Affine optimization method for probability interval power flow of distribution network based on holomorphic embedding

Abstract

With the large-scale integration of renewable energy into distribution networks, the impact of uncertainty on power systems is becoming increasingly significant. Addressing uncertainty in power flow calculations is critical for analyzing how the integration of distributed energy resources such as photovoltaic and wind power affects power flow distribution in distribution networks. This paper proposes an affine optimization method for probability interval power flow of distribution network based on holomorphic embedding. First, the affine model of system bus voltage and power is established, and an embedding factor introduced to construct the holomorphic embedding affine optimization power flow model. The focal element model of distributed photovoltaic output is established, transforming the probabilistic interval power flow model based on the focal element model into the holomorphic embedding affine optimization power flow model. The hybrid box-ellipsoid set correlation model for interval variables is established to describe distributed photovoltaic output correlation; this model is converted into affine constraints for joint solution within the holomorphic embedding affine optimization power flow model. Finally, the probabilistic boundaries of the distribution network probabilistic interval power flow solution are obtained based on evidence theory. Simulation results demonstrate the holomorphic embedding affine optimization power flow algorithm exhibits lower conservatism than the Taylor expansion affine power flow algorithm, making it more suitable for uncertain power flow analysis in larger fluctuation intervals. Simultaneously, the hybrid box-ellipsoid set correlation model achieves higher accuracy than other models and effectively reflects the influence of correlation coefficients on the calculation results.