Optimal Phase-Balancing in Three-Phase Distribution Networks Considering Shunt Reactive Power Compensation with Fixed-Step Capacitor Banks

The black hole optimization (BHO) method is applied in this research to solve the problem of the optimal reactive power compensation with fixed-step capacitor banks in three-phase networks considering the phase-balancing problem simultaneously. A master–slave optimization approach based on the BHO in the master stage considers a discrete codification and the successive approximation power flow method in the slave stage. Two different evaluations are proposed to measure the impact of the shunt reactive power compensation and the phase-balancing strategies. These evaluations include a cascade solution methodology (CSM) approach and a simultaneous solution methodology (SSM). The CSM approach solves the phase-balancing problem in the first stage. This solution is implemented in the distribution network to determine the fixed-step capacitor banks installed in the second stage. In the SSM, both problems are solved using a unique codification vector. Numerical results in the IEEE 8- and IEEE 27-bus systems demonstrate the effectiveness of the proposed solution methodology, where the SSM presents the better numerical results in both test feeders with reductions of about 32.27% and 33.52%, respectively, when compared with the CSM. To validate all the numerical achievements in the MATLAB programming environment, the DIgSILENT software was used for making cross-validations. Note that the selection of the DIgISLENT software is based on its wide recognition in the scientific literature and industry for making quasi-experimental validations as a previous stage to the physical implementation of any grid intervention in power and distribution networks.