A Data-Driven Probabilistic Power Flow Analysis Considering Voltage-Dependent Loads

Probabilistic power flow analysis (PPFA) stands as a promising method for assessing the steady-state performance of distribution networks (DNs) amidst uncertainties associated with renewable energy sources, particularly wind power units (WPUs). However, the reliability of the PPFA results hinges significantly on the accuracy of the power flow model. This paper proposes a new approach to PPFA that integrates voltage-dependent load (VDL). Although incorporating VDL in PPFA formulation enhances the precision of the model, it introduces additional computational complexity due to the introduction of new nonlinear terms into the optimization problem. Therefore, initially, a dataset of wind speed measurements is fitted to a Weibull probability distribution function (PDF). Subsequently, a new nonlinear model is developed, which integrates Monte Carlo (MC) simulation along with the specified PDF for PPFA, accounting for VDL effects. Finally, the proposed model is efficiently convexified using Newton's generalized binomial theorem, piecewise linearization, and appropriate approximations to extract the corresponding linear programming (LP) model. This LP model is then tested on a modified WPU-integrated 33-bus DN, revealing that the inclusion of VDL significantly influences the PPFA results. A comparative analysis between PPFA models with and without VDL incorporation illustrates that overlooking VDL can lead to underestimation of power losses and voltage drops in the analysis.