Probabilistic seismic assessment of seismically isolated electrical transformers considering vertical isolation and vertical ground motion

Engineering Structures 152 (2017) 888–900

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Probabilistic seismic assessment of seismically isolated electrical transformers considering vertical isolation and vertical ground motion Shoma Kitayama a,⇑, Donghun Lee a, Michael C. Constantinou a, Leon Kempner Jr. b a b

Department of Civil, Structural and Environmental Engineering, University at Buffalo, State University of New York, Buffalo, NY 14260, USA Bonneville Power Administration, Vancouver, WA, 98662, USA

a r t i c l e

i n f o

Article history: Received 29 May 2017 Revised 9 August 2017 Accepted 4 October 2017

Keywords: Electrical transformer Seismic isolation Three-dimensional isolation Vertical motion Risk assessment Failure probability

a b s t r a c t This study presents a probabilistic response analysis of seismically isolated electrical transformers with emphasis on comparing the performance of equipment that are non-isolated to equipment that are isolated only in the horizontal direction or are isolated by a three-dimensional isolation system. The performance is assessed by calculating the probability of failure as function of the seismic intensity with due consideration of: (a) horizontal and vertical ground seismic motions, (b) displacement capacity of the seismic isolation system, (c) limit states of electrical bushings, (d) details of construction of the isolation system, (e) weight of the isolated transformer, and (f) bushing geometry and configuration. Calculations of the probability of failure within the lifetime of isolated and non-isolated transformers at selected locations are also performed. The results of this study demonstrate that seismic isolation systems can improve the seismic performance for a wide range of parameters and that systems which isolate in both the horizontal and vertical directions can be further effective. The seismic assessment methodology presented can be used for: (a) deciding on the need to use seismic isolation and selecting the properties of the isolation system for transformers depending on the design limits, location, and configuration of transformer and (b) calculating the mean annual frequency of functional failure and the corresponding probability of failure over the lifetime of the equipment. The results may also be used to assess the seismic performance of electric transmission networks under scenarios of component failures. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Electric power systems are important elements of the infrastructure. They are expected to supply electricity at any time, to have low vulnerability to disasters and to be resilient. Empirical evidence in past earthquakes demonstrates that electrical equipment is vulnerable to earthquakes and several have been reported damaged worldwide [1–5]. Failure to supply electricity following an earthquake causes degradation of public safety and quality of life, and results in economic losses. Estimated immediate economic losses in earthquakes such as the 1993 Kushiro-Oki, Japan, 1994 Northridge, USA, 1995 Kobe, Japan, 1999 Kocaeli, Turkey and the 1999 Chi-Chi, Taiwan were in the range of hundreds of millions of dollars for each event just due to interruption of electric power [6,7].

⇑ Corresponding author at: Department of Civil, Structural and Environmental Engineering, 212 Ketter Hall, University at Buffalo, State University of New York, Buffalo, NY 14260, USA. E-mail address: [email protected] (S. Kitayama). https://doi.org/10.1016/j.engstruct.2017.10.009 0141-0296/Ó 2017 Elsevier Ltd. All rights reserved.

The electric power system consists of generating stations, transmission lines and distribution lines. Electrical transformers for step-up and step-down are located in-between these elements [8]. The key component of an electrical transformer is the high voltage bushing that is mounted on top of the transformer and provides electrical connection between the high-voltage lines and the transformer [9]. Bushings are most vulnerable to seismic shaking [7,8] so that many efforts have been undertaken in academia and the industry to develop means of seismically protecting the bushings and the transformers [8,10–13]. Past studies of the seismic performance of electrical equipment demonstrated that horizontal isolation systems can improve the seismic performance in terms of reduction of absolute horizontal acceleration and relative displacement of bushings and of the transformer body (e.g., [8,11,12]). These studies, however, (a) did not consider the effect of vertical ground motion or showed that the vertical ground motion was transmitted unchallenged through the horizontal isolation system, including some amplification, and (b) did not relate the reduction of the seismic performance index (e.g., acceleration at the bushing’s center of mass) to the prevention of failure of the bushing or failure of the transformer itself.

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Moreover, other experimental studies [14,15] investigated the failure modes of electrical bushings but did not relate the findings of component failure to the seismic response of transformers. The vertical ground motion affects a seismically isolated structure by (a) altering the behavior of the isolation system in the horizontal direction, and (b) magnifying (or at best not modifying) the vertical response of the structure above the isolators. The first effect is well documented and understood for sliding seismic isolation systems. For example, a review of the shake table test data reported in [8,16–18] for the friction pendulum isolation system reveals that the vertical earthquake causes a general increase in lateral forces, accelerations and drift (for strong excitation by an average of 15% but could be much larger for special cases) and that this increase is well predicted by analysis models. The earthquake vertical acceleration also has important effects on the lateral acceleration of structures isolated by elastomeric (lead-rubber) isolation systems as reported in [18–21], although we currently lack analytical models capable of predicting these effects. In general, the vertical excitation has insignificant effects on the isolation system displacement demands. The second effect mentioned above is documented in experimental studies [8,18,20,21]. For sliding isolation systems which are vertically very stiff, the vertical acceleration is transmitted through the isolators with minor modification. It is then magnified in the vertically flexible components above the isolators leading to large vertical response and potential for damage to secondary systems. In elastomeric isolation systems which have some limited vertical flexibility, there is magnification of the vertical acceleration directly above the isolators and then further magnification in vertically flexible components. In general, it is well understood that current seismic isolation systems do not provide any protection in the vertical direction. Providing for an effective vertical isolation system comparable to horizontal seismic isolation is a challenge. The main difficulty comes from the fact that the vertical isolation system must support the weight of the structure with limited static deflection so it becomes impractical to provide a sufficient low vertical frequency without excessive static deflections. A significant effort in Japan resulted in the development of three-dimensional seismic isolation systems by each of the large construction companies. These efforts are documented in [22] for applications related to nuclear structures and in [23] for buildings. These systems are often very complex consisting of combinations of air springs, elastomeric isolators, active components, vertical and horizontal coil spring and dampers. In the simplest and practical configurations, the systems consist of elastomeric isolators for horizontal isolation and a coil spring-damper system for vertical isolation, with the two separated by a stiff base. Additional vertical elements together with a stiff base ensure that there is no rocking in the isolation system. Typically, the vertical isolation system is stiff and highly damped but at least one tested design had the vertical frequency equal to 0.5 Hz, resulting in a static displacement of 1 m. Such an isolation system has a height of nearly 4 m, which is impractical. None has been implemented. Some of the systems developed in Japan were intended for use in equipment. Given the light weight of equipment, the horizontal isolation system took forms of low friction sliding bearings and horizontal coil springs or multistage elastomeric bearings in order to achieve sufficiently low horizontal frequency-about 0.5 Hz. The resulting horizontal-vertical isolation systems were complex and of considerable height. They are considered impractical for use in electrical transformers where the height of the isolation system is important to be within acceptable limits so that easy access to the equipment is not compromised. Such considerations led to an effort at the University at Buffalo, funded by the Bonneville Power Administration (BPA), to develop a compact three-dimensional

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seismic isolation system for electrical transformers of weight in the range of about 1300 kN to 3500 kN, using readily available technologies. The system developed and tested consists of four triple friction pendulum isolators, each placed on top of a vertical coil spring-linear viscous damper assembly that is restrained by a telescopic system to only move vertically. This system allows for unrestrained rotation (rocking) of the isolation system. Another version of the system employs a stiff base in-between the friction pendulum isolator and the vertical spring-damper system so that rocking is restrained. The version of the system without the added stiff base is preferable as it is easier to implement, including the option of embedding the vertical spring-damper system in the foundation so that there is minimum gain in the transformer height. This paper presents procedures for the analysis and results of an analytical study of the performance of electrical transformers with particular emphasis on comparing the options of a non-isolated transformer to one isolated only in the horizontal direction or a transformer with a three-dimensional isolation system. The isolation systems considered are those developed in the BPA-funded project and do not include any other possible alternatives. Details will be provided later in this paper. An important feature of this study is that the vertical ground motion is included in the analysis. The study uses incremental dynamic analysis (IDA) [24], which gradually scales up a large number of ground motions, conducts nonlinear response history analysis for each set of scaled motions and calculates the number of times that a specified limit state (or states) is reached. The data are used for constructing fragility curves (probability of functional failure versus the seismic intensity) based on procedures in FEMA P695 [25], and then the probability of failure over the lifetime of equipment is calculated using procedures in FEMA P58 [26]. The numerical model of the analyzed transformers is based on information acquired in the testing of components of electrical transformers [5,14,15]. The limit states used to describe functional failure of transformers are based on information for the field performance of electrical equipment in past earthquakes ([27–30]). Particularly, [28] reports on the development of empirical fragility curves for conventionally supported electrical equipment which are used in seismic vulnerability assessments by electric utility companies in a program called SERA [28,29]. Information utilized in program SERA for non-isolated electrical transformers is used in this study to calibrate the failure model, which is then used for constructing fragility curves for seismically isolated transformers.

2. Methodology for seismic performance evaluation IDA [24] is conducted for a set of ground motions, each one of which consists of a horizontal and a vertical component as originally recorded and progressively increased in intensity while maintaining the original ratio of peak vertical to peak horizontal acceleration. The intensity is defined as the peak value of the horizontal ground acceleration, the PGA, or per the terminology used in IEEE seismic design standard [31], the zero-period acceleration ZPA. Failure is defined when either the bushing transverse and longitudinal accelerations reach certain limits (based on calibration of the model using field empirical data) or the displacement of the isolators exceeds their stability limit either by too much horizontal displacement or too much uplift, whichever occurs first. The fragility curves (cumulative distribution functions) are then generated from information obtained in the IDA and analytical descriptions of the fragility curves are obtained by fitting the data with lognormal representations. The fragility curves present the probability of failure (i.e., the probability of exceeding a threshold of either acceleration or isolator displacement) versus the PGA, where the probability of failure is determined at each PGA level as the number of

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analyses that resulted in failure divided by the total number of analyses. Note that the presentation of the fragility curves (probability of failure versus the intensity of ground motion) is based on the use of the PGA for the measure of ground motion intensity. This differs from the approach in FEMA P695 [24] where the intensity is measured by the spectral acceleration at the fundamental period of the studied system. The use of PGA as the intensity measure is considered appropriate in this study because: (a) PGA is the ground motion intensity measure typically used in fragility analysis of electrical equipment ([27,32,33]), (b) it allows for calibration of the bushing failure model based on empirical fragility data that use PGA as the measure of seismic intensity and (c) it allows the presentation of fragility analysis results when the analyzed system has two distinct and important modes of vibration at two very different frequencies (horizontal and vertical). In the analysis, the following parameters are calculated: (1) PGAF: The median value of PGA of each of 40 ground motions (described in Section 3) that cause failure of the transformer. (2) b: Dispersion factor that is calculated as the standard deviation of the natural logarithm of the values of PGA causing failure of the transformer. The analytical fragility curve (cumulative distribution function or CDF) is calculated as:

Z CDFðxÞ ¼ 0

x

" # 2 1 ðln s  ln PGAF Þ pffiffiffiffiffiffiffi exp  ds 2b2 sb 2p

ð1Þ

The fragility curves present information on the probability of failure for specific levels of earthquake intensity as measured in this work by the PGA. However, engineers, utility officials, government officials, owners and insurers are interested in assessing risk, defined in this case as the mean annual frequency of failure, kF [26]. This kF is related to another important parameter, the probability of failure for a given number of years, n, or PF(n years) [26]. Assuming that the earthquake occurrence follows a Poisson distribution, the following equation relates kF to PF(n years):

PF ðnyearsÞ ¼ 1  expðkF nÞ

ð2Þ

The calculation of the kF requires consideration of the hazard from all possible seismic events. The hazard data are obtained from the website of the United States Geological Survey [34] in the form of the annual frequency of exceedance kPGA as function of the PGA for the specified site location and the soil condition. The calculation of the mean annual frequency of failure, kF, requires integration of the failure fragility of the structure over the seismic hazard curve [35]:

Z kF ¼ 0

1

   dkPGA    dðPGAÞ ðP F jPGAÞ dðPGAÞ

ð3Þ

In Eq. (3), |dkPGA/d(PGA)| is the absolute value of the slope (tangent) of the seismic hazard curve. Seismic hazard curves for three selected locations in Western US are presented in Fig. 1. The IEEE 693 standard [31] defines the life of equipment as over 30 years. Accordingly, sample calculations of probabilities of failure over the lifetime of the equipment are performed for 50 years of lifetime (i.e., n = 50 in Eq. (2)) for the locations in Fig. 1. 3. Selection and scaling of ground motions The procedures in FEMA P695 [24] only include the horizontal components of ground motions but the analysis conducted in this study requires that vertical components are also included. This is essential in assessing the performance of the combined

Fig. 1. Seismic hazard curves used in this study.

horizontal-vertical isolation systems. Far-field horizontal ground motions were selected from the suite of motions used in FEMA P695 [25] and the corresponding vertical components were obtained from the PEER website [36]. The vertical components of two ground motion sets (Superstition Hills in Poe Road Station and Cape Mendocino in Rio Dell Overpass Station) were not available. Accordingly, these two sets of motions were removed from the suite and a total of 20 ground motion sets (each consisting of two horizontal and one vertical components) were used. These resulted in a total of 40 pairs of combined horizontal and vertical ground motion histories for use in the analysis. Details of these ground motions can be found in [25,37]. The earthquake magnitude of the motions is in the range of 6.5–7.6 with an average of 7.0, and the sites are characterized as very stiff to stiff soil sites. The scaling method used in this study is to increase the PGA of the horizontal component of each pair of horizontal-vertical motions while keeping the vertical to horizontal peak acceleration ratio the same as in the originally recorded motion. The scaling approach for the horizontal component is similar to the Sa-Component Scaling approach in FEMA P695 [25]. The scaled motions are used to repeatedly analyze the transformer model with the peak acceleration of the horizontal component of each pair increased by increments of 0.05 g until failure occurred.

4. Modeling of electrical transformers The transformer model used in the analysis was developed in program OpenSees [38] with due consideration for the ultimate behavior of the isolation bearings. Some details are provided below-the interested reader is referred to [37] for more details. Fig. 2 illustrates a bushing and its model, and defines its parts and dimensions (not in scale). The parameters to describe the behavior are based on [14,15] and the modeling is based on recommendations in [5,39]. These include treating the transformer body as rigid and incorporating the effects of any possible body flexibility in the assumed value of the as-installed bushing frequency. The bushing is divided into upper and lower parts that are separated by a plate to which the bushing is connected. This plate is shown in Fig. 2 to have a thickness 2HF. Other geometric parameters are: HUB is the length of the bushing’s upper part, HLB is the length of the bushing’s lower part, HCM_UB is the distance of the flange to the center of gravity of the bushing’s upper part, HCM_LB is the distance of the flange to the center of gravity of the bushing’s lower part, mUB is the mass of the bushing’s upper part, mLB is the mass of the bushing’s lower part and mCH is the mass of the connection housing. Data in [14,15] for several bushings include geometric

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Fig. 2. Model of bushing: (a) Illustration of bushing; (b) Fixed condition model; (c) As-installed condition model.

properties, mass and frequencies of free vibration when installed fixed (called fixed frequency, fFix: fixed at the point of mCH in Fig. 3) and when installed connected to a flexible plate (called as-installed frequency, fAI: top plate of transformer has flexibility in vertical and rotational directions). Table 1 presents information on the properties of three bushings that are considered in this study. The range of the as-installed frequency of these three bushings represents the normally expected range. Data for additional bushings including an unusually flexible one are provided in [37] together with fragility analysis results. The development of the model for analysis requires the selection of the rotational and vertical stiffness of springs at the interface of the bushing model to the plate as shown in Fig. 2(c) (a horizontal spring at the same location has very large stiffness).

The moment of inertia IUB is selected (having assumed arbitrary Young’s modulus EUB) so that the bushing model when fixed to the plate has a fundamental frequency equal to the fixed frequency fFix (Fig. 2 (b)). The rotational stiffness Kh is then selected so that the rocking frequency of the bushing in the complete model is equal to the as-installed frequency fAI. The vertical stiffness of the spring KV representing the plate is then selected so that the vertical frequency of the bushing is equal to 15 Hz based on observations reported in [14,15] where this frequency was reported as being in the range of 10–20 Hz. Details of the calibration procedure are presented in [37]. The model of the transformer was constructed based on [8]. The representation of the transformer is two-dimensional with horizontal, vertical and rotational degrees of freedom. Fig. 3 illustrates

Fig. 3. Two-dimensional transformer models: (a) Fixed base (non-isolated); (b) Horizontally isolated; (c) Horizontally-vertically isolated models.

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Table 1 Properties of three bushings used in this study (after [14,15]).

Voltage capacity Total height Length over mounting flange: HUB Length below mounting flange: HLB Total weight Upper bushing weight: mUBg Location of upper bushing center of gravity: HCM_UB Lower bushing weight: mLBg Location of lower bushing center of gravity: HCM_LB Connection housing weight: mCHg Weight per unit length Distance to the flange (half of center pocket): HF Fixed frequency: fFix As-installed frequency: fAI Material of insulator

Unit

Bushing 3

Bushing 6

Bushing 8

kV meter meter meter kN kN meter kN meter kN kN/m meter Hz Hz –

550 6.22 4.95 1.27 12.5 9.59 2.23 2.46 1.50 0.44 1.94 0.29 9.36 4.25 Porcelain

196/230 3.85 2.32 1.52 3.74 1.99 0.86 1.30 0.71 0.44 0.86 0.34 21.00 11.25 Porcelain

550 6.48 4.83 1.65 9.70 6.98 2.16 2.27 0.99 0.44 1.43 0.29 9.35 7.70 Porcelain

the three transformer models considered: (a) fixed-base or non-isolated, (b) isolated only in the horizontal direction and (c) isolated in the horizontal and vertical directions. The elastic beam elements representing the transformer frame are designated rigid. Only flexible elements are those representing the bushing (see Fig. 2). Mass is lumped at joints as shown in Fig. 3. Each model represents half of a transformer. Each model contains one bushing modeled with the representation of Fig. 2(c) with an angle of inclination h equal to zero (vertical bushing) or 20 degrees (inclined bushing). The height and length (or width) of the transformer are denoted as HT and LT, respectively. Note that HT is the height to the center of mass of the transformer body. Similarly, HC, HTFP and HSD are the heights from the ground to the center of mass of concrete base (platform that the transformer sits on above the isolation system), the mid-height of the triple friction pendulum isolators (hereafter, triple FP) and the mid-height of the springdamper units, respectively. The mass of the body of the transformer (excluding the bushing) is 2 mT and is considered lumped at two locations. For the isolated transformer there is additional mass representing a concrete slab supporting the transformer on top of the isolators. This mass is 2mC and is lumped at two locations on top of the supports. Small masses to represent the triple FP isolators (mTFP) and the springdamper units (mSD) are added at the isolator locations. The properties used in this study are summarized in Table 2. The dimensions, concrete base weight and isolator weight are those of a transformer described in [8], which has been seismically isolated with a horizontal-only version of the isolation systems studied in this paper. That transformer had a total weight of 1868 kN but this study extended the weight to include two additional total weight cases while maintaining the same dimensions. The width of 2.79 m is the least encountered in the range of transformers of interest and it has been kept unchanged in the study as it results in the lar-

Table 2 Properties of transformer model. Height of transformer: HT Length (width) of transformer: LT Height of concrete slab: HC Height of triple FP isolator: HTFP Height of spring damper: HSD Angle of inclination of bushing: h Lumped mass for transformer body: mT Lumped mass for concrete slab: mC Lumped mass for triple FP: mTFP Lumped mass for spring damper: mSD Total weight of isolated structure: WT + WC = (mT + mC)g

2.06 meters 2.79 meters 0.15 meters 0.12 meters 0.38 meters 0 or 20 degrees 31741, 43077, 54412 kg 4534 kg 317 kg 227 kg 1423, 1868, 2313 kN

gest potential for uplift of the isolators. It also results in a frequency of rocking equal to about 2.6 Hz (for system allowed to freely rock and using the least shear stiffness for the horizontal isolators), resulting in magnification of the response of flexibly mounted bushings (as-installed frequency close to 2.6 Hz). The isolated model shown in Fig. 3(c) with the combined horizontal-vertical isolation system distinguishes between the cases of allowing for free rocking and of completely restraining rocking. The latter case is achieved by installing a rigid base between the spring-damper units and the triple FP isolators above. When the rigid base is removed, the structure is free to undergo rocking by differential vertical motion of the spring-damper units, which only move vertically. This is possible with the triple FP isolators on top as they behave essentially as rollers. Truly the base has to be of finite stiffness which will allow for some limited rocking to occur. In this work only results for the two bounding cases of zero and infinite base stiffness are presented, which correspond to the cases of allowing for free rocking and of completely restraining rocking, respectively. Details of isolation systems are described in the next section. Inherent damping was specified by adding vertical and rotational dashpots at the connection between the bushing and the transformer body, and horizontal dashpots between the nodes with mCH and mUB, as shown in Fig. 2, so that the damping ratio is 3% of critical in each mode of vibration. This value of damping is consistent with observations in the field study of [40]. Note that the inherent damping was not specified using Rayleigh damping as it was impossible to realistically damp the structure and also avoid leakage of damping in the isolation system, which then significantly affects the isolation system response [37]. Two aspects of the numerical model of the analyzed transformers require additional comments. One is the use of a single bushing whereas transformers typically have one to three bushings. Bushings are light by comparison to the transformer weight (4–12.5 kN per Table 1 versus 1400–2300 kN transformer weight per Table 2) so that they cannot affect the transformer motion. Even if more than one bushing were used, failure would have been controlled by one of the bushings depending on its dynamic characteristics (as all were assumed to have the same acceleration limits). Accordingly, a single bushing was used and its as-installed frequency was varied in a practical range. Second is the use of a two-dimensional representation, which is typical in the assessment of performance of structures [25]. This is considered appropriate given that most transformers have a balanced design with the center of mass close to the geometric center of their footprint. Also, the two-dimensional model had the least possible distance between supports and a relatively high location of the center of mass so that the results of analysis are considered conservative

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in terms of the potential for rocking and uplift of the isolation system, which both may contribute to failure of the transformer.

Table 3 Lower bound frictional properties of triple FP bearings. Load (kN)

l1 = l4

l2 = l3

Comments

5. Description of seismic isolation system

355.9

0.130

0.095

The seismic isolation system consists of triple FP bearings for providing isolation in the horizontal direction. When a threedimensional isolation system is used, the triple FP isolators are supported by spring-damper units to provide for some degree of vertical isolation. Fig. 4(a) shows the section of the smallest size triple FP isolator. It has been used in a transformer described in [8]. Note that this version of the isolator has an inner restrainer ring, which does not offer any advantage and could be removed. Fig. 4(b) shows the internal construction of a modification of the smaller size isolator without an inner restrainer ring. Both the isolators of Fig. 4(a) and (b) have been tested and their frictional properties are identical [8]. Additionally, the larger bearings without an inner restrainer that are shown in Fig. 4(c) and (d) are considered for the purpose of examining the effect of isolator displacement capacity on the fragility of transformers. The lower bound frictional properties of the bearings of Fig. 4 are presented in Table 3 for high speed conditions. The upper bound properties, excluding effects of low temperature (as those are dependent on location) have been calculated based on the procedures described in [41] using the following system property modification factors: ktest,max = 1.10, kae,max = 1.12, kspec,max = 1.00, kmax = 1.23. Thus, the upper bound values should be obtained from the lower bound values of Table 3 by multiplying by factor of 1.23. The subscripts in coefficient of friction denote the FP isolator surfaces, starting from 1 at the bottom [42]. The spring-damper unit consists of a centrally located vertical damper within a telescopic sleeve to resist shear force without any lateral deformation and surrounded by coil springs as illustrated in Fig. 5 and shown in the photographs of Fig. 6 from testing at the University at Buffalo. Each coil spring has its length available for shear deformation restricted so that each unit has sufficiently

489.3

0.120

0.080

578.3

0.110

0.065

For 1423 kN transformer. Adjusted from test data at 490 kN load For 1868 kN transformer. Based on test data at 490 kN load For 2313 kN transformer. Adjusted from test data at 490 kN load

Fig. 5. Schematic of spring-damper unit.

large torsional stiffness. The units are designed to support the transformer and the isolators on top (including a base if desired) and have the stiffness, damping constant and stroke values in Table 4. The devices with these characteristics are intended for use to support transformers of total weight of 1423–2313 kN (on four supports). These values of properties result in a frequency in the vertical direction of 2.0 Hz with a corresponding damping ratio

Fig. 4. Sections of considered triple FP isolators.

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Fig. 6. Views of isolation system when rocking is allowed (left) and rocking is restrained (right).

Table 4 Parameters of spring-damper device unit. Stiffness per unit, KS Damping constant per unit (linear viscous damping), CD Stroke capacity, DSD,Capacity

7.7 kN/mm 0.6 kN-sec/mm 127 mm

of 0.50 when the total supported load is 1868 kN (WT + WC in Table 2). For the range of weights considered, the vertical frequency and the corresponding damping ratio are 2.3 Hz and 0.56, respectively, when the weight is 1423 kN, and are 1.8 Hz and 0.44, respectively, when the weight is 2313 kN. The decision to develop a system with a 2.0 Hz vertical frequency in the average weight application was based on considerations of limits for static deflections and size of the system. Any frequency that is substantially less than 2.0 Hz results in large static deflections and in unacceptable height for the vertical isolation system. The selection of the damping ratio at 0.5 was based on studies to achieve limited dynamic deflections with some insensitivity of response to the details of the vertical ground motion. It is apparent that the vertical component of the isolation system does not function by lengthening the period of the isolated equipment in the vertical direction but rather it functions as a highly damped viscous damping system. The springs have linear elastic behavior and the damper has linear viscous behavior. The damper stroke capacity DSD,Capacity is 127 mm, part of which is consumed for static deflection under the weight of the equipment. For the transformer weight of 1868 kN, the static deflection is 61 mm, thus having a remaining capacity to deflect another 66 mm in the downward direction and 61 mm in the upward direction under dynamic conditions. Fig. 7 illustrates the behavior of the two possible installation methods for allowing rocking (Fig. 7(a)) and for restraining rocking (Fig. 7(b)) of the isolated equipment. The bottom concave plate of the triple FP isolators is allowed to rotate by an angle of rotation w that is limited by the telescopic sleeve system of the

spring-damper unit. In general, angle w is small and limited to 0.1 degrees. In the configuration in which rocking is allowed (Fig. 7(a)), the top plate of the triple FP isolators is free to rotate as the triple FP isolators provide no resistance to rotation. This is possible because the spring-damper system allows for relative vertical motion at each support. The rocking angle / is then only limited by the ability of the spring-damper unit to move vertically. Most of the displacement capacity will be then consumed by the average vertical motion of the four supports. Realistically, the relative vertical displacement between any two supports will be less than about 50 mm. For the shortest distance between supports of LT = 2.79 m (see Fig. 4), the angle of rocking / is about equal or less than 1 degree. The total angle of rotation / + w is thus less than about 1.1 degrees. This will result in additional displacements and acceleration at parts of the transformer furthest away from the isolation system. When a stiff base is installed to span between supports as shown in Fig. 7(b) (and Fig. 6(b) during testing), rocking of the superstructure is restrained so that angle / is essentially nil. The vertical isolators move in unison with essentially the same displacement. The total rotation / + w is now small and dependent on the stiffness of the connecting system. Effectively, it can be reduced to about 0.1 degrees.

6. Modeling of isolation system The triple FP isolators were modeled in OpenSees [38] using a modification of the series model [42] in order to simulate the ultimate behavior of the isolator as predicted by the theory of [43,44], including uplift. Specifically, the modified series model includes the stiffness of the inner restraining ring kr and its ultimate capacity. The shear stiffness of the restraining ring is calculated by the following equation [43,44], which is based on the shear strength of a 60° wedge of the restrainer ring divided by an appropriate value of a yield displacement Yr:

Fig. 7. Illustration of behavior vertical-horizontal isolation system when (a) rocking is allowed; (b) rocking is restrained.

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kr ¼

pðb  tr Þtr F ry 6Y r

ð4Þ

In Eq. (4), b and tr are the outside diameter and thickness of the inner restraining ring, respectively, and Fry is the shear yield stress of the material (172 MPa is a representative value for ductile iron [43]). The strength of the restraining ring is equal to krYr. The value of Yr was set equal to the thickness tr. The restrainer is considered acting as long as the restraining ring deformation is less than the thickness tr. When this displacement is exceeded for the first time, the restraining ring is removed from the model. The model is assumed valid until the displacement reaches a critical value which results in collapse or overturning of the internal parts of the bearing. This is considered to be at a displacement DUltimate equal to the displacement capacity DCapacity as predicted by the theory in [42] plus half of the diameter of the rigid slider. Specifically, the isolators of Fig. 4(a) and (b) have DUltimate equal to 450 mm, the isolator of Fig. 4(c) 704 mm and the isolator of Fig. 4(d) 795 mm. Note that the model does not explicitly simulate collapse. Simply when this limit of displacement is exceeded, the isolator is considered failed and execution of the program is terminated. Given that collapse is not directly simulated, a user of this model may opt to use a different limit for the ultimate displacement as for example the one calculated by more advanced models in [43]. The interested reader is referred to [37] for more details about this modified series model. Program OpenSees [38] has the following elements that were used in modeling the behavior of the spring-damper units: (a) ‘‘Elastic uniaxial material” to represent the spring with stiffness KS, (b) ‘‘viscous material” to represent the linear viscous damper with constant CD and (c) ‘‘elastic-perfectly plastic gap material” to represent the compressive stroke capacity DSD,Capacity of the damper. These are illustrated in Fig. 8. Moreover, the rigid ‘‘elastic-beam column element” is used in parallel of these materials to prevent horizontal and rotational movement of the spring damper unit. Note that the spring-damper unit can only deform in compression up to a maximum of DSD,Capacity from the unloaded position. When this displacement capacity is consumed, there is impact and this simulated in the model by using an arbitrarily large stiffness (100KS). When the element for the spring-damper unit is combined with the triple FP element there is modification of the behavior in tension. When uplift occurs in the triple FP isolator, there is zero tensile force in the spring-damper unit. Examples of force-displacement loops of the spring-damper unit simulated by the model are shown in Fig. 9 where one unit is subjected to cyclic vertical motion of 2 Hz frequency and amplitude of 58 mm from the starting static position due to gravity loads of 357 kN, 468 kN and 580 kN (corresponding to the three cases of transformer weight considered). Compressive loads and displacements are negative. The static deflections in the three cases are 46, 61 and 75 mm. In the first case the amplitude of motion (58 mm) is larger than the static displacement so that the displacement is capped by zero as the unit only operates in compression.

Fig. 8. Elements in parallel representing a spring-damper unit.

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In all cases the calculated positive force exceeds zero so that it is capped by zero as the isolator uplifts. In the case of the largest static load, the unit reaches its displacement capacity of 127 mm in compression resulting in impact and the shown increase in force.

7. Seismic performance evaluation Transformers may fail in an earthquake in a variety of ways. Often damage or failure of bushings is considered to be failure for the transformer [33]. The major failure modes of bushing are shown in Fig. 10 based on the observations in past earthquakes [14,45]. The modes of failure shown in Fig. 10 are the result of the development of large overturning moment and/or shear force at the base of the bushings. The moment and shear force are the resultants of the distributed inertia forces in the transverse direction along the height of the bushing. An investigation in [37] established a strong correlation between the acceleration at the center of mass of the upper bushing and the moment at the base of the bushing. Thus, we assume that bushing failure is caused by the acceleration at the center of mass of the upper bushing exceeding some critical value. Several options for the limits of acceleration in the longitudinal and transverse bushing directions were considered and analysis was conducted per the procedures described in this paper and fragility curves were constructed for the non-isolated transformer model. Specifically, the study considered that bushings fail when the acceleration at the center of mass of the upper part per Fig. 3 exceeds the limit of 1 g, 2 g or 3 g in the direction perpendicular to the longitudinal bushing axis and when it exceeds the limit of 5 g in the bushing longitudinal direction. The reason for the distinction between the limits in the lateral and longitudinal directions is based on observations of bushing failures. The values of PGAF and b obtained in the analysis of several nonisolated transformer models were compared with the empirical values of PGAF and b utilized in program SERA [27–30]. The empirical fragility curves in program SERA are based on observations of damage to electrical equipment in earthquakes over the past 30 years. An example of empirical fragility data is shown in Table 5. The data are based on observations of failure attributed to either gasket leakage or breakage of bushings. A comparison of the analytical fragility data and the empirical field data revealed an agreement when the limit of bushing transverse acceleration is between 1.0 g and 2.0 g. The 2.0 g limit appears to be high for some cases of bushing failure but it is representative of other types of failures not attributed to bushing breakage. The analytically predicted dispersion factors were in the range of 0.35–0.45, which compares to the empirical value of 0.30. This indicates that the transformer model is reasonably valid, that the selection and scaling of earthquake motions for the analysis are appropriate and that the analysis procedure is appropriate. It is considered that the transformer failure model based on the peak bushing acceleration values at the center of mass of the upper part has been validated. Analyses were thus conducted with bushing acceleration limits to be 1.0 g and 2.0 g in the transverse direction and 5.0 g in the longitudinal direction. More details may be found in [37]. For the seismically isolated transformers, the following failure criteria were also considered in addition to the acceleration limits described before: (a) the horizontal displacement of triple FP isolators exceeds the DUltimate limit as described before and (b) the uplift displacement of triple FP isolator exceeds 51 mm, which is the height of the outer restraining ring. While it is possible to have stable behavior for larger uplift calculated based on the theory in [43], this was not considered due to the complex nature of the calculations involved. Fig. 11 presents the fragility curves of transformers for the two cases of 1 g and 2 g transverse bushing acceleration limits (the

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S. Kitayama et al. / Engineering Structures 152 (2017) 888–900

Fig. 9. Examples of behavior of spring-damper unit.

Fig. 10. Failure modes of porcelain bushings. Table 5 Empirical fragility data for non-isolated transformers utilized in program SERA [28,29]. Type of transformer

Bushing voltage (kV)

Median PGAF (g)

Dispersion factor b

230 500

0.50–0.85 0.45–0.75

230 500

230 500

Type of transformer

Bushing voltage (kV)

Median PGAF (g)

Dispersion factor b

0.30 0.30

230 500

0.50–0.85 0.40–0.65

0.30 0.30

0.50–0.85 0.45–0.75

0.30 0.30

230 500

0.50–0.85 0.40–0.70

0.30 0.30

0.50–0.85 0.30–0.60

0.30 0.30

230 500

0.50–0.95 0.50–0.85

0.30 0.30

Fig. 11. Fragility curves of transformer with 7.7 Hz inclined bushing; Triple FP bearings without inner restrainer, lower bound friction properties and isolator ultimate displacement capacity of 450 mm; 1 g (left) and 2 g (right) transverse acceleration limits.

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frequencies, two bushing inclinations (at 20 degrees and vertically), two bushing transverse acceleration limits (1g and 2 g, the longitudinal limit is 5 g), three triple FP isolator displacement capacities, upper and lower bound friction values and isolators with and without an inner restraining ring. The data in these tables have not been adjusted either for uncertainties in the analysis methodology, models and in the test data or for the spectral shape effects of the ground motions. The former are easily adjusted by increasing the dispersion coefficient per procedures described in FEMA P695 [25]. The latter could not be accounted for by using the procedures in [25] as those are based on the analysis of the collapse of buildings systems and are not applicable to the problem studied. The results demonstrate that: (a) in general, the values of PGAF for transformers with a seismic isolation system are larger than those of non-isolated transformers, indicating a degree of protection provided by the isolation system (with the exception of the case of the 11.3 Hz bushing with 2 g transverse acceleration limit); (b) the restrainer ring has a minor negative effect on the fragility of the isolated transformer by slightly reducing the value of PGAF, which was more pronounced for the horizontally-vertically isolated with restrained rocking; (c) the inclination of the bushing had small effects of the fragility of the transformer with mixed results (the vertical placement resulted in slightly increased fragility for the non-isolated, slightly improved fragility for the horizontally isolated and about the same for the horizontally-vertically isolated) (this is expected as the angle of inclination is small); (d) the values of friction within the considered range of lower and

longitudinal bushing acceleration limit is 5 g). The bushing is inclined and has an as-installed frequency of 7.7 Hz, and the triple FP isolators are per Fig. 4(b) without an inner restraining ring and with displacement capacity of 450 mm. The friction coefficients have the lower bound values. Values of PGAF and b are shown in the figure. The results in Fig. 11 demonstrate a marked reduction of the probability of failure when seismic isolation is used, which is further reduced when the three-dimensional isolation system is used. For example, consider the case of bushing transverse acceleration limit of 1 g (left Fig. 11). Consider a seismic intensity with PGA = 0.6 g. The probability of failure (on the basis of the empirical data) is about 84% for the non-isolated transformer, it is about 21% for the horizontally isolated transformer and is less than 8% for the three-dimensionally isolated transformer with either rocking allowed or completely restrained. Failure is by exceedance of the transverse bushing acceleration limit of 1 g in both the nonisolated and the isolated transformers. The probabilities of failure are substantially reduced when a bushing acceleration limit of 2 g is considered (right of Fig. 11). It is about 26% for the nonisolated transformer, is about 9% for the horizontal-only isolated transformer and is about 5% for the two types of threedimensionally isolated transformers. Tables 6–8 present values of parameters PGAF and b of the lognormal distribution with that best fit the analysis data for each of the analyzed transformers. The results are shown for transformers that are non-isolated, are horizontally isolated or are horizontallyvertically isolated with rocking allowed or completely restrained. Data are presented for three transformer weights, three bushing

Table 6 Fragility data for analyzed transformers in case of lower bound friction, inclined bushing and isolators without inner restrainer (values in parenthesis are for vertically placed bushings). Transformer weight (kN)

Bushing Freq. (Hz)

Isolator Displ. capacity (mm)

Bushing Accel. limit (g)

1423

7.7

450

1868

4.3

450

7.7

450

2.0 1.0 2.0 1.0 2.0

2313

450

7.7

450

Horizontal-vertical isolation rocking allowed

b

PGAF (g)

b

PGAF (g)

b

PGAF (g)

b

1.0

0.45 0.45 0.34 0.34 0.45 (0.41) 0.45 (0.41) 0.45 (0.41) 0.45 (0.41) 0.45 (0.41) 0.45 (0.41)

1.06 0.81 1.06 0.97 1.01 (1.01) 0.82 (1.00) 1.19 (1.22) 0.84 (1.21) 1.32 (1.32) 0.88 (1.26)

0.39 0.47 0.38 0.37 0.38 (0.38) 0.45 (0.39) 0.40 (0.39) 0.46 (0.40) 0.45 (0.43) 0.49 (0.43)

1.17 1.01 1.26 1.13 1.22 (1.23) 1.03 (1.11) 1.56 (1.57) 1.40 (1.53) 1.70 (1.71) 1.49 (1.68)

0.42 0.42 0.46 0.43 0.44 (0.45) 0.43 (0.45) 0.42 (0.42) 0.42 (0.42) 0.45 (0.46) 0.46 (0.46)

1.38 1.08 1.29 0.94 1.36 (1.45) 1.07 (1.18) 1.75 (1.70) 1.54 (1.56) 2.06 (1.99) 1.66 (1.67)

0.43 0.38 0.45 0.45 0.45 (0.45) 0.39 (0.44) 0.44 (0.44) 0.41 (0.42) 0.47 (0.47) 0.45 (0.45)

2.0 1.0 2.0 1.0

(0.36) 1.44 0.72 0.80 0.40

0.35 0.35 0.45 0.45

0.97 0.81 0.99 0.82

0.39 0.40 0.40 0.45

1.14 1.11 1.21 1.05

0.44 0.44 0.46 0.44

1.45 1.35 1.15 1.06

0.46 0.44 0.43 0.40

1.0

11.3

Horizontal-vertical isolation rocking restrained

0.80 0.40 0.98 0.49 0.80 (0.72) 0.40 (0.36) 0.80 (0.72) 0.40 (0.36) 0.80 (0.72) 0.40

2.0

795

Horizontal isolation only

PGAF (g)

1.0 704

Non isolated

2.0

Table 7 Fragility data for analyzed transformers in case of upper bound friction with inclined bushing of 7.7 Hz frequency and isolators without inner restrainer. Transformer Weight (kN)

Bushing Freq. (Hz)

Isolator Displ. Capacity (inch)

Bushing Accel. Limit (g)

1868

7.7

450

2.0 1.0

Non Isolated

Horizontal Isolation Only

Horizontal-Vertical Isolation Rocking Restrained

Horizontal-Vertical Isolation Rocking Allowed

PGAF (g)

b

PGAF (g)

b

PGAF (g)

b

PGAF (g)

b

0.80 0.40

0.45 0.45

1.04 0.82

0.37 0.43

1.23 1.06

0.43 0.42

1.46 1.07

0.43 0.37

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Table 8 Fragility data for analyzed transformers in case of lower bound friction with inclined bushing of 7.7Hz frequency and isolators with inner restrainer. Transformer Weight (kN)

Bushing Freq. (Hz)

Isolator Displ. Capacity (inch)

Bushing Accel. Limit (g)

1868

7.7

450

2.0 1.0

Non Isolated

Horizontal Isolation Only

Horizontal-Vertical Isolation Rocking Restrained

Horizontal-Vertical Isolation Rocking Allowed

PGAF (g)

b

PGAF (g)

b

PGAF (g)

b

PGAF (g)

b

0.80 0.40

0.45 0.45

0.96 0.83

0.39 0.43

1.23 1.00

0.47 0.45

1.24 1.02

0.44 0.43

upper bound values have insignificant effect on the fragility of the isolated transformers; (e) the weight of the isolated transformer within the considered range has insignificant effect on the fragility of the horizontally isolated transformer but had small effect on the fragility of the horizontally-vertically isolated transformer (this is expected as the changes in weight only have small effects on the friction values of the horizontal isolators and on the vertical frequency and damping ratio), (f) increasing the displacement capacity of the triple FP isolators systematically results in decreases of the probability of failure and is particularly pronounced in the case of the horizontally-vertically isolated transformer, and (g) the asinstalled frequency of the bushings has important effects. As the as-installed bushing frequency is reduced in the case of the system with allowance for free rocking and is approaching the rocking frequency of the isolated transformer (about 2.6 Hz), there is an increase in the probability of failure. The reader is referred to [37] for more data on the effect of the bushing frequency where an atypical bushing with 2.6 Hz as-installed frequency results in unacceptably large probabilities of failure for some cases. Calculations for the mean annual frequency of failure, kF, as obtained by use of Eq. (3) for the three locations for which the seismic hazard curves are shown in Fig. 1, were performed for several cases of the 1868 kN transformer with the inclined

bushing when non-isolated and when isolated by the horizontal-only isolation system and by the horizontal-vertical isolation system with and without restraint for rocking. When isolated, the triple FP isolators were without an inner restrainer. Based on these values of the mean annual frequency, calculations for the probability of failure in a lifetime of 50 years were preformed using Eq. (2). Results for the probability of failure are presented in Table 9. The calculated probabilities of failure in a 50-year lifespan are substantially less for the case of transformers with the horizontal-only and the horizontal-vertical isolation system than for the non-isolated transformers with the exception of a two cases: (a) when the as-installed bushing frequency is 11.3 Hz and the transverse bushing acceleration limit is 2 g, and (b) in the case of the low frequency 4.3 Hz bushing with 1 g transverse acceleration limit in the case of the horizontally-vertically isolated transformer that is allowed to freely rock. The latter case is easily explained by the resonance phenomena occurring due to the proximity of the as-installed frequency to the isolated transformer rocking frequency (these are the cases where the rockingrestraining system may be used). The former case was investigated in [37] and found that (a) the non-isolated transformer has high enough frequency to fall in the constant acceleration portion of

Table 9 Probability of failure (in %) in 50 years of 1868kN transformer with inclined bushing for locations in Western US. Location

Bushing Freq. (Hz)

Isolator Displ. Capacity (mm)

Bushing Accel. Limit (g)

NonIsolated

Horizontal Isolation Only

Horizontal-Vertical Isolation Rocking Restrained

Horizontal-Vertical Isolation Rocking Allowed

Loma Linda, CA

4.3

450

7.7

450

2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0 2.0 1.0

4.70 26.07 10.76 39.80 10.76 39.80 10.76 39.80 1.32 11.31 1.18 7.39 2.80 12.77 2.80 12.77 2.80 12.77 0.34 2.90 0.37 1.92 0.73 3.84 0.73 3.84 0.73 3.84 0.17 0.72

4.16 5.11 4.85 10.18 3.07 9.72 2.64 9.33 5.49 9.38 1.04 1.28 1.22 2.64 0.77 2.52 0.67 2.42 1.38 2.40 0.33 0.38 0.37 0.69 0.27 0.67 0.24 0.65 0.40 0.62

3.24 4.11 3.32 5.30 1.31 1.94 1.15 1.90 3.94 4.33 0.82 1.03 0.84 1.34 0.34 0.49 0.30 0.48 0.99 1.09 0.27 0.33 0.28 0.39 0.16 0.20 0.14 0.19 0.32 0.34

2.87 7.21 2.38 4.09 1.00 1.36 0.63 1.22 2.06 2.39 0.73 1.84 0.60 1.03 0.26 0.35 0.17 0.31 0.52 0.61 0.25 0.51 0.22 0.33 0.13 0.16 0.09 0.14 0.20 0.22

704 795

Chehallis, WA

11.3

450

4.3

450

7.7

450 704 795

Eugene, OR

11.3

450

4.3

450

7.7

450 704 795

11.3

450

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the spectrum of the motions used in analysis, and (b) the probability of failure of the isolated transformers improved when the displacement capacity of the FP isolators was increased. The information presented in terms of probability of failure given the intensity of the earthquake and the probability of failure for particular locations (see [37] for data at more locations) within the lifetime of the equipment is important in making decisions on the use and the form of seismic isolation depending on the particular equipment considered and its location. However, given that transformers are considered critical structures, acceptably low probabilities of failure can be achieved only with the use of a combined horizontal-vertical isolation system with the triple FP isolators having some increased displacement capacity. Also the use of a second base to restrain rocking should be considered when the as-installed bushing frequency is close to the rocking frequency of the transformer or the isolators need to be relocated at a greater distance to increase the transformer rocking frequency. 8. Conclusions This study presented procedures and results of an analytical study of the response of seismically isolated electrical transformers for assessing the performance of equipment that is non-isolated to equipment that is isolated only in the horizontal direction or is isolated by a three-dimensional isolation system. The isolation system consisted of triple FP isolators in the horizontal direction and spring-damper system in the vertical direction. The performance was assessed by calculating the probability of failure as function of the seismic intensity with due consideration of (a) horizontal and vertical ground seismic motion effects, (b) displacement capacity of the seismic isolation system, including uplift capacity, (c) acceleration limits for failure of electrical bushings, (d) details of construction of the isolation system that allow or restrain rocking of the isolated structure, (e) weight of the isolated transformer in the range of 1423–2313 kN, (f) bushings with various asinstalled frequencies, (g) inclined and vertical placed bushings and (h) details of the isolators, including upper and lower bound properties and details of construction of the isolators. The acceleration failure limits for the transformer bushings were determined on the basis of a comparison of calculated fragility data in this study to empirical fragility data based on observations in past earthquakes for non-isolated transformers. Moreover, sample calculations of the probability of failure within a 50-year lifetime of isolated and non-isolated transformers at three locations in the Western US were performed. The results demonstrate that seismic isolation, whether horizontal-only or combined horizontalvertical, results in most cases, but not all, substantial reduction of the probability of failure by comparison to non-isolated transformers. Also, of the many parameters studied, all had small effects on the calculated probability of failure with the exception of the as-installed frequency of bushings. The performance assessment procedures demonstrated in this study may be used to (a) decide on the benefits offered by the seismic protective system depending on the limits of the protected equipment, location of the equipment (value of PGA) and configuration and properties of the seismic protective system, (b) calculate the mean annual frequency of functional failure and the corresponding probability of failure over the lifetime of the equipment and (c) assess the seismic performance of electric transmission networks under scenarios of component failures. As an example consider the case of a transformer located in Eugene, OR (Table 9). Given that there is considerable uncertainty in the value of the asinstalled frequency of bushings, the entire range of bushing frequencies is considered. Also consider the 1 g bushing acceleration limit. A non-isolated transformer has as much as 3.84% probability of failure in 50 years. When isolated only in the horizontal direc-

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tion, the probability of failure is 0.69% (and can be only marginally improved by increasing the size of the isolators). When isolated in the horizontal and vertical directions, the probability of failure may be further reduced depending on the configuration used but the improvement is not sufficient to warrant its use. Rather, just horizontal isolation with the smallest considered isolator is sufficient for this location. However, for the location of much higher seismic hazard in Loma Linda, CA, use of the three-dimensional isolation system is justified for most cases in Table 9. Acknowledgements This work was made possible with financial support by the Bonneville Power Administration (BPA). This support is gratefully acknowledged. We acknowledge Mr. Michael Riley of BPA and Dr. Anshel Schiff, consultant of BPA for providing numerous comments and suggestions during the course of this study that resulted in substantial improvements in the final product. We also acknowledge support provided by the Center for Computational Research at the University at Buffalo. References [1] Wilcoski J, Smith SJ. Fragility testing of a power transformer bushing – Demonstration of CERL equipment fragility and protection procedure. US army Corps of Engineers, Construction Engineering Research Laboratories; USA-CERL Technical Report 97/57 February 1997. [2] Gilani AS, Whittaker AS, Fenves GL, Fujisaki E. Seismic evaluation of 550 kV porcelain transformer bearings. PEER 1998/05 October. 1999, PEER, Pacific Earthquake Engineering Research Center. [3] Gilani AS, Whittaker AS, Fenves GL, Fujisaki E. Seismic evaluation of 230 kV porcelain transformer bearings. PEER 1998/14 December. PEER, Pacific Earthquake Engineering Research Center; 1999. [4] Filiatrault A, Matt H. Experimental seismic response of high-voltage transformer-bushing system. Earthq Spectra 2005;21(4):1009–25. https:// doi.org/10.1193/1.2044820. [5] Reinhorn AM, Oikonomou K, Roh H, Schiff A, Kempner Jr L. Modeling and seismic performance evaluation of high voltage transformers and bushings [MCEER-11-0006 2011]. Buffalo, NY: Multidisciplinary Center for Earthquake Engineering Research; 2011. [6] Shumuta Y. A study on seismic retrofit planning method of substation components on the basis of the seismic risk assessment of electric power system. CRIEPI Report U33, Japan; 1998 [in Japanese]. [7] Oikonomou K, Roh H, Reinhorn AM, Schiff A, Kempner L Jr. Seismic performance evaluation of high voltage transformer bushings. In: Proceeding of ASCE 2010 Structures Congress 2010, May 12-15; Orlando, FL. DOI: https://doi.org/10.1061/41130(369)246. [8] Oikonomou K, Constantinou MC, Reinhorn AM, Kempner Jr L. Seismic isolation of high voltage electrical power transformers [MCEER-16-0006 2016]. Buffalo, NY: Multidisciplinary Center for Earthquake Engineering Research; 2016. [9] Whittaker AS, Fenves GL, Gilani ASJ. Earthquake performance of porcelain transformer bushings. Earthq Spectra 2004;20(1):205–23. https://doi.org/ 10.1193/1.1647578. [10] Suzuki H, Sugi T, Kuwahara H, Kaizu N. Studies on aseismic isolation device for electric substation equipment. In: Cakmak AS, editor. Soil-structure interaction. Elsevier; 1987. [11] Ersoy S, Saadeghvaziri MA, Liu GY, Mau ST. Analytical and experimental seismic studies of transformers isolated with friction pendulum systems and design aspects. Earthq Spectra 2001;17(4):569–95. https://doi.org/10.1193/ 1.1423653. [12] Murota N, Feng MQ, Liu GY. Earthquake simulator testing of base-isolated power transformers. IEEE Trans Power Delivery 2006;21(3):1291–9. https:// doi.org/10.1109/TPWRD.2006.874586. [13] Koliou M, Filiatrault A, Reinhorn AM. Seismic response of high-voltage transformer-bushing systems incorporating flexural stiffeners I: Numerical study. Earthq Spectra 2013;29(4):1335–52. https://doi.org/10.1193/ 072511EQS184M. [14] Kong D. Evaluation and protection of high voltage electrical equipment against severe shock and vibrations [Ph.D. Thesis]. State University of New York, Buffalo, NY: University at Buffalo; 2010. [15] Fahad M. Seismic evaluation and quantification of transformer bushings [Ph.D. Thesis]. State University of New York, Buffalo, NY: University at Buffalo; 2013. [16] Fenz DM, Constantinou MC. Development, implementation and verification of dynamic analysis models for multi-spherical sliding bearings. MCEER-08-0018 2008; Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY. [17] Sarlis AA, Constantinou MC. Shake table testing of triple friction pendulum isolators under extreme conditions. MCEER-13-0011 2013; Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY.

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