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The intelligent control of power systems is one of the main tasks for realizing a smart grid. Because of the high dimensional dynamics and discrete control of power systems, realizing an optimal control to support system voltages is a hard combinatorial optimization problem. In this paper a new intelligent scheme based on a genetic learning progress for optimal voltage control is proposed. This learning control scheme combines the genetic algorithm (GA) with a memory which saves knowledge accumulated from past experiences. In each run of search by GA, past experiences in memory is exploited to speed up the searching of GA and improve the quality of the solutions while the knowledge in memory is also refined by the new solutions. With the help of this learning capability, a fast and self-healing voltage control is realized and the control performance can be improved gradually over time. A case study on the New England 39-bus power system showed that the purposed learning control can successfully prevent the system from voltage instability and at the same time a fast and adaptive system response is provided.