Natural frequencies of power transformers and their consequence M.G. Koller Résonance Ingénieurs-Conseils SA, Carouge, Switzerland M. Hässig Axpo grids, Baden, Switzerland S. Thomassin Résonance Ingénieurs-Conseils SA, Carouge, Switzerland ABSTRACT: High voltage power transformers are among the seismically most vulnerable elements of electricity distribution systems. Unanchored transformers can uplift. This significantly enhances the displacement demand at the top of the bushings and increases the inertial forces on the transformer. In order to better estimate what ground accel-erations are necessary to provoke partial uplift of power transformers, the frequencies of the fundamental rock-ing motions were measured for five typical transformers in Switzerland, covering all tension levels from the highest voltage down to the distribution level. The experiments, the results as well as their interpretation are pre-sented here. It turned out that all transformers had natural rocking frequencies within the plateau range of com-mon seismic design spectra. The conclusion is that power transformers should be anchored against uplift even in areas of moderate sismicity. Keywords: power transformers, natural frequencies, seismic uplift. 1. INTRODUCTION Inappropriate or even missing anchorage of power transformers (henceforth referred to as “trans-formers”) is common in areas of moderate seismicity. This can lead to partial uplift during an earth-quake, causing potentially severe damage to the transformers. Partial uplift significantly enhances the displacement demand at the top of the bushings. The slack pre-sent in the conductor connections is then usually insufficient, and strong interaction forces appear that typically lead to leakage or damage of the bushings, particularly due to porcelain failure. Uplift also increases the inertial forces on the bushings. Finally, the falling back to the foundation slab after par-tial uplift induces high acceleration peaks that can lead to failure of the transformer or its accessories. That's why high voltage transformers are among the seismically most vulnerable elements of electric-ity distribution systems. In areas of moderate seismicity, with a nominal peak ground acceleration (PGA) of, say, 1 m/s2 (zone 2 in Switzerland), it depends on the fundamental natural rocking frequencies of the transformer whether partial uplift occurs or not – and therefore, wether anchorage against uplift is necessary or not. Thus, it is important to know the fundamental frequencies of typical transformers. 1.1. Implicit natural frequency assumptions in the IEEE Std 693-2005 According to the American Standard IEEE Std 693-2005, paragraph D.4.1.1, “the transformer tank, core, coils, anchorage, and other components other than appendages, bushings, and surge arresters shall be qualified using static analysis according to the requirements of A.1.3.1.” Paragraph A.1.3.1 states: “The forces on each component of the equipment shall be obtained by multiplying the values of the mass of the component by the acceleration specified in the principal directions. The resulting force

shall be applied at the center-of-gravity of the component.” From the examples given, it becomes clear that the nominal PGA is meant by the term “acceleration”. In contrast to this, the appendages would have to be qualified, according to paragraph D.4.1.2, with acceleration values multiplied by 3. The use of PGA for the design of the anchorage implicitely assumes that the fundamental natural fre-quencies of the tranformer block (the transformer without the appendages) would be superior to 33 Hz (the response spectra given in the IEEE Std 693-2005 assume spectral accelerations equal to PGA for frequencies above 33 Hz). Furthermore, the application of the seismic force at the center-of-gravity assumes a quasi rigid behaviour. Are these assumptions reasonable? Natural frequencies within the “plateau range” are taken into account only for the appendages, the factor of 3 corresponding to a typi-cal design spectra plateau amplification for a damping value of 2 % of critical. It is interesting to note that an earlier version of the same standard, the IEEE Std 693-1997, indicated a multiplying factor of 2 for the acceleration at the top of the transformer block, i.e. typically at the foot of the bushings (Villaverde et al., 2001). 1.2. Natural frequencies according to the literature Only a few publications can be found in the literature that deal with experiments on the dynamic ba-haviour of high voltage transformers. In most cases, forced vibrations were caused with the aid of a shaker acting either on the transformer turret or on the foundation slab. Ibáñez et al. (1972) reported the results of forced vibration testing of 500 kV transformers in California. They found the first three natural frequencies at 2.70, 3.35 and 3.38 Hz, with corres-ponding damping ratios of 10 %, 2 % and 3 % of critical, respectively. Unfortunately, it is not clear from their publication whether the modes with these natural frequencies correspond to movements of the whole transformer or only of parts of it, like for instance the bushings – although the relatively high damping value of 10 % for the first mode rather suggests some rocking of the whole transformer with its foundation slab on the underlying soil. Bellorini et al. (1998) carried out experimental field tests with a three-phase ATR 160 MVA 230/135 kV transformer in Italy, using multi point random excitation as well as forced vibration tests. They performed these experiments primarily in order to find out the amplification factor between the ground and the transformer bushing flange. They found a fundamental natural frequency of the trans-former of 3.5 Hz and the corresponding damping ratio was around 2 % of critical. Villaverde et al. (2001) conducted forced vibration field tests on two different single-phase 500/230 kV transformers of Pauwels and of Westinghouse in California. Their aim was to quantify the ground motion amplification at the base of the bushings mounted on the transformers as a result of the flexibility of the transformer tank and turrets to which they were connected. They found fundamental natural frequencies of 3.4 Hz with damping ratios of 1.5 % and 2.1 % of critical for the Pauwels trans-former and 2.4 Hz with damping ratios of 3.6 % of critical for the Westinghouse transformer. All these experimental results are in contradiction to the assumptions adopted in the American Stan-dard IEEE Std 693-2005. 2. OBJECTIVE OF THE FREQUENCY MEASUREMENTS The experimental study presented here is part of an ongoing evaluation of the seismic vulnerability of electricity distribution systems in Switzerland. Since high voltage transformers are among the seismi-cally most vulnerable elements of electricity distribution systems, one of the key points was to realisti-cally estimate the vulnerability of these transformers. Since Swiss transformers are not anchored against uplift, and since the possibility of partial uplift for

Swiss design earthquakes strongly depends on the fundamental natural frequencies of the transform-ers, it was decided to measure these frequencies for five transformers representative for Switzerland. 3. MEASUREMENT OF NATURAL FREQUENCIES 3.1. Measured transformers Natural frequency measurements were carried out for five transformers covering all tension levels from the highest voltage level (380/220 kV) present in Switzerland down to the distribution level (11 /0.4 kV). These transformers were (the indicated lettters refer to Figure 1): (a) a BBC-MFO, 380/220 kV (600/3 MVA) single-phase auto-transformer (Axpo), (b) a Sécheron, 380/220 kV(1000/3 MVA) single-phase auto-transformer (Axpo), (c) a SMIT 220/110/16 kV (160 MVA) 3-phase transformer (Axpo), (d) a Siemens 150/22 kV (50 MVA) 3-phase transformer (ewz), (e) a Rauscher&Stöcklin 11/0.4 kV (1 MVA) distribution transformer (ewz).

Figure 1. Transformers whose fundamental natural frequencies were measured (see text for details). 3.2. Experimental technique Snap back tests were carried out with the Axpo transformers – pictures (a), (b) and (c) of Fig. 1. To this end, a rope (visible in the pictures b and c of Fig. 1) was fixed at the height of the turret or slightly

below. This rope was connected to a pair of strong magnets. By increasingly pulling at the farther magnet, a growing, approximately horizontal force could be applied to the transformer. Once the mag-netic attraction (between 10 to 15 kN) was overcome, the force in the rope was suddenly released, causing free oscillations of the whole transformer. The free oscillations were recorded with the aid of accelerometric sensors (Brüel&Kjær 4378) at about half the height of the turret, on the turret, as well as at the top of one of the bushings. This sensor con-figuration made it possible to get an idea about the principal mode shapes, in particular to distinguish between modes involving the whole transformer body (essentially rocking modes) and modes primar-ily due to flexural oscillations of the bushings. Figure 2 shows the accelerations recorded simultane-ously on the turret and at the top of a bushing; in the latter case, a superposition of a "transformer mode" and a "bushing mode" can be seen. The analysis of the free oscillations allowed to determine the frequencies of the main modes as well as to estimate their damping.

Transformer (turret)

-200-150-100-50

050

100150200

mm/s^2

Bushing

-2.00-1.50-1.00-0.500.000.501.001.502.00

m/s^2

30.0 32.0 34.0 36.0 38.0 40.0

s

Figure 2. Accelerations recorded simultaneously on the turret and at the top of a bushing of transformer (a). The accelerations at the top of the bushing, 1.5 m/s2, turned

out to be 10 times stronger than on the turret (about 0.15 m/s2). In addition to these "active" tests, ambient vibrations were successfully measured on all five trans-formers with the aid of a highly sensitive velocity sensor (Lennartz LE-3D/5s). Because of the rela-tively large size of this sensor – blue box on picture (e) of Fig. 1 –, only measurements on the turrets were possible. In contrast, ambient vibration measurements with the accelerometric sensors did not give any suitable results. 3.3. Results Table 1 gives an overview of the measured natural frequencies. The term "longitudinal" refers to the direction of energy flow (e.g. HV-side to LV-side), whereas "transversal" means perpendicular to the energy flow. Astonishingly enough, the fundamental rocking frequencies of all measured transformers, from the largest to the smallest, turned out to be very similar, situated between 3.3 and 5.5 Hz. These results are consistent with those reported for large and very large transformers in section 1.2. All measured fundamental rocking frequencies are within the interval corresponding to the accelera-tion plateau of usual seismic design spectra. Therefore, rocking motions of transformers are very "effi-ciently" excited by usual design earthquakes. This fully contradicts the implicit assumptions in the American standard IEEE Std 693-2005, presented in section 1.1.

Table 1. Measured natural frequencies. TRANSFORMER Mode

Frequency [Hz] longitudinal transversal

Transformer (a): BBC-MFO, 380/220 kV, 600/3 MVA Fundamental transformer rocking mode 4.3 5.0 Fundamental bushing flexure mode 7.0 6.0 Conservator mode 5.5 7.1 Transformer (b): Sécheron, 380/220 kV, 1000/3 MVA Fundamental transformer rocking mode 3.7 4.9 Fundamental bushing flexure mode 6 – 7 7.4 Transformer (c): SMIT, 220/110/16 kV, 160/160/53.3 MVA Fundamental transformer rocking mode 3.3 5.0 Fundamental bushing flexure mode 6.3 ? Transformer (d): Siemens, 150/22 kV, 50 MVA Fundamental transformer rocking mode 4.3 5.5 Transformer (e): Rauscher&Stöcklin, 11/0.4 kV, 1 MVA Fundamental transformer rocking mode 3.3 5.0

Table 2 shows the values of damping that were deduced from the observed free oscillations. Although accelerations as high as 15 % of g were recorded at the top of the bushings, these values are still sig-nificantly lower than what is expected during a damaging earthquake. Therefore, the damping ratios reported in Table 2 have to be considered as lower bounds of what is expected during a damaging earthquake. Table 2. Damping values observed for the free fundamental rocking oscillations.

Transformer Damping [% of critical] longitudinal transversal

Transformer (a): BBC-MFO, 380/220 kV, 600/3 MVA 1.7 % 1.2 % Transformer (b): Sécheron 380/220 kV, 1000/3 MVA 0.9 % 0.75 % Transformer (c): SMIT, 220/110/16 kV, 160/160/53.3 MVA 1.1 % ?

4. CONCLUSIONS Most high voltage power transformers in Switzerland have slenderness ratios of the order of 3.5 (ratio of the height of the centre of gravity to the half width of the effective support). Hence, for purely geo-metrical reasons, assuming rocking motion, the onset of partial uplift is possible for effective peak ground accelerations (PGA) exceeding about 1.2 m/s2. High voltage power transformers are key elements of electricity distribution systems, and their damage causes large direct and indirect costs. Consequently, within the framework of Eurocode 8, they should be designed or checked for an importance factor of 1.4. Dividing the afore-mentioned value of 1.2 m/s2 by 1.4 as well as by a soil factor of 1.35 or 1.4 (subsoil class D or E, respectively) leads to 0.6 m/s2. This means that the onset of partial uplift of typical high voltage transformers must be ex-pected for seismic zones with a nominal ground acceleration (zone value) that is as low as 0.6 m/s2. Therefore, in zones with zone values exceeding 0.6 m/s2, anchorage of high voltage transformers against uplift is mandatory. Transformers for lower voltage levels, for local distribution, are often less slender than high voltage transformers. However, slender ones should be anchored against uplift as well. Although the individ-ual lower voltage transformer is less important, many of them can be found within relatively small areas, and therefore, many of them might be damaged during an earthquake, leading to widespread power disruption.

ACKNOWLEDGEMENTS This study was financed by the Federal coordination centre for earthquake mitigation (Swiss Federal Office for the Environment). The authors are grateful for the strong support obtained from the head of the coordination centre, B. Duvernay. The active contributions of the companies "Axpo grids" (A. Guérig, H. Koch and H. Hefti) and "ewz" (P. Müller) are kindly acknowledged. REFERENCES IEEE Std 693-2005: IEEE Recommended Practice for Seismic Design of Substations, recognized as an

American National Standard, IEEE Power Engineering Society, New York, U.S.A. Ibáñez, P., Vasudevan, R. and Vineberg, E.J. (1973). A Comparison of Experimental Methods for Seismic

Testing of Equipment, Nuclear Engineering and Design. 25, 150-162. Bellorini, S., Salvetti, M., Bettinali, F. and Zafferani, G. (1998). Seismic Qualification of Transformer High

Voltage Bushings. IEEE Transactions on Power Delivery. 13:4, 1208-1213. Villaverde, R., Pardoen, G.C. and Carnalla, S. (2001). Ground Motion Amplification at Flange Level of

Bushings Mounted on Electric Substation Transformers. Earthquake Engineering and Structural Dynamics. 30, 621-632.