A Precision-Compensated Linear Power Flow Model Based on Mapping Voltage Magnitudes from Logarithmic Space to Squared Space

Linear power flow is widely applied in various areas of power systems. The DC power flow model is a classical linear power flow model, but its main limitation is the inability to account for voltage magnitude. Other classical models that consider voltage magnitude are typically linearized in the original voltage magnitude space, leading to a computational accuracy bottleneck. To address this issue, this study first proposes an improved linear power flow model. The model remaps the voltage magnitude from logarithmic space to square space, preserving the nonlinear characteristics of the original current equation and compensating for the voltage phase angle. This approach overcomes the accuracy bottleneck of classical models. Then, through matrix partitioning and transformation, the model achieves complete decoupling of the voltage magnitude and phase angle, avoiding nonconvex quadratic programming problems in optimization and enhancing computational efficiency. Finally, the accuracy and speed of the proposed model are validated through simulations across multiple test systems.