Data-Driven Piecewise Linearization for Distribution Three-Phase Stochastic Power Flow

As the penetration of distributed renewable energy increases, the stochastic power flow (SPF) method is becoming an increasingly essential tool to analyze the uncertainties in active distribution networks. This paper proposes a data-driven power flow (PF) linearization approach for three-phase SPF calculation. This three-phase piecewise linear power flow (LPF) model mitigates the errors of model-based PF linearization approaches by approximating the nonlinear PF equations in a data-driven manner. Considering the challenges caused by the collinearity of the training data and the nonlinear nature of the PF model, an improved K-plane regression algorithm is proposed to achieve piecewise linear regression, which is implemented to obtain the piecewise LPF model offline. Based on the trained piecewise LPF model, we propose an online SPF calculation process that incorporates the Nataf transformation and the Monte Carlo method. The proposed SPF can handle complex operational conditions such as the correction of random variables and three-phase unbalance. Numerical tests demonstrate the proposed approach can tackle the issues of data collinearity and correlation, as well as achieve satisfactory calculation accuracy with high computational efficiency under different scenarios, which indicates its promising implementation value in SPF analysis in active distribution networks.