**Analysis of Polarization and Depolarization Currents of Samples of NOMEX**®**910 Cellulose–Aramid Insulation Impregnated with Mineral Oil**

### **Stefan Wolny \* and Adam Krotowski**

Faculty of Electrical Engineering, Automatic Control and Computer Science, Opole University of Technology, Proszkowska 76 B2, 45-758 Opole, Poland; d565@doktorant.po.edu.pl

**\*** Correspondence: s.wolny@po.edu.pl

Received: 3 November 2020; Accepted: 18 November 2020; Published: 20 November 2020 -

**Abstract:** The article presents results of laboratory tests performed on samples of NOMEX®910 cellulose–aramid insulation impregnated with Nynas Nytro 10× inhibited insulating mineral oil using the polarization and depolarization current analysis method (PDC Method). In the course of the tests, the insulation samples were subjected to a process of accelerated thermal degradation of cellulose macromolecules, as well as weight-controlled dampening, thereby simulating the ageing processes occurring when using the insulation in power transformers. The effects of temperature in the ranges typical of normal transformer operation were also taken into account. On the basis of the obtained data, the activation energy was then fixed together with dominant time constants of cellulose–aramid insulation relaxation processes with respect to the temperature and degree of moisture, as well as thermal degradation of cellulose macromolecules. It was found that the greatest and predictable changes in the activation energy value were caused by the temperature and the degree of moisture in the samples. A similar conclusion applies to the dominant time constant of the relaxation process of cellulose fibers. Degree of thermal degradation samples was of marginal importance for the described parameters. The final outcome of the test results and analyses presented in the article are regression functions for the activation energy and the dominant time constants depending on the earlier listed parameters of the experiment, which may be used in the future diagnostics of the degree of technical wear of cellulose–aramid insulation performed using the PDC method.

**Keywords:** dielectric polarization; relaxation methods; activation energy; cellulose–aramid paper; moisture insulation; ageing effect; power transformer insulation testing

### **1. Introduction**

Power transformers are undoubtedly one of key elements of the electric energy distribution system. Their unfailing operation determines not only continuous energy deliveries for recipients, but also stable operation of the whole power system. The effects of a possible breakdown of a power transformer are always multidimensional, starting from purely economic ones, to logistics, to threats to property and life, as well as possible environmental contamination. For this reason, transformer units which are regarded as key (e.g., power plants' step-up transformers or distribution transformers working in critical power system nodes), are equipped with automatic security systems, monitoring systems for a number of parameters determining the technical condition of the unit, and are subjected to diagnostic procedures recommended by respective standards or operating instructions. Bearing in mind the complex design of power transformers as well as their almost unique structure, ensuring unfailing continuous operation for a few dozen years is a difficult problem, which requires extensive scientific and expert knowledge.

Particularly for new power transformers, the technical condition of the electric insulation saturated with dielectric fluids is regarded as the basic hazard to safe operation, where the key factors are the level of moisture as well as the degree of ageing, defined as the degree of the materials' thermal degradation [1–6]. Despite decades of designing and manufacturing power transformers, cellulose electric paper saturated with insulating mineral oil continues to be used as the basic electric insulation system. However, various kinds of synthetic and natural esters have become more and more recognized as substitutes for mineral oil [4–8]. One of the key factors accelerating the process of departing from mineral oils as the impregnating fluid, apart from improved electric, physical and chemical parameters of esters as compared to mineral oil, is their considerably better biodegradability. Likewise, we are constantly looking for a material that would effectively replace the commonly applied cellulose. At present, the highest hopes are related to synthetic papers manufactured on the basis of aramid fibers. This material was invented and patented by DuPont™ in the 1960s. DuPont™ produce a broad assortment of products to be used as electric insulation material in electric machines (also in power transformers) under the commercial name NOMEX® [6–9]. As compared to the classic cellulose paper, aramid paper is characterized by considerably better electrical properties (e.g., higher dielectric strength, higher volume and surface resistivity), physical properties (e.g., considerably higher breaking strength) and chemical properties (better resistance to ageing as a result of higher thermal resistance over continuous operation). Possible disadvantages of the aramid material include a higher price, lower ability to absorb dielectric fluids (worse impregnation as compared to cellulose), significantly higher rigidity than cellulose paper of similar thickness, which substantially complicates the process of manufacturing the insulation system for a transformer with complex geometry. In addition, intensification of the phenomenon of generating electrostatic charges as a result of stream electrification in transformers with induced circulation of dielectric fluid has also been observed [10,11]. Too high a presence of electrostatic charges in the solid insulation of a working transformer may lead to the development of partial discharges, accelerated ageing processes and, consequently, to complete discharge.

In order to use the unquestionable advantages of aramid papers in the insulation of power transformers with induced circulation of dielectric fluid, DuPont™ proposed a hybrid material, in the form of cellulose paper coated on both sides with a thin layer of synthetic aramid paper. This has resulted in a higher temperature class as compared to clean cellulose paper, an improved material dielectric fluid absorption capacity, and the impregnation capacity as compared to clean aramid paper, among other benefits. The article presents tests conducted on samples of insulation manufactured from this kind of material, which DuPont™ sells under the trade name NOMEX®910 [12]. A more detailed description of cellulose–aramid paper is presented in Section 2 of this article.

Because NOMEX®910 electro-technical paper contains a considerable amount of cellulose, its use in the insulation of a power transformer involves practically the same hazards as in a classic oil-saturated cellulose–aramid insulation. In brief, over the course of use, cellulose fibers, as a result of the presence of oxygen molecules, water, and elevated temperature, are subjected to the processes of oxidization, hydrolysis and pyrolysis, resulting in the bonds of cellulose macromolecules being torn apart (reduced degree of polymerization) and deterioration, first of all, of mechanical parameters (e.g., breaking strength). In addition, the described cellulose ageing processes generate a continuous increase in the degree of the material's moisture due to the fact that water is one of the products of decay of the bonds of cellulose macromolecules. The increased moisture of cellulose paper significantly reduces electrical parameters (e.g., dielectric strength or volume resistivity), becoming a significant threat to further safe operation of the transformer's insulation. In order to monitor the so-called degree of insulation's technical wear in transformers, a number of diagnostic methods are applied, which estimate the degree of moisture as well as the ageing of cellulose paper impregnated with dielectric fluids. Therefore, a question arises: can the diagnostic methods applied so far, developed for impregnated cellulose papers, also be applied for new cellulose–aramid papers? The article presents the results of tests using the polarization diagnostic method analyzing the profiles of polarization and

depolarization currents over time. This method is broadly used in diagnostic practice, and is referred to using the abbreviation PDC [7,13–15].

### **2. Materials Used for the Tests**

As earlier described in the article's abstract, for experimental tests the authors used solid insulation made of NOMEX®910 cellulose–aramid electro-technical paper, manufactured by DuPont™. The basis of this material is a high quality thermally improved cellulose pulp. A sheet of electro-technical paper formed from it is then coated on both sides with a thin layer of a binder from a high temperature meta-aramid polymer (NOMEX®). This procedure leads to an increase in the temperature class of the new material, which, for operation in mineral oil, increases to 130 ◦C (for operation in the environment of esters, it is 140 ◦C) [12]. In the case of electro-technical paper made of cellulose only, for Kraft type papers, the temperature class is 110–120 ◦C for operation in mineral oil. Figure 1 presents the cross-section of NOMEX®910 material structure and a real photograph of a small sample. °C

**Figure 1.** NOMEX®910 material structure: (**a**) cross-section; (**b**) photograph of a small sample.

An approx. 10 ◦C increase in the temperature class of cellulose–aramid papers as compared to Kraft type cellulose papers is obviously not their single advantage. The basic objective of the designers was to obtain an increased mechanical strength of the new material, more precisely, tearing, breaking and tensile strength. It was assumed that, while in the case of the new cellulose–aramid material the listed parameters values will be similar to classical cellulose paper, along with the maintenance-related ageing process, the new material will definitely keep the values required by the standards for a longer time. This results from the fact that aramid fibers demonstrate a considerably higher resistance to the effect of temperature (the temperature class of electro-technical papers made of aramid only for operation in the air is 220 ◦C, e.g., NOMEX®410 [9]), at the same time, they provide significant strengthening for thermally weakened cellulose. As a result, during operation of the transformer and the inevitably increasing degradation of cellulose (chains of cellulose macromolecules being torn apart as a result of the oxidization, hydrolysis and pyrolysis phenomena), the aramid component will continue to be intact, ensuring the paper's strengthened mechanical structure, and, consequently, will extend the technical life of the insulation and the whole transformer. The material's good saturability with dielectric fluids was observed, as well as an increased dielectric strength during electric tests in the environment of mineral oil, which is particularly important [16]. At present, the substantially higher price as compared to Kraft type electro-technical papers should be considered the only disadvantage of NOMEX®910 material. However, because the material appeared on the market just several years ago, there are no statistically significant data describing many aspects related to its maintenance in power transformers. The most important aspects include: migration water processes between oil–aramid–cellulose and the time of setting the hydrodynamic balance depending on the temperature of the whole insulation; heat dissipation processes from the inside of the insulation (particularly when the surface of cellulose–aramid paper is contaminated with insulating oil ageing products); and, finally, the effectiveness of the methods applied so far to diagnose the level of moisture and ageing of the impregnated insulation. In the latter case, this article attempts to answer this very significant aspect with reference to the PDC method. Doubts in this respect can still be a valid factor that discourages potential transformer manufacturers from applying the insulation concerned to a broader extent. Table 1 presents basic technical parameters of 0.08 mm thick NOMEX®910 paper, which has been used in the tests.


**Table 1.** Typical mechanical and electrical properties of NOMEX®910 paper (thickness 0.08 mm). Data from official DuPont™ online data sheet available online [16].

<sup>1</sup> Machine direction, <sup>2</sup> Cross machine direction.

Nynas inhibited mineral insulating oil with commercial symbol Nytro 10× was chosen as the impregnating fluid. Mineral oils of this Swedish company are very often applied in power transformers, and installed in European electric energy distribution systems. Table 2 states basic technical parameters of this dielectric fluid.

**Table 2.** Typical physical, chemical, and electrical properties of Nynas Nytro 10× mineral oil. Data are from the official Nynas data sheet, available online [17].


#### **3. Sample Preparation Method**

The insulation samples were made of 80 µm thick Nomex®910 transformer cellulose–aramid paper. It is the most frequently used type of cellulose–aramid insulation applied in contemporary new power transformers. The insulation paper was cut into 1300 mm × 100 mm strips. Then, before impregnation, the samples were subjected to a process of accelerated ageing by placing them in a sterilizer and heating at four different temperatures (130 ◦C, 150 ◦C, 170 ◦C and 190 ◦C) with the access of air for a definite time. In this way, 5 degrees of sample ageing were obtained: 0–1 h of ageing (fresh paper); 2–25 h of ageing at 130 ◦C; 3–25 h of ageing at 150 ◦C; 4–25 h of ageing at 170 ◦C; and 5–25 h of ageing

at 190 ◦C. After the stage of accelerated ageing, the samples were placed in vacuum and heated at 120 ◦C for 2 h to be dried before impregnation.

Directly after the accelerated thermal ageing processes and drying in vacuum, the samples were subjected to a process of weight-controlled dampening, which consisted of the paper absorbing moisture directly from the surrounding air for a definite time. The degree of sample moisture was determined as the percentage growth in paper weight to a predefined amount. This has resulted in 4 degrees of sample moisture for all 5 degrees of ageing: 1—initial residual moisture (sample impregnation directly after the vacuum drying process, the adopted degree of sample moisture was close to 0%); 2—1.5% sample moisture; 3—2% sample moisture; and 4—2.5% sample moisture. Directly after the weight-controlled dampening process, the samples were subjected to the process of impregnation with the dielectric fluid. Nynas inhibited mineral insulating oil with commercial symbol Nytro 10× was used for this purpose. Before the impregnation process, insulating oil was initially degassed and dried in a vacuum at a temperature of 60 ◦C for 2 h, reducing the content of water dissolved in oil to approx. 10 ppm. Figure 2 shows the entire sample preparation process as a diagram.

**Figure 2.** Sample preparation diagram.

The earlier described parameters of the sample ageing and moisture processes are certainly not accidental. Accelerated thermal ageing of cellulose paper in the environment of atmospheric air causes a significant loss in the degree of polymerization of cellulose macromolecule chains. On the basis of the authors' past long-term studies and literature data [18,19] it can be stated that the selected ageing time as well as temperature range resulted in a gradual, proportional loss in the degree of cellulose polymerization from a value equal to approx. 1000 (non-aged samples) to approx. 200 (ageing in 190 ◦C for 25 h). The described scope of changes in the degree of cellulose polymerization corresponds to the whole technical life of cellulose insulation in power transformers [20]. Likewise, it can be assumed that the degree of moisture of cellulose–oil insulation in the range between approx. 0% and 2.5% in practice corresponds to moisture recorded in the statistical majority of power transformers working in electric energy distribution systems of many states [21,22]. Due to some technical problems and the long process of sample moistening, the decision was made to resign from values exceeding 2.5% of water in paper, knowing that values reaching as much as approx. 5% are recorded in strongly worn out transformers. It was decided to consider higher degrees of sample moisture in future tests.

After the impregnation process, the samples were wound on the low potential electrode, which was a brass roll of 160 mm length and 40 mm diameter. In this way, 10 layers of insulation were obtained. The high potential electrode was made of a thin 80 mm aluminum foil. The foil was wound on the roll with the sample. Figure 3 shows a cross section of the electrode system and Figure 4 shows the system ready for testing. The tests were carried out in a hermetic chamber equipped with a system for temperature adjustment and stabilization. The tests were performed in the temperature range from 20 ◦C to 60 ◦C, which is consistent with the values typical of PDC diagnostics [13–15].

**Figure 3.** View of the measuring electrode system and the insulation sample studied: 1—a roll made of brass (LV—low potential electrode), 2—aramid–oil insulation sample, 3—metal foil (HV—high potential electrode), 4—heater, 5—temperature sensor, 6—insulator, 7—hermetic vessel plus thermal insulation.

**Figure 4.** Photograph of the insulation sample prepared for testing: (**a**) zoom on sample; (**b**) after placing the sample in the measuring system.

(**a**) (**b**)

#### **4. PDC Method**

Figure 5 presents a diagram of the connections used in diagnostics of the condition of the paper–oil insulation using the PDC method and time characteristics of currents and voltages which were recorded while performing the tests. The PDC method consists of applying to the examined object (in the industrial diagnostics, these are clamps of a power transformer) a source of DC voltage and measuring and recording I<sup>P</sup> polarization current for a certain period of time tP. After time tP, the voltage source is disconnected, and the examined object's measuring clamps are shortened. Then, the measurement and registration of I<sup>D</sup> depolarization current begins, also for a certain period of time tD. I<sup>P</sup> current decreases over the time of impact of the voltage source until the course is fixed at a certain level I<sup>K</sup> resulting from a finite resistivity value of the insulation being examined. On the other hand, I<sup>D</sup> current has the opposite sign to I<sup>P</sup> current and also decreases over time. Finally, the course of I<sup>D</sup> current decreases until zero is achieved, when the examined system discharges completely.

**Figure 5.** Diagnostics of the state of paper–oil insulation samples using the polarization and depolarization current analysis (PDC) method: (**a**) connections diagram; (**b**) time characteristics of currents and voltages. 1—measuring-switching system, 2—object being examined, 3—computer.

(**a**) (**b**)

From the point of view of diagnosing the condition of oil insulation in power transformers, it is extremely important to select the right value of U<sup>C</sup> charging voltage and I<sup>P</sup> and I<sup>D</sup> current recording times. On the one hand, too low a value of U<sup>C</sup> voltage will cause substantial measuring difficulties (in the PDC method typical recorded current values are nA fractions), and thereby growth in interference (external and resulting from the presence of electrostatic loads in the insulation being examined). On the other hand, too high a U<sup>C</sup> value will cause the "masking" effect of the conductivity element of I<sup>P</sup> current (problems in precise registration of the absorption element of I<sup>P</sup> current) and can cause non-linear relaxation phenomena, significantly hindering the correct interpretation of the received measurement results. For this reason, it is recommended for the U<sup>C</sup> voltage value in the diagnostics of the condition of the paper–oil insulation in power transformers not to exceed 1 kV. The relaxation mechanism time constant values existing in such insulation require the polarization and depolarization time not to be shorter than min. 1000 s.

When relay P<sup>1</sup> is switched on (Figure 5a), the U<sup>C</sup> charging voltage is put on the object being examined and I<sup>P</sup> polarization current flowing in the measuring circuit is registered (Figure 5b). After time tP, the control system switches P<sup>1</sup> relay off and P<sup>2</sup> on. Then, I<sup>D</sup> depolarization current is recorded in the circuit. The measurement is ended after time tD, when P<sup>2</sup> relay is opened. The PDC method requires very careful shielding of the measurement cables, the examined object, and the measurements to be made with reference to the joint earth potential.

In the first approx. 100 s of the polarization and depolarization current measurement, the recorded values are mainly determined by the properties of the insulating oil, i.e., first of all its conductivity, provided that in this case important factors are the following: degree of moisture, contamination, acid value or the effect of temperature. Increasing oil conductivity causes almost proportional increases in the initial polarization current values, therefore it is possible to fix oil conductivity from I<sup>P</sup> values registered directly after applying the U<sup>C</sup> voltage. The condition of cellulose–aramid insulation is determined for considerably longer times, sometimes even exceeding 1000 s [13–15]. The degree of

cellulose moisture determines the current leakage value, which increases along with the increasing moisture. A much faster depolarization current decay is also observed.

With sample polarization current time characteristics, it was decided to determine activation energy *E<sup>A</sup>* at which the low-frequency cellulose–aramid insulation relaxation process is subject to change. The purpose of the calculations was the assumption that the activation energy *E<sup>A</sup>* value is determined by the degree of moisture as well as the ageing of the samples, defined as the degree of cellulose macromolecule thermal degradation. The Low-Frequency Dispersion Jonscher equation was used as the sought sample polarization current regression function [23] in the form of:

$$I\_P(t) \propto A\_1 \cdot t^{-N\_1} + A\_2 \cdot t^{-N\_2},\tag{1}$$

where *A*1, *A*2, *N*1, *N*2—function parameters.

The activation energy *E<sup>A</sup>* can be calculated utilizing linear approximation of the Arrhenius temperature graph [24], applying the following dependencies:

$$
\ln(t\_A) = f\left(\frac{1000}{T}\right) \tag{2}
$$

$$E\_A = 1000 \cdot a \cdot k\_\prime \tag{3}$$

where *tA*—characteristic time (after which the relaxation process change occurs), *T*—sample temperature (in Kelvin degrees), *EA*—activation energy (eV), *a*—directional coefficient of linear regression function, and *k*—Boltzmann constant.

Characteristic time was calculated using the formula:

$$t\_A = \sqrt[{-N\_1 + N\_2}]{\overline{A\_2}} \sqrt{\frac{A\_2}{A\_1}} \tag{4}$$

Using sample depolarization current time characteristics, it was decided to analyze the dominant time constants separately for the relaxation processes of aramid and cellulose fibers, depending on the degree of moisture as well as ageing of the cellulose–aramid insulation being examined. To this end, a Debye equation with two relaxation times was used as the sought depolarization current regression function:

$$I\_D(t) \propto B\_1 \cdot e^{-\frac{t}{\tau\_1}} + B\_2 \cdot e^{-\frac{t}{\tau\_2}} \,. \tag{5}$$

where *B*1, *B*2—function parameters, τ1, τ2—dominant time constants of the relaxation processes, for aramid fibers and cellulose fibers, respectively.

#### **5. Experimental Results**

An MIC-15k1 high resistance meter from Sonel® was used for the measurements of the polarization and depolarization currents. Thanks to the embedded battery of accumulators, the meter provided a solid and stable U<sup>C</sup> charging voltage value, which amounted to 500 V for all the experiments. The registration of the polarization and depolarization currents in time was realized with the dielectric discharge factor measurement function (DD factor—Dielectric Discharge). The meter's software allowed any adjustment of the polarization and depolarization times, while data communication was over a wireless Bluetooth connection. The meter's sampling frequency was approximately 2 Hz, which, in the case of measurements of low-frequency currents, was a fully sufficient value.

#### *5.1. E*ff*ect of Temperature*

Figure 6 presents exemplary time characteristics of the polarization and depolarization currents for a non-aged insulation sample with an average degree of moisture (residual moisture plus 1.5% paper weight increase as a result of water absorption from the environment, before the impregnation process). We can observe on the characteristics how the sample temperature affects the recorded current values, in the range from 20 ◦C to 60 ◦C, at steps every 10 ◦C. The scope of temperature changes of the samples adopted in the experiments is typical of diagnosing the condition of oil insulation in power transformers performed using polarization diagnostic methods (including the PDC method) [13–15,18–22]. It is important to remember that polarization diagnostic methods require the transformer to be detached from the network (off-line state) and, consequently, the insulation temperature must be lower than typical, which is assumed at approx. 60 ◦C for the transformer's normal operation mode. If the transformer is disconnected for a long time from the network, the insulation temperature may be reduced even further to an ambient temperature, e.g., 20 ◦C.

**Figure 6.** Effect of temperature on the characteristics of the PDC method for a selected cellulose–aramid insulation sample (non-aged with 1.5% moisture) mineral oil-impregnated: (**a**) polarization current; (**b**) depolarization current.

The characteristics presented in Figure 6a prove that, along with an increase in insulation sample temperature, the depolarization current also increased across the whole time range. The reason for this phenomenon is the declining resistivity of mineral oil and cellulose itself. The observed change was almost proportional in relation to temperature, which is typical of insulation made of mineral oil-impregnated cellulose only [14,15]. In the case of the depolarization current (Figure 6b), temperature growth generated, just as before, an initial increase in the current, but a much faster decay was observed for times exceeding approx. 20 s. The reason is that the phenomenon related to the destructive effect of temperature on the polarization process of dielectric dipoles, making the following depolarization faster, because temperature facilitates the achievement of the initial state of dipoles disorder. As before, it can be stated that this is typical of mineral oil-impregnated cellulose insulation, which also proves the correctness of the completed measurements. It turned out that a small layer of aramid fibers does not significantly disturb the characteristics of the registered polarization and depolarization currents, with reference to the previously known effect of temperature in the PDC method for insulation made of mineral oil-impregnated cellulose paper only. The above conclusion was confirmed for all the examined samples, i.e., regardless of the degree of their moisture or ageing.

Figure 7a presents Debye regression functions according to Formula (5), which were used in order to fix time constants of two relaxation mechanisms based on the depolarization current of the cellulose–aramid insulation sample being examined. Certainly, the data presented in Figure 7a are only exemplary, while the regression functions being described were used for all the insulation samples, i.e., for each degree of moisture and ageing and for all temperatures. The sample of the insulation being examined was a thin layer of aramid fibers and mineral oil-impregnated cellulose, therefore it was assumed that the time characteristics of the depolarization current would contain at least three dominant time constants of the relaxation processes of the previously mentioned materials, i.e., aramid, cellulose and oil. Because the impregnation of the samples was made using fresh inhibited mineral oil, the time constant of the relaxation process of this poorly polar fluid was very small (below 1 s). Therefore, bearing in mind the primary nature of the tests being conducted (cellulose–aramid material), it was decided to ignore it. Recognizing that water collected in the insulation is stored mostly in cellulose (considerably higher absorbability compared to aramid fibers), a longer time constant τ<sup>2</sup> was needed to describe this process only. Then, a shorter time constant τ<sup>1</sup> was assigned to the relaxation process of aramid fibers. Figure 7b presents the effect of temperature on the value of the previously described time constants for a selected cellulose–aramid insulation sample, initially thermally aged in 150 ◦C with the smallest moisture. *τ τ*

**Figure 7.** Analysis of time characteristics of the depolarization current by means of Debye regression function for a selected cellulose–aramid insulation sample (aged at 150 ◦C with the smallest moisture), mineral oil-impregnated: (**a**) depolarization current in the measurement temperature 30 ◦C; (**b**) temperature dependence of the dominant time constants for two relaxation processes.

*τ τ τ τ τ τ* Analyzing the characteristics from Figure 7b, two opposing tendencies can be noticed. Temperature growth in the sample being examined resulted in an insignificant increase in time constant τ<sup>1</sup> value and a significant decrease in time constant τ<sup>2</sup> value. In the first case, the change in time constant τ<sup>1</sup> can be explained by the fact that the growing measurement temperature increased at the same time as the relative permeability of aramid fibers, and slightly reduced the material's volume resistivity [9]. Assuming that the time constant value in the electric equivalent circuit defines the product of the current capacity and resistance of the material, permeability growth probably determined a slight change in time constant τ<sup>1</sup> value. In the case of time constant τ2, which was correlated with the relaxation of cellulose fibers and the water collected in the material, temperature growth stimulated the process of water migration to the impregnating fluid, i.e., mineral oil [25]. Therefore, the amount of water in the insulation decreased (highly polar liquid with high permeability), and at the same time volume resistivity also decreased. The result of these phenomena was a considerable decrease in time constant τ<sup>2</sup> value. The described observations were confirmed for all the examined insulation samples, regardless of the degree of ageing and moisture.

#### *5.2. E*ff*ect of the Degree of Moisture*

Figure 8 presents exemplary characteristics of the polarization current measured for cellulose–aramid insulation samples with initial thermal ageing at 150 ◦C and with various moisture degrees. For comparison purposes, Figure 8 presents the results of tests for two different temperatures. The increased moisture of the samples resulted in a significant growth in the polarization current values at the initial stage of the measurement (until approx. 10 s) and a growth in the current conductivity element, which could be observed for considerably longer times (close to 1000 s). It is a typical phenomenon of the effect of increased moisture for the classic cellulose–oil insulation, widely described in many publications [13–15]. Therefore, it can be assumed that practically all the water is stored in the Nomex®910 paper cellulose layer. The measurement temperature growth stimulates the process of water migration from the cellulose layer to mineral oil, thereby reducing the differences in the polarization current characteristics being described (Figure 8b). The term "initial moisture" means the degree of cellulose–aramid insulation sample moisture, which was left in the material after the vacuum drying process, still before the oil impregnation process. As the drying method utilized for cellulose materials in industry, was applied, it may be assumed that the initial moisture of Nomex®910 paper did not exceed 0.5%.

**Figure 8.** Characteristics of the polarization current of cellulose–aramid insulation sample with initial thermal ageing at 150 ◦C and with various moisture: (**a**) polarization currents in the measurement temperature 20 ◦C; (**b**) polarization currents in the measurement temperature 40 ◦C.

In a similar manner, it is also possible to interpret the depolarization current characteristics, which are presented in Figure 9 for the same selected insulation samples. The increased moisture in the samples also generated an increased value of the depolarization current in the initial part of the analysis (until approx. 10 s); sometime later, a faster decay process of the depolarization current was observed for these samples.

**Figure 9.** Characteristics of the depolarization current of cellulose–aramid insulation samples with initial thermal ageing at 150 ◦C and with various moisture: (**a**) depolarization currents in the measurement temperature 20 ◦C; (**b**) depolarization currents in the measurement temperature 40 ◦C.

The measurement temperature growth (Figure 9b) also reduced the differences between the depolarization currents of samples with various moisture degrees within approx. 10 s, and this is due to the water migration process from cellulose to oil intensifying with increased temperature. The phenomenon described was observed for all the examined insulation samples, regardless of the degree of ageing (thermal degradation of cellulose fibers). The characteristics presented on Figures 8 and 9 are only general in nature.

Using the sample depolarization current characteristics depending on the measurement temperature, it was decided to analyze, using Equations (1)–(4), the dependence of the activation energy *E<sup>A</sup>* on the degree of moisture of the cellulose–aramid insulation. Figure 10 presents the manner of fixing characteristic time *t<sup>A</sup>* (Figure 10a) and the activation energy *E<sup>A</sup>* value (Figure 10b) with the use of the Arrhenius graph [24] for a selected non-aged sample with the smallest degree of moisture.

**Figure 10.** Method of fixing the activation energy *E<sup>A</sup>* for a selected non-aged cellulose–aramid insulation sample with the smallest degree of moisture: (**a**) way of fixing *t<sup>A</sup>* characteristic time from the polarization current; (**b**) Arrhenius graph.

The result of calculation of the activation energy *E<sup>A</sup>* depending on moisture for a selected non-aged cellulose–aramid insulation sample is presented in Figure 11a. A significant increase in the activation energy value along with the growing degree of insulation moisture should be noted. A similar phenomenon was observed for the classic mineral oil-impregnated cellulose insulation; however, the calculated *E<sup>A</sup>* values are slightly higher here [26]. Therefore, it can be assumed that the introduction of additional layers of aramid fibers in Nomex®910 paper raises the activation energy value at which the low-frequency insulation relaxation process is subject to change.

*τ τ* **Figure 11.** Dependence of the activation energy *E<sup>A</sup>* (**a**) and dominant time constants τ<sup>1</sup> and τ<sup>2</sup> (**b**) on the degree of moisture for a selected non-aged cellulose–aramid insulation sample.

*τ τ* Figure 11b presents the effect of the degree of sample moisture on the value of two dominant time constants of the relaxation processes, determined on the basis of the depolarization current characteristics according to Equation (5). Increased moisture resulted in a slight decrease in time constant τ1, which was correlated with the relaxation process of aramid fibers, and, on the other hand, a considerably more intensive decrease in time constant τ2, which was correlated with the relaxation of cellulose fibers. The presented difference is probably related to a significantly higher water absorbability by cellulose than aramid fibers.

#### *5.3. E*ff*ect of the Degree of Ageing*

Figure 12 presents exemplary characteristics of the polarization currents (Figure 12a) and the depolarization currents (Figure 12b) measured for unmoistened samples with various ageing degrees. It was decided to analyze the effect of the degree of ageing in the temperature range of initial degradation of cellulose fibers (before the impregnation process) from 130 ◦C to 190 ◦C, with steps every 20 ◦C.

**Figure 12.** Characteristics of the polarization currents (**a**) and the depolarization currents (**b**) measured for unmoistened cellulose–aramid insulation samples for different degrees of initial ageing in the measurement temperature 20 ◦C.

The greatest and the predictable effect of the degree of sample ageing was observed for the depolarization current within approx. 10 s (Figure 12b). Therefore, it can be concluded that a growth in the degree of thermal degradation of cellulose fibers significantly reduces the depolarization current value in this time range. For longer times, mostly due to small values of the registered depolarization currents at the level of 20–40 pA, the characteristics overlap, which makes their correct analysis difficult. In the case of the polarization currents (Figure 12a), within the observation time range up to approx. 10 s of the measurement, only the application of the initial degradation temperature of cellulose fibers equal to 190 ◦C caused a significant reduction in the current value as compared to the other samples. As thermal degradation of cellulose, namely a decrease in the degree of polymerization of its macromolecules, results mainly in a significant loss of mechanical properties (e.g., breaking strength), while the material's volume resistivity remains at a similar level, the polarization current characteristics in longer time ranges (approx. 1000 s) will stabilize close to the value equal to the leakage current. Similar conclusions were achieved for the other measurement temperatures, i.e., up to 60 ◦C inclusive. Unfortunately, the introduction of additional sample moisture in the range from 1.5% to 2.5% rendered the effect of the degree of ageing practically unfeasible to be observed on the polarization and depolarization current characteristics. Water molecules, because of their strongly polar nature, effectively conceal any minor effect of the degree of ageing, with any possible changes in the characteristics being within the boundaries of the meter's measuring error. This phenomenon was already observed in earlier publications from a co-author of this article [7,19].

Figure 13 presents the effect of the degree of sample ageing on the activation energy *E<sup>A</sup>* value (Figure 13a) and values of two dominant time constants of the relaxation processes (Figure 13b), which were determined on the basis of the depolarization current characteristics according to Equation (5).

*τ τ* **Figure 13.** Dependence of the *E<sup>A</sup>* activation energy (**a**) and dominant time constants τ<sup>1</sup> and τ<sup>2</sup> (**b**) on the degree of ageing for unmoistened cellulose–aramid insulation samples.

*τ τ* The most important change that was observed on the characteristics from Figure 13 is that the growing degree of thermal degradation of cellulose fibers resulted in a minor, but constant, decrease in the activation energy value, after which the low-frequency relaxation process of the insulation being examined was subject to change. A probable reason is that the activation of cellulose macromolecules with a smaller degree of polymerization as a result of ageing is less energy-intensive in the polarization process. In the case of the dominant time constants from Figure 13b, it was observed that the growing degree of sample ageing does not cause any significant changes. The explanation of this fact for time constant τ1, which is correlated with the relaxation processes of aramid fibers, is quite obvious. The initial sample ageing temperature is simply too low to cause any significant changes in the structure of this material's fibers [9]. In the case of time constant τ2, correlated mainly with the cellulose fiber relaxation process, the change is also negligible due to the similar process of decay of the depolarization current (Figure 12b) and the earlier described measuring difficulties.

#### **6. Conclusions**

The results of the tests presented in the article confirm that Nomex®910 cellulose–aramid electro-technical paper produced by DuPont™ is a material that can successfully be used and safely operated in the electro-insulation systems of power utilities for a long time. The basic goal of the company's engineers, i.e., strengthened cellulose material structure by two-sided covering of the paper surface with a thin layer of aramid, has certainly been accomplished. This article authors' opinion is particularly strong because of the fact that, after heating Nomex®910 paper in the temperature of 190 ◦C for 25 h with air access, the material changed to a darker color, however the structure of the surfaces did not change to a significant extent as compared to the samples heated at lower temperatures. The same process applied to classic Kraft type cellulose paper resulted in the material cracking when being handled after it was taken out of the furnace. Certainly, this statement applies to roll papers, with a thickness comparable to the cellulose–aramid paper used for the tests (0.08 mm).

At present however, there is still the problem of practical adaptation of the diagnostic methods applied so far for the classic cellulose–oil insulation, used, for example, in power transformers, as compared to hybrid semi-synthetic insulation, which Nomex®910 cellulose–aramid paper from DuPont™ is. It seems obvious that that the future of electro-insulation systems of power transformers will be synthetic materials. In the case of liquid materials, in many new and already operating

transformer units, oil of mineral origin is being replaced by biodegradable esters. Likewise, aramid material is being introduced to solid electric insulation systems at the stage of transformer design and production. Unfortunately, because the new materials are more expensive than the classic materials (cellulose and mineral oil), the number of transformers with semi-synthetic insulation operating at present is still small, limiting expert knowledge connected with the maintenance of these units.

The test results presented in the article have proved that the PDC diagnostic method (polarization and depolarization method) can be successfully used to estimate the degree of moisture of cellulose–aramid insulation impregnated with insulating mineral oil. The profiles of polarization and depolarization currents depending on moisture of the samples are predictable and similar to the characteristics measured for the classic cellulose–oil insulation. The introduction of a thin layer of aramid in Nomex®910 paper does not induce any significant changes in the characteristics of the hydrodynamic balanced paper–oil, which is certainly, from the point of view of adaptation of the PDC method, a very promising feature. In the analysis of the depolarization current using the regression method with Debye double function, described by Formula (5), in the case of a longer time constant of τ<sup>2</sup> relaxation processes, its practically linear dependence on the degree of sample moisture was observed (Figure 11b). This gives hope for the use of this information in future practical diagnostics of the degree of moisture in transformer insulation, although the article authors are aware that in the case of such complex systems, the linear dependence can change. The characteristics of the activation energy *E<sup>A</sup>* depending on moisture (Figure 11a) and depending on the degree of ageing (Figure 13a) are only cognitive in nature. In practical diagnostics, measurements of polarization and depolarization currents for several temperatures of the transformer's insulation are usually impossible. The process of cooling down the transformer's insulation system in offline mode is very time-consuming, which would require multiple diagnoses using the PDC method to be performed over several days, while, for the needs of diagnostics, transformers are switched off for as short a time as possible, subject to the company's economic calculations. At present, like for the classic cellulose–oil insulation, the estimation of the degree of ageing for samples made of Nomex®910 paper impregnated with insulating mineral oil is a great challenge for the PDC method. The cellulose ageing processes are always accompanied by increased moisture, because water is one of the products of decay of its macromolecules. Water is a strongly polar liquid, and therefore has a "masking" effect for significantly smaller changes in the characteristics of, for example, the depolarization currents that are caused by ageing changes. In this respect, there is a need to continue further research.

**Author Contributions:** Conceptualization, S.W.; methodology, S.W.; formal analysis, S.W. and A.K.; investigation, S.W. and A.K.; writing—original draft preparation, S.W.; visualization, A.K.; supervision, S.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** The NOMEX®910 for testing was provided by DuPont™ Poland Sp. z o.o., ul. Postepu 17b, 02-676 Warszawa, Poland.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **The Influence of the Window Width on FRA Assessment with Numerical Indices**

**Szymon Banaszak \* , Eugeniusz Kornatowski and Wojciech Szoka**

Faculty of Electrical Engineering, West Pomeranian University of Technology, 70-310 Szczecin, Poland; Eugeniusz.kornatowski@zut.edu.pl (E.K.); wojciech.szoka@zut.edu.pl (W.S.)

**\*** Correspondence: szymon.banaszak@zut.edu.pl

**Abstract:** Frequency response analysis is a method used in transformer diagnostics for the detection of mechanical faults or short-circuits in windings. The interpretation of test results is often performed with the application of numerical indices. However, usually these indices are used for the whole frequency range of the recorded data, returning a single number. Such an approach is inaccurate and may lead to mistakes in the interpretation. An alternative quality assessment is based on the estimation of the local values of the quality index with the moving window method. In this paper, the authors analyse the influence of the width of the input data window for four numerical indices. The analysis is based on the data measured on the transformer with deformations introduced into the winding and also for a 10 MVA transformer measured under industrial conditions. For the first unit the analysis is performed for various window widths and for various extents of the deformation, while in the case of the second the real differences between the frequency response curves are being analysed. On the basis of the results it was found that the choice of the data window width significantly influences the quality of the analysis results and the rules for elements number selection differ for various numerical indices.

**Keywords:** transformer winding; deformation; frequency response analysis (FRA); numerical index; window width

#### **1. Introduction**

In electric power systems transformers are very important elements. Their technical condition has a direct influence on the reliability of a power system. A power transformer's design and construction are quite complex and must meet many requirements related to the electrical, mechanical, thermal or environmental properties. In recent decades, the average age of a transformer in operation continues to increase, which means a growing demand for the development of diagnostic methods that can determine the actual technical condition of the transformer. Diagnostics plays a major role in the technical and economic aspects of power distribution companies' asset management [1]. Modern approaches in this field introduce health indices, which allow the managing staff to plan the operation and repairs [2]. Some such indices are used in complex systems introduced in power companies, taking into account the importance of the transformer in the power system [3]. The key issue in many methods is the interpretation of the obtained results, which includes the application of various signal processing methods. One such method is a moving window approach, used in linear digital filtration [4]. This method can be successfully used also in other numerical indices, including frequency response analysis.

The heart of a transformer is its active part (a core with all windings) with its designed mechanical strength. The design of the active part of transformers should be resistant to many mechanical forces, especially those caused by short-circuit currents. The strength of the structure is ensured by the appropriate connection of elements and the clamping system of the windings. However, with the passage of time, the mechanical integrity of the windings deteriorates due to the aging of the insulation and the cumulative effects of

**Citation:** Banaszak, S.; Kornatowski, E.; Szoka, W. The Influence of the Window Width on FRA Assessment with Numerical Indices. *Energies* **2021**, *14*, 362. https://doi.org/10.3390/en 14020362

Received: 3 December 2020 Accepted: 8 January 2021 Published: 11 January 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

the previous network or mechanical events (e.g., transport). In some cases, production errors [5] and the resulting insufficient resistance to factors not significantly different from the nominal conditions are revealed. When a short-circuit current of considerable magnitude occurs in the winding, as a consequence, significant electrodynamic forces also appear, which are proportional to the square of this current [6]. These forces deform the original shape of the winding and can also damage various components. One of the consequences of this process is the occurrence of electrical discharges in the reduced insulation gap. In other cases, initially a slight deformation of the windings does not necessarily lead to an immediate failure of the transformer. Such insulation can continue its operation, however, reduced gaps (e.g., similar turns of adjacent coils) and the disturbance of the turn insulation due to its aging lead to a reduction in electrical strength, which may end in a catastrophic failure [7].

One of the diagnostic methods used for testing of power transformers is frequency response analysis (FRA), which is widely used for the analysis of the mechanical condition of a transformer's active part, especially its windings. It is possible to detect faults, like radial deformations, axial displacements or short-circuits in windings. The FRA measurement results are usually presented in the form of Bode plots, where the amplitude is calculated as a scalar ratio of the signal measured at the output of the circuit to the signal given to the input, and presented in the form of attenuation (in dB). The phase shift of the frequency response results from the difference between these signals and is presented in degrees [8]. FRA is a comparative method, where two curves in a frequency domain are compared and the observed differences can be an indicator of a failure, for example a local deformation or a short-circuit in a winding. For this reason, there are no simple criteria for the determination of the winding's condition, the comparison is done in a wide frequency spectrum, which consists of many local series and parallel resonances, capacitive or inductive slopes of the frequency response (FR) curve. It should be mentioned that the proper connection scheme also influences the FR shape [9].

The assessment of the measurement data is a hard task, usually performed by experienced personnel. This assessment is aided by the application of several numerical indices, which usually return a single value that describes the condition of a winding. These indices and their applicability to FRA assessment are compared and analysed in many publications. The biggest set of indices—over 30—is gathered, described and compared in [10]. In [11] some tests of numerical indices with real FRA data coming from controlled deformations are performed, while in [12] these indices are tested with six case studies. In [13] the sensitivity tests of FRA results are performed and [14] proposes the criteria for interpretation of basic indices. From the point of view of the industrial user of the FRA method, it is hard to use over 20 different numerical indices, which can provide contrary conclusions, because they are sensitive to various differences between the compared frequency response curves. In addition, these differences are related to unknown faults, because—depending on the construction of the transformer, its power rating, winding connection, etc.—there is no universal direct correlation between a fault's type, size or location and its influence on the FR curve changes.

The authors of this paper performed the comparison of 14 of the most popular indices in [15], which was based on data coming from controlled deformations introduced into transformer windings and also from some industrial measurements. This allowed grouping indices into four categories and the selection of a single index from each category, which covers the behaviour of all indices from the given group. Thus, by using only four indices it is possible to perform a comprehensive assessment of the FRA data. This approach is called the grouped indices method—GIM. However, the result is still a single number returned by each index for the analysed frequency range. This limitation can be avoided by calculation of given index value not for the whole analysed range, but for a defined data window. In such a way it is possible to obtain a curve in a frequency domain for each numerical index. The question is what should be the width of such a window (number of analysed elements)?

Another problem in using numerical indices is the selection of the input data. The authors use only a medium frequency (MF) range, in which local deformations in the windings would create visible differences. The borders of this range depend on the geometrical size of the transformer and its construction; generally, the bigger the transformer, the lower in the frequency domain its response lies. The low frequency range is strongly influenced by an iron core, so—for example—all short-circuits in windings can be easily detected, as they generate a large difference between the compared curves in this range. A high frequency range shows the influence of wave phenomena in the windings and the connection setup of the diagnostic equipment and is usually omitted in the analysis. Details of the selection of the borders for an MF range are described in [15] by authors of this paper and wider in doctoral thesis [16]; this starts with the inflection point on the capacitive slope of the first deep resonance (visible for an end-to-end open test circuit and being the result of interaction of the bulk capacitance of the winding with magnetizing inductance of the core) and ends with the beginning of the wave phenomena influence on the FR curve (visible as the character change of the curve)—the example is presented in Figure 1, which presents the FRA data measured on the transformer used for tests described in Section 3 of this paper (details of the measurement configuration are also given there). — — —

" " **Figure 1.** FRA data measured in "end-to-end open" test circuit on a transformer used for the laboratory tests (Section 3 of this paper).

" " Although the input data are limited to the MF range, is still too wide to allow GIM indices to performing an accurate analysis with just a single (global) value. The borders of this range should be used rather as the beginning and end of the assessment performed in narrower windows. The efficient comparative analysis necessary for FRA results assessment needs determination of the local differences between the curves: reference and analysed ones. In such a case, a "moving window" technique may be introduced. This is well known in digital signal processing and digital filtration algorithms, widely described in the literature (for example, see [17]). Similarly, the problems of digital signal quality assessment can also be found in many papers [18].

" " In this paper, the authors introduce the "moving window" technique to FRA data analysis with numerical indices. The research results presented in the article include:


" "

—

criteria, and consequently—the impact of the window size on the readability of the FRA analysis results, and

• results of experimental research using a moving window and quality criteria used in the GIM method.

The data used for the analysis comes from controlled deformations performed on the active part of the distribution transformer and from industrial measurements coming from 10 MVA transformer. The aim of the research was to check the influence of a number of the window elements on the quality and applicability of a frequency response comparative analysis with chosen quality criteria.

#### **2. Frequency Response Analysis and Assessment of Measured Data**

In FRA results assessment usually only the amplitude is taken under investigation. It is commonly designated as FRA, so it can be written as follows:

$$\text{FRA (dB)} = \text{20log}(\mathcal{U}\_{\text{out}} / \mathcal{U}\_{\text{in}}) \,\tag{1}$$

where *U*in is the voltage on the input and *U*out is the voltage on the output.

Differences between the curves can be observed as frequency shifts of resonances or changes in curve damping [19].

The FRA measurements methodology is standardized [20]. The standard provides details of performing the FR measurements to obtain repeatable results, allowing the comparison of test results measured by various diagnostic companies or by equipment coming from various producers. All measurement data used in this paper was obtained according to this standard and using the end-to-end open test setup, presented in Figure 2.

**Figure 2.** FRA "end-to-end open" measurement configurations on typical transformer: ( " " **a**) Y-connected winding; (**b**) D-connected winding.

The FRA data was measured with a FRAnalyzer test device from Omicron (Austria), using standard settings, usually chosen by personnel for performing industrial measurements. This means that the total number of points, measured in the logarithmic scale of frequency (from 20 Hz to 2 MHz) was 1000. This number can be modified by advanced users, which allows for focusing on a given frequency range. These points are divided into frequency ranges as presented in Table 1.


**Table 1.** Standard distribution of test points in frequency ranges for the Omicron FRAnalyzer test device.

FRA diagnostics using local assessment of quality indices is the actual scientific problem. The research in this field can be found in papers from top publishers [21,22] or from international conferences, for example [23]. An assessment based only on a single value returned by any numerical index may be misleading and result in a wrong interpretation of the measured FR data.

The application of the moving window technique generates a series of quality indices QI(f) (where f—frequency) for subsequent positions of the algorithm window. The values of QI(f) are calculated by a chosen quality criterion, for example MSE (mean squared error), CC (correlation coefficient), ASLE (absolute sum of logarithmic error) or SD (standard deviation) as proposed in the GIM method [10]. The formulas representing these indices are given in Table 2.

**Table 2.** Numerical indices used in the grouped indices method (GIM) [15].


The input values are two sequences of FRA measurement data: The reference FRAY0(*f*) = {Y0: *y*0*<sup>i</sup>* | *i* = 1, 2, . . . , I}, and the diagnosed one, FRAY1(*f*) = {Y1: *y*1*<sup>i</sup>* | *i* = 1, 2, . . . , I}, where I is the index of the subsequent element of the set and also index (number) of FRA test frequency. Regardless of used quality index F (Table 2), the analysis result—in general—will be a set QI(*f*) = {QI: *qii*|*i* = N < *i* < I − N}. Calculation of the elements of this set is performed by the general formula:

$$\mathbf{Q}\mathbf{I}\_{i} = \mathbf{F}(\mathbf{y}\mathbf{0}\_{i-\mathrm{N}\ltimes i+\mathrm{N}\ltimes}\mathbf{y}\mathbf{1}\_{i-\mathrm{N}\ltimes i+\mathrm{N}})\tag{2}$$

with the assumption that the algorithm window contains K = 2 N + 1 elements and N ≤ *i* ≤ I − N.

The process of QI(*f*) calculation is similar to an algorithm of Finite Impulse Response filter (FIR) with two inputs [4]. The input data are sets Y0 and Y1. The input data are used for the successive calculation of QI, according to the rule F, using the window containing K = 2 N + 1 of consecutive elements of data vectors (values Y0 and Y1)—see Figure 3a. The window is being moved along the input vectors by one element and in the calculation process there is created the vector of output data QI, containing 2·N elements less than each of the input vectors. The process of selection of elements from input vectors, which are used for the calculation of QIi value is shown in Figure 3b.

(**b**)

" " **Figure 3.** (**a**) A flow chart of calculation of local values of the quality index, (**b**) the moving window algorithm: successive positions of the window in the process of elements acquisition from data vectors Y0 and Y1. The symbol "+" marks the central (current) window element, while total window width is K = 9 (N = 4).

> are done with the step Δ mal, equal to the number of measured points. If Δ The application of the moving window technique needs the determination of two parameters: a step of the algorithm and a number of window elements. If changes of index *i* are done with the step ∆*i* = 1, the frequency resolution of calculated index QI(*f*) is maximal, equal to the number of measured points. If ∆*i* > 1, the frequency resolution is lower.

> The choice of the window size is not an easy task. It can be predicted that large values of K will lead to a smoothening of the results. On the contrary, the low values of this parameter would lead to a very precise QI representation of the differences between FRAY0 and FRAY1. In such a case, obtained result QI(*f*) may be hard to interpret, similarly to the raw input data (measured curves of FRA(*f*)). The question arises: what should be the value of K?

— — — — If all probabilistic properties of the FRA dataset are taken under consideration, as well as the definitions of the chosen quality indices CC, SD, MSE and ASLE, the dependency of the indices variance changes as a function of N parameter (defining the number of window elements K = 2 N + 1) are given in Figure 4. The vertical axis represents—normalized to maximal values—the variance of the chosen quality indices. It can be seen that in the case of SD, MSE and ASLE, the application of a small size window would lead to a precise representation by these indices of the changes between the reference and diagnosed FRA datasets. For windows having large number of elements (e.g., with K > 11 (N > 5) elements), the curves representing these indices value changes would be smoothened, which in FRA diagnostics—in some cases—may be advantageous.

(QI) =

" " 1 ≤ i ≤ L,

1 L − 1 L

1

∑(QI<sup>i</sup> − QI

̅̅̅ ) 2

**Figure 4.** The dependency of normalized variance of quality indices values from N (the number of window elements K = 2 N + 1).

The variance values for each QI quality index (CC, SD, MSE or ASLE) were calculated using the definition of unbiased estimation of variance:

$$Var(\mathbf{QI}) = \frac{1}{\mathbf{L} - 1} \sum\_{1}^{\mathbf{L}} \left( \mathbf{QI}\_{\mathbf{i}} - \overline{\mathbf{QI}} \right)^{2} \tag{3}$$

where:

QI ̅̅̅

QI<sup>i</sup> are the values of CC, SD, MSE or ASLE calculated for all positions of the window having K = 2 N + 1 elements, "shifted" along the input data vector according to formula (6), which contains L elements, 1 ≤ i ≤ L,

" " — " " — QI is the mean value of CC, SD, MSE or ASLE, calculated for given window size K = 2 N + 1.

Finally, for such calculated vectors of variance (separately for individual quality indicators), graphs shown in Figure 4 were prepared, normalizing the results against the maximum QI value for each of the quality criteria.

A different character of window size influence on variance may be observed for the index CC. A maximum can be clearly seen on its graph in Figure 4. This means that for the N equal to approximately 10 the variance of CC index values is maximal, which results in the most exact representation of its changes in the frequency function. The curves shown on Figure 4 were obtained by averaging the results of the normalized variances calculations of four quality criteria for eight transformers (which have various power ratings) and for the standard measurement point distribution in frequency ranges, as shown in Table 1. If the frequency spectrum will be divided in a different way, the maximum value of CC index normalized variance is for N different than 10. In the case of the remaining indices curves would be similar to those presented on Figure 4 and will still be valid for the rule: "small" window—big variance, "large" window—small variance.

The conclusion from this comparison is that the optimal value of N cannot be defined. It depends on the expected final effect: a very exact representation of the changes or a smoothened analysis result. In the first case for three criteria: SD, MSE and ASLE, the value of N shall be lower than 5 (the increase of the variance in Figure 4). Where the analysis results need smoothening, it is the contrary. A significant increase in the value of N (much more than 5) will not influence the quality of the results: the smoothening level will change slowly, while the amount of calculations will change proportionally to the number of elements in the algorithm window.

In the case of the CC index window width estimation, the character of its variance changes needs to be considered in the function of N. A choice of N = 10 would allow for detailed representation of its values changes in the frequency domain, so its "sensitivity" would be maximal (for a standard distribution of test point in frequency ranges given in Table 1).

" "

#### **3. The Influence of the Window Size on GIM Indices**

The four indices, chosen for the GIM method, were used for assessment of the data coming from the deformational experiment, performed on a 6/0.4 kV, 800 kVA, Dyn transformer. Its active part was removed from the tank and various deformations were introduced into windings. One of them was chosen for testing the abovementioned indices with different sizes of analysis window. The results measured in controlled deformations are especially useful for described numerical indices analysis, because they are connected to a known deformation in the winding. This deformation was based on compression of the top disks, by removing spacers between them—it is presented in Figure 5. It was applied to disks 1-2 (Def. 1), 1-3 (Def. 2), 1-4 (Def. 3) and 1-5 (Def. 4), so there were four levels of this deformation, compared to the reference measurement. —

— **Figure 5.** Example of deformation introduced into windings of a transformer: compression (reduced inter-disc distances in three gaps)—Def. 3.

The analysis of the four GIM indices was conducted in the medium frequency range, which for this transformer was set from 20 kHz to 600 kHz (according to [15,16]). Various values of N were analysed. In the following section, three of these are presented in the graphs: N = 1, 10 and 20. The presentation of more results would make the graphs unclear.

– Figure 6 presents the FR data measured on this unit and used for the analysis. The graph shows only the MF range, used for further analysis (it is a part of curves from Figure 1). At the lower and higher frequencies no significant changes between the curves are present. To make the graph clear, only two deformations are presented (Def. 2 and Def. 4) with the reference curve (healthy winding). The differences between the curves are visible as damping shifts of the whole frequency ranges (for example from 70 kHz to 200 kHz) or at the resonant points (270 kHz, 340 kHz, 470 kHz).

—

—

**Figure 6.** FR curves measured on the healthy winding of 6/0.4 kV, 800 kVA transformer and with axial deformations.

— Figures 7–10 present the values of the four numerical indices for various values of N (K = 2 N + 1). Each case also contains the average value, which is a single value calculated from the given index for the whole analysed range. In other words, it represents the typical industrial approach to analysis with numerical indices and is presented on the graphs with dashed line. The curves used for comparison with the indices are the reference one and Def. 4—the biggest deformation. —

**Figure 7.** The results of assessment with ASLE for various values of N. The dashed line represents the average value (global).

**Figure 8.** The results of assessment with MSE for various values of N. The dashed line represents the average value (global).

**Figure 9.** The results of assessment with SD for various values of N. The dashed line represents the average value (global).

It is expected that with the increase of the value of N, the graph will get flattened. The cause of such behaviour is illustrated in Figure 4: for the large values of N, the variance of the indices values decreases, so the smoothening level gets higher.

The first example (Figure 7) is calculated with the ASLE index. The differences between N = 1 and N = 20 are clearly visible, especially in the frequency range where a narrow and steep value change appears—for example at approx. 270 kHz or 340 kHz. The smoothening is very strong, if compared to less steep areas (for example at approx. 100 kHz).

**Figure 10.** The results of assessment with CC for various values of N. The dashed line represents the average value (global).

– — The next graph (Figure 8) presents the calculation conducted with the MSE index. In this case, the graph flattening is also very strong in the case of narrow and steep areas, such as at approx. 270 kHz. The difference between the average value (dashed line) and the maximum value for N = 1 is huge.

– Figure 9 presents the results of assessment with the SD index. The conclusions are similar to the two previous cases, however, the smoothening is not so radical with the increase of N elements. For example, at approx. 270 kHz the change of the window size from 3 (N = 1) to 21 (N = 10) results in the drop of the SD value by approximately half.

The last example is the values of the CC index, shown in Figure 10. For this numerical index, the influence of the number of N is not so obvious.

Depending on the frequency range, the number of N influences to a different extent. For example, the resonance of the FR data at 270 kHz gives the biggest change to the CC result if the value of N = 10, while the two other resonances (340 kHz, 470 kHz) give the biggest change in CC for N = 1. This is related to the width of the resonance (see Figure 6), as the first of these (270 kHz) does not have slopes as steep as the other two.

— — — — — — — — To summarize the results from Figures 7–10, it can be stated that the window size depends on ones needs, whether it is necessary to smoothen or sharpen the output curve. However, the best value for the average approach is N = 10—especially in the case of CC index. For this quality index the value N = 10 guarantees the optimal precision of local values changes representation (Figure 2), which advantageously influences the legibility of CC (f) curve and the accuracy of diagnostic conclusions. In order to compare indices ASLE, SD, MSE and CC this value is used for testing all the indices for various extents of the deformation, which is presented in Figures 11–14. The curves presented on these graphs are the results of the assessment of the FR data with the four indices. Each curve represents the values calculated from comparison of the data measured in the healthy state with the data measured after introducing the deformation. For example, the curve marked as Def. 1 is the result of analysis with a given index, for N = 10, of the reference line and the line for deformation 1. Figures contain the results for Def. 1, Def. 3 and Def. 4 (minimal deformation, maximal deformation and one in-between) to make them easier to analyse. In addition, for each case the global value of the given index is given, in other words the average value, for the window width equal to the total number of points in the analysed MF range.

—

—

**Figure 11.** The results of assessment with ASLE for various deformations.

**Figure 12.** The results of assessment with MSE for various deformations.

**Figure 13.** The results of assessment with SD for various deformations.

**Figure 14.** The results of assessment with CC for various deformations.

The first example is shown in Figure 11, presenting the results obtained with the ASLE index. Depending on the frequency range (input FR data), there are visible various behaviours of curves calculated for the three deformation scales. However, if these shapes are compared to the global values (for the whole range), which are Def. 1—0.140, Def. 3—0.225 and Def. 4—0.230, it can be seen that latter two do not reflect the complexity of the changes visible on the graph, where—for example—Def. 3 has its maximum at 180 kHz, while for Def. 4 it is at 240 kHz. Their global values are almost the same, so an analysis based on them would not show any differences between these two cases. In other words application of the moving window technique is proven to be effective in the analysis of the FRA data.

A similar effect can be observed in Figure 12, where the MSE index was used for the assessment. The global values are in this case: Def. 1—2.92, Def. 3—5.11, Def. 4—5.04, so, again, the latter two are almost similar, while the curves show the maximums for different frequencies. The same conclusions may be drawn for the third index, SD (see Figure 13), where the global values are, respectively: 1.71, 2.26 and 2.25.

cover all possible scenarios, which can be encountered in the transformers' frequency re- The last case, the CC index, also has similar behavior. Def. 1 has its maximum at approx. 540 kHz, Def. 3 at 340 kHz, while Def. 4 is at 270 kHz. In this case, the global values are: 0.99961, 0.99944 and 0.99945, so again Def. 3 and Def. 4 are very similar—see Figure 14.

– From the above examples, it can be seen that for N = 10 all four indices act in the same way: their local extremums depend on the actual deformation and its influence on the FR curve. The comparison to global values clearly shows that analysis done for the narrower window, not for the whole analysed range, gives more information. It can be seen that for deformations introduced into the winding, the global value of the quality index may be insufficient to detect the fault. The quality indices for Def. 3 and Def. 4 are almost similar, while the measurements were taken for different geometries of windings.

#### **4. The Application to Industrial FRA Results**

The research described in the Section 3 was repeated for data coming from the industrial measurements. The tested transformer was 15/6 kV, 10 MVA unit, which has clearly visible differences between two measurements, namely reference and fault curves. The medium frequency range, which in this case is from 20 kHz to 600 kHz, can be observed in Figure 15. The exact cause of differences seen on this Figure is unknown for the authors, because the owner of the transformer did not share decisions taken on transformer further operation and possible results of the internal inspection. However, these results are good for the moving window technique analysis, because differences between both curves cover all possible scenarios, which can be encountered in the transformers' frequency response

analysis: a shift in the frequency domain (60–120 kHz) related to capacitance changes, a change of a shape with a new resonance (approx. at 200 kHz), which can be affected by many factors that constitute that parallel resonance (e.g., capacitance and inductance interaction in that frequency) and a damping change (approx. at 360 kHz) being an effect of changed parameters forming given resonance, e.g., capacitance and turn-to-turn magnetic couplings, if there was a deformation in the winding or local resistance change in the case of partial (via small resistance) local short-circuit. With such data the comparison of changing window widths showed all possible behaviours of the output data.

**Figure 15.** FR curves of industrial transformer 15/6 kV, 10 MVA in the medium frequency range.

The first tested numerical index was ASLE. Its results are shown in Figure 16. For value N = 1 the output results are very sharp, strongly pointing all present differences between curves. By increasing the N value to 10 and 20 the curve is smoothened and follows the frequencies of changes visible in FR graph from Figure 15. For diagnostic purposes the better result is obtained for value N = 10, because for changes at 200 kHz and 360 kHz is shown two separate maximums. Additionally, if compared to the average value, used in the standard approach to numerical indices application, there are clearly visible frequency ranges in which curves vary from this value.

**Figure 16.** The results of assessment of data from Figure 15 with ASLE for various values of N. The dashed line represents the average value (global).

"suspicious" frequency ranges differ from the average value of this index.

"suspicious" frequency ranges differ from the average value of this index.

"

"

"

Similar conclusions may be drawn for data presented in Figure 17 and representing the assessment with MSE index. For N = 1 the output graphs reaches very high amplitudes and is strongly sensitive on any differences between two input curves. Again, for N = 10 some local maximums may be observed in frequency ranges correlating to FR curves measured on the transformer and comparison to the average value clearly indicated "suspicious" frequency ranges.

**Figure 17.** The results of assessment of data from Figure 15 with MSE for various values of N. The dashed line represents the average value (global).

The third numerical index is SD, with results for various window sizes presented on Figure 18. Also this case shown the best efficiency in the detection of differences between input curves for N = 10, both indicating frequency ranges connected to faults and giving the good contrast if compared to the average value (global).

**Figure 18.** The results of assessment of data from Figure 15 with SD for various values of N. The dashed line represents the average value (global).

The last case is CC numerical index, analysed in Figure 19 and showing different behaviour. The value N = 1 gives the smaller sensitivity to differences between input curves, pointing out mainly the change of the shape (new resonance). However, the increase of N to 10 or 20 returns more differences in the curve shape. Additionally, in this case N = 10 gives better results, because the index is more sensitive to local changes. For example there

are visible local minimums at approx. 200 kHz and 250 kHz. All such local "suspicious" frequency ranges differ from the average value of this index.

**Figure 19.** The results of assessment of data from Figure 15 with SD for various values of N. The dashed line represents the average value (global).

The analysis of results presented on Figures 16–19 leads to the conclusion that the best quality of detection of differences between compared curves is achieved for the value N = 10, for which all categories of changes are indicated in the graphs: resonance shifts, damping changes and curve shape change.

#### **5. Summary**

The paper presents the research on the data window width for the analysis of frequency response results of transformer windings performed with numerical indices. Four quality indices were chosen to test the results measured on the active part of the transformer with deformations introduced into the winding. The results were analysed for various window widths (K = 2 N + 1).

In the first stage, the variance of the four indices was tested, depending on the N value, which allowed for testing their sensitivity to this parameter. In the case of the correlation coefficient (CC) index, the results were not unequivocal.

The analysis of data for various extents of deformation introduced into laboratory tested transformer showed that the approach based on moving the window is more accurate and allows for detection of the winding geometry changes, which are undetected by a standard approach with a single (global) value of a given index. This is clearly presented in the case of deformations 3 and 4. The choice of the N value depends on the needs of the analysis, however, the proposed N = 10 seems to be the most universal and useful for most practical analyses, however, some users of the frequency response analysis (FRA) method may need other effects (smoothening vs. sharpening). The similar conclusions may be drawn from observation of the industrial measurements performed on the second transformer. The value N = 10 allowed for the best effect of differences detection between compared frequency response curves (datasets). For such value the output curve of each numerical index clearly showed the local difference of the value, strongly differing from the average value, for any type of possible changes to the output data: a frequency shift, damping change or change in the shape (new resonance).

For practical application of obtained results authors propose to compare output data of each index in frequency range for N = 10 to average value (local maximum to average value ratio). By setting the fault detection criteria, for example on level 30%, it will be possible to identify the frequency ranges of input frequency response data having "suspicious" values differences. It can be applied to the automatic detection systems. The results of

experimental tests presented in Section 3 relate to an exemplary transformer with a power rating of 800 kVA. It should be clearly emphasized that the proposed "optimal" window sizes apply to transformers with such power and design features and—in particular—with the adopted frequency resolution of the frequency response analysis method.

The value of fault detection criteria should be further analysed, because it depends for example on geometrical size of the unit (power rating) or its construction. This topic is the subject of further research of the authors. In this paper, the authors wanted to draw the attention of other researchers dealing with diagnostics using the frequency response analysis method to the problem of window size selection when using objective (numerical) quality indicators. The readability of the obtained results for local frequency ranges depends on the number of window elements and there is no intuitive rule: the precision of mapping local numerical changes in quality indicators is inversely proportional to the number of window elements. This is evidenced by the presented analysis of the variance of changes in the correlation coefficient value, for which the maximum variance occurs for a given number of window elements.

**Author Contributions:** Conceptualization, S.B. and E.K.; Formal analysis, E.K.; Investigation, S.B., E.K. and W.S.; Methodology, S.B., E.K. and W.S.; Project administration, S.B.; Supervision, S.B. and E.K.; Validation, S.B. and E.K.; Writing—original draft, S.B., E.K. and W.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


*Article*
