Two-steps Power Flow Calculation

With the continuous expansion of power system scale and complexity of its structure, the convergence difficulty and the computational inefficiency of the power flow calculation have become major obstacles to ensuring the stable operation of the power system. Therefore, we propose a two-step power flow solving algorithm to provide a reliable adjustment scheme when the grid current calculation is unsolved and computationally inefficient. Firstly, the penalized least squares method is used to fit the power balance constraint term to construct the extended power flow calculation model. Then, we adopt the Augmented Lagrangian method (ALM) to decompose the optimization problem into two sub-problems. Sub-problem A is solved with the proposed adaptive BFGS algorithm based on the Armijo-Goldstein (AG) criterion, while sub-problem B is solved using the Coordinate Descent (CD) method. These two sub-problems are alternately updated to obtain the optimal voltage magnitude and phase angle of the system. Furthermore, to achieve a more accurate approximation of the system's real solution, we formulate a nonlinear least squares problem and determine the initial value to improve the algorithm's robustness to the initial value. The method was validated in various IEEE power node systems, and the results demonstrate that it can significantly enhance computational efficiency while ensuring high-precision computational outcomes. The results obtained using the conventional Newton-Raphson method serve as a benchmark for comparison. The algorithm demonstrated an average accuracy of 89% and a reduction in the required convergence time of 33%.