Transformer winding deformation accompanied by magnetic flux leakage field distribution variation and its diagnostic analysis of deformation degree

Abstract

During the transformer winding deformation process, the leakage magnetic field around the winding will change accordingly. Therefore, it is an effective method to monitor and track the change of the leakage magnetic field and then analyze and judge the state of the transformer. This paper firstly uses Comsol Multiphysics software to establish a 110 kV transformer electromagnetic simulation calculation model. Based on the simulation results of magnetic leakage distribution, an installation plan for the internal magnetic leakage sensor of a 110 kV true transformer is determined. The measurement results of the true single short-circuit test under different working conditions verify the accuracy of the simulation model. Subsequently, a number of B-phase high-centered three-phase short circuit (H-M B) true type tests were carried out, and the relationship between the magnetic leakage distribution characteristics and the impedance change rate after each impact was analyzed. The results show that before the transformer is seriously deformed due to multiple short circuit shocks, the sensitivity of the impedance change rate to the winding deformation is low, and the first five shocks only increase from 0.11% to 0.39%. However, the difference ratio between the simulation value and the test value of magnetic flux leakage (MFL) has obvious changes in each small deformation. BX3 increases from 1.77% to 5.62%, and BX4 increases from 2.08% to 6.55%. The difference ratio of four shocks before winding deformation is more than 6%. Therefore, by monitoring the flux leakage magnetic induction intensity, when the difference ratio is greater than 6%, strengthen the vigilance, which can provide a certain basis for winding monitoring before serious deformation.

Keywords

Transformer comsol magnetic leakage sensor magnetic flux leakage intensity deformation monitoring

1. Introduction

A transformer is a transformation hub of an electrical power system. Its stable and reliable operation significantly affects the operating efficiency of that electrical power system [1, 2, 3]. With the development of the electrical power industry, the voltage class of transmission lines has increased and capacity of a single transformer has also been increasing. When the transformer is short-circuited suddenly, its internal magnetic flux leakage field will in-crease rapidly, and the short circuit current can reach tens of times the rated operating value [4] so the windings generate a lot of heat in a short time and the insulation material is degraded. The windings also generate irreversible deformation with a huge, short circuit force [5, 6, 7].

Currently, transformer winding deformation diagnoses are commonly used at home and abroad and have a certain degree of maturity, mainly including a low-voltage pulse method, a frequency response method and a short circuit impedance method [8, 9, 10, 11]. In Literature [12], the author points out through tests and calculations that a double exponential pulse with a rising edge of approximately 250 ns and a half-pulse width of 2.5 ms is suitable for detecting winding deformation. However, the shortcomings of the low-voltage pulse method used in this literature in actual use are poor immunity from interference and repeatability. Although it continues to develop and can achieve a judgment on the deformation degree to some extent after the application of wavelet analysis technology, it still requires rich experience to analyze and summarize the deformation. In Literature [13], the author considers the phase on the existing basis of only considering the amplitude of frequency response results, and proposes a new numerical index, which improves detection sensitivity for small deformations. The frequency response method requires the transformer to stop running before monitoring, which reduces detection efficiency. In Literature [14], the author researches and designs an online winding deformation monitoring system including voltage and current data acquisition, data processing and host computer software based on the impedance method. For the short circuit impedance method, the evaluation and testing method is simple and clearly stipulated in the IEC and Chinese standards. When a measured value deviates from a set range, the winding can obviously show a fault and its degree of danger needs to be evaluated. However, the disadvantage of this method lies in its weak sensitivity to small deformations while it is apparently effective for any deformation that has a prominent overall impact. The existing detection quantities for monitoring winding deformations are mostly lumped parameters. The advantage of lumped parameters lies in obtaining relevant information reflected after a winding deformation, but it is relatively difficult to obtain local deformation-related information.

Deformation of the transformer winding is manifested in the change of the geometrical size of the winding and the relative position of the winding and the iron core, which will directly change the internal electromagnetic field distribution [15, 16]. In addition, the internal spatial magnetic field of the transformer is related to distribution of its inductor and capacitor on the windings and the electromotive force applied. In summary, performing an analysis and research of the internal magnetic field distribution before and after transformer deformation is the basis of proposing a winding deformation monitoring test and theory based on change in the magnetic field. In Literature [17], the author calculates the magnetic flux leakage field distribution under normal operation of the transformer and different axial deformations of four typical windings and four common winding deformation but does not quantitatively analyze the relationship between winding deformation and leakage inductance parameters of winding.

In this paper, a simulation calculation model of a solid transformer is established based on field-circuit coupling theory. The obtained distribution law of the internal magnetic flux leakage of the transformer under short circuit conditions is used to guide installation of magnetic flux leakage sensors inside a 110 kV transformer. A transformer anti-short circuit ability test is then carried out and simulation results under multiple short-circuit conditions and actual measurement results of the magnetic flux leakage sensors are compared to verify feasibility of the model. Finally, magnetic flux leakage characteristics during high to medium three-phase short circuits with Phase B as a test phase are analyzed and summarized. It is proposed to judge the winding deformation by monitoring the magnetic induction intensity of the internal magnetic flux leakage field of the transformer. The method proposed in this paper is of great significance to safe and stable operation of transformers.

2. Simulation model of the internal magnetic circuit of the transformer

Tests performed when studying the transformer winding intensity will cause irreversible damage to the winding. Considering true test conditions are strict and cost is high, it is necessary to make simulation calculations and then conduct test verification after mastering basic theoretical laws. Because the structure of the transformer is quite complex and characteristics of different structural parts are anisotropic, analysis of the transient magnetic flux leakage field is a huge task. To reduce calculation time and computational complexity, the structure of the power transformer will be appropriately simplified in this paper to establish a matching three-dimensional transient simulation model.

In this section, COMSOL software is used to establish a transformer electromagnetic field simulation calculation model based on the magnetic field-circuit coupling theory. The model is appropriately simplified during the modeling process:

The height of the high and low voltage winding coils is deemed to be consistent, and the coils are evenly distributed.

The upper and lower pressure plates, insulation between the winding phases and other components having little effect on both the winding force and magnetic field distribution are ignored.

To reduce the eddy current loss of the transformer core, its material is set to 30 mm thick, non-destructive soft iron that is stacked.

The winding material is set to copper. The three-dimensional model parameters of the transformer are shown in Table 1. Its simplified model is shown in Fig. 1.

Table 1
The model parameters of transformer

Parameter name	Value
Inner diameter of low voltage winding/mm	331
Outer diameter of low voltage winding/mm	396
Inner diameter of medium voltage winding/mm	435
Outer diameter of medium voltage winding/mm	500
Inner diameter of high voltage winding/mm	547
Outer diameter of high voltage winding/mm	640	.5
Turns of low voltage winding	107
Turns of medium voltage winding	226
Turns of high voltage winding	647
Window height/mm	1670
Iron core diameter/mm	600

Figure 1.

Simplified model of transformer.

The working condition of the model is high to medium three-phase short-circuit, and the model setting of field-circuit coupling circuit takes phase B as an example, as shown in Fig. 2. The Phase B high voltage winding in the three-dimensional field model of the transformer is equivalent to the B-H in the circuit model. The DC resistance of the Phase B high voltage winding is 0.9014 $\Omega$ . The voltage source, B-H, and the DC resistance of the Phase B high voltage winding are connected in series to obtain a circuit model on the high to medium short circuit high-voltage side. A model on the medium voltage side is similarly obtained. Consistent with the operating principle of the transformer, there is no power supply on the medium voltage side. The high and medium voltage windings establish their coupling relationship through the transformer core. The low voltage winding obtains the induced electromotive force through the transformer core flux. This induced electromotive force is an excitation source on the low voltage winding side.

Figure 2.

Field – path coupling circuit model setting.

After the short circuit occurs for about half a cycle, when the frequency is 50 Hz and the time is about 0.01 s, the short circuit current reaches the maximum value. According to calculation results, visualized post-processing can be performed to obtain the xz plane cross-sectional view of the internal magnetic flux leakage field distribution of the transformer at 0.01 s after the Phase B high-to-medium short circuit, as shown in Fig. 3.

Figure 3.

Distribution diagram of leakage magnetic field inside transformer at 0.01 s after short circuit.

According to distribution of the magnetic flux leakage field, the radial magnetic flux leakage field is mainly distributed at the end of the winding and a huge axial electromagnetic force is generated and applied to the end of the winding. The main magnetic field distributed in the empty path is the axial magnetic flux leakage field, which generates a radial electromagnetic force on the winding.

Simulation calculation results can be used to guide selection of the installation position of the magnetic flux leakage sensors for the true transformer short circuit test, as shown in the red area in Fig. 3. The magnetic flux leakage field of the transformer is distributed in various parts of the space. The installation position of the magnetic flux leakage sensors should meet certain requirements. First, in case of repeated short circuit impacts, the transformer winding is very likely to produce local irreversible deformations, such as winding bulge, breakage and collapse. If sensors are installed at these positions, it will inevitably cause position offset, affecting data collection. Therefore, the installation position should be secure. The installation point should not produce displacement in any direction with deformation of the winding. Second, the number of installed sensors should be reasonable and sensors should be evenly distributed in feasible installation areas. Considering the internal installation between the windings is difficult and radial magnetic flux leakage is concentrated at the ends of the windings, magnetic flux leakage sensors can be fixedly installed on the iron core upper iron yoke and pulling plate. Considering symmetry of the transformer, magnetic flux leakage sensors are also arranged at the same positions when short-circuit tests on other phases are performed. The sensor installation diagram is shown in Fig. 4.

Figure 4.

Schematic diagram of sensor installation area.

3. Test arrangement and method

In this test, an SFSZ7-31500/110 transformer is selected for the anti-short circuit ability test, and real-time monitoring of transformer internal magnetic flux leakage sensor measurement results under a variety of short-circuit conditions, and the relationship between transformer winding deformation accompanied by magnetic flux leakage field distribution variation and its deformation degree is investigated. The test site is located in Shenyang Transformer Research Institute.

3.1 Test arrangement

To monitor change of the magnetic flux leakage field in the internal space when any three-phase short circuit occurs in the transformer suddenly, a transformer prototype is modified before the test, and magnetic flux leakage sensors are installed inside it to monitor and record its internal magnetic flux leakage field. Magnetic flux leakage sensors for the test use a 10 $\times$ 50 mm multiturn air-core coil and are reliably fixed to selected measuring points inside the transformer directly with sealant during installation. Physical objects arranged on the test site layout mainly include a transformer, transmission lines, and a microcomputer, as shown in Fig. 4. The main parameters of the test transformer are shown in Table 2.

Table 2
The main parameters of three-phase transformer

Parameter name	Value
Rated capacity (MVA)	31.5/31.5/31.5
Rated frequency (Hz)	50
Rated voltage (V)	(110 $\pm$ 3 $\times$ 2.5%)/(38.5 $\pm$ 2 $\times$ 2.5%)/10.5
Rated current (A)	165/472/1732

Figure 5.

Physical drawing of test layout.

The connection group of the test prototype is YNyn0d11. Take Phase B high to medium three-phase short-circuit conditions as an example. For the Y-connected winding, high voltage neutral grounding, medium voltage short circuit grounding and low-voltage open circuit are used between the high voltage Phase B line terminal and the line terminal obtained after Phases A and C are connected. The principle of H-M test wiring is shown in Fig. 6.

Figure 6.

H-M test schematic diagram.

3.2 Sensor installation

The electromagnetic induction method is a traditional and simple method of measuring the magnetic flux leakage field based on the Faraday electromagnetic induction principle. The electromagnetic induction method can be used to monitor various magnetic fields such as constant, variable, uniform and non-uniform magnetic fields. It has a large measurement range and measure the constant magnetic field in the range of 10-9 $\sim$ 10T and the variable magnetic field up to 5T [18, 19]. It can meet requirements for measurement of magnetic flux leakage field when a transformer operates in a low frequency environment, the internal magnetic flux leakage field basically has a uniform magnetic field distribution, and measurement requirements are not high. In this test, coil-type magnetic flux leakage measurement sensors are made based on the electromagnetic induction principle. And its measurement range is 10-6 $\sim$ 1T, and the resolution is 1 $\times$ 10-6T. Induced electromotive force is generated through the changed magnetic field and magnetic field density is obtained by inverse integration. The main components and functions are as follows: sensors collecting magnetic flux leakage signals, shielded pairs transmitting signals, state monitoring and wave recording systems, and finally a microprocessor performing post-processing of the data.

According to the above-mentioned installation requirements and considering lead-out convenience of the measurement line, installation measuring points of the built-in magnetic flux leakage sensors are selected on the transformer Phase B upper iron yoke and iron core leg. The cables are shielded twisted pairs that are firmly tied, and the shielding layer is grounded at one end. Both the sensors and cables must be at ground potential, such as the iron core, clamp, pulling plate and other positions. The small coil of the sensors for measuring magnetic induction intensity of the magnetic flux leakage field is attached to the internal structure. The magnetic induction intensity value at the center of the coil can be measured by this method. Any change of the magnetic flux leakage field at the sensor configuration points can be monitored in real time during any sudden short circuit fault of the transformer. The monitoring position description of the magnetic flux leakage sensors is shown in Tables 3 and 4. The installation position correspondence is shown in Figs 7 and 8.

Table 3
The corresponding position table of magnetic flux leakage monitoring of iron yoke

Marking	Position
BE1	At Phase B coil center and perpendicular to the low voltage outer diameter (close to Phase A)
BE2	At Phase B coil center and perpendicular to the medium voltage outer diameter (close to Phase C)

Figure 7.

Mounting position of magnetic flux leakage sensor on iron yoke.

Table 4

Correspondence table of MFL monitoring position on core pillar

Marking	Position
BX1	Phase B pulling plate flush with coil end
BX2	Another Phase B pulling plate flush with coil end
BX3	Phase B pulling plate 100 mm below coil end
BX4	Another Phase B pulling plate 100 mm below coil end

Figure 8.

Installation location of magnetic flux leakage sensor for phase center Pillar B.

According to test requirements of GB/T 1094.5 2008, circuit tests are performed on the transformer. Short circuit duration is 250 ms. Test interval is about 20 min. Magnetic induction intensity measured by magnetic flux leakage sensors configured in six positions of the Phase B upper iron yoke and iron core leg is collected and recorded in every short circuit test. Sampling time is 0.1 ms and sampling frequency is 10 kHz. A resistance value of the winding is measured after each impact test.

4. Analysis of magnetic flux leakage characteristics under short circuit impact

4.1 Comparison of test and simulation data

Short circuit impact tests are performed under various short circuit conditions, including high-to-low three-phase short circuit with Phases C and B as test phases respectively, high-to-medium three-phase short circuit with Phases B and C as test phases, respectively, and medium to low three-phase short circuit with Phases A and C as test phases, respectively. A simulation calculation of corresponding test group conditions is made using the established transformer three-phase short circuit calculation model. A point probe is added in the model in the form of coordinates to obtain the magnetic induction intensity of magnetic flux leakage corresponding to test measuring points. Any two measuring points under the first impact under various short circuit conditions are selected. Table 5 is created for grouping.

Table 5
Statistical table of magnetic flux leakage data under various working conditions

Test group	Short circuit conditions	Test current/A	Sensor	Measured value/T	Simulation value/T
1	HL-C	701	BE1	0.064689	0.0693
2			BE2	0.06787	0.0714
3	HL-B	693	BE1	0.017697	0.0165
4			BE2	0.017852	0.0169
5	HM-B	914	BX3	0.152453	0.1498
6			BX4	0.149911	0.1531
7	HM-C	1273	BX3	0.104318	0.1009
8			BX4	0.106584	0.1113
9	ML-A	2802	BX3	0.014496	0.0139
10			BX4	0.010918	0.0118
11	ML-C	4085	BX3	0.019629	0.0189
12			BX4	0.021058	0.0223

An error graph between the calculated and test values of magnetic flux leakage under various short circuit conditions is plotted, as shown in Fig. 9. Simulation calculation results at any selected measuring point of magnetic flux leakage under different working conditions fit in well with actual measurement results. Group 10 has the largest error, which is 7.63%. Error values of magnetic induction intensity of magnetic flux leakage in each group are within 15%, meeting engineering requirements. In addition, this model is suitable for a variety of different short circuit conditions, which further shows validity of the established model and correctness of the calculation results. In engineering applications, it can be considered to avoid arrangement of magnetic flux leakage sensors and obtain the distribution of internal magnetic flux leakage of the transformer after short circuit impact in advance through simulation.

Figure 9.

Comparison diagram of magnetic flux leakage intensity data in various working conditions.

4.2 Analysis of magnetic induction intensity data of magnetic flux leakage

According to test requirements of GB/T 1094.5 2008, Phase B high to medium short circuit tests are performed on the transformer at different short circuit currents. 60%, 80%, 85%, 90%, 100% and 105% of the short circuit current are applied, respectively. Four 105% short circuit current tests are performed, corresponding to 1 to 9-time impact test groups. The HM-B three-phase short-circuit test and simulation data are recorded as shown in Table 6. When the transformer suffers from multiple short-circuit shocks in actual operation, the deformation accumulation leads to changes in the winding structure, that is, the relative position of the current changes slightly, which changes the difference between the measured value of magnetic flux leakage induction intensity and the simulated value during the test. In order to study the diagnosis of winding deformation degree under multiple short-circuit impact caused by magnetic leakage, the relation curve between the difference ratio of the measured value and the simulated value of magnetic flux leakage induction intensity and the rate of impedance change was drawn, as shown in Fig. 10.

Table 6
HM-B three-phase short circuit test and simulation data record sheet

Test group	BX3		BX4
	Measured value/T	Simulation value/T	Measured value/T	Simulation value/T
1	0.152453	0.1498	0.149911	0.1531
2	0.193827	0.199733	0.197712	0.204133
3	0.204203	0.212216	0.207302	0.216891
4	0.216019	0.2247	0.218932	0.22965
5	0.235625	0.249666	0.238454	0.255166
6	0.246193	0.26215	0.249849	0.267925
7	0.244657	0.26215	0.24874	0.267925
8	0.245775	0.26215	0.248946	0.267925
9	0.243714	0.26215	0.247922	0.267925

Figure 10.

Difference ratio of the magnetic flux leakage and impedance change rate curve.

The proportion of the absolute value of the difference between the measured value and the simulated value in the simulation value is the difference ratio. As can be seen from Fig. 10, difference ratio of the magnetic flue leakage and the impedance change rate measured after every test, show an increasing trend of high consistency. In the first four impact tests, the impedance change rate after every short circuit impact slightly increases to 0.25% from 0.11%. The growth rate of difference ratio is obviously faster than the change rate of impedance. When the fourth short-circuit impact occurs, the difference ratio of BX3 sensor reaches 3.86% and that of BX4 sensor reaches 4.66%. After the fifth short circuit impact (100% of the short-circuit current), both the impedance change rate and difference ratio of the magnetic flux leakage increased. The impedance change rate reaches 0.39%. The difference ratio of the BX3 and BX4 sensors increases sharply to 5.62% and 6.55%, respectively. In the ninth impact, the impedance change rate is abruptly changed to 2.28% and the difference ratio suddenly increases to 7.03% and 7.46%, respectively. At this moment, the transformer winding produces obvious deformation under the huge, short circuit electromagnetic force and the winding structure is destroyed. From the above analysis, it can be seen that when the winding is subjected to multiple short-circuit impacts and no obvious winding deformation has occurred, the difference ratio is faster than the increase rate of impedance change rate. The winding can be determined to have produced a certain degree of deformation by studying the difference ratio between the measured value of magnetic flux leakage and the simulated value.” on page 8.

5. Conclusions

In this paper, a transformer short circuit calculation model is established based on the field-circuit coupling theory. By referring to simulation conclusions, magnetic flux leakage sensors are installed in a 110 kV transformer and short circuit impact tests are carried out. By taking as an example the high to medium three-phase short circuit conditions with Phase B as a test phase, the relation between the magnetic induction intensity of magnetic flux leakage and the impedance change rate is analyzed according to tests and simulations and the main conclusions obtained are as follows:

Coil-type magnetic flux leakage sensors developed and used based on the electromagnetic induction method can achieve real-time monitoring of internal magnetic flux leakage of the transformer. Calculation results of the internal magnetic induction intensity of magnetic flux leakage of the transformer under short circuit conditions fit in well with test results of magnetic flux leakage sensors, which effectively verifies the accuracy of the transformer model established in this paper. The magnetic field distribution of the transformer can be easily calculated based on this model.

After the ninth short-circuit impact, the impedance change rate increased sharply to 2.28%. Compared with the difference ratio of magnetic flux leakage (MFLM) magnetic induction intensity, it was easier to judge the serious deformation of the winding, and the difference ratio of MFLM magnetic induction intensity was greater than 6% in the four shocks before the serious deformation of the winding. Therefore, when the difference ratio is greater than 6%, we should be vigilant about serious winding deformation.

Before the transformer is seriously deformed due to multiple short-circuit shocks, the sensitivity of the impedance change rate to the winding deformation is low, and every small deformation will have a more obvious change in the difference ratio between the simulation value of magnetic flux leakage induction intensity and the test value. Therefore, by monitoring the flux leakage magnetic induction intensity, it can provide some basis for winding monitoring before serious deformation.” on page 9.

Footnotes

Acknowledgments

The authors acknowledge the Science and Technology Project of State Grid Hebei Electric Power. (Grant: Kj2019-060).

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Transformer winding deformation accompanied by magnetic flux leakage field distribution variation and its diagnostic analysis of deformation degree

Abstract

Keywords

1. Introduction

2. Simulation model of the internal magnetic circuit of the transformer

Table 1 The model parameters of transformer

3.1 Test arrangement

Table 2 The main parameters of three-phase transformer

Table 3 The corresponding position table of magnetic flux leakage monitoring of iron yoke

4.1 Comparison of test and simulation data

Table 5 Statistical table of magnetic flux leakage data under various working conditions

Table 6 HM-B three-phase short circuit test and simulation data record sheet

Footnotes

Acknowledgments

References

Table 1
The model parameters of transformer

Table 2
The main parameters of three-phase transformer

Table 3
The corresponding position table of magnetic flux leakage monitoring of iron yoke

Table 5
Statistical table of magnetic flux leakage data under various working conditions

Table 6
HM-B three-phase short circuit test and simulation data record sheet