A data-driven probabilistic harmonic power flow approach in power distribution systems with PV generations

Large-scale electrification in the end-user and renewable energy fields is one of the key pathways to achieving carbon neutrality by 2050. Meanwhile, a large number of power electronic devices are used in residential, commercial, and office loads and photovoltaic (PV), which leads to the power quality harmonics in the power distribution system (PDS) becoming more prominent than ever before. Due to the nature of the random behavior of users and random changes in external factors, e.g., illumination and temperature, the harmonics in the PDS are strongly random and time-varying, which makes it hard to evaluate and mitigate the harmonics using the individual deterministic harmonic power flow (HPF) approach. This paper proposes a data-driven piecewise probabilistic HPF method for the PDS with PVs. First, a data-driven piecewise probabilistic harmonic cross coupling model is proposed for analyzing the harmonics generated by different harmonic sources, and the probabilistic and time-varying features can be manifested via this model. Moreover, this proposed harmonic model has a certain predictive capability. Then, the decoupled method based on graph theory and injection current is developed for computing the HPF. Finally, a field theory-based piecewise probabilistic HPF is applied for assessing the probabilistic harmonics of the PDS with PVs. Actual measurements for various harmonic sources and simulations in three different sizes of IEEE systems validate the precision, effectiveness, and efficiency of the proposed models and methods.