An Improved Voltage Phasor Estimation Technique
to Minimize the Impact of CCVT Transients in
Distance Protection
E. Pajuelo
Member IEEE
G. Ramakrishna
Member IEEE
Power System Research Group
University of Saskatchewan
Saskatoon, SK S7N 5A9, Canada
Abstract-This paper describes the impact of the transient
response of coupling capacitor voltage transformers (CCVTs) on
the performance of distance relays. Several factors that affect the
frequency and time responses of CCVTs are considered. The
effect of the transient response on phasor estimation is illustrated.
A new least squares phasor estimation technique, which uses the
knowledge of the frequency of the CCVT transients, is presented.
A sample case, taken from a set of studies, is included to
demonstrate the performance of the proposed approach.
I.
INTRODUCTION
Distance relays are the most widely used devices for
protecting transmission lines. The parameters measured by
these relays are derived from the phasors of voltages and
currents of the fundamental frequency. An error in the
measurement of these phasors either causes undesired
overreach or underreach. The accuracy and speed with which
the magnitude and angle of these phasors is measured are,
therefore, very important issues.
Power systems are frequently subjected to changes in their
operating states either due to normal switching operations or
due to the occurrence of faults. The transitions between two
states are accompanied with transient changes in voltages and
currents. High speed relays have to make decisions when a
system state changes. Because voltages and currents are
experiencing transients at those times, the performance of
relays is affected adversely.
On EHV transmission systems, voltages are scaled down,
typically to 110 V in North America, by CCVTs before they
are applied to relays. In high speed devices, the performance is
affected by, among other factors, the transient response of the
CCVTs.
This paper outlines the factors that affect the transient
response of the CCVTs. Specifically considered are the design
parameters, secondary burden, fault incidence angle and
magnitude of voltage change. The impact of the CCVT
transients is demonstrated by evaluating the phasors by the
Discrete Fourier transform (DFT) approach. Some methods
that are being used to overcome this problem, such as prefiltering and/or adaptive delays, are discussed.
A new method of estimating the phasors is proposed in this
paper. The method is based on the least squares technique and
M.S. Sachdev
Life Fellow IEEE
uses the knowledge of the frequencies in the voltages, provided
by the CCVTs, during the transitions between the operating
states of power systems.
A representative case for a transmission line fault is
presented in this paper. The voltages and currents were
determined by simulating a power system on the Alternative
Transients Program (ATP) software. The results are compared
with those obtained by using a least squares technique that
does not take into account the transient behavior of the
CCVTs. The results show that there are improvements in
terms of speed and accuracy when the proposed method is
used.
II. CCVT RESPONSE
A. Modeling
Figure 1 shows a detailed model of a CCVT (the modeling
considerations are discussed in Reference 1).
Figure 1: Detailed model of a CCVT
A CCVT is basically a capacitive divider that has two
elements in series. Each element has a capacitance, C1 and C2.
Because there are losses in the capacitive stack, resistors R1
and R2 are added in the model. The series inductance is
modeled by a combination of LLE and RLE. The potential
transformer modeled by primary inductance, LPE, and
resistance, RPE, secondary inductance, LSE, and resistance, RSE,
along with an ideal transformer PT. The magnetizing branch
RM and XM is assumed to be linear in this model. This
assumption is reasonable for the purpose of this study because
the transients of interest are faults which cause voltage drops
that are typically within the linear region of the CCVTs [2].
Stray capacitances are not included because its effect is only
noticeable at high frequencies [3] that are removed by simple
filters. The ferroresonance suppression circuit (FSC) is
represented in detail by the inductance LF and RLF, the
capacitance CF and RCF and the resistance RF. This type of
circuit is called “active” FSC [1, 4] and is the one that
introduces bigger distortions in the voltages when a transient is
experienced. The burden is represented by the inductance LO,
RLO and resistance RO.
B. Frequency Response
The ideal frequency response of a CCVT is a zero gain and
zero angle shifts for all frequencies. The series inductance LLE
and capacitors C1 and C2 are typically chosen to obtain this
condition at the fundamental frequency. The response for the
full range of frequencies depends on the overall design of the
CCVT [3]. An analysis of the model shows that some
frequencies are amplified; the most significant amplification is
of the components of the subharmonic frequencies. Also, the
high order frequencies and the DC component are attenuated.
Moreover, the phase angle response is non linear. A
significant factor that affects the frequency response of the
CCVT is the burden [3, 5]. More resistance in the load results
in more attenuation of the high frequency components whereas
more inductance in the load results in higher amplification of
the subharmonic components. The effect of the burden on the
phase angle response is not as significant as the effect on the
gain response.
C. Time Response
The CCVT time response shows a decaying transient riding
the steady state voltage experienced during a fault. This
transient is affected by the incidence angle at which the fault
occurs and by the magnitude of the change of voltage. The
voltage change is the difference between the non faulted and
steady state fault signal at the time of the inception of the fault.
To obtain this difference the pre-fault voltage is extrapolated in
time and the steady state fault voltage is subtracted from it. A
smaller voltage change results in less distortion of the signal.
A zero incidence angle results in maximum distortion of the
signal from all possible angles [4]; this is shown in Figure 2.
Figure 2: CCVT output for a step change in voltage at zero degree phase angle
III. IMPACT OF TRANSIENT ON DISTANCE PROTECTION
A. Basic Concepts
A basic distance relay measures the voltage at the relay
location and the current flowing in the protected line. A signal
processing technique is used to convert the sampled values of a
voltage to fundamental frequency phasor VR, and the sampled
values of a current to fundamental frequency phasor IR. From
these phasors, the relay compares IRZL (ZL being the reach of
the relay) with VR to decide if the fault is in the protected zone
of the relay.
The errors in the estimates of the magnitude and angle of the
phasor affect the operation of the distance function in many
situations. These errors cause undesired overreach or
underreach as shown in Figure 3.
(a)
(b)
Figure 3: The effects of the errors in the estimates of (a) magnitudes of the
phasors and (b) the phase angles of the phasors
B. Impact of CCVT Transients
The transient response of the CCVT affects the performance
of distance protection by producing transient overreach and/or
underreach. To illustrate these phenomena, a fault at the
remote end of a line is considered and performances of CCVTs
and distance functions with and without the transients are
evaluated. For comparison, the quality of phasor estimates is
considered. The voltage phasor is estimated using the DFT
technique [8] that uses a one cycle data window. The impact
of the transients in the current is eliminated by using the steady
state phasor of the fault current.
The voltage at the relay location is a function of the source
to line impedance ratio SIR (=ZS/ZL). A higher SIR translates
into a larger voltage change at the relay location on the
inception of a fault; the voltage at the relay location is lower
compared to the voltage experienced if the SIR were smaller.
Figure 4 shows the phasors if the voltage waveform were
ideal and if the waveform were distorted due to the transient
behavior of the CCVT shown in Figure 2. A transient
overreach of 16% on the pre-fault scale is observed. This
corresponds to 177% (= 16% / 9%) of the line impedance ZL.
The risk of false operation of the protection function is,
therefore, very high unless appropriate countermeasures are
taken. On the other hand the response of an ideal PT
converges to the correct value after one cycle, which is the
nominal delay of the full cycle DFT technique.
An over-defined set of linear equations is put together based
on the selected waveform using the measured samples of the
voltage v, the time dependent sine and cosine coefficients and
the unknown parameters VR and VI. The coefficients are
functions of time t-tO (= k∆t, k = 1 … N) and ∆t that is the
sampling period. The number of measured samples, N, used in
estimating the phasor is also called the data window size,
which is sometimes expressed in cycles of the nominal
frequency. The set of linear equations can be written as
Figure 4:.Estimated voltage phasors at the relay location when SIR is 10
C. Techniques used to Minimize the Impact of CCVT
Transients
One possible approach is to reduce the relay reach by a
percent of the line impedance if the maximum error due to the
CCVT transient is known. For applications in which the SIR is
small, reduced coverage of the first zone is usually an
acceptable approach. However, if the SIR is large, it may be
impossible to prevent incorrect operations; the alternative is to
disable the zone 1 relays that are set to operate without any
intentional time delay.
The second approach is to delay the relay operation until the
transients caused by the CCVTs subside. A fixed delay is
simpler to implement, but the minimum power system clearing
times could be exceeded for severe faults [7]. Use of adaptive
delays that verify the stability of the phasor estimates after the
inception of a fault can help in deciding on the appropriate
delay to be used in an application.
The third approach is to use special pre-filters [2] that
remove the CCVT transient frequencies, before the phasors are
estimated.
Other techniques, which take advantage of some
characteristics of small and large SIR conditions, use a mixture
of signal processing techniques with combinational or
sequential logic [6, 7]. It is also possible to use the improved
least squares technique proposed in Section IV of this paper.
IV. IMPROVED LEAST SQUARES TECHNIQUE
A. Basic Least Squares Approach
This algorithm is based on fitting a set of measurements to a
waveform. The best fitting is obtained by minimizing the sum
of squares of the differences between the measurements and
the waveform. For achieving this objective, the mathematical
description of the waveform must be selected upfront [9].
For the estimation of the fundamental frequency phasor, the
waveform is assumed to be a time dependent sine function of
known frequency ωO, but of an unknown magnitude and phase
angle. This waveform is decomposed in two orthogonal sine
and cosine functions with unknown amplitudes VR and VI. The
difference from the observed signal, say voltage v, and the
proposed waveform is assumed to be noise ε.
sin(ωO ∆t )
sin(ω 2∆t )
O

#

sin(ωO N∆t )
cos(ωO ∆t ) 
v(t O + ∆t ) 

cos(ωO 2∆t )  VR  v(t O + 2∆t ) 
=

 VI  #
#



cos(ωO N∆t )
v(t O + N∆t )
(4.1)
In the matrix notation, this is
[A][x] = [b]
(4.2)
The vector of unknowns is determined by using the left
pseudo-inverse of [A] as follows
[x] = [ [A]T [A] ] [A]T [b]
−1
(4.3)
One of the important advantages of this non-recursive least
squares algorithm is that the pre-filtering and phasor estimation
are done in one step.
B. Improved Least Squares Technique
The information concerning the CCVT transfer function and
burden can be included in the phasor estimating algorithm if it
is available. Considering the example described in Section II
(C), the model of the CCVT output can be expressed as a sum
of the waveform of the fundamental frequency ωO, a few
oscillatory decaying components and a decaying DC
component. Including the frequencies ω1 and ω2, and the time
constants of the decays, σ1, σ2 and σ3, provides the following
equation.
v = VR sin( ω O t ) + VI cos(ω O t )
+ VR1e (σ 1) t sin( ω1t ) + VI 1e (σ 1) t cos(ω1t )
+ VR 2 e (σ 2 ) t sin( ω 2t ) + VI 2 e (σ 2 ) t cos(ω 2t )
(4.4)
+ V3e (σ 3) t + ε
The matrix A is now defined by
  
 A =  A0
 Nx 7   Nx 2

A1 A2 A3
Nx 2
Nx 2
(4.5)
Nx1
Where [A0] is identical to the basic least squares matrix [A],
and the others are defined by Equations 4.6 to 4.8. The vector
of the unknown is defined by Equation 4.9. Once the matrices
are defined, finding the unknown requires the calculation of the
pseudo-inverse using Equation 4.3.
e ∆t ⋅σ 1 sin(ω1 ∆t )
 2 ∆t ⋅σ 1
e
sin(ω1 2∆t )
[A1] = 
#

e N∆t ⋅σ 1 sin(ω1 N∆t )
e ∆t ⋅σ 2 sin(ω 2 ∆t )
 2 ∆t ⋅σ 2
sin(ω 2 2∆t )
[A2] = e
#

e N∆t ⋅σ 2 sin(ω 2 N∆t )


e 2 ∆t ⋅σ 1 cos(ω1 2∆t ) 

#

e N∆t ⋅σ 1 cos(ω1 N∆t )
e ∆t ⋅σ 1 cos(ω1 ∆t )


e
cos(ω 2 2∆t )  (4.7)

#

e N∆t ⋅σ 2 cos(ω 2 N∆t ) 
e ∆t ⋅σ 2 cos(ω 2 ∆t )
2 ∆t ⋅σ 2
e ∆t ⋅σ 3 
 2 ∆t ⋅σ 3 

[A3] = e

#


e N∆t ⋅σ 3 
[x ] = [V R
VI
(4.6)
V R1 V I 1 V R 2
VI 2
V3 ]
T
Figure 7: Estimated angles of the phasors
(4.8)
The magnitude and angle of the phasors show that they are
within a reasonable margin to decide the operation of the relay
two cycles after the inception of the fault. Compared to this,
the phasors calculated by using the basic least squares
technique stabilize four cycles after the inception of the fault.
(4.9)
V. CONCLUSIONS
C. Simulation and Results
The technique was tested from simulations of faults on a 500
kV network using the ATP/EMTP software and the proposed
technique was used to calculate the phasors. An example is
presented in this section. The sampling rate used in this
example was 3840 Hz.
Figure 5 shows the voltages provided by an ideal PT and the
modeled CCVT. The phasors calculated with the proposed
algorithms are shown in Figures 6 and 7.
This paper has described the significant impact of CCVT
transients on the performance of distance relays. The
traditional techniques that do not correctly estimate the phasors
during the first few cycles after the inception of a fault are
likely to operate incorrectly.
The knowledge of the CCVT design and the connected
burden can be incorporated in the relay algorithm. This
improves the correctness of the calculated phasors. A least
squares technique that includes this knowledge has been
proposed and demonstrated in this paper. The results show
significant improvements in both accuracy and speed.
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[2]
[3]
Figure 5: Voltages provided by an ideal PT and the CCVT.
[4]
[5]
[6]
[7]
[8]
[9]
Figure 6: Estimated magnitudes of the phasor
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