A Family of Newton and Quasi-Newton Methods for Power Flow Analysis in Bipolar Direct Current Networks with Constant Power Loads

This paper presents a comprehensive study on the formulation and solution of the power flow problem in bipolar direct current (DC) distribution networks with unbalanced constant power loads. Using the nodal voltage method, a unified nonlinear model is proposed which accurately captures both monopolar and bipolar load configurations as well as the voltage coupling between conductors. The model assumes a solid grounding of the neutral conductor and known system parameters, ensuring reproducibility and physical consistency. Seven iterative algorithms are developed and compared, including three Newton–Raphson-based formulations and four quasi-Newton methods with constant Jacobian approximations. The proposed techniques are validated on two benchmark networks comprising 21 and 85 buses. Numerical results demonstrate that Newton-based methods exhibit quadratic convergence and high accuracy, while quasi-Newton approaches significantly reduce computational time, making them more suitable for large-scale systems. The findings highlight the trade-offs between convergence speed and computational efficiency, and they provide valuable insights for the planning and operation of modern bipolar DC grids.