An improved differential evolution using self-adaptable cosine similarity for economic emission dispatch

As increasing demand of electric energy and deterioration of environment pollution in global, economic emission dispatch (EED) problem has become one of the most important problems in power systems. In order to improve the quality of life and further reduce emissions, plug-in electric vehicle (PEV) has become a popular transportation. But the frequent and random charging of PEVs will bring potential risk that undermines the stability of the power grid. Therefore, dynamic economic emission dispatch considering plug-in electric vehicles (DEED-PEV) as a new hot-spot issue has gradually become more and more important in the power system. In this paper, an improved differential evolution using self-adaptable cosine similarity (DE-SCS) is proposed for EED and DEED-PEV problems. First, a dynamic cosine similarity calculated replaces the F of the differential evolution algorithm (DE) to scale the perturbation by self-adaptability. Second, a result-driven selection operation for multiple mutation strategies is implemented in each iteration. Third, a modified environment selection changes the usual way to ranking in the vectors pool during the update on Pareto front. Last, an evaluation mechanism that involves two series of solution sets and three types of comparing approaches is conducted on our proposed algorithms in the experiment. DE-SCS improves the equilibrium between exploration and exploration of the DE. The cosine similarity makes the convergence more self-adaptive. The modified environment selection maximizes the worth of previous generation vectors and brings the randomness into the next iteration. DE-SCS matching various environmental selection are tested on twelve unconstrained multi-objectives problems, six EED cases and six DEED-PEV cases containing charging load, discharging power, valley filling, and peak shaving. Experimental results confirm that DE-SCS is capable of obtaining such excellent and feasible solutions that it has good potential to deal with EED and DEED-PEV problems.