Capacitor placement in large-scale distribution systems using variable scaling hybrid differential evolution

This paper presents an effective method, variable scaling hybrid differential evolution (VSHDE), with integer programming for solving large capacitor placement problems in distribution systems. The variable scaling factor is used in VSHDE to overcome the drawback of the fixed and random scaling factor in the hybrid differential evolution (HDE). And, the use of variable scaling factor can also alleviate the problem of selection of mutation operator of the hybrid differential evolution. The rule of updating scaling factor is based on 1/5 success rule of evolution strategies (ESs). Various-scale application systems are used to compare the performance of the proposed method with the HDE, simulated annealing (SA), and ant system (AS). Numerical results show that the performance of the proposed VSHDE method is better than the other methods. Also, the VSHDE method is superior to some other methods in terms of solution power loss and costs.