Abstract
Economic dispatch is the optimal scheduling for generating units with technical constraints. Combined heat and power economic dispatch (CHPED) refers to minimization of the total energy cost for generating electricity and heat supply to load demand. This planning model integrates heat and power energy to balance energy supply and demand, mitigate climate change and improve energy efficiency of sustainable cities and green buildings. In this paper for the first time, self-regulating particle swarm optimization (SRPSO) algorithm is utilized for solving the CHPED problem by considering valve point effects and prohibited zones on fuel cost function of pure generation units and electrical power losses in transmission systems. The main advantage of SRPSO algorithm to PSO algorithm is the inertia weight flexibility with respect to search conditions. In this algorithm, unlike PSO algorithm that inertia weight reduces in each iteration, this value increases or reduces proportional to particles’ positions, which will lead particles to achieve optimal value with higher speed. The capability and effectiveness of the proposed algorithm are evaluated on a large-scale energy system using MATLAB environment. The results obtained by SRPSO algorithm are outperformed by other optimization methods from the economic, sustainable energy and time consumption point of view.
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Abbreviations
- \(F_{{{\text{p}}i}}\) :
-
Fuel cost function of pure power unit i
- \(F_{{{\text{c}}j}}\) :
-
Fuel cost function of cogeneration unit j
- \(F_{{{\text{h}}k}}\) :
-
Fuel cost function of pure heat unit k
- \(P_{\text{D}}\) :
-
Power demand
- \(P_{\text{L}}\) :
-
Transmission loss
- \(B_{ij}\), \(B_{0i}\), \(B_{00}\) :
-
Power loss coefficients
- \(\omega_{\text{i}} \left( t \right)\) :
-
Inertia weight
- \(N_{\text{Iter}}\), \(Max\_it\) :
-
Number of iterations
- \(\omega_{\text{I}}\) :
-
Initial inertia weight
- \(\omega_{\text{F}}\) :
-
Final inertia weight
- \(\eta\) :
-
Acceleration rate
- \(P_{id}^{\text{se}}\) :
-
Perception for the self-cognition
- \(P_{id}^{\text{so}}\) :
-
Perception for the social cognition
- \(\gamma\) :
-
Binary value for defining the confidence
- λ :
-
Threshold value
- \(H_{\text{D}}\) :
-
Heat demand
- \(B\) :
-
Loss coefficient matrix
- \(a_{{{\text{p}}i}} , b_{{{\text{p}}i}} , c_{{{\text{p}}i}}\) :
-
Cost function coefficients of pure power unit i
- \(e_{{{\text{p}}i}} , f_{{{\text{p}}i}}\) :
-
Non-convex cost function coefficients of pure power unit i
- \(a_{{{\text{c}}j}} ,b_{{{\text{c}}j}} ,c_{{{\text{c}}j}} ,d_{{{\text{c}}j}} ,e_{{{\text{c}}j}} ,f_{{{\text{c}}j}}\) :
-
Cost function coefficients of cogeneration unit j
- \(a_{{{\text{c}}k}} ,b_{{{\text{c}}k}} ,c_{{{\text{c}}k}}\) :
-
Cost function coefficients of pure heat unit k
- \(P_{{{\text{p}}i}}\) :
-
Power output of pure power unit i
- \(P_{{{\text{p}}i,\hbox{min} }}\) :
-
Lower power output of pure power unit i
- \(P_{{{\text{p}}i,\hbox{max} }}\) :
-
Upper power output of pure power unit i
- \(H_{{\text{h}}k}\) :
-
Heat output of pure heat unit k
- \(H_{{{\text{h}}k,\hbox{min} }}\) :
-
Lower heat output of pure heat unit k
- \(H_{{{\text{h}}k,\hbox{max} }}\) :
-
Upper heat output of pure heat unit k
- \(P_{{{\text{c}}j}}\) :
-
Power output of cogeneration unit j
- \(H_{{{\text{c}}j}}\) :
-
Heat output of cogeneration unit j
- \(P_{{{\text{c}}j,\hbox{min} }}\) :
-
Lower power output of cogeneration unit j
- \(P_{{{\text{c}}j,\hbox{max} }}\) :
-
Upper power output of cogeneration unit j
- \(H_{{{\text{c}}j,\hbox{min} }}\) :
-
Lower heat output of cogeneration unit j
- \(H_{{{\text{c}}j,\hbox{max} }}\) :
-
Upper heat output of cogeneration unit j
- \(P_{\text{D}}\) :
-
Power demand
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Lashkar Ara, A., Mohammad Shahi, N. & Nasir, M. CHP Economic Dispatch Considering Prohibited Zones to Sustainable Energy Using Self-Regulating Particle Swarm Optimization Algorithm. Iran J Sci Technol Trans Electr Eng 44, 1147–1164 (2020). https://doi.org/10.1007/s40998-019-00293-5
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DOI: https://doi.org/10.1007/s40998-019-00293-5