Unified Power Flow Algorithm Based on the NR Method for Hybrid AC/DC Grids Incorporating VSCs

Runze Chai, Baohui Zhang, Jingming Dou, Zhiguo Hao, Tao Zheng

Research output: Contribution to journalArticlepeer-review

66 Scopus citations


This paper proposes a unified power flow algorithm based on the Newton-Raphson (NR) method to obtain a feasible solution for hybrid AC/DC grids incorporating voltage source converters (VSCs). The power flow model of hybrid AC/DC grids is composed of an AC grid model, a VSC station model, and a DC grid model. Detailed converter losses are involved in VSC station modeling. In the DC grid model, a unified dc control expression is applied to adapt to different control methods. To obtain sparse Jacobian matrix, the mismatch equations and unknown variables are classified into three categories corresponding to AC, VSC, and DC models. Then the proposed algorithm achieved quadratic convergence with the NR method. Once the solution is infeasible (variable out-of-limit) or diverging, the constrained load flow (CLF) method is applied automatically to achieve a feasible solution by revising the references of ac/dc grids. Simulations were carried out for the hybrid AC/DC test system composed of two AC grids and two DC grids. The results under different DC voltage control modes show that the proposed algorithm is able to obtain a feasible solution with high accuracy and convergence speed.

Original languageEnglish
Article number7377126
Pages (from-to)4310-4318
Number of pages9
JournalIEEE Transactions on Power Systems
Issue number6
StatePublished - Nov 2016
Externally publishedYes


  • DC grid
  • DC voltage control
  • unified power flow algorithm
  • voltage source converter


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