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This paper addresses the problem of the power flow analysis of bipolar direct current (DC) networks considering unbalanced loads and the effect of a neutral wire, which may be solidly grounded or non-grounded. The power flow problem is formulated using the nodal admittance representation of the system and the hyperbolic relations between power loads and voltages in the demand nodes. Using Taylor series expansion with linear terms, a recursive power flow method with quadratic convergence is proposed. The main advantage of the hyperbolic approximation in dealing with power flow problems in DC bipolar networks is that this method can analyze radial and meshed configurations without any modifications to the power flow formula. The numerical results in three test feeders composed of 4, 21, and 85 bus systems show the efficiency of the proposed power flow method. All of the simulations were conducted in MATLAB for a comparison of the proposed approach with the well-established successive approximation method for power flow studies in distribution networks. Full article

Bipolar direct current (DC) networks are emerging electrical systems used to improve the distribution capabilities of monopolar DC networks. These grids work with positive, negative, and neutral poles, and they can transport two times the power when compared to monopolar DC grids. The distinctive features of bipolar DC grids include the ability to deal with bipolar loads (loads connected between the positive and negative poles) and with unbalanced load conditions, given that the loads connected to the positive and neutral poles are not necessarily equal to the negative and neutral ones. This load imbalance deteriorates voltages when compared to positive and negative poles, and it causes additional power losses in comparison with balanced operation scenarios. This research addresses the problem of pole-swapping in bipolar DC networks using combinatorial optimization methods in order to reduce the total grid power losses and improve the voltage profiles. Bipolar DC networks with a non-solidly grounded neutral wire composed of 21 and 85 nodes are considered in the numerical validations. The implemented combinatorial methods are the Chu and Beasley genetic algorithm, the sine-cosine algorithm, and the black-hole optimization algorithm. Numerical results in both test feeders demonstrate the positive effect of optimal pole-swapping in the total final power losses and the grid voltage profiles. All simulations were run in the MATLAB programming environment using the triangular-based power flow method, which is intended for radial distribution system configurations. Full article