Linearization of AC Power Flow Equation Based on Least-squares Approximation

Linearization of nonlinear power flow equation is of great significance to power system analysis because it can reduce computational burden and guarantee theoretical convergence, the improvement of whose accuracy is a crucial research topic. The existing Taylor expansion based linear power flow models may not perform accurately when the system operating point is far from the expansion point. In this paper, we propose a linear power flow model with minimum mean square error in the approximation region from the perspective of function approximation theory, which is different from the local mathematical properties inherent in the Taylor expansion principle. The proposed model can consider the information of the AC power flow equation in the defined approximation region instead of just using a base point. Therefore, the overall accuracy of the model can be greatly improved. Numerical results verify the effectiveness of the proposed least-squares approximation based linear power flow model.