### Coulomb’s and Franklin’s Laws Based Optimization for Nonconvex Economic and Emission Dispatch Problems

#### Abstract

*The economic and emission dispatch (EED) problem addresses to minimize the fuel cost as well as the emission from the thermal power plants referring the equality and inequality constraints. Thus, the multi-objective EED problem optimizes the contradicting objectives concurrently. The non-smooth and non-convex fuel cost function such as valve point loading (VPL) effect acts as additional impediment for EED problem. These limitations drive the EED problem to be a highly nonlinear and a multimodal optimization problem. In this article, a new heuristic approach, Coulomb’s and Franklin’s laws based optimization (CFLBO) algorithm is bestowed to solve the nonconvex economic and emission dispatch problem. The proposed EED considers the non-smooth and nonconvex cost characteristics to ape the VPL effects. The CFLBO approach is concocted from the Coulomb’s and Franklin’s theories, and comprises attraction /repulsion, probabilistic ionization and contact stages. Applying these CFLBO stages has inflicted in upgrading the robustness and search proficiency of the approach, and substantially lessening the number of generations required to accomplish the optimal solution. The fuel cost and the environmental emission functions are viewed as objective functions and developed as a bi-objective EED problem. The bi-objective EED problem is tackled after converting EED problem to a solitary objective function optimization issue by weighted sum approach with price penalty factors. A fuzzy based concessive approach is employed to choose the best compromised solution from the non-dominated solution sets. To demonstrate its competence, the proposed CFLBO algorithm is employed to 10 and 40-units test systems with nonconvex characteristic. The simulation results signify that the CFLBO algorithm affords the best concessive solution and outruns the other compared state-of –the-art approaches.*

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