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This paper presents a new method for planning single-tuned passive harmonic filters to control harmonic voltage distortion throughout a power system. In the problem, the probabilistic characteristics of the harmonic source currents and network harmonic impedances in the filter planning are taken into account. The objective is to minimize the total filter installation cost, while the harmonic voltage limits and filter component constraints are satisfied with predetermined confidence levels. To obtain the optimal size of each filter component of the planning problem, the proposed procedure is first to find the candidate filter buses based on the sensitivity analysis. Next, the formulated probability-constrained problem is transformed into a deterministic nonlinear programming problem and is solved by a genetic-algorithm-based optimizer. The proposed solution procedure is tested with an actual distribution network and is verified by the conventional deterministic approach and by the Monte Carlo simulation. Numerical experiences show that the proposed method yields favorable results compared with the other two approaches.