## 1 Introduction  
Electric power systems involve all aspects of people's lives and are the main energy supply system in modern society [1]. Once a power system is damaged, it has a major impact on daily life and productivity and it even endangers the national economy and social security. In electric power systems, a substation is a part of an electrical transmission and distribution system that can transform (raise or lower) voltage and perform other important functions. A typical substation structure system includes transformers, bushings, lightning arresters, switches, circuit breakers, and other devices that may be interconnected by air-insulated bare conductors strung on support structures. Among them, a high-voltage (HV)ushing is an outlet device that guides the lead lines of the high-voltage and low-voltage windings in a transformer to the outside of the fuel tank, and a line entrance surge arrestor protects substation equipment. In substations, HV bushings and lightning arresters are often connected to in-station jumpers by \"\(\lambda\)\"-shaped down lead transmission lines (DLTLs) (Figure 1). HV bushings and lightning arresters not only insulate DLTLs against the ground but also immobilize them, so the working performance of HV bushings and arrestors directly affects the long-term reliable operation of the whole transformer substation system. In practical engineering, HV bushings, lightning arrestors, and the other electric devices mentioned above feature relatively heavy, high, and large structures and are mostly made of brittle ceramics, which are easily damaged under the action of earthquakes [2]. In recent years, damage to substation facilities caused by earthquakes has occurred from time to time [3]. In 2007, the Niigata earthquake in Japan caused a transformer to catch fire and affected the operation of the nuclear power plant nearby. In 2008, a large amount of porcelain switchgear equipment was damaged in the Wen Chu earthquake [4]. In 2010, earthquakes in Mexico and New Zealand caused serious damage to electrical equipment such as broken insulators. In 2011, the Tohoku earthquake caused a total of 621 electrical equipment damage events [5,6]. On 20 April 2013, a 7.0-magnitude earthquake occurred in Lu Shan County, Ya'an City, Sichuan Province, China and caused serious losses, including damage to a total of 626 substations. It was necessary to shut down 34 substations of 35 kV and above [7]. On 15 November 2019, an earthquake of magnitude 5.2 occurred in Jing xi City, Guangxi Province, China, which caused displacements between the porcelain jacket and flange of a main transformer HV bushing [8]. Oil seepage occurred at the neutral point of the high- and medium-voltage sides of the bushings [9]. Therefore, earthquake-induced failure of HV electrical equipment has become a common issue around the world. Researchers in China and other countries have performed experimental research and theoretical analyses regarding the dynamic response of HV electrical devices under seismic loading. [PERSON] et al. [10] conducted static and seismic simulator tests on two 230 kV, U-shaped transformer bushings to evaluate the seismic performance of the bushings. The Pacific Earthquake Engineering Research (PEER) Center, headquartered at the University of California, Berkeley, evaluated the standard industry procedures for seismic identification of substation equipment based on seismic simulator analysis and triaxial tests and gave some suggestions on the suitability of in-service HV transformer bushings. [PERSON] et al. proposed a Construction Engineering Research Laboratory (CERL) equipment fragility and protection program, CERL Equipment Fragility and Protection Procedure (CEFAPP), for large-scale power transformer bushing tests. [PERSON] et al. simulated the interactions between transformers and bushing structures in detail using the finite element (FE) method and noted the problems warranting attention in practical engineering applications.