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An improved real-coded genetic algorithm with random walk based mutation for solving combined heat and power economic dispatch

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Abstract

Combined heat and power economic dispatch (CHPED) is an energy management problem that minimizes the operation cost of power and heat generation while a vast variety of operational constraints of the system should be met. The CHPED is a complicated, non-convex and non-linear problem. In this study, a new real-coded genetic algorithm with random walk-based mutation (RCGA-CRWM) is under study, which is effective in solving large-scale CHPED problem with minimum operation cost. In the presented optimization method, a simple approach is introduced to combine the positive features of different probabilistic distributions for the step size of random walk. Using the presented approach, while the genetic algorithm is speeded up, the premature convergence is also avoided. After verifying the performance of the presented method on the benchmark functions, two large-scale and two medium-scale case studies are used for determining the algorithm strength in solving the CHPED problem. Despite the fact that the complexity of the CHPED rises dramatically by increasing its dimensionality, the algorithm has solved the problems accurately. The application of RCGA-CRWM method improves the results of the CHPED problem in terms of both operation cost and convergence speed in comparison with other optimization methods.

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Abbreviations

i :

Index of the thermal units

j :

Index of the CHP units

k :

Index of the boilers

\(a_{j},\ b_{j},\ c_{j},\ d_{j},\ \mathrm{and}\ f_{j}\) :

Cost coefficients of the \(j\mathrm{th}\) CHP plant

\(\alpha _{i},\ \beta _{i},\ \mathrm{and}\ \gamma _{i}\) :

Cost coefficients of the \(i\mathrm{th}\) thermal plant

\(\lambda _{i}\ {\rm and}\ \rho _{i}\) :

Coefficients of the valve-point influence of the \(i\mathrm{th}\) thermal plant.

\(a_{k},\ b_{k},\ {\rm and}\ c_{k}\) :

Cost coefficients of the \(k\mathrm{th}\) boiler

\(C_{i}\) :

Power production cost of the \(i\mathrm{th}\) thermal unit

\(C_{j}\) :

Power production cost of the \(j\mathrm{th}\) CHP unit

\(C_{k}\) :

Power production cost of the \(k\mathrm{th}\) boiler

\(P_{i}^{p}\) :

Power generation of the \(i\mathrm{th}\) conventional plant

\(P_{j}^{c}\) :

Power generation of the \(j\mathrm{th}\) CHP unit

\(H_{j}^{c}\) :

Heat generation of the \(j\mathrm{th}\) CHP unit

\(H_{k}^{h}\) :

Heat generation of the \(k\mathrm{th}\) boiler

\(P_{d}\) :

Power demand

\(H_{d}\) :

Heat demand

\(P_{i}^{pmin}\) :

Minimum power generation of the \(i\mathrm{th}\) conventional power unit

\(P_{i}^{pmax}\) :

Maximum power generation of the \(i\mathrm{th}\) conventional power unit

\(P_{j}^{cmin}\) :

Minimum power generation of the \(j\mathrm{th}\) CHP unit

\(P_{j}^{cmax}\) :

Maximum power generation of the \(j\mathrm{th}\) CHP unit

\(H_{j}^{cmin}\) :

Minimum heat generation of the \(j\mathrm{th}\) CHP unit

\(H_{j}^{cmax}\) :

Maximum heat generation of the \(j\mathrm{th}\) CHP unit

\(H_{k}^{hmin}\) :

Minimum heat generation of the \(k\mathrm{th}\) boiler unit

\(H_{k}^{hmax}\) :

Maximum heat generation of the \(k\mathrm{th}\) boiler unit

\(N_{p}\) :

Number of conventional power units

\(N_{c}\) :

Number of CHP units

\(N_{h}\) :

Number of boiler units

\(P^{loss}\) :

Transmission loss

\(B_{ij},\ B_{0i},\ B_{00}\) :

Transmission loss coefficients

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Authors and Affiliations

  1. Faculty of Electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran

    A. Haghrah & M. A. Nekoui

  2. Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran

    M. Nazari-Heris & B. Mohammadi-ivatloo

  3. Institute of Research and Development, Duy Tan University, Da Nang, 550000, Vietnam

    B. Mohammadi-ivatloo

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  1. A. Haghrah
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  2. M. A. Nekoui
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  3. M. Nazari-Heris
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  4. B. Mohammadi-ivatloo
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Correspondence to B. Mohammadi-ivatloo.

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Appendix

Appendix

Detailed data for test systems I and II, and the results achieved by the proposed algorithm are demonstrated in this section.

See Tables 8, 9, 10, 11, 12, 13.

Table 8 Cost function parameters of test system I
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Table 9 The results of the proposed algorithm implemented for solving test system I
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Table 10 Cost function parameters of test system II
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Table 11 The results of the proposed algorithm implemented for solving test system II
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Table 12 The results of the proposed algorithm implemented for solving 24-unit test system
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Table 13 The results of the proposed algorithm implemented for solving 48-unit test system
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Haghrah, A., Nekoui, M.A., Nazari-Heris, M. et al. An improved real-coded genetic algorithm with random walk based mutation for solving combined heat and power economic dispatch. J Ambient Intell Human Comput 12, 8561–8584 (2021). https://doi.org/10.1007/s12652-020-02589-5

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