Experimental Seismic Response of High-Voltage Transformer ...

Experimental Seismic Response of High-Voltage Transformer-Bushing Systems Andre Filiatrault,a… M.EERI, and Howard Mattb…

This paper describes the shake table testing of a full-scale high-voltage electrical transformer-bushing system. The main objective of the study was to investigate the amplification between the ground motion and the motion at the base of the bushing under various ground-motion time histories and intensities. Another objective of the testing was to assess the predictions of a three-dimensional finite-element model of the transformer-bushing system. The experimental results obtained indicated that the rocking motion of the bushing and turret, facilitated by the top plate flexibility of the transformer, influenced significantly the dynamic characteristics of the bushing. The finite element model was able to predict absolute accelerations, relative displacements, and stress distributions in the systems with reasonable accuracy considering its complexity. 关DOI: 10.1193/1.2044820兴 INTRODUCTION The IEEE-693 Standard 共IEEE 1997兲, which provides seismic design recommendations for substation equipment, states that bushings with voltage ratings exceeding 161 kV must be seismically qualified by shake table testing. Since placing a full-scale transformer-bushing system on a shake table is not economically feasible on a routine basis, bushing qualification tests are generally performed by placing the bushing on a rigid frame in lieu of the transformer body itself. Although the transformer body is assumed to be rigid, it is acknowledged that the supporting structure of the bushing, consisting of the turret and transformer tank, amplifies the ground acceleration. For this purpose, the IEEE-693 Standard assumes that the motion at the base of the bushing is equal to the ground motion multiplied by a factor of 2. Shake table testing of porcelain bushings on a rigid base using the IEEE-693 seismic qualification procedure has demonstrated a generally good performance of these components 共Whittaker et al. 2004兲. This good experimental performance is contrary to the failure of bushings observed in the field following past earthquakes. It is believed that the actual seismic vulnerability of porcelain bushings might be caused by the flexibility of transformer tanks and of bushing attachments, which affect their dynamic characteristics. Although numerical studies have indicated that the dynamic response of porcelain

a兲

Department of Civil, Structural and Environmental Engineering, University at Buffalo, State University of New York, Buffalo, NY 14260. b兲 Department of Structural Engineering, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093.

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Earthquake Spectra, Volume 21, No. 4, pages 1009–1025, November 2005; © 2005, Earthquake Engineering Research Institute

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A. FILIATRAULT AND H. MATT

Figure 1. Transformer test specimen on shake table: 共a兲 general view, and 共b兲 mock bushing attachment details.

bushings mounted on transformer tanks is greatly different than that on a rigid base 共Ersoy and Saadeghvaziri 2004兲, no experimental data is currently available to validate these models. This paper describes the uniaxial shake table testing of a 525-kV transformerbushing system. The opportunity to test on a shake table a full-scale, high-voltage transformer bushing is significant. Never before has a high-voltage electrical transformer of this size been shake-table tested in the United States. The shake table tests performed allowed for the identification of the dynamic properties of the system as well as a better understanding of the seismic response of a bushing mounted on a transformer. DESCRIPTION OF TEST SPECIMEN As shown in Figure 1a, a 525-kV transformer-bushing system was made available for the shake table tests. Because of the payload limitation of the shake table, the transformer tank was stripped of all extraneous appendages such as its radiators, bushings, surge arrestors, and control cabinet, as well as its internal components 共core, coil, and oil兲. The test specimen was not, therefore, completely representative of a true transformer due to missing components. However, provided the interior core is not braced and does not stiffen the tank, as is often encountered in currently installed transformers, the lateral stiffness of the transformer originates from the steel tank structure itself. Furthermore, the mounting conditions of the bushing to the top plate of the transformer are of greater importance to its seismic response. The transformer tank specimen included all stiffening elements on top of the transformer; therefore, realistic bushing boundary conditions were captured during testing.

EXPERIMENTAL SEISMIC RESPONSE OF HIGH-VOLTAGE TRANSFORMER-BUSHING SYSTEMS

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The dimensions of the transformer tank are 2.69 m ⫻ 3.02 m ⫻ 6.96 m in height. The total weight of the tank is 300 kN. The steel tank sides and top plates are 12 mm thick, while the bottom plate of the tank is 30 mm thick. Several stiffening elements were welded to the interior of the top plate. These stiffening elements are composed of thin plates and channels. In addition to the stiffening elements attached to the top plate, several compounded steel lamina were tack-welded to the interior of the tank. These acted as a buffer between the steel tank and the core and coils mounted within the tank. Details of the transformer tank specimen construction are described elsewhere 共Matt and Filiatrault 2004兲. To support the transformer test specimen, a steel frame was constructed and mounted on top of the shake table. The frame was constructed from W12⫻ 26 steel beam members welded to one another with their lower flanges bolted to the shake table. The shake table frame provided a mounting surface, upon which the bottom plate of the transformer specimen could be welded. The transformer was mounted on the shake table such that the input motion acted in the longitudinal 共3.02 m兲 direction of the tank. Transformer bushings are expensive and inherently brittle, making them vulnerable to failure under repetitive shaking. For these reasons, it was decided to construct and use a mock bushing in lieu of a real porcelain bushing for the seismic tests. The mock bushing was designed such that it exhibited dynamic properties similar to a real 525-kV porcelain transformer bushing’s. The mock bushing closely matched the total mass, stiffness, and center of gravity of a real bushing. By doing this, the natural frequency and mode shape associated with the fundamental mode of vibration for the real 525-kV transformer bushing could be represented by the mock bushing. In addition, the mock bushing was designed to exhibit roughly the same inertial forces and overturning moment induced by a real 525-kV bushing during the seismic shaking 共Matt and Filiatrault 2004兲. Note that the mock bushing was not designed to exhibit the damping characteristics of real bushing construction. Results of qualification tests have shown that damping of bushings is between 2 and 5% of critical 共Filiatrault and Stearns 2002兲. It is expected that the damping in the mock bushing will be lower than these values. The real 525-kV porcelain bushing prototype considered has a total weight of 13.7 kN and a total height of 4.1 m. Its fundamental frequency was estimated to be 3.1 Hz when supported on the 525-kV transformer top plate. The center of gravity of the 525-kV bushing is located at 2.8 m above its base. The mock bushing comprised three annular steel sections used as mounting plates, two steel tubular sections, and a steel plate upon which a concrete block was attached. The diameter of the main tube is 355 mm with a wall thickness of 9.5 mm. The concrete block dimensions are 1 m ⫻ 1.5 m ⫻ 300 mm. A 12-mm-thick steel plate connected the concrete block to the steel tube. The total height of the mock bushing including the concrete block and attachment plates is 3.1 m. Figure 1b shows a photograph of the mock bushing attached to the transformer tank specimen. As seen in the photograph, the turret attachment plate was bolted

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Table 1. Properties of mock and prototype 525- kV bushings Property

Mock Bushing

Prototype 525-kV Bushing

Total Height Total Weight Height of Center of Mass Fixed Base Fundamental Frequency Transformer Mounted Fundamental Frequency 共Hz兲 Lateral Stiffness 共kN/mm兲

3.1 m 13.9 kN 2.9 m 8.8 Hz 2.9 Hz

4.1 m 13.7 kN 2.8 m 8.9 Hz 3.1 Hz

4.0 kN/ mm

4.4 kN/ mm

to the turret upon the transformer top plate. The turret and mock bushing are tilted 7.8 degrees from the vertical axis. The bushing is also rotated along a plane oriented 45 degrees from both orthogonal axes of the transformer tank. The total weight of the mock bushing assembly is 13.9 kN and its calculated fundamental frequency is 2.9 Hz when attached to the transformer tank. Table 1 summarizes the physical and dynamic properties of the mock bushing and of the prototype 525-kV bushing. The flexibility of the top plate of the transformer has a significant effect in reducing the fundamental frequency of the bushing. INSTRUMENTATION The test specimen was instrumented with over 50 sensors to measure accelerations, displacements and strains at various locations of interest. Because of space limitations, details of the instrumentation are given elsewhere 共see Matt and Filiatrault 2004兲. EARTHQUAKE GROUND MOTIONS Five different earthquake acceleration time histories were selected as input motions for the shake table tests. Three of the records were historical ground motions recorded during California seismic events, while the other two records were synthetic records

Table 2. Characteristics of earthquake ground motions Record No. 1 2 3 4 5 a

Seismic Event

Moment Magnitude MW

1992 Cape Mendocino 1994 Northridge

7.1 6.7

1992 Landersa Synthetica

7.2 —

Recording Station

Peak Ground Acceleration 共g兲

Fortuna Blvd Mulhol Canoga Park — —

0.12 0.36 0.42 1.00 1.00

Modified to match the IEEE-693, 2% damped, response spectrum for high seismic zone


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generated to match the IEEE-693 response spectrum for high seismic zones 共IEEE 1997兲. Table 2 lists the main characteristics of these five ground motions; other details are given elsewhere 共Matt and Filiatrault 2004兲. Due to the height and large mass of the transformer, the limiting factor for ground motion intensities was the overturning moment capacity of the shake table. It was determined from the transformer test model that the peak ground acceleration that could be safely implemented on the shake table without exceeding the table overturning capacity was approximately 0.4 g 共Matt and Filiatrault 2004兲. SHAKE TABLE TESTING PROGRAM Three different shake-table test series were performed on the transformer–mock bushing test system. The first series consisted of frequency evaluation tests to determine the natural frequencies of the system along with its corresponding mode shapes. The second series included damping evaluation tests from which the percentage of critical damping for each mode of vibration identified could be determined. The final test sequence was a series of seismic tests using the earthquake records described in the previous section. The frequency evaluation tests were performed using an acceleration-controlled flat, clipped white noise as input motion. The excitation frequency range was between 0 and 50 Hz. During the 11-minute white noise excitation, acceleration time histories were recorded from each of the accelerometers. Specialized analysis software 共Experimental Dynamic Investigations 1993兲 was utilized to determine the natural frequencies from power spectral density plots of the absolute acceleration time histories of various accelerometers. The corresponding mode shapes were found by comparing the relative amplitudes and phases of the spectral density plots between different accelerometer measurements. The damping evaluation tests were performed by exciting the test specimen with low-amplitude sinusoidal excitation at specific frequencies corresponding to the natural frequencies of the system identified during the frequency evaluation tests. Once a steady-state resonance had occurred, the shake table excitation was abruptly stopped causing a decaying free vibration response of the test specimen. Acceleration time histories recorded after the shake table had come to a complete stop were then used to evaluate the percentage of critical damping for that particular mode using the logarithmic decrement method 共Filiatrault 2002兲. The seismic tests were conducted using the five ground acceleration records described earlier at seven different intensities. The target peak input acceleration of the records ranged from 0.05 g to a maximum of 0.25 g by increment of 0.05 g. Data was acquired during the seismic tests at a sampling rate of 100 Hz and filtered with a 50-Hz low-pass filter.

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Figure 2. Mode 1: first mode of mock bushing, 2.61 Hz.

RESULTS OF FREQUENCY EVALUATION TESTS Results of the frequency evaluation tests identified the first two lowest natural frequencies of the system associated with the vibration of the mock bushing. These two frequencies are 2.61 Hz and 3.30 Hz, respectively. The transverse frequency of the transformer tank is 14.61 Hz and the longitudinal frequency is 6.74 Hz, much lower than anticipated. Reasons for why the longitudinal frequency of the tank was much lower than expected will be discussed in later sections. The mode shapes were evaluated for the three lowest natural frequencies of the transformer–mock bushing system. Due to the difficulty in identifying the transverse fourth mode of vibration 共14.61 Hz兲 from the white noise test conducted in the longitudinal direction of the transformer tank, its mode shape could not be calculated. The first three modes of the system are shown in Figures 2–4. The mode shapes were calculated by first computing the spectral densities for seven accelerometers attached throughout the height of the transformer and mock bushing. The accelerometer channels A3, A5, and A7 measured the north-south 共NS兲 acceleration of the transformer tank. Accelerometer channels A14 and A15 measured the NS acceleration of the bottom and top of the mock bushing tube, respectively. Accelerometer channels A16 and A17 measured the NS and EW 共east-west兲 motion of the mock bushing concrete block, respectively. The first mode of vibration corresponds to the bushing oscillating in the NW-SE plane. The second mode is also associated with almost pure motion of the mock bushing. However, the mock bushing vibrates in a plane perpendicular to the first mode. The mode shape lies in the NE-SW plane. The third mode of vibration corresponds to the transformer tank vibrating in the longitudinal 共NS兲 direction. Note that for this mode, the mock bushing vibrates in the opposite direction of the tank in the NS plane.


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Figure 3. Mode 2: second mode of mock bushing, 3.30 Hz.

RESULTS OF DAMPING EVALUATION TESTS The equivalent viscous damping varied depending upon the amplitude of the response. Using the log-decrement method, the equivalent damping ratio for each mode of vibration was calculated as a function of the amplitudes recorded during the damping evaluation tests. Figure 5 shows the percentage of critical damping computed for each of the first three modes of vibration of the test system as a function of input acceleration amplitude. For each mode of vibration, the damping ratio increases almost linearly with increasing acceleration amplitude. The damping associated with the mode of vibration of the transformer tank 共Mode 3兲 is significantly higher than that associated with the modes of vibration of the mock bushing. RESULTS OF SEISMIC TESTS This section presents the results of all the shake table seismic tests performed. Because of the large mass of the transformer tank that caused significant dynamic interaction between the test system and the shake table, the peak shake table accelerations measured during the seismic tests were larger than those of the target PGA 共Matt and Filiatrault 2004兲. For this reason, the results of the seismic test are presented relative to the measured shake table absolute acceleration. Table 3 presents the main results obtained during the seismic tests. For each ground motion record and intensity considered, the table lists the following measured values: 共1兲

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Figure 4. Mode 3: first longitudinal mode of transformer tank, 6.74 Hz.

the peak acceleration on the shake table, 共2兲 the peak acceleration measured on the top plate of the transformer tank, 共3兲 the peak acceleration on the turret at the base of the mock bushing, 共4兲 the peak acceleration on the concrete block at the top of the mock bushing, 共5兲 the relative displacement of the top plate of the transformer tank, 共6兲 the

Figure 5. Equivalent viscous damping as a function of excitation amplitude for the first three modes of vibration of the transformer–mock bushing system.

Peak Horizontal Acceleration 共g兲 Target PGA Top Base of Top of Input Motion 共g兲 Table Plate Bushing Bushing

Peak Horizontal Relative Peak Vertical Relative Displacement 共mm兲 Displacement 共mm兲

Top Plate

Top of Bushing

Top Plate

Peak Stresses 共MPa兲 Bending Principal Base of Turret Bushing

0.05 0.10 0.15 0.20 0.25

0.12 0.21 0.28 0.34 0.42

0.38 0.72 1.00 1.13 1.28

0.36 0.68 0.87 1.05 1.12

0.34 0.76 1.00 1.27 1.40

1.9 3.8 5.3 6.9 7.8

7.3 18.0 26.9 33.8 38.1

0.53 1.19 1.88 2.44 2.77

32 62 94 115 136

21 46 66 85 101

Northridge Mulhol

0.05 0.10 0.15 0.20 0.25 0.30 0.35

0.17 0.25 0.34 0.44 0.51 0.54 0.59

0.27 0.41 0.59 0.75 0.95 1.17 1.32

0.26 0.39 0.54 0.75 0.94 1.13 1.32

0.21 0.40 0.56 0.75 0.92 1.11 1.34

1.4 2.4 3.6 4.8 5.6 6.4 8.1

5.1 10.4 15.2 18.8 24.9 37.9 39.7

0.38 0.64 1.24 1.52 1.58 1.78 2.24

19 30 55 77 85 97 115

14 24 41 57 68 84 104

Northridge Canoga Park

0.05 0.10 0.15 0.20 0.25

0.15 0.25 0.38 0.49 0.52

0.30 0.53 0.85 1.19 1.46

0.28 0.48 0.82 1.14 1.52

0.30 0.62 1.05 1.48 1.72

1.5 2.8 5.1 7.6 10.2

7.4 15.8 23.9 36.3 38.1

0.71 1.07 1.52 2.16 2.54

23 57 88 119 146

22 49 68 101 124

Landers

0.05 0.10 0.15 0.20 0.25

0.15 0.26 0.38 0.43 0.56

0.33 0.64 0.94 1.16 1.35

0.30 0.62 0.87 1.10 1.33

0.45 0.72 0.95 1.33 2.00

0.8 2.5 5.3 7.6 9.1

9.4 17.8 26.7 40.4 59.2

0.61 1.17 1.52 2.31 3.30

34 77 108 130 163

28 57 85 103 149

Synthetic

0.05 0.10 0.15 0.20 0.25

0.14 0.23 0.34 0.39 0.48

0.32 0.54 0.79 0.95 1.26

0.29 0.50 0.65 0.93 1.11

0.38 0.82 1.17 1.41 1.55

1.7 3.1 4.3 6.0 8.9

9.4 20.6 25.4 30.7 39.6

0.61 1.37 1.60 2.03 2.54

27 66 83 101 126

27 66 83 100 117

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Cape Mendocino


Table 3. Results of seismic tests

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Figure 6. Spectral amplification plot for Landers ground motion, nominal PGA= 0.25 g.

relative displacement of the concrete block at the top of the mock bushing, 共7兲 the peak principal stress in the turret, and 共8兲 the peak bending stress at the base of the mock bushing. COMPUTATION OF SPECTRAL AMPLIFICATIONS Using the shake table test results presented in the previous section, a horizontal dynamic amplification factor between the input motion at the base of transformer and the motion recorded on the top plate of the transformer tank was computed. For a given shake table test, the dynamic amplification was obtained by taking the ratio of the 2% damped response spectrum computed from the horizontal acceleration recorded at the base of the mock bushing to the corresponding 2% damped response spectrum from the acceleration recorded on the shake table. This spectral ratio is defined as a spectral amplification, which explicitly expresses the dynamic amplification of the horizontal acceleration as a function of frequency. Figure 6 shows the spectral amplification plot under the Landers record at a nominal PGA of 0.25 g. There are three distinct peaks in the spectral amplification. These peaks occur at the first two natural frequencies of the mock bushing 共2.61 Hz and 3.30 Hz兲, and at the longitudinal natural frequency of the transformer 共6.74 Hz兲. The horizontal line shown at 2.0 represents the frequency independent amplification factor defined within the IEEE-693 Standard 共IEEE 1997兲. The spectral amplification values occurring at the frequencies of the mock bushing are of highest interest since this amplification dictates the bushing response. When comparing the two peaks associated with the bushing frequencies, the spectral amplification is generally larger at the first natural frequency of the mock bushing. Figure 7 shows the spectral amplification values at the first natural frequency of the


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Figure 7. Spectral amplifications at first natural frequency 共2.61 Hz兲 of mock bushing.

mock bushing for all earthquake records and intensities considered in the shake table testing program. In addition, the mean spectral amplification across all records and intensities is also plotted and is compared to the constant amplification factor 2.0 defined in the IEEE-693 Standard 共IEEE 1997兲. The maximum spectral amplification at the first natural frequency of the mock bushing is 3.1 under the Cape Mendocino record at a nominal PGA of 0.10 g. The corresponding minimum spectral amplification is 1.6 under the Northridge 共Mulhol兲 ground motion at a nominal PGA of 0.20 g. Since the spectral amplification is based on the ratio of the spectral acceleration at the base of the mock bushing to that of the transformer base spectral acceleration, it should remain constant for a given ground motion regardless of its intensity, provided that the system responds in the elastic range. Although this is apparently clear for the Northridge No. 2 共Mulhol兲, Northridge No. 3 共Canoga Park兲, and Landers earthquake records, the synthetic 共IEEE兲 and Cape Mendocino records show a decline in spectral amplification as the ground motion intensity increases. This may indicate some nonlinear responses of the test system with increasing amplitudes of these records. All ground motion records with exception of the Northridge No. 2 共Mulhol兲 record resulted in spectral amplification values larger than 2.0 at the first natural frequency of the mock bushing. The mean spectral amplification computed from all five records is above the IEEE-693 amplification factor of 2.0 for all amplitudes. The maximum mean spectral amplification at the first frequency of the bushing is 2.4 and occurs at an intensity of 0.24 g. As expected, the mean spectral amplification remains fairly constant with respect to the ground motion intensity.

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Figure 8. Finite element model of transformer–mock bushing system.

DESCRIPTION OF NUMERICAL MODEL A three-dimensional finite-element model of the transformer-bushing system was constructed using the structural analysis software SAP2000 共Computers & Structures 2003兲. Figure 8 shows the finite element mesh of the complete model. Eight-node shell elements with the appropriate thickness and mass were used to model the transformer tank walls. The shell elements allow for in-plane deformations and out-of-plane bending. Tri-dimensional beam elements as well as eight-node shell elements were used to model the stiffeners attached to the tank sides. The geometry, thickness, location, and mass of all walls, plates, and beams were obtained through a physical survey of the transformer tank. Note that the model represents the conditions of the test specimen and does not include the various appendages. Appendages were initially included in the numerical model and were found to have a negligible effect on its seismic response. The mock bushing was modeled as multiple beam elements with the appropriate geometry, stiffness, and mass. Point masses at the top of the mock bushing were added to account for the mass of the concrete block. Pin supports were used at bolt locations, and fully fixed conditions were used at weld locations. Roller supports were added at each node under the tank base at locations supported by the steel frame on the shake table. Other details of the finite element model can be found elsewhere 共Matt and Filiatrault 2004兲.


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Table 4. Comparison of measured and predicted natural frequencies Natural Frequency 共Hz兲 Predicted Mode Description

Measured

Initial Model

Modified Model

First Mode of Mock Bushing Second Mode of Mock Bushing First Longitudinal Mode of Transformer Tank First Transverse Mode of Transformer Tank

2.61 3.30 6.74

2.52 3.04 20.21

2.52 3.04 9.33

14.61

13.81

12.38

COMPARISON OF NATURAL FREQUENCIES A free-vibration analysis of the finite element model described above was performed to obtain numerical predictions of the fundamental frequencies and mode shapes of the transformer–mock bushing system. These predicted natural frequencies are compared in Table 4 to the measured natural frequencies obtained from the frequency evaluation tests described above. The first and second natural frequencies of the bushing were computed to be 2.52 Hz and 3.04 Hz, respectively, which agree very well with the corresponding measured frequencies. The first transverse natural frequency of the transformer tank was computed to be 13.81 Hz, which agrees relatively well with the measured frequency of 14.61 Hz. The first longitudinal natural frequency of the transformer tank was computed to be 20.21 Hz, which is much higher than the measured frequency of 6.74 Hz. From this latter comparison, it became clear that the initial finite-element model was not capturing all of the details of the test setup. MODIFICATION OF NUMERICAL MODEL In an attempt to capture the first longitudinal frequency of the transformer tank, the rigid-base finite-element model was modified to include the steel base frame and shake table foundation frame. Because of space limitations, details of this modeling can be found elsewhere 共Matt and Filiatrault 2004兲. After making the modifications stated above, another modal analysis was performed to identify the fundamental frequencies of the transformer–mock bushing system. As shown in Table 4, the first longitudinal natural frequency of the transformer tank predicted by the modified numerical model was greatly reduced to 9.33 Hz, compared to that of the initial model 共20.21 Hz兲. The corresponding mode shape predicted by the modified numerical model incorporates rocking motions of the supporting frame and shake table. The first two natural frequencies for the mock bushing were unchanged by the modifications of the numerical model. Because of the characteristics of the shake

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Table 5. Peak absolute accelerations predicted by numerical model and measured during seismic tests at nominal PGA= 0.25 g Peak Horizontal Acceleration 共g兲 Input Motion Cape Mendocino Northridge 共Mulhol兲 Northridge 共Canoga Park兲 Landers Synthetic

Top Plate

Base of Bushing

Top of Bushing

Numerical

Experimental

Numerical

Experimental

Numerical

Experimental

1.46

1.28

1.39

1.12

1.21

1.40

1.53

0.95

1.48

0.94

1.09

0.92

1.81

1.46

1.75

1.52

1.18

1.72

2.20 1.97

1.35 1.26

2.18 1.94

1.33 1.11

2.17 2.29

2.00 1.55

table foundation construction, the predicted first transverse natural frequency of the tank only reduced slightly for the modified numerical model 共12.38 Hz兲 compared to that of the initial numerical model 共13.81 Hz兲. Based on these results, it was concluded that the modified numerical model was adequate to model with sufficient accuracy the dynamic characteristics of the transformer– mock bushing test system. The influence of the supporting frame and shake table flexibility on the first longitudinal frequency of the transformer tank points to the need for incorporating stiff foundation systems to support real transformers. The natural frequency of a transformer tank could be reduced substantially if its foundation system is too flexible, which could lead to undesirable rocking motions. PREDICTION OF SEISMIC TESTS Time-history dynamic analyses were performed using the modified finite-element model in order to predict the results of the seismic tests. The input ground motions used for the analyses were the acceleration time histories recorded by an accelerometer located underneath the shake table for each of the seismic tests performed. The mean modal damping ratios measured during the damping tests were used in the numerical model 共see Figure 5兲. These values were 0.26% and 0.37% of critical for the first and second modes of the mock bushing, respectively, and 1.42% of critical for the longitudinal mode of the transformer tank. All other modes of vibration were assigned a constant damping ratio of 2% of critical. The comparison between the numerical and experimental is limited herein to the seismic tests involving a nominal PGA of 0.25 g. More details can be found elsewhere 共Matt and Filiatrault 2004兲. Tables 5–8 compare the envelope of the peak responses predicted by the finite ele-


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Table 6. Peak relative displacements predicted by numerical model and measured during seismic tests at nominal PGA= 0.25 g Peak Relative Displacements 共mm兲 Horizontal Top Plate

Input Motion Cape Mendocino Northridge 共Mulhol兲 Northridge 共Canoga Park兲 Landers Synthetic

Vertical Top Plate

Horizontal Top of Bushing

Numerical

Experimental

Numerical

Experimental

Numerical

Experimental

7.9

4.3

0.8

5.6

38.1

36.8

5.6

4.6

1.5

3.1

24.9

33.0

10.2

5.6

2.5

3.8

38.1

30.3

9.1 8.9

7.1 6.1

3.3 2.5

5.8 7.1

59.2 39.6

54.4 62.0

ment models to those measured during the seismic tests. For most cases, the peak absolute acceleration values predicted by the numerical model are higher than the measured values, as shown in Table 5. Table 6 compares the envelope of the peak relative displacements predicted by the finite element model and those measured during the seismic tests. In general, the relative horizontal displacement values predicted by the model are larger than those recorded during the seismic tests. Table 7 compares the envelope of peak stresses predicted by the finite element model and those measured during the seismic tests. The principal stresses found at the base of turret were overpredicted by the model while the peak bending stress at the base of the bushing tended to be less than the results from the seismic tests.

Table 7. Peak stresses predicted by numerical model and measured during seismic tests at nominal PGA= 0.25 g. Peak Stresses 共MPa兲 Principal, Base of Turret Bending, Base of Bushing Input Motion Cape Mendocino Northridge 共Mulhol兲 Northridge 共Canoga Park兲 Landers Synthetic

Numerical Experimental Numerical Experimental 187 129 164 248 260

133 84 145 161 124

67 44 97 108 119

100 68 123 149 116

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Table 8. Spectral amplifications predicted by numerical model and measured during seismic tests at nominal PGA= 0.25 g. Spectral Amplifications

Input Motion Cape Mendocino Northridge 共Mulhol兲 Northridge 共Canoga Park兲 Landers Synthetic Mean

Bushing, First Natural Frequency

Bushing, Second Natural Frequency

Tank, First Longitudinal Frequency

Numerical

Experimental

Numerical

Experimental

Numerical

Experimental

1.7

2.0

1.7

1.8

10.5

11.1

1.9

1.6

1.9

1.6

9.4

7.4

1.7

2.1

1.6

2.2

8.8

6.8

1.6 2.2 1.8

2.4 1.9 2.0

1.6 1.8 1.7

2.0 2.0 1.9

11.1 14.3 10.8

8.1 8.5 8.4

Table 8 compares the spectral amplifications predicted by the finite element model and those measured during the seismic tests. The spectral amplification results are given at the first two natural frequencies of the mock bushing and at the first longitudinal natural frequency of the transformer tank 共see Figure 6兲. The spectral amplification values predicted by the numerical model at the first natural frequency of the mock bushing are slightly lower that the experimental values. At this frequency, the measured mean spectral amplification computed across all earthquake records is 2.00, while the predicted mean spectral amplification is 1.8. CONCLUSIONS The results of the shake table tests conducted herein confirmed that the dynamic characteristics of a bushing are greatly influenced by the flexibility of the top plate of the transformer tank. A horizontal dynamic amplification factor between the input motion at the base of transformer and the motion recorded at the base of the bushing was computed. It was found that this dynamic amplification factor is frequency dependent and reaches maxima at the natural frequencies of the bushing and transformer tank. Four of the five ground motion records used in this study generated spectral amplification values larger than the IEEE-693 amplification factor of 2.0 at the first natural frequency of the mock bushing. The dynamic interaction between the test system and the shake table was significant and caused a substantial reduction in the first longitudinal natural frequency of the transformer tank. This result points to the need for incorporating stiff foundation systems to support real transformers. The natural frequency of a transformer tank could be reduced


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substantially if its foundation system is too flexible, which could lead to undesirable rocking motions and possible dynamic interaction with the bushing itself. Once the finite element model was modified to include realistic boundary conditions at the base of the transformer tank, it was able to predict the experimental results with reasonable accuracy considering its complexity. ACKNOWLEDGMENTS This research project was sponsored by the Pacific Earthquake Engineering Research Center’s Program of Applied Earthquake Engineering Research of Lifeline Systems, supported by the California Energy Commission, California Department of Transportation, and the Pacific Gas & Electric Company. This work made use of Earthquake Engineering Research Centers Shared Facilities, supported by the National Science Foundation under Award Number EEC-9701568. REFERENCES Computers & Structures, Inc., 2003. SAP2000 Nonlinear V. 8.2.6, Berkeley, CA. Ersoy, S., and Saadeghvaziri, M. A., 2004. Seismic response of transformer-bushing systems, IEEE Transactions on Power Delivery, Power Engineering Society, Institute of Electrical and Electronics Engineers, 19 共1兲, 131–137. Experimental Dynamic Investigations 共EDI兲, 1993. U2 Program User’s Manual, Vancouver, BC. Institute of Electrical and Electronics Engineers 共IEEE兲, 1997. Recommended Practice for Seismic Design of Substations, IEEE-693 Standard, Piscataway, NJ. Filiatrault, A., 2002. Elements of Earthquake Engineering and Structural Dynamics—Second Edition, Polytechnic International Press, Montreal, Canada, 365 pp. Filiatrault, A., and Stearns, C., 2002. Substation Equipment Interaction—Experimental Flexible Conductor Studies, Structural Systems Research Project Report No. SSRP-2002/09, Department of Structural Engineering, University of California, San Diego, La Jolla, CA, 164 pp. Matt, H., and Filiatrault, A., 2004. Seismic Qualification Requirements for Transformer Bushings, Research Project Report No. SSRP-2003–12, Department of Structural Engineering, University of California, San Diego, La Jolla, CA, 186 pp. Whittaker, A. S., Fenves, G. L., and Gilani, A. S. J., 2004. Earthquake performance of porcelain transformer bushings, Earthquake Spectra 20 共1兲, 205–223.

共Received 1 October 2004; accepted 19 January 2005兲