This study proposes a new approach, based on a hybrid algorithm combining of Improved Quantum-behaved Particle Swarm Optimization (IQPSO) and simplex algorithms. The Quantum-behaved Particle Swarm Optimization (QPSO) algorithm is the main optimizer of algorithm, which can give a good direction to the optimal global region and Nelder Mead Simplex method (NM) which is used as a local search to fine tune the obtained solution from QPSO. The proposed improved hybrid QPSO algorithm is tested on several benchmark functions and performed better than particle swarm optimization (PSO), QPSO and weighted QPSO (WQPSO). To assess the effectiveness and feasibility of the proposed method on real problems, it is used for solving the power system load flow problems and demonstrated by different standard and ill-conditioned test systems including IEEE 14, 30 and 57 buses test systems, and compared with the conventional Newton–Raphson (NR) method, PSO and some versions of QPSO algorithms. Furthermore, the proposed hybrid algorithm is proposed for solving load flow problems with considering the reactive limits at generation buses. Simulation results prove the robustness and better convergence of IQPSOS under normal and critical conditions, when conventional load flow methods fail. 
A hybrid Improved Quantum-behaved Particle Swarm Optimization–Simplex method (IQPSOS) to solve power system load flow problems