An Analytical Strategy for Passive Harmonic Filter Placement in Transmission Systems with Stochastic Aggregate Load Models Considering Resonant Conditions

High percentage of voltage harmonics has been observed in transmission networks due to harmonic currents penetrated from the load side amplified by resonant conditions. This requires the use of suitable harmonic filters in transmission networks. However, filter placement in a transmission system for harmonic mitigation is a planning procedure of high complexity. Since filter placement discounting the overall system response may deteriorate harmonic conditions at remote buses due to frequency characteristics alteration. The stochastic behavior of harmonic loads demands adequate models and calculations. The interlinked topology of a transmission system also necessitates an extensive system-wide study. This paper presents an analytical methodology for determining the appropriate number, location, and parameters of C-Type passive filters in a transmission system to improve the overall harmonic condition. The proposed strategy targets minimizing the expected value of a system-wide index given the stochastic behavior of loads, while limiting the 95th percentiles of voltage distortions to the standard levels prescribed by IEEE Std. 519 and satisfying the fundamental power flow constraints. A restricted hierarchical direct search algorithm is utilized to find the near global solution whose subsets are also effective. The performance of the proposed approach is evaluated on the IEEE 118-bus test system and its validity is checked by Monte Carlo simulations and compared with harmonic modal analysis.