For a hybrid ac/dc power system incorporating voltage source converter-based multi-terminal direct current (VSC-MTDC) grids, it is essential to solve the power flow problems efficiently for reliable operation. This paper presents an efficient ac/dc power flow algorithm considering the complementary constraints of VSC's reactive power limit and ac node voltage. It can be distinguished from the existing works in terms of both modeling and algorithm aspects. First, the VSC model is formulated, in which the interactions between the reactive power limit and the ac node voltage of VSC are viewed as complementary relations. The complementary relations are expressed using a smooth Fischer-Burmeister function. Then, power flow models of the ac grid and dc grid with a constant Jacobian matrix are formulated based on the VSC model, respectively. To efficiently solve the power flow of an ac/dc grid, the structure characteristic of the Jacobian matrix of ac/dc power flow computation is analyzed. It shows that the Jacobian matrix can be approximated as a block-upper triangular one. Based on this characteristic, a decoupled ac/dc power flow computation algorithm is provided. Test results on two hybrid ac/dc systems under different scenarios validate the correctness, convergence, and efficiency of the proposed power flow algorithm.

中文翻译：

---

考虑VSC无功功率和交流节点电压互补约束的AC/MTDC高效潮流算法


对于采用基于电压源换流器的多端直流（VSC-MTDC）电网的混合交直流电力系统，有效解决功率流问题对于可靠运行至关重要。本文提出了一种考虑VSC无功功率限制和交流节点电压互补约束的高效交流/直流潮流算法。它在建模和算法方面都可以与现有的工作区分开来。首先，建立VSC模型，其中无功功率限制与VSC交流节点电压之间的相互作用被视为互补关系。使用平滑的 Fischer-Burmeister 函数来表达互补关系。然后，基于VSC模型分别建立了具有恒定雅可比矩阵的交流电网和直流电网的潮流模型。为了高效求解交直流电网潮流，分析了交直流潮流计算雅可比矩阵的结构特点。它表明雅可比矩阵可以近似为块上三角矩阵。基于这一特性，提出了一种解耦的交直流潮流计算算法。不同场景下两个混合交直流系统的测试结果验证了所提出的潮流算法的正确性、收敛性和效率。