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This paper presents a new approach based on the linear approximation method and chance-constrained programming model for the optimal planning of single-tuned harmonic passive filters in an industrial power system. In the problem, the effects of the probabilistic characteristics of the nonlinear load currents and harmonic impedances of the system and linear loads are considered in the filter planning. The objective is to minimize the total filter installation cost, while the harmonic currents limits and filter component constraints are satisfied with predetermined confidence levels. The formulated probability-constrained problem is then transformed into a deterministic nonlinear programming problem and is solved by a sequential quadratic programming (SQP) solver. The proposed solution procedure is tested with an actual industrial power system and is verified by the conventional deterministic approach and by the Monte Carlo simulation. Numerical experiences show that the proposed method yields favorable results for the filter planning.