Probabilistic Harmonic Forecasting of the Distribution System Considering Time-Varying Uncertainties of the Distributed Energy Resources and Electrical Loads

Distributed energy resources (DER) and electrical loads have grown rapidly in response to concerns about energy sustainability and rising energy demand. However, to realize energy conversion, a large number of power electronic converters are used, resulting in serious harmonic issues in the distribution system. Meanwhile, the random and intermittent characteristics of DER and electrical load bring strong uncertainties to the distribution system. It not only affects the safe and stable operation but also leads to the new stochastic characteristics of harmonics. The study proposes a novel probabilistic harmonic power flow method that takes into account DER and electrical load uncertainties in order to effectively forecast and analyze the uncertain harmonic distortion. Firstly, the time-varying states with stochastic characteristics are determined to represent the uncertainties of electrical load, distributed photovoltaic power, and distributed wind power. The proposed method adapts to time-varying uncertain variable analysis while requiring less computation. Then, a novel constant-weight point estimate method based on the Nataf transformation is proposed to obtain the statistical features of the uncertainties. By simplifying the approximation process, the uncertain variable can be estimated more rapidly and effectively. Moreover, the interaction between multiple uncertain variables is also considered with the correlation coefficient matrix, which can analyze the harmonic coupling interaction in the system. Finally, the probabilistic harmonic power flow is developed considering the time-varying stochastic characteristic of uncertainties. On this basis, the proposed method can be used to forecast the harmonic distortion and also analyze the daily or seasonal statistical features. The proposed probabilistic harmonic power flow method's effectiveness is validated using real-field measured data.