Improved Particle Swarm Optimization for Combined Heat and Power Economic Dispatch

Abstract

KEYWORDSAbstract. This paper presents eight Improved Particle Swarm Optimization (IPSO) algorithms for solving Combined Heat and Power Economic Dispatch (CHPED) problem with valve point loading e ects on fuel cost function and transmission losses. The main objective of the problem is to nd the power output and the heat output of available units so that the total fuel cost is minimized while satisfying power and heat demands and power and heat limits. The proposed IPSO algorithms are based on some modi cations on the parameters and the use of Cauchy distribution. The e ectiveness of the IPSO methods has been validated through six di erent test systems including three systems with quadratic fuel cost function of pure power units neglecting transmission losses, two systems with nonconvex fuel cost function of pure power units considering transmission losses, and one large-scale system with nonconvex fuel cost function of pure units and without transmission losses. The result comparisons between the IPSO methods and other methods in the literature have indicated that the proposed methods can obtain higher solution quality with faster computational time than many other methods. Therefore, the proposed IPSO methods would be very e cient methods for solving the nonconvex CHPED problem.

A Novel Method for Economic Dispatch of Combined Heat and Power Generation

“…Observing this table, the fuel cost comparison indicates that MBA finds a better optimal solution than most methods excluding two methods, that are GCPSO [23] and GWO [25] with slightly less costs of $33.54 and $66.09 than MBA, respectively. Despite the disadvantage, MBA is still a the strongest method since its CPU time is the fastest among the compared methods, especially 1.01 s for GCPSO [23] and 5.26 s for GWO [25] while that is only 0.1 second for MBA. Moreover, as indicated in the FE max and SCT (s) columns, MBA used 4000 fitness evaluations and spent a runtime of 0.1 second, which are lower than all other methods like BCO [14] and AIS [17], that used 5,000 fitness evaluations and take 6.45 s and 6.62 s, respectively.…”

“…Moreover, as indicated in the FE max and SCT (s) columns, MBA used 4000 fitness evaluations and spent a runtime of 0.1 second, which are lower than all other methods like BCO [14] and AIS [17], that used 5,000 fitness evaluations and take 6.45 s and 6.62 s, respectively. When compared to GCPSO [23] and GWO [25], FE max and SCT(s) are 20,000 and 0.76 s when using GCPSO, respectively. Whilst there was no population size reported when using GWO, it has taken a quite long time of 5.04 s to search the solution.…”

“…If the velocity is high, the Bats' positions, i.e., solutions could move the feasibility area outside whereas the small velocity could limit the discovery areas. For the BA, there is no information discussing the optimal range of velocity, while this term has been constantly improved in PSO [23]. In [23], authors have mentioned that the optimal range of the velocity can be fixed from 10% to 15% of the difference between the boundary positions.…”

“…For the BA, there is no information discussing the optimal range of velocity, while this term has been constantly improved in PSO [23]. In [23], authors have mentioned that the optimal range of the velocity can be fixed from 10% to 15% of the difference between the boundary positions. For this study, we suggest that the updated velocities of the Bats should be narrowed in a range of V min…”

“…In recent years, some most promising methods have proposed for the CHPGED, like the group search optimization [20], oppositional teaching learning based optimization [21], opposition-based group search optimization [22], and eight versions of PSO [23], grey wolf optimization [24], machine learning algorithm [25], and the cuckoo search algorithm [26]. It is observed that the performance of these methods seems to be better than all the methods given in [8][9][10][11][12][13][14][15][16][17][18][19] for most cases.…”