Method for fault location on series compensated power transmission lines with two-end unsynchronized measurement
View Patent ↗A method for fault location in series compensated power transmission lines using two-end unsynchronized voltage and current measurements in stations A and B. The method includes performing a subroutine I for determining whether the fault occurred in a line section LA between the station A and a SC&MOV and the distance d A to the fault from station A. Subroutine II determines whether the fault occurred in a line section LB between the station B and the SC&MOV and the distance d B to the fault from station B. The synchronization angle e jδ A is determined in subroutine I, and the synchronization angle e jδ B is determined in subroutine II. Then, the distance to fault d A or d B is determined. Finally, an equivalent impedance of compensating banks at fault stage Z SC1 — ph SUB — A and Z SC1 — ph SUB — B , and pre-fault stage Z SC1 — pre is calculated in order to determine whether distance d A or d B is the final result.
1. A computer program product comprising non-transitory computer-readable program code which when executed on a computing device carries out the steps of detecting a location of a fault in one or more power transmission lines that extend between a station A and a station B and have a series capacitor and metal oxide varistor device (SC&MOV) connected therein, using unsynchronized voltage and current measurements in the stations A and B, before and after occurrence of the fault, performing a subroutine I for determining if the fault occurred in a line section (LA) between the station A and the SC&MOV and determining a distance (d A ) to the fault from station A, performing a subroutine II for determining if the fault occurred in a line section (LB) between the station B and the SC&MOV and determining a distance (d B ) to the fault from station B wherein subroutine I comprises the following steps:
(A1.) determining a synchronization angle (δA) in term (e jδ A ) for a known type of fault which is phase-to-ground faults or phase-to-phase faults, from the formula:
[
ⅇ
jδ
A
]
ph
-
g
,
ph
-
ph
=
a
_
F
2
I
-
SET
I
_
SC
2
_B
-
a
_
F
1
II
-
SET
I
_
SC
1
_B
a
_
F
1
II
-
SET
N
_
A
1
-
a
_
F
2
I
-
SET
N
_
A
2
where:
subscript ph-g denotes phase to ground faults: a-g, b-g, c-g, and subscript ph-ph denotes phase to phase faults a-b, b-c, c-a,
a F2 I-SET , a F1 II-SET —denote coefficients dependent on fault type,
I SC1 — B —denotes the positive sequence current from the station B after analytical transfer towards the SC&MOV,
I SC2 — B —denotes the negative sequence current from the station B after analytical transfer towards the SC&MOV,
N A1 , N A2 —denote coefficients dependent on positive and negative sequence currents and voltage taken at station A respectively as well as parameters of the one or more power transmission lines, or
for faults not being the phase-to-ground faults or phase-to-phase faults from the formula:
ⅇ
jδ
A
=
(
1
+
Z
_
1
B
Y
_
1
B
)
(
Y
_
1
B
V
_
B
1
pre
-
I
_
B
1
pre
)
+
Y
_
1
B
V
_
B
1
pre
(
1
+
Z
_
1
A
Y
_
1
A
)
(
I
_
A
1
pre
-
Y
_
1
A
V
_
A
1
pre
)
-
Y
_
1
A
V
_
A
1
pre
where:
V A1 pre , V B1 pre —denote pre-fault positive sequence quantities of voltage measured at the ends A and B, respectively,
I A1 pre , I B1 pre —denote pre-fault positive sequence quantities of current measured of the faulted one or more power transmission lines at the ends A and B, respectively,
Z 1A , Y 1A —denote impedance and admittance, respectively, of line section LA,
Z 1B , Y 1B —denote impedance and admittance, respectively, of line section LB,
(A2.) then taking into account a distributed parameter line model and solving the formula:
d A =p SC d LA ,
where:
p sc —denotes a distance (p.u.) per unit of total line length l at which the SC&MOV is installed in the transmission line from the station A, and
d LA —denotes a hypothetical distance to fault, expressed in relation to length p SC l and which value is received using known iterative method by solving the fault loop formula:
∑
i
=
0
2
a
_
i
(
V
_
Ai
cosh
(
γ
_
iL
d
LA
p
SC
l
)
-
Z
_
ciL
I
_
Ai
sinh
(
γ
_
iL
d
LA
p
SC
l
)
)
·
ⅇ
jδ
A
-
R
FA
∑
i
=
1
2
a
_
Fi
M
_
i
cosh
(
γ
_
iL
(
1
-
d
LA
)
p
SC
l
)
=
0
for single line,
in which:
P SC l—denotes a length (km) from station A at which SC&MOV is installed in the transmission line,
V Ai —zero, positive, and negative voltage sequences measured at the end A, and wherein i=0, 1, 2, denoting the i-th symmetrical component,
Z ciL —zero, positive, and negative sequence line impedances, and wherein i=0, 1, 2, denoting the i-th symmetrical component,
I Ai —zero, positive, and negative sequence currents measured at the end A, and wherein i=0, 1, 2, denoting the i-th symmetrical component,
γ iL —zero, positive, and negative sequences of line admittance, and wherein i=0, 1, 2, denoting the i-th symmetrical component;
∑
i
=
0
2
a
_
i
(
V
_
Ai
cosh
(
γ
_
iL
d
LA
p
SC
l
)
-
Z
_
ciL
I
_
Ai
sinh
(
γ
_
iL
d
LA
p
SC
l
)
)
·
ⅇ
jδ
A
-
R
FA
∑
i
=
1
2
a
_
Fi
M
_
i
cosh
(
γ
_
iL
(
1
-
d
LA
p
SC
l
)
-
a
_
m
0
d
LA
p
SC
Z
_
0
m
I
_
A
paral_
0
·
ⅇ
jδ
A
=
0
for double-circuit line,
in which:
R FA —denotes an unknown fault resistance, which a value is received using known iterative method by solving the fault loop formula above,
a 1 , a 2 , a 0 , a m 0 —denotes weighting coefficients dependent on fault type,
M i —denote numerical components for positive and negative sequences,
a F0 , a F1 , a F2 —denotes the share coefficients dependent on fault type,
Z 0m —mutual coupling impedance for zero sequence,
I Aparal — 0 —denotes zero sequence current from the station A measured in a healthy parallel line,
V Ai —zero, positive, and negative voltage sequences measured at the end A, and wherein i=0, 1, 2, denoting the i-th symmetrical component,
Z ciL —zero, positive, and negative sequence line impedances, and wherein i=0, 1, 2, denoting the i-th symmetrical component,
I Ai —zero, positive, and negative sequence currents measured at the end A, and wherein i=0, 1, 2, denoting the i-th symmetrical component,
γ iL —zero, positive, and negative sequences of line admittance, and wherein i=0, 1, 2, denoting the i-th symmetrical component,
(A3.) then an equivalent impedance of the SC&MOV at fault stage ( Z SC1 — ph SUB — A ) is calculated from the equation:
Z
_
SC
1
_ph
SUB_A
=
Δ
V
_
SC_ph
SUB_A
I
_
SC_ph
SUB_A
where
:
Δ
V
_
SC_ph
SUB_A
=
a
_
1
Δ
V
_
SC_
1
SUB_A
+
a
_
2
Δ
V
_
SC_
2
SUB_A
+
a
_
0
Δ
V
_
SC_
0
SUB_A
,
I
_
SC_ph
SUB_A
=
a
_
1
Δ
I
_
SC_
1
SUB_A
+
a
_
2
Δ
I
_
SC_
2
SUB_A
+
a
_
0
I
_
SC_
0
SUB_A
,
Δ V SC — ph SUB — A and I SC — ph SUB — A denote the phase quantities of voltage and currents calculated from the i-th symmetrical components of voltage drop and i-th symmetrical component of current entering the SC&MOV bank while neglecting the shunt capacitances of the line,
Δ V SC —i SUB — A = V Bi − V Ai e jδ A −Z iL I Bi +d A ( Z iL I Ai e jδ A +Z iL I Bi ) denotes the i-th symmetrical component of voltage drop across the SCs&MOVs,
I SC — i SUB — A = I Bi denotes i-th symmetrical component of current entering the SC&MOV bank, while neglecting the shunt capacitances of the line,
a 1 , a 2 , a 0 are complex coefficients that depend on fault type and are selected by case type:
in a single-phase to ground fault, the faulted phase, for example, for a phase ‘a’ to ground fault the equivalent impedance of SC&MOV in phase ‘a’ is determined and
in an inter-phase fault, any of the faulted phases, for example, for a phase ‘a’ to phase ‘b’ fault, the equivalent impedance of SC&MOV in phase ‘a’ is determined,
next, an-equivalent impedance of SC&MOV at pre-fault (Z SC1 — pre ) is calculated from the equation:
Z
_
SC
1
_pre
=
Δ
V
_
SC
1
pre
I
_
SC
1
_B
pre
where
:
Δ
V
_
SC
1
pre
=
V
_
SC
1
_B
pre
-
V
_
SC
1
_A
pre
ⅇ
j
δ
A
,
V
_
SC
1
_A
pre
=
cos
h
(
γ
_
1
L
p
SC
l
)
·
V
_
A
1
pre
-
Z
_
c
1
L
sin
h
(
γ
_
1
L
p
SC
l
)
·
I
_
A
1
pre
,
V
_
SC
1
_B
pre
=
cos
h
(
γ
_
1
L
(
1
-
p
SC
)
l
)
·
V
_
B
1
pre
-
Z
_
c
1
L
sin
h
(
γ
_
1
L
(
1
-
p
SC
)
l
)
·
I
_
B
1
pre
,
I
_
SC
1
_B
pre
=
-
1
Z
_
c
1
L
sin
h
(
γ
_
1
L
(
1
-
p
SC
)
l
)
·
V
_
B
1
pre
+
cos
h
(
γ
_
1
L
(
1
-
p
SC
)
l
)
·
I
_
B
1
pre
,
in which:
Z c1L denotes the characteristic impedance of the line for the positive sequence, and
γ 1L denotes the propagation constant of the line for the positive sequence, in order to determine the final result (d A ) which is chosen in the following steps:
first, check whether the fault resistances (R FA ) is of positive value and if not, then subroutine I is rejected,
next, features “real” and “imag” of the estimated equivalent circuit, ( Z SC1 — ph SUB — A ), of the SC&MOV is checked for the following dependency:
real( Z SC1 — ph SUB — A )>0,
imag( Z SC1 — ph SUB — A )<0,
and imag( Z SC1 — ph SUB — A )>imag( Z SC1 — pre )
and if the above dependency is met, then it is determined that the fault has occurred between the station A and the SC&MOV and the result (d A ) indicates the distance to fault, and the information about the real fault case is supplied to fault locator FL,
wherein subroutine II comprises the following steps:
(B1.) determining a synchronization angle (δ B ) in term (e jδ B ) for a known type of fault which is phase-to-ground faults or phase-to-phase faults from the formula:
[
ⅇ
jδ
B
]
ph
-
g
,
ph
-
ph
=
a
_
F
2
I
-
SET
I
_
SC
2
_A
-
a
_
F
1
II
-
SET
I
_
SC
1
_A
a
_
F
1
II
-
SET
N
_
B
1
-
a
_
F
2
I
-
SET
N
_
B
2
where:
a F2 I-SET , a F1 II-SET —denote coefficients dependent of fault type,
I SC1 — A —denotes positive sequence current from the station A after analytical transfer towards the SC&MOV,
I SC2 — A —denotes negative sequence current from the station A after analytical transfer towards the SC&MOV,
N B1 , N B2 —denote coefficients dependent on positive and negative sequence currents and voltage taken at station B respectively as well as parameters of the one or more power transmission lines, and
for faults not being the phase-to-ground faults or phase-to-phase faults from the formula:
ⅇ
-
jδ
B
=
(
1
+
Z
_
1
B
Y
_
1
B
)
(
Y
_
1
B
V
_
B
1
pre
-
I
_
B
1
pre
)
+
Y
_
1
B
V
_
B
1
pre
(
1
+
Z
_
1
A
Y
_
1
A
)
(
I
_
A
1
pre
-
Y
_
1
A
V
_
A
1
pre
)
-
Y
_
1
A
V
_
A
1
pre
where:
V A1 pre , V B1 pre —denote pre-fault positive sequence quantities of voltage measured at the ends A and B, respectively,
I A1 pre , I B1 pre —denote pre-fault positive sequence quantities of current measured of the faulted one or more power transmission lines at the ends A and B, respectively,
Z 1A , Y 1A —denote impedance and admittance, respectively, of line section LA,
Z 1B , Y 1B —denote impedance and admittance, respectively, of line section LB,
(B2.) then taking into account the distributed parameter line model and solving the formula:
d B =(1 −p SC ) d LB
where:
(1−p SC )—denotes a distance (p.u.) per unit of total line length l, at which the SC&MOV is installed in the transmission line from the station B,
d LB —denotes a hypothetical distance to fault, expressed in relation to length (1−p SC l) and which value is received using known iterative method by solving the fault loop formula:
∑
i
=
0
2
a
_
i
(
V
_
Bi
cosh
(
γ
_
iL
d
LB
(
1
-
p
SC
)
l
)
-
Z
_
ciL
I
_
Bi
sinh
(
γ
_
iL
d
LB
(
1
-
p
SC
)
l
)
)
·
ⅇ
jδ
B
-
R
FB
∑
i
=
1
2
a
_
Fi
M
_
i
cosh
(
γ
_
iL
(
1
-
d
LB
)
(
1
-
p
SC
)
l
)
=
0
for single line,
∑
i
=
0
2
a
_
i
(
V
_
Bi
cosh
(
γ
_
iL
d
LB
(
1
-
p
SC
)
l
)
-
Z
_
ciL
I
_
Bi
sinh
(
γ
_
iL
d
LB
(
1
-
p
SC
)
l
)
)
·
ⅇ
jδ
B
-
R
FB
∑
i
=
1
2
a
_
Fi
M
_
i
cosh
(
γ
_
iL
(
1
-
d
LB
)
(
1
-
p
SC
)
l
)
-
a
_
m
0
d
LB
(
1
-
p
SC
)
Z
_
0
m
I
_
Bparal_
0
·
ⅇ
jδ
B
=
0
for double-circuit line
where:
V Bi denotes the zero, positive and negative sequence of voltage, respectively, measured at the end A, and wherein i=0, 1, 2 denotes the i-th symmetrical component,
Z ciL denotes the zero, positive and negative sequence of line impedance, respectively, and wherein i=0, 1, 2 denotes the i-th symmetrical component,
I Bi denotes the zero, positive, and negative sequence currents measured at the end A, respectively, and where i=0, 1, 2 denotes the i-th symmetrical component,
γ iL denotes the zero, positive, and negative sequence of line admittance, respectively, and wherein i=0, 1, 2 denotes the i-th symmetrical component,
R FB —denotes an unknown fault resistance, which a value is received using known iterative method by solving the fault loop formula above,
M i —denote numerical coefficients for positive and negative sequences,
a 1 , a 2 , a 0 , a m 0 —denotes weighting coefficients dependent on fault type,
a F0 , a F1 , a F2 —denotes share coefficients dependent on fault type,
Z 0m —mutual coupling impedance for zero sequence,
I Bparal — 0 —denotes zero sequence current from the station B measured in a healthy parallel line,
(B3.) then an equivalent impedance of the SC&MOV at fault stage (Z SC1 — ph SUB — B ) is calculated using post fault measured voltage and currents from the equation:
Z
_
SC
1
_ph
SUB_B
=
Δ
V
_
SC_ph
SUB_B
I
_
SC_ph
SUB_B
and an equivalent impedance of SC&MOV bank at pre-fault (Z SC1 — pre ) is calculated from the equation:
Z
SC
1
_pre
=
Δ
V
_
SC
1
pre
I
_
SC
1
_B
pre
where
:
Δ
V
_
SC
1
pre
=
V
_
SC
1
_B
pre
-
V
_
SC
1
_A
pre
ⅇ
j
δ
A
,
V
_
SC
1
_A
pre
=
cos
h
(
γ
_
1
L
p
SC
l
)
·
V
_
A
1
pre
-
Z
_
c
1
L
sin
h
(
γ
_
1
L
p
SC
l
)
·
I
_
A
1
pre
,
V
_
SC
1
_B
pre
=
cos
h
(
γ
_
1
L
(
1
-
p
SC
)
l
)
·
V
_
B
1
pre
-
Z
_
c
1
L
sin
h
(
γ
_
1
L
(
1
-
p
SC
)
l
)
·
I
_
B
1
pre
,
I
_
SC
1
_B
pre
=
-
1
Z
_
c
1
L
sin
h
(
γ
_
1
L
(
1
-
p
SC
)
l
)
·
V
_
B
1
pre
+
cos
h
(
γ
_
1
L
(
1
-
p
SC
)
l
)
·
I
_
B
1
pre
,
Zc1L denotes the characteristic impedance of the line for the positive sequence,
γ 1L denotes the propagation constant of the line for the positive sequence, in order to determine the final result (d B ) which is chosen in the following steps:
first, check whether the fault resistances (R FB ) is of positive value and if not, then subroutine II is rejected,
next, features “real” and “imag” of the estimated equivalent circuit of the SC&MOV is checked for the following dependence:
real( Z SC1 — ph SUB — B )>0,
imag(Z SC1 — ph SUB — B )<0
and imag( Z SC1 — ph SUB — B )>imag( Z SC1 — pre ),
then it is determined that the fault has occurred between the station (B) and the SC&MOV and the result (d B ) indicates the distance to fault, and the information about the real fault case is supplied to fault locator FL.
2. A protection relay equipped with a fault locator comprising means for performing the steps of claim 1 .