An experimental study of winding vibration of a single-phase power transformer using a laser Doppler vibrometer

Applied Acoustics 87 (2015) 30–37

Contents lists available at ScienceDirect

Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust

An experimental study of winding vibration of a single-phase power transformer using a laser Doppler vibrometer q Jing Zheng a, Jie Pan b,⇑, Hai Huang a a b

Department of Instrument Science and Engineering, Zhejiang University, Hangzhou 310027, China School of Mechanical and Chemical Engineering, The University of Western Australia, WA 6009, Australia

a r t i c l e

i n f o

Article history: Received 26 April 2014 Received in revised form 13 June 2014 Accepted 16 June 2014 Available online 8 July 2014 Keywords: Power transformer Transformer vibration Laser Doppler vibrometer Fault diagnosis Vibration and noise control

a b s t r a c t Transformer tank vibration has been used for the condition monitoring and fault diagnosis of power transformers, as well as for the evaluation of radiated sound power from such power transformers. In both applications, seeking a correlation between transformer tank vibration and the vibration of the transformer windings and core becomes a challenge for fault identification and noise control at the sources of vibration and noise. The purpose of this paper is to experimentally investigate the winding vibration of an electrically live power transformer and characterize the changes in the spatial and frequency features of the vibration as various mechanical faults are introduced to the transformer winding. To avoid the effects of transducer loading and electromagnetic fields on the measurement results, a laser Doppler vibrometer was used to make non-contact measurements of the winding vibration. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Power transformers are vital components of power network infrastructure. Failures of transformers may cause considerable economic losses and disruption of power supply. Low-frequency humming noise from power transformers in service also causes serious environmental issues. The evolution of transformer faults and variations in the radiated transformer noise can often be related to changes in the transformer tank vibration. This is why several vibration-based techniques have been developed for transformer condition monitoring and fault diagnosis [1,2], and passive and active noise control [3–5]. The main sources of transformer tank vibration and its noise radiation are the magnetostrictive and electrodynamic forces in the core and windings [6,7]. The vibration generated by these forces is transmitted to the transformer tank through the mechanical joints and transformer oil [1]. Recognizing the sources of faults and noise, researchers have begun to look inside a transformer for insights into the generation, distribution, and transmission of the vibrations. It has become a common belief that mechanical changes in the active parts of a transformer may significantly change the spatial and frequency q Some of the contents in this paper has been presented at Acoustics 2012, Fremantle, Australia. ⇑ Corresponding author. Tel.: +61 08 6488 3600; fax: +61 08 6488 1024. E-mail address: [email protected] (J. Pan).

http://dx.doi.org/10.1016/j.apacoust.2014.06.012 0003-682X/Ó 2014 Elsevier Ltd. All rights reserved.

properties of their vibration, which may in turn be observed in the transformer tank vibration and radiated sound. Previous work on the internal vibrations of transformers has largely focused on analysis of the axial vibration of transformer windings [8–11]. The radial vibration of transformer winding plays an important role in transmitting winding vibration to the transformer tank via the cooling oil. However, there is a lack of experimental and modeling evidence for the radial components of transformer-winding vibration. Using traditional accelerometers for vibration measurements of live transformer windings requires direct contact with high voltage components. Thus, a non-contact laser Doppler technique is often preferred. However, only few studies on laser-based measurements of transformer vibration have been found. Mizokami Masato et al. [12] developed a laser-based vibration measurement system. They applied the system to a three-phase three-limb transformer core, in order to examine the vibration pattern of a transformer core under a normal steady-state condition. Hackl and Hamberger [13] measured the velocity of an experimental tank surface with a laser scanner vibrometer, to understand the fundamental effects of changes in the surface velocity pattern and fluctuations in sound pressure level. Those previous works shed some light on the vibration performance of both the transformer’s core and its assembled structure. However, no detailed measurements on the vibration of the transformer winding have yet been made.

31

J. Zheng et al. / Applied Acoustics 87 (2015) 30–37

This paper presents the spatial and frequency properties of vibration on the surface of a winding of a single-phase 10-kV A disk-type power transformer measured using a laser Doppler vibrometer (LDV). The advantage of using LDV technique is that the measurement of vibration is free from the effect of leakage magnetic field. As the first part of a complete transformer vibration measurement program, this paper will focus on the winding vibration excited by magnetostriction in the transformer core. This was achieved by leaving the secondary winding in the open circuit condition and thus applying negligible current and negligible electromagnetic forces in the winding. This stage of the measurement already has practical significance as the vibration of many power transformers is dominated by magnetostriction in the core material. Extraction of current-induced winding vibration from the combined excitation of electromagnetic forces and magnetostriction is the second part of this measurement program. In order to investigate vibration performance under abnormal operating conditions, the winding vibration was also measured as various artificial faults were introduced into the winding. The results were then analyzed by comparing the vibration patterns of the winding with and without faults. 2. Description of experiments Fig. 1 shows the single-phase 10-kV A power transformer for the test. The rated voltages of the transformer are 415/240 V. During the test, the primary voltage of the transformer was set at the rated value (415 V), while the secondary was left in the open-circuited condition. The LDV was utilized to measure vibrations of the winding with and without faults. To acquire an adequate detailed radial vibration pattern of the transformer winding, one side of the winding surface was selected as the scanning area. Fig. 2 shows the 11  11 scanning points on the winding surface. The distance between two adjacent scanning points in the horizontal direction was approximately 1.6 cm, and the vertical distance was about 2 cm, which is nearly twice the thickness of the winding disk. Although only part of the winding surface is measured, useful spatial information of the winding vibration can be extracted by the symmetrical structure of the winding. The vibration amplitude and frequency are extracted point by point by the focused laser beam that moves rapidly in the scanning process defined in Fig. 2. It should be noted that the scanning surface is slightly curved in the horizontal direction. The measured winding vibration at the scanning points away from the center

y=20 cm

y=0 x=16 cm

x=0

Fig. 2. Diagram of the measurement system for the vibration pattern in the transformer winding.

vertical line did not exactly equal the winding vibration in the radial direction. As a result, the measured winding vibration at these locations may be interpreted as the vector contribution of the radial (major) and in-plane (minor) components of the winding vibration. Four cases of transformer winding vibration are studied. The first case is for transformer operation in a normal condition. The other three cases are for transformer operation in various abnormal conditions. Case 1 The settings of the winding, including the winding clamping pressure and insulation blocks, were all at normal operating

(a)

(b) 1st block 2nd block 3rd block 4th block

Winding clamping bolt Core clamping bolt

Fig. 3. Photos showing (a) the winding clamping bolts and core clamping bolts and (b) the four insulation blocks to be removed for the four settings in Case 3.

-5

2.5

x 10

Velocity (m/s)

2

1.5

1

0.5

0

100

200

300

400

500

600

700

800

Frequency (Hz) Fig. 1. The single-phase 10-kV A disk-type power transformer used for the test.

Fig. 4. Spatially averaged spectrum of winding vibration velocity for Case 1.

32

J. Zheng et al. / Applied Acoustics 87 (2015) 30–37

Fig. 5. The velocity pattern of winding vibration for Case 1 (a) RMS value, at (b) 100 Hz, (c) 200 Hz, and (d) 300 Hz.

Fig. 6. Vibration distributions of the winding at 100 Hz for winding clamping pressures (a) from Case 1 to settings 1, 4 and 5 of Case 2; (b) for the second stage of winding looseness, settings 6, 8 and 10 of Case 2; and (c) for the third stage of winding looseness with settings 11, 18 and 21 of Case 2.

conditions. The core laminations were also under the normal clamping pressure. Case 2 Various degrees of clamping pressure (36 settings) were applied to the winding by tightening the winding clamping bolts (as shown in Fig. 3). The increment of the clamping pressure was measured by the angular displacement (clockwise from the top) of the nuts on the four bolts. Such pressure was also calibrated by the tensions on the bolts measured by the strain gauge method. Settings 1 to

36 corresponded to the number of fixed angular displacements of the four nuts in the counter-clockwise direction from 100% tightness. The angular displacement of the ith setting is thus hi = i  22.5°, and h36 = 36  22.5° corresponds to 100% looseness of the winding clamping pressure. Case 3 To study the change in vibration behavior of the winding due to loose insulation blocks, settings 1 to 4 were designed corresponding to the number of insulation blocks removed from the winding

33

J. Zheng et al. / Applied Acoustics 87 (2015) 30–37

(see Fig. 3(b)). Before the removal of the insulation blocks, the clamping pressures on both winding and core were applied at the 100% level.

2

s1;1 ð f Þ . . . 6. .. 6 sðf Þ ¼ 4 .. . s11;1 ð f Þ   

3

s1;11 ð f Þ 7 7: ... 5 s11;11 ð f Þ

ð1Þ

Case 4 Case 1 To study the relationship between the core clamping looseness and the changes in the winding vibration, the core clamping bolts on the upper yoke were loosened step-by-step, while the winding clamping pressure remained at 100%. For settings 1 to 9, the angular displacement of the bolts for the ith setting is measured by /i ¼ i  90 , where i = 1, 2, . . .9.

3. Results and discussion The frequency spectrum of the vibration velocity at the (n, m)th scanning point of the winding is noted by sn,m, where n is the row index number (increasing from left to right) and m is the column index number (increasing from bottom to top). For a total of 11  11 scanning points on the winding, the following matrix can be constructed to describe the spatial distribution of the winding’s vibration at frequency f:

The magnetostrictive force in the core is approximately related to the square of the primary voltage. As a result, for the primary voltage dominated by the 50 Hz component, the measured winding vibration is mainly dominated by the frequency components at 100 Hz and its harmonics. Such frequency characteristics of the winding vibration are demonstrated by the spatially averaged spectrum as shown in Fig. 4. The vibration components at the harmonics are caused by the saturation and hysteresis between the magnetic flux in the core and magnetizing current in the winding. The spatially distributed root-mean-square (RMS) velocity of the winding is shown in Fig. 5(a). The x and y coordinates are the locations of the scanning points in the horizontal and vertical directions, respectively. The origin of the coordinates is defined at the bottom-left corner of the winding as shown in Fig. 2. The z coordinate shows the magnitude of the winding vibration velocity. The vibration is contributed to by spatial distribution of winding

Fig. 7. Vibration distribution of the winding at 100 Hz for settings 22–36 of Case 2.

34

J. Zheng et al. / Applied Acoustics 87 (2015) 30–37

velocity at 100 Hz and its harmonics. The spectra s(1 0 0), s(2 0 0) and s(3 0 0) are plotted in Fig. 5(b)–(d). The distribution at 100 Hz (Fig. 5b) has approximately bilateral (left–right) symmetry across the horizontal axis, and decreases linearly from the top of the winding (y = 0). Such an increase of the winding vibration from the bottom to the top is consistent with the magnetostrictive strain induced vibration in the core material. As the bottom of the core is fixed to the rigid support, the magnitude of the displacement induced by magnetostrictive strain e is derived as:

dðyÞ ¼ eðy þ yo Þ;

ð2Þ

where yo is the distance from the bottom of the core to the bottom of the winding. The contribution of the vibrations at 200 Hz and 300 Hz to the overall winding vibration is less significant than that at 100 Hz. However, their magnitudes are also well above the background noise level and their spatial distributions can be used to explain the fluctuation of the distributed vibration in Fig. 5(a). The spatial distribution of the transformer vibration is caused by the modal properties and distribution of the excitation forces. Both causes are frequency dependent. This may explain why the spatial distributions of the 200 Hz and 300 Hz components do not follow the same trend of the 100 Hz component in Fig. 5(b). Case 2 Fig. 6 shows the evolution of velocity patterns of the winding vibration at 100 Hz when the winding clamping force is changed from the normal Case 1 to settings 1, 2, . . . and 36 of Case 2. As shown in Fig. 6(a), when the winding clamping bolts are sufficiently tightened (settings 1–4), the vibration distribution follows the pattern observed in Case 1 (Fig. 5b). The vibration amplitude, especially at the bottom and top parts of the winding, varies with the clamping force. The result in Fig. 6 also suggests that, although the global vibration distribution is not changed, the magnitudes of winding vibration at locations close to the clamping surfaces are sensitive to a slight variation of winding clamping forces. At the second stage of winding looseness (settings 6 to 10 for Case 2), significant changes occur at the bottom end of the

winding, as shown in Fig. 6(b). The top part of the winding vibration tends not to follow the linear distribution in the vertical direction. With the decrease of the clamping forces, the asymmetry of the winding vibration at the bottom becomes more obvious (as shown in Fig. 6(c)). For example, the amplitude (in dB) difference of the vibration between ðx; yÞ ¼ ð0; 20Þ cm and ðx; yÞ ¼ ð16; 20Þ cm is 1 dB and 7.8 dB respectively for setting 10 and setting 21, while this difference becomes 0.9 dB for setting 5. This increased asymmetry in the winding vibration may be caused by the fact that the resultant clamping forces created by the four bolts are not the same, even though for each setting the angular displacements of the nuts are the same. In the final stage (settings 22 to 36), the clamping forces created by the four bolts gradually approached zero. Fig. 7(a)–(e) demonstrate that the velocity pattern varies dramatically with the clamping forces and gradually adjusts to a shape of symmetry, as shown in Fig. 7(f). In this final stage, the tension in the winding bolts has been almost completely released. What is most remarkable is that the velocity pattern has been thoroughly inverted from that of Case 1. Fig. 7(f) demonstrates that vibration amplitudes at the top part (y ¼ 20 cm) of the winding become excessively large, nearly 1.5 times that of the bottom part. The decrease in the winding clamping forces also brings changes in the velocity pattern at other frequency components. As presented in Fig. 8(a) and (b), the winding vibration is generally of equal amplitude at 200 Hz from setting 1 to setting 6, and undergoes a slight rise as the clamping force deceases from setting 6 to setting 21. However conspicuous changes in winding vibration can be found in Fig. 8(c) as the clamping force further decreases from setting 22 to setting 27. For this case, the middle part of the winding vibration, in particular, experiences a large increase in velocity. Ultimately, as shown in Fig. 8(d), the velocity pattern at 200 Hz is converted to a shape similar to that at 100 Hz. Case 3 Removal of the insulation blocks changes the mechanical properties of the winding structure. As shown in Fig. 9(a), removing the blocks (settings 1–4) leads to a rise in vibration amplitudes at

Fig. 8. Vibration distribution of the winding at 200 Hz for Case 2 for settings (a) 1, 4 and 6, (b) 6, 14, 18 and 21, (c) 22, 24, 25 and 27, and (d) 28, 29, 31, 34 and 36.

35

J. Zheng et al. / Applied Acoustics 87 (2015) 30–37

Fig. 9. Vibration distribution of the winding for Cases 1 and settings 1–4 of Case 3, at (a) 100 Hz and (b) 200 Hz.

Fig. 10. Vibration distributions of the winding at 100 Hz for settings 1 to 9 of Case 4.

-90

(b) (10log(velocity 2))/dB

(10log(velocity)2)/dB

(a)

-100

-110

-120

-130

10

20

30

-100

-110

-120

-130

-140

Setting 1 - 36

10

20

30

Setting 1 - 36

Fig. 11. Spatial variance for Case 2, for (a) a(1 0 0) and (b) a(2 0 0).

100 Hz, and a fall in amplitudes at 200 Hz. In spite of the obvious increase in vibration at 100 Hz, the velocity distribution at 100 Hz stays almost unchanged. Moreover, the vibration at 200 Hz (Fig. 9(b)) only yields a minor difference from that of Case 1 for small changes in the structure (setting 1). However, after more than three blocks are removed (setting 4), the velocity pattern becomes quite different from that of Case 1. This observation

indicates that the vibration patterns at higher frequencies are more sensitive to local changes in the winding’s structure. Case 4 Fig. 10 shows the velocity patterns of the winding vibration at 100 Hz for the ten settings of core clamping pressure. Small

36

J. Zheng et al. / Applied Acoustics 87 (2015) 30–37

changes in core clamping pressure lead to small variations in winding vibration, as shown in Fig. 10(a). When the bolts on the core become loose, significant changes in winding vibration are found (Fig. 10(b)–(d)). Vibration of the core is due to the magnetostriction in the core material. When the core laminations become loose when the core clamping pressure is reduced, the magnetostrictive force will increase the vibration in the core laminations. Since the winding and core are structurally connected, the more vibration will be transmitted to the winding from the increased core vibration. However, it is surprising that the winding velocity patterns at 100 Hz for Case 1, and for settings 1–9 of Case 4 are similar to each other, except for some changes in the symmetry of the patterns of settings 2–9. The asymmetry of the winding vibration may be caused by the non-uniform clamping conditions on the core laminations. For Case 2, the winding velocity pattern at 100 Hz changes dramatically while the winding’s clamping pressure decreases. However, as shown in Fig. 10, the pattern of winding vibration is less sensitive to the variation in core clamping pressure. Spatial variance is used to describe the difference between the pattern s0(f) of Case 1 and winding vibration pattern si(f) of the ith setting in Case n, where n = 2, 3, 4. This variance is given by:

ai ð f Þ ¼

n¼1

m¼1

Dsn;m;i ð f Þ  Dsi ð f Þ 112

(10log (velocity 2))/dB

-105

-115

-120

-125

1

2

3

Setting 1 - 4

4

6

8

Case 1 with full loading

-90 -95

Case 1 without loading

-100

5

x ( ×16mm)

5

10 10

0

y ( ×20mm)

Fig. 14. The vibration distributions of winding at 100 Hz under secondary opencircuit and loaded conditions.

of loading current on the winding vibration. In general, the vibration of transformer structure (core and winding) is mainly exited by the magnetostrictive and electromagnetic forces in the core material. The direct excitation of the winding by normal loading current (e.g. nominal secondary current for transformer under test was about 20 A) is usually much smaller than the excitation in the core. Fig. 14 shows a comparison of the winding vibration at 100 Hz under secondary open-circuit and loaded (20 A) conditions. The distributed vibration for the latter case is only little different from the former. However, if the current becomes extremely large, such as that in the short-circuit situation, the current induced winding vibration will then become important.

(b)

-110

4

-105 0

(10log(velocity 2))/dB

(10log(velocity 2))/dB

-105

2

-85

where Dsn,m,i(f) = sn,m,i(f)  sn,m,0(f) is the difference between vibrations of setting i and that of Case 1 at location (xn, ym) and P11 P11 Dsn;m;i ðf Þ m¼1 Dsi ðf Þ ¼ n¼1 11 is the mean difference of the vibration pat2

(a)

-120

Fig. 13. Spatial variance a(1 0 0) for Case 4.

ð3Þ

terns between two settings. In Fig. 11, a(1 0 0) and a(2 0 0) both increase with the looseness of winding clamping pressure. Fig. 12 indicates that the local changes in the winding’s structure (due to the loss of insulation blocks) also result in a variation of the winding velocity distribution at the dominant frequencies. For this case, the spatial variance also follows the severity trend of the settings. The low amplitudes of a(1 0 0) and a(2 0 0) for Case 3 represent the slight changes of the winding velocity pattern. A different trend in a(1 0 0) is found for Case 4 as illustrated in Fig. 13. Although the looseness of the core clamping bolts does cause fluctuation in the winding vibration distribution, a considerable difference from the trend in Fig. 11(a) was found. The core looseness has less impact on the winding velocity pattern than the winding looseness does. Moreover, the non-monotonic behavior in Case 4 also manifests, in that the spatial variance is not a proper indicator of the core looseness. Although aforementioned results are for open circuit condition when loading current is zero, it is worthwhile to discuss the effects

-115

Setting 1 - 9

2 ;

-110

-125

20log (velocity) (dB)

P11 P11 

-100

-110

-115

-120

-125

-130

1

2

3

Setting 1 - 4

Fig. 12. Spatial variance for Case 3, for (a) a(1 0 0) and (b) a(2 0 0).

4

J. Zheng et al. / Applied Acoustics 87 (2015) 30–37

4. Conclusions This paper provided the first detailed vibration characteristics of a single-phase transformer winding under normal and abnormal operating conditions. The laser scanning technique allowed measurement of the vibration patterns on the testing surface of a transformer winding at 100 Hz and its harmonics. Some results under open-circuit conditions can be summarized as follows: (1) The radial vibration patterns depended heavily on the overall health of the winding structure. When the transformer was operating in a healthy condition, the velocity distribution on the winding at 100 Hz followed a pattern with approximate bilateral (left–right) symmetry across the horizontal axis and an apparent linear decrease along the vertical axis. Once a fault was introduced into the winding, the velocity pattern altered and became asymmetric. (2) Intrinsic faults (such as looseness in winding clamping pressure or removal of insulation blocks) in the winding structure are related to the characteristics of the winding’s vibration patterns at the dominant frequencies. The spatial variance was used to describe the variance of the difference between the winding velocity distributions si(f) and s0(f), which turned out to be a sensitive and accurate measure of the winding faults. Furthermore, the results indicate that the mechanical defects of windings can be diagnosed under open-circuit conditions. (3) Looseness in core clamping pressure is detectable by observing the changes in the winding vibration. However, the spatial distribution of transformer winding vibration is less affected by such faults. The distribution varies with the level of fault severity. The spatial variance is not capable of determining the severity of the core looseness. As far as vibration transmission from the transformer winding to the tank is concerned, the amount of energy flow between them is directly determined by the spatial and frequency properties of the winding vibration. Such properties control the coupling strength between the winding and the surrounding cooling oil and therefore the vibration of the transformer tank. A significant change in the winding vibration resulting from the introduction of artificial faults and variations in clamping pressure strongly suggests: (1) That the mechanical faults and changes in the clamping pressure of the transformer winding are most likely detectable from the changes in the transformer tank vibration; and

37

(2) The possibility of minimizing the coupling between the transformer tanks and the winding/core for achieving control of transformer noise radiation from the sources of sound and vibration.

Acknowledgements This work was completed while the first author was under an exchange program at the University of Western Australia, and was supported in part by CRC for Infrastructure Engineering Asset Management (CIEAM) and Public Projects of Zhejiang Province (Grant No. 2013C31008). The first author would like to thank the financial support from the China Scholarship Council (CSC). References [1] Berler Z, Golubev A, Rusov V, Tsvetkov V, Patterson C. Vibro-acoustic method of transformer clamping pressure monitoring. In: Conference Record of the 2000 IEEE International Symposium on Electrical Insulation, Anaheim, California, USA; 2000. p. 263–6. [2] Munir BS, Smit JJ. Evaluation of various transformations to extract characteristic parameters from vibration signal monitoring of power transformer. In: Electrical insulation conference, Annapolis, Maryland, USA; 2011. p. 289–3. [3] Ming RS, Pan J, Norton MP, Wende S, Huang H. The sound-field characterisation of a power transformer. Appl Acoust 1999;56:257–72. [4] Ming RS, Pan J, Norton MP, Teh M. The passive control of tonal sound radiation from vibrating structures. Appl Acoust 2000;60(3):313–26. [5] Chen Y, Zhang JZ, Wu CG, Cheng M. Research of active noise control for transformer based on piezoelectric ceramic actuator. Appl Mech Mater 2013;416–417:800–5. [6] Lord T, Hodge G. Interfacing on-line monitoring technologies to power transformers. [accessed 9.07.10]. [7] Bagheri M, Naderi MS. On-line transformer winding deformation diagnosis: a profound insight to methods. In: 26th International power system conference, Tehran, Iran; 2011. p. 1–14. [8] Li Y, Zhou W, Jing Y, Sun X. Axial vibration analysis of power transformer active part under short-circuit, In: International conference on electrical machines and systems, Beijing, China; 2011. p. 1–4. [9] Uchiyama N, Saito S, Kashiwakura M, Takizawa A, Morooka H, Itoh Y, et al. Axial vibration analysis of transformer windings with hysteresis of stress-andstrain characteristic of insulating materials. In: Power engineering society summer meeting, Seattle, WA, USA; 2000. p. 2428–33. [10] Li H, Li Y, Yu X. Axial vibrations modal analysis and computation of power transformer windings under different levels of pre-compression. In: International conference on applied superconductivity and electromagnetic devices, Chengdu, Sichuan, China; 2009. p. 229–32. [11] Liang Z, Li J, Tang R. Axial vibrations of transformer windings under shortcircuit conditions. In: International conference on electrical machines and systems, Beijing, China; 2003. p. 332–5. [12] Masato M, Masao Y, Yasuo O. Vibration analysis of a 3-phase model transformer core. Electr Eng Jpn 1997;119:1–8. [13] Hackl A, Hamberger P. Investigation of surface velocity pattern of power transformers tanks, In: International conference on electrical machines, Rome, Italy; 2010. p. 1–3.