Download A Method to Enhance Ground

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IEEE PES Letters
A Method to Enhance Ground-Fault Computation
Shyh-Jier Huang, Senior Member, IEEE, and Hsing-Ho Wan
Abstract—This letter presents a simple criterion for reviewing
balanced three-phase fault and unbalanced ground-fault current
using the ratio of zero sequence impedance to positive sequence
impedance as seen from the fault location, which can be employed
to enhance the power system design and protection. The method
has been verified by real power systems in Taiwan with
satisfactory results.
Index Terms—Balanced three-phase
ground-fault, sequence impedance.
fault,
unbalanced
A
A
B
B
C
C
Ib
Ia
Ia
Ic
Zf
(a)
(b)
Fig. 1 The unbalanced ground fault (a) single line-to-ground fault (b) double
line-to-ground fault
A
A
B
B
HORT circuit faults in a power system include single
line-to-ground (SLG), line-to-line (LL), double
line-to-ground (DLG), and three-phase short-circuit
(3SC). Among these types of faults, the SLG occurs most often
while the 3SC is commonly deemed the most severe one with
largest magnitude of fault current, significantly influencing the
decision on the equipments and protective relays setting for
power system planning and operation. However, exceptions do
exist. The magnitude of SLG current may exceed 3SC current
when they occur in the vicinity of a solidly grounded machine or
transformer [1]-[2]. Meanwhile, since a ground fault would
cause a voltage shift between neutral and ground, the voltage
insulation of neutral needs to evaluate more prudently. In this
letter, a fast measure is proposed to investigate the relationships
among unbalanced ground fault, balanced three-phase fault, and
neutral voltage shift, anticipating serving as a more reliable
design for power systems protection.
C
C
II. PARADIGM AND METHODOLOGY
The symmetrical components analysis is an effective way to
evaluate an unbalanced system by using positive, negative, and
zero sequence impedances seen from the fault point. Fig. 1
shows unbalanced ground faults, including single
line-to-ground and double line-to-ground fault. In the figure, the
SLG current in term of sequence impedances can be expressed
as
I SLG =
3
Z1 + Z 2 + Z 0
where Z1 , Z2 , and Z0 are positive, negative, and zero sequence
impedances in ohms per phase. By neglecting fault
impedance Zf as well as assuming Z1=Z2 [3], (1) can be
rewritten as
I SLG
 1 
3 
Z
=  1
Z 
2+ 0 
 Z1 
Zf
(2)
The authors are with the Department of Electrical Engineering, National
Cheng Kung University, Tainan, Taiwan, R. O. C.
Ib
Ia
Ic
Zf
Ib
Ia
Ic
(a)
(b)
Fig. 2 The balanced three-phase fault (a) short-circuit without ground (b)
short-circuit with ground
The expressions in (1) and (2) are the per-unit currents by
assuming that voltage is one per-unit at the fault point. Next, for
a balanced three-phase fault, Fig. 2 depicts a short circuit
connected with and without the ground. The ratio of SLG
current to 3SC current can be expressed as
I SLG
=
I 3SC
3
Z 
2+ 0 
 Z1 
(3)
The voltage shift between neutral and ground is accordingly
derived to be equal to zero-sequence voltage [4], hence the
following equation is written
 Z0 


Z
V0
=  1
VN
Z 
2+ 0 
 Z1 
(4)
where VN is the phase-to-neutral voltage in the system. Similarly,
the ratio of the magnitude of DLG to 3SC becomes
I DLG
=
I 3SC
(1)
Ic
Zf
I. INTRODUCTION
S
Ib
3
Z
1+ 2 0
 Z1
2
Z  Z 
×  0  +  0  +1

 Z1   Z1 


(5)
Meanwhile, the neutral voltage shift can be expressed as
 Z0 


V0
 Z1 
=
VN
Z 
1+ 2×  0 
 Z1 
(6)
Equations (3)-(6) illuminate the relationships of currents and
neutral voltage shift under unbalanced ground fault scenario
using the ratio of Z0 to Z1 . Note that since the resistance values
can be neglected for fault current calculations in real power
systems, impedances are approximately seen as inductance in
IEEE PES Letters
this study. Fig. 3 delineates the graphical relationships. From
the plot of Fig. 3 (a), contrary to the common knowledge that
three-phase fault is the worst possible case, the magnitudes of
unbalanced ground fault currents are occasionally larger than
those of I 3SC . It seems only when X0 becomes larger than X1 ,
then unbalanced ground fault currents would be smaller than
three-phase fault ones [5]. This observation is very beneficial to
determine the interrupt capacity of breakers. Meanwhile,
through the investigation of neutral voltage shift as Fig. 3(b)
plots, when the condition of X0/X1=3 is encountered [6], the
neutral voltage shifts of SLG and DLG is 0.6 and 0.428 per unit,
respectively.
1
1.5
DLG / 3SC
1
SLG / 3SC
0.5
0
0 1 2 3 4 5 6 7 8 9 10
X0/X1
Ratio of Voltages (pu)
2
Ratio of Currents (pu)
1
2
3
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0.8
0.6
Vo/Vn (SLG)
0.4
Vo/Vn (DLG)
0.2
0
0 1 2 3 4 5 6 7 8 9 10
X0/X1
taking that SLG fault currents may be larger than 3SC ones into
consideration, this letter suggests that a simple condition of
X0/X1>1may consider to add.
TABLE I: SEVERAL LOCATIONS WITH I3SC>ISLG IN TAIPOWER SYSTEM (2008)
Single
Three-Phase
Impedance Ratio
Line-Ground
Location
Fault Current
ISLG
V0
R0/X1
X0/X1
I3SC(kA)
(kA)
(kV)
Nantou E/S
33.73
31.08
35.9
0.141
1.249
Tienlun E/S
37.93
32.41
40.0
0.236
1.491
Ermei E/S
46.83
44.80
33.6
0.124
1.128
Renwu E/S
42.28
38.89
36.0
0.126
1.257
Nangkang P/S
34.55
31.91
35.9
0.211
1.236
Hsinchu P/S
35.57
28.50
43.3
0.319
1.716
Tainan P/S
31.71
22.18
49.6
0.486
2.238
Wujia P/S
39.70
28.99
47.7
0.333
2.083
Yingtsai D/S
38.34
37.07
33.2
0.226
1.085
Sanju D/S
25.22
21.82
39.4
0.213
1.455
Hsiaobei D/S
26.71
20.88
44.6
0.355
1.806
Kenting D/S
8.19
5.72
49.3
0.403
2.243
REMARKS: TAIPOWER REQUIRES THE EFFECTIVE GROUNDING SATISFY R0/X1<1
AND X0/X1<3
TABLE II: LOCATIONS WITH I3SC<ISLG IN TAIPOWER SYSTEM (2008)
Single
Three-Phase
Impedance Ratio
Line-Ground
Location
Fault Current
ISLG
V0
R0/X1
X0/X1
I3SC(kA)
(kA)
(kV)
(a)
(b)
Fig. 3 Relationships in term of X0/X1 (a) Unbalanced ground faults and
balanced three-phase fault currents. (b) Neutral voltage shifts.
III. REAL CASES VALIDATION
To validate the effectiveness of the method, this study has
employed the approach to analyze the fault current data
recorded at Taipower in the year of 2008. Both SLG and 3SC
faults occurred at 161 kV side of primary transmission system
have been extensively surveyed. Table I and II list the fault data,
where E/S, P/S and D/S individually stand for extra
high-voltage, primary, and distribution substations. From the
list of Table I, it indicates that 3SC currents are larger than SLG
ones at most locations; yet from that of Table II, the recorded
data at seven substations have demonstrated different features in
which 3SC are smaller than SLG. Next, with a closer
observation, all ratios of X0/X1 in Table 2 are found to be
smaller while those of X0/X1 in Table 1 are larger than one. This
outcome implies that the ratio of X0/X1 could serve as a useful
indicator as all of cases tested in Taipower come with no
misidentification found. In the mean time, this proposed method
has been applied to compute neutral voltage shifts. Consider a
SLG fault occurred at 161 kV side of Sijhih E/S in Table II as an
example. By substituting the value of X0/X1 into (4), the
magnitude of neutral voltage shift is computed to be
0.946/(2+0.946)= 0.3211 per unit, meaning that the calculated
value is equal to 29.84 kV in terms of 161/ 3 kV base. This
computed value is very close to the on-site measure of 29.9 kV
listed in Table II, further confirming the feasibility and
practicality of the method.
IV. CONCLUSION
Inspection of effective grounding is always an important task
from the perspectives of scheduled maintenance of utilities. In
practice, the conditions of R0/X1< 1 and X0/X1< 3 are often
recommended to justify the effective grounding. However, by
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Sijhih E/S
36.33
36.96
29.9
0.083
0.946
Banciao E/S
35.59
36.13
30.1
0.122
0.949
Jongke E/S
19.69
19.74
30.8
0.078
0.989
Hsingyi E/S
12.61
13.07
28.7
0.031
0.892
Hsinmin D/S
29.74
30.41
29.6
0.189
0.914
Jingsing D/S
32.12
33.17
29.1
0.148
0.896
Hserho D/S
30.07
31.14
28.8
0.172
0.880
In other words, rather than solely adopt the conditions of
X0/X1<3, it may be more prudent to express the conditions as
1<X0/X1<3 when the effective grounding is performed. Besides,
the letter has concluded that for effective grounding system, the
neutral voltage shift can only reach 0.6 per unit at most. These
test results are beneficial to enhance the short-circuit fault
computation, anticipating that the forewarning signals can be
flagged at an early stage such that system damage can be more
effectively restricted.
V. ACKNOWLEDGMENT
The authors are greatly indebted to technical assistance from
System Operation Department in Taiwan Power Company.
[1]
[2]
[3]
[4]
[5]
[6]
REFERENCES
IEEE Recommended Practice for Industrial and Commercial Power
Systems Analysis, IEEE Std. 399, 1997.
M. Mitolo, “Grounding the Neutral of Electrical Systems through
Low-Resistance Grounding Resistor: An Application Case,” IEEE Trans.
Ind. Appl., vol. 44, no. 5, pp. 1311-1316, Sep./Oct. 2008.
Paul M. Anderson, Analysis of Faulted Power Systems, IEEE Power
System Engineering Series, Piscataway, NJ: IEEE Press, 1995.
J. Lewis Blackburn, Symmetrical Components for Power Systems
engineering. New York: M. Dekker, c 1993.
M. J. Lantz, "Analysis of Fault Currents for High-Voltage Circuit-Breaker
Interruption," AIEE Trans. PAS, vol. 74, no. 3, pp. 41-45, Jan. 1955.
IEEE Recommended Practice for Grounding of Industrial and
Commercial Power Systems, IEEE Std. 142, 2007.