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IEEE TRANSACTIONS ON POWERDELIVERY, VOL. 23, NO. 1, JANUARY 2008 347
Fault Distribution Modeling Using Stochastic
Bivariate Models for Prediction of Voltage
Sag inDistribution Systems
Bach Quoc Khanh, Dong-Jun Won, Member, IEEE, and Seung-Il Moon, Member, IEEE
Abstract—This paper presents a new method regarding fault dis-
tribution modeling for the stochasticprediction study of voltage
sags in the distribution system. 2-D stochastic models for fault mod-
eling make it possible to obtain the fault performance for the whole
system of interest, which helps to obtain not only sag performance
at individual locations but also system sag performance through
system indices of voltagesag. By using the bivariate normal dis-
tribution for fault distribu
ti
on modeling,this paper estimates the

Manuscript received August 2, 2005; revised December 5, 2006. This work
was supported by the Korea Foundation for Advanced Studies’ International
Scholar Exchange Fellowship for the academic year of 2004–2005. Paper no.
TPWRD-00456-2005.
B. Q. Khanh iswith the Electric Power System Department, Faculty of Elec-
trical Engineering, Hanoi University of Technology, Hanoi,Vietnam (e-mail:
).
D J. Won iswith the School of Electrical Engineering,
INHA Univ
ersity,
Incheon 402–751, Korea (e-mail: ).
S I. Moon iswith the School of Electrical Engineering and Computer Sci-
ence, Seoul National University, Seoul 151-742, Korea (e-mail: moonsi@plaza.
snu.ac.kr).
Digital Object Identifier 10.1109/TPWRD.2007.905817
information about the voltage sag ismainly obtained by
monitoring and stochastic prediction. With recently advanced
computer-aided simulation tools, the stochastic prediction of
voltage sag becomes the preferable approach that can obtain
the results at required accuracy for various network topologies
and operational conditions.“The method of fault positions”
and “the method of critical distances” are known as the most
widely used methods for stochastic prediction studies.
It is notable that regardless of which method is used, a sto-
chastic prediction study always has to solve two critical
prob-
lems
: 1) the modeling of causes leading to voltage sags and
2) the simulation of the power system for computing voltage sag
characteristics. Among important cause of voltage sags, short-

only one fault position for each distribution transformer and one
fault position for each line segment.
Different fault types should be applied to each fault position
mainly depending on the number of phases available at the se-
lected fault positions. The fault rate of each fault type is nor-
mally referred from the observed historical data.
0885-8977/$25.00 © 2007 IEEE
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348 IEEE TRANSACTIONS ON POWERDELIVERY , VOL. 23, NO. 1, JANUARY 2008
The fault rate mainly depends on fault position, fault type,
and fault cause. While two earlier factors have been discussed
at length in past research, the distribution of the fault rate for
the selected fault positions has received less interest. The most
common assumption that has been argued so far is that because
the fault can occur anywhere in the system, stochastically, it is
possible to model the fault rate as the uniform distribution [3],
[4]. In this sense, the fault rate at each position is identical to
the component failure rate that is based on component relia-
bility. However, in reality, many factors can lead to faults, not
just the component failure, and fault rates at different positions
in
the
system are rarely the same. Recently, a report [5] pro-
posed some interesting 1-D models of fault distribution along
individual line segments (between two nodes). However, this re-
search could not consider the distribution of transformer faults.
Furthermore, by using 1-D fault distribution, it is hard to ob-

of equipment follows the uniform distribution depending on the
equipment type although itstill may cause some errors (e.g., not
all equipment is put into
operation at the same time or has the
same
maintenance conditions).
Besides equipment failure, there are many other causes from
the ambient environment that also may lead to faults in power
systems. This paper calls them the external causes. Some can in-
fluence the fault performance of the power system in a large area
such as severe weather (wind storms, lightning, etc.). Mean-
while, others mainly have local impacts, such as trees and ani-
mals (birds, mice, etc.). Human factors (scheduled interruption,
human errors, mischief, and vandalism) can cause faults that
only influence the power system in small parts as well as se-
vere faults for a large power system. All of these causes occur
randomly and they can be simulated by stochastic models. 1-D
stochastic models seem to not be suitable as explained
before.
Fig. 1.Example of bivariate normal distribution.
This paper proposes the idea of using 2-D stochastic models in-
stead (e.g., the bivariate normal distribution model as illustrated
in Fig. 1).
For large power systems, it is hard to obtain a converged 2-D
fault distribution model for various causes in a large area. How-
ever, for small-to-medium-size networks, such as the section of
distribution network fed from a bulk-point distribution substa-
tion, of which the monitored historical data of fault performance
shows that faults due to external causes occur concentratively on
one location (e.g., some lines pass through a small area which

sumption only neglects voltage sags caused by faults in
the
transm
ission system. It will be considered if the stochastic
prediction of voltage sag in large transmission systems [4]
is included.
• In terms of reliability, the test system is modeled on two
main components: lines and distribution transformers. The
reliability of any other distribution equipment is suppos-
edly included in the reliability of these two components.
• The fault positions are selected as mentioned in Part II.For
transformers, one fault position
at each load node (i.e., the
nodes
connected with distribution transformers) is applied.
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KHANH et al.:FAULT DISTRIBUTION MODELING USING STOCHASTIC BIVARIATE MODELS 349
For lines, one fault position is also applied for each line
segment. Due to the short line segments, this paper selects
the fault position at the end of each line segment (For the
test system, there are 122 line segments and 87 load nodes.
Therefore, 209 fault positions in total are selected).
• Fault types (single phase to ground, phase to phase, two
phases to ground, and three phases to ground) are applied
to fault positions depending on the number of available
phases. The fault impedance is assumed to be negligible.
• The fault rate of a distribution transformer is a random

The line failure rate is normally expressed in the number of
faults per year per foot (or meter) length. However, because of
the short length of line segments, the line failure rate is calcu-
lated for the whole line segment
as follows:
(2)
where
number of line faults of the test system;
total line segments;
length of the line segment (in feet).
The distribution of the fault rate due to external causes de-
pending on fault positions is supposedly in compliance with the
2-D stochastic model. This paper uses bivariate normal distribu-
tion because it is the most common stochastic model which has
such critical advantages as it accepts continuous variables and is
easy to build up the distribution based on monitored historical
data. Besides that, it is also simple to convert to other models
using continuous variables.
So the fault rate at each fault position is
as follows.
For
the transformer
(3)
For the line segment
(4)
where
contributory percentage of faults due
to external causes
;
, weighted factors of the fault rates of

following approximation where and are the coordinates of
the fault position
.
• Faults rate for the transformer
(8)
• Fault rate for the line segment
(9)
C. Development of Voltage Sag Indices
PQ indices are used to estimate the quality of supplied elec-
tric energy for the power system. To date, many PQ indices
have been proposed for various PQ events. A well-known index
of voltage sag is the system average rms voltage variation fre-
quency index for voltage sag down to under X% of the nominal
voltage value
. It is often used for evaluating the PQ
of a three-phase power system based on monitored limited seg-
mentation [3]. The assessed system is segmented so that every
point in the system is contained within a section monitored by
an actual PQ measuring instrument.
In distribution systems, because various phase loads (phase
to neutral, phase to phase, three-phase loads) are available,
asymmetrical faults, which account for most faults, never result
in voltage sags to all single-phase loads (e.g, phase A-to-ground
faults may not cause voltage sags to the loads connectedbetween
phase B and neutral or phase C and neutral or loads connected
between phase B and phase C). Therefore, using
regardless of the number of phases involved, may not exactly
reflect the voltage sag performance of the distribution system.
From the demand sides, the indices are more interesting because
they can estimate the voltage sag performance for phase loads.

that, contributory percentages of different fault types are also
assumed as follows:
•single phase to ground (N1): 80%;
• two phase to ground (N11): 10%;
• two phase together (N2): 8%;
• three phase to ground (N3): 2%
and the component fault rates are supposed to be
• transformer: 50%;
•line: 50%.
The listed percentages shown are, in
fact, based on actual survey
data
[9]. Based on the aforementioned assumptions, the system
fault rates of transformers and lines for different fault types due
to different fault causes (equipment failure or external causes)
are calculated and shown in columns 2 and 3 of Table I. Param-
eters (
, ) that are included make it possible to consider
the influence of fault causes due to external factors.
Second, the fault rate of each fault type is calculated for each
fault position using the fault distribution models as stated in
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KHANH et al.:FAULT DISTRIBUTION MODELING USING STOCHASTIC BIVARIATE MODELS 351
Fig. 3. Sag frequency spectrum and of different phase loads for the case the mean value is at node 13 and deviation .
Table I. The test system with actual dimensions in feet is mapped
out in Fig. 2. The fault positions are assigned with coordinates.
Third, the voltage sag magnitude and phase shift at all load

variate normal distribution. This paper considers four op-
tions of the mean value at nodes 13, 51, 67, and 85 as in-
dicated in Fig. 2.
• Vary the deviations
, of the bivariate normal distri-
bution. This paper also considers the options of the devi-
ation that are equal to 0.2, 0.5, and 0.8 of the maximum
value among deviations
.
C. Results Analysis
Based on aforementioned procedures of stochastic prediction,
the following are remarkable results.
In Fig. 3, the indices of voltage sag for different phase loads,
including voltage sag frequency spectrums, corresponding
, , and for X ranging
from 10% to 90% of the nominal voltage are shown. In this
case study,
, .
Besides that,
for the whole test system for dif-
ferent mean values (at nodes 13, 51, 67, and 85) of the fault
distribution models regardless of the number of involved
phases are also depicted in Fig. 4. Obviously, there are big
differences between
of different phase loads or
between
of phase loads and of the whole
system.
of phases A, B, and C are different
because the number of single-phase loads on each phase are

352 IEEE TRANSACTIONS ON POWERDELIVERY , VOL. 23, NO. 1, JANUARY 2008
Fig. 4. Sag frequency spectrum and of the whole system for different mean positions for the case that the deviation is .
Fig. 5. Voltage sag frequency spectrum of the load-bus 63 on phase A for dif-
ferent deviations. The mean value is at node 67 (upper) and node 13 (lower).
Fig. 6. Voltage sag frequency spectrum for loads on phase A for different de-
viations. The mean value is at node 67 (upper) and node 13 (lower).
Figs. 5 and 6 plot the voltage sag frequency for load node
63 (see Fig. 2) on phase A and for all loads on phase A for
Fig. 7. Voltage sag frequency spectrum and for the whole system for
different deviations for the mean value at node 67.
Fig. 8. Voltage sag frequency spectrum and for the whole system for
different deviations for a mean value at node 13.
different deviation values of fault distribution
in the case the mean values are identical to
the coordinates of node 13 and node 67. Similarly, Figs. 7 and 8
demonstrate the voltage sag frequency spectrum and
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KHANH et al.:FAULT DISTRIBUTION MODELING USING STOCHASTIC BIVARIATE MODELS 353
Fig. 9. Voltage sag frequency distribution for sags lower than 10%, 40% to 50%, 60% to 70%, and 70% to 80%, , , mean at
node 67.
for the whole test system also for different deviation values
and for the mean values at
node 13 and node 67. Increasing the deviation values
and
will turn the normal distribution into the uniform distribu-
tion. It causes shape variations to the voltage sag frequency
spectrum. The clear increase of the frequency of deep sags is

of the distribution model should be selected properly to match
the monitored historical data of fault performance of the system
of interest. By using the bivariate normal distribution for mod-
eling fault distribution, this paper also analyzed the influences
of its
parameters on voltage sag performance. It i
s notable that
the alteration of the deviation value of the distribution has a
much stronger impact on sag performance, especially for the
deep sag frequencies pattern than switching the position of the
mean value. The more concentrated occurrence of faults on one
location in the distribution system of interest will increase the
number of deep sags. The results are also evidence that the typ-
ical radial network topology of the distribution system is also
another important reason for the high frequency of deep sags.
2-D stochastic models, such as the bivariate normal distribu-
tion used for modeling fault distribution, can provide a good
o
v
erview of fault performance of the whole system of interest.
Thus, it is possible not only to analyze the relation between
faults and voltage sags at individual locations of the system,
such as a specific load node or a segment of line, but also to
compute system indices of voltage sags, such as
.
The application of 2-D stochastic models has some limits to
the size of the system of interest.For the sections of the dis-
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System Quality. New York: McGraw-Hill, 1996.
[2] M. H. J. Bollen, Understanding Power Quality Problems—Voltage
Sags and Interruptions. New York: IEEE Press, 2000.
[3] D. L. Brooks, R. C. Dugan, M. Waclawiak, and A. Sundaram, “Indices
for assessing utility distribution system RMS variation performance,”
IEEE Trans. Power Del.,vol. 13, no. 1, pp. 254–259,
Jan. 1998.
[4] M. R. Qader, M. H. J. Bollen, and R. N. Allan, “Stochastic prediction
of voltage sags in a large transmission system,” IEEE Trans. Ind. Appl.,
vol. 35, no. 1, pp. 152–162, Jan./Feb. 1999.
[5] J. V. Milanovic, M. T. Aung, and C. P. Gupta, “The influence of fault
distribution on stochastic prediction of voltage sags,” IEEE Trans.
Power Del.,vol. 20,
no. 1,
pp. 278–285, Jan. 2005.
[6] R.E.Brown, ElectricPower Distribution Reliability. New York:
Marcel-Dekker, 2002.
[7] IEEE Distribution Planning Working Group Report, “Radial distribu-
tion test feeder,” IEEE Trans. Power Syst.,vol. 6, no. 3, pp. 975–985,
Aug. 1991.
[8] W. H. Kersting,Distribution System Modeling and Analysis. Boca
Raton, FL: CRC, 2002.
[9]
T
. A. Short, ElectricPower Distribution Handbook. Boca Raton, FL:
CRC, 2004.
[10] G. Olguin, “Voltage dip (sag) estimation in power system based on sto-
chastic assessment and optimal monitoring,” Ph.D. dissertation, Dept.
Energy Environ.,Div.Elect. Power Eng., Chalmers Univ. Technol.,
Gotteborg, Sweden, 2005.

with the Advanced Power Technologies Center,
Department of Electrical Engineering, University of
Washington, Seattle. His
research i
nterests include
power quality, dispersed generation, renewable energy, and hydrogen economy.
Seung-Il Moon (M’93) received the B.S. degree
in electrical engineering from Seoul National Uni-
versity, Seoul, Korea, in 1985 and the M.S. and
Ph.D. degrees in electrical engineering from The
Ohio State University, Columbus, in 1989 and 1993,
respectively.
Currently, he is an Associate Professor of the
School of Electrical Engineering and Computer
Science at Seoul National University. His special
fields of interest include power quality, flexible ac
transmission systems (FA
CTS), renewable energy,
and dispersed generation.
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The 2009 ASEAN Symposium on Power and Energy Systems - EEE.RC.ASPES 2009
Paper No. PS-1

Abstract This paper presents a method of assessing a
power quality phenomena in distribution systems - voltage sag.
The voltage sag performance is obtained by the problem of
stochastic prediction of voltage sag in power systems [2] basing

Researches about the voltage sag are usually related with
a basic process known as a “compatibility assessment” [1]
which includes three steps: i. Obtain the voltage sag
performance of the system of interest, ii. Obtain equipment
voltage tolerance, iii. Compare equipment voltage tolerance
with the voltage sag performance and estimate expected
impacts of the voltage sag on the equipment. Researches to
date have already evidenced that obtaining the voltage sag
performance is still needing much further improvement. The
information about the voltage sag is mainly obtained by
monitoring and stochastic prediction [1]. This paper
presents a method of predicting voltage sags in distribution
system using SARFI
X-CURVE
that is derived from SARFI
X
with regard to tripping time of protective devices currently
used in power distribution networks in Vietnam.

Bach Quoc Khanh is with Electric Power System Department,
Electricity Faculty, Hanoi University of Technology, 1 Dai Co Viet Rd.,
Hanoi, Vietnam (e-mail: ).
II. INDICES FOR VOLTAGE SAG ASSESSEMENT
Voltage sag assessment often bases on its characteristics:
magnitude and duration. There are many indices proposed
for voltage sag quantification [1], [2] and one of frequently
used indices is SARFI
X
that is defined as follows
N

[4], [6] which is defined below
Figure 1. ITI curve for susceptibility of computer equipment.
Prediction of Voltage Sags in Distribution
Systems With Regard to Tripping Time of
Protective Devices
Bach Quoc Khanh (Hanoi University of Technology)
A
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The 2009 ASEAN Symposium on Power and Energy Systems - EEE.RC.ASPES 2009
Paper No. PS-1
N
N
SARFI
m
i
iX
CURVEX
¦



1
'
)(
(2)
where
'

significant steps
- Modeling the fault distribution on of a given
segment of distribution system (see part B)
- Calculating the short-circuit current and voltage
sags at all influenced load nodes.
- Cumulating system voltage sags with different
characteristics and obtaining SARFI
X
.
- Cumulating system voltage sags that cause
equipment to trip and obtaining SARFI
X-CURVE
.
To obtain SARFI
X-CURVE
, this work uses the typical
tripping curve (t
PD
= f(I
F
)) of protective devices like fuses,
feeder circuit breakers currently used in distribution
systems. Each sag is plotted as a point characterized by a
pair of co-ordinates (magnitude of voltage sag and tripping
time). If the point falls out of voltage tolerant envelop
(Figure 1), the sag is cumulated to calculate SARFI
X-CURVE
.
B. Fault Distribution Modeling
Modeling the fault distribution is to determine the short-

Besides fault distribution modeling, for the distribution
system, following assumptions are possibly considered [3].
- Voltage sags are only caused by faults in the
distribution system.
- If the distribution system is supposedly a section of a
large distribution system, only faults occurred within it are
considered. The faults in sections fed from other distribution
substations can be skipped as the transformer impedance in
distribution substations, in reality, is rather high. Similarly,
the faults in low voltage networks are also ignored because
of the large impedance of distribution transformers. This
assumption only neglects voltage sags caused by faults in
the transmission system. It will be considered if the
stochastic prediction of voltage sag in large transmission
systems [7] is included.
- In terms of reliability, the distribution system is
modeled on two main components: lines and distribution
transformers. The reliability of any other distribution
equipment is supposedly included in the reliability of these
two components.
- The fault positions are selected as mentioned in the Part
III.B. For transformers, one fault position each load node
(i.e. the nodes connected with distribution transformers) is
applied. For lines, one fault position is also applied for each
line segment. Because of short line segments, the paper
selects the fault position at the end of each line segment.
- Fault types (single phase to ground, phase to phase, two
phases to ground and three phases to ground) are applied to
fault positions depending on the number of available phases.
~

D. System voltage sag calculations
Short-circuit calculations and resulting voltage sag
magnitude at load nodes in distribution systems is
performed by MatLab programming that used in [3]. The
program consists of two modules
- Short circuit calculation
- Fault distribution modeling
Its block diagram is briefly depicted as Figure 3

IV. A C
ASE STUDY
A. Case study definition
This work illustrates the method by predicting voltage
sag performance and resulting SARFI
X-CURVE
for a 24kV
feeder network in Hanoi, Vietnam. Preliminary data is as
follows
The network segment under consideration: Feeder 482-
E14, 24kV, underground cable, outgoing from 110/35/22kV
Giam substation. It’s a radial network with 99 nodes and 98
branches. Fault positions can be selected at load nodes for
distribution transformer fault and at all nodes for line fault.
Besides, contributory percentages of different fault type
are also assumed as follows
- Single phase to ground (N1) : 65%
- Two phase to ground (N11) : 10%
- Two phase together (N2) : 20%
- Three phase to ground (N3) : 5%
and the component fault rates are supposed to be

results. The system fault rate is then distributed uniformly to
all fault positions as assuming in Part III.B. Short-circuit
calculation is made at every fault positions and resulting
voltage sags at all load nodes are identified by their
magnitudes. Besides, the fault current is used to determine
voltage sag duration as per (3) and each voltage sag
identified above are again checked to see whether it is to fall
inside the voltage tolerant envelope of ITI curve or not. If it
is inside, it is taken into account for calculating SARFI
X-
CURVE
. Finally two indices SARFI
X
and SARFI
X-CURVE
are
obtained and plotted in the same graphics for analysis. The
results are depicted on two graphics. Figure 5 depicts the
system voltage sag frequency spectrum. Figure 6 depicts
SARFI
X
and SARRFI
X-CURVE
.
The results also indicate some following remarks
- Deep sag frequency rises highly due to the radial
network topology with short distances of cable
lines in distribution systems.
- 40-50% sag is also a little greater than other sags
because the feeder consists of one trunk line with

CALCULATION
Sag quantification by duration
TRIPPING TIME
t
PD
=
f
(
I
N
)
24kV bus of
110kV Giam
substation
Circuit
b
reake
r
Fuse
Fuse
Distribution
transforme
r
Distribution
transforme
r
Figure 4. Brief description of
24kV feeder protection system
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X-CURVE
that combines SARFI
X
and equipment compatibility curves.
Therefore, the results of assessment provide a better
understanding of the influence of voltage sag on loads.
This method is also found useful for power quality
assessment and power supply contracting principles for
power distribution utilities in Vietnam in the process of
electricity market establishment because the management of
distribution system is becoming financially separated from
the power system.
The application of the method has some limits that can be
developed in further researches. For a larger network, a
more suitable fault distribution should be considered [3],
[5]. In addition, a combination of the problems of predicting
voltage sags in distribution systems and transmission system
[7] will provide a more comprehensive understanding of
voltage sag performance of a power system.
VII. R
EFERENCES
[1] M.H.J. Bollen, Understanding power quality problems - voltage sags
and interruptions, IEEE Press, 2000.
[2] Recommended practice for the establishment of voltage sag indices,
Draft 6, IEEE P1564, Jan 2004.
[3] Bach Quoc Khanh, Dong Jun Won, Seung Il Moon, “Fault
Distribution Modeling Using Stochastic Bivariate Models For
Prediction of Voltage Sag in Distribution Systems”, IEEE Trans.
Power Delivery, pp. 347-354, Vol.23, No.1, January 2008.
[4] Juan A. Martinez, Jacinto Martin-Arnedo, “Voltage Sag Studies in

20
25
30
35
40
45
0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90
Sag
Sag leading load failure
System voltage sag frequency
V
Sag
(percentage of U
n
)
Figure 5. System voltage sag frequency spectrum
0
20
40
60
80
100
120
<10<20<30<40<50<60<70<80<90
SARFI
SARFI
X
SARFI
X-CURVE
V

phương pháp dự báo ngẫu nhiên SANH [2] trong hệ thống điện (HTĐ). Việc đánh giá này dựa trên chỉ
tiêu tần suất SANH trung bình của HTĐ với đặc tính X (SARFI
X
) và SARFI
X-CURVE
[3] cho phép xét đến
không chỉ đặc trưng biên độ của SANH mà còn cả đặc trưng thời gian tồn tại SANH. Đối tượng tính
toán là hệ thống truyền tải điện 220kV của Việt Nam theo tổng sơ đồ 6 với tỷ lệ suất sự cố ngắn mạch
thực tế của năm 2008. Việc đánh giá này là một cố gắng đầu tiên định lượng hóa tình hình một hiện
tượng chất lượng điện năng phổ biến trên một lưới điện diện rộng thực tế giúp cho việc đánh giá chất
lượng điện năng nói chung của hệ thống điện Việt Nam hiện nay.
ABSTRACT
This paper presents a method of predicting a power quality phenomena in distribution systems,
voltage sag [1]. The calculation of voltage sag performance follows the model of stochastic prediction
of voltage sag in power systems [2]. The voltage sag performance is predicted basing on the System
Average RMS variation Frequency Index (SARFI
X
) and SARFI
X-CURVE
[3] that considers not only the
characteristics - magnitude, but also the characteristics – duration of voltage sag. The objective of
research is the whole 220kV transmisson systems in Vietnam as per the 6
th
master-plan with actual
data of fault rate of the year 2008. This prediction is the first effort of quantifying the voltage sag
performance for such a large transmission system that helps assess the power quality of the electric
power system in Vietnam now.

I. ĐẶT VẤN ĐỀ
Theo IEEE-1159, 1995, SANH (voltage

Trong khi đó, việc nhận dạng tình hình
CLĐN là nhiệm vụ của phía cung cấp điện.
Ở Việt Nam, đã bắt đầu có những nghiên
cứu chuyên sâu về đánh giá tình hình SANH
trong HTĐ [2, 3], tuy nhiên việc định lượng hóa
tình hình SANH trên HTĐ thực tế ở Việt Nam
vẫn chưa được thực hiện. Nguyên nhân chính
hiện nay
là k
hông có một cơ sở dữ liệu về
CLĐN nói chung và SANH nói riêng của HTĐ
Việt Nam do hệ thống giám sát và lưu trữ thông
tin về CLĐN vẫn còn rất thiếu. Bên cạnh việc
giám sát CLĐN, một cách gián tiếp để xác định
tình hình SANH trên HTĐ có thể dùng mô hình
dự báo CLĐN dựa trên các nguyên nhân sinh ra
nó. Trong các nguyên nhân này, trên 90%
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SANH là do sự cố ngắn mạch trong HTĐ. Do
đó, có thể đánh giá SANH thông qua mô phỏng
và tính toán ngắn mạch trên HTĐ theo phương
pháp điểm sự cố [1, 2].

trưng biên độ của SANH (Hình 2) được xác
định bởi vị trí và loại sự cố ngắn mạch [1, 4].
Đặc trưng thời gian tồn tại SANH thì phụ thuộc
vào thời gian loại trừ ngắn mạch của các thiết bị
bảo vệ.
Các đặc trưng trên đây của SANH được
xác định tại các nút phụ tải của lưới truyền tải
220kV là các trạm biến áp 220kV để từ đó xác
định các chỉ tiêu SARFI
X
và SARFI
X-CURVE
cho
cả hệ thống truyền tải điện 220kV của Việt
Nam.
Hình 2. Các đặc trưng của SANH
2.2. Xây dựng mô hình điểm sự cố đối với
lưới điện truyền tải 220kV của Việt Nam
- Chọn vị trí sự cố : Chỉ xét sự cố ngắn mạch
trên lưới 220kV. Các ngắn mạch xảy ra ở lưới
có điện áp thấp hơn có thể giả thiết là ít ảnh

Ngắn mạch 2 pha - đất : 10%
Ngắn mạch 3 pha : 5%
Vùng mất an toàn
Vùng mất
an toàn
Vùng
an toàn
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- Phân bố sự cố ngắn mạch : Sự cố ngắn mạch
mang tính ngẫu nhiên phụ thuộc vào nhiều yếu
tố [2] nên suất sự cố nhìn chung khác nhau đối
với từng loại sự cố và vị trí sự cố. Trong nghiên
cứu này, do số liệu thống kê về phân bố sự cố
trên lưới truyền tải 220kV chưa đủ chi tiết nên
sự phân bố sự cố được đề xuất theo mô hình
phân bố đều. Theo thống kê của tổng công ty
truyền tải điện quốc gia lưới truyền tải 220kV
trong năm 2008 có tổng số 45 sự cố xảy ra tại
các nút trạm 220kV và 143 sự cố trên các
đường dây 220kV. Suất sự cố đường dây là
0,0179 sự cố/km/năm và của trạm biến áp là
0,682 sự cố/trạm/năm. Phân bố sự cố cho từng

thấp hơn. Lưới 220kV lại có dạng mạch vòng
nên nhìn chung trên mỗi nhánh đường dây
220kV, bảo vệ được đặt tại cả hai đầu và khi
xảy ra sự cố ngắn mạch trên nhánh đường dây
nào thì nhánh đó sẽ bị cô lập riêng. Do đó, tất
cả các nút (66 trạm 220kV) trên lưới điện đều
bị SANH khi sự cố, không có nút nào bị mất
điện duy trì và ta phải tính SANH cho 66 nút
này.
2.3 Tính toán ngắn mạch và xác định đặc
trung biên độ SANH trong lưới điện truyền
tải 220kV của Việt Nam
Việc tính ngắn mạch và SANH tại các
nút phụ tải trong lưới truyền tải 220kV được
thực hiện bằng chương trình PSS/E. Sơ đồ khối
các bước tính toán như hình 3.
- Xác định SARFI
X
: Việc chọn vị trí và xác
định suất sự cố cho từng vị trí và từng loại sự
cố được thực hiện như ở 2.2. Dùng chương
trình PSS/E tính ngắn mạch tại từng điểm sự cố
với từng loại sự cố và từ đó xác định biên độ
SANH tại tất cả 66 nút phụ tải do từng điểm và
từng loại sự cố ngắn mạch gây ra. Gán suất sự
cố cho từng vị trí và từng loại sự cố sẽ rút ra
được tần suất SANH tại từng nút phụ tải do sự
cố đang xét gây ra. Lặp lại việc tính ngắn mạch
và SANH với các điểm sự cố khác rồi tổng hợp
lại ta được tần suất SANH với các đặc tính biên

hệ thống bảo vệ lưới 220kV và dạng đặc tính
chịu điện áp lựa chọn. Đối với lưới 220kV của
Việt Nam hiện nay, bảo vệ chính là bảo vệ cắt
nhanh (so lệch dòng điện hoặc tổng trở cực
tiểu) với tổng thời gian cắt ngắn mạch từ 120ms
đến 150ms. Trong nghiên cứu sử dụng đặc tính
chịu điện áp của các phụ tải nhậy cảm là SEMI,
và với thời gian loại trừ sự cố như trên, các
SANH có biên độ dưới 70% đều rơi vào vùng
mất an toàn và làm các phụ tải nhậy cảm ngừng
làm việc. Do đó, khi xác định SARFI
X-CURVE
,
với X từ 70% đến 100% điện áp định mức thì
SARFI
X-CURVE
không đổi.
Mô phỏng phân bố sự cố trên
lưới truyền tải 220kV
Mô phỏng lưới điện, tính
ngắn mạch bằng PSS/E
Start
Tính SANH cho từng nút tải
bằng PSS/E
Tính SARFI
X
cho lưới truyền
tải điện 220kV
Tính SARFI
X-CURVE


Hình 5. Tần suất SANH nút 220kV Mai Động
theo đặc trưng biên độ lũy tiến Hình 6. Tần suất trung bình SANH theo từng
khoảng đặc trưng biên độ SANH
hơn SARFI
X
của toàn hệ thống vì lưới 220kV ở
miền Bắc có nhiều phụ tải hơn do địa bàn rộng
hơn. N
(3)

N
(1,1)

N
(2)

N
(1)

Tần suất SANH
X
Tần suất SANH
X
SARFI
X

SARFI
X-CURVE

X

tải điện của Việt Nam trải trên một phạm vi
rộng lớn với tình hình sự cố khác nhau. Các mô
hình ngẫu nhiên với các luật phân bố xác suất
phù hợp với tình hình xảy ra sự cố thực tế có
thể được xem xét [2, 6, 8].
TÀI LIỆU THAM KHẢO
1. M. H. J. Bollen; Understanding power quality problems - voltage sags and interruptions; IEEE
Press, 2000.
2. Bach Quoc Khanh, Dong Jun Won, Seung Il Moon; Fault Distribution Modeling Using Stochastic
Bivariate Models For Prediction of Voltage Sag in Distribution Systems; IEEE Trans. Power
Delivery, Vol.23, No.1, pp.347-354, Jan. 2008.
3. Bach Quoc Khanh; Prediction of Voltage Sags in Distribution Systems With Regard to Tripping
Time of Protective Devices; Proceeding, EEE.CR.ASPES2009, Tech. Section 2.1., Hua Hin,
Thailand, Sep. 28-29, 2009.
4. D. L. Brooks, R. C. Dugan, Marek Waclawiak, Ashok Sundaram; “Indices for Assessing Utility
Distribution System RMS Variation Performance”; IEEE Trans. Power Delivery, Vol.13, No.1,
pp.254-259, Jan. 1998.
5. M.R.Qader, M.H.J.Bollen, and R.N.Allan; “Stochastic Prediction of Voltage Sags in a Large
Transmission System”; IEEE Trans. Industry Applications, Vol.35, No.1, pp.152-162, Jan./Feb.
1999.
6. Juan a. marTíNez-Velasco; “Computer-Based Voltage Dip Assessment in Transmission and
Distribution Networks”, Electrical Power Quality and Utilisation, Journal Vol.XIV, No.1, 2008.
7. J.V.Milanovic, M.T.Aung and C.P.Gupta; “The Influence of Fault Distribution on Stochastic
Prediction of Voltage Sags”; IEEE Trans. Power Delivery, vol.20, no.1, pp.278-285, Jan. 2005.
8. Recommended practice for the establishment of voltage sag indices, Draft 6, IEEE P1564,
Jan
2004.
9. Tổng sơ đồ phát triển Hệ thống điện Việt Nam, Bản IV, Viện Năng lượng, 2006.
10. T. A. Short; Electric Power Distribution Handbook, CRC Press, 2004.


frequency, stochastic prediction, fault distribution, fault clearing
time, ITIC, SEMI curve.
I. INTRODUCTION
mong power quality phenomena, voltage sag (dip) is
defined by IEEE 1159 (1995) as a decrease in RMS
voltage to between 0.1 to 0.9 of nominal voltage at power
frequency for duration of 0.5 cycle to 1 minute. Interests in
voltage sag has been getting much greater recently in Vietnam
due to its impact on the performance of sensitive electronic
equipment like variable speed drives, computer-controlled
production lines that are widely used, especially in industry.
Although voltage sags are more common in distribution
system, many causes leading to voltage sag are derived from
transmission systems. An assessment of voltage sag in
transmission systems is important for utilities and customers
in Vietnam now.
Voltage sag assessment normally comes prior looking for
the solution of voltage sag mitigation. Voltage sag assessment
is usually related with the basic process known as a
“compatibility assessment” [1] which includes three steps: (i).
Obtain the voltage sag performance of the system of interest,
(ii). Obtain equipment voltage tolerance and (iii). Compare
equipment voltage tolerance with the voltage sag performance Bach Quoc Khanh is a faculty member with Electric Power Systems
Department, Electrical Engineering Faculty, Hanoi University of Science and
Technology, 1 Dai Co Viet Rd., Hanoi, Vietnam (e-mail: bq_khanh-
).
Nguyen Hong Phuc is a master student with Electric Power System

i
iX
X


)(
(1)
where
X rms voltage threshold; possible values – 10-90% nominal
voltage
N
X(i)

Number of customers experiencing voltage sag with
magnitudes below X% due to measurement event i.
N
number of customers served from the section of the system
to be assessed
Despite being widely used, SARFI
X
only considers the
magnitude of voltage sag. Unfortunately, the magnitude value
maybe much greater than the actual number of tripped
electrical appliances, especially when the duration of sags is
small enough (less than a half second), such as for
transmission system in Vietnam where the total fault clearing
time of protection system is typically less than 5 to 7 cycles of
the mains frequency. To take the voltage sag duration into
account, SARFI
X

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event i.
If we plot voltage sag as a point with co-ordinates being its
magnitude and duration on the graph of the equipment
compatibility curve, SARFI
CURVE-X
corresponding to voltage
sags falling out of the equipment voltage tolerant area (Fig. 1)
will be obtained. So far, well known curves are CBEMA, ITIC
and SEMI [1]. Obviously, SARFI
CURVE-X
can provide a better
understanding of the influence of voltage sag on the operation
of electric equipment in electric networks. This paper presents
the method of calculating SARFI
X-CURVE
using ITIC and SEMI
curve (SARFI
ITIC-X
and SARFI
SEMI-X
) as case studies.
3. Quantifying voltage sag frequency at load nodes (site
indices) and cumulating system sags with different
characteristics and obtaining SARFI
X
(system indices)
4. Cumulating system voltage sags that cause equipment to
trip and obtaining SARFI
CURVE-X
.
To obtain SARFI
X-CURVE
, the voltage sag duration that
depends on the fault clearing time of protective system should
be considered. This work takes the typical tripping time of
protective devices (instantaneous protective relay) and high
voltage circuit breakers currently used in the transmission
system in Vietnam into its calculation.
B. Fault Distribution Modeling and Assumptions
- Fault distribution modeling: Fault distribution modeling
considers the occurrence of all faults in the whole transmission
system of Vietnam that cover 500kV and 220kV networks.
The scope of the transmission system of Vietnam starts from
the points of energy receiving from generating centers or
interconnection points with the transmission system of South
China to load nodes that are step-down 220kV substations. An
individual fault (short-circuit) is characterized by a pair of
parameters: fault position, fault type and its occurrence is
assigned a fault rate. All faults with their assigned rate of
occurrence build up a fault distribution model. Following are
analyses of each fault characteristics for the transmission

that are under the management of National Power
Transmission Corporation (NPT). Other twelve 220kV
substations are under the management of power generation.
Therefore, transformer fault positions will be 11 for 500kV
substations and 63 for 220kV substations respectively. For
OHL faults, fault positions are selected depending on the
length of each branch. According to the above said principle
of fault position selection, we divide the line branches into
some segments and each segment is represented by one fault
position, normally at one of two ends of the line segment. For
220kV OHL, the line segment length shoud be from 10km to
40km depending on the line branch length. For 500kV OHL,
each line segment should be 50km. In this case study, fault
positions are selected at 76 locations for 500kV OHL and 169
locations for 220kV OHL. Therefore, there are 319 fault
positions in total.

SARFI
X-CURVE

qualified
SARFI
X-CURVE

disqualified
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Fig 2. The Transmission System of Vietnam in 2008
Vietnam National Power Transmission

within each regions in Vietnam. For example, phase-to-ground
faults remain unchanged anywhere in the section of
transmission system within a region. The transmission system
is Vietnam is divided in four regions. The data of fault
performance recorded by NPT and its subsidiary agencies
(Power Transmission Companies, PTC) for 2008 is shown in
the Table 1 below.
TABLE 1. R
EGIONAL FAULT RATE PERFORMANCE
Regional Power
Transmission
Company
Line fault rate
(per km.year)
Substation
fault rate
(per year)
500kV 220kV
PTC1 (North) 0.00093 0.02504 0.0397
PTC2 (North Center) 0.00562 0.00536 0.0408
PTC3 (South Center) 0.00173 0.01279 0.0161
PTC4 (South) 0.0077 0.00808 0.0229
NPT 0.00407 0.01478 0.0306
It is noticeable that the fault rates stated in Table 1 are for
all four fault types as mentioned above. Therefore, for each
fault type, the fault rate should multiply by contributory
percentage of different fault types. For the fault that represents
OHL faults within a line segment, fault rate should be
calculated based on the length of the line segment.
- Selection of load nodes for voltage sag calculation: In the


,
PP-G
,
P-P
,
3P-G
)
Short-circuit
calculation and
determine voltage sag
magnitude at selected
load node by PSS/E
Fault distribution
modeling, determine
fault rate of the fault
under calculation
Calculate the frequency
of voltage sag at
the selected load node
Are
all fault type
selected ?
Are
all fault position
selected ?
Are
all load nodes
selected ?
Sag frequency
spectrum by

Vietnam.
(system index)
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load on the system is, the higher short-circuit current will be
generated and the deeper voltage sags will be at load nodes.
Therefore, the most interested prefault loading condition is
obviously that of full loaded and this work performs the short-
circuit calculation in the maximum loading condition.
C. Short circuit calculation and voltage sag determination for
the transmission system of Vietnam
Short circuit calculation and voltage sag determination for
the whole transmission system of Vietnam is carried out by
program PSS/E (Power System Simulation for Engineering).
The block diagram of the calculation is depicted in Fig. 3.
- SARFI
X
calculation: With fault distribution modeling for
the transmission system proposed in Part B, this work
performs short-circuit calculation using the program PSS/E for
a certain individual fault (fault position, fault type) and then
voltage sag magnitude at a selected load node is calculated.
After assigning fault rate to this fault, the frequency of sag at
the selected load node resulted by this fault will be obtained.
By repeating this calculation for all other faults (fault position
and fault type), and gather them together, we obtains the
frequency spectrum of voltage sag with different magnitude
characteristics at the selected load nodes caused by all faults in Fig 5. Voltage sag frequency spectrum (per year) for all fault
events at 220kV Mai Dong Substation, Hanoi, Vietnam
(per unit) intervals for different fault types. Fig. 5 is voltage
sag frequency spectrum for all fault types. Fig. 6 is the
cumulative voltage sag frequency.

Fig 6. Cumulative Voltage Sag Frequency (per year)
at 220kV Mai Dong Substation, Hanoi, Vietnam
For other load nodes, the calculation is similarly performed
and then we obtain voltage sag frequency spectrum of all other
load nodes. Finally, the average frequency spectrum per load
node is calculated and plotted on the Fig. 7 and SARFI
X
of the


Fig 8. SARFI
X
and SARFI
CURVE-X
of
the transmission system of Vietnam
Sag Magnitude
(p.u)
Sag Magnitude
(p.u)
Sag Magnitude
(p.u)
SARFI
X

SARFI
ITIC-X

Sag Magnitude
(p.u)
SARFI
ITIC-0.7


differential protection as above said using the tele-
communication links of power line carrier or fibre-optical
ground wire integrated in power carrying lines or the distance
protection using differential relays of SIEMENS (SIPROTEC
7SA6) or ALSTOM (EPAC 3000, MiCOM P440). All those
protective relay system is of instantaneous tripping type that is
typically less than 100ms. The switching devices are almost
SIEMENS, SCHNEIDER or ABB products manufactured in
Europe with typical breaking time of 40ms for 500kV to 60ms
for 220kV circuit breakers. Besides the above mentioned
operating times of protective relays and circuit breakers,
additional time delays are also included for auxiliary relay
trips and operating time of tele-protection with total additional
operating time not exceeding two more cycles (20-24ms).
Therefore, the total fault clearing time is 160ms to 180ms that
defines the voltage sag duration. If posing this duration on the
ITIC curve, it’s obviously that only sags lower than 0.7 p.u.
will be out of load voltage tolerance and qualified for
SARFI
ITIC-X
. The upper 0.7 p.u. sags with duration defined by
the above said fault clearing time definitely fall inside the
voltage tolerance envelope and thus, they are not qualified as
SARFI
ITIC-X
. Therefore, SARFI
ITIC-X
is a part of SARFI
X
with

lower than 0.5 p.u are qualified for SARFI
CURVE-X
using the
SEMI curve (SARFI
SEMI-X
). With X greater than 0.5 p.u,
voltage sags fall inside SEMI’s ridethorugh area and not
qualified for SARFI
SEMI-X
. So, for X from 0.5 p.u to 0.9 p.u,
the value of SARFI
SEMI-X
remains unchanged and equal to
SARFI
ITIC-0.5
. SARFI
SEMI-X
is also shown on Fig 8.
D. Result Analysis
From the results, there’re some following remarks:
- The SARFI
X
and SARFI
CURVE-X
values obtained from this
calculation are useful for utilities as a benchmark for reducing
the frequency of fault for solving the problem of voltage sag.
This result also helps customers know the voltage sag
performance and choose suitable location for less voltage sag
frequency.


Fig 9. Voltage sag frequency of selective load nodes
(220kV substations) throughout of Vietnam

Sag magnitude
(p.u)
Sag magnitude
(p.u)
Sag magnitude
(p.u)
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