Non-linear Modeling of Oil-paper Insulation for ... - IEEE Xplore

IEEE Transactions on Dielectrics and Electrical Insulation Vol. 22, No. 4; August 2015

2165

Non-linear Modeling of Oil-paper Insulation for Condition Assessment using Non-sinusoidal Excitation A. Pradhan Department of Electrical Engineering Jadavpur University, Kolkata, 700032, India

C. Koley Department of Electrical Engineering National Institute of Technology, Durgapur, 713209, India

B. Chatterjee and S. Chakravorti Department of Electrical Engineering Jadavpur University, Kolkata, 700032, India

ABSTRACT In high voltage engineering, dielectric response analysis is a widely used tool for insulation diagnostic. Voltages used for studying dielectric response in the laboratory are usually sinusoidal in nature. But the insulation system in operation on site is often stressed by voltages that may deviate significantly from a sinusoid. Thus the use of nonsinusoidal waveform in obtaining the dielectric response is a desirable study for advanced insulation diagnostic technique. Present work involves assessing the condition of electrical insulation using dielectric response analysis under the influence of nonsinusoidal voltage waveform. In dielectric response analysis, characteristics curve of phase response over a frequency band is used to predict the insulation condition, which involves expertise. In this respect parameterization of insulation condition can make the assessment technique much simpler. But the nonlinear behavior of insulation restricts such an attempt to be accurate enough for reliable assessment of minute degradation of insulation condition. Therefore, the present work proposes a non-linear system identification technique, in an attempt to parameterize insulation condition. In this work, a suitable excitation signal has been designed so that the observed response becomes representative of the behavior of the whole system dynamics over the frequency band of interest. Tests have been performed with insulations having different moisture contents. The obtained system parameters, through nonlinear Hammerstein model, were found to be consistent over several experiments, and also accurate enough to detect small variation of moisture content. The proposed method is based on the time domain measurement of input excitation voltage and corresponding response current through the insulation. Index Terms - System identification, nonlinear systems, frequency domain spectroscopy, Hammerstein model, insulation condition monitoring, transformer oilpaper insulator.

1 INTRODUCTION AS the lifetime of power transformers is directly related to the insulation quality, continuous monitoring of insulation quality of power transformer is a practically significant issue. In this context application of new diagnostic tools and monitoring techniques gain increasing importance [1-5]. Manuscript received on 17 December 2014, in final form 9 August 2014, accepted 11 January 2015.

Numbers of modern diagnostic techniques used to assess the insulation condition of transformers include, but not limited to, dissolved gas analysis (DGA), degree of polymerization (DP) measurement, and Furan Analysis, the classical techniques like insulation resistance, power frequency dissipation factor and polarization index measurements [1, 2, 6]. Since the solid insulation within the transformer is not accessible, the main aim of any diagnostic procedure is measurement of moisture in the oil-impregnated paper/pressboard insulation without having to open the

DOI 10.1109/TDEI.2015.004504

2166

A. Pradhan et al.: Non-linear Modeling of Oil-paper Insulation for Condition Assessment using Non-sinusoidal Excitation

transformer to take samples from critical locations. With time researchers have developed more reliable and appropriate tools to diagnose power equipment insulation non-destructively in the field. The time domain based polarization/depolarization current (PDC) and frequency domain spectroscopic (FDS) measurements have been developed over the last decades [712]. This is facilitated significantly by the availability of modern computer controlled instrumentation. Dielectric spectroscopy in frequency domain offers new opportunities for off-line, on-site insulation condition assessment of HV electric power equipment facilitating predictive maintenance. Based on the dielectric theory, it is not essential to use a sine wave excitation to obtain frequency domain data. A nonperiodic excitation can also be used in time domain for measuring the polarization and depolarization current. Researchers [13] have suggested the use of arbitrary waveform impedance spectroscopy (AIWS), which they found to be less time consuming and applicable for online condition assessment. Voltages used in FDS technique are usually sinusoidal in nature, but today¶s insulation system in operation on site is often stressed by voltages, which deviate significantly from a sinusoid, mainly due to increasing use of power electronic devices. Thus the use of non-sinusoidal waveform in obtaining the dielectric response is a desirable study for advanced insulation diagnostic technique, which is also evident from the work of [14], for measurement of dielectric parameters for characterization of non-linear stress grading systems. The authors [15] applied periodic semi-square voltage waveform with time period around 0.01 s, and found that AIWS measurement system provides results consistent with the FDS technique, while it requires less time for the measurement. Accurate assessment of insulation condition is more important than measurement time. The dielectric frequency response reported by many authors [7, 9, 10, 12, 16] are significantly different from system to system. Even for similar power transformers responses as obtained were found to be different due to the fact that dielectric responses in either time or frequency domains are influenced by many factors, such as temperature, moisture content, chemical composition of dielectrics, structure of insulation system, frequency, etc. [17]. Therefore insulation condition assessment from the frequency response results in FDS could be ambiguous. Very recently researchers [12] have presented empirical equations between three characteristic frequencies of FDS (10-3, 10-2, and 10-1 Hz) with aging of oil-pressboard sample when tested at laboratory. The authors of [16] realized a Debye circuit model for oil paper condenser bushing. They also identified model parameters which they found to be sensitive to temperature and moisture content. They obtained the model parameters through system identification from the frequency domain response, which again involves frequency domain data to be obtained first. On the other hand the authors [18] applied time domain based method with the help of depolarization current curve to identify the circuit model of insulation. In the present work, it has been observed that the oil paper insulation of power transformer behave as non-linear system.

The system non-linearity has also been reported in [19-20]. Therefore, for accurate assessment of insulation condition by applying non-sinusoidal waveform having frequency band similar to that experienced by transformers in the field, some alternative method is preferable. In this context, the present paper describes the findings of non-liner gray box identification results when applied on power transformer with oil-paper insulation having different moisture content. Moreover, in this work suitable model has been identified from the time-domain voltage and current data rather than using frequency domain data which require testing with variable sinusoidal frequency to obtain gain and magnitude responses. Therefore, the proposed insulation condition assessment system is easier to implement, less time consuming and can be used to identify insulation condition through fixed set of parameters, rather than observing shifting of curves as used in the case of FDS.

2 EXPERIMENTAL SETUP A schematic diagram of the experimental arrangement is shown in Figure 1, which consists of a computer to generate arbitrary waveform from previously stored waveform data file through DCA module (NI PCI-5412) and to acquire the two voltage signals, i.e. voltage applied across the test object and the voltage across shunt resistance representing current through it. The voltage output of DAC goes to the power amplifier containing a current amplifier followed by step-up transformer for the low and medium frequency range. For very low frequency range (DC to < 1 Hz) an arbitrary waveform generator (6517B Keithley Instruments) has been used instead of PC to generate it.

Figure 1. Schematic diagram of the experimental setup.

2.1 TRANSFORMER MODEL FOR TESTING A model transformer has been designed for testing, with a core of Galvanized Iron (GI) sheet. The LV and HV winding sections were modeled by forming layers of Press board Kraft paper - Copper foil - Kraft paper of suitable thicknesses. A suitable gap was maintained in between LV and HV winding sections to model the oil duct. The whole insulation structure was then placed in oil filled GI tank over several days for proper impregnation and seasoning. A schematic diagram of the model transformer layout is shown in Figure 2. The detailed description of the test sample can be found in [21].


2167

3.1 DATA ACQUISITION AND PREPROCESSING The two voltage signals, i.e. the voltage applied across the test object and the voltage across the shunt resistance representing the response current have been acquired with the following sampling frequency; ݂௦ ൌ ͳͲͲͲ ൈ ݂‫݁݃ܽݐ݈݋ݒ݈݀݁݅݌݌݂ܽ݋ݕܿ݊݁ݑݍ݁ݎ݂݈ܽݐ݊݁݉ܽ݀݊ݑ‬

In each case recording time was set in such a way that at least two complete cycles of the voltage can be recorded, from the automatically selected triggering point at zero crossing of the applied voltage. Figure 2. Top view of the model transformer layout design.

2.2TEST SAMPLE PREPARATION The paper insulations were first placed inside a low pressure sealed chamber and heated at 90 qC continuously for sufficient time to remove any residual moisture that might have ingressed during sample preparation. After the heating process, weight (Wb) of each sample is measured with a precision balance. The samples are then exposed to air and kept for sufficient time to absorb moisture. After allowing sufficient time to achieve moisture ingress, weight (Wa) of each sample is measured. From Wb and Wa, the moisture content of each sample is calculated using (1). The moisture-content (MC) of the sample at a particular temperature

w w w a

b

u 100%

(1)

b

Three different set of samples havingmoisture contents (MC) of 1, 2 and 3.2%, have been prepared in the laboratory for experimental purpose. The samples are then placed into the GI tank as shown in Figure 1. The tank is having cross-section area of 130 mm × 130 mm and height of 110 mm. The tank is filled with same volume of transformer oil for each sample to impregnate paper and pressboard material. The whole specimen is placed inside a sealed chamber for several days for proper impregnation with no further moisture ingress. Different type of tests as performed on these insulations while maintaining the temperature at 50 0C, are discussed in the following section.

After acquiring the signals, high frequency noises were removed by suitably designed low pass digital FIR filter (6thorder). Since, a FIR filter produces frequency dependent phase shift, which is not at all desirable in this application, therefore to avoid phase distortion, zero-phase filtering was performed by processing the input data through the FIR Filter, in both the forward and reverse directions [22]. After removal of noises, all the signals were normalized by a scale factor obtained from the individual experimental data. Up and down sampling of the signal as and when required, has been performed by interpolation technique using a 4 thorder FIR filter. 3.2 MEASUREMENT OF LOSS ANGLE The method is based on the measurement of two signal, i.e. voltage (Vc) across and current (Is) through the test object. The current (Is) is measured by measuring the voltage (Vs) across the small shunt resistance (Rsh). Then equivalent impedance of the test sample is obtained from; ܸܿ െ ܸ‫ݏ‬ ܼ݁‫ ݍ‬ൌ ‫ݏܫ‬ whereǡ ‫ ݏܫ‬ൌ ܸ‫ݏ‬ൗܴ‫݄ݏ‬. The basic equivalent circuit of the measuring system is shown in Figure 3. )LQDOO\WKHGLHOHFWULFORVVDQJOHį has been obtained by the measurement of phase difference between Vc and Is,with the help of high-accuracy Fourier Analysis based on synchronous sampling techniques [23]. This method has been followed to obtain loss factors of test specimen under variable frequency sinusoidal and triangular excitation waveforms.

3 EXPERIMENTAL PROCEDURE Various tests have been performed over several months.These can be categorized indifferent groups according to the type of excitation voltage applied, which are sinusoidal and triangular waveformof varying frequency from 0.001 Hz to 10 kHz and pseudo square waveform of variable frequency in the range of 0.005 to 500 Hz. Several experiments have been performed with these inputs, by altering the method of varying the time period or the pulse width of the pseudo square waveform along with the amplitude varying from 150 to 10 V. Tests have been repeated for three different moisture content of paper insulation, which are of 1, 2 and 3.2%. For each of the samples, tests have been repeated three times over considerable period of time for better generalization of the experimental data.

Figure 3. Basic equivalent circuit of the experimental measurement.

3.3 SYSTEM IDENTIFICATION IN TIME DOMAIN The insulation condition could be better analyzed if it can be represented with the help of mathematical model, which requires identification ofsystem structure and the value of

2168


its parameters. The system identification has long been applied in various fields of engineering, mainly in the field of control engineering [24], where lot of advanced algorithm can be found to identify black-box or gray-box system. The theoretical background of linear system identification has been advanced in last few decades, but as most of the practical systems are nonlinear in nature therefore to improve accuracy, nonlinear system identification is gaining more importance, where the basic concepts of linear system identification has been extended. The concept of system identification in time domain has been represented with the help of Figure 4.In this method for some given input, the objective is to form a mathematical model such that, it is able to provide same response as obtained from actual test system.

Figure 4. Functional block of system identification and Hammerstein model.

In the initial stages of the work, linear system identification technique has been applied first, but it has been observed that the response of the system contains some amount of static nonlinearity. Therefore nonlinear system identification approach has been considered. Among the various nonlinear approaches, most popular and conventional algorithms are Winner, Hammerstein, and Hammerstein-Winner model. The Hammerstein model consists of static nonlinear sub-system followed by a dynamic linear sub-system, which is reverse in the case of Winner model, which is also quite popular. In some of the application Hammerstein-Winner model has been used where the linear sub-system is placed in between two nonlinear sub-systems.In the following section the theoretical background of system identification through Hammerstein model is presented, the details can be found in [25, 26]. The nonlinear Hammerstein model takes input signal ܸሺ‫ݐ‬ሻand the generated output signal ‫ܫ‬ሺ‫ݐ‬ሻ for estimation of the nonlinear model. It parameterizes the pre-defined model structure by determining suitable estimated output ‫ܫ‬መሺ‫ݐ‬ሻ in order to minimizing the error ݁ሺ‫ݐ‬ሻ. For the Hammerstein system as shown in Figure 4, ܸത ሺ‫ݐ‬ሻ is the output of the nonlinear sub-system due to inputܸሺ‫ݐ‬ሻ and ‫ݎ‬ሺ‫ݐ‬ሻ is the white noise with zero mean and standard GHYLDWLRQ RI ı2, whose value is determined from the measurement of signal-to-noise ratio. The inner ഥ ሺ‫ݐ‬ሻ,‫ݓ‬ሺ‫ݐ‬ሻ, and ‫ݕ‬ሺ‫ݐ‬ሻ are not measurable. The variablesܸ ߯ሺǤ ሻis static nonlinearity function generally represented as

sum of nonlinear basis functions, therefore the output ܸത ሺ‫ݐ‬ሻcanbe written as; ܸത ሺ‫ݐ‬ሻ ൌ ‫݌‬ଵ ߯ଵ ൫ܸሺ‫ݐ‬ሻ൯ ൅ ‫݌‬ଶ ߯ଶ ൫ܸሺ‫ݐ‬ሻ൯ ൅ ‫ ڮ‬൅ ‫݌‬௔ ߯௔ ൫ܸሺ‫ݐ‬ሻ൯ ൌ ࢖࣑൫ܸሺ‫ݐ‬ሻ൯ The linear sub-system is generally expressed with the help ofnumerator and denominator polynomials of the form; ܰሺ‫ݖ‬ሻ ൌ ͳ ൅ ݊ଵ ‫ି ݖ‬ଵ ൅ ݊ଶ ‫ି ݖ‬ଶ ൅ ݊ଷ ‫ି ݖ‬ଷ ൅ ‫ ڮ‬൅ ݊௕ ‫ି ݖ‬௕ ‫ܦ‬ሺ‫ݖ‬ሻ ൌ ͳ ൅ ݀ଵ ‫ି ݖ‬ଵ ൅ ݀ଶ ‫ି ݖ‬ଶ ൅ ݀ଷ ‫ି ݖ‬ଷ ൅ ‫ ڮ‬൅ ݀௖ ‫ି ݖ‬௖ whereǡ ܽ,ܾ, and ܿ are the degree of the polynomials and ‫ି ݖ‬ଵ is the zero order hold system.In the case on linear-only-model identification the ߯ሺǤ ሻ ൌ ͳ, therefore ܸത ሺ‫ݐ‬ሻ ൌ ܸሺ‫ݐ‬ሻ. Remaining procedures are same as nonlinear model identification, as described in the following section. Now, the objective is to find the values of࢖ ‫ א‬Թܽ ,࢔ ‫א‬ Թܾ ,andࢊ ‫ א‬Թܿ with givenܸሺ‫ݐ‬ሻ, ‫ܫ‬ሺ‫ݐ‬ሻ, ܽ, ܾ and ܿ, so that the ݁ሺ‫ݐ‬ሻ is minimum. This search process can be performed in many ways. As present application involves input and output data of finite length (‫)ܮ‬, use of Newton¶V iterative algorithm for the Hammerstein model is an attractive choice. For the linear discrete time sub-system this input and output relationship can be represented as, ത ሺ݇ሻ ൅ ‫ݎ‬ሺ݇ሻ, ݇ ൌ ͳǡ ʹǡ ǥ ǡ ‫ܮ‬ ‫ܦ‬ሺ‫ݖ‬ሻ‫ܫ‬መሺ݇ሻ ൌ ܰሺ‫ݖ‬ሻܸ (2) In order to represent this input output relationship in matrix form, new set of matrix variables has been formed, which are; Measured output ࡵሺ‫ܮ‬ሻ ؔ ሾ‫ܫ‬ሺͳሻǡ ‫ܫ‬ሺʹሻǡ ǥ ǡ ‫ܫ‬ሺ‫ܮ‬ሻሿ ‫ א‬Թ௅ , the coefficients of the polynomials ࢔ ࢽ ؔ ൥ࢊ൩ ‫ א‬Թ஽ ǡ ‫ ܽ ؔ ܦ‬൅ ܾ ൅ ܿǡthe estimated output ࢖ information vector, ் ࢼሺ݇ሻ ؔ ൣെ‫ܫ‬መሺ݇ െ ͳሻǡ െ‫ܫ‬መሺ݇ െ ʹሻǡ ǥ Ǥ Ǥ ǡ െ‫ܫ‬መሺ݇ െ ܿሻ൧ ‫ א‬Թ௖ , and input information matrix

࣑൫‫ݑ‬ሺ݇ െ ͳሻ൯ ‫ۍ‬ ‫ې‬ ‫࣑ ێ‬൫‫ݑ‬ሺ݇ െ ʹሻ൯ ‫ۑ‬ ௕ൈ௔ ࢻሺ݇ሻ ؔ ‫ێ‬ ‫אۑ‬Թ ‫ڭ‬ ‫ێ‬ ‫ۑ‬ ‫࣑ۏ‬൫‫ݑ‬ሺ݇ െ ݊௕ ሻ൯‫ے‬ Then Hammerstein systems in matrix form can be written as; ‫ܫ‬መሺ݇ሻ ൌ ࢊࢼ் ሺ݇ሻ ൅ ࢔் ࢖ࢻሺ݇ሻ ൅ ‫ݎ‬ሺ݇ሻ

Further combining all the matrixes, for the L number of measurement data. ઴଴ ሺ‫ܮ‬ሻ ؔ ሾࢼሺͳሻǡ ࢼሺʹሻǡ ǥ ǡ ࢼሺ‫ܮ‬ሻሿ் ‫ א‬Թ௅ൈ௖ ࢖் ࢻ் ሺͳሻ ‫ې ் ் ۍ‬ ሺͳሻ‫ۑ‬ ઴ሺ࢖ሻ ؔ ‫ࢻ ࢖ێ‬ ‫ א‬Թ௅ൈ௕ ‫ڭ‬ ‫ێ‬ ‫ۑ‬ ‫ ்ࢻ ்࢖ۏ‬ሺ‫ܮ‬ሻ‫ے‬ Now, a least square cost function can be formed as; ‫׋‬ሺࢽሻ ൌ ԡࡵሺ‫ܮ‬ሻ െ ઴଴ ሺ‫ܮ‬ሻࢊ െ ઴ሺ࢖ሻ࢔ԡଶ , and an iterative loop can be made to minimize ‫׋‬by updatingࢽ, which will iterate until change in ߛ values becomes sufficiently small. The system identification process in general isperformed in four steps, which are as follows; 3.3.1 DATA PROCESSING It involves measurement of suitable set of input and output variables, with suitable sampling interval. Design of a suitable


input excitation voltage signal is necessary so that it becomes representative signal, which will be able to represent the total system performance in the operating region. In the present work variable frequency pseudo square (VFPS) excitation signal of variable amplitudehas been designed, which covers the frequency bandwidth of interest. Moreover this kind of signal contains various steps of different duration. 3.3.2 MODEL STRUCTURE SELECTION In this step a suitable model structure has to be defined, which consists of defining type of static nonlinearity for the nonlinear function߯ሺǤ ሻ, which was chosen to be polynomial, as it is conventional and also defining the number of numerator and denominator coefficients for the dynamic liner part. Due to non-availability of any prior information about this model structure and the order of the polynomial function a trial and error method has been adopted, details of which is discussed in a later section. 3.3.3 MODEL ESTIMATION For a given model structure and measured input output data a suitable optimization algorithm needs to be used, which can find the values of the model parameters so that some suitable error function is minimized. In this work Newton¶Viterative method and gradient search algorithm have been adopted with minimization leastsquare error function.

2169

frequency range, which is also shown in Figure 5. The loss factors of the insulation at different frequencies were obtained by varying the frequency of triangular waveform with coarse interval in such a manner that by utilizing up to 7th harmonics of the particular triangular waveform could give the loss factor in fine interval as obtained using sinusoidal waveform over the logarithmic scale. An example of such triangular waveform of 100 Hz is presented in Figure 6a, the frequency response of which is presented in Figure 6b.

Figure 5. Measurement of dielectric loss factor by sinusoidal and triangular waveforms.

3.3.4 MODEL VALIDATION After searching optimal model parameters, the model is verified with fresh set of input data and the deviation from the measured output is observed for acceptability of the model.

4 RESULTS The following section discusses the obtained results in three parts: the first one presents the results from the tests of assessing loss factor under sinusoidal and triangular waveform excitation, followed by results obtained by system identification using variable frequency pseudo square (VFPS) waveform of different pulse width and amplitude and finally the estimation of moisture content using different kind of waveforms. 4.1 MEASUREMENT OF LOSS FACTOR The dielectric loss factor, i.e. ሺߜሻǡ measured using the sinusoidal excitation over the frequency range of 0.001 Hz to 10 kHz is presented in Figure 5. The frequency interval in this case is chosen to be fine over the logarithmic scale. The temperature was maintained constant at 50oC.When the test was repeated over time on same insulationat same condition,the average mean-square-error(MSE) between such characteristic curves of loss factor found to be within 0.05%. In order to investigate the behavior of loss factor when some non-sinusoidal excitation such as triangular waveform is applied on the same insulator, the obtained characteristics curve over the frequency range found to vary in a similar fashion, but the estimated loss factor by the triangular waveform when compared to the sinusoidal waveform was higher in the lower frequency range and lower in the higher

Figure 6. Applied triangular waveform of (a) 100 Hz and (b) corresponding frequency spectrum.

In Figure 6b presence of several frequency components can be observed, but the magnitude of the fundamental (100 Hz) and its odd harmonics are much significant when compared to other frequency components. It can be also observed that the magnitude of the odd harmonics decreases with the increase of the order.Thereforeestimation of loss factor above 7th harmonics with the help of respective Fourier Transform coefficients becomes not a practical proposition.

2170


4.2 NONLINEAR SYSTEM IDENTIFICATION The non-linear system identification results are divided intothree parts. The first part presents the analysis of excitation and response signal, second part discusses the issues involved with the system identification, while the third part summarizes the results obtained through the simulation of the identified system models. 4.2.1 EXCITATION AND RESPONSE SIGNAL ANALYSIS In this work, an excitation signal has been designed by combining pseudo square waveform of several frequencies, in such a manner that the harmonic composition becomes almost constant over the frequency band of interest. An example of such input excitation as measured is presented in Figure 7, along with the recorded current signal, (both the signals have been scaled and arranged from low to high frequency for presentation purpose). The frequency response of the excitation voltage signal is presented in Figure 8, which shows that the frequency composition and the weightage are almost constant over the frequency band.

Figure 7. Measured (scaled) sample excitation signal and corresponding measured current signal.

of insulation. Thereafter respective excitation and response signals have been stored into a database for model identification purpose, in a group of training and testing dataset. One part of each recording was kept in training database and the remaining part in testing dataset. The data in training and testing sets are mutually exclusive. 4.2.2 MODEL IDENTIFICATION For model identification the model structure, i.e. type of nonlinearity for the nonlinear block of Hammerstein model and the order of the numerator and denominator for the linear block has to be defined before optimization process.Unfortunately these are not available apriori.Therefore, trial and error method has been used to find the best possible reduced order model structure. This search process was performed by iteratively varying the model structure. Initially the iteration started from much higher order nonlinearity i.e. withܽ ൌ ͳͲ, and lowest possible order for the linear block, i.e. with b=0 and c=1, and thereafter incrementand decrementof the model order for the linear and nonlinear model by observing the performance. Among the three sets of training datasetfrom three different experiments for the same insulation under same condition, one data set has been used for training and the remaining two for validation. The average MSE over the two validation data sets has been used as performance criterion. It has beenobserved by various researchers that the optimization process often does not converge to same point in all the runs even when the initial condition was set to zero. Therefore, in each case, the optimization process has been repeated for 10 times and then average performance and the average of the standard deviations of the values of the parameters have been observed. The average performances and standard deviations obtained with some of the modelsare presented in Table 1forܽ ൌ ͳͲ. Table 1.Performance measures with different model structures. Numerator (b) Denominator (c) MSE (%) Std. Dev. (±) 1 2 0.0874 0 2 3 0.0551 0 3 4 0.0507 0.003 4 5 0.046 0.09 5 6 0.0333 0.014 6 7 0.0358 0.021 7 8 0.0262 0.028 8 9 0.0254 0.013 9 10 0.0253 0.016

Figure 8. Frequency domain response of the measured input voltage signal.

A signal of similar type but with randomly variable frequency (within pre-specified range) has been applied on the oil paper insulation system, and consequently response of the insulation system has been recorded. This kind of test has been performed on three different moisture content, i.e. 1, 2 and 3.2 % insulation system, and for each of the insulation the same experiment has been repeated three times separated over considerable period of time, which produce three recordings for each value of moisture content

From Table 1 it can be observed that the performance improves initiallywith the increase of the model order, but thereafter the performance is mixed. It can be observed that up to model of order 3 the standard deviation is zero.Therefore in all the cases the optimization converges to the same point. However, in the case of higher order model the optimization converges to different points and therefore provides different values of model parameters. In the case of model of order 4 the standard deviation is significantly small in comparison with the variation of the model parameters due to changes in moisture content. It can


also be observed that the after the model order of four (c=4) the average standard deviation increases significantly, indicating wide variation of the model parameters obtained after optimization, which is not desirable in the present case. When the insulation condition degrades slightly, the variation of model parameters will be less and if the optimization algorithm reaches to several solutions then the reliability of the overall assessment system will be poor.By considering all these factors and keeping in mind the main objective of selecting lowest order, the order of the model was chosen three for the linear part and 10 for the nonlinear one. A small section of the validation data (excitation and physical model response) along with the simulated responses of the nonlinear model and its corresponding OLQHDU PRGHOV¶ UHVSRQVH are presented in Figure 9. The responses are found to be quite close to the measured ones. A zoomed view of the initial part of the Figure 9 is presented in Figure 10, for closer examination of the deviations for both the simulated models. Apparently it seems that boththe identified models (linear and nonlinear)are quite successful, but a closer view of the polarization current shows some amount of deviation, which has been effectively identified by the nonlinear model.

Figure 9. Measured excitation signal and corresponding physical model response along with simulated responses of linear and non-linear models.

Figure 10. Zoomed view of the Figure 9 for initial time period of 1 to 1.2 s.

4.2.3 TESTING OF MODELS With the selected suitable model structure and the excitation and response signals, three different models of the three different insulationsamples having moisture content of 1, 2 and 3.2% have been identified with the

2171

help of training dataset, following the process as discussed earlier. After identifying the model parameters, the respective identified digital models have been analyzed to compare the magnitude and phase responses, which are presented in Figures 11 and 12, respectively. From the graphs it can be observed that increase of the moisture content is not only shift the phase responsesto the higher side, as thoroughly investigated by various researchers in the past decade [16-17], but also changes the slope of the magnitude response to the lower side. The low frequency region (below 0.01 Hz) and high frequency region (above 10 Hz) of phase response curve of oil-paper insulation are mainly dominated by the polarization and depolarization of cellulose material, whereas the middle region is dominated by the conductivity of oil insulation. The phase response curves of Figure 12, re-confirm the observations of past researchers [32] that the phase response move upward due to increase of moisture content in cellulose material of oil-paper insulation system and the shift of the middle region toward right side indicate higher conductivity, which might be due to ingress of paper moisture into the oil. From the phase responses of Figure 12, it can be observed that sinusoidal based method is indicating lower moisture content in cellulose part of oil-paper insulation and higher conductivity in oil insulation in comparison with non-linear model. Further, the linearonly-model response is in between the non-linear model and sinusoidal responses. The static nonlinear functions for the models in the form of polynomial ‫ ݕ‬ൌ ‫݌‬ଵ଴‫ݔ‬ଵ଴ ൅ ‫݌‬ଽ ‫ ݔ‬ଽ ൅ ‫ ڮ‬൅ ‫݌‬ଵ ‫ݔ‬ଵ ൅ ‫݌‬଴ for the three different insulations are presented in Table 2, From the Table 2, it can be observed that the system nonlinearity also varies with moisture content. The values of the model parameters as obtained for the three different MC samples are presented in Table 3, in the form of mean and standard deviation obtained from the respective three set of datasets. From the Table 3, it can be observed that the parameters of the numerator polynomial almost insensitive to the variation in the MC, whereas the parameters of the denominator polynomial changes with the variation in MC. The variations of the݀ଵ and݀ଷ w.r.t. moisture content are presented in Figure 13. Such well-defined variation of identified parameters could be utilized for moisture estimation when a suitable database is formed by testing real life transformers.It can be also observed that the variations of these parameters (standard deviation) over multiple tests for the same moisture content samples are insignificant over the variation of these parameters due to changes in the moisture contents of the sample, which makes the proposed system robust.This fact can be observed from the scatter plot of ݀ଵ vs. ݀ଷ as shown in Figure 14. Figure 14 shows the Scatter plot of d1 and d3 coefficients for the identified nonlinear model along with the linear-only-modelcoefficients (without consideration of nonlinear function). From Figure 14, it can be observed that d1 and d3 coefficients of linear-only-modelhave higher

2172


uncertainties when different datasets are considered for the same moisture content of insulation. Therefore, consideration of non-linear model reduces uncertainties in the estimation of the model coefficients. Further a linear model fitting the datasets of d1 and d3w.r.t % PRLVWXUH FRQWHQW ȟ LQ ZDV obtained by minimizing MSE for the nonlinear model and the linearonly-model. The model equation in estimation of moisture-content for the non-linear model is presented in equation (3). Ɍ ൌ െͷʹͲǤͷͳ െ ʹʹ͵Ǥ͹ͳ ൈ ݀ͳ ൅ ͻͻͳǤͳ͸ ൈ ݀ʹ െ ͳʹ͸Ǥͺͳ ൈ ݀ͳ ʹ െ ͷ͹͹Ǥ͹͸ ൈ ݀ʹ ʹ

(3)

Figure 11. Magnitude response of the identified models of insulation having different moisture contents.

corresponding minimum ߜ value is evaluated. It was reported by W.S. Zaengl that moisture present in paper, maintains a relationship with the minimum ߜ ( ߜ௠௜௡ ) as given in (4) [7]. (4) Ɍ ൌ ͳͷǤʹ͹ͻ ൅ ʹǤͷ͵ʹ͸͹ ൈ ݈݊ሺ ߜ݉݅݊ ሻ Paper moisture of the test samples having known moisture content have been predicted using equation (4) for sinusoidal excitation and corresponding prediction error has been tabulated in Table 4. In the case of triangular excitations, the fundamental components corresponding to the applied non-sinusoidal excitation and measured dielectric response current are extracted using FFT [15, 29, 33] over the frequency range of 1 mHz - kHz. From these corresponding fundamental components, the dielectric dissipation factors are calculated using the same techniques as reported in [15, 29, 33]. The ߜ values are then plotted against frequency for each sample and corresponding minimum ߜare calculated. From the corresponding minimum ߜ, paper moisture of the test samples having known moisture content are predicted using (4) and corresponding prediction errors are evaluated that has been given in Table-4. Table-4 also shows the results obtained from the proposed system identification approach using equation (3) for the respective models obtained from the separately kept testing dataset. From the table it can be observed that proposed system identification approach using the VFPS excitation signal provides minimum amount of error, in determination of MC. Table 2.Coefficients of the non-linear functions for different moisture content. Polynomial Coefficients MC (%) ‫݌‬ଵ଴ ‫݌‬ଽ ‫଼݌‬ ‫଻݌‬ ‫଺݌‬ ‫݌‬ହ ‫݌‬ସ ‫݌‬ଷ ‫݌‬ଶ ‫݌‬ଵ ‫݌‬଴ 1.0 -2.2 3.2 5.2 -5.6 -4.5 2.9 1.6 -0.32 -0.24 -0.31 -0.22 2.0 -2.0 4.9 4.5 -8.8 -3.8 4.9 1.4 -0.78 -0.20 -0.32 -0.14 3.2 -2.0 3.0 5.0 -5.1 -4.5 2.4 1.8 -0.12 -0.3 -0.38 -0.05 Table 3. Parameters of the linear model (Mean ± Standard Deviation) in %. Model parameters MC ܰሺ‫ݖ‬ሻ ‫ܦ‬ሺ‫ݖ‬ሻ in (%) ݊ଵ ݊ଶ ݀ଵ ൈ ͳͲିଶ ݀ଶ ൈ ͳͲିଶ ݀ଷ ൈ ͳͲିଶ 90.61±0.07 1.0 1±0 -1±0 -96.56±0.19 - 93.81±0.01 2.0 1±0 -1±0 -94.57±0.37 - 93.73±0.01 89.33±0.21 3.2 1±0 -0.99±0 -89.67±0.33 - 93.53±0.01 86.22±0.14

Figure 12. Phase response of the identified models of insulation having different moisture contents.

4.3 DETERMINATION OF MOISTURE CONTENT USING DIFFERENT WAVEFORMS For conventional FDS, pure sinusoidal excitation voltages over a wide frequency range (typically 1 mHz ± 1 kHz) are applied to the oil-paper insulation and corresponding dielectric response currents are measured. From the applied sinusoidal excitations and corresponding dielectric response currents, dielectric dissipation factors are calculated at different frequencies over the frequency range of 1 mHz ± 1 kHz using the same procedure as followed in [9, 16]. The dielectric dissipation factors ( ߜ) are plotted against frequency and

Figure 13. Variation of the most sensitive model parameters (݀ଵand ݀ଷ ) with respect to moisture content of the insulation.


Figure 14. Scatter plot of d1 and d3 coefficients for different moisture content. Table 4.Mean % errors obtained for estimation of MC using different waveforms. Moisture-content (%) Signal Type 1 2 3.2 Sinusoidal 4.8 4.4 4.2 Triangular 3.2 3.1 2.7 VFPS (Linear-only-model) 2.4 2.1 1.9 VFPS (Non-linear model) 1.3 1.2 0.9

5 DISCUSSIONS In the present contribution, various facts as observed from differenttests repeated on transformer oil-paper insulation with different types of input signal, in precisely controlled laboratory environment over considerable amount of time,are presented.The dielectric response observed through sinusoidal excitation was different from the dielectric response obtained using triangular waveform. This indicate system nonlinearity, i.e. the effect produced by several harmonics when acting together as in the case of triangular waveform is not same when the harmonics are applied separately. In the present scenario due to increasing use of power electronic devices the excitation signals are mostly deviated from sinusoidal. Thismotivated to explore other form of condition assessmenttechnique using the non-sinusoidal waveform. The system identification long being applied to obtain mathematical model of different systems, mainly in the field of control engineering, has been used. Main point of attraction is the mathematical model, which can be used to assess insulation condition in much simpler way than the dielectric response characteristic curves.The nonlinear system identification approach has been used by studying the system static nonlinearity. The primary objective of this work is to estimate the moisture content in the insulation through non-invasive method. For this purpose frequency domain spectroscopy using nonlinear waveform has been performed on oil-paper insulation in the frequency range of 1 mHz ± 1 kHz in order to assess the condition of insulation more accurately. Toobtain the mathematical model, variable frequency pseudo square (VFPS) waveform has been designed which consist of several step signals of different duration. This kind of input excitation signal often found to be effective [30], [31] in order to obtain proper response which represents the system dynamics over the frequency band of

2173

interest. The mathematical models obtained for different moisture content of oil-paper insulation are presented, which provide more insight about the insulationcondition, with the increase in moisture content. It can be observed that not only the phase response changes with the moisture content but also the magnitude response changes. More interesting is the system nonlinearity functions, which is also sensitive to the moisture content. The identified static nonlinearity reveals the nonlinearity in system behavior with the magnitude of the excitation signal, which is also been observed by previous researchers as problem to accessing insulation condition. The proposed method is based on the estimated linear model of the insulation system. The moisture content has been estimated from the parameters of the linear part of the estimated nonlinear model. In the system, nonlinearity can be present in the input excitation, insulation and in the measurement process. In this work it has been observed that using only linear model the deviation between actual responses and the estimated liner model response is higher in comparison with the non-linear model. Therefore, the static nonlinearity present in system has been separated by higher order nonlinear function, so that linear system dynamics can be modeled more accurately. In the work, nonlinear system identification concept has been extended to obtain digital model of insulation having different moisture content. The results shows that some of the parameters of the identified model changes with the change in moisture content, while others remain insensitive to the moisture content. The obtained result in predicting moisture content using different approach such as applying sinusoidal and triangular waveforms, reveals that the proposed system is more accurate and robust. Moreover, the proposed method takes less time for testing as the duration of the excitation signal was approximately 8 minutes compared 3/4 hours as required in the case ofsinusoidal and triangular waveform. In comparison with previous works, the present work advances the application of arbitrary waveform as originally proposed in [13] and [15] by improving accuracy, and also by providing more insights by providing mathematical model. This work also advances the concept of finding mathematical model of insulation through nonlinear system identification approach from the time domain data [18]. The proposed system is much simpler as it takes the primary time domain data rather than the secondary frequency domain data [16]. The success of the proposed system is primarily dependent on the proper convergence of the optimization process, and main point of concern is the convergence at different pointsduring multiple runs. Another area of concern is the large amount of data to be used in optimization in the present model structure. As the entire input excitation signal and model response signal are to be sampled at uniform rate, therefore in order to accommodate 1 kHz signal with proper sampling frequency, the number of samples in one cycle of the extreme low frequency of 0.001 Hz will be huge, and the optimization process will take very long time, with presently available computational

2174


power. In the present contribution the frequency range has been chosen from 0.005 to 500 Hz, for which the 3rd order model has taken on an average 15 minutes to converge, in computer platform with Intel 2.4 GHz, i5 processor, 8 GB RAM,and Windows 7 64 bit OS with MATLAB 2012 environment. Setayeshmehr et al reported that as temperature varies, activation energy in the dielectric material changes [9]. Due to change in activation energy, dc conductivity of the dielectric material as well as the polarization processes changes [9]. These variations of dc conductivity and polarization processes with temperature affect the dielectric response current. Those phenomena consequently may affect the model parameters (d1 and d2 of (3) as well as polynomial coefficients of Table 2). Variation of these parameters can be used for investigating the effect of temperature when a suitable database is formed by testing real life transformer. In this work a classical optimization technique has been implemented which has several limitations in finding optimal solution. But in spite of the fact that the model order was compromised byapproximating it to lower order, it converged to the same point, and the performance obtained was well above the acceptance limit. Therefore by using some advanced optimization technique such as heuristics methods, one can improve the performance by considering higher order model structure, which falls within the scope of future work.

6 CONCLUSIONS The present contribution provides insights about insulation condition assessment through non-sinusoidal excitation. A suitable input excitation signal has been designed, which have uniform magnitude response over the frequency band of interest. Nonlinear system identification concept has been applied in assessment of insulation condition with variation of moisture content of the oil-paper insulation system and it revealed more information. The proposed method is more proper in the sense that,it uses non-sinusoidal excitation for assessment of insulation condition, which is desirable in the present day scenario, where the wide spread application of advanced power electronics devices is throwing a challenge to the conventional condition assessment methods. On the other hand it is much simpler in the sense that it takes into consideration only the time domain data to obtain the values of the model parameters. Among the different parameters, two parameters have been identified through the experiment, which are found to vary almost linearly with the moisture content of the insulation. Therefore, this known variations can be used to identify the MC of unknown samples. The main point of concern with the proposed method is the choice of optimization method and the amount of computation required. But these can be overcome by finding suitable optimization technique and using the increasing computational power. Among various factors, which affect the FDS response, major one is the temperature dependency of it. In FDS, it is

suggested to maintain the temperature constant during test. But at site difficulties arise to achieve it. In future work, the temperature of the insulation will be taken as another input to the system and Multi Input Single Output (MISO) model will be developed instead of present Single Input Single Output model. Proper estimation of such MISOmodel, along with the real life transformer test database can help ininvestigating the effect of temperature also.

ACKNOWLEDGMENT Financial support for conducting this research work was provided by DST, Govt. of India (Grant No. SR/S3/EECE/0097/2010).

REFERENCES [1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

T. K. Saha, "Review of Modern Diagnostic Techniques for Assessing Insulation Condition in Aged Transformers", IEEE Trans. Dielectr. Electr. Insul., Vol. 10, pp. 903-917, 2003. A. Bouaïcha, I. Fofana, M. Farzaneh, A. Seytashmehr, H. Borsi, E. Gockenbach, A. Béroual and N. T. Aka, "On the Usability of Dielectric Spectroscopy Techniques as Quality Control Tool", IEEE Electr. Insul. Mag., Vol. 25, No. 1, pp. 6-14, 2009. M. de Nigris, R. Passaglia, R. Berti, L. Bergonzi and R. Maggi, ³Application of modern techniques for the condition assessment of power transformers", CIGRE, Paper A2- 207, Paris, France, 2004. W.S. Zaengl, "Dielectric Spectroscopy in Time and Frequency Domain for HV Power Equipment, Part I: Theoretical Considerations", IEEE Electr. Insul. Mag., Vol. 19, No. 5, pp. 5-19, 2003. &LJUH 7DVN )RUFH ³'LHOHFWULF 5HVSRQVH 0HWKRGV IRU 'LDJQRVWLFV RI 3RZHU 7UDQVIRUPHUV´ Electra, No. 202, pp. 25-36, 2002. M. Wang, A.J. Vandermaar and K.D. Srivastava, "Review of Condition Assessment of Power Transformers in Service," IEEE Electr. Insul. Mag., Vol. 18, No. 6, Nov. 2002. W. S. Zaengl, "Applications of dielectric spectroscopy in time and frequency domain for HV power equipment", IEEE Electr. Insul. Mag., Vol. 19, No. 6, pp. 9-22, 2003. T. K. Saha and P. Purkait ³,QYHVWLJDWLRQ RI 3RODUL]DWLRQ DQG Depolarization Current Measurements for the Assessment of Oilpaper Insulation RI $JHG 7UDQVIRUPHUV´ IEEE Trans. Dielectr. Electr. Insul., Vol. 11, No. 1, pp. 144-154, 2004. A. Seytashmehr, I. Fofana, C. Eichler, A. Akbari, H. Borsi and E. *RFNHQEDFK ³'LHOHFWULF 6SHFWURVFRSLF 0HDVXUHPHQWV RQ Transformer Oil-Paper Insulation under Controlled Laboratory &RQGLWLRQV´IEEE Trans. Dielectr. Electr. Insul., Vol. 15, pp. 11001111, 2008. S. Q. Wang, G. J. Zhang, J.L. Wei, S. S. Yang, M. Dong, ³,QYHVWLJDWLRQ RQ 'LHOHFWULF 5HVSRQVH &KDUDFWHULVWLFV RI 7KHUPDOO\ Aged Insulating Pressboard in Vacuum and Oil-impregnated $PELHQW´ IEEE Trans. Dielectr. Electr. Insul., Vol. 17, No. 6, pp. 1853-1862, 2010. J. L. Wei, G. J. Zhang, H. Xu, H. D. Peng, S. Q. Wang and M. Dong, ³1RYHO &KDUDFWHULVWLF 3DUDPHWHUV IRU 2LO-paper Insulation Assessment from Differential Time-domain Spectroscopy Based on 3RODUL]DWLRQDQG'HSRODUL]DWLRQ&XUUHQW0HDVXUHPHQW´ IEEE Trans. Dielectr. Electr. Insul., Vol. 18, No. 6, 1918-1928, 2011. R. Liao, J. Hao, G. Chen and L. Yang, "Quantitative Analysis of Ageing Condition of Oil-paper Insulation by Frequency Domain Spectroscopy," IEEE Trans. Dielectr. Electr. Insul., Vol. 19, No. 3, pp. 821-830, 2012. B. Sonerud, T. Bengtsson, J. Blennow, and S. M. Gubanski, "High and low voltage dielectric response measurements utilizing arbitrarily shaped waveforms", Int¶O. Sympos. High Voltage Engineering (ISH), Ljubljana, Slovenia, 2007. F. P. Espino-Cortes, Y. Montasser, S. H. Jayaram, and E. A. Cherney, "Study of stress grading systems working under fast rise time pulses", IEEE Int¶O Sympos. Electr. Insul. Toronto, Ont., Canada, pp. 380-383, 2006.

IEEE Transactions on Dielectrics and Electrical Insulation Vol. 22, No. 4; August 2015 [15] %6RQHUXG7%HQJWVVRQ-%OHQQRZDQG60*XEDQVNL³'LHOHFWULF response measurements utilizing semi-VTXDUH YROWDJH ZDYHIRUPV´ IEEE Trans. Dielectr. Electr. Insul., Vol. 15, pp. 920-926, 2008. [16] I. Fofana, H. Hemmatjou1, F. Meghnefi1, M. Farzaneh, A. Setayeshmehr, H. Borsi, and E. Gockenbach, "On the Frequency Domain Dielectric Response of Oil-paper Insulation at Low Temperatures," IEEE Trans. Dielectr. Electr. Insul., Vol. 17, No. 3, pp. 799-807, 2010. [17] M. K. Pradhan and K. J. H. Yew, "Experimental Investigation of Insulation Parameters Affecting Power Transformer Condition Assessment using Frequency Domain Spectroscopy", IEEE Trans. Dielectr. Electr. Insul., Vol. 19, No. 6, pp. 1851-1859, 2012. [18] 7.6DKD33XUNDLWDQG)0XOOHU³$Q$WWHPSWWR&RUUHODWH7LPH & Frequency Domain Polarization Measurements for the Insulation DiagnRVLV RI 3RZHU 7UDQVIRUPHU´ ,((( 3RZHU (QJ 6RF *HQ Meeting, Vol. 2, pp. 1793-1798, 2004. [19] % 3DKODYDQSRXU 0 0DUWLQV DQG 1 (NOXQG ³6WXG\ RI 0RLVWXUH Equilibrium in Oil-SDSHU6\VWHPZLWK7HPSHUDWXUH9DULDWLRQ´,(((WK ,QW¶O&RQI3URSHUWLHV$SSODielectr. Materials, Vol. 3, pp. 1124-1129. [20] A. Kumar and S. M. Mahajan, "Time Domain Spectroscopy Measurements for the Insulation Diagnosis of a Current Transformer," IEEE Trans. Dielectr. Electr. Insul.,, Vol. 18, No. 5, pp. 1803-1811, 2011. [21] A. Pradhan, %&KDWWHUMHHDQG6&KDNUDYRUWL³&RPSDUDWLYHVWXG\RQWKH effect of temperature on frequency domain spectroscopy results under VLQXVRLGDODQGWULDQJXODUH[FLWDWLRQ´,QW¶O&RQI3RZHU(QHUJ\,&3(1 in North Eastern Regional Inst. Sci. Technology, pp. 1-6, 2012. [22] A. V. Oppenheim, and R.W. Schafer, Discrete-Time Signal Processing, Prentice-Hall, 1989. [23] $)HUUHURDQG54WWRERQL³+LJK$FFXUDF\)RXULHU$QDO\VLV%DVHG RQ6\QFKURQRXV6DPSOLQJ7HFKQLTXHV´ IEEE Trans. Instrumentation Measurement, Vol. 41, No. 6, pp. 780-785, 1992. [24] L. Ljung, System Identification: Theory for the User, Second edition, PTR Prentice Hall, NJ, 1999. [25] F. Ding, X. Peter, C. Liu, and G. Liu, "Identification methods for Hammerstein nonlinear systems," Digital Signal Processing, Vol. 21, pp. 215±238, 2011. [26] Y. Liu and (: %DL ³,WHUDWLYH LGHQWLILFDWLRQ RI +DPPHUVWHLQ V\VWHPV´$XWRPDWLFD9RO, No. 2, pp. 346±354, 2007. [27] A. Pradhan, B. Chatterjee, S. Chakravorti and &.ROH\³)UHTXHQF\ domain dielectric spectroscopy using Triangular wavHIRUP´$QQXDO IEEE India Conf. (INDICON), pp. 931-935, 2012. [28] -+