Analysis of hybrid polarization frequency domain spectrum characteristics of oil-paper insulation transformers

This paper utilizes a hybrid Debye model to accurately simulate the relaxation response process of the oil-paper insulation of a transformer to explore the application of frequency domain dielectric spectroscopy (FDS) in nondestructive diagnosis of the aging condition of oil-paper insulation. Via FDS test data, the model parameters can be identiﬁed, and the inﬂuence laws of FDS can be obtained through the variation of model parameters. To explore the effects of insulating paper moisture content, insulating paper layers, and test temperature on FDS characteristics, an FDS experimental platform is established. The results show that the hybrid Debye model can effectively reﬂect the relaxation response process of oil-paper insulation under different conditions, as well as that a physical relationship between the model parameters and oil-paper dielectric polarization exists. In addition, the parameters of the hybrid Debye model can be used as the characteristic quantities for the non-destructive evaluation of the oil-paper insulation state, providing new ideas for the non-destructive evaluation of the oil-paper


INTRODUCTION
As the pivotal equipment of a power system, the power transformer is the key to ensuring the stability, reliability, and safety of a power system. Since aging and dampening of the oil-paper insulation system are the main cause of transformer failure [1][2][3][4][5][6], it is particularly important to reasonably, effectively, nondestructively, and comprehensively diagnosis the state of the oil-paper insulation system. Doing so has great practical significance and economic benefits. The measurement conclusions of RVM [7][8][9][10][11] (return voltage method), PDC [12][13][14][15][16] (polarization and depolarization current), and FDS [17][18][19][20][21][22][23] (frequency domain spectroscopy) based on dielectric response are consistent when it comes to transformer aging diagnosis. RVM can only evaluate the overall condition of the insulation and cannot distinguish the condition of insulating oil from that of insulating paper. Moreover, it is susceptible to the accuracy limitation of signal measurement and electromagnetic interference in the time domain, making interpretations of experimental results very complicated [7,8].
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. PDC, on the other hand, has certain advantages in diagnosing the insulation state of transformers. However, when measuring the polarization and depolarization current for a long time, the long test process and the large temperature variation will seriously affect the measurement results. Moreover, the field test will inevitably be affected by electromagnetic interference because the polarization and depolarization current values are quite small, the accuracy of the measurement is questionable in this case. Therefore, how to suppress the field temperature interference and electromagnetic interference needs to be further studied [14,15]. Meanwhile, FDS, as a nondestructive electrical diagnosis technology, has the characteristics of a strong anti-interference ability, wide measurement frequency band, and abundant information compared to the other methods [18][19][20][21][22][23][24][25][26][27][28][29].
The research method based on FDS test data can be summarized as follows. First, the characteristics are extracted directly from the FDS curve to find the relationship between the characteristics and the insulation characteristics. The second is to establish an equivalent model of the oil-paper insulation system based on the FDS measurement curve, and to explore the change rule of the oil-paper insulation characteristics reflected by the model parameter changes. The latter has received extensive attention and research due to its specific microphysical theoretical basis to explain the change of dielectric insulation characteristics. At present, the equivalent models used in oil paper insulation system mainly include extended Debye model (EDM), Maxwell Wagner model, X-Y model, Cole-Cole model and so on. Bognar et al. [25] utilized the extended Debye model consisting of a few RC branches to monitor the insulation state of equipment. However, in the actual polarization process of transformer oil paper insulation system, insulation oil, insulation paper and a series of aging products will form interface polarization [27]. Obviously the application of EDM ignores the existence of interface polarization. The Maxwell-Wagner model [26], composed of two RC series circuits, can be used to calculate voltage distribution and dielectric loss, but its calculation accuracy is limited, owing to its neglect of the nonlinear characteristics of resistance and the relaxation process [27][28][29]. Besides, Zhang et al. [30] used the X-Y model to simulate the polarization characteristics of the complex oilpaper insulation structure, which is composed of separators, oil gaps, and braces. X-Y model can better reflect the structure of oil paper insulation system. However, in some early transformers, it is difficult to know the size parameters of oil paper insulation, so the parameters of X-Y model can not be accurately obtained. Ojha et al. [31] drew the Cole-Cole circle of the repolarization rate of oil-paper insulation, and found that the insulation state is obviously related to the size, relaxation time, and distribution parameters of the Cole-Cole circle. However, the distribution parameters of Cole-Cole model has no physical meaning and can not further explain the polarization process of oil paper insulation. During the operation of oil paper insulation, a series of aging products (including water, acid etc.) are produced. The relative dielectric constant of these products are different, so complex interface polarization are formed. Moreover, the uneven distribution of water in the material also makes the polarization process of the dielectric more complex [32][33]. The interface polarization process of oil-paper insulation is very important for judging the degree of moisture and aging of oil-paper insulation. Therefore, it is necessary to establish an equivalent model that can accurately reflect the interface polarization process of oil-paper insulation.
Based on the above background, this paper presents a hybrid Debye model (HDM) to reflect the complex polarization process of oil-paper insulation, which appends hybrid branches to characterize complex interface reactions on account of the difference between the interface polarization and dielectric polarization. This paper is organized as follows. First, the construction of the hybrid Debye model based on FDS and the identification of its parameters are introduced; then the relationship between the equivalent model parameters and the polarization process of the oil-paper insulation system is explored through the simulation platform; finally, the effects of different external factors on the oil-paper insulation system are analysed through experiments. The influence of the FDS spectral line of the insu-lating sample, and the establishment of the HDM model, and verify the accuracy and validity of the equivalent model through the degree of agreement.
The various code symbols mentioned in this paper and their corresponding meanings are shown in Table 1.
According to dielectric physics theories [34], the relationship between the equivalent admittance Y of the HDM and complex capacitance C are expressed as: In terms of the Maxwell circuit principle [35], the real part of dielectric complex capacitance C′ can be described as: The imaginary part of dielectric complex capacitance C′′ is depicted as: In Equations (2)-(3), the time constant τ is denoted as: The dielectric loss factor, tan δ, can be derived from the ratio of the imaginary part to the real part of the complex capacitance, Furthermore, test and calculated complex capacitance and dielectric loss factor data are selected for parameter identification.
We can also construct the objective optimization function, as shown in Equation (6): where C ' M (ω i ), C '' M (ω i ), tanδ M (ω i ) are the FDS measured values at each corresponding frequency, and C ' tanδ C (ω i ) are the calculated values of model equivalent parameters as substituting them into Equations (2)-(5) at each corresponding frequency. The optimal solutions can be obtained as the objective optimization function approaches 0. The consistency, W, of comparing the measured and calculated values of each group of characteristic quantities can be extracted as: where X C and X M are the calculated and measured values of each characteristic quantity. The results with the highest consistency can be selected as the model parameters. Based on the above strategy, the model parameters of the HDM were identified by FDS test data of a retired oil-immersed induction transformer (TSJA-20/0.5), as shown in Table 2.
Model parameters based on the EDM are exhibited in Table 3.
To further demonstrate that the hybrid Debye circuit of oilpaper insulation can more veritably reflect FDS characteristics, a comparison of the consistency between FDS measured values and calculated values obtained from the HDM and the EDM is displayed in Figure 2. In addition, the consistency of different   Table 4, where the consistency of the HDM observably exceeds the consistency of the EDM, thus proving that the HDM possesses greater practicability and superiority compared when with the EDM.

SIMULATION OF FDS CHARACTERISTICS OF OIL-PAPER INSULATION
This simulation study on the influence of the circuit parameters of the HDM on FDS curves lays a foundation for exploring the influence of different environmental factors on FDS characteristics and equivalent model parameters. In the dielectric polarization response process, the insulation system is affected   by moisture, aging, and environmental temperature [23]. Hence, FDS characteristics are also affected, which results in the variation of model parameters. To accurately explore the physical relationship among the measured polarization parameters and the dielectric polarization of an oil-paper insulation system, and to determine the effects of the variation of insulation resistance R g , geometric capacitance C g , and parameters of the polarization branches on FDS characteristics, simulations were carried out utilizing parameter identification results of a TSJA-20/0.5 induction transformer. R g , R p , and Rh decrease while C g , C p , and C h increase with the aging of an oil-paper insulation system [36]. Table 5 shows the variations of the parameters used in simulations.
The real part of the complex capacitance remains constant, and the imaginary part grows with the decrease of R g in the range of 10 −3 -10 0 Hz, as displayed in Figure 3. R g diminishes with the extension of electric conductivity altered by water, acid, or other aging products produced during the oil-paper insulation aging process, which magnifies the imaginary part of the complex capacitance, while the real part remains immune to the variation. Figure 4 demonstrates that the real part of the complex capacitance heightens if C g increases, while the imaginary part is maintained. The enlargement of C g , owing to storage capacity, was intensified in the period of the insulation state of the transformer turning worse, which lifts the real part of the curve of the complex capacitance, but the imaginary part keeps impregnable.
With the ascent of R p and the descent of C p , the real and imaginary parts of the complex capacitance simultaneously rise,  Figure 5.Similarly, Figure 6 reveals that the real and imaginary parts of the complex capacitance grow in the process of R h decreasing and C h increasing. Furthermore, dielectric polarization and interfacial polarization deepen due to insulation aging, which consequently results in the enhancement of electric conductivity; hence, as R p and R h decline, C p and C h are amplified, which is represented through the rise of the complex capacitance.

EXPERIMENT ON FDS CHARACTERISTICS OF OIL-PAPER INSULATION
In order to verify the effectiveness of HDM, we prepared oil paper insulation samples under different conditions. Figure 7 displays a three-electrode test system, where H, L, and G represent the voltage applying end, the current measuring end,  In this experiment, professional insulating boards with a thickness of 1 mm and 25 naphthenic mineral insulating oil were adopted as research objects. First, as part of our preprocessing, the oil-paper insulation samples were pretreated, and the insulating boards were dried for 24 h in a temperature controlled drying oven at 100 • C under standard atmospheric pressure. Secondly, the dried insulating boards were placed on the high-precision balance electronic scale to absorb moisture in the air naturally at different times to prepare insulating boards with different moisture gradients. The prepared insulating paper was infused in a hermetic vessel, where degassed mineral oil was injected at 30 • C for 48 hours in an oil-paper ratio of 5:1. FDS test data of the samples were employed to explore the influence of moisture content, insulation paper layers, and test temperature on the dielectric properties of oil-paper insulation.

Analysis of FDS data and HDM model parameters of oil paper insulation samples with different moisture content
The oil-paper insulation system of the transformer will be invaded by external moisture and mixed with water molecules produced by the insulation aging of the transformer itself after a long period of service. The moisture content of the paper insulation of transformers will rise from less than 0.5% to more than 4%. Therefore, the moisture content of oil-paper insulation was controlled in 0.1-4% in this experiment. After repeated attempts, the moisture content of the four samples was 0.244%, 1.58%, 2.77%, and 3.63%, respectively, which was measured by a high precision balance electronic scale. The insulation paper of the test samples was set to have five layers, and the testing ambient temperature was 30 • C. Moisture produced by the overall aging of an oil-paper insulation system or found in the air is the main factor that damages insulation during the operation of a transformer [15]. An increase in the moisture content of insulation paper leads to an ascent in the number of impurity particles contained in the insulation paper, which in turn leads to the strengthening of the electrical conductivity and polarization loss of an insulation system [33,37]. Hence, the real and imaginary parts of the complex capacitance of the oil-paper insulation grow, as displayed in Figure 8. It can be seen from the table 6, Geometric capacitance C g is immune to moisture content in the oil-paper insulation, owing to the structure and size of the oil-paper insulation system not being impacted by moisture content. This finding was acquired by analyzing the fitting model parameters under different moisture content. On the other hand, insulation resistance, R g , is sensitive to the variation of moisture content. R g trails off monotonously with the elevation of moisture content on account of the increased moisture content promoting the injection and migration of charged particles inside the medium more rapidly, which significantly improves the conductivity of oil-paper insulation. Meanwhile, polarization resistance, R p , decreases, and polarization capacitance, C p , increases monotonously with moisture content in the branch with the maximum time constant (the fifth branch in Table 6) by the principle that water molecules are highly polar molecules and tend to combine with hydrophilic groups to form charged ions. At the same time, water molecules promote the cracking of large insulating molecules in oil paper, resulting in an augment in the number of polarized molecules in the system, a strengthening in the capacity of dielectric bounding charge,  and a deepening in the degree of polarization. Furthermore, charged ions formed through the combining of water molecules and hydrophilic groups facilitate large molecule cracking, multiply polarized molecules, and intensify the ability of dielectric bound charge, which are seen through the enhancement of the polarization extent, relative permittivity, as well as the descent of the corresponding polarization resistance and the ascent of the polarization capacitance. The influence laws of the growing moisture content on the complex capacitance are consistent with the effects of R g , R p , and R h reductions (C p and C h increments) on the FDS characteristics simulated in Section 3, which verifies the validity of utilizing the HDM to simulate FDS characteristics of an oil-paper system. Table 7 shows the consistency values of the FDS curve reconstructed by the identified parameters based on HDM oil-paper insulation samples with different moisture content and the original measurement curve.
In the Table 7, all the consistency values were above 94%, reflecting the feasibility and accuracy of the equivalent model constructed in this paper. It also proves that HDM can effectively reflect the polarization process of oil paper insulation system with different moisture content.

Analysis of FDS data and HDM model parameters of oil paper insulation samples with different layers of insulating paper
Researching the FDS characteristics of different layers of insulation paper is a profitable means by which to obtain the FDS peculiarity of a transformer insulation system composed of a multilayer oil channel and insulation paper, as presented in Figure 9. The number of insulation paper layers in the test sample was set as 1, 3, 4, and 5 layers, and the testing ambient temperature was 30 • C. The test revealed that the real part of the complex capacitor moves downward with the augmentation of paper layers throughout the whole frequency band, while the imaginary part shifts down only in the low frequency band. Table 8 shows the HDM parameter identification results of four insulation samples with different insulation layers based on FDS test data obtained at 30 • C Insulation resistance R g enlarges with the increase of the number of insulation layers, while geometric capacitance C g decreases slightly. During the period of dielectric charging between parallel plates, the complex capacitor can be described as: where ε 0 , ε r , S, and d are the vacuum dielectric constant, relative dielectric constant, plate area, and dielectric thickness, respectively. The real part of the complex capacitor declines on account of the growth of dielectric thickness d, in accompaniment with the multiplication of the insulation paper layers, according to Equation (8). However, the imaginary part of the complex capacitor remains constant, owing to the loss between the insulation cardboard and the number of insulation paper layers. Table 9 demonstrates the consistency values of the FDS curve reconstructed using the identified parameters based on HDM oil-paper insulation samples with different numbers of insulation paper layers and the original measurement curve.
In the Table 9, all the consistency values were above 91%. The variation rules of the growing number of insulation paper layers on the complex capacitance are in accordance with the effects of C g 's reduction of the FDS characteristics simulated in Section III, which confirms that the characteristics of the complex capacitance's real part can reflect the deformation or burnout of the transformer winding. Diverse insulation system temperatures inside a transformer can be caused by the varying load of the transformer during operation or different seasons [37,38]. It is also proved that HDM can effectively reflect the polarization process of oil paper insulation system with different shapes and structures.

5.3
Analysis of FDS data and HDM model parameters of oil paper insulation samples at different temperatures Figure 10 exhibits the conspicuous impact of different test temperatures on the FDS characteristics of the oil-paper insulation samples within 1% moisture content, measured at 40, 60, and 80 • C. The insulation paper of the test samples had five layers, and the moisture content was controlled within 1%. The real part and the imaginary part of the complex capacitor shift up with the ascent of the test temperature within the frequency  Table 10.
It can be seen from the Table 10, geometric capacitance C g depends on the structure and size of the oil-paper insulation system, remains invariant or float very slightly at various test temperatures, and cannot transform the insulation structure. Dissimilarly, insulation resistance R g is susceptible to the variation of the surrounding temperature, leading to its diminution in the case of an upward trend in temperature. Furthermore, polarization resistance R p decreases, and polarization capacitance C p increases, monotonously with the moisture content in the branch with the maximum time constant (the fifth branch in Table 10).The variation rules lie in the mechanism where the escalation of the temperature aggravates the thermal motion of polar molecules, accelerates the relaxation process, shortens the relaxation time, enhances the polarization intensity of the system, elevates the polarisability, promotes the Carrier migration rate of the system, magnifies the conductivity, and strengthens the conductance process. Table 11 displays the consistency values of the FDS curve reconstructed using the identified parameters based on HDM oil-paper insulation samples with different test temperatures and the original measurement curve.
It can be seen from the Table 11, all the consistency values were above 92%. And the influence laws of the growing test temperature on the complex capacitance are consistent with the effects of R g , R p , and R h reductions (C p and C h increments) on the FDS characteristics simulated in Section 3, which verifies that HDM can effectively reflect the polarization process of oil paper insulation system under different test temperatures.

CONCLUSION
This paper used the hybrid Debye model to analyses the hybrid polarization frequency domain spectrum characteristics of oilpaper insulation systems under different conditions through simulation and experiments. The findings can be summarised as follows: 1. FDS simulation results disclose that the variation of the parameters in each branch of the hybrid Debye model of oilpaper insulation can simulate the oil-paper insulation aging process, which was presented regularly on the frequency domain curves of the complex capacitance. 2. The experimental results show that the complex capacitance and dielectric loss factor of the oil-paper insulation system change with the moisture content, the layers of insulating paper, and the test temperature, and are reflected in the corresponding HDM parameters. In addition, using the HDM parameters of the oil-paper insulation samples under different conditions to reconstruct the FDS curve and the original measurement curve has a higher consistency value, which further proves that HDM can effectively reflect the hybrid polarization of the oil-paper insulation system.