Hybrid Coordinate Affine Power Flow Algorithm Based on Coordinate Conversion

Affine power flow algorithm is critical for addressing the uncertainty of power flow. However, for existing affine power flow algorithms which are based on rectangular affine arithmetic, it is difficult to analyze the interactions between the magnitude and angle of voltage and the injected power. This paper proposes an affine coordinate conversion (ACC) method that allows an affine variable to be transformed between different coordinate systems. Based on the ACC method, the hybrid coordinates affine arithmetic (HCAA) is proposed, which uses rectangular affine arithmetic in addition operation and uses polar affine arithmetic in multiplication and division operation. Finally, an affine power flow algorithm based on HCAA is proposed, which is computed by Ybus-Gauss iteration algorithm. In numerical experiments, the Monte Carlo method are used as benchmarks for evaluating the completeness of the exact solution, and the results demonstrated the method proposed in this paper presents a more compact solution region than existing affine power flow algorithms. Meanwhile, the simulation results on IEEE33-bus distribution network with injected power fluctuation shows the accuracy of the proposed method in solving the uncertain power flow.