An effective and accurate power flow algorithm provides control references for active power dispatch and initial steady state operating points, used for stability analysis, short-circuit calculations, and electromagnetic transient simulations, which is not only a fundamental precondition to analyze the system operating conditions, but also the basis to improve the accuracy of power flow and DC voltage control of the multi-terminal voltage source converter-based high voltage direct current (VSC-HVDC). This paper proposes a nodal voltage-based universal steady-state power flow algorithm for the newly-developed bipolar multi-terminal VSC-HVDC (VSC-MTDC). Firstly, as the positive-pole and negative-pole DC network of the bipolar VSC-MTDC can be operated individually, a bipolar power flow alternating iterative method is proposed here to obtain the positive/negative-pole DC network power flow. Secondly, a series of nodal equivalent methods involving various control strategies are proposed for the universal power flow algorithm. Then the detailed calculation procedure and a general MATLAB(TM) program for the universal power flow algorithm is presented. A typical 4-terminal bipolar VSC-MTDC system was built in the PSCAD/EMTDC to verify the validity of the proposed algorithm, and the results are discussed here. Moreover, the calculation results of more complex bipolar VSC-MTDC systems under different operating conditions, employing the proposed universal power flow algorithm, are presented to illustrate its universality and efficiency.

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