Research on identification method of transformer winding material based on vibration characteristic

Abstract

At present, there are shoddy transformers in the market, of which the windings are replaced by aluminum and copper clad aluminum. The commissioning of these transformers may cause poor power supply performance and excessive winding heating. The existing detection methods of windings are complex, time-consuming to operate and destructive. Therefore, a winding material identification method based on vibration characteristics is proposed. Firstly, the vibration accelerations of transformer cores and windings with different winding materials are theoretically derived. Furthermore, through the coupling simulation of magnetic field and structure field of distribution transformers, the calculated vibration characteristics of copper, aluminum, and copper clad aluminum are verified. Finally, by comparing the time domain, the frequency domain and time-frequency domain of acceleration signals, preliminary identification of winding materials is conducted, which lays a theoretical foundation for establishing a precise identification model for winding materials in the future. This work provides guarantee for the safe operation of the distribution network.

Keywords

Transformer identification of winding material vibration characteristics multi-physical field coupling time-frequency analysis

1. Introduction

Transformers undertake important tasks such as voltage level regulation, energy distribution, and transfer in the power system, based on the principle of electromagnetic induction. It is one of the core electrical equipment in the power system [1,2]. Transformer is mainly composed of iron cores, windings, fixed supports, and boxes. Wherein, the winding is the core of the transformer, whose number of turns and insulation determine the capacity of the transformer. Usually, copper is used as the winding material, due to its better conductivity. If aluminum even copper clad aluminum (CCA) is used instead of copper as the winding material, the performance of the transformer will deteriorate, thus posing the heating problem and safety hazards [3].

It is widely believed in Europe and America that aluminum can replace copper for windings of transformers. In this regard, it is clearly pointed out that transformers with aluminum winding can be used when the demand of capacity is small and the voltage level is low [4]. Therefore, the main research direction in this area is the comparison and selection of performance and economy of copper aluminum transformers, while little research on winding material identification [5]. In some regions, there is a high demand for transformers. But due to the high price of copper, some manufacturers use aluminum wire instead of copper wire to make transformer windings for profit, resulting in many transformers using aluminum instead of copper [6–8]. According to statistics, State Grid Corporation conducted a special spot check on newly purchased distribution transformers by companies in various provinces in 2012. Among them, 476 units were disassembled and inspected, and 53 units of aluminum coil products were found, accounting for 11.13%. In recent years, there have even been half copper and half aluminum transformers in the distribution transformer market, where only the high-voltage winding (or low-voltage winding) is aluminum conductor [9,10]. The conductivity, mechanical properties, and temperature characteristics of copper windings are superior to those of aluminum windings. If aluminum or CCA is used instead of copper, it can affect the various performance indicators of transformers and cause economic losses. In the field of distribution transformer winding material identification applications, the current method for industrial mostly uses hanging covers, dismantling and testing, which damage the insulation of transformer windings, and the operation is complex and the cost is high [11,12].

There is currently no effective non-destructive testing equipment for distribution transformer windings in the market. Therefore, many researches have been conducted on non-destructive testing methods. With the massive data statistics, theoretical analysis, and test verification methods, the advantages, disadvantages, and feasibility of various methods for identification of winding material are compared. The simulations and experiments are conducted to demonstrate that the identification and on-line monitoring of distribution transformer winding materials is feasible and effective [13]. Based on the thermoelectric effect, the reference [14] proposed to judge whether the transformer winding is aluminum winding according to the thermoelectric potential under a certain temperature difference. However, in practical application, it is inaccurate due to the difficult to control the temperature difference of the winding circuit and the impurities of winding material. Moreover, when applied to the oil immersed transformer, the heating method is limited, and further disassembly of the hanging cover is still required. The attenuation law of X-rays in the material was utilized to identify the winding material of transformers in [15]. This method explored the X-ray transmission mode of copper and aluminum as coils, and provided and published a comparative analysis of the blackness of X-ray transmission images of winding transformers made of two materials. However, the operation process is complex, costly, and the detection cycle is long, which can only be carried out in the laboratory, resulting in poor engineering practicality. The resistance coefficient method was proposed in [16], which calculated the theoretical resistance ratio of copper and aluminum at different temperatures, and then compared the actual resistance ratio of the transformer through experiments to determine the material of the transformer winding. However, the DC resistance of the low-voltage winding of the transformer was small, requiring a quite high measurement accuracy.

The above detection methods require high accuracy in recognizing the parameters, and the parameters are difficult to extract and need high operating costs. The vibration signals during transformer operation are easy to collect. And characteristics values are easy to extract, which can effectively reflect the operating status of the transformer. A clever method to identify core materials of transformer is proposed based on comparison of the vibration characteristics, which deduces the correlation of transformer vibration characteristics under different winding materials. It is easily to implement compared with currently common used thermoelectric method.

2. Vibration characteristics of transformers with different windings materials

2.1. Vibration of iron core

Vibration of transformer is mainly caused by that of the transformer core and winding. Amongst, the vibrations of the iron core are mainly caused by the magnetostriction of the silicon steel sheet. Assuming the power supply voltage u = U sin 𝜔t, the magnetic flux density in the iron core B can be expressed as follows, according to Faraday’s law of induction. $\begin{eqnarray}B=\frac{{\varphi}}{S}=\frac{U}{{\omega}\mathit{NS}}\cos {\omega}t=B_{0}\cos {\omega}t\end{eqnarray}$ (1) Where, 𝜑 is the magnetic flux of the iron core. S is the cross-sectional area of the iron core. N is the number of stacked layers of silicon steel sheets. $B_{0}=\frac{U}{{\omega}\mathit{NS}}$ is the maximum magnetic flux density.

Due to the magnetic field strength being the ratio of magnetic flux density to medium permeability 𝜇, the magnetic field strength H in an iron core can be expressed as $\begin{eqnarray}H=\frac{B}{{\mu}}=\frac{BH_{c}}{B_{s}}=\frac{B_{0}H_{c}\cos {\omega}t}{B_{s}}\end{eqnarray}$ (2) Where, B _s is the saturation magnetic flux density of iron core. H _c is coercivity.

The magnetostriction rate of an iron core 𝜀 can be expressed as $\begin{eqnarray}{\varepsilon}=\frac{{\rm\Delta}L}{L}=\frac{2{\varepsilon}_{s}}{H_{c}^{2}}\int _{0}^{H}|H|dH=\frac{{\varepsilon}_{s}}{H_{c}^{2}}H^{2}\end{eqnarray}$ (3) Where, 𝜀_s is the saturation magnetostriction rate. H _c is the saturation magnetic field strength.

From Eqs (2) and (3), it can be obtained that the axial expansion of the silicon steel sheet ΔL caused by magnetostriction is as followed. $\begin{eqnarray}{\rm\Delta}L=L\frac{{\varepsilon}_{s}H^{2}}{H_{c}^{2}}=\frac{L{\varepsilon}_{s}^{2}U^{2}}{({\omega}\mathit{NSB}_{s})^{2}}\cos ^{2}{\omega}t.\end{eqnarray}$ (4)

The vibration acceleration of the core a _c is further derived as followed. $\begin{eqnarray}a_{c}=\frac{d^{2}{\rm\Delta}L}{dt^{2}}=-\frac{2L{\varepsilon}_{s}U^{2}}{(\mathit{NSB}_{_{s}})^{2}}\cos 2{\omega}t.\end{eqnarray}$ (5)

2.2. Vibration of windings

The vibration of the winding is mainly caused by the dynamic electromagnetic force on the coil with alternating current in the leakage magnetic field. When the transformer winding is energized with current, radial and axial leakage fields are generated in the dielectric and envelope space where the winding is located. In the leakage magnetic field, vibrations will be generated between the windings, namely the wire turns and the wire cakes under the action of electromagnetic forces, as shown in Fig. 1.

Fig. 1.

Analysis of transformer winding forces.

When the load current flows through the windings, a leakage magnetic field is generated around the winding. Under the effecting of current and leakage magnetic field, the Lorentz force is generated inside the winding, as followed. $\begin{eqnarray}d\overset{\rightarrow }{F}=\mathit{id}\overset{\rightarrow }{l}\times \overset{\rightarrow }{B}\end{eqnarray}$ (6) Where, $\stackrel{\rightarrow }{F}$ is the Lorentz force (N); $\stackrel{\rightarrow }{B}$ is the magnetic flux density (T). $\begin{eqnarray}\overset{\rightarrow }{F}=\int _{v}J_{{\phi}}\overset{\wedge }{{\phi}}\times (B_{r}\overset{\wedge }{r}+B_{z}\overset{\wedge }{z})dv=F_{r}\overset{\wedge }{r}+F_{z}\overset{\wedge }{z}\end{eqnarray}$ (7) Where, J _𝜙 is the current density inside the short-circuit coil in the direction of 𝜙. $\stackrel{\wedge }{r}$ , $\stackrel{\wedge }{{\phi}}$ , $\stackrel{\wedge }{z}$ is the unit vector under the cylindrical coordinate system. F _r, F _z are axial and radial electromagnetic forces, respectively.

Ignoring the difference between axial and radial electromagnetic forces, the electromagnetic force F can be expressed as $\begin{eqnarray}\displaystyle F & = & \displaystyle \mathop{\sum }_{i=1}^{n}B_{ri}\cdot I_{i}\cdot L_{i}\approx 2{\pi}r_{p}I_{d}\sum _{i=1}^{n}B_{ri}\nonumber\\ \displaystyle & = & \displaystyle 2{\pi}r_{p}\cdot I\cdot N\cdot \left(\frac{\mathop{\sum }_{i=1}^{n}B_{ri}}{m}\right)=2{\pi}r_{p}\mathit{INB}_{pr}\end{eqnarray}$ (8) Where, r _p is the winding radius. I _d is the current of a single wire. Iis the winding current. N is the number of winding turns. m is the number of parallel wires. B _pr is the equivalent average magnetic flux density in the inner diameter direction of the winding. B _ri is the radial magnetic flux density of the center of the root conductor.

Under current i = I cos 𝜔t, the vibration acceleration of the winding a _w can be expressed as followed. $\begin{eqnarray}a_{w}=\frac{2{\pi}r_{p}\mathit{INB}_{pr}}{m_{w}}\cos {\omega}t=\frac{{\pi}r_{p}\mathit{IN}}{m_{w}}\cos 2{\omega}t+\frac{{\pi}r_{p}\mathit{IN}}{m_{w}}\end{eqnarray}$ (9) Where m _w is the mass of windings.

For transformers with different winding materials, there are differences in the vibration acceleration of the windings. It is necessary to calculate the relationship between the vibration acceleration of copper winding, aluminum winding, and CCA winding. In the calculation, the density of copper is 8.96 g/cm³, and the resistivity is 2.135 × 10⁻⁸ Ω⋅m. The density of aluminum is 2.70 g/cm³, and the resistivity is3.44 × 10⁻⁸ Ω⋅m. The density of copper clad aluminum is 3.63 g/cm³, and the resistivity is 2.68 × 10⁻⁸ Ω⋅m. For a transformer with a certain capacity, the change in capacity can be calculated as followed if the winding material is changed from copper to aluminum. $\begin{eqnarray}\frac{C_{Al}}{C_{Cu}}=\sqrt{\frac{{\rho}_{Cu}}{{\rho}_{Al}}}=\sqrt{\frac{2.135\times 10^{-8}}{3.44\times 10^{-8}}}=0.787\end{eqnarray}$ (10) Where C _Al and C _Cu are the capacity of transformers with aluminum and copper wires. 𝜌_Al and 𝜌_Cu are the electrical resistivity of aluminum and copper wires, respectively.

According to Eq. (10), the capacity will increase to 0.787 times than that of the original capacity. To maintain the transformer capacity unchanged, it is necessary to increase the weight of the iron core silicon steel sheet, with a weight increase value as followed. $\begin{eqnarray}\frac{G_{Al}}{G_{Cu}}=\sqrt[4]{\frac{1}{0.787^{3}}}=1.20\end{eqnarray}$ (11) Where G _Al and G _Cu are the gravitational forces acting on aluminum and copper, respectively.

According to Eq. (11), the weight of the silicon steel sheet increases by 1.20 times, and the no-load loss also increases by 1.20 times. The statistics indicate that the no-load loss of transformers generally increases by 26%, and the load loss generally increases by 20% [16], after replacing the copper with aluminum.

Based on the above analysis, to maintain the same capacity and no-load loss, the cross-section of the iron core should be reduced by 1.2 times and the number of coil turns should be increased by 1.2 times. Due to the fact that the diameter of the wire is much smaller than that of the iron core, the length of the wire after replacing it with aluminum wire should be 1.2 times the length of the original copper wire, ignoring the influence of the wire diameter. In addition, to maintain the resistance of the coil unchanged, the ratio of the wire cross-sectional area to the wire weight is as followed. $\begin{eqnarray}\frac{S_{Al}}{S_{Cu}}=\frac{{\rho}_{Al}\times L_{Al}}{{\rho}_{Cu}\times L_{Cu}}=\frac{3.44\times 10^{-8}}{2.135\times 10^{-8}}\times 1.2=1.93\end{eqnarray}$ (12) Where, S _Al and S _Cu are the cross-sectional areas of aluminum and copper wires. L _Al and L _Cu are the lengths of aluminum wire and copper wire, respectively.

The ratio of masses of aluminum winding and copper winding is as followed. $\begin{eqnarray}\frac{m_{Al}}{m_{Cu}}=\frac{{\rho}_{Al}^{\prime }\times S_{Al}\times L_{Al}}{{\rho}_{Cu}^{\prime }\times S_{Cu}\times L_{Cu}}=\frac{2.70}{8.96}\times 1.93\times 1.2=0.70\end{eqnarray}$ (13) Where, m _Al and m _Cu are the masses of aluminum and copper wires. ${\rho}_{Al}^{\prime }$ and ${\rho}_{Cu}^{\prime }$ are the densities of aluminum and copper wires, respectively.

According to Eqs (9) and (13), the ratio of vibration acceleration amplitudes of aluminum winding and copper winding is as followed. $\begin{eqnarray}\frac{a_{Al}}{a_{Cu}}=\frac{\displaystyle \frac{{\pi}r_{p}\mathit{IN}}{m_{Al}}\cos 2{\omega}t+\frac{{\pi}r_{p}\mathit{IN}}{m_{Al}}}{\displaystyle \frac{{\pi}r_{p}\mathit{IN}}{m_{Cu}}\cos 2{\omega}t+\frac{{\pi}r_{p}\mathit{IN}}{m_{Cu}}}=1.429\end{eqnarray}$ (14) Where, a _Al and a _Cu are the vibration accelerations of the aluminum and copper windings, respectively.

If the winding material is changed from copper to CCA, the ratio of vibration acceleration amplitudes between copper clad aluminum winding and copper winding can be obtained through the same calculation method. $\begin{eqnarray}\frac{a_{\mathit{CCA}}}{a_{Cu}}=\frac{\displaystyle \frac{{\pi}r_{p}\mathit{IN}}{m_{\mathit{CCA}}}\cos 2{\omega}t+\frac{{\pi}r_{p}\mathit{IN}}{m_{\mathit{CCA}}}}{\displaystyle \frac{{\pi}r_{p}\mathit{IN}}{m_{Cu}}\cos 2{\omega}t+\frac{{\pi}r_{p}\mathit{IN}}{m_{Cu}}}=1.63\end{eqnarray}$ (15) Where, m _CCA is the mass of CCA and a _CCA is the vibration acceleration of CCA windings.

3. Finite element analysis

3.1. Finite element modelling

In this work, a 10/0.4 kV oil-immersed distribution transformer is taken as an example. The finite element analysis (FEA) model is built according to the actual size 1:1, of which the key dimensions are shown in Table 1.

Table 1
Parameters of the distribution transformer

Definition Size/mm

The length of the upper and lower iron yokes 635

The width of the upper and lower iron yokes 125

Distance between two yokes 380

Width iron core column 125

Primary winding height 300

Inner diameter of primary winding 160

Outer diameter of primary winding 170

Secondary winding height 300

Inner diameter of secondary winding 130

Outer diameter of secondary winding 140

Definition	Size/mm
The length of the upper and lower iron yokes	635
The width of the upper and lower iron yokes	125
Distance between two yokes	380
Width iron core column	125
Primary winding height	300
Inner diameter of primary winding	160
Outer diameter of primary winding	170
Secondary winding height	300
Inner diameter of secondary winding	130
Outer diameter of secondary winding	140

During the modeling process, the structure of the iron core and winding is certain simplified. If the iron core is modeled by stacking actual silicon steel sheets, it will not only require high modeling accuracy, but also cause problems such as difficulty in grid division and long calculation time. Therefore, when establishing the iron core model, it is necessary to simplify the main column and side column into an overall form. The contour of the outer edge of the horizontal section is maintained to ensure that the length, width, height, diameter, and other dimensions of the iron core center column, side column, and iron yoke are strictly consistent with the drawings [17]. Besides, the coil of three-phase windings is simplified into a cylindrical shape, with the cylinder height being the same as the actual size. The FEA model of transformer is shown in Fig. 2.

Fig. 2.

FEA model of transformer.

Corresponding material properties to each component of the transformer are assigned, according to the design drawings, as shown in Table 2.

Table 2

Material properties of transformer components

	Density kg/m³	Elastic modulus Pa	Poisson’s ratio
Silicon steel sheet	7650	1.95e11	0.26
Copper	8300	1.1e11	0.34
Insulating paper	1450	1.2e11	0.3
Structural steel	7850	2e11	0.3

3.2. Model verification

Conducting transient structural field analysis for the established FEA model of the transformer, of which the winding material is copper. And the transformer is in a light load operating state. The vibration time and frequency domain signal results of the copper winding transformer are obtained. Reference [18] also analyzed the vibration time-domain and frequency-domain signals of copper winding transformers under light load by experiments. The comparison of experimental and simulation results is shown in Fig. 3.

Under light load state, the current passing through the transformer winding changes slightly. If the leakage flux remains unchanged, the electromagnetic force on the transformer winding is relatively small, resulting in the vibration signal mainly concentrated in the low frequency range, which is an integer multiple of 100 Hz. The variation trend of the vibration time-domain signal obtained by the model in this paper is consistent with the experimental results in the literature. From the frequency-domain results, the vibration signals are mainly concentrated at 100 Hz and 200 Hz, which are consistent with the literature.

Fig. 3.

The comparison of experimental and simulated results.

The above results indicate that the FEA model of the transformer established here is in line with reality. By changing the winding material, the vibration characteristics of transformers with different winding materials can be further analyzed based on this model.

4. Analysis of vibration characteristics of transformers with three different windings

The main analysis objects are the vibration acceleration of the core and the acceleration measured from the transformer box. The monitoring of the acceleration of the transformer box is similar to the actual engineering application. In the actual detection, vibration signal test points are usually arranged on the top of the transformer box or around the box. In the simulation, three grids on the top of the transformer box are taken, as shown in Fig. 4.

Fig. 4.

Collection points for box vibration signal.

In order to obtain the vibration characteristics of transformers with different windings during the simulation process, it is necessary to set the winding materials as copper, aluminum, and CCA. The physical properties differences between copper, aluminum, and CCA are presented in Table 3.

Table 3

Differences in physical properties of copper, aluminum and CCA

Physical characteristics	Copper	Aluminum	CCA
Density	8.96 g⋅cm⁻³	2.70 g⋅cm⁻³	3.63 g⋅cm⁻³
Magnetic order	Diamagnetism	Paramagnetism	Paramagnetism
Magnetic susceptibility	−1.0 ×10⁻⁵	2.2 × 10⁻⁵	0.5 × 10⁻⁵
Resistivity	2.135 × 10⁻⁸ Ω⋅m	3.44 × 10⁻⁸ Ω⋅m	2.68 × 10⁻⁸ Ω⋅m
Young’s modulus	110–128 GPa	70 GPa	205 GPa
Shear modulus	48 GPa	26 GPa	42 GPa
Bulk modulus	140 GPa	76 GPa	69.6 GPa
Poisson’s ratio	0.34	0.35	0.33

Under light load state, the time domain vibration signals of the three winding materials are shown in Fig. 5. The vibration acceleration amplitude of copper wire winding transformer is 0.0175 m/s², aluminum wire winding transformer is 0.0246 m/s², and CCA winding transformer is 0.0285 m/s². There are significant differences in the time-domain vibration signals of the three different winding materials. The ratio of vibration acceleration amplitude between transformers with aluminum winding and copper winding, and between transformers with CCA winding and copper winding are 1.41 and 1.62, respectively, which are consistent with the theoretical calculation results before.

Fig. 5.

Time domain vibration signal.

The frequency domain vibration signals of the three winding materials of the transformer are shown in Fig. 6. The fundamental frequency of the vibration of the three winding materials of the transformer under light load is 100 Hz. The vibration frequency distribution of the copper winding and aluminum winding transformers does not change. The vibration signal of the CCA winding shows obvious integer harmonics of 100 Hz.

Fig. 6.

Frequency domain vibration signal.

By combining time-domain and frequency-domain signals, a time-frequency map of vibration is obtained, which clearly describes the relationship between signal frequency and time, and also expresses the corresponding amplitude size through spectrogram. The vibration time-frequency diagram of transformers with different winding materials is shown in Fig. 7. The frequency of the vibration signal of copper winding transformers is mainly concentrated within 300 Hz, with the maximum amplitude appearing between 0–150 Hz. The frequency of the vibration signal of aluminum winding transformers is mainly concentrated within 400 Hz, with the maximum amplitude appearing between 0–300 Hz. The frequency of the vibration signal of CCA winding is mainly concentrated between 100–400 Hz, and the maximum amplitude appearing between 200–300 Hz. There are significant differences in the distribution of vibration energy of transformers made of three winding materials.

Fig. 7.

Time-frequency diagram of vibration signal.

5. Conclusion

In this paper, comparisons of the vibration characteristics of copper winding, aluminum winding, and CCA winding transformers through theoretical calculation and simulation analysis are presented. The main conclusions are as follows:

Under the same capacity, the vibration acceleration amplitude of transformers with CCA winding and aluminum winding is significantly greater than that of copper winding. The time-domain signal waveform is significantly different, and the ratio of vibration acceleration amplitude is consistent with the theoretical calculation results. However, there is no significant change in the vibration frequency distribution.

The vibration energy distribution of the three types of winding transformers is different. The maximum amplitude of copper winding appears between 0–150 Hz, while aluminum winding appear between 0–300 Hz and CCA winding appear between 200–300 Hz.

There are significant differences in the vibration characteristics of transformers with copper winding, aluminum winding, and CCA winding. In actual engineering applications, vibration signal sensors can be used to obtain the vibration signal of the transformer. By analyzing the vibration characteristics, the winding material can be preliminarily determined.

Footnotes

Acknowledgement

This work has been supported by Science and Technology Project of State Grid Jiangsu Electric Power Co., Ltd. (Grant No. J2022126).

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