Short-Circuit Current Calculation of Single-Phase to Ground Fault in Petal-Shaped Distribution Network

Petal-shaped distribution networks are receiving increasing attention due to their enhanced reliability. However, the integration of distributed generators (DGs) significantly alters the fault characteristics during single-phase to ground faults. Traditional short-circuit calculation methods become inadequate due to the unmodeled effects of negative sequence current control in DGs. To address this challenge, this study establishes, for the first time, a mathematical model for single-phase to ground faults in a petal-shaped network with DG integration under both positive and negative sequence control. It explicitly derives the DGs’ output current under three control goals: maintaining constant active power, maintaining constant reactive power, and injecting a symmetric three-phase current. Utilizing the symmetrical component method, a composite sequence network incorporating the DGs’ negative sequence current output is developed. Based on the node–voltage relationships, an analytical short-circuit current calculation method suitable for multiple control goals is proposed. Validation via MATLAB R2022a simulations demonstrates high-fidelity accuracy: in Case 1 with different fault locations, the maximum relative error is 0.31%, while in Case 2, it is 2.04%. These results quantify the critical impact of the negative sequence current—reaching up to 14.78% of the DG output during severe voltage sags—providing theoretical support for the protection design of a petal-shaped distribution network with high DG integration.