Resonance Measurement of Capacitance Current in
Ineffectively Earthed Power Systems
WT Yi1, XJ Zeng1, SS Choi2, ZL Liu1
1 School of Electrical & Info. Engineering Changsha Univ. of Science andTechnology
Changsha,410077, P.R.China.
2 School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore
yafeifei@hotmail.com , eexjzeng@csust.edu.cn, esschoi@ntu.edu.sg
Abstract- Capacitance current is an important parameter
for single phase ground fault protection and control in
ineffectively earthed power systems. A novel method for the
capacitance current measurement is presented in the paper. An
adjustable reactor is in series connection with the open-delta
side of a zero sequence voltage transformer. System resonance
frequency is sought by injecting a current signal with variable
frequency. By changing the reactor inductance value, another
resonance frequency can also be sought. The ground
capacitance and ground capacitance current can thus be
calculated using the two resonance frequencies for the power
systems. Experimental work shows that the proposed method
has produced results of high precision in real-time, without the
need to interrupt power supply.
Index Terms—Capacitance current, Distribution system,
Grounding capacitance, Grounding fault protection, Voltage
transformer, Resonance measurement
The method is complex; it can impact on the safety to
operating personnel and equipment and can easily cause
over-voltage. The other method for the capacitance
measurement is proposed in [1]. The resonance frequency is
sought by injecting a current signal with varying frequency
to the open-delta secondary side of a voltage transformer. It
can satisfy the requirement for on-site safety. However, the
leakage impedance of the voltage transformer influences on
the accuracy of the measurement with the result that the
measurement error is large.
In order to improve on the accuracy, a novel method for
the capacitance current measurement is now proposed. The
method will reduce the influence of the voltage transformer
leakage impedance on the measurement error. Dynamic
power system experiments have been carried out to verify
the validity of the method.
II. NOVEL RESONANCE MEASUREMENT METHOD
The proposed test circuit to measure the capacitance to
I.
INTRODUCTION
Many power distribution systems have been operated with
either neutral unearthed, or with high resistance earthed or
resonance earthed. The systems are usually called
ineffectively earthed power systems. Most Chinese
Medium Voltage (MV) power systems have been operated
with neutral point ungrounded. With the system expansion
and topology changes, system parameters will change and
therefore phase-ground fault residual current will vary
dynamically. If the system parameters are taken in
consideration in the protection system design or equipment
insulation is imperfect, the arcing ground fault will easily
cause over-voltage and induce multiple faults. According
to the China Electrical Standard, the residual current
caused by single-phase earth fault needs to be limited to
twenty amperes and ten amperes in 10KV and 35KV
distribution networks respectively. Otherwise, power
systems should utilize Petersen-coil to compensate for the
capacitance current. So method of measuring the
capacitance current with high precision and speed is the
basis of deciding the capacity of the Petersen-coil.
At present, there are two main methods to measure
capacitance current. One is by direct measurement of the
capacitance to earth in high voltage power system but it
requires interruption to power supply. An additional
capacitance is connected with a feeder, the capacitance to
earth can be calculated by measuring the voltages variations.
earth is shown in Figure.1. A reactor( L )is connected in
series to the open-delta side of a voltage transformer. The
corresponding equivalent circuit is shown as Figure.2
without considering the leakage impedance of voltage
transformer. In the figure, C is the single phase capacitance
to earth of the distribution system under consideration. By
injecting a current signal ( I ) with variable frequency, the
phase difference between the signal current ( I ) and the
returned signal voltage ( U ) is measured. When it is zero
(that is resonance), this signal frequency (
ω0
) is the
resonance frequency of the system. Whence, the single
phase capacitance to earth can be calculated
from C =
1
ω 02 L
. The equivalent capacitive reactance
( X C 50 ) of the system at the fundamental frequency of 50
Hz is:
X C 50 =
1
ω 50C
=
1
ω 50
1
ω 02 L
=
ω 02 L
ω50
(1)
Where ω50 is fundamental angular frequency, i.e.314
rad./sec in the 50-Hz system.
L'
U ′
R
1
C
3
I
Figure.4 Simplified equivalent circuit of Figure.3
Select an additional reactor la , inject a current signal ( I )
with variable frequency, and seek the resonance frequency
( ω1 ) of the power system. Two equations can be derived:
U L = jω 1 La ⋅ I
Figure.1 Proposed capacitance current measurement method
(2)
1 U ′ = − j
⋅ I ⋅ 3 + I ⋅ R + jω1 L ′ ⋅ I (3)
ω 1C
Where La is the equivalent reactance of l a referred to the
primary side, U L is the voltage across the adjustable
reactor ( l a). Changing the additional reactor to lb , repeat
the measurement process and the resonance frequency
Figure.2 Equivalent circuit for resonance measurement: with the voltage
transformer leakage impedance ignored
When including the leakage impedance of the voltage
transformer, the equivalent circuit is shown as Figure.3. In
the figure, L1 , R1 are the leakage inductance and the
leakage resistance of the voltage transformer secondary coil
respectively; Lm , Rm are the excitation inductance and the
excitation resistance of the voltage transformer respectively;
ω2
can also be obtained. The following equations can be
obtained:
U L = jω 2 Lb ⋅ I
(4)
1 U ′ = − j
⋅ I ⋅ 3 + I ⋅ R + jω 2 L′ ⋅ I (5)
ω 2C
Where Lb is the equivalent inductance of lb referred to the
primary side. The measured voltage ( U ) is composed of
L2 , R2 are the leakage inductance and the leakage
two parts, U = U L + U ′ . From the four equations (2)-(5),
resistance
one can derive the following two equations:
of
the voltage transformer
primary coil
respectively; and U ′ is the secondary voltage of voltage
transformer referred to the primary side. The excitation
current in the transformer is very small, so the excitation
impedance can be neglected. The equivalent circuit can thus
be simplified as Figure.4. Where R and L ′ are the leakage
resistance and the inductance of the voltage transformer
respectively.
L1
U ′
I
R1
L2
Lm
Rm
R2
1
C
3
Figure.3 Equivalent circuit for voltage transformer with the capacitance to
earth (per phase)
ω（1 La＋L′） =
1
1
ω 1C
3
1
ω（2 Lb＋L′） =
1
ω 2C
3
(6)
(7)
Therefore, the three-phase capacitance to earth of the
distribution network can be calculated from
3C = 9 ⋅
ω12 − ω 22
ω12ω 22 ( Lb − La )
(8)
The total capacitive current ( I c ) caused by a ground fault
can be obtained:
IC = 9 ⋅
TABLE I
ω (ω12 − ω 22 )U Φ
ω 12ω 22 ( Lb − La )
(9)
Where ω and U Φ are the frequency and the phase voltage
of
the
power
system
respectively.
If
the
voltage
transformation ratio of voltage transformer is k , (8) and (9)
can be calculated as:
ω −ω
ω ω k (lb − l a )
(10)
ω (ω − ω )U Φ
ω12ω k 2 (lb − l a )
(11)
3C = 9 ⋅
IC = 9 ⋅
2
1
2
1
2 2
2
2
1
2
2
2
2
2
2
III. EXPERIMENT
Experiments have been carried out on a dynamic power
system model in laboratory, and the experiment model is
shown in Figure.5. Where C A , C B , C C are the single
phase capacitance to earth of the network. The voltage
transformation ratio of the zero sequence voltagetransformer is 100 3 ; The distribution system voltage is
10kV; lumped capacitances replace the ground capacitance.
The adjustable reactor ( l ) is connected in series with the
secondary side of the voltage transformer, and its inductance
ranges from 1mH to 20mH . A variable frequency current
signal of 0.5 ampere is injected into the secondary side.
Figure.5 Circuit diagram of the experimental set-up
Test results are shown in TABLE I. Where l1 , l2 are the
selected reactors; f1 , f 2 are the resonance frequency
corresponding to l1 , l2 respectively; 3C is the actual threephase capacitance to earth used in the test; 3C cal is the
calculated three-phase capacitance to earth. Note that the
influence of the voltage transformer leakage impedance has
been considered, the largest error of the test measurements
does not exceed 2.74%.
MEARSUREMENT RESULTS
l1 ( mH
)
5.4
5.4
5.4
5.4
5.4
l2 ( mH
)
14
14
14
14
1
f1 ( Hz )
78
36.6
25.8
20.4
12
f 2 ( Hz )
49.2
23.1
16.2
12
27.6
3C cal ( µ F)
0.219
0.996
2.039
4.012
9.726
3C ( µ F)
0.22
1
2
4
10
IV. CONCLUSIONE
A novel method of capacitance current measurement for
an ineffectively grounded power system is proposed in the
paper. It uses an adjustable reactor which is in series
connection with the open-delta side of a zero sequence
voltage transformer. By injecting a signal with variable
frequency, the power system resonance frequency can be
sought. By changing the value of the reactor to another
value, another resonance frequency is also obtained. Using
the two resonance frequencies, the capacitance to earth can
be calculated, where the leakage inductance of the voltage
transformer will not influence the accuracy of the
measurement. Experimental results show that the proposed
method can achieve high measurement accuracy, and can be
carried out without the need to interrupt power supply.
REFERENCES
[1] Zhang Xuhui. “Measurement device for grounding capacitance current”,
(in Chinese) Patents in China, July.2001.
[2] B Michael Aucion, Rober H Jones.High impedance fault detection
implementation
issues[J].
IEEE
Trans
on
Power
Delivery.1996.11(1):139-145
[3] IEEE recommended practice for grounding of industrial and
commercial power systems, IEEE Std 142~1991. PP.17-80, 1991.
[4] Joseph Sottile Jr., and Lawrence E. Holloway, “An overview of fault
monitoring and diagnosis in mining equipment,” IEEE Transactions
on Industry Applications, Vol.30, No.5, 1994, pp.1326-1332.
[5] Zeng Xiangjun, Li K.K., Chan W.L., Yin Xianggen. “On-site safety
evaluation for earth fault in mining power systems”. IEEE
Transaction on Industry Applications Vol.39, No.6, Nov./Dec. 2003
1563-1569.
[6] Novak T., and Kohler J. L., “Technological innovations in deep coal
mine power systems,” IEEE transactions on industry applications,
Vol.34, No.1, 1998, pp.196-204.
[7] Zeng Xiangjun,Li K.K.,,Chan W.L.,Su Sheng "Grounding Faulted
Feeder Detection with Fault Resistance Measurement in Mining
Power Systems". Industry Applications Conference, Fortieth IAS
Annual Meeting, 2005 Vol 1, 2-6 Oct. 2005 PP.657 – 661
[8] R.Willheim, and M.Waters, “Neutral grounding in high-voltage
transmission,” New York: Elsevier, 1956.
[9] John P. Nelson, and Pankaj K.Sen, “High-resistance grounding of
lowvoltage systems: a standard for the petroleum and chemical
industry,” IEEE transaction on industry application, Vol.35, No.4,
1999, pp. 941-948.
[10] Zhao Zhengjun, Jiang Xinyu. “Research on capacitance current
mearsurement with signal injection in distribution network”, (in
Chinese) Guang Dong Electric Power, Vol.17, No.6, Dec.2004
[11] Lu Li, Sun Jiezhong. “ A new method to measure capacitance current
in distribution network”, (in Chinese) Power System Technology,
Vol.25, No.5, May.2001