Ill-Conditioned Power Flow Calculation in Urban Rail Traction Power Supply System

In the traction power supply system (TPSS) of urban rail transit, heavy load fluctuation and the dynamically changing system structure are inherent. Traditional power flow (PF) calculation based on Newton-Raphson (N-R) method frequently experiences non-convergence issues, resulting in severe ill-conditioned PF scenarios. It impedes accurate deduction and analysis of the operational state. This article offers a thorough examination of the TPSS under ill-conditioned PF scenarios and proposes an enhanced approach to PF calculation. First, a thorough analysis is conducted to identify the primary factors contributing to ill-conditioned PF under three typical circumstances: improper initial value, nonlinear characteristics, and large system scale. It uncovers the fundamental causes of ill-conditioned PF in urban rail systems, thereby providing opportunities for enhancing the PF algorithm. Subsequently, an improved PF algorithm is adopted that integrates the Levenberg-Marquardt (L-M) method. This approach leverages the convergence advantages of the L-M method near singular points to refine the iterative step update strategy in the N-R method. Finally, simulation and field test demonstrates that the proposed method not only ensures calculation accuracy but also significantly enhances convergence speed and simulation efficiency. This article contributes valuable perspectives and approaches for enhancing algorithms in PF calculation, thus facilitating the stable operation of urban rail systems.