A Piecewise Probabilistic Harmonic Model of Aggregate Residential Loads

Harmonics produced by residential loads have become an increasing concern in recent years due to the extensive adoption of power-electronic-based home appliances. Harmonic modeling of aggregate residential loads (ARLs) is of great significance since it is the prerequisite for harmonic evaluation and necessary mitigation measures in the residential areas. In this paper, a piecewise probabilistic harmonic model is proposed to analyze the aggregate harmonics of residential loads. Based on the field measurement data, a unified dominant harmonic coupled matrix model (UD-HCMM) is established. This model directly exhibits the coupled relationship between the harmonic voltages and currents of residential loads. In view of the random and fluctuating harmonic characteristics of home appliances, the multi-Gaussian curve fitting method is used to fit the UD-HCMM parameters. Thereafter, the probabilistic UD-HCMMs are reconstructed using the Newton-Raphson method. Finally, a piecewise UD-HCMM is derived to characterize the time-varying harmonics of ARLs. The accuracy and validity of the proposed method are verified through simulations and field measurements. In addition, the proposed method is applied to evaluate the harmonics of a medium voltage distribution system with massive residential loads.