Optimal Neutral Grounding in Bipolar DC Networks with Asymmetric Loading: A Recursive Mixed-Integer Quadratic Formulation

This paper presents a novel approach to tackle the problem of optimal neutral wire grounding in bipolar DC networks including asymmetric loading, which naturally involves mixed-integer nonlinear programming (MINLP) and is challenging to solve. This MINLP model is transformed into a recursive mixed-integer quadratic (MIQ) model by linearizing the hyperbolic relation between voltage and powers in constant power terminals. A recursive algorithm is implemented to eliminate the possible errors generated by linearization. The proposed recursive MIQ model is assessed in two bipolar DC systems and compared against three solvers of the GAMS software. The results obtained validate the performance of the proposed MIQ model, which finds the global optimum of the model while reducing power losses for bipolar DC systems with 21, 33, and 85 buses by 4.08%, 2.75%, and 7.40%, respectively, when three nodes connected to the ground are considered. Furthermore, the model exhibits a superior performance when compared to the GAMS solvers. The impact of grounding the neutral wire in bipolar DC networks is also studied by varying the number of available nodes to be grounded. The results show that the reduction in power losses is imperceptible after grounding the third node for the three bipolar DC systems under study.