Dependent Discrete Convolution Based Probabilistic Load Flow for the Active Distribution System

Active distribution system (ADS) plays a significant role in enabling the integration of distributed generation. The stochastic nature of renewable energy resources injects the complex uncertainties of power flow into ADS. This paper proposes a discrete convolution methodology for probabilistic load flow (PLF) of ADS considering correlated uncertainties. First, the uncertainties of load and renewable energy are modeled using the distribution of the corresponding forecasting error, and the correlation is formulated using a Copula function. A novel reactive power-embedded DC power flow model with high accuracy in both branch flow and node voltage is introduced into ADS. Finally, the distribution of power flow is calculated using dependent discrete convolution, which is capable of handling nonanalytical probability distribution functions. In addition, a reduced dimension approximation method is proposed to further reduce the computational burden. The proposed PLF algorithm is tested on the IEEE 33-nodes system and 123-nodes system, and the results show that the proposed methodology requires less computation and produces higher accuracy compared with current methods.