Node Power Injection Modification Model Based on Direct Derivation for Lossy Power Flow in Hybrid AC-DC Distribution Networks

Lossy power flow naturally extends lossless linear power flow to lossy distribution networks, further improving the accuracy of approximate computation and analysis. However, these enhanced versions are only applicable at the alternating current (AC) transmission level, and the accuracy is limited in distribution networks, especially in hybrid AC-direct current (DC) distribution networks. In this paper, we revisit the lossy power flow model and extend it to hybrid AC-DC distribution networks with multi-terminal voltage source converters. The proposed lossy power flow model can be reformulated as an iteration problem with node power injection as the fixed point. For this purpose, a node power injection modification model based on direct derivation is proposed by exploiting the negligibility of the phase angle differences, and iteratively solving lossy power flows for both AC and DC sub-networks. For coupling devices, to guarantee that the power flow is matched on both AC and DC sides, we formulate a rigorous fixed-point problem to solve the lossy power flow of voltage source converters. Finally, the high accuracy and computational efficiency of the proposed model are verified on multiple test cases.