Energy and Power Engineering, 2013, 5, 1182-1186
doi:10.4236/epe.2013.54B224 Published Online July 2013 (http://www.scirp.org/journal/epe)
A Novel Pilot Protection for VSC-HVDC Transmission
Lines Based on Correlation Analysis*
Xingfu Jin , Guobing Song
School of Electrical Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, P. R. China
Received February, 2013
ABSTRACT
The control system of voltage source converter HVDC (VSC-HVDC) is complex and its fault tolerance ability is not
sufficient, and correct rate of line protection device is not high. A novel pilot protection for VSC-HVDC transmission
lines based on correlation analysis is proposed in this paper. In the principle, external fault is equivalent to a positive
capacitance model, so the correlation coefficient of the current and voltage derivative is 1; while the internal fault is
equivalent to a negative capacitance model, so the correlation coefficient of the current and voltage derivative is -1.
Internal faults and external faults can be distinguished by judging the correlation coefficient. Theoretical analysis and
PSCAD simulation experiments show that the new principle, which is simple, not affected by transition resistance, con-
trol type and line distributed capacitance current, can identify internal faults and external faults reliably and rapidly,
having certain practical value.
Keywords: VSC-HVDC; DC Transmission Lines; Correlation Coefficient; Pilot Protection
1. Introduction
Voltage Source Converter HVDC (VSC-HVDC) is a
flexible and efficient DC transmission and distribution
technology using full-controlled switching devices and
high frequency PWM modulation technology, and it is
very promising in the fields such as the grid connection
of renewable energy, the island power supply, the urban
power supply, the interconnection among synchronous
grids and multi-terminal dc transmission [1-5]. Recently,
ABB has successfully developed a HVDC circuit breaker
[6], which provides the possibility for the formation of
the DC grid.
Generally, the dc transmission lines are over long dis-
tance with a high fault rate, and need a set of perfect and
reliable relay protection device to ensure the safe opera-
tion of the whole system. However, the relay protection
of VSC-HVDC transmission line still adopt protection
principle on CSC-HVDC lines which takes the traveling
wave protection as the main protection and current dif-
ferential protection as a backup protection, without tak-
ing into account the characteristics of VSC-HVDC [7-8].
The traveling wave protection is of fast response, not
affected by CT saturation and long term distributed ca-
pacitance and so on, while it requires a high sampling
frequency, is easily disturbed by the noise and loses effi-
cacy with high resistance grounding. The current differ-
ential protection is effective for high resistance ground-
ing, but is easily affected by distributed capacitance, re-
quiring the long delay, which does not meet the fast con-
trol characteristics in dc transmission. In [9], a VSC-
HVDC cable lines differential protection principle is
proposed based on frequency variable parameters model,
reducing the effect of the distributed capacitance, but it
increases a large amount of calculation and performs
slowly with a low constant value and a long time delay to
escape the transient process in order to ensure the un-
wanted operation in sound pole. In [10], a VSC-HVDC
cable lines pilot direction protection principle is pre-
sented with RL model in circuit, but there is principle
error and RLC in the model error function derive from a
set of differential equations with a large amount of cal-
culation [11]. Develop a pilot protection principle for
VSC-HVDC cable lines using the current natural fre-
quency. It also needs much calculation and the reliability
depends on the accurate extraction of the natural fre-
quency. Moreover, it needs extra auxiliary criterion and
complex setting, and there exists the dead zone in both
ends and the midpoint. In [12], a pilot protection method
for the transmission lines is proposed on the basis of the
principle of model identification. In this method, the in-
ternal faults are equivalent to the inductance models and
the external faults are equivalent to the capacitance mod-
*This work was supported by the National Natural Science Foundation
of China (No. 51177128) and the Key Program of National Natural
Science Foundation of China (No. 51037005).

X. F. JIN , G. B. SONG 1183
els, so internal faults and external faults can be distin-
guished through calculating model error.
On the basis of the idea of model identification, this
paper proposes a novel pilot protection principle for dc
transmission lines combining with the characteristics of
the VSC-HVDC whose double ends connect the shunt
large capacitance. This new principle can accurately dis-
tinguish internal faults from external faults by judging
the correlation coefficient of the current and the voltage
derivative. It has the following characteristics:
 It is conducted in time dominant, needs a short
data window, and has a fast response.
 The principle, simple and easily to be achieved, is
not affected by the distributed capacitance.
 It has a strong patience to transition resistance,
and can take action only on the fault pole.
2. The Structure of VSC-HVDC and the
Correlation Analysis
2.1. The Structure of VSC-HVDC
Figure 1 is the simplified diagram of the structure of
VSC-HVDC. Mp and Mn are respectively the meas-
ured voltage of the positive pole and the negative pole in
M terminal. Mp and Mn are respectively the measured
current of the positive pole and the negative pole in M
terminal. Np and Nn are respectively the measured
voltage of the positive pole and the negative pole in N
terminal.
uu
i i
u u
N
p and Nn are respectively the measured
current of the positive pole and the negative pole in N
terminal. f1-f5 are the fault location. f1 is inside the dc
transmission line, f2 and f3 are outside the capacitors, f4
and f5 are in ac lines in front of primary side of the con-
verter transformer in M terminal and N terminal. The
reference directions of voltage and current are as shown
in Figure 1.
ii
The shunt large capacitance, on both sides of voltage
source converter HVDC transmission lines, are mainly
used to provide dc voltage for the converter, and at the
same time, they can buffer the fluctuation in dc side
when the fault occurs, reduce the voltage ripple of the dc
side and support dc voltage of the receiving end [2].
Figure 1. VSC-HVDC transmission system with two elec-
trodes.
2.2. The Correlation Analysis
Correlation analysis is used to describe the relevance of
two variables or more. Linear correlation analysis is used
to represent the linear correlation degree of two variables,
and usually employs the correlation coefficient as a nu-
merical index. From [13], it can be noted that the correla-
tion coefficient between two variables can be expressed
as follows:
22
() ()
() ()
xy
xt ytdt
x
tdty tdt




 


(1)
After discretization:
1
22
11
()()
() ()
N
k
xy NN
kk
xkyk
x
kyk





(2)
The correlation coefficient

is a dimensionless
value, varying from -1 to 1. If

is 1, it stands for posi-
tive linear relationship between variables, while if

is
-1, it represents negative linear relationship between va-
riables. If

is 0, it stands that the two variables have
no relation at all.
3. The Analysis of the Fault Characteristics
of VSC-HVDC Transmission Lines
3.1. Model of the External Fault
On the basis of superposition theorem, the dc lines
shown in Figure 1 can be equivalent to the superposition
of a circuit network in normal operation and a fault net-
work [14]. Setting the external fault in M end as an ex-
ample, its fault components network is shown in Figure
2, where uf is the voltage source of fault components
network, Cp is the shunt large capacitance of the line
ends; the lines adapt π model, and L, R and C are the
corresponding equivalent inductance, resistance and ca-
pacitance with the lumped parameter; the inductive con-
verters can be equivalent to the Rsn resistance and the Lsn
inductance [2].
In this paper, we suppose that the positive direction of
current is from the converter to the line. From the basic
circuit principle, we can obtain the following equations:
Figure 2. The fault components net of external faults.

X. F. JIN , G. B. SONG
1184
M
MM
N
NN
MN
d
'C
d
d
'C
d
''0
u
ii t
u
ii t
ii









(3)
The fault components differential current and differen-
tial voltage is defined as follows:
cdM N
cdM N
iii
uuu



 (4)
Then we can obtain the following equation with the
external fault:
cd
cd
d
Cd
u
it

 (5)
From the analysis of the Equation (5) we can achieve
the following equivalent positive capacitance model of
the external fault, as shown in Fig u r e 3
From the Equation (5) we can obtain the correlation
coefficient of the differential current and differential
voltage derivative as follows:
cd
cd
d
,
d
u
it






1



(6)
3.2. The Model of the Internal Fault
The fault components network is shown in Figure 4
when the internal fault occurs in dc transmission lines.
RsM, LsM, RsN and LsN are respectively the equivalent re-
sistance and inductance of the M and N terminal.
At the moment of a sudden fault, the shunt large ca-
pacitance will rapidly discharge to the fault point, pro-
ducing a huge impulse current. As shown in Figure 4,
the impulse current cM and cN are respectively far
larger than M
ii
s
i and sN , and the system side can be
equivalent to the shunt large capacitance [9-11].
i
From Figure 4, we can obtain the following equations
based on the basic circuit principle with M
s
i and sN i

neglected.
M
McMp
N
NcNp
d
Cd
d
Cd
u
ii t
u
ii t

 



 


(7)
Figure 3. Positive capacitance model of external faults.
According to the definition of the differential current
and voltage, the following equation is made as:
cd
cd p
d
Cd
u
it

  (8)
From the analysis of the Equation (8), we can achieve
the following equivalent negative capacitance model of
internal faults, as shown in Figure 5.
From the Equation (8) we can obtain the correlation
coefficient of the differential current and differential
voltage derivative as follows:
cd
cd
d
,
d
u
it 


1




(9)
4. Principle and Criterion of the Pilot
Protection
On the basis of part III, the correlation coefficient of the
current and voltage derivative is 1 when an external fault
occurs; while the correlation coefficient of the current
and voltage derivative is -1 when an internal fault occurs.
Then we can make the criterion of the pilot protection
based on this characteristic.
The criterion by comparing correlation coefficient is as
follows:
cd
cd
d
,d
s
et
u
it







(10)
where
s
et

is the threshold, usually assuming from -0.8
to 0, and the length of the data window is 5 ms.
The specific process of this algorithm is as follows:
firstly, we can use the difference algorithm to calculate
the voltage and current fault components; then extract
low frequency components through filtering in low pass
band and calculate the correlation coefficient of the differ-
ential current and differential voltage derivative with the
least squares algorithm; lastly, we can distinguish the faults
by comparing the calculated value with the set value.
Figure 4. The fault components network of internal faults.
Figure 5. Negative capacitance model of internal line faults.

X. F. JIN , G. B. SONG 1185
It is necessary to make instructions that lines in this
paper adopt π model equivalent circuit corresponding to
a certain applicable band, so the method needs low pass
filtering [15].
5. Simulations
The  60 kV bipolar VSC-HVDC transmission system
simulation models are shown in Figure 1. The system
capacity is 60 MW, and the line length is 300 km.
PSCAD is employed for electromagnetic transient simu-
lation and MATLAB is used for data processing.
In this simulation model, the frequency-dependent pa-
rameters line model is used, and its structure and control
strategy is detailed in [9]. The shunt capacitances of both
the positive and negative pole are 1000 F and the sam-
pling rate is 10 kHz. The fault occurs at 2.5 s with dura-
tion of 0.1 s in the system. The data window is about 5
ms and the action threshold
s
et

is set to be -0.7. Be-
cause of the limited space, this paper only presents the
fault simulation results under the condition of the most
unfavorable to the protection action.
5.1. The Simulation Results of Internal Faults
The simulation results are shown in Figure 6 when an
internal fault occurs at the 30 km point from the terminal
M with a transition resistance of 300 in the positive pole.
The Figure 7 presents the simulation results when a me-
tallic grounding fault occurs at the 270 km point from the
terminal M in the positive pole.
From Figures 6 and 7, it can be noted that when a
fault with different fault distance and different transition
resistance occurs, for the fault pole, the correlation coef-
ficient

is far less than the threshold
s
et

and
protection devices can accurately distinguish fault; for
the sound pole, it is equivalent to the external faults, and
the correlation coefficient

is far more than the thre-
shold
s
et

, which can ensure the protection do not
2.52.5052.512.5152.522.525 2.53 2.5352.542.545 2.552.55
-1
-0.5
0
correlation coefficient, ρ
Positive electrode
2.52.5052.512.5152.522.525 2.53 2.5352.542.545 2.552.55
-1
-0.5
0
0.5
1
Ti m e(s)
correlation coefficient, ρ
Negative electrode
correlation coefficient
threshold
correlation coefficient
threshold
Figure 6. Simulation results when a fault at 30 km from the
M-side with 300resistances occurs.
2.52.505 2.51 2.5152.522.5252.53 2.535 2.542.5452.552.55
-1
-0.5
0
correlation coefficient,ρ
Positive electrode
2.52.505 2.51 2.5152.52 2.525 2.53 2.535 2.54 2.545 2.552.55
-1
-0.5
0
0.5
1
Time(s)
correlation coefficient,ρ
Negative electrode
correlation coefficient
threshold
correlation coefficient
threshold
Figure 7. Simulation results whe n a metallic ground fault at
30km from the M-side occurs.
take action.
5.2. The Simulation Results of External Faults
Simulation results when a metallic ground fault in DC
lines beyond the M-side(corresponding to f2 in Figure 1)
occurs are shown in Figure 8; Figure 9 presents the si-
mulation results when a metallic ground fault in AC lines
beyond the N-side(corresponding to f5 in Figure 1) oc-
curs.
From Figure 8 and Figure 9, it can be seen that the
correlation coefficient

is far more than the threshold
s
et

when the external fault occurs with different fault
distance and different transition resistance, which can
ensure the protection do not take action.
A lot of simulation results show that the protections
can correctly take action when internal faults in dc line
occur, and can reliably ensure inaction when external
faults in dc line occur.
5. Conclusions
This paper proposes a novel pilot protection principle for
VSC-HVDC transmission lines based on correlation
analysis. Theoretical analysis and simulation results can
help draw the following conclusions:
 The positive capacitance model reflects the ex-
ternal faults and negative capacitance model re-
flects the internal faults. Comparing the correla-
tion coefficient of differential current and differ-
ential voltage derivative with the threshold, we
can rapidly and reliably distinguish internal faults
from external faults.
 The faults for the fault pole are internal, but ex-
ternal for the sound pole, and the correlation co-
efficient of differential current and differential
voltage derivative is 1. Therefore this protection
can take action only on the fault pole.

X. F. JIN , G. B. SONG
1186
2.52.505 2.512.5152.522.5252.532.5352.54 2.5452.552.55
-1
-0.5
0
0.5
1
correlation coefficient,ρ
Positive electrode
2.52.505 2.512.5152.522.525 2.53 2.535 2.54 2.5452.552.5
5
-1
-0.5
0
0.5
1
Tim e(s)
correlation coefficient,ρ
Negative electrode
correlation coefficient
threshold
correlation coefficient
threshold
Figure 8. Simulation results when a metallic ground fault in
DC lines beyond the M-side occurs.
2.52.505 2.512.5152.522.525 2.532.535 2.542.5452.5
5
2.5
5
-1
-0.5
0
0.5
1
correlation coefficient,ρ
Positive electrode
2.52.505 2.512.5152.522.525 2.532.535 2.542.5452.5
5
2.5
5
-1
-0.5
0
0.5
1
Tim e(s )
correlation coefficient,ρ
Negative electrode
correlation coefficient
threshold
correlation coefficient
threshold
Figure 9. Simulation results when a metallic ground fault in
AC lines beyond the N-side occur s.
 The proposed novel pilot protection principle re-
gards the correlation coefficient as criteria with-
out compensating capacitor current. This princi-
ple is simple and easy to be achieved. Simulation
results indicate that this principle is not affected
by transition resistance, control type and it can
identify internal faults and external faults reliably
and rapidly under various working conditions,
having certain practical value.
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