A Study on the Effect of Distributed Generation on
Short-Circuit Current
Insu Kim
Ronald G. Harley
Electrical Engineering
Alabama A&M University
Normal, AL, 35711, USA
insu.kim@aamu.edu
Electrical and Computer Engineering
Georgia Institute of Technology, Atlanta, GA, USA
Professor Emeritus at the University of KwaZulu-Natal in
South Africa, rharley@ece.gatech.edu
Abstract-In short-circuit studies, phase shifts in transformers
and insisted that transformers connected in different ways
have a significant impact on fault current [11]. Another recent
study discussed the accuracy of transformer models presented
from the Alternative Transients Program that shift phases in
positive- and negative-sequence networks [12]. However,
these studies have not analyzed distribution networks not only
heavily or weakly meshed but also enhanced by DG resources
with relatively high capacity (e.g., 30 and 50 percent). Thus,
the objective of this study is (a) to present an accurate short­
circuit analysis algorithm able to calculate the magnitude and
the phase angle of fault current in meshed or radial networks,
including phase shifts through transformers, and (b) to analyze
the effect of not only various capacities (e.g., 10, 30, and 50
percent) of DG resources but also various locations of faults
on current that flows during the short circuit.
(e.g., connected in wye-delta or vice versa) make difficult to
calculate fault current flowing in sequence-component networks.
Therefore, they are often ignored because the magnitude of fault
current is much more of interest than phase angles from the
protection point of view (e.g., overcurrent relays). As high­
capacity
distributed
deployed
into
generation
direction
and the phase
distribution
(DG)
networks,
angle
resources
they
may
are
being
change
the
of fault current and cause
abnormal operations of directional or distance relays. Thus, the
objective of this paper is to develop a short-circuit analysis
algorithm able to (a) calculate changes in phase shifts caused by
transformers in
sequence
networks
with high-capacity DG
sources and (b) analyze the effect of not only various capacities
(e.g., 10, 30, and 50 percent) of DG resources but also various
locations of faults on current that flows during a short circuit.
To verify the developed algorithm, using MATLAB, case studies
that generate a single line-to-ground fault on (a) the high- and
low-voltage
sides
and
(b)
a
weakly
meshed
network
are
presented.
Index
Terms-Distributed
generation
(DG),
phase
shift,
sequence network, short circuit, and single line-to-ground fault.
I.
INTRODUCTION
As high-capacity distributed generation (DG) resources
such as small-scale synchronous generators, solar, and wind
farms are being deployed into distribution networks, they may
change current that flows during a short circuit or an electrical
fault. Thus, many studies have presented various methods for
short circuit studies, which can be classified by the following
three methods:
(1) solving sequence networks using symmetrical components
[1-3],
(2) iterative compensation methods using bus admittance
matrices [4, 5],
(3) iterative compensation methods using bus impedance
matrices [6-9].
However, these study ignored phase shifts through
transformers since the magnitude of fault current is much
more of interest than phase angles from the protection point of
view (e.g., overcurrent relays). To examine phase shifts of
transformers, a study presented a mathematical model and
graph theory (which is referred to as a V-equivalent) of the
delta-wye transformer that shift phases [10]. Another study
modeled the transformer and the load in short circuit analysis
978-1-5090-0687-8/16/$31.00 ©2016
IEEE
This paper is organized as follows: Section 2 describes a
problem statement, and Section 3 presents the short-circuit
theory for analyzing phase shifts of transformers and meshed
networks. Section 4 provides a flowchart of the implemented
short-circuit analysis algorithm. Section 5 introduces case
studies for calculating short-circuit current using the proposed
algorithm. Section 6 summarizes major conclusions of this
study.
II.
PROBLEM STATEMENT
If a fault occurs on an external line of a distribution system
with high-capacity DG resources, fault current flowing from
DG resources will flow to the faulted line, which is a reverse
direction when compared to the case without DG resources.
Furthermore, since phase angle changes in fault current caused
by DG resources may affect the protection coordination of
directional or distance relays, they should not be ignored.
Thus, this study is to develop a short-circuit analysis algorithm
able to calculate a phase angle of fault current, including phase
shifts through transformers. For this purpose, it applies a
phase-shifting method to positive- and negative-sequence
networks. In addition, this study changes the capacity of DG
resources and fault locations in a case study in order to
examine their effect on the magnitude of fault current.
III.
SHORT-CIRCUIT STUDY
A. Current of a Single Line-to-Ground Fault
In the circuit theory, a power system network with n nodes
can be expressed by currents injected at nodes and voltages
induced at nodes with regard to the reference:
V=Zb,J,
(l)
where Zbus is referred to as the bus impedance matrix.
The bus impedance matrix is useful to find the fault current.
For example, if the phase a of line i is faulted to the ground,
single line-to-ground (SLG) fault currents of zero, positive,
and negative sequences are given by
I o =I I =I 2 =
VJ
'
Zo(i, i)+ZI(i, i)+Z2(i, i)+3Zr
(c) Zero sequence
Fig. I. Equivalent sequence networks of a transformer connected in delta­
grounded wye.
C. Meshed Topology
(2)
where
10, hand h = zero-, positive-, and negative-sequence currents
of faulted bus or line i, respectively,
V;= prefault voltage of Thevenin's equivalent voltage source
in the positive-sequence network (typically lLO° PU),
Zo(i, i) , ZI (i, i) , and Z2(i, i) = zero-, positive-, and negative­
sequence open-circuit driving-point impedances of faulted bus
or line i in bus impedance matrices, respectively,
Zr= fault impedance.
The fault current If of line i is
IJ =310 =311 =312,
Fig. 2 presents a meshed topology consisting of four buses
and branches, which can be used to increase the reliability of
distribution systems by adding switches between the branches
or lines. In the short-circuit study, if (a) each branch or line
has an impedance of ideally 0 and (b) a fault occurs on one of
the branches or buses, currents flowing through each branch
cannot be calculated from the Ohm's equation (e.g.,
I2.I=VdZ2/, but the impedance of Z2/ is 0). Therefore, this
study applies the Kirchhoffs Current Law (KCL) to the
meshed topology. For example, if a fault occurs on bus 3 in
Fig. 2, currents flowing through the branches is determined by
the following KCL:
[ 1j
I I. 3
o 1
0 /2•1
12
1 0
0 1 12•4
IF - 13
o 0 -1 1 �3
�
where Ii,j = the current that flows from buses ito j,
1
(3)
B. Representation of Transformers in Sequence Networks
In short-circuit studies, since the main concern of which is
usually the magnitude of fault current, phase shifts through
transformers are often ignored. In other words, transformers
are replaced by simply zero-, positive-, and negative-sequence
impedances. To examine such phase shifts of transformers,
Fig. 1 illustrates a method that shifts phases between two
buses in positive- and negative-sequence networks in the case
of a transformer connected in delta-grounded wye. In the
positive-sequence network of the transformer balanced in
three phases, a phase of +30° will be shifted from buses ito j,
shown in (a). The negative sequence shifts by -30°.
-1
0
0
(4)
Ii = the current incoming to or outgoing from bus i.
Since It, h h h and IF can be determined by solving the
sequence networks, the currents flowing through branches,
(e.g., 12, 1 ) can be found by an inverse transformation of (4).
Fig, 2, 4-bus meshed topology [13].
(a) Positive sequence
IV.
IMPLEMENTATlON OF THE SHORT-CIRCUIT ANALYSIS
ALGORITHM
Using MATLAB, this study implements an algorithm that
(a) builds bus impedance matrices for positive-, negative-, and
zero-sequence networks, (b) calculates SLG fault current, and
(c) applies the proposed phase-shifting method to sequence
networks. This study used the four rules presented in [1] in
order to build the bus impedance matrix. Fig. 3 presents a
(b) Negative sequence
flowchart of the developed short-circuit algorithm, which will
be verified in the following case studies.
V.
A.
CASE STUDY
A Distribution Network with DG
In Fig. 4, this study presents a case study of the
distribution system with a DG source in order to (a) verify the
proposed algorithm that calculates phase shifts through
transformers, (b) evaluate changes in fault current when a fault
occurs on either high- or low-voltage sides, and (c) examine
the effect of the capacity of DG and the location of faults on
fault current. For this purpose, this study initially generates a
SLG (single line-to-ground) fault on the high-voltage side of
the distribution system, phase a of feeder 1, and on the low­
voltage side, feeder 2. A fault impedance, Zf, of 0 is assumed
and a synchronous generator with a capacity of 10 MVA,
which is 10 percent of a total generation capacity of 100 MVA,
is used as an example of a DG source. In this case study, load
current is ignored because it is often negligible when
compared to large fault current. Then, this study builds bus
impedance matrices according to the steps presented in Fig. 3,
decomposes the distribution system into zero-, positive-, and
negative-sequence networks, shown in Fig. 5, and applies
phase shifts of transformers to positive- and negative­
sequence networks. Finally, it calculates fault current flowing
from a faulted line to the ground.
Fig. 5. Equivalent sequence network of the distribution system after a SLG
fault occurs on feeder 1.
TABLE I to TABLE IV show fault currents after a SLG
fault. If a SLG fault occurs on the high-voltage side (feeder 1)
of the distribution system with a lO-MW synchronous
generator, a current of 1.4489L-47.04° PU in phase a flows to
the ground. But if the same type fault occurs on the low­
voltage side of the distribution system, feeder 2, a current of
1.2128L-85.34° PU flows, which is lower than 1.4489L47.04° pu. That is, in the distribution system with DG
sources, a SLG fault close to the substation seems to increase
the magnitude of fault current. Next, the proposed algorithm
calculates phase shifts, particularly 30°, in voltage and current
of transformers balanced in delta-grounded wye or vice versa,
in positive- and negative-sequence networks, which can be
seen in the columns of hh VI, and V2 of each table. Note that
* sign in the Bus column of TABLE II and TABLE IV
indicates a current direction. For example, "Generator*-7 Bus
S" indicates a line current outgoing from the generator, which
does not contain phase shifts through the delta-wye
transformer.
Bus
Generator
BusS
Feeder I
(Fault)
BusR
Feeder 2
DG
Fig. 3. A flowchart of the developed short-circuit analysis algorithm.
Fig. 4. A distribution system with a synchronous generator at the end.
Bus
Generator*
�BusS
BusS*
� Feeder I
Feeder 1*
� Fault
BusR*
� Feeder 2
Feeder 2*
�BusR
DG'
� Feeder 2
TABLE T PHASE VOLTAGES AFTER A FAULT ON FEEDER I
Volta e in PU
Phase A
Phase B
Phase C
V,(Zero) v 1 (Positive) V,(Negative)
OLO°
lLO°
OLO°
ILO°
IL-120°
IL120°
L-21.26°
L-149.41°
L89.74°
L-136.59°
L27.76°
L-135.0Io
L-155.38°
L96.78°
L-152.02
L29.40°
L-148.53°
L-18.62°
L-144.27°
L83.81°
L-137.52
L28.38°
L-145.18°
LI4.81°
L-120.00°
LI08.42°
L-1.l5°
L-1l5.18°
0.6343
OLO°
0.3683
0.7495
ILO°
1.0008
1.0895
0.9399
1.0000
IL-120.00°
0.9907
1.0535
0.9567
0.7109
ILI20.00°
0.1219
0.4208
0.1405
OLO°
OLO°
0.8735
0.7103
0.7494
0.8072
ILO°
0.1317
0.2898
0.2518
0.1937
OLO°
TABLE IT LINE CURRENTS AFTER A FAULT ON FEEDER I
Current in PU
1,(Zero)
Phase A
Phase B
Phase C
I, (positive) h(Negative)
0.6709
0.6709
OLO°
L-45.0Io
LI34.99°
L-45.39°
LI37.82°
LI37.82°
OLO°
OLO°
1.0235
1.4489
L-47.04°
0.4269
0.1388
0.1388
L-50.99°
L-42.18°
L-55.18°
LI24.82°
L-55.18°
LI24.82°
0.1677
0.1677
0.1677
0.1677
OLO°
0.3873
0.3873
L-75.0Io
L-15.0Io
L-46.59°
L-45.0Io
L-45.0Io
L-47.04°
L-47.04°
L-47.04°
L-42.18°
L-47.52°
L-55.18°
L-55.18°
OLO°
OLO°
L-85.18°
L-25.18°
OLO°
OLO°
L-85.18°
L-25.18°
0.1388
0.1388
0.2488
0.4830
0.2341
0.3873
0.4830
0.0968
0.0968
0.0968
0.3873
0.4830
0.0968
0.0968
0.0968
Fig, 6. Flows of fault currents after a single line-to-ground fault on feeder 1,
Bus
Generator
TABLE TIT PHASE VOLTAGES AFTER A FAULT ON FEEDER2
Volta e in PU
Phase A
Phase B
Phase C
Vo(Zero) V,(Positive) V,(Negative)
BusS
Feeder I
(Fault)
BusR
ILO°
0,8811
L-32,83°
0,7813
L-144,80°
0,7592
ILI20,00°
1,0000
L90,00°
1,0000
L-140.49°
L90,00°
L-52,23°
L-134,18°
L90,00°
L-I13.44°
LI12,04°
0,7038
OLO°
DG
ILO°
Bus
0,9060
L-41.44°
Feeder 2
Generator*
�BusS
BusS*
� Feeder I
Feeder 1*
�BusR
BusR*
� Feeder 2
Feeder 2*
� Fault
DG*
� Feeder 2
IL-120,00°
0,6186
0,9117
IL-120,00°
1.0000
0,9662
ILI20,00°
OLO°
OLO°
OLO°
OLO°
0,2426
L-175,34°
OLO°
ILO°
0,9275
OLO°
0,0737
L29,21°
LI60,04°
L30,67°
LI46,52°
L32.49°
LI42,62°
LO,91°
L178,5JD
0,8382
0,7496
0,6210
ILO°
0,1621
0,2532
0,3793
OLO°
TABLE TV LINE CURRENTS AFTER A FAULT ON FEEDER 2
Current in PU
lo(Zero)
Phase A
Phase B
Phase C
l,(posilive) h(Negative)
0.4333
L-79,96°
0,3753
L-79,95°
0,3753
L-79,95°
0,3753
L-79,95°
1.2128
L-85,34°
0,7824
L-88,32°
0,2167
LI00,04°
OLO°
OLO°
OLO°
OLO°
0,2167
L-79,96°
0,2167
LI00,04°
0,3753
LI00,05°
0,3753
LI00,05°
0,3753
LI00,05°
OLO°
0,2167
L-79,96°
OLO°
0,2167
0,2167
L-79,96°
L-79,96°
L-49,95°
L-109,95°
L-49,95°
L-109,95°
L-49,95°
L-109,95°
L-85,34°
L-85,34°
L-85,34°
L-85,34°
L-91.49°
L-91.49°
OLO°
OLO°
OLO°
0.4043
0.4043
0,2167
0,2167
0,2167
0.4043
0,1896
0,2167
impedance compared to the substation in the case of SO
percent DG, the magnitude of current caused by a fault
occurred close to the DG source is greater than that caused by
a fault close to the substation. For example, the substation has
jO.34 PU of positive-sequence impedance and j0.49 PU (zero­
sequence) but SO percent DG has jO.4 PU (positive-sequence)
and jO.12 PU (zero-sequence). If a fault occurs on feeder 2 in
the case of SO percent DG, an equivalent impedance of the
zero-sequence network is only jO. l2 Pu. Therefore, it shows
the highest magnitude of fault current in all the cases. In
addition, in the all cases, the higher capacity a DG source has,
fault current with the higher magnitude flows. Note that in the
case of without DG, the fault location of feeder 2 was moved
to the secondary side of the grounded wye-delta transformer in
Fig. 4, (to avoid that fault current does not flow in the case of
a fault on feeder 2 of the test feeder without DG because the
side of the DG source is open in the zero-sequence network).
0,2167
0,2167
0.4043
0,1896
Fig. 6 shows fault currents that flow in each phase of the
distribution system after a single SLG fault occurs on feeder 1.
A fault current of 6,708.28L-47.04° A, which is the
summation of currents flowing from the substation,
4,738.S1L-4S.39° A, and the DG source, 1,976.42L-SO.99°,
flows to the ground. Since this study assumes a DG source
with a capacity of 10 MVA at 0.38 kV, a large fault current of
2S,486.11L-SS.18° A flows from the distributed generator.
In the previous case study, this study fixed the capacity of
a DG source to 10 percent of a total generation capacity of 100
MVA. To examine the effect of not only varying capacities of
DG resources but also the location of faults on the magnitude
of fault current, this study changes not only the capacity of
DG resources in a range of 10 MW (10 percent) to SO MW (SO
percent) but also fault locations. Fig. 7 shows the trends in the
magnitude of fault currents. In the cases of without DG and 10
percent DG, if a SLG fault occurs close to the substation (e.g.,
Bus S), the magnitude of fault current is greater than that
caused by a fault occurred far from the substation (e.g., Feeder
2). However, since the DG source has relatively low
Fig, 7. Fault currents when capacities of a DG source and locations of a fault
are varying.
B.
Meshed Network
To verify the proposed algorithm that analyzes faults
occurring on the meshed network, this study presents a case
study of the IS-bus meshed distribution system in Fig. 8 and
generates a SLG fault on bus 13 of the network. TABLE V
shows the results of fault currents of each branch with an
impedance of 0, calculated from equation (4). Note that h=
h.13 + 115,13 + 113 . In this case study, load current is also
ignored.
ground, and three-phase faults. In addition, this study did not
analyze sufficiently large distribution networks. However, the
developed algorithm can be extended for such cases by taking
into account of load current, implementing the other fault
types, and modeling large distribution networks, all of which
are still our future work.
REFERENCES
[1]
[2]
[3]
Fig. 8. A meshed IS-bus distribution network.
TABLE V LINE CURRENTS AFTER A SLG FAULT OCCURS ON Bus 13
Current in PU
Bus
Phase Phase
Phase A
lo(Zero)
[,(Positive)
h(Negative)
B
C
OLO°
OLO°
0.0078L-58.96°
0.0078L-58.96°
0.0026L-58.96°
0.0026L-58.96°
,7
19
0.0078L-58.96° OLO° OLO° 0.0078L-58.96° 0.0026L-58.96° 0.0026L-58.96°
19.15
0.0233L-58.96° OLO° OLO° 0.0233L-58.96° 0.0078L-58.96° 0.0078L-58.96°
1,.13
115.13 0.0233L-58.96° OLO° OLO° 0.0233L-58.96° 0.0078L-58.96° 0.0078L-58.96°
0.0155L-58.96° OLO° OLO° 0.0155L-58.96° 0.0052L-58.96° 0.0052L-58.96°
1/3
0.062IL-58.96° OLO° OLO° 0.0621L-58.96° 0.0207L-58.96° 0.0207L-58.96°
IF
VI.
CONCLUSION
The main objective of this study is to develop a short­
circuit analysis algorithm able to (a) calculate phase shifts of
transformers in sequence networks and (b) analyze the
behavior of fault current of distribution systems enhanced by
DG resources. For this purpose, this study has applied a phase­
shifting method to positive- and negative-sequence networks
and has presented case studies in which the capacity of DG
resources and fault locations are changed. The results from the
case studies show that in a distribution system with low­
capacity DG sources (e.g., less than or equal to 10 percent of
total generation capacity), if a SLG fault occurs close to the
substation, the magnitude of fault current can be greater than
that caused by a fault occurred far from the substation.
However, if the DG source has relatively low impedance when
compared to the substation, in a distribution system with high­
capacity DG sources (e.g., 30 and 50 percent), the magnitude
of current caused by a fault occurred close to the DG source
can be greater than that caused by a fault occurred close to the
substation. Finally, the proposed algorithm has calculated
phase shifts, particularly 30°, in voltage and current of
transformers balanced in delta-grounded wye or vice versa in
positive- and negative-sequence networks, including a meshed
network.
Although this study presented a short-circuit analysis
algorithm able to analyze a SLG fault on the distribution
system with DG sources, it ignored load current (because it is
negligibly lower than fault current) and did not implement the
other fault types such as double line-to-line, double line-to-
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