Data-driven Power Flow Analysis Based on Improved Affine Arithmetic

This paper proposes a novel data-driven power flow analysis method based on improved affine arithmetic. In contrast to traditional Taylor-based or linear affine methods, the proposed approach analytically extracts key nonlinear components from the power flow equations and embeds them into an enhanced affine mapping structure. A regression-based optimization model is then constructed using historical operating data to accurately approximate state-variable mappings under uncertainty. Experimental validation on a modified IEEE 33-bus distribution test system demonstrates that the proposed method significantly outperforms recent benchmark techniques—including linear affine, Taylor-series, and Koopman-based methods—in terms of accuracy and robustness. These results highlight the method's strong potential for reliable power flow estimation in active distribution networks with high PV penetration. The proposed method exhibits superior performance in modeling active/reactive power flows and nodal voltages.