Measurement of Electric Field Distribution Along ...

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R. Zeng et al.: Measurement of Electric Field Distribution Along Composite Insulators by Integrated Optical Electric Field Sensor

Measurement of Electric Field Distribution Along Composite Insulators by Integrated Optical Electric Field Sensor Rong Zeng, Yun Zhang, Weiyuan Chen and Bo Zhang State Key Lab of Power Systems, Dept. of Electrical Engineering, Tsinghua University, Beijing 100084, China

ABSTRACT In order to meet the demands for the electric field measurement along the composite insulators simultaneously, such as intensive signal, fine insulation, passive and small size, a novel measurement system based on the core device, the integrated electro-optic sensor, was developed. First, the theory of the system and the sensor were introduced. Second, after fabrication, the input/output character was obtained and the calibration was implemented between two parallel square metal planes under power frequency. By optimum design, this kind of novel sensor was suitable for insulated, intensive (> 250 kV/m), small size (55 mm x 2 mm x 1 mm) electric field measurement. Third, the axial and radial electric field distribution of the insulators were measured carefully in laboratory, and by combining the BEM and CSM method, the electric field of the same insulators was numerically calculated. Finally, the measurement and calculated results of electric field distribution were compared and the relationship between them were analyzed. This comparison verified the suitability and importance of the measurement system. Index Term - composite insulators, electric field measurement, integrated electro-optic field sensor, BEM, CSM.

1 INTRODUCTION COMPOSITE insulators have been widely used in high voltage transmission lines in China for many years [1], because of its lightness, advantage in anti-pollution, and little maintenance in operation. The uneven distribution of the electric field upon the surface of the insulators, which is caused by the structure design and the material, is one of the reasons for partial discharge, or even breakdown. So, it is very important to get to know the electric field distribution at power frequency, which will be very useful for the optimum design of the insulators, the confirmation of the parameters of the grading ring and supplying guidance for the research of online diagnosis. Measurement is the most useful and directly method to acquire the distribution of the electric field and can be sorted into direct and indirect methods. The indirect method gets the field by means of the measurement of the distribution of potential on the insulators. The most popular used instrument for voltage distribution method were metal spherical dipole [2-6] and parallel high resistance divider [7]. These kinds of methods were simple, but Manuscript received on 20 December 2006, in final form 8 August 2007.

there were some disadvantages. The contact of the sensor with the insulator will affect the original voltage distribution because of the dispersed capacitance changed by the sensor. And these methods were almost not suitable for the composite insulators. The direct methods were studied from 1990’s, mainly used for the online diagnosis of the insulators, for example, the tester for porcelain suspension insulators were developed by Hydro-Quebec [8]. The electric field of 735 kV and 315 kV insulators were measured online by this tester [9]. And power corporations of America and Mexico diagnosed the nonceramic insulators aged in a salt fog chamber by field sensor [10]. In recent years, great advancement has been accomplished and some new sensors, such as the thermocouple field sensor and the diode rectified field sensor have been developed. For instance, the potential free spherical sensor has been developed by Feser and Hartings for the electric field measurement of the insulators and the research of corona character near high voltage electrode [11-13]. But there are still some problems to be overcome. First, the size of the sensor was a little big that it could not be used in the precisely measurement and the intrusion of the metal sensor will distort the original field so much that the error of the measurement was too big. Second, these sensor and transmission system were active, and the energy supply for the sensor will affect the field too seriously [14].

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IEEE Transactions on Dielectrics and Electrical Insulation

Vol. 15, No. 1; February 2008

303

For the difficulty of precisely measurement of the electric field, many numerical methods, such as charge simulation method (CSM), finite element method (FEM), boundary element method (BEM) and finite difference method (FDM), are used to calculate the electric field distribution of the insulators [15]. But as we can see, according to the complex structure of the insulators and connected conductors, the numerical methods still can not calculate the electric field very accurately. In order to overcome above difficulties, following special demands for the measurement system, such as intensive signal measurable, fine insulation, and small size, as smaller distortion as possible to the original field, must be satisfied simultaneously. In this paper, a novel integrated electro-optic sensor, based on electro-optical crystals such as LiNbO3, LiTaO3 [16,17] have been developed. Compared with traditional measurement method, the proposed integrated electro optic sensor is a passive one and has a compact size. The field distortion due to the sensor is therefore minimized. The laboratory measurement of the electric field of composite insulators was carried out carefully, and the electric field of the same insulators is calculated by combining BEM and CSM. The comparison between the measurement and the calculation results are illustrated in detail in this paper too.

modulated laser signal is transposed into a voltage signal by the optical receiver. In the proposed configuration, a distributed feedback (DFB) laser diode (LD) optical receiver is adopted which has low noise and narrower spectral width. And the voltage signal detected by the digital signal processing system will reflect the original electric field signal. The mostly adopted electro-optic effect for electric field measurement is the well-known Pockels effect [18,19]. Traditionally, by using the electro-optic crystal, the sensor is suitable for very intensive electric field measurement. However, in order to couple the light into the sensor-head from fibers, this kind of measurement system must be constructed with many of dispersed optical components, which makes it such a complex optic system, and obviously a great limitation for their application in field measurement. Based on the semiconductor technology, integrated optics sensor, on the other hand, has the advantage of not requiring lensing systems. It is easy to install and no need for earth-quake proofing because the whole system is fully integrated before being placed in the measurement environment. Besides, the size of the passive sensor head can be significantly minimized and this leads to less distortion to the electric field distribution. Therefore, it is a suitable method to apply the electro-optic sensor to the measurement of intensive electric field in high voltage environment.

2 THEORY AND IMPLEMENTATION OF THE MEASUREMENT SYSTEM

2.2 THE THEORY OF THE SENSOR The fundamental principle of the electro-optic modulation can be found in some other papers [20]. The refracting index of some Electro-optic crystals, such as Lithium Niobate, will change when an electric field is put on it.

2.1 THE STRUCTURE OF THE MEASUREMENT SYSTEM The configuration of the measurement system is illustrated in Figure 1. It has four parts: laser source, electro-optic sensor, optical receiver, and digital signal processing system. A 50 m-long polarization maintaining fiber (PMF) connects the sensor to the optical laser source, and a 50 m-long single mode fiber (SMF) connects the sensor to the optical receiver. The length of the two fibers ensures the security distance from the high voltage devices to the observation point.

Δne = rE

(1)

where Une is the change of the refractive index of the crystal and r is the electro-optic coefficient corresponding to the polarization of the electric field E. According to the fundamental principle of Mach-Zehnder modulator, the modulator output of optical power can be expressed as the following equation [21].

Po =

Pi [1 + cos(Δϕ 0 + ϕ )] 2

(2)

where Po and Pi are the output and input laser power respectively. Uφ0 is the intrinsic phase difference between two waveguides and φ is phase difference added by the environmental electric field, liner to Une. When the intrinsic phase difference between the two optical paths is π/2, the output of optical power will be Figure 1. The configuration of the measurement system.

The laser source operates in CW mode and the output laser is a linear polarized optical beam at the wavelength of 1550 nm, which is widely used for telecommunication systems. The input laser signal is modulated in the integrated electro-optic field sensor by the environmental electric field, and the output

Po =

Pi [1 − sin ϕ ] 2

(3)

Obviously, the output power of laser is linear to the electric field imposed on the sensor.

Po = a + kha E

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(4)

304


From above equation it can be found that the value of the electric field can be acquired by measuring the output laser power, when the sensor is working in the static working zone.

3 THE CALIBRATION OF THE MEASUREMENT SYSTEM

2.3 THE DESIGN AND IMPLEMENTATION OF THE SENSOR

In order to acquire the input/output characteristics of the measurement system and to evaluate the feasibility for insulators electric field measurement, the calibration experiment based on parallel square metal planes was carried out as following.

One of the structure of the sensors using a Mach-Zehnder interferometer is illustrated in Figure 2. To obtain a large driving voltage, the two optical paths are 40 mm long and the distance between them was 60 µm. There is a path difference of one-quarter of the wavelength of light between these two arms in order to form an optical bias of π/2, which is desirable for the sensor to be driven without a DC bias voltage and for the output of the sensor to be linear with the input electric field.

Electrode Waveguide Output Y branch

Input Y branch

z

Dipole

y

3 LiNbO3 substrate

Figure 2. One kind of he structure of the sensor.

The electrodes on the modulator were formed by depositing 5 mm long gold film, and the distance between two adjacent electrodes is 90 µm. The dipole was made up of triangle-shaped gold film, which was connected to the electrode. When an electric field is applied to the dipole, a voltage is induced across the electrode of the modulator. The optical modulator converts this voltage to an optical signal, the ac component of which is proportional to the electric field strength. Crystal /Waveguide

Electrode/Dipole

Figure 3. The integrated electro-optic field sensor after fabrication.

Having finished the design of the sensor, the sensor is fabricated by forming two optical paths obtained by diffusing titanium in a 55 mm×6 mm×1 mm X-cut LiNbO3 as illustrated in Figure 3[22].

3.1 THE CONFIGURATION OF THE CALIBRATION EXPERIMENT According to standard GB/T12720 (1991), the standard electric field for calibration was derived from the parallel square planes. The calibration system must meet the following requirements. First, the space between the electrodes must be longer than 1.5 times of the side size of the sensor. Second, the side size of the metal plane must be more than 3 times of the space of the sensor. Third, the distance between the sensor and the edge of the square plane will be not less than 3 times of the space between the electrodes. In consideration of above requirements and the size of the sensor, a standard power frequency calibration system was built. The square planes were made of steel, and the thickness was 1 mm. The upper electrode was connected with power frequency high voltage signal and the lower one was connected with ground wire. The distance between these electrodes was 140 mm, and the side size is 800 mm, which can ensure to acquire uniform electric field at the central area. The edge of each plane was polished to be smooth and the corner of the plane was shaped as circular arc to avoid the existence of corona.

3.2 THE CALIBRATION RESULT OF THE MEASUREMENT SYSTEM During the calibration, the output power of the laser kept at 5 mW. In the power frequency electric field, the output signal of the optical receiver was a sine signal added on the dc bias, as illustrated in equation (4). The dc bias was filtered by setting the input mode of the digital signal processing system to be ac coupling. The sensor was placed at the center of the square, equal distance to each electrode. The voltage was boosted up by the transformer and put on the parallel square electrodes. Different amplitude of electric field was acquired by regulating the autotransformer. The input voltage was increased step by step from 100 V to 50 kV and then decreased to 100 V with same sequence. At each step point, the input voltage and the output of optical receiver were recorded. The high voltage was detected by the resistance divider and the electric field was acquired by the sensor. Both voltage signals were sent to the same digital signal processing device in different channel. These sequences were repeated 3 times and the average value of each measure point were calculated.




Se n s o r

out put

(mV)

Totally, three different directions of the sensor were calibrated, one was the maximum output direction and other two were crossed directions. All the results were drawn in Figure 4. The input electric field and sensor output voltage were both power frequency RMS value. 1200 1100 1000 900 800 700 600 500 400 300 200 100 0

305

where E is the input electric field in RMS (kV/m), and Vo is the sensor output voltage in RMS (mV).

4 ELECTRIC FIELD MEASUREMENT OF THE INSULATORS 4.1 THE SCHEME OF THE MEASUREMENT

Ma x i mu m Di r e c t i o n

The experiment simulated the arrangement of suspension insulators on the tower. The configuration was shown in Figure 6. The insulators were suspended on the crossbeam, which was well grounded. The radius of the crossbeam was 2 cm and length was 2 m. A thin horizontal transmission line connected the power frequency transformer and the bottom of the insulators. The electric field sensor was fixed by an insulated bracket, which ensured the proper position of the sensor. The output voltage of the power frequency transformer kept 35 kV during the experiment, and the output of the optical receiver was recorded at different measuring points.

Di r e c t i o n 2 Di r e c t i o n 3

0

50

100

150

200

250

300

350

El e c t r i c f i e l d (kV/m)

Figure 4. The input/output characteristics of the measurement system.

It can be found that there was a most sensitive direction of the sensor, which was same to the direction of the dipole and the maximum changed direction of Une. At other two cross directions, the output of the sensor just were 3.7% and 2.3% of that of the maximum direction, respectively. That is to say, the sensor was direction sensitive, which was a very good property for power frequency measurement. But we can see from the input/output curve that the sensor output began to be saturated from 250 kV/m electric field input. That can be explained by equation (3), the sensor output was sine relation to the input electric field. But in our insulators measurement, the amplitude is no more than 200 kV/m. The curves between 0-250 kV/m are shown in Figure 5 and the linear fit curve is drawn in the figure too. Figure 6. The arrangement of the experiment and the shape of the insulators. Maxium Direction Direction 2 Direction 3 Linear Fit Curve

Sensor output (mV)

500 400

The insulators composed of 5 big sheds and 4 small sheds. The diameter of the big shed was 145 mm and the diameter of small shed was 110 mm. The thickness of shed edge was 2 mm and the thickness of the shed root was 12 mm. The diameter of the Fiberglass-Reinforced Plastics (FRP) rod was 27 mm. Some other sizes of the insulators were drawn in Figure 6.

300 200 100 0

0

50

100

150

200

4.2 THE MEASUREMENT OF AXIAL ELECTRIC FIELD COMPONENT

250

Electric field (kV/m) Figure 5. The input/output curve in linear zone.

From Figure 5, it can be found that the output of the sensor was linear to the input electric field, when the electric field is less than 250 kV/m. By linear fitting, the relationship of the sensor output voltage and the electric field is as below.

Vo = 2.243E

(5)

The axial component (direction z in Figure 6.) of the electric field was measured first. The measured positions were selected at the middle of each two sheds, and were number from 1 to 10 at the sequence from high to low potential, which were illustrated in Figure 6 as hollow circles. The measurement repeated 6 times at direction r, when the distance to the center of the insulators’ axis varies from 20 mm to 70 mm, every 10 mm. And 6 groups of data have been acquired, which are shown in part 6 of this paper.


306


4.3 THE MEASUREMENT OF RADIAL ELECTRIC FIELD COMPONENT The radial electric field component (direction r in Figure 6.) below each shed was measured too. The measurement positions were selected just below each shed, and were number from 1 to 9 at the sequence from high to low potential, which were illustrated in Figure 6 as solid circles. The surface of the sensor contacted with the surface of the shed as close as possible. The measurement repeated 4 times at direction r when the distance to the center of the insulators’ axis varies from 20 mm to 50 mm, every 10 mm. And 4 groups of data have been acquired, which were also shown in part 6 of this paper.

5 NUMERICAL CALCULATION METHOD OF THE ELECTRIC FIELD 5.1 THE DESCRIPTION OF THE CALCULATION THEORY Because of the complexity, the available method to calculate the electric field around the insulators is numerical method. There were some papers that calculated the electric field around the transmission lines or insulators, but they rarely considered the transmission line, tower and insulators at the same time. In our research work, different types of components, such as, the composite insulators, the transmission lines and crossbeam which can be modeled as metal lines, must be considered simultaneously in the numerical simulation. Based on the original research work [23], the combination of boundary element method (BEM) and method of moments (MoM) was adopted here to solve this problem. For simulation, the surface of the insulator was dissected into many boundary elements, and the conductors were dissected into many segments. First, for the composite insulators, equations were built based on the indirect BEM by introducing charges on the interface of the insulator to substitute the effect out of the interface. So, the key problem changed to find the quantity of the sources on the elements, which must satisfy the boundary conditions and the equations inside the boundary. For the jth element, the following equation can be acquired [24],

q j ε0 − εc + Enj = 0 2ε 0 ε 0 + ε c

(6)

where εc, ε0 are the dielectric constants of the insulators and air, respectively, qj is the charge in the jth element. And Enj is the electric field at the jth element, caused by the charges on other elements, the ground image and the leakage currents on the segments. Assume the number of the elements of the insulators is M and that of the segments of the conductors is N. The matrix equation can be acquired as,

[A21

⎡I ⎤ A22 ] ⎢ ⎥ = 0 ⎣q⎦

leakage currents on the segments and q is the vector of the charge on boundary elements. Second, according to the circuit model, the equations of conductors were built by MoM.

[A11

⎡I ⎤ A12 ] ⎢ ⎥ = U ⎣q⎦

where A11 is a coefficient matrix of the segments, and A12 is the coefficient matrix of the boundary elements, U is the vector of voltages on the segment. Finally, by combining equations (7) and (8), after all the coefficients in the matrix were obtained, then M+N equations can be built. So, the leakage currents on the segments and the surface charges of the boundary elements can be obtained, from which the electric field and potential of the composite insulators can be calculated.

5.2 THE MODEL CONSTRUCTION OF THE NUMERICAL SIMULATION As the theory mentioned above, the simulation objects can be modeled into two kinds, insulator and conductors. The insulator include three different parts, the sheds, FRP rod and electrode. All the conductors were modeled as cylinder. And the final model which was used in the simulation was shown in Figure 7.

Figure 7. The simulation model of the insulators.

In boundary element setting, the dielectric constants of the air, FRP rod and insulators were 1, 4, and 4.5, respectively. The RMS value of high voltage was set to be 35 kV and ground wire was zero. Table 1. The dissection of each component. Component

where A21 is a coefficient matrix of the segments, and A22 is the coefficient matrix of the boundary elements, I is the vector of

Number of

Number of

elements

segments

FRP rod

400

Shed

792

High potential connector

48

Low potential connector

16

High voltage conductor

(7)

(8)

4

Grounded conductor

4

Grounded crossbeam

16

Suspension conductor

16



6 THE COMPARISON ANALYSIS OF THE MEASUREMENT AND SIMULATION RESULT

Me a s u r e d

90

Calculated

80 70 60 50 40 30 20

1

Calculated

120 100 80

8

9

10

Calculated

70 60 50 40 30 20 1

2

3

4

5

6

7

8

9

10

Me a s u r e d a n d c a l c u l a t e d p o i n t

1

2

3

4

5

6

7

8

9

10

Figure 11. The axial electric field distributed along the insulators, r = 50 mm.


100

120

Measured Calculated

90

(kV/m)

me a s u r e d

110

Calculated

100 90

El e c t r i c f i e l d

(kV/m)

7

80

10

Mea s ur ed and c al c ul at e d po i nt


6

Me a s u r e d

40

80 70 60 50 40 30 20

5

90

60

20

4

100

(kV/m)

Meas ur ed

140

3




(kV/m)

160

2


6.1 THE RESULTS OF AXIAL ELECTRIC FIELD COMPONENT As illustrated in the last two parts, the measurement and numerical simulation results have been obtained based on a 35 kV composite insulators. The measurement and calculation results of the RMS value of the axial electric field were illustrated from Figure 8 to Figure 13, when r = 20 mm, 30 mm, 40 mm, 50 mm, 60 mm and 70 mm, respectively.

307

100

(kV/m)

Based on the rectangle fundamental element, the insulators were dissected. And the conductors were segmented as shown in Table 1. From the Table 1, the number of boundary elements M were 400+792+48+24=1256, and the number of conductors N were 40. Thus, the total variables were 1296. The numerical program was developed based on Matlab software. And the result obtained based on this program were illustrated as following.



80 70 60 50 40 30 20 10 0

1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

10

Me a s u r e d a n d c u l c a l t e d p o i n t



Figure 12. The axial electric field distributed along the insulators, r=60 mm.



308

The difference between the measurement and calculation was caused by the model of the simulation. At the end of the insulators, the real shape of high potential and low potential connector was more complex than the simulation model. And the crossbeam and other conductors were irregular shape, but they were modeled as cylinder in the simulation. These kinds of hypothesis result in the error of numerical simulation. That is to say, in order to get more credible result of the distribution of the electric field along the insulators, the measurement is essential.

Me a s u r e d

90

Calculated

80 70 60 50 40 30

6.2 THE RESULTS OF RADIAL ELECTRIC FIELD COMPONENT

10

1

2

3

4

5

6

7

8

9

10


Figure 13. The axial electric field distributed along the insulators, r=70 mm.

From all the figures, it can be found that the curves of the measured and calculated were similar to each other, both were U shape. That is to say, compared with the middle part, each end of the insulators tolerates much higher electric field. Especially, when r is 20 mm, the electric field of measured and calculated value at position 1,2 (high potential)and 10 (low potential) were 157.3 kV/m, 92.6 kV/m and 92.1 kV/m, respectively, almost 2 to 5 times as that at position 8. That is to say, the optimum design of the grading ring is very important for EHV of UHV insulators to avoid this kind of un-equilibrium. And with the increase of r, the electric field decrease sharply at the terminal of insulators than at the middle part do. The electric field is almost in inverse proportion to r at the high potential end of the insulators. By comparing the measurement and calculation result, the difference between them was listed in Table 2. It can be found that the difference was U shape too. The difference at the end of the insulators was much bigger than in the middle. For instance, the difference was less than 20% from position 3 to 7, but at position 1, 8, 9, and 10, the difference was much higher.

The measurement and calculation results of the RMS value of the radial electric field were illustrated from Figure 14 to Figure 17, when r = 20 mm, 30 mm, 40 mm and 50 mm, respectively. Compared with the axial curve, it can be found that the distribution of radial electric field component decrease monotonously along the insulators from high potential end to low potential end, not as the U shape of axial one. 140

(kV/m)

20



(kV/m)

100

Meas ur ed

120

Calculated

100 80 60 40 20 0

1

2

3

4

5

6

7

8

9

Mea s ur ed an d c al c ul a t ed po i nt

Figure 14. The radial electric field distributed along the insulators, r = 20 mm. Table 2. The difference between the measurement and calculation of the axial

100

electric field.

Meas ur ed

20

30

40

50

60

70

1

0.4%

8.5%

12.2%

23.0%

21.2%

22.0%

2

17.8%

12.8%

4.2%

3.3%

18.5%

23.1%

3

1.9%

7.6%

13.9%

14.4%

4.7%

0.2%

4

13.5%

6.5%

0.7%

10.8%

19.1%

13.8%

5

6.8%

0.0%

7.5%

1.9%

2.2%

2.4%

6

17.1%

9.6%

6.6%

1.5%

5.9%

6.3%

7

15.8%

10.5%

10.3%

12.1%

18.0%

16.8%

8

28.5%

24.9%

19.9%

18.1%

16.6%

16.2%

9

29.3%

26.0%

26.9%

28.1%

29.8%

33.9%

10

48.1%

42.0%

35.8%

37.4%

36.0%

33.6%


number

Distance to the axis, r（mm）

(kV/m)

90 Point

Calculated

80 70 60 50 40 30 20 10 0

1

2

3

4

5

6

7

8

9

Meas ur ed and c al c ul at ed poi nt

Figure 15. The radial electric field distributed along the insulators, r=30 mm.




309

Table 3. The difference between the measurement and calculation of the radial electric field.

100


(kV/m)

90

Me as u r ed

Point

Calculated

80

number

50

1

60

1.0%

0.0%

9.5%

1.9%

2

41.6%

19.7%

18.9%

0.5%

3

53.7%

15.2%

17.2%

1.3%

4

68.8%

14.4%

11.9%

8.8%

5

63.7%

17.3%

11.8%

12.4%

6

68.5%

8.4%

23.3%

17.6%

7

65.1%

13.2%

25.5%

21.8%

8

70.5%

25.6%

40.7%

5.3%

9

48.3%

76.4%

92.7%

76.4%

50 40 30 20 10

1

2

3

4

5

6

7

8

9

Mea s u r e d a n d c a l c u l a t ed p oi n t

Figure 16. The radial electric field distributed along the insulators, r = 40 mm.

80 Me as ur ed

70

(kV/m)

Distance to the axis, r（mm） 30 40

70

0


20

Calculated

60 50 40 30 20 10 0

1

2

3

4

5

6

7

8

9

Me as u r e d an d c al c ul at ed po i n t

Figure 17. The radial electric field distributed along the insulators, r = 50 mm.

7 CONCLUSIONS A novel measurement system based on the integrated electro-optic sensor for the measurement of electric field of the insulators has been developed and presented. This kind of sensor was high voltage insulated, able to measure intensive electric field, small size, and passive design. After fabrication, by carefully calibration and the field measurement of real composite insulators, it has been verified that this system is very suitable for the electric field measurement and diagnosis of insulators. By combining the BEM and CSM numerical method, the numerical simulation of complex structures which include insulators and connected conductors is possible. By comparing the measurement and calculation results, it can be concluded that the measurement is essential to get credible result, although the simulation is a very important method too. A new sensor that can measure more intensive electric field to 2 MV/m is in developing by the authors, which will be a powerful tool for the research work of insulation.

ACKNOWLEDGMENTS It can be found from these curves that the amplitude changed sharply at high potential end, and changed slowly at low potential end. For example, the amplitude at position 1 (the first shed of high potential) was the biggest, reached about 119.09 kV/m, at the position r=20 mm, which was almost about 3 times as that at position 2 (second shed near high potential). And the amplitude at position 9 (the first shed to low potential) was near zero. That is to say, the radial electric field component near high potential end should be paid more attention, but it almost can be ignored at low potential end of the composite insulators. The difference between the measured and calculated results of the radial electric field was shown in Table 3. It can be found that the difference was big at the position of r=20 mm and at position number 8 and 9. As illustrated before, the simulation model and location error of the sensor were the main reasons for this difference.

This work was supported by the National Natural Science Foundation of China under Grant 50407002 and Fund of the National Priority Basic Research of China (2004CB217906).

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Rong Zeng (M’02, SM’06) was born in Shaanxi, China in 1971. He received the B.Sc., M. Eng., and Ph.D. degrees from the Department of Electrical Engineering, Tsinghua University in Beijing, respectively in 1995, 1997, and 1999. He became a lecturer in the Department of Electrical Engineering, Tsinghua university in Beijing in 1999, and an associate professor in 2002. Now he is vice dean of the Electrical Engineering Department, Tsinghua University. He is currently working in the fields of lightning and grounding research, lightning protection, and electromagnetic compatibility (EMC) in power system, with main emphasis on the hybrid research of electric and magnetic field measurement by integrated optical sensor and numerical simulation of long air gap discharge process. He is the author and coauthor of more than 20 IEEE transaction papers.

Yun Zhang was born in Huangshan, Anhui, China, in 1981. He received the B.Sc. degree from the Department of Electrical Engineering, Tsinghua University in Beijing in 2003. He is now a Ph.D. candidate in the Department of Electrical Engineering, Tsinghua University, Beijing, China. His research interests include gas discharge physics, power system over voltage and compact transmission line.

Weiyuan Chen was born in Ningbo, Zhejiang, China, in 1979. He received the B.Sc., M.Eng., and Ph.D. degrees from the Department of Electrical Engineering, Tsinghua University in Beijing, respectively in 2001, 2003, and 2006. He is working in the Nanrui Group, Nanjing, China. His research interests include high voltage measurement technology, power system protection and automation.

Bo Zhang was born in Datong, China, in 1976. He received the B.Sc. and Ph.D. degrees in theoretical electrical engineering from the North China Electric Power University, Baoding, in 1998 and 2003, respectively. From 2003 to 2005, he was a postdoctoral researcher in the Department of Electrical Engineering at Tsinghua University. Currently, he is an assistant researcher in the Department of Electrical Engineering at Tsinghua University. His research interests include computational electromagnetics, grounding technology, and EMC in power systems.
