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This paper presents Function Optimization by Learning Automata (FOLA) for the power flow problem which aims to achieve economic power system dispatch and voltage stability enhancement in dynamic wind power integrated systems. Dividing each dimension into a certain number of cells, FOLA undertakes the dimensional search, and has the ability of memorizing history through the values of cells that have been visited, in contrast to evolutionary algorithms (EAs) which adopt population-based search and aggregate the individuals of a population towards the best one selected in a current population. In this paper, FOLA is compared with improved Particle Swarm Optimization (PSO) and Genetic Algorithm (GA). Simulation studies have been carried out on the modified IEEE 30-bus and 57-bus power systems respectively, which are integrated with time-varying wind power. The experimental results have demonstrated that FOLA outperforms PSO and GA, as it tracks the changing system configuration more rapidly and accurately than the improved PSO and GA.