Optimal Power Flow for Hybrid AC/DC Electrical Networks Configured With VSC-MTDC Transmission Lines and Renewable Energy Sources

This article presents the single objective optimal power flow (OPF) formulation incorporating both renewable energy sources, and voltage source converter-based multiterminal direct current transmission lines, simultaneously. To solve the formulated OPF problem, powerful metaheuristic optimization algorithms including adaptive guided differential evolution, marine predators algorithm, atom search optimization, stochastic fractal search (SFS), and fitness-distance balance-based SFS (FDB-SFS) are employed. The performance of the algorithms is tested for the minimization of fuel cost, pollutant emissions of thermal generators, voltage deviation, and active power loss in a modified IEEE 30-bus power network. The simulation results give that FDB-SFS achieved the best results on the fuel cost ($786.5361 \, {\$}/\text{h}$), the fuel cost with valve point effect ($815.6644 \,{\$}/\text{h}$), and the fuel cost with emission-carbon tax ($820.5991 \,{\$}/\text{h}$). In addition, FDB-SFS reduced voltage deviation and active power loss values by 14.2587% and 6.7438% compared to SFS. The nonparametric Wilcoxon and Friedman statistical test results confirmed that FDB-SFS is an effective and robust algorithm that can be used in the optimization of the introduced OPF problem.