In this paper, we solve the optimal power flow problem using by the new hybrid fuzzy particle swarm optimisation and Nelder–Mead (NM) algorithm (HFPSO–NM). The goal of combining the NM simplex method and the particle swarm optimisation (PSO) method is to integrate their advantages and avoid their disadvantages. The NM simplex method is a very efficient local search procedure, but its convergence is extremely sensitive to the selected starting point. In addition, PSO belongs to the class of global search procedures, but it requires significant computational effort. In the other side, in the PSO algorithm, two variables ( Φ 1 , Φ 2 ) are traditionally constant; in this case, due to the importance of these two factors, we decided to obtain these two as fuzzy parameters. The proposed method is firstly examined on some benchmark mathematical functions. Then, it is tested an IEEE 30-bus standard test system by considering different objective functions for normal and contingency conditions to solve optimal power flow. The simulation results indicate that the FPSO–NM algorithm is effective in solving the mathematical functions and the OPF problem. 
Optimal power flow under both normal and contingent operation conditions using the hybrid fuzzy particle swarm optimisation and Nelder–Mead algorithm (HFPSO–NM)