The bipolar DC distribution network offers high power supply reliability, extensive transmission capacity, and adaptable voltage levels. Developing a bipolar DC distribution network represents an effective strategy for constructing a new type of distribution network. Voltage unbalance constitutes a distinctive power quality issue within bipolar DC distribution networks. Power flow calculation serves as the fundamental tool for analyzing voltage imbalance. Nevertheless, conventional power flow calculation methods merely illustrate the transfer outcomes of voltage unbalance, failing to depict its transfer process within the network. Furthermore, in practical engineering, power is often the measured electrical quantity rather than current, making the existing power flow model based on injected current unsuitable for meeting the application requirements. Hence, this paper proposes a power-injection equation to analyze and quantify the transfer characteristics associated with voltage unbalance.

Initially, the generation and transfer mechanism of voltage unbalance within the bipolar DC distribution network is studied. The voltage unbalance transfer matrix grounded on sensitivity is established to depict the transfer characteristics of voltage unbalance factors at individual nodes. Furthermore, the analytical formulations for each component of the voltage unbalance transfer matrix are derived, and a power flow calculation technique based on the Newton-Raphson method is proposed for determining the matrix. The suggested method employs a power-injection equation for power flow modeling and integrates droop control and comprehensive load models of distributed generation. Finally, the effectiveness of the proposed approach is validated via the modified IEEE 33-node test system. Three case studies are conducted.

Numerical results reveal the following findings. (1) The proposed power flow calculation method exhibits a negligible sacrifice in accuracy, with no more than a 0.83% deviation and a calculation efficiency enhancement of 44%. Additionally, it offers the advantage of accommodating constant power loads, which is suitable for high prevalence power load or load data readily available scenarios. (2) The voltage unbalance transfer matrix effectively illustrates voltage unbalance factors’ alterations and transfer conditions at each node under disturbance conditions. Disturbances induce voltage unbalances that propagate throughout the network following the direction of power flow. Measures must be implemented to block or suppress it at critical network nodes. For instance, strategies such as load switching and energy storage scheduling encourage multi-point loads to adjust in a more balanced manner simultaneously, curtailing unbalanced transfer. Moreover, incorporating a power spring in series with a constant resistance load near the line's terminus can introduce intelligent load management, affording greater flexibility in system voltage unbalance adjustment. The deployment of voltage-regulating equipment, such as DC transformers and voltage balancers, is instrumental in obstructing unbalanced voltage transfer.