## 1 Introduction  
With the rapid development of the world economy and increasing security requirements, the safety of substations has received increasing attention. Estimating the reliability of substations is vital to urban stakeholders, such as utility companies, urban planners, and policymakers, as well as residents and business owners. Over the past 30 years, the disruption of substations and equipment by natural hazards has had severe socioeconomic consequences worldwide [1, 2, 3]. Power systems also play a critical role in disaster planning, mitigation, response, and recovery [4, 5]. A substation consists of many interconnected pieces of equipment and structures, such as transformers, steel frames, and control rooms. The anti-seismic capability of a single structure or piece of equipment has received widespread attention, and a large number of anti-seismic devices have been applied to reduce earthquake disasters [6, 7, 8]. However, due to the redundancy of equipment and structures and physical interactions in the substation system, their seismic reliability is still unclear. In some studies on the seismic reliability of power grids, each substation is regarded as a node on a topological map, and its vulnerability is simplified by defining the overall performance of the substation [9; 10; 11]. The binary test method expresses each state of the basic system through different state vectors. Although this method has been adopted in previous studies [12; 13], the total number of system states is \(2^{n}\), and the calculation amount increases sharply with the number of units, far exceeding the existing capabilities of computers. For complex systems, a fault tree can clearly and completely express the composition of the system and the relationship between the units [14; 15; 16]. In the fault tree, each square represents an event (unit), and the top event is the object to be studied; \"OR\" means that any event below it that occurs causes the event above it to fail, and \"AND\" means that the event above it fails only if all events below it occur. Specifically, for substation systems, research on their seismic reliability can be generally divided into two areas: seismic damage statistics and theoretical analysis. Regarding seismic damage statistics for substation systems, [PERSON] et al. [17] obtained seismic fragility curves for 230 kV and 500 kV substations using empirical statistical methods based on the Loma Prieta earthquake seismic damage database. [PERSON] [18] studied the seismic reliability of substations with two fixed forms of equipment using HAZUSMH's model, combined with expert judgment and empirical models based on mathematical statistics of seismic data. [PERSON] et al. [19] determined the damage ratios of major primary equipment in 121 110 kV substations under different earthquake intensities in the Wenchuan earthquake. The normal distribution function and its cumulative function were used to fit the damage probability density curve and the damage probability curve of various high-voltage electrical equipment based on earthquake intensity. Regarding theoretical analysis, the Federal Emergency Management Agency (FEMA) [20] improved the methodology for assessing the seismic performance of substations. Substations are divided into five kinds of damage states: intact, slight damage, medium damage, serious damage, and complete damage. The damage degrees of the main primary electrical equipment, such as transformers and circuit breakers, are considered to directly affect the damage state of a substation. [PERSON], [PERSON] et al. [21; 22] discussed the seismic reliability analysis of the main wiring system of high-voltage substations, and through the established system reliability analysis criterion, several typical main wiring types of substations were abstracted into simple logical relationship diagrams, and Boolean algebraic analysis was applied to analyze and calculate the seismic fragility of substations.