Improved stochastic fractal search algorithm with chaos for optimal determination of location, size, and quantity of distributed generators in distribution systems

Abstract

In the power system operation, the reduction of the power loss in distribution systems has significance in the reduction of operating cost. In this paper, a novel chaotic stochastic fractal search (CSFS) method is implemented for determining the optimal siting, sizing, and number of distributed generation (DG) units in distribution systems. The objective of the optimal DG placement problem is to minimize the power loss in distribution systems subject to the constraints such as power balance, bus voltage limits, DG capacity limits, current limits, and DG penetration limit. The proposed CSFS method improves the performance of the original SFS by integrating chaotic maps into it. On the other hand, ten chaotic maps are utilized to replace the random scheme of the original SFS to enhance its performance in terms of accuracy of solution and convergence speed, corresponding to ten chaotic variants of the SFS where variant being chosen is the best chaotic variant regarding search performance. For solving the problem, the CSFS is implemented to simultaneously find the optimal siting and sizing of DG units and the optimal number of DG units will be obtained via comparing optimal results from different numbers of DG in the problem. The proposed method is tested on the IEEE 33-bus, 69-bus, and 118-bus radial distribution systems. The obtained results from the CSFS are verified by comparing to those from the original SFS and other methods in the literature. The result comparisons indicate that the proposed CSFS method can obtain higher quality solutions than the original SFS version and many other methods in the literature for the considered cases of the test systems. Moreover, the incorporation of chaos theory allows performing the search process at higher speeds. Therefore, the proposed CSFS method can be a very promising method for solving the problem of optimal placement of DG units in distribution systems.