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Reactive power planning (VAR Planning) is one of the most challenging issues in the domain of power system research. It is a mixed integer nonlinear optimization problem with a large number of variables and uncertain parameters. In this paper, first, the fuzzy clustering method is employed to select candidate locations for installing new shunt VAR sources. Specifically, U/U0 index, G index, and a critical voltage magnitude index are employed to form data matrix of fuzzy clustering. Second, a multi-objective optimization model is proposed for VAR optimization considering generation cost, VAR device cost, voltage stability and active power loss. A P-model learning automata algorithm is used to provide the multi-objective optimization solutions. Test results on a IEEE 57-bus system clearly demonstrate that a learning automata is a feasible method to produce a multi-objective trade-off analysis; and the combination of fuzzy clustering and learning automata can be a prospective method for multi-objective reactive power planning.