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Combined heat and power economic dispatch problem with binary method using flower pollination algorithm and differential evolution

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Abstract

Nowadays, the need for electrical energy became crucial in the world. The co-generation plants, which simultaneously produce electrical and heat energies, are one of the alternative solutions to supply people and industry with both energies. The present work addresses the cost minimization of the nonconvex combined heat and power dispatch problem (CHPED). The nonconvex operating region is handled using the binary method, and the optimization problem is solved using two nature-inspired algorithms, namely the flower pollination algorithm (FPA) and the differential evolution (DE). Penalty functions are adopted to handle all the operating constraints, units’ limits, and demands. The results obtained compare the algorithms and those of the literature. It is observed that the fuel cost obtained by the flower pollination algorithm (FPA) is less than the one obtained by the differential evolution (DE) and the particle swarm optimization (PSO).

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Abbreviations

CHPED:

Combined heat and power economic dispatch

FPA:

Flower pollination algorithm

DE:

Differential evolution

PSO:

Particle swarm optimization

PFCOA:

Cuckoo optimization algorithm with a penalty function

FA:

Firefly algorithm

IABC:

Improved artificial bee colony

GAs:

Genetic algorithms

MNOPQR:

Search space of the CHPED problem

P j :

Power generated by unit

H j :

Heat generated by unit j

P 1 :

Power unit

P 2, P 3 :

Power of co-generations 1 and 2, respectively

H 2, H 3 :

Heat of co-generations 1 and 2, respectively

H 4 :

Heat unit

Cost1(P 1):

Cost of power unit

Cost2(P 2, H 2):

Cost of co-generation unit 1

Cost3(P 3, H 3):

Cost of co-generation unit 2

Cost4(H 4):

Cost of heat unit

x 1, x 2 :

Binary variables

P d :

Power demand

H d :

Heat demand

p, ε :

Random values given in [0, 1]

\(\begin{aligned} x_{i}^{t + 1} = & x_{i}^{t} + L(g* - x_{i}^{t} ) \\ x_{i}^{t + 1} = & x_{i}^{t} + \varepsilon (x_{j}^{t} - x_{k}^{t} ) \\ \end{aligned}\) :

New positions of the pollen using Levy flight

ϕ l (l = 1, 2,…,15):

Penalty factors

\(\tilde{F}(X)\) :

Fitness function with penalties

X :

Vector of decision variables

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Authors and Affiliations

  1. LMSS, Faculty of Technology, M’Hamed Bougara University, Boumerdes, Algeria

    Mohamed Arezki Mellal, Marwa Khitous & Meriem Zemmouri

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  1. Mohamed Arezki Mellal
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  2. Marwa Khitous
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Contributions

Mellal implemented the method and wrote the concept/manuscript. Khitous and Zemmouri implemented the method and reported the results.

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Correspondence to Mohamed Arezki Mellal.

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Mellal, M.A., Khitous, M. & Zemmouri, M. Combined heat and power economic dispatch problem with binary method using flower pollination algorithm and differential evolution. Electr Eng 105, 2161–2168 (2023). https://doi.org/10.1007/s00202-023-01801-x

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