Impact of Large Power Transformer Bushing Seismic Vulnerability on the Electrical Grid

Impact of Large Power Transformer Bushing Seismic Vulnerability on the Electrical Grid | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Impact of Large Power Transformer Bushing Seismic Vulnerability on the Electrical Grid Bjorn Vaagensmith, Akram Batikh, Jon Bender, Chandrakanth Bolisetti, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7753894/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Numerous studies suggest that the Pacific Northwest Subduction and the San Andreas Fault systems are past due for a severe seismic event. In the time that has passed since the last highly destructive event near an urban area (Northridge, 1994, M6.7), major changes to our electrical grid have introduced uncertainty in the impact such an event would have on critical infrastructure. While design practices have improved since 1994, the seismic vulnerability of large power transformers remains in question. These critical substation components are essential for power delivery but are extremely expensive and becoming difficult to procure with lead times that can be as long as five years. Thus, it is essential to understand the seismic risk transformers represent to the bulk electrical grid where bushing failure was of primary concern. This work presents a parametric study of the commonly used high voltage transformer-bushing systems on the 10,000 synthetic bus system (138kV and 345kV), from which the probability of a given transformer bushing to exceed design amplification standards was used to approximate whether the transformer would fail during a seismic event. These risk values are then applied to the 10,000 synthetic bus system of the western interconnect through Monte Carlo sampling. Depending on line protection settings, the resulting showed 7.2–11.7% and 2.4–10.7% of cases did not exhibit load loss for San Andre’s and Seattle Washington, respectively. However, 80.5–89.8% and 88.6–91.1% of cases exhibit losses greater than 100 MW of lost load for the San Andrase and Seattle Washington areas, respectively. Physical sciences/Engineering/Energy infrastructure/Energy grids and networks Physical sciences/Engineering/Civil engineering Physical sciences/Energy science and technology/Energy modelling Physical sciences/Engineering/Electrical and electronic engineering large power transformers bushings earthquakes grid resilience Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 1. Introduction Earthquakes can devastate critical infrastructure and result in large scale outages [1]. The Los Angeles California Northridge earthquake of 1994, for example, was only rated a 6.7 on the moment of magnitude scale but resulted in power outages extending to Idaho, Utah, and Colorado [2]. Events like Northridge provide salient reminders on the importance of understanding how seismic events can disrupt the power grid [3]. Prior studies have predominantly focused on specific modes of failure for individual components [4], or on predicting wide spread impact to the grid using graph theory, statistical methods, and fragility curves [5–8]. The importances of specific component vulnerabilities and their ripple effects on bulk grid outages, however, remains largely unstudied. Earthquakes can impact many different power grid components such as power transformers [9], power lines [10], breakers [4], and power plants [11]. While all grid components are important, large power transformers are of particular interest due to their high cost and long lead times [12]. Protecting large transformer assets is of high importance to power utilities to ensure grid reliability and resilience. Historically, earthquakes have damaged large power transformers through bushing failures [13], anchor failures [14], oil conservator tank failures [15], and fires from oil leaks [15], all of which require replacing the transformer or major time-consuming repairs. Comparatively, bushing failures are by far the most frequent [9]. Several real-world examples of earthquakes like the 1986 North Palm springs and 1994 Northridge events, where the bushings of over 20 different 230 kV transformers failed, show how transformers are vulnerable to seismic events [16]. The 2008 Wenchuan earthquake damaged several 500 kV transformers, which were studied with finite-element analysis (FEM) post event by Ma et. Al. [15]. Their study found structural shortcomings in the bushings and the conservator oil tanks based on the typical earthquakes’ input frequencies. The accelerations and bushing demand amplifications experienced were much greater than the seismic design standards IEEE 693 or GB 50260 − 2013 consider for bushing qualification. IEEE 693 recommends that bushings be qualified with a ‘fixed base’ condition subjected to earthquakes that match twice the performance level response spectrum [17]. This recommendation assumes that the ground motion experienced by the bushing is amplified by the transformer tank and turret dynamics no more than two times. Many studies on transformer tank-turret-bushing dynamics suggest that bushing demand amplification can exceed a factor of two [9, 18, 19]. In addition to individual device failure modes, others have studied the impact seismic activity has on the bulk grid. CIPCast was a tool developed to assess power grid seismic resilience based on component serviceability and grid connectivity post event [6]. It overlays earthquake intensity maps with the grid topology, qualitatively assesses power grid asset damage (for nodal points like substations and generators), and recovery rates (for connection points like power lines) over time. Nazemi et. Al. leveraged Monte Carlo sampling to randomly generate earthquake scenarios and studied how degraded (or failed) generation resources impacted the bulk grid [7]. The Monte Carlo simulation selected peak ground acceleration (PGA) values based on historic seismic hazard maps and used fragility curves to qualitatively assign varying degrees of functionality to generators on the power grid. The resulting power grid functionality was assessed using DC approximation. They found a combination of generation rebalancing and system reconfiguration enabled the fastest grid recovery. Espinoza et. al. leveraged a similar randomly generated earthquake scenario but included substations and generators degradation [8]. They studied component importance by granting specific generators or substations seismic immunity within the DC approximation grid simulations. They observed which substation immunities enhanced the grid’s ability to resist degradation the most. Ghafory-Ashtiany et. al. leveraged graph analysis methods to study the seismic impact on the Iranian grid [20]. They used fragility curves to consider the impact on substations, transmission lines, sub-transmission lines, and generators and developed resilience metrics that considered component damaged along with how the damaged component may affect downstream connections. Their scenarios tended to fail powerlines more frequently than generators or substations, although system connectivity (i.e., paths from generators to loads) was affected more significantly by generator or substation failures. Previous studies have tended to focus on one of two areas: specific component vulnerabilities or impacts on the bulk grid. To the authors best knowledge, no studies have attempted to bridge the gaps between these two realms by analyzing how specific component vulnerabilities cascade up into impacting the bulk power grid. This work attempts to address both issues by leveraging power flow simulation software coupled to dynamic finite element models (FEM) that analyze vibration coupling between power transformer tanks, turrets, and bushings. While the number of designs and interactions between the tank, turret, and bushing are complex, this work attempts to approximate the dynamics of a “typical” system within a given voltage class through parametric analyses using many reduced-order models (ROMs) based off a few actual transformer designs and running many bulk grid earthquake scenarios. The diversity and complexity of actual transformer-bushing system scattered through the grid might in some cases positively, and in other cases negatively, impact grid resilience. A large sample base of ROMs was used to average out how these nuances affect the bulk grid. Earthquake scenarios may then be linked directly to transformer bushing failures and used to understand how these vulnerabilities translate into best, average, and worst load loss outcomes. 2. Methodology A unique four step methodology was developed to assess the impact bushings will have on the bulk grid. (1) selecting a grid model for which the analysis will be performed. (2) selecting an earthquake scenario and determining the shaking intensity at the base of each transformer. (3) build a contingency scenario by computing the seismic demand on the transformer bushings from the earthquake and determine whether the bushing exceeded its design qualification prescribed by IEEE 693 (via a random sampling of available ROMs performance under seismic demand). Lastly, (4) performing a bulk grid contingency analysis based on which transformers had assumed bushing failures (based on the seismic demand exceeding its design qualification in step 3). Steps 3–4 were repeated to get a more statistically significant sample set. This section outlines how seismic demand on the transformer bushing was calculated, how contingency scenarios were generated, and how power grid contingency analysis was performed. 2.1. Determining Seismic Demands on the Bushing and Identifying “At-Risk” Bushings To determine if a bushing failed due to an earthquake would require an adequate understanding of the bushing properties, including the ultimate strength of each bushing, which requires testing the bushings to failure. While this data may be available for some bushings, little information is publicly available, and it would be a monumental undertaking to estimate the failure strength of each bushing in the grid. This study contends with this shortcoming by identifying the bushings (and therefore, the transformers) that are “at risk”. “At-risk” bushings are defined as those that experience a seismic demand greater than what they are qualified for per IEEE 693. Therefore, shaking intensity via peak ground acceleration (PGA) identified at the base of each transformer was used to calculate the amplification from the transformer base to the bushing and the resulting seismic demand on the bushing. It was assumed that every bushing within any given area was qualified per IEEE 693 to its associated seismic hazard level. If the bushing amplification was greater than it was qualified for, the transformer with the bushing in question was assumed to have failed and was taken out of service when performing power flow contingency analysis. 2.1.1. Calculation of bushing amplification distributions Calculation of bushing demands requires ground motion at the base of each transformer and a structural analysis model (e.g., finite-element analysis models) for each transformer including the tank, turret, and bushing. Using the USGS ShakeMap scenario database [21], which provides spectral accelerations and velocities at 0.3, 1.0, and 3.0 sec periods (3.33, 1.0, and 0.33 Hz), an approximate response spectrum at the base of each transformer can be estimated for a specific earthquake scenario. However, each transformer is custom designed and acquiring structural models for each one in the grid would be virtually impossible. To address this challenge, a statistical distribution of transformer’s seismic response by voltage class was created using parametric analysis starting with a smaller sample population for which detailed drawings were available. Since bushing failures were the focus of this study, the acceleration amplification at the base of the bushing was chosen as the transformer response parameter. Three 138 kV and nine 345 kV designs were selected, and complex finite element models were developed for each using the commercial structural analysis software, SAP2000 (example shown in Fig. 1 ). Each transformer model closely approximated the stiffness and mass distribution of the represented components according to three-dimensional (3D) computer automated design (CAD) fabrication drawings, bushing seismic test data, and component cutsheets. Insulating oil was also considered in terms of both weight and hydrostatic pressure. These complex models were used to develop reduced order models (ROMs) in Idaho National Laboratory’s Multi-hazard Analysis for STOchastic time-DomaiN phenomena (MASTODON) application [22]. MASTODON is a MOOSE (Multiphysics Object-Oriented Simulation Environment) [23] application tailored for seismic analysis and risk assessment. These ROMs were used to perform parametric analysis and calculate the bushing amplification distribution for each kV class. The ROMs were created by idealizing the three main components of each transformer—the tank, turret, and the bushing—using a lumped mass stick model (LMSM; i.e., a stack of beam elements with masses lumped at the nodes) that replicates the first vibration mode of the component. The tank LMSM had the same height and total mass of the tank, and its stiffness was calibrated to achieve the tank natural frequency calculated by the SAP2000 model. The turret LMSM was created using the turret height, cross-section, and mass. The bushing LMSM was a single-degree-of-freedom structure with its mass equal to the air-side mass of the bushing, length equal to the distance between the base of the bushing and its center of mass, and the stiffness calibrated to replicate the fixed-base fundamental frequency of the bushing. Two zero-length rotational spring elements between the bushing and turret and the turret and tank were calibrated to replicate the mounted bushing frequency and the mounted turret frequency, respectively. These natural frequencies were calculated from a modal analysis of the SAP2000 models. After calibrating the LMSMs and the springs individually, they were stacked together to create the full ROM of the transformer as shown in Fig. 2 . To further increase the sample size, all possible combinations of these ROM components were created in MASTODON. For example, since nine detailed transformer models were available in the 345 kV class, ROMs corresponding to all possible combinations of the nine tanks, turrets, and bushings were created, resulting in an extended population size to 9 3 =729. Since all the tanks, turrets, and bushings considered in these models were from real transformers, the parameterized ROMs were also assumed to be representative of real transformers. After developing the extended population of ROMs for each kV class, bushing amplifications for these ROMs were calculated. A broad spectrum Ormsby Wavelet was the input to each ROM and the bushing amplification was calculated as the ratio of the bending moment at the bushing mounted on the turret-transformer model to the same bushing mounted to a fixed base. Since all the ROMs are linear, the amplification ratio is the same regardless of the magnitude of the PGA. The amplification ratios for all the ROMs of the same kV are then used to build a voltage class specific bushing amplification distribution, from which transformer amplification responses to a PGA ground motion can be randomly sampled from. 2.1.2. Identification of “at-risk” bushings During a specific earthquake scenario, the following inequality check is performed for every bushing within the seismic zone to evaluate if it is at risk. If the check is true, the bushing is at risk. If the check is false, the bushing is not at risk. $$\:SPG{A}_{i}\cdot\:{\alpha\:}_{ij}>QPG{A}_{i}\cdot\:2.0$$ Here, the SPGA i is the PGA at the base of the i th transformer for a specific earthquake scenario, α ij is the j th sampling of the bushing amplification (from the amplification distribution of the corresponding transformer voltage class) for the i th transformer, and QPGA i is the PGA assumed at the transformer base during IEEE qualification testing. Since the bushing amplification is uncertain, a Monte Carlo sampling is performed from the amplification distribution for the corresponding transformer voltage class. Since the IEEE 693 qualification procedure assumes that all turret-transformers systems have an amplification no greater than 2.0, the peak acceleration that the bushing is qualified to is calculated as the transformer base PGA multiplied by 2.0. In the qualification process, the transformer base PGA can be either 0.5g (medium seismic hazard) or 1.0g (high seismic hazard), and therefore, bushings are typically qualified to a base acceleration of either 1.0g or 2.0g. This work assumes all transformers bushings were qualified to a base acceleration of 1.0g (medium seismic hazard). 2.2. Translating parametric analysis into power grid contingencies Figure 3 provides a high-level summary of the input data and how it is processed to produce a power grid contingency. Python code intakes power model files (which also have GPS data linked to bus information), the number of contingency scenarios to be generated, ShakeMap scenario data, and amplification distributions. ShakeMap data was taken from USGS scenario database for the San Andreas (M 7.9 Scenario Earthquake – N. San Andreas: SAN + SAP + SAS scenario) [24] and the middle Seattle (M 7.2 Scenario Earthquake – Seattle fault zone-middle scenario) [25] and are shown in Fig. 4 . Amplification distributions were calculated using the parametric analyses described in Section 2.1.1. The amplification ratios were generated for each transformer via MCS of their corresponding voltage class amplification distributions. A contingency file was created for each sampling with the list of transformers to remove from service. To account for the uncertainty in the amplification distributions, 2000 such contingencies were generated. To determine the number of contingencies, we conducted a convergence study. The analysis showed that there was no difference in power outage distributions between 2,000 scenarios to 10,000 scenarios. 2,000 scenarios were deemed adequate to achieve stable results without added computational expense. 2.3. Impact on the bulk grid PowerWorld Simulator 23 software was used to compute contingency analysis for a synthetic 10,000 bus system of the western United States [26, 27]. Once the contingency file (in .con format) was uploaded to PowerWorld, a custom monitor was used to trip off lines that exceeded 125% capacity or 150% capacity. This was done to prevent simulations that allowed unrealistic current flows through power lines. Simulation convergence was not always reached for contingencies that failed many transformers and tripped off many lines. For these contingencies, the amount of load lost reported prior to the software failing to converge on a solution (using Newton-Raphson method) was used. DC approximation solvers were not compatible with custom monitors in PowerWorld (i.e., despite being able to solve all contingencies they would not trip lines exceeding the capacity limit) and thus was not used. A custom aux script (i.e., a PowerWorld scripting language) extracted load flow data from each simulated contingency to provide the geolocation of each load not served due to the earthquake scenario and power line trip settings. Load loss and failed transformer locations were plotted on satellite image maps for different cases that aligned with the average and highest load (the lowest cases resulted in zero load loss, so no maps were generated). Distribution plots of the total load loss for the two different earthquake scenarios, assuming 125%-line trip and 150%-line trip settings were plotted along with the distributions of transformers lost by voltage class and MVA size. While the 10,000-bus system has many different voltage classes of transformers, the San Andreas California and Seattle Washington areas were only populated with only 138 kV and 345 kV large power transformers, thus these voltage classes will be the focus of this analysis. 3. Results 3.1. Comparison between ROMs and high-fidelity models Before performing the parametric study to calculate amplification distributions, the performance of the ROMs was benchmarked against SAP2000 to ensure comparable results. The benchmarking was done for each kV class (138 kV and 345kV) by comparing the percentage of samples for which the amplification was greater than 2 (shown in Table 1 ). A good agreement for 345 kV was observed, but not for 138 kV. This is because only 3 high-fidelity models were available for the 138 kV class (which were expanded to 27 for the MASTODON ROMs as described in Section 2.1) and therefore, there is not a large enough sample size to enable a reasonable comparison. Nevertheless, given that the first modes of the tank, turret, and bushing were captured explicitly, ROMs could still be considered representative of real 138 kV transformers for this demonstrative study. 138 kV transformers are not considered in IEEE 693 because historically they have not exhibited much seismically vulnerable. While the small SAP2000 model sample size shows these transformers as more problematic, the expanded ROMs likely produced a more realistic result with fewer 138 kV transformers showing concern (see section 3.2 and 3.3). Table 1 Comparison of amplifications calculated using MASTODON ROMs and high-fidelity finite element SAP2000 models. Class MASTODON SAP2000 138 11% 67% 345 96% 100% 3.2. Transformer Bushing Amplification Figure 5 shows the different amplification distributions generated from parametric analyses. The 138 kV voltage class shows an 11.1% chance of exceeding the 2x industry standard with mean amplification of 1.42x and a maximum amplification of 2.39x. The 345 kV transformers, on the other hand, have a much larger structure and mass which can allow for some amplifications greater than 20x. 345 kV transformers show a 91.2% likelihood of exceeding the 2x industry standard with a mean amplification of 4.63x. 3.3. Impact on Bulk Grid For the two scenarios chosen, the 10,000-bus eastern interconnect contained only 138 kV and 345 kV transformer types. Figure 6 shows the frequency of transformer failures by voltage class. In both the San Andreas and Seattle cases, few 138 kV transformers failed (Fig. 6 a). This is attributed to 138 kV transformers having low application distributions (Fig. 5 ) and smaller population sizes in both areas. The San Andreas area contained 123 138 kV and 215 345 kV transformers. The Seattle Washington area contained 44 138 kV and 110 345 kV transformers. In each case, 138 kV transformers only accounted for 36% (San Andreas) and 28% (Seattle) of the total assessed transformer populations. These results are also consistent with the fact that 138 kV transformers are not considered seismically vulnerable and thus excluded from IEEE 693 requirements. Conversely, the structural properties of 345 kV transformers lend themselves to more sever seismic amplification (see Fig. 5 ), are subject to IEEE 693 requirements, and exhibited more failures across the 2000 generated contingencies shown in Fig. 6 b. Figure 7 shows the number of failed transformers based on MVA size. Most cases exhibit 0–4 transformer failures in sizes ranging from 0-199 MVA, 400–599 MVA, and 600–799 MVA. This was attributed to smaller population sizes of these transformer sizes for their respective locations. Most transformer failures were 345 kV as seen in Fig. 6 b where 25% and 40% of scenarios contained no 138 kV failures for San Andreas (Fig. 7 a) and Seattle Middle (Fig. 7 b), respectively. Interestingly, the smaller sizes ranging from 0-199 MVA and 200–399 MVA were the most frequent failures in San Andreas (Fig. 7 a). The Seattle scenario (Fig. 7 b) shows only 200–399 MVA transformer size as the dominate failure type. These trends were attributed to the smaller transformer MVA sizes being the most dominant population in these areas and may also help explain how many scenarios resulted in lower load loss from Fig. 8 and Fig. 9 . Figure 8 shows the frequency of occurrence vs the range of lost load for the San Andreas fault scenario assuming power lines trip offline after exceeding 125% or 150% of their capacity. Both cases showed 0–50 MW bin as the most frequent with 7.2% and 11.7% likelihood for the 125% (Fig. 8 a) and 150% (Fig. 8 b) trip cases, respectively. While not shown explicitly in the figure, this 0–50 MW bin was mostly composed of scenarios exhibiting no load loss. As expected, the 125% trip case showed the highest second most likely next bin between 301–350 MW at 4.58% likelihood compared to the 201–250 MW at 5.9% for the 150% trip case. This was likely due to the 125% trip scenario taking lines out of service sooner compared to the 150% trip case. Both cases show a positive skewed distribution with an impulse around the 0–50 MW bin. While the positive skew is a good thing in that it favors smaller power outages, the amount of load loss is still relatively high. For the 125% trip case, the likelihood of an outage causing some amount of load loss between 201–600 MW is 25%. This is only reduced to 23% for the 150% trip case. Figure 9 shows the frequency of load lost vs the range of lost load for the Seattle middle fault zone also assuming power lines trip offline after exceeding 125% or 150% of their capacity. Unlike San Andrase neither case showed 0–50 MW bin as the most frequent or second most frequent with 2.4% and 10.6% likelihood for the 125% and 150% trip cases, respectively. Like the previous case, the 125% trip case showed higher load loss potential with the 351–400 MW bin with a 26.2% likelihood of occurrence and the 151–200 MW bin at 14.6% for the 150% trip case. The Seattle case shows a much tighter grouping of outages compared to the San Andrase case. This is attributed to the failure of more transformers supporting loads being centralized in the earthquake epicenter. Both cases show a positive skewed distribution like the San Andreas case. Compared to the San Andreas case the likelihood of an outage causing some amount of load loss between 201–600 MW is 65% for the 125% outage and is only reduced to 50% for the 150% trip case. These results warrant serious consideration of transformer resilience against seismic events. They also illustrate the impact of how changes in grid topology can impact the severity of power outages during an earthquake. Figure 10 shows satellite maps with the coordinates of lost load (circles) and transformers (blue Xs) plotted for both average and worst-case scenarios of the 150% trip case. The satellite images provide an alternative means to understand the effects of the two seismic scenarios. As expected, the most concentrated areas of load loss and transformer failures occurred near the earthquake epicenters (see Fig. 4 ). However, in the worst-case scenarios, the impacts extended well beyond the epicentral regions. With few exceptions, most of the transformer failures occurred around the epicenters. The main differences between the worst-case scenarios and average case scenarios were the size and number of the transformers that were taken offline. Larger sized transformers supporting greater amounts of load and were likely connected to critical powerline corridors, which contributed to the cascade further outside the epicenter. 4. Discussion These results demonstrate the potentially devastating effect large earthquakes could have on the power grid. While not a real grid, the 10,000 bus model was designed to have similar properties of a real grid [26, 27]. Actual transmission grids in California and Washington are not purely composed of 138 kV and 345 kV transformers. Other voltage classes, such as 230 kV, are more commonly represented. A more accurate transformer voltage class distribution within the synthetic grid would create a better picture of the actual impact of a significant seismic event. Moreover, this study does not account for remedial actions taken by grid operators to minimize load loss. Despite including 138 kV transformers in this study, it should be noted that 138 kV transformers are not held to the same standard as voltages above 138 kV in IEEE 693 [17]. 138 kV was listed as the cutoff for seismic amplification testing. Our results corroborate this finding, as Fig. 6 shows that the maximum number of 138 kV transformer failure in any given scenario was four, with many scenarios showing zero failures. Conversely, the 345 kV transformer voltage class failed 15–19 and 30–34 on average for the San Andrase and Seattle Middle scenarios, respectively (see Fig. 6 a-b). Additionally, the amplification distribution plots in Fig. 5 show 138 kV transformers exhibiting lower amplification ratios compared to 345 kV transformers. While these results do not directly demonstrate imminent disaster given the limitations mentioned above, it does, however, show that a component vulnerability (like bushing amplification) can lead to large scale grid impact. In this regard, this work serves as a call to serious consideration of component-level vulnerabilities in the power grid and the consequential threat from large seismic events. Many of the scenarios above resulted in zero load loss (i.e., a large number of contingencies comprising the 0–50 MW bins of Fig. 8 and Fig. 9 showed no load loss) and the likelihood of zero load loss never exceeded 15%. The median load loss depends on powerline trip settings. For the 125%-line trip setting both earthquake scenarios predicted load loss ranging from 351–400 MW as the most likely case. For the 150%-line trip settings, both scenarios show similar outcomes of 201–250 MW and 151–200 MW load loss as most likely for the San Andreas and Seattle Middle case, respectively. In both cases, the amount of load loss would be considered significant from a utility perspective. 5. Summary and conclusions Large power transformers are critical assets for the power grid and cannot be quickly replaced after a sudden failure. This study presents a novel methodology for studying how seismic activity impacts the bulk power grid through bushing failures on power transformers. Complex models built in SAP2000 were used to tune ROMs, the core components of which were mixed and matched to expand the sample set. The expanded ROMs were then used to generate amplification distribution histograms based on transformer voltage class. These distributions showed 138 kV transformers had an 11% chance of exceeding 2x amplification (1.42 mean amplification) whereas 345 kV exhibited a 91.2% chance (4.63 mean amplification). The 138 kV results was consistent with the fact that they do not pose as much of a seismic risk due to their smaller size and are thus not required to meet the same standards of IEEE 693 imposed on larger transformer voltages. Random sampling of these amplification distributions was used to determine which transformer was at risk of failure for a given earthquake scenario. 2,000 contingency scenarios were created to study the seismic impact to the synthetic 10,000 bus Western interconnect. The San Andreas scenarios showed 0–50 MW of lost load was the most likely case at 7.2% and 11.7% likelihood for cases where ampacity power line trip settings were set to 125% and 150%, respectively. The Seattle Middle case showed the most likely loss ranging from 351–400 MW (26.2% likelihood) and 151–200 MW (14.6% likelihood) for the 125%- and 150%-line trip cases, respectively. These results closely corresponded to the next most likely load loss scenarios for the San Andreas 125%- and 150%-line trip setting (351–400 MW (4.85% likelihood) and 201–250 MW (5.9% likelihood), respectively). The amount of lost load observed in these cases was significant, however this study has some limitations. 1) 138 kV transformers are not held to the same standards as higher voltage class transformers (but were evaluated according to IEEE 693 for this study). 2) The frequency of transformer voltage class within the San Andreas and Seattle areas do not closely align with reality (only containing 138 kV and 345 kV transformer as the largest voltage classes). 3) Grid operator remedial actions were not considered, which could potentially preserve more grid functionality during a natural disaster. 4) Power flow simulation convergence was often not reached due to many transformers being taken out of service and resulting power lines tripping offline. The final reported load loss before the power flow software failed to converge was used. While this study does not directly predict eminent disasters from a significant seismic event, it does suggest that a potentially significant threat to the grid exists, and a more detailed investigation is warranted. Moreover, this study also supports a growing body of work that suggests transformer tank-turret-bushing amplification dynamics can easily exceed the 2x industry standard for large power transformers. 6. Future work This study could improve if performed on a more realistic synthetic power grid that includes a more significant population of 230 kV transformers and some 500 kV transformers. This work plans to leverage the California Test System for future studies because it includes a wider variety of transformer voltage class types [28]. Additionally, power grid simulation convergence was a significant issue due to the removal of many grid elements in a single contingency. This work plans to modify contingency files to progressively solve the mode after removing a limited number of elements rather than attempting to solve with all the elements removed at once. Additionally, leveraging experimental data to improve the accuracy of SAP models is needed. A jointly funded project by DOE-CESER and DOE-OE-TRAC led by Idaho National Laboratory plans to experimentally test seismic response (via shake table) of an oil filled 230 kV large power transformer. This test will provide the first ever full-scale experimental data to inform FEM studies on transformer tank-turret-bushing interactions. The experimental data can be used to improve the accuracy of simulated large power transformer failure probabilities during a seismic event. This work plans to leverage this experimental data to improve transformer failure likelihood estimates from seismic events on large grid simulations. Declarations Acknowledgements This work was supported through the INL Laboratory Directed Research & Development (LDRD) Program under DOE Idaho Operations Office Contract DE-AC07-05ID14517. Author Contributions Akram Batikh contributed ROM modeling, data analysis, python scrip methodology and writing, and manuscript writing; Bjorn Vaagensmith contributed to the concept formulation, python code methodology, power systems modeling, aux script writing, manuscript writing, funding acquisition, and project supervision; Jon Bender contributed to concept formulation, python code methodology, SAP 2000 modeling, and funding acquisition; Chandrakanth Bolisetti contributed to the concept formulation, python scrip methodology and funding acquisition; Alexander Harvey contributed python code methods and writing; Joeseph Liebergen contributed to python code methods and writing; Hassan Khan contributed to python code methods and writing, and Mihai Diaconeasa contributed to manuscript reviewing, manuscript editing, review of methods, and supervision. 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Additional Declarations There is NO Competing Interest. Supplementary Files SupplimentaryinformationBushingfailureimpactongridlargescalev6.docx Supplementary information - Impact of Large Power Transformer Bushing Seismic Vulnerability on the Electrical Grid markuplanguageSeismicAlgorithms.pdf Supplementary Information - Algorithms Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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05:43:00","extension":"html","order_by":33,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":80264,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7753894/v1/409f8483cafb3b5fa722fcd2.html"},{"id":95504150,"identity":"959fef5c-0ea1-4c6a-b359-398230e09f35","added_by":"auto","created_at":"2025-11-10 05:42:59","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":341831,"visible":true,"origin":"","legend":"\u003cp\u003eExample of a Complex Finite Element Model of a Power Transformer analyzed via SAP2000\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7753894/v1/c79520b515789a2408a3aebb.png"},{"id":95504156,"identity":"9c26ad37-de48-4bf3-83b9-6f5c7a2f03df","added_by":"auto","created_at":"2025-11-10 05:42:59","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":371512,"visible":true,"origin":"","legend":"\u003cp\u003eComplex Finite Element Model and Reduced Order Model of a Power Transformer.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7753894/v1/6d64741bb57d63281a2bd0e5.png"},{"id":95529891,"identity":"d4f57ba3-3dd1-4806-925e-b0cb48f5be1d","added_by":"auto","created_at":"2025-11-10 10:17:37","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":301395,"visible":true,"origin":"","legend":"\u003cp\u003eInput data and process flow for converting transformer-tank-bushing models into a power grid contingency scenario.\\\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7753894/v1/bb36e67db6ea2aea699e92c4.png"},{"id":95528398,"identity":"26a317d4-edab-4815-b6eb-bb9bdf2b721a","added_by":"auto","created_at":"2025-11-10 10:16:01","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":760808,"visible":true,"origin":"","legend":"\u003cp\u003eSeismic shake maps used in the grid impact assessment: (a) M 7.2 Seattle fault zone scenario and (b) M 7.9 N. San Andreas scenario.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-7753894/v1/c1e5694c719b975fbe9eab60.png"},{"id":95504169,"identity":"03de8169-1e23-41fa-83bd-5c425b0e4962","added_by":"auto","created_at":"2025-11-10 05:42:59","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":103424,"visible":true,"origin":"","legend":"\u003cp\u003eBushing amplification ratio histograms for 138 kV and 345 kV transformer voltage classes.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-7753894/v1/4dd93b6657e9a3396b974bf2.png"},{"id":95529015,"identity":"9937ab2f-7157-4804-92ca-92310907e251","added_by":"auto","created_at":"2025-11-10 10:16:42","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":90832,"visible":true,"origin":"","legend":"\u003cp\u003eNumber of failed transformers for (a) all 138 kV in both the San Andreas and Seattle scenarios, (b) 345 kV for San Andreas and Seattle scenarios.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-7753894/v1/6f2da36c1611e3d125f40f5d.png"},{"id":95504164,"identity":"fc17478c-ccda-4e2b-a26d-cd3865414222","added_by":"auto","created_at":"2025-11-10 05:42:59","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":99815,"visible":true,"origin":"","legend":"\u003cp\u003eFailed transformers by MVA size for (a) San Andreas and (b) Seattle scenarios.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-7753894/v1/946a5ab03150ca1c692080b6.png"},{"id":95529748,"identity":"e1608c0a-7478-48bd-ba63-9d1fa882b2df","added_by":"auto","created_at":"2025-11-10 10:17:28","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":103455,"visible":true,"origin":"","legend":"\u003cp\u003eFrequency of occurrence for various ranges of lost load (MVA) for the San Andreas sceanrio assuming powerlines will trip off when capacitiy exceeds (a) 125% and (b) 150%.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-7753894/v1/976d97986a60937af68115a7.png"},{"id":95504161,"identity":"d16e37e7-22c6-444c-9ff0-e0a6d7395470","added_by":"auto","created_at":"2025-11-10 05:42:59","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":99943,"visible":true,"origin":"","legend":"\u003cp\u003eFrequency of occurrence for various ranges of lost load (MVA) for the middle fault zone in Seattle sceanrio assuming powerlines will trip off when capacitiy exceeds (a) 125% and (b) 150%.\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-7753894/v1/4b08b10949c4d7c85ce622ef.png"},{"id":95504182,"identity":"d38fc933-a935-4e10-856d-27f762f85265","added_by":"auto","created_at":"2025-11-10 05:43:00","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":954034,"visible":true,"origin":"","legend":"\u003cp\u003eImpact of earthquake shaking on the electrical grid. The figure displays simulated power outages (colored circles indicating load loss) and failed transformers (blue crosses) for two earthquake scenarios. The top row shows the (a) worst-case and (b) average load loss contingencies for the M 7.2 Seattle fault zone scenario, while the bottom row depicts the (c) worst-case and (d) average load loss contingencies for the M 7.9 N. San Andreas scenario\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-7753894/v1/c1d64a35bf245fe02fc593be.png"},{"id":104397925,"identity":"7997b5c3-f751-4a2a-b85d-775cbf7a70ba","added_by":"auto","created_at":"2026-03-11 11:58:49","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4006904,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7753894/v1/21e493c3-05e8-4adf-a14d-2fbd53e659e1.pdf"},{"id":95528400,"identity":"bf93312e-1d57-4262-8add-74a8f551cd81","added_by":"auto","created_at":"2025-11-10 10:16:01","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":22386,"visible":true,"origin":"","legend":"Supplementary information - Impact of Large Power Transformer Bushing Seismic Vulnerability on the Electrical Grid","description":"","filename":"SupplimentaryinformationBushingfailureimpactongridlargescalev6.docx","url":"https://assets-eu.researchsquare.com/files/rs-7753894/v1/e5a124a0797956880f0a8fa7.docx"},{"id":95504153,"identity":"fc8bcee9-a53a-4ea0-817c-b4d9e7da4a96","added_by":"auto","created_at":"2025-11-10 05:42:59","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":158347,"visible":true,"origin":"","legend":"Supplementary Information - Algorithms","description":"","filename":"markuplanguageSeismicAlgorithms.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7753894/v1/77b8fbfff8b1f8ea2251bb84.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Impact of Large Power Transformer Bushing Seismic Vulnerability on the Electrical Grid","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eEarthquakes can devastate critical infrastructure and result in large scale outages [1]. The Los Angeles California Northridge earthquake of 1994, for example, was only rated a 6.7 on the moment of magnitude scale but resulted in power outages extending to Idaho, Utah, and Colorado [2]. Events like Northridge provide salient reminders on the importance of understanding how seismic events can disrupt the power grid [3]. Prior studies have predominantly focused on specific modes of failure for individual components [4], or on predicting wide spread impact to the grid using graph theory, statistical methods, and fragility curves [5\u0026ndash;8]. The importances of specific component vulnerabilities and their ripple effects on bulk grid outages, however, remains largely unstudied.\u003c/p\u003e\u003cp\u003eEarthquakes can impact many different power grid components such as power transformers [9], power lines [10], breakers [4], and power plants [11]. While all grid components are important, large power transformers are of particular interest due to their high cost and long lead times [12]. Protecting large transformer assets is of high importance to power utilities to ensure grid reliability and resilience. Historically, earthquakes have damaged large power transformers through bushing failures [13], anchor failures [14], oil conservator tank failures [15], and fires from oil leaks [15], all of which require replacing the transformer or major time-consuming repairs. Comparatively, bushing failures are by far the most frequent [9]. Several real-world examples of earthquakes like the 1986 North Palm springs and 1994 Northridge events, where the bushings of over 20 different 230 kV transformers failed, show how transformers are vulnerable to seismic events [16]. The 2008 Wenchuan earthquake damaged several 500 kV transformers, which were studied with finite-element analysis (FEM) post event by Ma et. Al. [15]. Their study found structural shortcomings in the bushings and the conservator oil tanks based on the typical earthquakes\u0026rsquo; input frequencies. The accelerations and bushing demand amplifications experienced were much greater than the seismic design standards IEEE 693 or GB 50260\u0026thinsp;\u0026minus;\u0026thinsp;2013 consider for bushing qualification. IEEE 693 recommends that bushings be qualified with a \u0026lsquo;fixed base\u0026rsquo; condition subjected to earthquakes that match twice the performance level response spectrum [17]. This recommendation assumes that the ground motion experienced by the bushing is amplified by the transformer tank and turret dynamics no more than two times. Many studies on transformer tank-turret-bushing dynamics suggest that bushing demand amplification can exceed a factor of two [9, 18, 19].\u003c/p\u003e\u003cp\u003eIn addition to individual device failure modes, others have studied the impact seismic activity has on the bulk grid. CIPCast was a tool developed to assess power grid seismic resilience based on component serviceability and grid connectivity post event [6]. It overlays earthquake intensity maps with the grid topology, qualitatively assesses power grid asset damage (for nodal points like substations and generators), and recovery rates (for connection points like power lines) over time. Nazemi et. Al. leveraged Monte Carlo sampling to randomly generate earthquake scenarios and studied how degraded (or failed) generation resources impacted the bulk grid [7]. The Monte Carlo simulation selected peak ground acceleration (PGA) values based on historic seismic hazard maps and used fragility curves to qualitatively assign varying degrees of functionality to generators on the power grid. The resulting power grid functionality was assessed using DC approximation. They found a combination of generation rebalancing and system reconfiguration enabled the fastest grid recovery. Espinoza et. al. leveraged a similar randomly generated earthquake scenario but included substations and generators degradation [8]. They studied component importance by granting specific generators or substations seismic immunity within the DC approximation grid simulations. They observed which substation immunities enhanced the grid\u0026rsquo;s ability to resist degradation the most. Ghafory-Ashtiany et. al. leveraged graph analysis methods to study the seismic impact on the Iranian grid [20]. They used fragility curves to consider the impact on substations, transmission lines, sub-transmission lines, and generators and developed resilience metrics that considered component damaged along with how the damaged component may affect downstream connections. Their scenarios tended to fail powerlines more frequently than generators or substations, although system connectivity (i.e., paths from generators to loads) was affected more significantly by generator or substation failures.\u003c/p\u003e\u003cp\u003ePrevious studies have tended to focus on one of two areas: specific component vulnerabilities or impacts on the bulk grid. To the authors best knowledge, no studies have attempted to bridge the gaps between these two realms by analyzing how specific component vulnerabilities cascade up into impacting the bulk power grid. This work attempts to address both issues by leveraging power flow simulation software coupled to dynamic finite element models (FEM) that analyze vibration coupling between power transformer tanks, turrets, and bushings. While the number of designs and interactions between the tank, turret, and bushing are complex, this work attempts to approximate the dynamics of a \u0026ldquo;typical\u0026rdquo; system within a given voltage class through parametric analyses using many reduced-order models (ROMs) based off a few actual transformer designs and running many bulk grid earthquake scenarios. The diversity and complexity of actual transformer-bushing system scattered through the grid might in some cases positively, and in other cases negatively, impact grid resilience. A large sample base of ROMs was used to average out how these nuances affect the bulk grid. Earthquake scenarios may then be linked directly to transformer bushing failures and used to understand how these vulnerabilities translate into best, average, and worst load loss outcomes.\u003c/p\u003e"},{"header":"2. Methodology","content":"\u003cp\u003eA unique four step methodology was developed to assess the impact bushings will have on the bulk grid. (1) selecting a grid model for which the analysis will be performed. (2) selecting an earthquake scenario and determining the shaking intensity at the base of each transformer. (3) build a contingency scenario by computing the seismic demand on the transformer bushings from the earthquake and determine whether the bushing exceeded its design qualification prescribed by IEEE 693 (via a random sampling of available ROMs performance under seismic demand). Lastly, (4) performing a bulk grid contingency analysis based on which transformers had assumed bushing failures (based on the seismic demand exceeding its design qualification in step 3). Steps 3\u0026ndash;4 were repeated to get a more statistically significant sample set. This section outlines how seismic demand on the transformer bushing was calculated, how contingency scenarios were generated, and how power grid contingency analysis was performed.\u003c/p\u003e\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1. Determining Seismic Demands on the Bushing and Identifying \u0026ldquo;At-Risk\u0026rdquo; Bushings\u003c/h2\u003e\u003cp\u003eTo determine if a bushing failed due to an earthquake would require an adequate understanding of the bushing properties, including the ultimate strength of each bushing, which requires testing the bushings to failure. While this data may be available for some bushings, little information is publicly available, and it would be a monumental undertaking to estimate the failure strength of each bushing in the grid. This study contends with this shortcoming by identifying the bushings (and therefore, the transformers) that are \u0026ldquo;at risk\u0026rdquo;. \u0026ldquo;At-risk\u0026rdquo; bushings are defined as those that experience a seismic demand greater than what they are qualified for per IEEE 693. Therefore, shaking intensity via peak ground acceleration (PGA) identified at the base of each transformer was used to calculate the amplification from the transformer base to the bushing and the resulting seismic demand on the bushing. It was assumed that every bushing within any given area was qualified per IEEE 693 to its associated seismic hazard level. If the bushing amplification was greater than it was qualified for, the transformer with the bushing in question was assumed to have failed and was taken out of service when performing power flow contingency analysis.\u003c/p\u003e\u003cdiv id=\"Sec4\" class=\"Section3\"\u003e\u003ch2\u003e2.1.1. Calculation of bushing amplification distributions\u003c/h2\u003e\u003cp\u003eCalculation of bushing demands requires ground motion at the base of each transformer and a structural analysis model (e.g., finite-element analysis models) for each transformer including the tank, turret, and bushing. Using the USGS ShakeMap scenario database [21], which provides spectral accelerations and velocities at 0.3, 1.0, and 3.0 sec periods (3.33, 1.0, and 0.33 Hz), an approximate response spectrum at the base of each transformer can be estimated for a specific earthquake scenario. However, each transformer is custom designed and acquiring structural models for each one in the grid would be virtually impossible. To address this challenge, a statistical distribution of transformer\u0026rsquo;s seismic response by voltage class was created using parametric analysis starting with a smaller sample population for which detailed drawings were available. Since bushing failures were the focus of this study, the acceleration amplification at the base of the bushing was chosen as the transformer response parameter. Three 138 kV and nine 345 kV designs were selected, and complex finite element models were developed for each using the commercial structural analysis software, SAP2000 (example shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Each transformer model closely approximated the stiffness and mass distribution of the represented components according to three-dimensional (3D) computer automated design (CAD) fabrication drawings, bushing seismic test data, and component cutsheets. Insulating oil was also considered in terms of both weight and hydrostatic pressure.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThese complex models were used to develop reduced order models (ROMs) in Idaho National Laboratory\u0026rsquo;s Multi-hazard Analysis for STOchastic time-DomaiN phenomena (MASTODON) application [22]. MASTODON is a MOOSE (Multiphysics Object-Oriented Simulation Environment) [23] application tailored for seismic analysis and risk assessment. These ROMs were used to perform parametric analysis and calculate the bushing amplification distribution for each kV class. The ROMs were created by idealizing the three main components of each transformer\u0026mdash;the tank, turret, and the bushing\u0026mdash;using a lumped mass stick model (LMSM; i.e., a stack of beam elements with masses lumped at the nodes) that replicates the first vibration mode of the component. The tank LMSM had the same height and total mass of the tank, and its stiffness was calibrated to achieve the tank natural frequency calculated by the SAP2000 model. The turret LMSM was created using the turret height, cross-section, and mass. The bushing LMSM was a single-degree-of-freedom structure with its mass equal to the air-side mass of the bushing, length equal to the distance between the base of the bushing and its center of mass, and the stiffness calibrated to replicate the fixed-base fundamental frequency of the bushing. Two zero-length rotational spring elements between the bushing and turret and the turret and tank were calibrated to replicate the mounted bushing frequency and the mounted turret frequency, respectively. These natural frequencies were calculated from a modal analysis of the SAP2000 models. After calibrating the LMSMs and the springs individually, they were stacked together to create the full ROM of the transformer as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. To further increase the sample size, all possible combinations of these ROM components were created in MASTODON. For example, since nine detailed transformer models were available in the 345 kV class, ROMs corresponding to all possible combinations of the nine tanks, turrets, and bushings were created, resulting in an extended population size to 9\u003csup\u003e3\u003c/sup\u003e=729. Since all the tanks, turrets, and bushings considered in these models were from real transformers, the parameterized ROMs were also assumed to be representative of real transformers.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eAfter developing the extended population of ROMs for each kV class, bushing amplifications for these ROMs were calculated. A broad spectrum Ormsby Wavelet was the input to each ROM and the bushing amplification was calculated as the ratio of the bending moment at the bushing mounted on the turret-transformer model to the same bushing mounted to a fixed base. Since all the ROMs are linear, the amplification ratio is the same regardless of the magnitude of the PGA. The amplification ratios for all the ROMs of the same kV are then used to build a voltage class specific bushing amplification distribution, from which transformer amplification responses to a PGA ground motion can be randomly sampled from.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section3\"\u003e\u003ch2\u003e2.1.2. Identification of \u0026ldquo;at-risk\u0026rdquo; bushings\u003c/h2\u003e\u003cp\u003eDuring a specific earthquake scenario, the following inequality check is performed for every bushing within the seismic zone to evaluate if it is at risk. If the check is true, the bushing is at risk. If the check is false, the bushing is not at risk.\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:SPG{A}_{i}\\cdot\\:{\\alpha\\:}_{ij}\u0026gt;QPG{A}_{i}\\cdot\\:2.0$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eHere, the SPGA\u003csub\u003ei\u003c/sub\u003e is the PGA at the base of the i\u003csup\u003eth\u003c/sup\u003e transformer for a specific earthquake scenario, α\u003csub\u003eij\u003c/sub\u003e is the j\u003csup\u003eth\u003c/sup\u003e sampling of the bushing amplification (from the amplification distribution of the corresponding transformer voltage class) for the i\u003csup\u003eth\u003c/sup\u003e transformer, and QPGA\u003csub\u003ei\u003c/sub\u003e is the PGA assumed at the transformer base during IEEE qualification testing. Since the bushing amplification is uncertain, a Monte Carlo sampling is performed from the amplification distribution for the corresponding transformer voltage class. Since the IEEE 693 qualification procedure assumes that all turret-transformers systems have an amplification no greater than 2.0, the peak acceleration that the bushing is qualified to is calculated as the transformer base PGA multiplied by 2.0. In the qualification process, the transformer base PGA can be either 0.5g (medium seismic hazard) or 1.0g (high seismic hazard), and therefore, bushings are typically qualified to a base acceleration of either 1.0g or 2.0g. This work assumes all transformers bushings were qualified to a base acceleration of 1.0g (medium seismic hazard).\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\u003ch2\u003e2.2. Translating parametric analysis into power grid contingencies\u003c/h2\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e provides a high-level summary of the input data and how it is processed to produce a power grid contingency. Python code intakes power model files (which also have GPS data linked to bus information), the number of contingency scenarios to be generated, ShakeMap scenario data, and amplification distributions. ShakeMap data was taken from USGS scenario database for the San Andreas (M 7.9 Scenario Earthquake \u0026ndash; N. San Andreas: SAN\u0026thinsp;+\u0026thinsp;SAP\u0026thinsp;+\u0026thinsp;SAS scenario) [24] and the middle Seattle (M 7.2 Scenario Earthquake \u0026ndash; Seattle fault zone-middle scenario) [25] and are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. Amplification distributions were calculated using the parametric analyses described in Section 2.1.1. The amplification ratios were generated for each transformer via MCS of their corresponding voltage class amplification distributions. A contingency file was created for each sampling with the list of transformers to remove from service. To account for the uncertainty in the amplification distributions, 2000 such contingencies were generated. To determine the number of contingencies, we conducted a convergence study. The analysis showed that there was no difference in power outage distributions between 2,000 scenarios to 10,000 scenarios. 2,000 scenarios were deemed adequate to achieve stable results without added computational expense.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003e2.3. Impact on the bulk grid\u003c/h2\u003e\u003cp\u003ePowerWorld Simulator 23 software was used to compute contingency analysis for a synthetic 10,000 bus system of the western United States [26, 27]. Once the contingency file (in .con format) was uploaded to PowerWorld, a custom monitor was used to trip off lines that exceeded 125% capacity or 150% capacity. This was done to prevent simulations that allowed unrealistic current flows through power lines. Simulation convergence was not always reached for contingencies that failed many transformers and tripped off many lines. For these contingencies, the amount of load lost reported prior to the software failing to converge on a solution (using Newton-Raphson method) was used. DC approximation solvers were not compatible with custom monitors in PowerWorld (i.e., despite being able to solve all contingencies they would not trip lines exceeding the capacity limit) and thus was not used. A custom aux script (i.e., a PowerWorld scripting language) extracted load flow data from each simulated contingency to provide the geolocation of each load not served due to the earthquake scenario and power line trip settings. Load loss and failed transformer locations were plotted on satellite image maps for different cases that aligned with the average and highest load (the lowest cases resulted in zero load loss, so no maps were generated). Distribution plots of the total load loss for the two different earthquake scenarios, assuming 125%-line trip and 150%-line trip settings were plotted along with the distributions of transformers lost by voltage class and MVA size. While the 10,000-bus system has many different voltage classes of transformers, the San Andreas California and Seattle Washington areas were only populated with only 138 kV and 345 kV large power transformers, thus these voltage classes will be the focus of this analysis.\u003c/p\u003e\u003c/div\u003e"},{"header":"3. Results","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\u003ch2\u003e3.1. Comparison between ROMs and high-fidelity models\u003c/h2\u003e\u003cp\u003eBefore performing the parametric study to calculate amplification distributions, the performance of the ROMs was benchmarked against SAP2000 to ensure comparable results. The benchmarking was done for each kV class (138 kV and 345kV) by comparing the percentage of samples for which the amplification was greater than 2 (shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). A good agreement for 345 kV was observed, but not for 138 kV. This is because only 3 high-fidelity models were available for the 138 kV class (which were expanded to 27 for the MASTODON ROMs as described in Section 2.1) and therefore, there is not a large enough sample size to enable a reasonable comparison. Nevertheless, given that the first modes of the tank, turret, and bushing were captured explicitly, ROMs could still be considered representative of real 138 kV transformers for this demonstrative study. 138 kV transformers are not considered in IEEE 693 because historically they have not exhibited much seismically vulnerable. While the small SAP2000 model sample size shows these transformers as more problematic, the expanded ROMs likely produced a more realistic result with fewer 138 kV transformers showing concern (see section 3.2 and 3.3).\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eComparison of amplifications calculated using MASTODON ROMs and high-fidelity finite element SAP2000 models.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eClass\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMASTODON\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eSAP2000\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e138\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e11%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e67%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e345\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e96%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e100%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\u003ch2\u003e3.2. Transformer Bushing Amplification\u003c/h2\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e shows the different amplification distributions generated from parametric analyses. The 138 kV voltage class shows an 11.1% chance of exceeding the 2x industry standard with mean amplification of 1.42x and a maximum amplification of 2.39x. The 345 kV transformers, on the other hand, have a much larger structure and mass which can allow for some amplifications greater than 20x. 345 kV transformers show a 91.2% likelihood of exceeding the 2x industry standard with a mean amplification of 4.63x.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003e3.3. Impact on Bulk Grid\u003c/h2\u003e\u003cp\u003eFor the two scenarios chosen, the 10,000-bus eastern interconnect contained only 138 kV and 345 kV transformer types. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows the frequency of transformer failures by voltage class. In both the San Andreas and Seattle cases, few 138 kV transformers failed (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea). This is attributed to 138 kV transformers having low application distributions (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e) and smaller population sizes in both areas. The San Andreas area contained 123 138 kV and 215 345 kV transformers. The Seattle Washington area contained 44 138 kV and 110 345 kV transformers. In each case, 138 kV transformers only accounted for 36% (San Andreas) and 28% (Seattle) of the total assessed transformer populations. These results are also consistent with the fact that 138 kV transformers are not considered seismically vulnerable and thus excluded from IEEE 693 requirements. Conversely, the structural properties of 345 kV transformers lend themselves to more sever seismic amplification (see Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e), are subject to IEEE 693 requirements, and exhibited more failures across the 2000 generated contingencies shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows the number of failed transformers based on MVA size. Most cases exhibit 0\u0026ndash;4 transformer failures in sizes ranging from 0-199 MVA, 400\u0026ndash;599 MVA, and 600\u0026ndash;799 MVA. This was attributed to smaller population sizes of these transformer sizes for their respective locations. Most transformer failures were 345 kV as seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb where 25% and 40% of scenarios contained no 138 kV failures for San Andreas (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ea) and Seattle Middle (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eb), respectively. Interestingly, the smaller sizes ranging from 0-199 MVA and 200\u0026ndash;399 MVA were the most frequent failures in San Andreas (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ea). The Seattle scenario (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eb) shows only 200\u0026ndash;399 MVA transformer size as the dominate failure type. These trends were attributed to the smaller transformer MVA sizes being the most dominant population in these areas and may also help explain how many scenarios resulted in lower load loss from Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e shows the frequency of occurrence vs the range of lost load for the San Andreas fault scenario assuming power lines trip offline after exceeding 125% or 150% of their capacity. Both cases showed 0\u0026ndash;50 MW bin as the most frequent with 7.2% and 11.7% likelihood for the 125% (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ea) and 150% (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eb) trip cases, respectively. While not shown explicitly in the figure, this 0\u0026ndash;50 MW bin was mostly composed of scenarios exhibiting no load loss. As expected, the 125% trip case showed the highest second most likely next bin between 301\u0026ndash;350 MW at 4.58% likelihood compared to the 201\u0026ndash;250 MW at 5.9% for the 150% trip case. This was likely due to the 125% trip scenario taking lines out of service sooner compared to the 150% trip case. Both cases show a positive skewed distribution with an impulse around the 0\u0026ndash;50 MW bin. While the positive skew is a good thing in that it favors smaller power outages, the amount of load loss is still relatively high. For the 125% trip case, the likelihood of an outage causing some amount of load loss between 201\u0026ndash;600 MW is 25%. This is only reduced to 23% for the 150% trip case.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e shows the frequency of load lost vs the range of lost load for the Seattle middle fault zone also assuming power lines trip offline after exceeding 125% or 150% of their capacity. Unlike San Andrase neither case showed 0\u0026ndash;50 MW bin as the most frequent or second most frequent with 2.4% and 10.6% likelihood for the 125% and 150% trip cases, respectively. Like the previous case, the 125% trip case showed higher load loss potential with the 351\u0026ndash;400 MW bin with a 26.2% likelihood of occurrence and the 151\u0026ndash;200 MW bin at 14.6% for the 150% trip case. The Seattle case shows a much tighter grouping of outages compared to the San Andrase case. This is attributed to the failure of more transformers supporting loads being centralized in the earthquake epicenter. Both cases show a positive skewed distribution like the San Andreas case. Compared to the San Andreas case the likelihood of an outage causing some amount of load loss between 201\u0026ndash;600 MW is 65% for the 125% outage and is only reduced to 50% for the 150% trip case. These results warrant serious consideration of transformer resilience against seismic events. They also illustrate the impact of how changes in grid topology can impact the severity of power outages during an earthquake.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e shows satellite maps with the coordinates of lost load (circles) and transformers (blue Xs) plotted for both average and worst-case scenarios of the 150% trip case. The satellite images provide an alternative means to understand the effects of the two seismic scenarios. As expected, the most concentrated areas of load loss and transformer failures occurred near the earthquake epicenters (see Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). However, in the worst-case scenarios, the impacts extended well beyond the epicentral regions. With few exceptions, most of the transformer failures occurred around the epicenters. The main differences between the worst-case scenarios and average case scenarios were the size and number of the transformers that were taken offline. Larger sized transformers supporting greater amounts of load and were likely connected to critical powerline corridors, which contributed to the cascade further outside the epicenter.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eThese results demonstrate the potentially devastating effect large earthquakes could have on the power grid. While not a real grid, the 10,000 bus model was designed to have similar properties of a real grid [26, 27]. Actual transmission grids in California and Washington are not purely composed of 138 kV and 345 kV transformers. Other voltage classes, such as 230 kV, are more commonly represented. A more accurate transformer voltage class distribution within the synthetic grid would create a better picture of the actual impact of a significant seismic event. Moreover, this study does not account for remedial actions taken by grid operators to minimize load loss.\u003c/p\u003e\u003cp\u003eDespite including 138 kV transformers in this study, it should be noted that 138 kV transformers are not held to the same standard as voltages above 138 kV in IEEE 693 [17]. 138 kV was listed as the cutoff for seismic amplification testing. Our results corroborate this finding, as Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows that the maximum number of 138 kV transformer failure in any given scenario was four, with many scenarios showing zero failures. Conversely, the 345 kV transformer voltage class failed 15\u0026ndash;19 and 30\u0026ndash;34 on average for the San Andrase and Seattle Middle scenarios, respectively (see Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea-b). Additionally, the amplification distribution plots in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e show 138 kV transformers exhibiting lower amplification ratios compared to 345 kV transformers.\u003c/p\u003e\u003cp\u003eWhile these results do not directly demonstrate imminent disaster given the limitations mentioned above, it does, however, show that a component vulnerability (like bushing amplification) can lead to large scale grid impact. In this regard, this work serves as a call to serious consideration of component-level vulnerabilities in the power grid and the consequential threat from large seismic events. Many of the scenarios above resulted in zero load loss (i.e., a large number of contingencies comprising the 0\u0026ndash;50 MW bins of Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e showed no load loss) and the likelihood of zero load loss never exceeded 15%. The median load loss depends on powerline trip settings. For the 125%-line trip setting both earthquake scenarios predicted load loss ranging from 351\u0026ndash;400 MW as the most likely case. For the 150%-line trip settings, both scenarios show similar outcomes of 201\u0026ndash;250 MW and 151\u0026ndash;200 MW load loss as most likely for the San Andreas and Seattle Middle case, respectively. In both cases, the amount of load loss would be considered significant from a utility perspective.\u003c/p\u003e"},{"header":"5. Summary and conclusions","content":"\u003cp\u003eLarge power transformers are critical assets for the power grid and cannot be quickly replaced after a sudden failure. This study presents a novel methodology for studying how seismic activity impacts the bulk power grid through bushing failures on power transformers. Complex models built in SAP2000 were used to tune ROMs, the core components of which were mixed and matched to expand the sample set. The expanded ROMs were then used to generate amplification distribution histograms based on transformer voltage class. These distributions showed 138 kV transformers had an 11% chance of exceeding 2x amplification (1.42 mean amplification) whereas 345 kV exhibited a 91.2% chance (4.63 mean amplification). The 138 kV results was consistent with the fact that they do not pose as much of a seismic risk due to their smaller size and are thus not required to meet the same standards of IEEE 693 imposed on larger transformer voltages. Random sampling of these amplification distributions was used to determine which transformer was at risk of failure for a given earthquake scenario. 2,000 contingency scenarios were created to study the seismic impact to the synthetic 10,000 bus Western interconnect. The San Andreas scenarios showed 0\u0026ndash;50 MW of lost load was the most likely case at 7.2% and 11.7% likelihood for cases where ampacity power line trip settings were set to 125% and 150%, respectively. The Seattle Middle case showed the most likely loss ranging from 351\u0026ndash;400 MW (26.2% likelihood) and 151\u0026ndash;200 MW (14.6% likelihood) for the 125%- and 150%-line trip cases, respectively. These results closely corresponded to the next most likely load loss scenarios for the San Andreas 125%- and 150%-line trip setting (351\u0026ndash;400 MW (4.85% likelihood) and 201\u0026ndash;250 MW (5.9% likelihood), respectively). The amount of lost load observed in these cases was significant, however this study has some limitations. 1) 138 kV transformers are not held to the same standards as higher voltage class transformers (but were evaluated according to IEEE 693 for this study). 2) The frequency of transformer voltage class within the San Andreas and Seattle areas do not closely align with reality (only containing 138 kV and 345 kV transformer as the largest voltage classes). 3) Grid operator remedial actions were not considered, which could potentially preserve more grid functionality during a natural disaster. 4) Power flow simulation convergence was often not reached due to many transformers being taken out of service and resulting power lines tripping offline. The final reported load loss before the power flow software failed to converge was used. While this study does not directly predict eminent disasters from a significant seismic event, it does suggest that a potentially significant threat to the grid exists, and a more detailed investigation is warranted. Moreover, this study also supports a growing body of work that suggests transformer tank-turret-bushing amplification dynamics can easily exceed the 2x industry standard for large power transformers.\u003c/p\u003e"},{"header":"6. Future work","content":"\u003cp\u003eThis study could improve if performed on a more realistic synthetic power grid that includes a more significant population of 230 kV transformers and some 500 kV transformers. This work plans to leverage the California Test System for future studies because it includes a wider variety of transformer voltage class types [28]. Additionally, power grid simulation convergence was a significant issue due to the removal of many grid elements in a single contingency. This work plans to modify contingency files to progressively solve the mode after removing a limited number of elements rather than attempting to solve with all the elements removed at once. Additionally, leveraging experimental data to improve the accuracy of SAP models is needed. A jointly funded project by DOE-CESER and DOE-OE-TRAC led by Idaho National Laboratory plans to experimentally test seismic response (via shake table) of an oil filled 230 kV large power transformer. This test will provide the first ever full-scale experimental data to inform FEM studies on transformer tank-turret-bushing interactions. The experimental data can be used to improve the accuracy of simulated large power transformer failure probabilities during a seismic event. This work plans to leverage this experimental data to improve transformer failure likelihood estimates from seismic events on large grid simulations.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAcknowledgements\u003c/h2\u003e\n\u003cp\u003eThis work was supported through the INL Laboratory Directed Research \u0026amp; Development (LDRD) Program under DOE Idaho Operations Office Contract DE-AC07-05ID14517.\u003c/p\u003e\n\u003ch2\u003eAuthor Contributions\u003c/h2\u003e\n\u003cp\u003eAkram Batikh contributed ROM modeling, data analysis, python scrip methodology and writing, and manuscript writing; Bjorn Vaagensmith\u003csup\u003e\u0026nbsp;\u003c/sup\u003econtributed to the concept formulation, python code methodology, power systems modeling, aux script writing, manuscript writing, funding acquisition, and project supervision; Jon Bender contributed to concept formulation, python code methodology, SAP 2000 modeling, and funding acquisition; Chandrakanth Bolisetti contributed to the concept formulation, python scrip methodology and funding acquisition; Alexander Harvey\u003csup\u003e\u0026nbsp;\u003c/sup\u003econtributed python code methods and writing; Joeseph Liebergen\u003csup\u003e\u0026nbsp;\u003c/sup\u003econtributed to python code methods and writing; Hassan Khan contributed to python code methods and writing, and Mihai Diaconeasa contributed to manuscript reviewing, manuscript editing, review of methods, and supervision.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003eDeclaration of Competing Interest\u0026nbsp;\u003c/h2\u003e\n\u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. The authors declare that they are bound by confidentiality agreements that prevent them from disclosing SAP 2000 models of actual transformers deployed in the grid used in this work.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eA. Mate, T. Hagan, E. Cotilla-Sanchez, T. K. A. Brekken, and A. V. Jouanne, \u0026quot;Impacts of Earthquakes on Electrical Grid Resilience,\u0026quot; in \u003cem\u003e2021 IEEE/IAS 57th Industrial and Commercial Power Systems Technical Conference (I\u0026amp;CPS)\u003c/em\u003e, 27-30 April 2021 2021, pp. 1-5, doi: 10.1109/ICPS51807.2021.9416632. \u003c/li\u003e\n\u003cli\u003eA. Schiff, \u0026quot;Lessons from the 1994 Northridge earthquake in California,\u0026quot; \u003cem\u003eIEEE Power Energy Mag, \u003c/em\u003evol. 9, no. 2, pp. 46-51, 2011.\u003c/li\u003e\n\u003cli\u003eA. F. 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Roald, \u0026quot;California Test System (CATS): A Geographically Accurate Test System Based on the California Grid,\u0026quot; \u003cem\u003eIEEE Transactions on Energy Markets, Policy and Regulation, \u003c/em\u003evol. 2, no. 1, pp. 107-118, 2024, doi: 10.1109/TEMPR.2023.3338568.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"large power transformers, bushings, earthquakes, grid resilience","lastPublishedDoi":"10.21203/rs.3.rs-7753894/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7753894/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eNumerous studies suggest that the Pacific Northwest Subduction and the San Andreas Fault systems are past due for a severe seismic event. In the time that has passed since the last highly destructive event near an urban area (Northridge, 1994, M6.7), major changes to our electrical grid have introduced uncertainty in the impact such an event would have on critical infrastructure. While design practices have improved since 1994, the seismic vulnerability of large power transformers remains in question. These critical substation components are essential for power delivery but are extremely expensive and becoming difficult to procure with lead times that can be as long as five years. Thus, it is essential to understand the seismic risk transformers represent to the bulk electrical grid where bushing failure was of primary concern. This work presents a parametric study of the commonly used high voltage transformer-bushing systems on the 10,000 synthetic bus system (138kV and 345kV), from which the probability of a given transformer bushing to exceed design amplification standards was used to approximate whether the transformer would fail during a seismic event. These risk values are then applied to the 10,000 synthetic bus system of the western interconnect through Monte Carlo sampling. Depending on line protection settings, the resulting showed 7.2\u0026ndash;11.7% and 2.4\u0026ndash;10.7% of cases did not exhibit load loss for San Andre\u0026rsquo;s and Seattle Washington, respectively. However, 80.5\u0026ndash;89.8% and 88.6\u0026ndash;91.1% of cases exhibit losses greater than 100 MW of lost load for the San Andrase and Seattle Washington areas, respectively.\u003c/p\u003e","manuscriptTitle":"Impact of Large Power Transformer Bushing Seismic Vulnerability on the Electrical Grid","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-10 05:42:54","doi":"10.21203/rs.3.rs-7753894/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"c9df1651-0611-469c-ad36-2cca7187b8d0","owner":[],"postedDate":"November 10th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":57515288,"name":"Physical sciences/Engineering/Energy infrastructure/Energy grids and networks"},{"id":57515289,"name":"Physical sciences/Engineering/Civil engineering"},{"id":57515290,"name":"Physical sciences/Energy science and technology/Energy modelling"},{"id":57515291,"name":"Physical sciences/Engineering/Electrical and electronic engineering"}],"tags":[],"updatedAt":"2026-02-26T17:56:04+00:00","versionOfRecord":[],"versionCreatedAt":"2025-11-10 05:42:54","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7753894","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7753894","identity":"rs-7753894","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}