Electrical Power and Energy Systems 32 (2010) 416–420
Contents lists available at ScienceDirect
Electrical Power and Energy Systems
journal homepage: www.elsevier.com/locate/ijepes
A novel error compensation algorithm for three-current transformer connection
Qing-quan Jia a,*, Chun-xia Dou a, Chun Wang a, Ning Wang a, Jie Tian a, Zhi-qian Bo b
a
b
Institute of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China
AREVA Protect/Control Ltd., Stafford ST17 4LX, UK
a r t i c l e
i n f o
Article history:
Received 30 October 2007
Received in revised form 30 July 2009
Accepted 25 September 2009
Keywords:
Current transformer
Error compensation
Saturation
EMTP
Current protection
a b s t r a c t
Under fault condition, primary current of a current transformer (CT) has high magnitude and may include
decaying dc offset. This can result in saturation of magnetizing core of the CT and the secondary current is
thus distorted. The distorted current is likely to cause malfunction of protection relays or control devices.
Therefore error compensation methods are studied. Most attentions are paid to a single CT. However, CTs
are usually connected together for different protections and control devices. For example, three CTs are
linked for three-phase current protection and zero-sequence current protection of transmission lines.
This paper proposes a novel error compensation algorithm for 3-CT connection. Due to the existence
of neutral circuit, the three CTs are affected each other and error compensation methods for a single
CT cannot be applied. The error compensation algorithm is derived based on the physical configuration
of the 3-CT connection. It is evaluated by EMTP simulation data and case studies are included. Protection
relays and control devices can achieve better performance using the compensated current
measurements.
Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction
Although novel protection and fault location schemes for power
systems were investigated widely [1,2], CT saturation and the
resulting distortion of the secondary current waveform have been
of concern to protection engineers. One approach of reducing the
impact of CT saturation is to use waveform compensation or
restructuring algorithms that attempt to reconstruct the secondary
current waveform. A compensation algorithm [3] using LeastSquare (LS) curve fitting method is introduced to convert a
sampled current waveform distorted by CT saturation to a compensated current waveform. Another algorithm [4] for compensating the distortion in the secondary current caused by saturation
and remanence in a CT is described. A second-difference function
applied to the current signal was used to detect the start of first
saturation. A busbar current differential protection relay suitable
for use with measurement type current transformers is described
[5,6]. The relay operates in conjunction with a saturation algorithm, which detects the start and end of each saturation period
using a technique based on the third-difference function applied
to the current signal. A blocking signal is activated after the onset
of saturation and is maintained active until the saturation period
plus an additional delay of one cycle has expired. Another scheme
for error compensation of current transformers is presented [7].
* Corresponding author. Tel.: +86 03358047169.
E-mail address: jiaqingquan@sina.com (Q.-q. Jia).
0142-0615/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijepes.2009.09.024
The method is to apply Hall Current Transducers (HCTs) based on
magnetic force balance to detect and compensate the error current
so as to eliminate the error of CT caused by its exciting current.
This compensation scheme is oriented to improve measuring precise and is applied for metering CT. Papers [8,9] describe an algorithm for detecting CT saturation using the third-difference
function. Kang presents a technique [10] of estimating the secondary current corresponding to the CT ratio under CT saturation. Marti described a current transformer model with fast solution
algorithms [11]. But this fast and non-iterative solution calculates
saturated secondary current from known primary current referred
to the secondary side.
The above mentioned contributions for CT error compensation
are concentrated on single CT. However, CTs are usually connected together for different protections and control function.
3-CT connection is very common in power systems for protection purpose. Due to the existence of neutral circuit, the three
CTs are affected each other and error compensation methods
for a single CT cannot be applied. This paper presents an error
compensation algorithm for 3-CT connection considering saturation. CT model in [11] is referred to, but the proposed algorithm
estimates the primary current from the measuring secondary
current. The process of secondary current compensation is
shown in Fig. 1.
The remainder of this paper is organized as follows. Section 2
describes the derivation of the error compensated algorithm in details. Evaluation results including EMTP simulation are presented
in Section 3. Conclusion is drawn in Section 4.
417
Q.-q. Jia et al. / Electrical Power and Energy Systems 32 (2010) 416–420
2.3. Core loss branches
For CT-1 shown in Fig. 3, the voltage cross the core loss resistance is
v m1 ¼ RFe1 iFe1
ð1Þ
and
v m1 ¼
d
k1
dt
ð2Þ
where k1 represents the magnetic linkage.
Putting (1) and (2) together in new sample and old sample
form:
1
1
ðk1:new k1:old Þ ¼ RFe1 ðiFe1:new þ iFe1:old Þ
2
Dt
Fig. 1. The process of secondary current compensation.
2. Derivation of error compensation algorithm
or
iFe1:new ¼ C Fe1 k1:new þ hFe1:old
ð3Þ
where
2.1. 3-CT connection scheme
hFe1:old ¼ C Fe1 k1:old iFe1:old ;
C Fe1 ¼
2
RFe1 Dt
3-CT connection scheme for current protection is shown in
Fig. 2, where Relay-1, Relay-2 and Relay-3 are phase current relays;
Relay-0 is zero-sequence current relay; is1 ; is2 and is3 are the secondary currents; is0 is the zero-sequence current through the coil
of the neutral relay; Z 1 ¼ R1 þ jxL1 ; Z 2 ¼ R2 þ jxL2 and Z 3 ¼ R3 þ
jxL3 are the total phase impedances of CT and phase current relay
in each phase and Z 0 ¼ R0 þ jxL0 is the total impedance of zero-sequence current relay and neutral leads.
iFe2:new ¼ C Fe2 k2:new þ hFe2:old
ð4Þ
iFe3:new ¼ C Fe3 k3:new þ hFe3:old
ð5Þ
hFe2:old ¼ C Fe2 k2:old iFe2:old ;
C Fe2 ¼
2.2. The equivalent circuit of CT
hFe3:old ¼ C Fe3 k3:old iFe3:old ;
C Fe3
The equivalent circuit of CT-1 can be expressed in Fig. 3. It is
0
0
0
identical of CT-2 and CT-3, where ip1 ; ip2 and ip3 are the primary
currents of CT-1, CT-2 and CT-3 referred to the secondary side;
iFe1 ; iFe2 and iFe3 are the currents through resistance RFe1 , RFe2 and
RFe3 which represent the losses of iron core; im1 ; im2 and im3 are
the magnetizing currents through the non-linear inductance Lm1 ,
Lm2 and Lm3 , which represent the magnetizing behavior of the iron
core; v m1 ; v m2 and v m3 are the voltages across the magnetizing
branches.
2.4. Magnetizing branches
Similarly, the current in the core loss branches in CT-2 and CT-3 are
where
2
RFe2 Dt
2
¼
RFe3 Dt
The flux–current relationship of the magnetizing branch can be
represented by the piecewise linear curve. There is following relation of magnetizing current and flux in the iron core:
im1:new im1:old ¼
im1:new ¼
1
ðk1:new k1:old Þ
Lm1
1
k1:new þ km1
Lm1
ð6Þ
where
km1 ¼ im1:old 1
k1:old
Lm1
Similarly, the magnetizing currents in CT-2 and CT-3 are
1
k2:new þ km2
Lm2
1
¼
k3:new þ km3
Lm3
im2:new ¼
ð7Þ
im3:new
ð8Þ
where
Fig. 2. 3-CT connection scheme.
1
k2:old
Lm2
1
¼ im3:old k3:old
Lm3
km2 ¼ im2:old km3
According to Fig. 3, the voltage on the secondary branch is
dis1
dðis1 þ is2 þ is3 Þ
þ R0 ðis1 þ is2 þ is3 Þ þ L0
dt
dt
dis1
dðis2 þ is3 Þ
þ R0 ðis2 þ is3 Þ þ L0
¼ ðR1 þ R0 Þis1 þ ðL1 þ L0 Þ
dt
dt
dðis2 þ is3 Þ
0
0 dis1
¼ R1 is1 þ L1
þ R0 ðis2 þ is3 Þ þ L0
dt
dt
v m1 ¼ R1 is1 þ L1
Fig. 3. Equivalent circuit of CT-1.
ð9Þ
ID
400583
Title
Anovelerrorcompensationalgorithmforthree-currenttransformerconnection
http://fulltext.study/article/400583
http://FullText.Study
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