Three-Phase Second-Order Analytic Probabilistic Load Flow With Voltage-Dependent Load

This paper proposes a fully analytic second-order probabilistic load flow (PLF) method to realize an accurate and fast three-phase load flow analysis considering unbalanced uncertainties from voltage-sensitive loads and photovoltaic (PV) generation in distribution systems. The load flow equations are modelled by an accurate quadratic expression based on the bus injection model (BIM). To work at the distribution level, the voltage dependence of the load is considered based on the constant impedance, constant current, and constant power (ZIP) model, with the ZIP parameters acting as more realistic random variables. The PV generation is also considered as a constant power model. The uncertainties are modelled in time series as conditional probabilities, reducing the complexity of their probability distribution functions (PDFs). The PLF is modelled in a fully analytic second-order stochastic formulation, which can accurately and easily handle the PDFs of voltage and current by computing the first two moments. The computation is accelerated by an analytical calculation of the quadratic coefficients over the ZIP parameters. Case studies on a practical distribution network show the significance of considering the voltage-dependent load model and the high accuracy of the proposed method.