An Accurate Calculation Method for Minimum Detectable Fault Ramp Rate of Coupled-Inductor Z-Source DC Circuit Breakers

Z-source dc circuit breakers (ZSCBs) have been widely studied for their automatic fault-breaking capability. Minimum detectable fault ramp rate (MD-FRR) is a crucial parameter for describing the protection threshold of ZSCBs, and its accurate calculation is essential to ensure reliable tripping. However, the conventional calculation method for MD-FRR is derived under a simplified circuit model and suffers from low accuracy. In the case of coupled-inductor ZSCBs, the calculation error can even reaches 70%. To solve this problem, an accurate calculation method for MD-FRR of coupled-inductor ZSCBs is proposed in this article. This method can significantly reduce calculation errors and provide precise guidance for breaker design. First, the limitations of the conventional calculation method are analyzed. On this basis, an accurate mathematical model based on Gamma-ZSCB is proposed. Then, a numerical calculation process is designed to solve the accurate model and obtain an approximate analytical solution of MD-FRR. Additionally, a simple parameter-equivalent method is presented, which can generalize the proposed method to all coupled-inductor ZSCBs. Finally, experiments are carried out to verify the accuracy of the proposed method. The results show that relative calculation errors are lower than 10%.