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A generalized frame of reference for the incorporation of, multi-terminal VSC-HVDC systems in power flow solutions

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Original languageEnglish
Pages (from-to)415-424
Number of pages10
JournalElectric Power Systems Research
Publication statusPublished - 1 Jul 2016
Publication typeA1 Journal article-refereed


This paper introduces a new and general frame-of-reference for true unified, iterative solutions of AC/DC power flows using the Newton-Raphson method. The emphasis is placed on the so-called multi-terminal VSC-HVDC systems. This frame-of-reference accommodates quite naturally any number of AC/DC sub-networks generated by an arbitrary number of VSC converters. Besides, each AC sub-network may contain any number of FACTS devices. The modeling approach adopted for the multi-terminal VSC-HVDC systems is incremental in nature. An AC system of arbitrary configuration is connected to the high-voltage side of the VSC's LTC transformer. In turn, the DC side of each pairing VSC is linked to a DC system of arbitrary configuration. The new model represents a paradigm shift in the way the fundamental frequency, positive sequence modeling of VSC-HVDC links are modeled, where the VSCs are not treated as idealized, controllable voltage sources but rather as compound transformer devices with which key control properties of the PWM-based converters are linked. In contrast to other contemporary approaches, the power flow iterative solutions carried out using the reference frame put forward in this paper exhibits a true quadratic convergence characteristic - in most credible cases, convergence to a tight power mismatch tolerance of e-12 would be achieved in five or less iterations.


  • MT-HVDC systems, Newton-Raphson method, Power flows, VSC-HVDC modeling

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