Finite Element Method Modeled Dielectric Response for ... - IEEE Xplore

2013 Annual Report Conference on Electrical Insulation and Dielectric Phenomena

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Finite Element Method Modeled Dielectric Response for Condition Evaluation of Transformer Insulation Yi Cui1, Chandima Ekanayake1, Tapan K. Saha1, Peidong Du2 and Hui Ma1 1

School of Information Technology and Electrical Engineering University of Queensland, Brisbane 4072, Australia 2 Electrical Power Research Institute of Gansu Province, China

(FDS) measurement has also attracted broad attention from world-wide scholars and experts for it merits of satisfactory assessment results and its easy use [5-7]. However, the traditional method of FDS test is based on the data analysis from field test. In this paper, a finite element model of both perfect and defect transformer insulation system is established. And the dielectric response from frequency domain is also analyzed with an expectation to provide as a supplementary tool to better understand the field test results of FDS.

Abstract-- Defects such as cracks and voids in the insulation medium of a power transformer may affect the dielectric response of transformer insulation system. This paper uses the finite element method (FEM) to analysis the influence of electric field distribution on the dielectric response of transformer oilpaper insulation system. Firstly a simple transformer winding insulation model consisting of several layers of pressboard and oil ducts is established in FEM. Here, two circumstances are taken into consideration to represent normal insulation and insulation with cracks penetrating all the layers. The complex capacitance (real part and imaginary part) is calculated to obtain general tendency of dielectric response of winding insulation in a transformer. Secondly, this paper proposes FEM model of a three phase oil-immersed power transformer insulation system. Based on the developed model, the dependency between electric field displacement, current density at the selected point with the applied electric field is discussed in detail. Moreover, the complex capacitance of transformer insulation is also studied. This will help to understand the correlations among insulation defects, electric field variations, and dielectric response of insulation.

II. ELECTRIC FIELD DISTRIBUTION OF OIL-PAPER INSULATION IN THE TRANSFORMER WINDINGS A. Simplified equivalent circuit of winding insulation The structure of transformer windings in each phase mainly consist of low-voltage windings revolved around the iron core, high-voltage windings and insulating medium between the high-voltage and low-voltage windings. The insulation structure is shown in Fig. 1. Located between the two windings (low-voltage windings and high-voltage windings), the insulation system includes many layers of paper/pressboard immersed in mineral oil. In addition, transformer spacers are used to strengthen the mechanical structure. The above two windings are revolved around the iron core. The oil-paper insulation material is surrounded by a complex electromagnetic field caused by electric field and magnetic flux leakage of windings.

Index Terms-- Dielectric response; Insulation degradation; Oil-paper insulation; FEM

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I. INTRODUCTION

ower transformer plays an important role in a power system. Their failure and replacement is an enormous expenditure. Within the life span of a transformer, preventive maintenance has been widely utilized for ensuring the stable power supply to consumers. The conventional diagnosis techniques including dissolved gas analysis (DGA), thermal measurement, partial discharge detection, capacitance and dielectric dissipation factor measurements and other dielectric response, are widely adopted to evaluate the transformer insulation condition from certain aspect . Dielectric response has been gaining its popularity in recent years which consists a group of methods used for investigating the behavior of dielectric materials as well as complex insulation systems [2]. Since 1990s, a variety of novel methods based on the dielectric response theory from time domain have gradually emerged such as polarization and depolarization current (PDC) and return voltage measurement (RVM) [3-4]. Meanwhile, Frequency Domain Spectroscopy

Fig. 1 Insulation structure of windings cross-section

B. Electric field distribution of intact winding insulation A three phase oil-immersed transformer with voltage ratios

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electric field displacement at point A under an external voltage with variable frequency is shown in Fig. 4(a). The frequencies are discretely set to 50 Hz, 100 Hz, 150 Hz and 200 Hz. The calculated result indicates no difference in the displacement response. The magnitude of electric field displacement is 2.28μC/m2 in all circumstances.

220 kV/35 kV is selected as FEM simulation model. The rated capacity of this transformer is 31.5 MVA. We consider the conductor of low voltage winding as a single unit which is wrapped by paper in oil. Electric field distribution between iron core and low voltage windings is calculated through Ansys software [8]. According to the national standard, the thickness of single-layer pressboard is 5 cm. The width of the oil duct is 1 cm [9]. Suppose the insulation consists of five cellulose paper layers and five oil ducts which is colored as yellow and brown respectively. The distance between conductor and core edge is 30 cm. The finite element model is established in Fig. 2.

(a) Electric field displacement

(b) Conduction current density

Fig. 4. Electric field displacement and conduction current density at point A applied by external voltage with various frequencies

Fig. 4(b) gives the conduction current density at point A at different frequencies. From Fig. 4(b) we can see the amplitude of conduction current density is proportional to the frequency of the applied voltage.

Fig. 2. FEM model of oil-paper insulation in transformer windings

C. Electric field distribution of defected windings insulation In this part, an internal defect is added to the insulation structure. Suppose the dielectric performance of the oilpressboard insulation is slightly degraded for certain reason. A small rectangular area with relative permittivity of 6 is created in the finite element model which denotes the defect area penetrating all the insulation layers. The conductivity of the defect is 10-9 S/m. The defect penetrates through all the insulation layers which accounts for 2% area of winding insulation. Then the electric field distribution and dielectric response is analyzed when it is subjected to external voltage at different frequencies. The defected insulation model is shown in Fig. 5.

In the FEM model, the relative permittivity of the pressboard is set to 4. The relative permittivity of mineral oil is set to 2.2. The conductivity of cellulose paper and mineral oil without degradation are set to 1.5×10-13 S/m and 10-11 S/m respectively [7]. A Volume outside winding is filled with oil (yellow rectangle) for simulating the oil-immersed insulation structure. A sinusoidal voltage with 35 kV (rms) is applied on the winding. Iron core which is well grounded and region edges far away from the winding are set as boundary with voltage zero. The simulation results of electric field distribution are presented in Fig. 3. From Fig. 3 it can be observed that the electric field strength distribution of the outer winding pressboard and oil flow is uniform. The maximum electric field strength in mineral oil is 0.06 kV/mm which is smaller than that at pressboard- core interface (0.11 kV/mm).

Fig. 5. Defected insulation FEM model for oil-paper insulation structure

Fig. 6 illustrates the electric field distribution when a defect exists in the insulation. It is obvious that the electric field at the defected area is more concentrated compared with that of the intact one. The maximum electric field of oil reaches up to 0.12 kV/mm. The electric field near the upper and bottom edge of the defect also reaches to 0.07 kV/mm. Here an observation line is marked along x axis from conductor to core to measure the variation of the concentrated electric field due to insulation defects. This line penetrates all insulation layers with total thickness of 300 mm. A comparison has been presented in Fig. 7 and Table I addressing the amplitude of electric field displacement and

Fig . 3. Electric field distribution of intact oil-paper insulation structure

An observation point named A (as in Fig. 2), at the interface between pressboard and core, is selected for the electric field analysis. It is just located at the central point of the interface between iron core and winding insulation. The 40

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conduction current density along the observation line when the insulation is intact and defected. From Fig. 7 we can see there is a downwards trend in the electric field displacement at 50 Hz along the radial direction of the observation line from the central conductor to outer edge of iron core. When the insulation has a defect, the electric field displacement is greater than that of the intact insulation. Similar results may be obtained when the frequency varies from 50 Hz to 200 Hz.

intact and transformer with defect insulation can be obtained in Fig. 8. It can be obtained from the figure that the real part of complex capacitance will decrease while the imaginary part will grow up when the insulation degrades.

(a) real part

(b) imaginary part

Fig. 8. Frequency spectrum of the complex capacitance

III. FREQUENCY SPECTRUM SIMULATION FOR MAIN INSULATION OF THREE-PHASE TRANSFORMER In this part, a three-phase oil-immersed transformer with capacity of 120 MVA is selected as simulation model. The rating voltage of this transformer is 220 kV/35 kV. The geometric configuration is shown in Table II.

Fig. 6. Electric field distribution of oil-paper insulation with internal defect

TABLE II.

GEOMETRICAL CONFIGURATION OF THREE PHASE OILIMMERSED TRANSFORMER MODEL

Component Iron core Low-voltage windings High-voltage windings Thickness of single layer pressboard Mineral oil duct width

TABLE I. COMPARISON OF ELECTRIC FIELD DISPLACEMENT AND CURRENT DENSITY BETWEEN INTACT AND DEFECTED OIL-PAPER INSULATION AT OBSERVATION POINT

50 100 150 200

Intact insulation Current Electric field density displacement(μC/m2) (mA/m2) 0.71 1.43 2.28 2.15 2.86

0.8 1

Based on Table II, oil-paper composite insulation model is shown in the Fig. 9 - (a). The insulation between the high voltage and low voltage windings consists of 25 layers pressboard. Total 50 layers pressboard between each of two phases is considered as the main insulation medium. Copper coils are assigned to windings in the 2D model which is colored as green (phase A) and yellow (phase B). Similarly, for comparison we consider two cases of which the insulation condition is intact (model 1) and defect (model 2). The insulation defects (orange areas) with total area accounting for 2% of the insulation medium are shown on the Fig. 9 - (b). In model 1, the relative permittivity of pressboard is set to 4 while the mineral oil is 2.2. In model 2, the degraded area is located between phase A and phase B with relative permittivity of 1.5. A rated voltage with peak value of 311 kV is applied on the windings to analysis the dielectric response.

Fig. 7. Electric field displacement along the observation line penetrating the insulation layers

Frequency (Hz)

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Guage cm 800 in length, 500 in width Cross-section: 25 in width, 280 in height Cross-section: 30 in width, 280 in height

Insulation with defects Electric field Current displacement density 2 (μC/m ) (mA/m2) 1.39 2.78 6.37 4.17 5.56

As we known, the displacement current density is associated with the time derivative of electric field displacement which is a function of electric field strength and polarization [7]. The displacement current is shown in (1). ur d φe ∂ E ur (1) I d = ε 0ε r = ε 0ε r ∫∫ ⋅d S dt ∂t s It can be seen from Table I that the current density amplitude increases with increasing frequency from 50 Hz to 200 Hz. When the insulation contains a portion of deterioration, the dielectric loss will also increase. So the insulation condition can be effectively assessed by comparing the dielectrics response using spectrum analysis. An AC voltage U = 100sin(ωt ) is applied on the conductor. A comparison of complex capacitance between

(a) intact insulation

(b) defected insulation

Fig. 9. 2D FEM model of insulation structure in transformer

A reference point A is selected to analyze the electric field strength, electric field displacement, conduction current density from the frequency domain when the insulation is

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degraded.


When the insulation is intact, the imaginary part of complex capacitance decreases from 2.23 nF to 1.38 nF when the frequency increases from 1 Hz to 1 kHz. The imaginary part also shows a downwards trend over the whole frequency spectrum when the insulation contains defects. The amplitude of imaginary part for defect condition under each frequency is greater than that of the intact insulation. So it is the same with the dispassion factor of the insulation system. It demonstrates the effectiveness of dielectric spectrum to assess the insulation condition of power transformer with different deterioration or internal defects.


Fig. 10. Electric field distribution with perfect and degraded insulation

It can be seen from Fig. 10, electric field at reference point A is 0.03 kV/mm at rated voltage when the insulation is perfect (Fig. 10 (a)). The electric field strength reaches 0.57 kV/mm when internal insulation defects exist (Fig. 10 (b)). It is obvious that insulating material has to tolerate intensive electric field strength when it is cracked. As shown in Fig. 11, the electric field displacement at point A is 15.82 μC/m2 when the insulation is intact (left one). However, it reaches 20.70 μC/m2 for the defect circumstance. Total current density of the medium increases with increasing frequency. Maximum current density is 0.09 A/m2 when frequency is 1 kHz. Maximum current density reaches up to 0.13 A/m2 in the defect insulation.


IV. CONCLUSIONS Frequency domain dielectric response method is an offline, effective testing method based on the dielectric response theory. In this paper, a finite element model of oil-immersed transformer is proposed to analyze the dielectric response of the oil-paper insulation system while the insulation is intact and degraded. The current density, electric field strength as well as electric field displacement are calculated using FEM algorithm. Then influence of electric field distribution on the complex capacitance regarding to frequency domain is discussed in detail. The FEM analysis provides a supplementary tool to get a direct visual observation of electromagnetic field distribution in the power transformer. In addition, it also gives an insight to forecast the effectiveness of FDS method which is useful for insulation condition assessment of aged transformers.


V. ACKNOWLEDGMENT

Fig. 11. Electric field displacement at point A with different insulation

We highly appreciate the supports provided by Australian Research Council, Powerlink Queensland, Energex, Ergon Energy, and TransGrid. VI. REFERENCES


[1] L. E. Lundgaard, W. Hansen, D. Linhjell and T. J. Painter, "Aging of oilimpregnated paper in power transformers," IEEE Transactions on Power Delivery, vol.19, pp. 230-239, 2004. [2] J. Singh, Y. R. Sood and R. K. Jarial, "Condition Monitoring of Power Transformers - Bibliography Survey," IEEE Electrical Insulation Magazine, vol.24, pp. 11-25, 2008. [3] T. K. Saha and P. Purkait, "Investigation of polarization and depolarization current measurements for the assessment of oil-paper insulation of aged transformers," IEEE Transactions on Dielectrics and Electrical Insulation, vol.11, pp. 144-154, 2004. [4] S. M. Gubanski and C. P. Boss, "Dielectric response methods for diagnostics of power transformers," IEEE Electrical Insulation Magazine, vol.19, pp. 12-18, 2003. [5] W. S. Zaengl, "Dielectric spectroscopy in time and frequency domain for HV power equipment. I. Theoretical considerations," IEEE Electrical Insulation Magazine, vol.19, pp. 5-19, 2003. [6] W. S. Zaengl, "Applications of dielectric spectroscopy in time and frequency domain for HV power equipment," IEEE Electrical Insulation Magazine, vol.19, pp. 9-22, 2003. [7] E. C., M. G. S., G. A. and W. K., "Frequency response of oil impregnated pressboard and paper samples for estimating moisture in transformer insulation," IEEE Transactions on Power Delivery, vol.21, pp. 1309-1317, 2006. [8] "ANSYS North America Training Center" available at http://www.ansys.com/Support/Training+Center. [9] Specification and Technical Requirement for Oil-immersed Power Transformers, GB/T 6451-2008, 2008.


Fig. 12. Current density at point A with perfect and degraded insulation

The real part of complex capacitance of intact and defect transformer is presented in Fig. 13 when the frequency varies from 1 Hz to 1 kHz. From Fig. 13 it can be obtained that there is a decrease in the real part of complex capacitance from 1.06 μF to 0.06 μF when the insulation is intact. Once the insulation degrades, the real part is reduced significantly from 0.76 μF to 0.05 μF when the frequency is lower than 300 Hz.

(a) real part

(b) imaginary part

Fig. 13. Frequency spectrum of complex capacitance of different insulation

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