## 5 Conclusions  
This study presents a new evaluation process for assessing the seismic reliability of substation systems based on the quasi-Monte Carlo (QMC) method. The proposed process considers the system's physical interdependence, evaluates the seismic vulnerability, and identifies key equipment, the seismic performance of which can be improved to enhance overall system reliability. The key findings and methodological advancements are summarized below:  
A new evaluation process for the seismic reliability of substation systems based on the QMC method is proposed. The system structure is expressed by an adjacency matrix, and the connectivity matrix is solved by the QMC simulation method and the triangle algorithm. By introducing the concept of a functional unit, a basic model of the substation network that comprehensively considers the influence of the building structure, electrical equipment, and main wiring topology is established. According to the assumed vulnerability parameters, the seismic reliability is evaluated and expressed by the fragility curve.  
The analysis results show that physical interdependence can be considered through the evaluation process. Substations are more susceptible to earthquakes than individual equipment, which shows that from the perspective of earthquake resistance, the redundancy of existing substations is insufficient. When the PGA is very low, the functionality of the substation depends on the line-out unit, and then because the line-in units and the transformer units are no longer redundant, the functionality of the substation system depends on whether the line-in unit and the transformer unit are destroyed.  
A sensitivity analysis determined that the 220 kV CT, CB, and DS and the 110 kV DS are the most critical pieces of equipment in the substation. Based on this result, the seismic performance of the key pieces of equipment can be improved through isolation technology, such as dampers and isolation devices, and the proposed process can be used to evaluate the effect. Therefore, the evaluation process proposed in this paper plays an important role in ensuring the safe and stable operation of substation systems in an earthquake and can be applied to other engineering systems. In addition, if more detailed facility fragility data are available, different types of electrical equipment can be further distinguished to accurately evaluate the results.  
X.L.: Methodology, Methodology, Software, Formal Analysis, Writing--Original Draft; S.Z.: Conceptualization, Resources, Project Administration, Funding Acquisition; Q.Q.: Visualization. P.H.: Data Curation. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China, grant number [52278530] and Key R&D Projects in Shaanxi Province, grant number [2021 ZDLSF06-10]. The APC was funded by [2021 ZDLSF06-10].  
Data Availability Statement: Data available in a publicly accessible repository. The data presented in this study are openly available at [[https://doi.org/10.6084/m9.figshare.20656707.v1](https://doi.org/10.6084/m9.figshare.20656707.v1)]([https://doi.org/10.6084/m9.figshare.20656707.v1](https://doi.org/10.6084/m9.figshare.20656707.v1)).  
The authors would like to thank the anonymous reviewers for their valuable comments.  
The authors declare no conflicts of interest.