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Condition monitoring of power transformer using MEMS sensor.


Transformer is critical unit in a power network. Failure of transformer would cause interrupted power supply and hence may lead to costly repairs and replacement. Therefore it is desirable to detect potential failures as early as possible. Model based fault diagnosis has become increasingly popular for condition monitoring of transformers (Arivamudhan.M and Santhi.S, 2013). Transfer function method in particular, is highly employed for the identification of winding deformation faults (Rahimpour.E et al., 2003; Florkowski.M and Furgal.J, 2003). Also high frequency modeling is shown to be useful for condition monitoring purposes (Huseyin Akcay et al., 1998).

Recently, condition monitoring of transformers through tank vibration analysis has drawn considerable attention of the researchers (Bartoletti.C et al., 2004; Aschwanden.T.H et al., 1998). Transformer tank vibration modeling is attempted to diagnose winding deformation due to short circuit (Garcia.B et al., 2006a, b). Since vibration signature of transformer has very close relation with its mechanical structure such as winding and the core, vibration measurement and analysis method of condition monitoring would be effective for the diagnosis of mechanical faults.

Analysis of power system signals and its harmonics by extended Prony method has been proven to be effective (Zhijian Hu et al., 2006; Wegelin.F.A et al., 2005; Barone.P, 1998). This paper focuses a new method for condition monitoring of transformer using MEMS (Micro Electro Mechanical Sensor) based sensor to acquire the transformer winding vibration signal and analyze by the extended Prony method.

Motivation and objective:

The MEMS sensors are increasingly becoming popular in wide range of applications. Since these sensors are less expensive and are available with adequate sensitivity, attention is focused on the use of MEMS sensor for the transformer winding vibration signal measurement. Prony analysis is an emerging methodology that extends Fourier analysis by directly estimating the frequency, amplitude, damping factor and phase of model components present in the signal (Hauer.J et al., 1990). Though it is not a spectral estimation technique, the method has close relationship to the least squares linear prediction algorithms used for autoregressive (AR) and autoregressive moving average (ARMA) parameter estimation. The Prony method seeks to fit a deterministic exponential model to the data in contrast to AR and ARMA methods that seek to fit a random model to the second order statistics (Zbigniew Leonowicz et al., 2003).

This paper aims at combining the advantages of the MEMS sensor for the measurement of the vibration signal and extended Prony method for the analysis of vibration signal to identify the mechanical faults in the transformer winding structure. The ADXL203, a dual axis accelerometer with signal conditioned voltage outputs on single monolithic IC is employed to measure the winding vibration.

Theory of extended prony method:

Prony method is a technique for modeling time series data as a linear combination of exponentials and it extends Fourier analysis. It is a technique of analyzing signals to determine magnitude, damping, phase, and frequency information contained in the signal.

Fourier analysis has several drawbacks when it is applied to the time-domain signal which is corrupted by noise. First, experimental time-domain signals are of finite duration. Fourier transformation of truncated time-domain signal leads to undesirable frequency-domain 'wiggles' which make it hard to observe a small peak in the vicinity of a large peak (Marshall.A.G and Verdun.F.R, 1990). Second, Fourier transforms distributes time-domain noise uniformly throughout the frequency domain which leads to limitation in the certainty with which peak frequencies, widths, magnitudes and phases could be computed. Third, discrete sampling of a time-domain continuous signal causes limitation in obtaining the spectral information content (Marshall.A.G and Verdun.F.R, 1990).

Due to the ability to identify the damping factors of transients, Prony analysis can accurately identify growing or decaying components of signals. Extended Prony method (EPM) uses the linear combination of a group of exponential functions to fit a cycle of sampling data. In addition the extended Prony method fits a reduced-order model to higher-order system both in time and frequency domains.

Consider a harmonic signal composed of p exponential functions with arbitrary amplitudes, phase angles and decaying factorials. The mathematical model in discrete time function form is

[??](n) = [[summation].sup.p.sub.i=1] [b.sub.i] [z.sup.n.sub.i] where n = 0,1, ... ... ... ... ... .. (N - 1) (1)

[??](n) is the approximation of x(n)

In equation (1) [b.sub.i] and [z.sub.i] are complex numbers and

[b.sub.i] = [A.sub.i] exp (j[[theta].sub.i]), [z.sub.i] = exp [([[alpha].sub.i] + j2[pi][f.sub.i])[DELTA]t]

where [A.sub.i] is amplitude, [[theta].sub.i] is phase angle, [[alpha].sub.i] is decaying factorial, [f.sub.i] is frequency, [DELTA]t is sampling interval and N is the number of sampling points. Transform (1) into a matrix form as follows,


To determine the solution of the Prony model, a cost function as defined below is to be constructed. e(n) = [[summation].sup.N-1.sub.n=0][[absolute value of (x(n) - [??] (n))].sup.2] (3)

The parameters [A.sub.i], [[theta].sub.i], [[alpha].sub.i] and [f.sub.i] are determined by solving a non-linear least square equation. This requires the determination of the roots [z.sub.i] of the polynomial equation which uses these coefficients as its parameters.

Substituting [z.sub.1], ...., [z.sub.p] into (2), the least square solution is

b = [([z.sup.T]z).sup.-1][z.sup.T][??]

Finally, the parameters of harmonics are obtained as follows


Implementation of extended prony algorithm through simulation:

In order to verify the effectiveness of the extended Prony method, the algorithm is developed and implemented through simulation using Matlab coding. A signal v(t) as defined below is simulated and is shown in Fig. 1. The signal is transformed to frequency domain by Fourier transformation. The transformed signal is shown in Fig. 2 which depicts the frequency contents present as 50 Hz, 750 Hz, 1050 Hz and 1500 Hz.

v(t)= 10cos(2[pi]f+[pi]/3) + 5cos(30[pi]f+[pi]/6) + 2cos(42[pi]f+[pi]/6) + cos (60[pi]f+[pi]/4)

The parameters such as frequency, amplitude, damping factor and phase characterizing the signal v(t) are extracted from the simulated signal by applying extended prony algorithm and these parameters are tabulated in Table 1. This clearly indicates that the signal v(t) can be expressed as a sum of eight (order) exponential functions with amplitude, frequency, damping factor and phase as tabulated in table. 1.

To elucidate the advantage of Prony method compared to FFT, a signal x(t) defined as x(t)= 15[e.sup.-20t]+10cos(2[pi]ft+[pi]/3) + 2cos(6[pi]ft+[pi]/6) as shown in Fig. 3 that consists of aperiodic component is simulated and considered for the analysis using FFT and Prony method. The FFT analysis provides only the frequency and amplitude information as shown in Fig. 4 whereas Prony analysis yields the damping factor information also as indicated in Table 2.

Hence one can appreciate that Fourier transformation provides only frequency amplitude and phase information whereas extended Prony analysis provide all of these and in addition damping factor too and suited precisely for the analysis of signals that contain aperiodic components.

It is observed that the computational precision is high if the chosen order is almost equal to the theoretical order and it is the characteristic feature of this method. Further the computation burden is reduced as compared to Fourier transformation. The extended Prony method thus can estimate the parameters of the signal effectively since it treats the whole information of the signal.

Mems sensor for vibration signal measurement:

As MEMS sensors provide low power, compact and robust sensing compared to conventional accelerometers it is preferred in this work. Further system integration is another feature that motivates its choice. This work employs ADXL203 a high precision, low power complete dual axis acceleration measurement system on a single, monolithic IC. It contains a polysilicon surface micro machined sensor and is used to sense both static and dynamic acceleration. This means that the sensor is suited for sensing tilt and brute acceleration. The ADXL203 has the capability of measuring both positive and negative accelerations to at least [+ or -] 1.7 g. It is a solid state MEMS accelerometer with analog output. The output must be filtered to limit the aliasing errors. It has provisions for band limiting the [X.sub.OUT] and [Y.sub.OUT] pins and capacitors must be added at these pins. This filtering improves measurement resolution and prevents aliasing. The bandwidth of the accelerometer is selected by using capacitor [C.sub.X] and capacitor [C.sub.Y] at the [X.sub.OUT] and [Y.sub.OUT] pins. The analog output may be selected for typical bandwidth of 0.5 Hz to 2.5 kHz to suit the application.

Validation of prony algorithm for the analysis of vibration signal:

The experimental setup to measure vibration of any vibrating component is shown in Fig. 5. The measurement system consists of MEMS sensor suitably configured with proper power supply and connected to Agilent DSO 3062A to acquire the signal from the vibrating surface. In order to verify measurement of vibration using MEMS sensor, the sensor system is arranged to acquire the vibration signal generated on the table by hitting the table surface with a hammer. The measured vibration signal through DSO is shown in Fig. 6. The signal is transformed to frequency domain by Fourier transformation and the frequency domain representation is shown in Fig. 7. It is observed from Fig. 7 that the spectrum of the measured vibration signal contains frequency components of which 15Hz, 28 Hz, 55 Hz, 76 Hz and 122 Hz are dominantly present. The parameters extracted through extended Prony analysis are tabulated in Table. 3. As mentioned earlier, the precision of extraction can be improved by proper choice of the order of the model. Thus the performance of MEMS sensor encourages that it can be suitably positioned to acquire vibration signal and the analysis be carried out by employing extended Prony method.

Device under test:

To validate the use of MEMS sensor for the measurement of transformer winding vibration under short circuit condition, the device under test (DUT) considered is a specially designed single phase transformer winding structure with rating 2 kVA, 50 Hz. The structure is popularly known as jumping ring model. It is a two winding transformer with provision for secondary winding deformation in a reproducible manner. The primary winding has 850 turns and the secondary winding has 10 turns, outer diameter of 10.5 cm and an axial length of 10.4 cm. The core length is 18.6 cm and the area is 2.9 cm X 2.9 cm. The secondary winding is 10 turns, 12-gauge coil of mass 30 g. The outer diameter is 4.4 cm and has an axial length of 1 cm. Fig. 8 shows the photograph of the DUT and schematic diagram of the DUT is shown in Fig. 9.

Vibration signal analysis by epm for winding deformation detection:

The experiment is conducted by exciting primary winding from a 230V, 50 Hz auto transformer. With secondary winding kept under short circuited condition, the excitation to the primary winding is gradually increased. The vibration generated in the secondary winding is captured using Agilent DSO 3062A. To verify the application of extended Prony method for the detection of winding deformation, the vibration of the secondary winding when there is no movement and when there is axial displacement are measured. It is observed that when the excitation to the primary is such as to send a current of more than 5A through it, the secondary winding experiences an axial force causing it to move up. The measured secondary winding acceleration when there is no axial movement (with primary winding current of 2A) is shown in Fig. 10. The vibration thus measured is considered to be vibration under normal condition. The frequency domain representation of the corresponding secondary winding acceleration is shown in Fig. 11. Table. 4 shows the details of the extracted secondary acceleration Prony model parameters.

The winding vibration is due to the electromagnetic forces which are caused by the interaction of the current through the winding and the leakage flux. The electromagnetic forces acting on the conductors of the winding are proportional to the square of the load current. Due to this the main vibration frequency of the winding is 100 Hz. This is obviously seen from Fig. 11. Also this is observed from the extracted secondary vibration signal parameters as in Table. 4. In addition to 100 Hz frequency component the method extracted other frequency components too with suitable amplitude, damping factor and phase. Thus it is evident that the vibration signal could be suitably analyzed and the parameters characterizing it are obtainable.

To demonstrate the suitability of the proposed method for winding deformation detection, the experiment is conducted by adjusting the excitation to the primary winding as 6A in order that the secondary winding experiences axial displacement. This creates vibration in the secondary winding and is regarded as vibration under fault condition. The measured secondary winding vibration under fault condition is shown in Fig. 12. The corresponding frequency domain representation is shown in Fig. 13. The extended Prony analysis is carried out for the secondary winding vibration under fault condition and the extracted parameters are shown in Table. 5. Comparison of tables 4 and 5 reveals that there are significant changes in the model parameters extracted from the secondary winding vibration under normal and fault condition. Thus it is evident that MEMS sensor can measure the vibration and further the extended Prony analysis could serve the purpose of condition monitoring of transformer.


This paper has demonstrated in a systematic manner the application of MEMS sensor and extended Prony algorithm for the condition monitoring of transformer. Initially the algorithm was validated for a simulated signal consisted of known frequency components. Next the performance of MEMS sensor was validated through the acquisition of a random vibration signal generated on a vibrating table. Finally the vibration measurement and subsequent analysis by extended Prony method was implemented to condition monitoring problem for a specially designed two winding transformer. Since extended Prony method attempts to fit a model to the signal by considering the complete information of it, the transient details could also be followed effectively. Since the results are encouraging the method could be satisfactorily applied for the condition monitoring of transformers and provides facility for the safe operation of the transformer.


Article history:

Received 3 September 2014

Received in revised form 30 October 2014

Accepted 4 November 2014


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Arivamudhan, M and Santhi, S

Annamalai University, Department of Electronics and Instrumentation Engineering, Annamalai Nagar, Tamil Nadu, India

Corresponding Author: Arivamudhan, M., Department of Electronics and Instrumentation Engineering, Annamalai university, Annamalai Nagar, Tamil Nadu, India.

Tel: +919842565051, E-mail:

Table 1: The mode of Prony model for signal v(t).

Frequency (Hz)   Amplitude   Damping factor   Phase (rad)

50                  10            0.0              1
750                  5            0.0             0.5
1050                 2            0.0             0.5
1500                 1            0.0             0.8

Table 2: The mode of Prony model for signal x(t).

Frequency   Amplitude   Damping factor   Phase
(Hz)                                     (rad)

0              15             20           0
50              5            0.0         1.0472
150             2            0.0         0.5236

Table 3: The mode of Prony model for measured vibration signal.

Frequency    Amp     Damping   Phase(deg)
(Hz)                 factor

15.3787     0.0006   0.6969     -124.717
28.1628     0.0007   1.2452     -212.357
55.8469     0.0004   -0.1901    -201.667
76.9949     0.0002   -0.4902    -124.265
122.1547    0.0002   -0.5770    -106.312

Table 4: Prony model parameters for vibration signal under normal

Frequency (Hz)   Amp   Damping factor   Phase (deg)

100.4            0.2       -11.8            0.2
791.1            0.1      -274.64           0.5
2473.5           0.1      -255.31           1.5

Table 5: The mode of Prony model for vibration signal under fault

Frequency (Hz)   Amp   Damping factor   Phase(deg)

100.7            0.2       -73.4           0.2
782              0.1        -339           0.5
2483.2           0.1        -268           1.5
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Author:Arivamudhan, M.; Santhi, S.
Publication:Advances in Natural and Applied Sciences
Article Type:Report
Geographic Code:9INDI
Date:Nov 15, 2014
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