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A comprehensive time domain model of a Custom Power Park, suitable for harmonic-oriented studies, is presented in this work. It comprises a Unified Power Quality Conditioner (UPQC), coupling transformers, a static transfer switch and a control system. The UPQC consists of two voltage source converters (VSC) connected throughout a DC capacitor. Whilst a shunt VSC maintains constant the bus voltage and the DC capacitor voltage, a series VSC feeds sensitive loads with distortion-free voltages. Furthermore, the transformer model incorporates its nonlinear characteristic and core losses. Limit cycle method based on the Poincaré map and a Newton method is applied to compute periodic steady-state solutions of the Custom Power Park. Important speed up factors up to 206 561 are reported to locate the limit cycle after a voltage disturbance. The application of the limit cycle method to custom power controllers paves the way to carry-out efficient power quality analysis at the distribution level.