Power Flow Models of Grid-Forming Inverters in Unbalanced Distribution Grids

Load unbalance in electric distribution systems is unavoidable. Unbalanced load currents will lead to negative sequence (NS) voltages that may damage electric equipment. Unbalanced power flow analysis is a common tool to detect and mitigate NS voltage issues and requires accurate models of grid components. While traditional source models are available, grid-forming (GFM) inverter models are not well developed. GFM inverters implement various control strategies, which affect their power flow models. In this article, a novel GFM inverter model considering control effects is proposed. We show that for some control methods, unbalanced system loading will lead to unbalanced terminal voltages of the GFM inverters, which are modeled through an equivalent negative sequence impedance. The proposed models are initially validated using a simple test circuit. Then, they are applied in the power flow analysis on the IEEE 13-bus and 34-bus systems to demonstrate the accuracy improvement over the state-of-the-art. Using time-domain simulations as benchmarks, we show that the proposed models reduce the calculation error of negative sequence voltages by at least 25% in unbalanced distribution systems.