Multi‐objective squirrel search algorithm to solve economic environmental power dispatch problems

Abstract

Major challenge in the modern power system assessment is to address the issue of Combined Economic and Environmental Power Dispatch (CEEPD). The prime intention of CEEPD is to mitigate the total expense in the power generation process considering the environmental collision caused owing to the discharge of gaseous pollutants of fossil energy. This paper bestows a new swarm intelligence technique, Squirrel Search Algorithm (SSA) to deal with multiobjective CEEPD problem in power systems. The SSA is devised from the foraging behavior of squirrels which is based on the dynamic jumping and gliding strategies. Multi-Objective SSA (MOSSA) approach employs the Pareto dominance and crowding distance concepts for finding the Pareto front solutions set. An external elitist depository mechanism is employed to preserve Pareto front solutions acquired during the optimization process. Then, an optimality based fuzzy decision maker is used to decide the best compromise solution. Furthermore, a renovate strategy and selection rules are utilized in the MOSSA approach to appropriately handle the CEEPD constraints. To access the practicability and effectiveness of the proposed MOSSA algorithm, it has been applied for 6, 10, and 40 units' power systems and compared with those of List of symbols and abbreviations: a i , b i , c i , cost coefficients of generator i; a ij , b ij , c ij , e ij and f ij , cost coefficients of the unit i for fuel type j; B ij , line loss coefficients; C D , drag coefficient; C L , lift coefficient; d i , e i , cost coefficients of the VPL effect of generator i; D, drag force; ed i , euclidean distance between nondominated solution and the nearest Pareto front solution in objective space; d, mean value of ed i ; d g , gliding distance; E i , emission of the generator i; F i , total fuel cost of the generators; F max j and F min j , maximum and minimum values of jth objective function respectively; F(P i)F(P i) max , cost function of the worst feasible solution in the population; F bcs and E bcs , fuel cost and emission attained by CEEPD; F min and E max , fuel cost and emission attained by ELD minimization respectively; F max and E min , fuel cost and emission attained by emission minimization respectively; G c , gliding constant; h g , gliding height; i and j, indices of unit and fuel type, respectively; k, index of prohibited zone; L, lift force; M, number of nondominated solutions; n, number of solutions in the nondominated set; nf, number of fuel types for each unit; ng, total number of generating units; nz, total number of POZs; P D , power demand; P dp , predator presence probability; P i , P 0 i , current and previous power output of ith unit respectively; P ij, min and P ij, max , minimum and maximum power output of unit i with fuel option j, respectively; P L i,k , P U i,k , lower and upper power outputs of the kth prohibited zone of the ith generator, respectively; Pi, max i, min , minimum and maximum generation of unit i; P L , transmission losses; r 1 , r 2 and r 3 , random numbers in the range...

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