Determination of an effective implementation of the differential evolution method to power shortage minimization

Constant development of electric power systems leads to their constant enlargement and complication; new ways of their control appear. In this regard, the existing models and software for adequacy assessment may work defective and ineffectively from the point of view of the adequacy of the obtained results, as well as the speed and accuracy of calculations. The key role in adequacy assessment of electric power systems (EPS) are played by optimization methods that allow to correctly determine the minimum of power shortage that occurs in various states of the EPS. A review of modern computational systems for adequacy assessment showed that the general concept of mathematical models is the same and can be described within the framework of the flow distribution problem. Despite this, each mathematical model is unique in its own way and requires an individual approach to its optimization. The purpose of this work is to analyze the efficiency of calculations in terms of accuracy and speed of various versions of the differential evolution (DE) method for the specified mathematical models within the framework of adequacy assessment of EPS. To achieve this goal, we solved several problems: two mathematical models were identified - a nonlinear model for minimizing the power shortage with the quadratic losses in flows and its modification with the controlled sections; differential evolution methods, including standard DE, composite DE, JDE, chaotic DE, adaptive DE; mutation strategies: DE/rand/1, DE/best/1, DE/rand/2, DE/best/2, DE/rand/3, DE/best/3, DE/current-to-rand/1, and DE/current-to-best/1. In this paper we tested the effectiveness of differential evolution methods, with different mutation strategies and different scales of EPSs. The experimental part was carried out using a software that was independent development by authors using C++. This complex includes the implementation of mathematical models and methods. The methods were tested on two systems with different numbers of adequacy zones, including those with three and seven adequacy zones. According to the research results, self-adaptive methods of DE are of the greatest interest for the further use and development of methods for this problem, due to automatic adjustment of the method parameters for each of the considered models and systems.