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Voltage Balancing for Bipolar DC Distribution Grids: A Power Flow Based Binary Integer Multi-Objective Optimization Approach

The re-emergence of two-phase bipolar dc distribution network, which utilizes the neutral wire for efficient distribution, has spurred research interest in recent years. In practice, system efficiency (power loss) and voltage unbalance are major concerns for the planning and design of the two-phase dc bipolar network. While most of the existing methodologies are power electronics solutions, there are very few works on resolving the problem from the power system perspective. This paper proposes a model-based optimization method by first formulating the power flow model for two-phase dc bipolar network using the single line modeling technique and nodal analysis. Second, a binary integer load distribution model is proposed to consider the re-distribution of unipolar loads across the two unipolar distribution poles. Together with the power flow model, the system power loss and system voltage unbalance indices are formulated as a binary integer quadratic model. Third, a multi-objective optimization model is formulated and solved using the weighted sum approach. The proposed method is applied to a dc LED lighting system design, which considers both voltage unbalance and power loss. Using a 15 bus single source and a 33 bus multi-source network as case studies, the developed power flow model is validated with very high accuracy. Compared to existing iterative methods, the proposed model-based approach is able to significantly improve the voltage balancing across the distribution system.