Modified Particle Swarm Optimization for Non-smooth Non-convex Combined Heat and Power Economic Dispatch

Abstract

This article presents modified particle swarm optimization to solve the non-smooth non-convex combined heat and power economic dispatch problem. Valve-point loading and prohibited operating zones of conventional thermal generators are taken into account. Particle swarm optimization performs well for small-dimensional and less complicated problems but fails to locate global minima for complex multi-minima functions. This article proposes Gaussian random variables in the velocity term, which improves search efficiency and guarantees a high probability of obtaining the global optimum without significantly impairing the speed of convergence and the simplicity of the structure of particle swarm optimization. The effectiveness of the proposed method has been verified on two test systems. The results of the proposed approach are compared with those obtained by other evolutionary methods. It is found that the proposed modified particle swarm optimization based approach is able to provide a better solution.

Keywords:

• modified particle swarm optimization
• combined heat and power economic dispatch
• cogeneration
• prohibited operating zone
• valve-point loading

NOMENCLATURE

ai, bi, di, ei, fi	=	cost coefficients of ith conventional thermal generating unit
CT	=	total production cost
Cti, Cci, Chi	=	fuel characteristics of the conventional thermal generating, cogeneration, and heat-only units, respectively
HD	=	system heat demand
Hhi	=	heat output of ith heat-only unit
Hminhi, Hmaxhi	=	lower and upper heat production limits of the ith heat-only unit
Pci, Hci	=	power output and heat output of ith cogeneration unit
PD	=	system power demand
PL	=	transmission loss
Pti	=	power output of ith conventional thermal generating unit
Pminti, Pmaxti	=	lower and upper power capacity limits of ith conventional thermal generating unit
Nt, Nc, Nh	=	numbers of conventional thermal generating, cogeneration, and heat-only units respectively
αi, βi, γi, δi, ϵi, ξi	=	cost coefficients of ith cogeneration unit
φi, ηi, λi	=	cost coefficients of ith heat-only unit

Additional information

Notes on contributors

Mousumi Basu

Mousumi Basu received her bachelor's degree, master's degree, and Ph.D. from Jadavpur Universty, Kolkata, India, in 1991, 1993, and 2003, respectively. Her research is focused on power system optimization and soft computing techniques.