Procedia Engineering 23 (2011) 24 – 28

1877-7058 © 2011 Published by Elsevier Ltd.doi:10.1016/j.proeng.2011.11.2459

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ProcediaEngineering

Procedia Engineering 00 (2011) 000–000

www.elsevier.com/locate/procedia

PEEA2011

Study on Tester Method of MOA Resistive Current

Xuepeng Liua, Dongmei Zhaoa

Zhongshan Polytechnic, No 25th, Road Bo’ai, City Zhongshan, Province Guangdong, China,528404

Abstract

Digital filtering algorithm is utilized for gathering data of MOA tester by least square method. The interphase interference is analyzed. With the combination of third harmonic wave, the algorithm is proposed about the third harmonic resistive current and capacitive current. Finally the circuit and hardware part is designed

Keywords: MOA tester. Interphase Interference. Harmonic resistive current;

1. Introduction

MOA takes advantage of overvoltage protection in electrical power system. However, resistor is subject to aging, heating, impact fracture, which can result in MOA explosion, breakdown and system short circuit fault. Therefore, the effective and strict test should be executed periodically. The leakage resistive current is an important factor, which can demonstrate MOA insulation, moistened,deterioration[1-

5]. Hence, it is an effective way to judge the MOA characteristic correctly by testing leakage resistive current.

Digital filtering algorithm is utilized for gathering data of MOA tester by least square method. The interphase interference is analyzed. With the combination of third harmonic wave, the algorithm is proposed about the third harmonic resistive current and capacitive current. Finally the circuit and hardware part is designed.

2. Data Smoothing Procession

There are some defaults from A/D, for example distortion, clutter, error. The data should be smoothened firstly.

25Xuepeng Liu and Dongmei Zhao / Procedia Engineering 23 (2011) 24 – 282 Author name / Procedia Engineering 00 (2011) 000–000

The data 1u , 2u ,… , iu ,… nu respond to time 1t , 2t , it ,… nt respectively. The curve fitting formula is

given for data m iu − ,… , mu ,… m iu + : 20 1 2U a a t a t= + ⋅ + ⋅ . According to least square method, in

order to minimize 2 20 1 2[ ( )]

m

ik m

M u a a t a t=−

= − + ⋅ + ⋅∑ , the following is obtained:

20 1 2

20 0 1 2

1

2 20 1 2

2

2 ( ) 0

2 ( ) 0

2 ( ) 0

m

k k kk m

m

k k k kk m

m

k k k kk m

Mu a a t a t

a

Mu a a a t a t t

a

Mu a a t a t t

a

=−

=−

=−

⎧ ∂= − − − =⎪ ∂⎪

⎪∂⎪ = − − − − =⎨ ∂⎪⎪ ∂

= − − − =⎪∂⎪⎩

∑

∑

∑So:

2 2

02 3 2 3

1

22 3 4 2 3 4

2 1 2 1Tm m m m

k k k kk m k m k m k m

m m m m m m

k k k k k kk m k m k m k m k m k m

m m m m m m

k k k k k kk m k m k m k m k m k m

m t t m t t

a

A a t t t t t t

a

t t t t t t

=− =− =− =−

=− =− =− =− =− =−

=− =− =− =− =− =−

⎛ ⎞ ⎛ ⎞+ +⎜ ⎟ ⎜

⎜ ⎟ ⎜⎡ ⎤⎜ ⎟ ⎜⎢ ⎥= = ⎜ ⎟ ⎜⎢ ⎥⎜ ⎟ ⎜⎢ ⎥⎣ ⎦ ⎜ ⎟ ⎜⎜ ⎟ ⎜⎜ ⎟ ⎜⎝ ⎠ ⎝ ⎠

∑ ∑ ∑ ∑

∑ ∑ ∑ ∑ ∑ ∑

∑ ∑ ∑ ∑ ∑ ∑

1

2

2 3

2 3 4 2

2 1Tm m m

k k kk m k m k m

m m m m

k k k k kk m k m k m k m

m m m m

k k k k kk m k m k m k m

m t t u

t t t u t

t t t u t

−

=− =− =−

=− =− =− =−

=− =− =− =−

⎛ ⎞ ⎛ ⎞ ⎛ ⎞+⎜ ⎟⎟ ⎜ ⎟ ⎜ ⎟

⎜ ⎟⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟⎟ ⎜ ⎟ ⎜ ⎟⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠ ⎝ ⎠⎝ ⎠

∑ ∑ ∑

∑ ∑ ∑ ∑

∑ ∑ ∑ ∑

Where

2

2 3

2 3 4

2 1m m

k kk m k m

m m m

k k kk m k m k m

m m m

k k kk m k m k m

m t t

X t t t

t t t

=− =−

=− =− =−

=− =− =−

⎛ ⎞+⎜ ⎟⎜ ⎟⎜ ⎟

= ⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

∑ ∑

∑ ∑ ∑

∑ ∑ ∑

,0

1

2

a

A a

a

⎡ ⎤⎢ ⎥= ⎢ ⎥⎢ ⎥⎣ ⎦

,

2

m

kk m

m

k kk m

m

k kk m

u

Y u t

u t

=−

=−

=−

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟

= ⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

∑

∑

∑

3. Algorithm Analysis

The resistive current is made up of odd harmonic. 31 5 ...r r r rI I I I= + + + . The MOA resistive

current is influenced by the following factor: Firstly, MOA has a nonlinear characteristic, which leads to harmonic component. Especially third

harmonic is sensitive to temperature change, and varies with resistive current caused by MOA deterioration.

Secondly, power network voltage harmonic. Since power network is seriously polluted, the harmonic exists: 3 1(1 ~ 2%)U U= , 3 1r rI I< , 3 1(1 ~ 2%)P P< .

Thirdly, Interphase Interference. There is stray capacitance between three-phase MOA. One phase MOA is subject to neighboring phase voltage caused by stray capacitance besides its voltage. In Fig.1, phase A and phase C is influenced by phase B. So the leakage current phase will advance and lag at a degree of 3-5° respectively. However phase B change slightly.

26 Xuepeng Liu and Dongmei Zhao / Procedia Engineering 23 (2011) 24 – 28 Author name / Procedia Engineering 00 (2011) 000–000 3

Fig.1. interphase capacitance Fig.2. current vector

Fourly. Temperature influence. Third harmonic resistive current is sensitive to temperature. According to the analysis above, the algorithm is described as follows: First step. The elimination of interphase influence. Fig.2 is the current vector distribution. Phase B is

middle MOA, XCI , XAI are leakage resistive current for phase A and C without phase intervence, while /XCI , /

XAI are current with interphase intervence, Aϕ , Cϕ are phase values with interphase intervence. 2 120C Aϕ ϕ θ− = + , θ is phase difference. Therefore:

sin sin( )XA A xA AI Iϕ ϕ θ′ = +

So sin( ) / sin( )XA XA A AI I ϕ ϕ θ′= + .

At the same time, sin( ) / sin( )XC XC c cI I ϕ ϕ θ′= −

Second step. Fourier Transformation.

∑∞

=

+⋅=1

)sin(k

kkxC kwtUu α

∑∞

=

+⋅=1

)sin(k

kkxXC kwtII β

kxU , kxI are amplitude of whole voltage and current. kα , kβ are harmonic phase angle. Capacitance current is cos( )C ck k

dui C i kwt a

dt= ⋅ = ⋅ + . sin( )R RK ki i kwt α= ⋅ +

)sin()cos()sin( kRKkckkkx kwtIkwtIkwtI ααβ +⋅++⋅=+⋅By triangular transformation, it is given:

(cos cos sin sin )RK kx k k k ki I α β α β= + (cos sin sin cos )ck kx k k k ki I α β α β= −

rki , cki are resistive and capacitive current value. K is harmonic order. Third step. Power network harmonic component is filter. Third harmonic current is:

3 1 3 3 3U r U rI I I= +First harmonic generats the current:

27Xuepeng Liu and Dongmei Zhao / Procedia Engineering 23 (2011) 24 – 284 Author name / Procedia Engineering 00 (2011) 000–000

1 1 1

1 1sin( )( )

1xI U wt ar

j cω= + +

Where phase angle is ( )arctg wcrσ = .

Third harmonic generats the current:

3 3 3

1 1sin(3 )( )

13

u xI U wtr

j wc

β= + +

Where phase angle is 3 3arctg wcrσ = . Therefore, 3 3 3 3cosU r uI I σ= .

The third resistive current caused by first harmonic is:

1 3 3 3 3 3 3 3cosU r U r R uI I I I I δ= − = −Third capacitive current caused by first harmonic is:

1 3 3 3sinU c C usI I I δ= −So phase A current is obtained by following equation:

sin( ) / sin( )XA XA A AI I ϕ ϕ θ′= +

∑∞

=

+⋅=1

)sin(k

kkxA kwtUu α

∑∞

=

+⋅=1

)sin(k

kkxXA kwtII β

)sinsincos(cos kkkkkxRK Ii βαβα +=(cos sin sin cos )ck kx k k k ki I α β α β= −

)(33 δσ tgarctg=Third harmonic capacitive current is:

33333331 sin)3sin(sin δβδ +−=−= wtUIIII xCusCcU

Third harmonic resistive current is: 333333331 cos)3sin( δβ+−=−= wtUIIII xRrUrU

4. Circuit system design

MOA tester measures 3 phase leakage current and main power voltage. Leakage current is sampled by CT, while leakage voltage is done by PT. The whole structure is shown in Fig.3.

5. Conclusion

The digital filtering is proposed. By utilizing FFT, voltage and current is analyzed. A method is proposed to extract first harmonic and third harmonic component. The method has a good resolution and good ability to resist noise, which is very effective after practical experiment.

28 Xuepeng Liu and Dongmei Zhao / Procedia Engineering 23 (2011) 24 – 28 Author name / Procedia Engineering 00 (2011) 000–000 5

Fig 3. Diagram

References

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HIGH VOLTAGE APPARATUS, 10:24-26(2005)

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ELECTRIC POWER. 22(6), 60-63 (2009)

[3]. Fu ZhongjunAccurately Measuring MOA's Resistive Fundamental Harmonic Leakage Current by Over-zero & Harmonic

Analysis Methods, INSULATORS AND SURGE ARRESTERS. 2, 35-39(2004)

[4]. MENG Yi, WEN Yuan-fang, GONG Li-wei: Study on Electric Characteristics in Low Current Region of MOV in Different

Dielectrics, INSULATORS AND SURGE ARRESTERS, 5, 17-20(2006)

[5]. Ji Shengcang, Yang Lanjun: Electrical field probe used in online MOA Resistive harmonic current, HIGH VOLTAGE

APPARATUS, 1,43-49(2000)