} & {0.14} & {0.11} & {0.13} & {0.12} & {0.38} & {0.16} & {0.16} & {0.18} \\ {0.18} & {0.16} & {0.14} & {0.12} & {0.13} & {0.12} & {0.16} & {0.40} & {0.15} & {0.16} \\ {0.19} & {0.18} & {0.16} & {0.14} & {0.15} & {0.14} & {0.16} & {0.15} & {0.42} & {0.19} \\ {0.20} & {0.18} & {0.16} & {0.15} & {0.16} & {0.15} & {0.18} & {0.16} & {0.19} & {0.44} \\ \end{array} } \right] $$

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Ali, E.S., Abd Elazim, S.M. Mine blast algorithm for environmental economic load dispatch with valve loading effect. Neural Comput & Applic 30, 261–270 (2018). https://doi.org/10.1007/s00521-016-2650-8

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