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IEEETRANSACTIONS ON POWER DELIVERY, VOL.23, NO.1, JANUARY 2008 347

Fault Distribution Modeling Using StochasticBivariate Models for Prediction of Voltage

Sagin Distribution SystemsBach Quoc Khanh, Dong-Jun Won, Member, IEEE, and Seung-Il Moon, Member, IEEE

AbstractThis paper presentsa newmethod regarding fault dis-tribution modeling for the stochastic prediction study of voltagesags inthedistribution system. 2-D stochastic modelsfor fault mod-eling make it possible to obtain the fault performance for the wholesystem ofinterest, which helps to obtain not only sagperformanceat individual locations but also system sag performance throughsystemindices of voltage sag. By using the bivariate normal dis-tribution for fault distribution modeling, this paper estimates theinfluence of model parameters on system voltage sag performance.The paper also develops the modified

regarding phaseloads that create better estimation for voltage sagperformance for

the distribution system.

Index TermsBivariate normal distribution, distributionsystem, fault distribution modeling, phase loads, power quality(PQ), stochastic prediction, voltage sag frequency.

I. INTRODUCTION

AMONG power-quality (PQ) phenomena, the voltage sag

(dip) is defined in IEEE1159, 1995 as a decrease in rms

voltage to between 0.1 and 0.9 of the nominal voltage at the

power frequency for thedurationof0.5cycleto1min. There has

been a greaterinterestin voltage sags recently due to problems

caused by the performance of sensitive electronic equipmentthat is widely used.

Research about the voltage sag is usually related to a basic

process known as a compatibility assessment[1], [2] which

includes three steps.

Step 1) Obtain the voltage sag performance of the system of

interest.

Step 2) Obtain equipment voltage tolerance.

Step 3) Compare equipment voltage tolerance with the

voltage sag performance and estimate the expected

impacts of the voltage sag on the equipment.

Current research has shown evidence that obtaining the

voltage sag performance still needs more improvement. The

Manuscript received August 2, 2005;revised December 5, 2006.This workwas supported by the Korea Foundation for Advanced Studies InternationalScholarExchangeFellowship for the academic year of 20042005. Paper no.TPWRD-00456-2005 .

B.Q.Khanhis with theElectric Power System Department, Faculty ofElec-trical Engineering, Hanoi University of Technology, Hanoi, Vietnam (e-mail:[email protected]).

D.-J. Won is with the School ofElectrical Engineering, INHA University,Incheon 402751, Korea (e-mail:[email protected]).

S.-I.Moon is with the School ofElectrical Engineering and Computer Sci-ence, Seoul National University, Seoul 151-742, Korea (e-mail:[email protected]).

Digital Object Identifier 10.1109/TPWRD.2007.905817

information about the voltage sag is mainly 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 obta in

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-

circuit faults in the power system account for the largest part and

the assessment of the voltage sag performance based on fault

distribution modelingis a well-known approach.However,itis

very difficult to build upaccuratefault modeling because the

data of faults can only obtained by monitoring and, thus,it has

the same uncertainties as to what the monitoring of voltage sags

can generate.

This paper presents a new approach on fault distribution mod-

eling for the stochastic prediction of voltage sags in the distri-

bution system using the method of fault positions.The simula-tion of the distribution system and fault distribution modelingare made on MATLAB for computing not only siteindices, but

also systemindices of voltage sags.

II. FAULTDISTRIBUTIONMODELING

Modeling the fault distributionis to determine the short-cir-

cuit fault frequency (i.e., fault rate or the number of short-circuitfaults per year) for all fault types at all poss ible fault positions

throughout the system ofinterest.It consists of the selection of

fault position and fault type and the distribution of fault rate for

the selected fault positions and fault types.Fault positions are generally chosenin a way that a fault po-

sition should represent short-circuit faults leading to sags with

similar characteristics [2]. For the distribution system with typ-

ical radialnetwork topology, small line segments, and distribu-

tion transformers along the trunk feeders, itis possible to apply

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 IEEETRANSACTIONS ON POWER DELIVERY, 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 lessinterest.The most

common assumption that has been argued so far is that because

the fault can occur anywhere in the system, stochastically,itispossible to model the fault rate as the un iform distribution [3],

[4]. In this sense, the fault rate at each position is identical tothe 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-

tain a systemindex about voltage sag performance since there

are plenty of line segmentsin the distribution system.The new

method of fault distribution modeling proposed by this paper

carefully analyzes concerned fault causes and builds up a suit-

able modeling of the fault distribution for the whole system of

interest from which systemindices can be obtained.

III. NEW FAULT DISTRIBUTIONMODELING BASED

ONFAULTCAUSES FORDISTRIBUTIONSYSTEMS

Although there are a variety of causes that result in faultsin

distribution systems,itis possible to group theminto two parts:namely 1) equipment failures and 2) external causes.

Equipment failure is basically due to defects that are prob-

ably created during manufacture, transportation, and installa-

tion. Equipment failure depends on the time of being placed

into operation, the aging period, and maintenance conditions.According to the reliability theory, it is often characterized by

the component failure rate.There are several distribution func-

tions to model this parameter but the most common one is the

exponential distribution which assumes the component failure

rate to be constant. This value is equal to the average failure

rate during the useful life of thebathtubcurve [6].Therefore,

if the same type of equipment is used throughout the system

(e.g., the same type of distribution transformers usedin the dis-

tribution system), it is possible to assume that the failure rate

of equipment follows the uniform distribution depending on the

equipment type although it still may cause some errors (e.g., not

all equipmentis putintooperation at the same time or has the

samemaintenance conditions).Besides equipment failure, there are many other causes from

the ambient environment that also may lead to faults in powersystems. This paper calls them the external causes. Some can in-

fluence the fault performance of the power system in a largearea

such as severe weather (wind storms, lightning, etc.). Mean-

while, others mainly have localimpacts, such as trees and ani-

mals (birds, mice, etc.).Human factors (scheduledinterruption,

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 explainedbefore.

Fig.1. Example of bivariate normal distribution.

This paper proposes theidea of using 2-D stochastic modelsin-

stead (e.g., the bivariate normal distribution model asillustrated

in Fig. 1).

For large power systems,itis hard to obtain a converged 2-D

fault distribution model for various causesin 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, ofwhichthe monitored historical data of fault performance

shows that faults due to external causesoccur concentratively on

one location (e.g., some lines pass through a small area whichis at high risk for faults due to industrial pollution or trunk fall),

it is the favorite condition to obtain a converged 2-D fault dis-

tribution model.

IV. PROBLEMDEFINITION ANDSOLUTION

A. Case Study Definition

To illustrate the new method of fault distribution modeling

in the stochastic prediction of voltage sag in the distributionsystem, this paper uses the IEEE 123-bus radial distribution

feeder [7] as the test system.It can be seen as the distribution

systemis fed from a bulk point.It does not narrow the scope of

application of the study with the following assumptions. Since line segments in the test system come in one, two,

and three phases, distribution transformers at load nodes

are the single phase type for separate single-phase loads.

For three-phase loads, the connection of the distribu-

tion transformer is 4.16-kV grounded wyelow-voltage

grounded wye.

Voltage sags are only caused by faultsin the test system.

If the test systemis supposedly a section of a large distri-

bution system, only faults occurring in it are considered.

The faults in sections fed from other distribution substa-

tions can be skipped as the transformer impedancein dis-

tribution substations, in reality, is rather high. Similarly, the

faultsin low-voltage networks are alsoignored because ofthe large impedance of distribution transformers.This as-

sumption only neglects voltage sags caused by faultsinthetransmission system.It will be consideredif the stochasticprediction of voltage sagin 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-

edlyincludedin the reliability of these two components.

The fault positions are selected as mentionedin Part II. For

transformers, one fault positionat each load node (i.e., the

nodes connected with distribution transformers)is applied.




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KHANHet al.: FAULT DISTRIBUTION MODELING USING STOCHASTIC BIVARIATEMODELS 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 positionsin total are selected).

Fault types (single phase to ground, phase to phase, twophases to ground, and three phases to ground) are applied

to fault positions depending on the number of availablephases.The faultimpedanceis assumed to be negligible.

The fault rate of a distribution transformer is a random

variable depending on the position of the load node it is

connected to. The fault rate of a line segment is also a

random variable depending on the fault position and the

length of this line segment.Based on the previous definitions and assumptions, the com-

putation of voltage sags at all load nodes on the primary side

of distribution transformers throughout the test system is per-

formedon MATLAB [8]. The voltage sag frequencyat each load

nodeis obtained when applying the fault rate to each fault posi-

tion.The fault rates at the fault positions are calculated based on

the new fault distribution modeling presentedin Part B. Finally,

related voltage sag indices are calculated.

B. Fault-Rate Modeling

Faults are random events and as previously indicated, they

can be simulated by stochastic distribution models.According

to the analysisin Section III, the fault rate of each fault type at

each fault positionis equal to the sum of equipment failure rate

and fault rate due to external causes.The equipment failure rate

is supposed to followthe uniform distribution model. Therefore,

for the fault position of the transformer , the failure rateis cal-

culated as follows:

(1)

where

number of transformer faults of the test system;

total distribution transformers;

contributory percentage of equipment failure.

The line failure rateis normally expressedin 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 positionsis supposedlyin compliance with the

2-D stochastic model. This paper uses bivariate normal distribu-

tion becauseitis 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 positionisas follows.

Forthe transformer

(3)

For the line segment

(4)

where

contributory percentage of faults due

to external causes ;

, weighted factors of the fault rates of

the transformer and the line segmentthat follow the bivariate normal

distribution model depending on fault

positions.

Thejoint probability density functio n o f bivariate normal dis-

tributionis expressed as follows:

where

(5)

, , , means and standard deviations of two

variables , ;

correlation coefficient. If the

coordinates of fault positions are

independent variables .

The probability for a fault tooccur atthe fault position

within an area can be calculated as follows:

(6)

If and is large enough,

then the distributionis normalized as follows:

(7)

For the distribution system, geographically,if network nodes

are disposed relatively uniform,it will be possible to apply the




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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

PQindices 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-knownindexof voltage sag is the system average rms voltage variation fre-

quency index for voltage sag down to under X% of the nominal

voltage value .Itis often used for evaluating the PQof a three-phase power system based on monitored limited seg-

mentation [3].The assessed system is segmented so that every

pointin the systemis contained within a section monitored by

an actual PQ measuringinstrument.

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-groundfaults maynot cause voltagesags to theloadsconnected between

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.In order to take the availability of various phase loads in the

distribution system into account, this paper newly develops

in regard to phase loads as follows:

(10)

(11)

(12)

where

, , number of sags down to under

X% that phase-to-neutral

(A,B,C), phase-to-phase (A-B,

B-C, C-A), or three-phase load

experiences;, , number of phase-to-neutral

(A,B,C), phase-to-phase (A-B,

B-C, C-A), or three-phase

customers served from the

system ofinterest.

TABLEISYSTEMFAULT-RATEBREAKDOWN

Fig.2. Mapping of the IEEE123-bus radial distribution test feeder.

V. RESULTDEMONSTRATION ANDANALYSIS

A. Procedures of Stochastic Prediction

The process of stochastic prediction study is performed

through the following steps.First, the system fault rate (the total of faults occurr ingin the

test system over a certain period of time) is assumed to be an

arbitrary number, say 500 faults. This value is just for calcu-

lation and easier graphic demonstration of the results. Besides

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%.

Thelisted 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 shownin columns 2 and 3 of Table I.Param-

eters ( , ) that are included make it possible to consider

theinfluence 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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Fig.3. Sag frequency spectrum and of different phase loads for the case the mean value is at node 13 and deviation 1 .

Table I. The test systemwithactual dimensions in feet is mapped

outinFig.2.The fault positions are assigned with coordinates.

Third, the voltage sag magnitude and phase shift at all load

nodes are computed for all selected fault positions.With the ap-

plication of fault rates to the selected fault positions, the voltage

sag frequencies corresponding to different characteristics are

obtained. The voltage sag frequency is calculated for the fol-

lowing:

individual load nodes;

all possible phase loads, including phase-to-neutral,

phase-to-phase, and three-phase loads; the whole test system.

B. Evaluationof Influences of the Fault Distribution Modeling

on the Voltage Sag Performance

The fault distribution modeling uses several parameters. In

practice,itis possible to adjust these parameters so that the re-

sulting modelis suitable for the fault performance of the distri-

bution system ofinterest. However, the variation of these param-

eters also makes the voltage sag performance change accord-

ingly. In modeling fault distribution, this paper also considers

the following options of fault distribution for estimating thein-

fluences of fault distribution on voltage sag performance. Change contributory percentages of the fault due to ex-

ternal causes (change or ).In this paper, three op-

tions , 50%, and 100% are considered. Switch the position of the mean value ( , ) of the bi-

variate normal distribution.This paper considers four op-

tions of the mean value at nodes 13, 51, 67, and 85 as in-

dicatedin 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 proceduresof stochastic prediction,

the following are remarkable results.

InFig.3, theindices 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 thiscase 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 bigdifferences 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

different. are rather low as single-phase loads

just experience sags due to single-phase-to-ground faults on

the same phase. Generally, are greater because

phase-to-phase loads are impacted by more faults (faults on

two phases) than phase-to-neutral loads (faults on one phase).

For phase-to-phase loads, there is a little deep sag frequency;

meanwhile, the shallow sag frequency rises greatly because al-

most phase-to-ground faults (80% system fault rate) just cause

shallow sags to phase-to-phase loads. for threephasesis the greatest and for is equal

to 500 sags per load because three-phase loads will experiencevoltage sag for any fault type. The aforementioned remarks

also explain why , defined for phase loads,is for more

usefulindices for estimating the voltage sag performancein the

distribution system where many single-phase loads exist.

Fig.4 also shows that different positions of the mean value of

fault distribution models resultin different spectrums of voltage

sag frequency. It is notable that if the position of mean value gets

closer to the bulk point of supply, the deep sag frequency will

increase, thatis, mainly because of the radial network topology

of the distribution system.




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Fig.4. Sag frequency spectrum and of the whole system for different mean positions for the case that the deviationis 1 .

Fig.5. Voltage sag frequency spectrum of the load-bus 63 on phase A for dif-ferent deviations.The mean valueis 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 valueis 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 fordifferent deviations for the mean value at node 67 .

Fig.8. Voltage sag frequency spectrum and for the whole system fordifferent deviations for a mean value at node 13.

different deviation values of fault distribution

in the case the mean values areidentical 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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Fig.9. Voltage sag frequency distribution for sags lower than 10%, 40% to 50%, 60% to 70%, and 70% to 80%, 1 , , mean atnode 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 andwill 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

shown in all cases of the sag performance demonstration. If

the mean position of the distribution model is located at node

13, which is very near the bulk point, the frequency of sags

below 10%is even raised by about 50% for the small deviation

.Thatis also explained as the result of

the radial network topology of the distribution system.

The spectrum of the voltage sag frequency for different case

studies (fromFigs.38)is quite similarin which deep sags ac-

count for a large number mainly due to short feedersin the dis-

tribution system.The frequency of 40% to 60% sags is also highas the network topology consists ofonetrunkline with many lat-

eral taps in the middle.That means the point of common cou-

pling of many load nodesis on the middle of the trunk line. Few

load nodes connected to the trunk line near the bulk point of

supply (the distribution substation) explain why the shallow sag

frequency is very low. Fig. 9 gives us a closer look at the voltage

sag frequency distribution for different sag magnitudes. It is,

without doubt, that deep sag frequencies appear at the nodes

on branches connected close to the far end of the trunk line.Voltage sags 40% to 50% are distributed rather uniformly ex-

cepting nodes near the bulk point.The shallow sag frequencies

mainly occur at several nodes near the bulk point of supply.

VI. CONCLUSION

This paper presented a new method of fault distribution mod-eling in the stochastic prediction of voltage sag for the distri-

bution system using 2-D distribution models.When using 2-D

distribution models for modeling fault distribution, parameters

of the distribution model should be selected properly to match

the monitored historical data of fault performance of the system

ofinterest.By using the bivariate normal distribution for mod-

eling fault distribution, this paper also analyzed the influences

ofits parameters on voltage sag performance.It is 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 ofinterest will increase thenumber of deep sags.The results are also evidence that the typ-

ical radial network topology of the distribution system is also

anotherimportant 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

overview of fault performance of the whole system ofinterest.

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 systemindices 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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tribution system, of which the size is so large as the one sup-

plied from a bulk distribution substation, it is practical to use

this fault distribution modeling. The accuracy will be further

improved for the distribution systems, of which the topology

features the uniform arrangement of components. In addition,

the stochastic prediction of the transmission system should be

includedif the influence of fault occurring in the transmission

system on voltage sag performancein the distribution system ofinterestis considered.

The presence of different phase loads in the distribution

system indicated that for the whole system without

considering the number of phase of the loads cannot reflect

voltage sag performance properly.To have a better assessment

of the voltage sag, this paper develops modified

regarding phase loads. The results proved that there are

big differences between , , and

for different phase loads and for the

whole system.This modification of is more practical

from the customers point of view when power-supply contracts

are set up.

REFERENCES

[1] R. C.Dugan, M. F.McGranaghan, and H.W. Beaty, Electric PowerSystem Quality. New York:McGraw-Hill, 1996.

[2] M. H. J. Bollen, Understanding Power Quality ProblemsVoltageSags and Interruptions. New York:IEEEPress, 2000.

[3] D.L.Brooks, R.C.Dugan, M.Waclawiak, and A.Sundaram,Indicesfor assessing utility distribution system RMS variation performance,

IEEE Trans.Power Del., vol.13, no.1, pp.254259, 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.152162, Jan./Feb.1999.

[5] J.V.Milanovic, M.T.Aung, and C.P.Gupta,Theinfluence of faultdistribution on stochastic prediction of voltage sags, IEEE Trans.Power Del., vol.20, no.1, pp.278285, Jan.2005.

[6] R. E. Brown, Electric Power Distribution Reliability. New York:

Marcel-Dekker, 2002.[7] IEEEDistribution Planning Working Group Report, Radial distribu-

tion test feeder,IEEE Trans. Power Syst., vol.6, no.3, pp.975985,Aug.1991.

[8] W. H . Kersting, Distribution System Modeling and Analysis. BocaRaton,FL:CRC, 2002.

[9] T.A.Short, Electric Power Distribution Handbook. Boca Raton,FL:CRC, 2004.

[10] G.Olguin,Voltage dip (sag) estimationin 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.

[11] M.R.Qader, M.H.J.Bollen, and R.N.Allan, Stochastic predictionof voltage sagsin reliability test system,presented at the PQA-97 Eu-rope,Elforsk, Stockholm, Sweden, Jun.1997.

[12] J.A. Martinez-Velasco and J. Martin-Arnedo,Stochastic predictionof voltage dips using an electromagnetic transient program,presentedat the 14th PSCC, Sevilla, Spain, Jun.2002, Paper 4, Session 24.

Bach Quoc Khanh received the B.S.and Ph.D.de-grees in powernetwork andsystems from HanoiUni-versity of Technology, Hanoi, Vietnam, in 1994 and2001, respectively. He received the M.S. degree i nsystem engineering from the Royal Melbourne Insti-tute of Technology (RMIT), Melbourne, Australia,in1997.

He is currently a Lecturer with the Faculty ofElectrical Engineering, Electric Power SystemDepartment, Hanoi University of Technology. Hewas a Postdoctoral Fellow with the Power System

Laboratory, School of Electrical Engineering and Computer Science, SeoulNational University, Seoul, Korea.His special fields ofinterestinclude powerdistribution system analysis, DSM, and power quality.

Dong-Jun Won (M05) was born in Korea on Jan-uary 1, 1975.He received the B.S., M .S., and Ph.D.degrees in electricalengineering from Seoul NationalUniversity, Seoul, Korea, in 1998,2000, and2004, re-spectively.

Currently, he is a Full-Time Lecturer with theSchool ofElectricalEngineering with INHA Univer-sity, Incheon, Korea. He was a Postdoctoral Fellowwith the Advanced Power Technologies Center,Department ofElectricalEngineering, University ofWashington, Seattle. His research interests include

power quality, dispersed generation, renewable energy, and hydrogen economy.

Seung-Il Moon (M93) received the B.S. degreein electrical engineering from Seoul National Uni-versity, Seoul, Korea, in 1985 and the M.S. andPh.D. degrees in electrical engineering from TheOhio State University, Columbus,in 1989 and 1993,respectively.

Currently, he is an Associate Professor of theSchool of Electrical Engineering and ComputerScience at Seoul National University. His specialfields of interest include power quality, flexible actransmission systems (FACTS), 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 apower quality phenomena in distribution systems - voltage sag.The voltage sag performance is obtained by the problem ofstochastic prediction of voltage sag in power systems [2] basingon System Average RMS variation Frequency Index (SARFIX).However, SARFIX is modified into SARFIX-CURVE thatconsiders not only the magnitude of voltage sag, but also itsduration. The resulting SARFIX-CURVE provides a betterunderstanding of the influence of voltage sag on the electricloads. The duration of voltage sag is modeled regarding thetripping time of protective devices in distribution systems. Thepaper also applies this method to assess voltage sagperformance of the 22kV feeder 482-E14 of 110/35/22kV Giamsubstation in Hanoi city, Vietnam.

Index Terms-- power quality, voltage sag, distributionsystem, equipment compatibility curve, fault distributionmodeling, tripping time.

I. INTRODUCTION

MONG power quality phenomena, the voltage sag

(dip) is defined at IEEE1159, 1995 as a decrease in

RMS voltage to between 0.1 and 0.9 of the nominal voltage

at the power frequency for the duration of 0.5 cycle to 1minute. Interests in the voltage sag have been getting much

greater recently due to its problems causing on the

performance of sensitive electronic equipments that are

widely used.

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. Theinformation 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 SARFIX-CURVE that is derived from SARFIXwith 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:[email protected]).

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 SARFIX that is defined as follows

N

N

SARFI iiX

X

)(

(1)

where

X rms voltage threshold; possible values 10-90%

nominal voltage

NX(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, SARFIX only considers the

magnitude of voltage sag and, of course, its value is maybe

much greater than the actual number of tripping electrical

appliances, especially when the duration of sags is small

enough (less than a half second). To take the sag duration

into account, SARFIX is developed into SARFI

X-CURVE [2],

[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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Paper No. PS-1

N

N

SARFI

m

i

iX

CURVEX

1

'

)(

(2)

where'

)(iXN :Number of customers tripped when experiencing

voltage sag with magnitudes below X% due to measurement

event i.

SARFIX-CURVE corresponds to voltage sags below anequipment compatibility curve. So far, frequently used

curves are CBEMA, ITIC and SEMI [1]. Obviously,

SARFIX-CURVE 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 SARFIX-CURVEusing ITI curve (Figure

1) as a case study.

III. REDICTION OF VOLTAGE SAG IN DISTRIBUTION SYSTEM

A. Problem definition

The problem of stochastic prediction of voltage sag can

obtain the voltage sag performance of a specific electricsystem by using data of events leading to sags. In fact, more

than 90% sag events are resulted from short-circuits and it is

possible to use fault modeling and short-circuit calculation

tools to predict voltage sags in the power system (Figure 2).

This work uses the method of fault position [1] for

voltage sag prediction in distribution systems with following

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 SARFIX.

- Cumulating system voltage sags that cause

equipment to trip and obtaining SARFIX-CURVE.

To obtain SARFIX-CURVE, this work uses the typical

tripping curve (tPD= f(IF)) 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 SARFIX-CURVE.

B. Fault Distribution Modeling

Modeling the fault distribution is to determine the short-

circuit fault frequency (i.e. fault rate or the number of short-

circuit faults per year) for all fault types at all possible fault

positions throughout the system of interest [3]. It consists of

the selection of fault position and fault type and the

distribution of fault rate for selected fault positions and fault

types.

Fault positions are generally chosen in the way that a

fault position should represent short-circuit faults leading to

sags with the similar characteristics [1]. For the distribution

system with typically radial network topology, small linesegments and distribution transformers along the trunk

feeders, it is possible to apply only one fault position for

each distribution transformer and also one fault position for

each line segment.

Different fault types should be applied to each fault

position mainly depending on number of phases available at

the selected fault positions. The fault rate of each fault type

is normally referred from the observed historical data.

Fault rate mainly depends on fault position, fault type

and fault cause. For a segment of distribution system that is

geographically seen as small area, it possible to assume that

fault rate of each fault type follows uniform distribution for

all fault positions. [3]. In this sense, the fault rate at eachposition is identical to component failure rate that is based

on component reliability. In reality, uniform fault

distribution is a practical assumption for distribution

systems because the service area of a certain distribution

line outgoing from a distribution substation is normally

small.

C. Assumptions

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 areconsidered. 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 thesetwo 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.

~ZS

ZF

Vt

E

Load at PCC

Short circuit

Figure 2. Model of voltage sagprediction in power systems

tPD

VSag

E

t

VttPD




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Paper No. PS-1

The fault impedance is assumed to be negligible.

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 modelingIts blockdiagram is briefly depicted as Figure 3

IV. A CASE STUDY

A. Case study definitionThis work illustrates the method by predicting voltage

sag performance and resulting SARFIX-CURVE for a 24kV

feeder network in Hanoi, Vietnam. Preliminary data is as

follows

The networksegment under consideration: Feeder 482-

E14, 24kV, underground cable, outgoing from 110/35/22kV

Giam substation. Its a radial networkwith 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

- Transformer : 50%

- Line : 50%

The tripping curve used for this work is the typical

inverse curve of in-service protective devices in distribution

systems like fuse-cutout for distribution transformer

protection, overcurrent relay for 24kV line feeder. The

common formula of tripping curve is

1)( *

bPDI

at (3)

where

I*: Ratio of fault current INand pickup current IP.

a, b: Constants that are selectable.

V. RESULT DEMONSTRATION AND ANALYSIS

Firstly, the system fault rate (the total of faults occurring

in the test system over a certain period of time) is assumed

to be an arbitrary number, say, 100 faults. This value is just

for calculation and easier graphic demonstration of the

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 SARFIX-

CURVE. Finally two indices SARFIX and SARFIX-CURVE are

obtained and plotted in the same graphics for analysis. Theresults are depicted on two graphics. Figure 5 depicts the

system voltage sag frequency spectrum. Figure 6 depicts

SARFIXand SARRFIX-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

many lateral taps in the middle. That means the

Figure 3. Block-diagram of voltage sag prediction

and SARFIX-CURVEin distribution systems

START

DETERMINE FAULT LINEFind nodes and branches on

fault current carrying line

STOP

ON FAULT-LINE CALCULATIONCalculate fault current IN and

sags VSat nodes on fault line

SARFIX CALCULATIONSag quantification by magnitude

calculation

OFF FAULT-LINE CALCULATIONCalculate voltage sags VSat

nodes not on fault line

SARFIX-CURVECALCULATIONSag quantification by duration

TRIPPING TIME

tPD=f(IN)

24kV bus of

110kV Giam

substation

Circuit

breaker Fuse Fuse

Distribution

transformer

Distribution

transformer

Figure 4. Brief description of

24kV feeder protection system




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Paper No. PS-1

point of common coupling of many load nodes is

on the middle of the trunkline.

- Voltage sags with X greater than 70% are very few

because the system and distribution transformer

impedances normally are much higher than

distribution lines.

- SARFIX and SARFIX-CURVE are slightly different

because the tripping time of protective devices in

distribution systems is typically 0.5 seconds and

frequencies of voltage sag of 70-80% and 80-90%

are very small. In ITI curve, sags with the

magnitude X lower than 70% nominal voltage

feature very short duration (less than one cycle)

and thus they are certainly taken in to account for

calculating SARFIX-CURVE.

VI. CONCLUSIONS

This paper presented a method of assessing voltage sags

in distribution systems with regard to tripping time of

protective devices. The assessment bases on SARFIX-CURVEthat combines SARFIXand 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. REFERENCES

[1] M.H.J. Bollen, Understanding power quality problems - voltage sagsand 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

Distribution Networks - Part II: Voltage Sag Assessment, Part III -

Voltage Sag Index Calculation, IEEE Trans. Power Delivery, pp.

1679-1697, Vol. 21, No. 3, July 2006.

[5] Jovica V. Milanovic, Myo Thu Aung, C. P. Gupta, The Influence of

Fault Distribution on Stochastic Prediction of Voltage Sags, IEEE

Trans. Power Delivery, pp. 278-285, Vol. 20, No. 1, Jan 2005.

[6] 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.

[7] 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.

[8] M.R.Qader, M.H.J. Bollen and R.N.Allan, Stochastic Prediction of

Voltage Sags in Reliability Test System, PQA-97 Europe, Elforsk,

Stockholm, Sweden, Jun. 1997.

VIII. BIOGRAPHIES

Bach Quoc Khanhreceived B.S. and Ph.D. degrees in power networkand systems from Hanoi University of Technology, Hanoi, Vietnam in 1994

and 2001 respectively. He received M.S. in system

engineering from RMIT, Melbourne, Australia in

1997. He is a teaching staff of Electric Power

System dept., Electrical Engineering Faculty,

Hanoi Univeristy of Technology. His specialfields of interest include power distribution

system analysis, DSM and power quality.

0

5

10

15

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

Systemv

olta

gesagfrequency

VSag(percentage of Un)

Figure 5. System voltage sag frequency spectrum

0

20

40

60

80

100

120


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TP CH KHOA HC & CNG NGH CC TRNG I HC K THUT S 77 - 2010

72

NH GI ST GIM IN P NGN HNTRN LI TRUYN TI IN 220KV VIT NAM

PREDICTION OF VOLTAGE SAGS IN THE 220KV TRANSMISSION SYSTEM OF VIETNAM

Bch Qu c Khnh

Trng i hc Bch Khoa H Ni

Phng Th Anh

Cng ty CP T vn Xy dng in ITM TT

Bi bo trnh byphng php nh gi mt hin tng cht lng in nng (CLN) trn litruyn tiin (LTT) l st p ngn hn (SANH - voltage sag) [1]. M hnh nh gi SANH da trnphng php d bo ngu nhin SANH [2] trong h thng in (HT). Vic nh gi ny da trn chtiu tn sut SANH trung bnh ca HT vi c tnh X (SARFIX) v SARFIX-CURVE[3] cho php xt nkhng ch c trng bin ca SANH m cn c c trng thi gian tn ti SANH. i tng tnhton l h thng truyn ti in 220kV ca Vit Nam theo tng s 6 vi t l sut s c ngn mchthc t ca nm 2008. Vic nh gi ny l mt c gng u tin nh lng ha tnh hnh mt hintng cht lng in nng ph bin trn mt li in din rng thc t gip cho vic nh gi chtlng in nng ni chung ca h thng in Vit Nam hin 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 predictionof voltage sag in power systems [2]. The voltage sag performance is predicted basing on the System

Average RMS variation Frequency Index (SARFIX) and SARFIX-CURVE [3] that considers not only thecharacteristics - magnitude, but also the characteristics duration of voltage sag. The objective ofresearch is the whole 220kV transmisson systems in Vietnam as per the 6

thmaster-plan with actual

data of fault rate of the year 2008. This prediction is the first effort of quantifying the voltage sagperformance for such a large transmission system that helps assess the power quality of the electricpower system in Vietnam now.

I. T VN

Theo IEEE-1159, 1995, SANH (voltage

sag) l hin tng CLN trong gi trinp hiu dng ca li in st gim cn t0,1n 0,9 in p nh mc trong thi gian t0,5chu k n 1 pht [1]. SANH c th lm chocc thit b in nhy cm nh in t cngsut, cc b iu tc hay my tnh c nhnngng hoc lm vic khng mong mun. Hintng ny li rt hay xy ra, trong khi nngcao hiu sut qu trnh hay vic ng dng cccng nghmi, cc thit bin ng dng intcng sut ngy cng c sdng nhiu, do SANH ngy cng c quan tm nghincu. Trc khi xem xt nhng gii php khcphc tc ng ca SANH, yu cu nh giSANH trong HT lun c t ra. Qu trnhnh gi CLN ni chung v SANH ni ringthng tri qua ba khu chyu [1] l i. Nhndng tnh hnh CLN c cung cp, ii. Xcnh yu cu CLN ca cc ph ti, iii. Sosnh yu cu CLN ca ph ti vi tnh hnh

CLN c cung cp v nh gi tc ng caCLN i vi ph ti. Vic xc nh yu cuCLN ca cc ph ti thuc v cc nh sn

xut thit bdng in m in hnh l c tnhchu in p ca ph ti CBEMA, ITIC hocSEMI [1] (Hnh 1).

Trong khi , vic nhn dng tnh hnhCLN l nhim vca pha cung cp in.

Vit Nam, bt u c nhng nghincu chuyn su v nh gi tnh hnh SANHtrong HT [2, 3], tuy nhin vic nh lng hatnh hnh SANH trn HT thc tVit Namvn cha c thc hin. Nguyn nhn chnhhin nay l khng c mt c s d liu vCLN ni chung v SANH ni ring ca HT

Vit Nam do hthng gim st v lu trthngtin vCLN vn cn rt thiu. Bn cnh vicgim st CLN, mt cch gin tip xc nhtnh hnh SANH trn HT c thdng m hnhdbo CLN da trn cc nguyn nhn sinh ran. Trong cc nguyn nhn ny, trn 90%




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73

SANH l do s c ngn mch trong HT. Do, c thnh gi SANH thng quam phngv tnh ton ngn mch trn HT theo phngphp im sc[1, 2].

Hnh 1. ng cong chu in p ca nhmthit b SEMI (Semiconduactor Equipment andMaterials International group)

Bi bo trnh by phng php d boSANH trn ton b li in truyn ti 220kVca HT Vit Nam theo Tng s VI dngphng php im scvi sliu scngnmch trn li truyn ti 220kV thc t canm 2008 v s dng ch tiu SARFIX vSARFIX-CURVE[3,4,8].

II. XY DNG M HNH BI TON

2.1 Phng php im s c dng cho dbo SANH trong li in truyn ti 220kV

Theo phng php ny, gi thit SANHgy ra l do ngn mch trong HT. Khi , ctrng bin ca SANH (Hnh 2) c xcnh bi v tr v loi s c ngn mch [1, 4].c trng thi gian tn ti SANH th ph thucvo thi gian loi tr ngn mch ca cc thit bbo v.

Cc c trng trn y ca SANH cxc nh ti cc nt ph ti ca li truyn ti

220kV l cc trm bin p 220kV t xcnh cc ch tiu SARFIXv SARFIX-CURVEchoc h thng truyn ti in 220kV ca VitNam.

Hnh 2.Cc c trng ca SANH

2.2. Xy dng m hnh im s c i vili in truyn ti 220kV ca VitNam

- Chn v tr s c : Ch xt s c ngn mchtrn li 220kV. Cc ngn mch xy ra lic in p thp hn c th gi thit l t nhhng n li 220kV do tng tr cc my bin

p khu vc v a phng l kh ln. V bnthn li 220kV rt ln nn trong nghincu ny cha xt cc s c ngn mch trn li500kV v ti cc ngun in. Bin SANHti cc nt ph ti ph thuc vo v tr imngn mch. V nguyn tc s c c th xy rati bt c u trn li 220kV, tuy nhin nutrong mtphm vi ca li in m ngn mch u dn n SANH ti cc nt ph ti ccng c trng bin th ch cn chn mt vtr in hnh. S h thng truyn ti in220kV theo tng s VI [9] tnh n nm2008 gm 66 trm 220kV, 98 nhnh ng dy

220kV vi tng chiu di l 7988km. S cngn mch trn li in truyn ti c xtcho c ng dy v trm bin p nn i vis c trm bin p xt tt c 66 nt c trm220kV, cn s c trn ng dy, ty theo tngchiu di mi nhnh ng dy m xt mthoc vi im s c trn nhnh . Nhn chung,cc im s c cch nhau t 10km n 40km.Tng s im ngn mch trn ng dy l 169im.

- Chn loi s c ngn mch: Li in cao pl 3 pha, vai tr cc pha nh nhau nn khi xtcc dng ngn mch th xt 4 dng vi t lphn b sut s c [10] :

Ngn mch 1 pha - t : 65%

Ngn mch 2 pha : 20%

Ngn mch 2 pha - t : 10%

Ngn mch 3 pha : 5%

Vng m t an ton

Vng m tan ton

Vng

an ton




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74

-Phn b s c ngn mch : S c ngn mchmang tnh ngu nhin ph thuc vo nhiu yut [2] nn sut s c nhn chung khc nhau ivi tng loi s c v v tr s c. Trong nghincu ny, do s liu thng k v phn b s ctrn li truyn ti 220kV cha chi tit nns phn b s c c xut theo m hnhphn b u. Theo thng k ca tng cng tytruyn ti in quc gia li truyn ti 220kVtrong nm 2008 c tng s 45 s c xy ra ticc nt trm 220kV v 143 s c trn ccng dy 220kV. Sut s c ng dy l0,0179 s c/km/nm v ca trm bin p l0,682 s c/trm/nm. Phn b s c cho tngloi ngn mch i vi ng dy v my binp c cho Bng 1.

Bng 1.Phn b s c theo loi s c

LoiSut s c

n d Tr m bin N(1) 92,95 29,25

N(1,1) 28,60 9,00

N(2) 14,30 4,50

N(3)

7,15 2,25

- Chn v tr nt ph ti cn xc nh SANH :Trn li truyn ti, nt ph ti l cc nt ctrm 220kV cp in xung cc li c in pthp hn. Li 220kV li c dng mch vngnn nhn chung trn mi nhnh ng dy220kV, bo v c t ti c hai u v khixy ra s c ngn mch trn nhnh ng dy

no th nhnh s b c lp ring. Do , ttc cc nt (66 trm 220kV) trn li in ub SANH khi s c, khng c nt no b mtin duy tr v ta phi tnh SANH cho 66 ntny.

2.3 Tnh ton ngn mch v xc nh ctrung bin SANH trong li in truynti 220kV ca Vit Nam

Vic tnh ngn mch v SANH ti ccnt ph ti trong li truyn ti 220kV cthc hin bng chng trnh PSS/E. S khicc bc tnh ton nh hnh 3.

- Xc nh SARFIX : Vic chn v tr v xcnh sut s c cho tng v tr v tng loi sc c thc hin nh 2.2. Dng chngtrnh PSS/E tnh ngn mch ti tng im s cvi tng loi s c v t xc nh bin SANH ti tt c 66 nt ph ti do tng im v

tng loi s c ngn mch gy ra. Gn sut sc cho tng v tr v tng loi s c s rt rac tn sut SANH ti tng nt ph ti do sc ang xt gy ra. Lp li vic tnh ngn mchv SANH vi cc im s c khc ri tng hpli ta c tn sut SANH vi cc c tnh bin khc nhau do s c ti tt c cc im ngnmch trn li truyn ti 220kV gy ra, v cuicng ta rt ra c ch tiu SARFIXca ton hthng.

Hnh 3. S khi nh gi SANH trn litruyn ti in 220kV Vit Nam

-Xc nh SARFIX-CURVE: xc nh SARFIX-CURVE, phi xt n thi gian loi tr s c cah thng bo v li 220kV v dng c tnhchu in p la chn. i vi li 220kV caVit Nam hin nay, bo v chnh l bo v ctnhanh (so lch dng in hoc tng tr cctiu) vi tng thi gian ct ngn mch t 120msn 150ms. Trong nghin cu s dng c tnhchu in p ca cc ph ti nhy cm l SEMI,v vi thi gian loi tr s c nh trn, ccSANH c bin di 70% u ri vo vngmt an ton v lm cc ph ti nhy cm ngnglm vic. Do , khi xc nh SARFIX-CURVE,vi X t 70% n 100% in p nh mc thSARFIX-CURVEkhng i.

M phng phn b s c trnli truyn ti 220kV

M phng li in, tnhngn mch bng PSS/E

Start

Tnh SANH cho tng nt tibng PSS/E

Tnh SARFIXcho li truy nti in 220kV

Tnh SARFIX-CURVEchotruyn ti in 220kV

Stop




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75

III. PHN TCH KT QU

Thc hin trnh t tnh ton nh s khi hnh 3, sau y l tm tt mt s kt qung lu :

- Tn sut SANH trung bnh ca mt nt ph tibt k:

Hnh 4 v 5 biu din kt qu tnh tontn sut SANH ti nt trm 220kV Mai ng,Thnh phH Ni.

Hnh 4. Tn sut SANH nt 220kV Mai ngtheo tng khong c trng bin

Hnh 5. Tn sut SANH nt 220kV Mai ngtheo c trng bin ly tin

Hnh 6. Tn sut trung bnh SANH theo tngkhong c trng bin SANH

Hnh 7. SARFIX v SARFIX-CURVE ca li

truyn ti in 220kV tnh cho nm 2008

Hnh 4 biu din tn sut SANH theotng khong c trng bin ca SANH.Hnh 5 biu din tn sut SANH khi SANH cbin nh hn tng mc c trng bin .

- Tn sut SANH trung bnh h thng:

i vi mi ph ti, tn sut SANHtrung bnh theo tng khong c trng bin SANH c cho Hnh 6. V cui cng l chtiu SARFIX ca ton b li truyn ti in220kV Vit Nam c cho Hnh 7.

T kt qu cho ta mt s nhn xt ngch sau :

- Tn sut SANH ng vi tng loi s c tngng vi tn sut ca tng loi s c.

- SANH nng (70%-90%) c tn sut kh lnv tn sut SANH d ca nt c th l 220kVMai ng hay trung bnh cho tng nt chkhong 25 ln/nm rt nh so vi tng s s ctrn li 220kV l 188. l v li 220kV triton quc nn ngn mch xy ra tng min tnh hng n cc ph ti ti cc min khc.

- Tn sut SANH nt 220kV Mai ng lnhn SARFIXca ton h thng v li 220kV min Bc c nhiu ph ti hn do a bn rnghn.

N(3) N(1,1) N(2) N(1)

Tn sut SANH

X

Tn su t SANH

X

SARFIX

SARFIX-CURVE

X

X

Tn su t




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76

V. KT LUN

Bi bo trnh by phng php nhgi SANH trn li truyn ti in 220kV caVit Nam thng qua ch tiu SARFIX vSARFIX-CURVE. y l cgng u tin nhlng ha vic nh gi tnh hnh SANH ni

ring v CLN ni chung trong HT Vit Namtrn mt din rng.

Nghin cu trong bi bo cng cn cpht trin thm. Kt qu nh gi SANH trong

li truyn ti in cn c xt thm ccSANH do ngn mch phn ngun v litruyn ti in 500kV. Hn na, nghin cucng cn c th pht trin vic xem xt cc yut nh hng n phn b s c khi li truynti in ca Vit Nam tri trn mt phm virng ln vi tnh hnh s c khc nhau. Cc mhnh ngu nhin vi cc lut phn b xc sutph hp vi tnh hnh xy ra s c thc t cth c xem xt [2, 6,8].

TI LIU THAM KHO

1. M. H. J. Bollen; Understanding power quality problems - voltage sags and interruptions; IEEEPress, 2000.

2. Bach Quoc Khanh, Dong Jun Won, Seung Il Moon; Fault Distribution Modeling Using StochasticBivariate 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 TrippingTime 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, MarekWaclawiak, AshokSundaram; Indices for Assessing UtilityDistribution 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 LargeTransmission System; IEEE Trans. Industry Applications, Vol.35, No.1, pp.152-162, Jan./Feb.1999.

6. Juan a. marTNez-Velasco; Computer-Based Voltage Dip Assessment in Transmission andDistribution 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 StochasticPrediction 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, Jan2004.

9. Tng s pht trin Hthng in Vit Nam, Bn IV, Vin Nng lng, 2006.

10. T. A. Short; Electric Power Distribution Handbook, CRC Press, 2004.

a chlin h: Bch Quc Khnh - Tel: 0904.698.900, email: [email protected] Hthng in, Khoa in, Trng i hc Bch khoa H NiS1, i CVit, H Ni




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Abstract In this paper, a novel effort for prediction of

voltage sag in the entire transmission system of Vietnam ispresented. As the Vietnamese electricity industry moves towardthe electricity market, prediction will help utilities have earlyassessment of power quality in transmission system. Theproposed prediction approach uses a fault position method inwhich the fault distribution in the transmission system is createdbased on an actual fault occurrence in the entire 220kV and500kV transmission system throughout Vietnam that took placein 2008. The research also makes use of the SARFICURVE withITIC and SEMI curve, which takes into account of the actualfault clearing time of protective devices used in transmissionsystem in Vietnam. By using SARFICURVE, a better assessment ofvoltage sag performance is obtained in the transmission systemwith regard to loads voltage tolerance.

Index Terms--transmission system, power quality, voltage sagfrequency, stochastic prediction, fault distribution, fault clearingtime, 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 involtage 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 SystemsDepartment, Electrical Engineering Faculty, Hanoi University of Science andTechnology, 1 Dai Co Viet Rd., Hanoi, Vietnam (e-mail: [email protected]).

Nguyen Hong Phuc is a master student with Electric Power SystemDepartment, Electricity Faculty, Hanoi University of Science and Technology,1 Dai Co Viet Rd., Hanoi, Vietnam (e-mail: [email protected]).

and estimate expected impact of voltage sag on the equipment.

The permissible voltage tolerance for electric equipment,

normally defined by the manufacturers and the well-known

PQ curves for susceptibility of computer equipment displays

are CBEMA, ITIC or SEMI [1] whereas power quality

assessment of power supply system is utilities duty. This paper

is the first effort to assess the voltage sag performance in the

transmission system of Vietnam by using the method of

stochastic prediction of voltage sags [1], [2], [3] using

SARFICURVE-X that is derived from SARFIX with regard to

fault clearing time of protective devices currently used in thetransmission system in Vietnam.

II. INDICES FOR VOLTAGE SAG ASSESSMENT

Voltage sag assessment often relies on voltage sag

characteristics: magnitude and duration. There are many

indices proposed for voltage sag quantification. [1], [4] In this

paper the authors use one of the frequently used indices,

SARFIX. It is defined as follows

N

N

SARFI iiX

X

)(

(1)

whereX rms voltage threshold; possible values 10-90% nominalvoltage

NX(i) Number of customers experiencing voltage sag withmagnitudes below X% due to measurement event i.

N number of customers served from the section of the systemto be assessed

Despite being widely used, SARFIX 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 ofthe mains frequency. To take the voltage sag duration into

account, SARFIX is developed into SARFICURVE-X [5], [6]

which is defined below

N

N

SARFI

m

i

iX

XCURVE

1'

)(

(2)

where'

)(iXN :Number of customers tripped when experiencing

voltage sag with magnitudes below X% due to measurement

Prediction of Voltage Sag in The TransmissionSystem of Vietnam, A Case Study

Bach Quoc Khanh, Nguyen Hong Phuc

A

978-1-61284-788-7/11/$26.00 2011 IEEE




21/120

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, SARFICURVE-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, SARFICURVE-Xcan provide a better

understanding of the influence of voltage sag on the operation

of electric equipment in electric networks. This paper presentsthe method of calculating SARFIX-CURVEusing ITIC and SEMI

curve (SARFIITIC-Xand SARFISEMI-X) as case studies.

Fig 1. ITI curve for susceptibility of computer equipment

III. PREDICTION OF VOLTAGE SAG INTHE TRANSMISSION SYSTEM OF VIETNAM

A. Problem definition

The problem with stochastic prediction of voltage sag isthat it can only obtain the voltage sag performance of a

specific electric system by using data of causal events leading

to sags. In fact, more than 90% sag events are resulted from

short-circuits, hereby called faults, and it is possible to use

fault modelling and short-circuit calculation tools to simulate

and predict voltage sags in the power system. This work uses

the method of fault position [1] for voltage sag prediction in

the transmission systems with following significant steps

1. Modeling the fault distribution of the transmission systemof Vietnam event modeling (Sub section B)

2. Calculating the short-circuit current and voltage sags at allinfluenced load nodes event indices (Sub section C)

3. Quantifying voltage sag frequency at load nodes (siteindices) and cumulating system sags with different

characteristics and obtaining SARFIX(system indices)

4. Cumulating system voltage sags that cause equipment totrip and obtaining SARFICURVE-X.

To obtain SARFIX-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 modelingconsiders the occurrence of all faults in the whole transmissionsystem of Vietnam that cover 500kV and 220kV networks.The scope of the transmission system of Vietnam starts fromthe points of energy receiving from generating centers orinterconnection points with the transmission system of SouthChina to load nodes that are step-down 220kV substations. An

individual fault (short-circuit) is characterized by a pair ofparameters: fault position, fault type and its occurrence isassigned a fault rate. All faults with their assigned rate ofoccurrence build up a fault distribution model. Following areanalyses of each fault characteristics for the transmissionsystem of Vietnam.- Fault position: The fault can occur anywhere in thetransmission system including 500kV and 220kV networks.Since load nodes of the transmission system are 220kV step-down transformers, faults in 110kV networks and distributionnetworks should not considerably impact on voltage sags intransmission system because of large impedance of 220kVstep-down transformers. Faults at the power generatingsources should be included in the faults at the 220kV step-uptransformers. Therefore, this work only considers faults thatoccur in the transmission system. According to [1], [3], [7],

basing on the concept of area of vulnerability, faultpositions should be generally chosen in the manner that a faultposition should be the representative for other nearby short-circuit faults in a portion of network that cause voltage sags toload nodes with the similar characteristics (similarmagnitudes). Voltage sag magnitude normally divides in 9ranges : 0-0.1, 0.1-0.2,, 0.8-0.9 p.u. Similar manitudes meanthe magnitudes that fall inside a same range of magnitudeabove said. Faults in the transmission system are divided intotwo groups. That are overhead line OHL faults (or faults on

branches) and transformer faults (faults on substations). In the

transmission system of Vietnam given in VI Master Plan [10]for the year 2008, 63 substations 220kV will be seen as loadnodes for voltage sag assessment. The transmission system(Fig. 2) includes the 500kV network (11 nodes as 500kVsubstation and 17 branches of OHL with total length of3246km) and the 220kV network (63 nodes as 220kVsubstations and 103 branches of 220kV OHL with total lengthof 6414km). In Figure 2, the number of 220kV substation is 51that are under the management of National PowerTransmission Corporation (NPT). Other twelve 220kVsubstations are under the management of power generation.Therefore, transformer fault positions will be 11 for 500kVsubstations and 63 for 220kV substations respectively. For

OHL faults, fault positions are selected depending on thelength of each branch. According to the above said principleof fault position selection, we divide the line branches intosome segments and each segment is represented by one fault

position, normally at one of two ends of the line segment. For220kV OHL, the line segment length shoud be from 10km to40km 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 169locations for 220kV OHL. Therefore, there are 319 fault

positions in total.

SARFIX-CURVEqualified

SARFIX-CURVEdisqualified




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Fig 2. The Transmission System of Vietnam in 2008

Vietnam National Power TransmissionCorporation

Total 500kV OHL length: 3441kmTotal 220kV OHL length: 76541km

Number of 500kV substation: 11Number of 220kV substation: 51Total 500kV transformer capacity: 8756MVATotal 500kV transformer capacity: 14761MVA

220/110/35kVMai Dong substation,2x250MVA, Hanoi




23/120

- Fault type: This calculation considers all types of shortcircuit with well known contributory percentages of differentfault type are assumed as follows

Single phase to ground (SP-G): 65%

Two phase to ground (PP-G): 10%

Two phase together (P-P): 20%

Three phase to ground (3P-G): 5%

For the transmission system that requires high reliability

and stability, short-circuits are prone to permanent fault.Therefore, in this work, transitory faults are not considered.

- Fault rate: The occurrence of short circuits depends onmany factors [3] and the rates of occurrence of different faults(fault position, fault type) are normally not the same.However, because, in reality, recorded fault data does notconsider detailed fault distribution, this work assumes thatfault distribution for each fault type follows uniform modelwithin each regions in Vietnam. For example, phase-to-groundfaults remain unchanged anywhere in the section oftransmission system within a region. The transmission systemis 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 inthe Table 1 below.

TABLE 1. REGIONAL FAULT RATE PERFORMANCE

Regional PowerTransmission

Company

Line fault rate(per km.year)

Substationfault 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 forall four fault types as mentioned above. Therefore, for eachfault type, the fault rate should multiply by contributory

percentage of different fault types. For the fault that representsOHL faults within a line segment, fault rate should becalculated based on the length of the line segment.

- Selection of load nodes for voltage sag calculation: In thetransmission system, load nodes are 220kV substationsfeeding to downstream 110kV and medium voltage networks.The topology of transmission network is complicated andmany branches also have switching devices at both ends.When a fault occurs on a certain branch (a line or a

transformer), the two switching devices at both ends of thatbranch will trip and isolate it from the network. Therefore,many load nodes normally experience voltage sags. Only theloads on or nearby the fault position (for transformer fault)suffers an interruption. So, voltage sags at all 63 load nodeshad to be considered in this work.

- System loading condition when faults occur: It is alsonotable that for short-circuit calculation in the transmissionsystem where limited power sources are connects to, the short-circuit current and voltage sags depend heavily on the pre-fault loading condition when the fault occurs. The heavier the

True

False

True

False

True

False

True

Select the load node (among63 nodes for sa calculation

START

Select the fault position(amon 319 ositions

Select the fault type(SP-G, PP-G, P-P, 3P-G

Short-circuitcalculation and

determine voltage sagmagnitude at selectedload node by PSS/E

Fault distributionmodeling, determinefault rate of the fault

under calculation

Calculate the frequencyof voltage sag at

the selected load node

Areall fault type

selected ?

Areall fault position

selected ?

Areall load nodes

selected ?

Sag frequencyspectrum by

the fault undercalculation

event index

Sag frequencyspectrum at

selected loadnode by all

Sag frequencyspectrum at allload nodes by

all faultssite index SARFIX

calculation

Check ITICcurve ?

SARFIX-CURVE

STOP

Fig 3.

Block diagram

of the problem

of prediction of

voltage sag in

the transmission

system of

Vietnam.

(system index)




24/120

load on the system is, the higher short-circuit current will begenerated and the deeper voltage sags will be at load nodes.Therefore, the most interested prefault loading condition isobviously 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 byprogram PSS/E (Power System Simulation for Engineering).The block diagram of the calculation is depicted in Fig. 3.

- SARFIXcalculation: With fault distribution modeling forthe transmission system proposed in Part B, this work

performs short-circuit calculation using the program PSS/E fora certain individual fault (fault position, fault type) and thenvoltage sag magnitude at a selected load node is calculated.After assigning fault rate to this fault, the frequency of sag atthe selected load node resulted by this fault will be obtained.By repeating this calculation for all other faults (fault positionand fault type), and gather them together, we obtains thefrequency spectrum of voltage sag with different magnitudecharacteristics at the selected load nodes caused by all faults inthe transmission system. Fig. 4, Fig. 5 and Fig. 6 show anexample of voltage sag performance for an individual loadnode (220kV Mai Dong substation in Hanoi, Fig. 3). Fig. 4shows voltage sag frequency spectrum by sag magnitude

NEW

Fig 4. Voltage sag frequency spectrum (per year)by fault types at load node 220kV Mai Dong substation

Fig 5. Voltage sag frequency spectrum (per year) for all faultevents at 220kV Mai Dong Substation, Hanoi, Vietnam

(per unit) intervals for different fault types. Fig. 5 is voltagesag frequency spectrum for all fault types. Fig. 6 is thecumulative 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 performedand then we obtain voltage sag frequency spectrum of all otherload nodes. Finally, the average frequency spectrum per load

node is calculated and plotted on the Fig. 7 and SARFIXof thewhole transmission system of Vietnam is calculated as theformula (1). The voltage sag performance of transmissionsystem SARFIXis shown in Fig. 8.

Fig 7. Transmission system average voltage sag frequencyby magnitude characteristics

Fig 8. SARFIXand SARFICURVE-Xofthe transmission system of Vietnam

SagMagnitude

(p.u

)

SagMagnitude

(p.u

)

SagMagnitud

e

(p.u

)

SARFIX

SARFIITIC-X

SagMagnitude

(p.u

)

SARFIITIC-0.7

SARFISEMI-X

SARFISEMI-0.5

Sag magnitude(p.u)

SP-G

PP-G

P-P

3P-G




25/120

- SARFIITIC-X calculation: SARFIX-CURVE can be achieved bytaking fault clearing time of protective system into account.For the transmission system of Vietnam, the primary functionscurrently used for transformer protection is biased differential

protection using differential relays of SIEMENS (SIPROTEC7UT613) or ALSTOM (MiCOM P340). For OHL line

protection, the primary functions currently in use are also thedifferential protection as above said using the tele-communication links of power line carrier or fibre-opticalground wire integrated in power carrying lines or the distance

protection using differential relays of SIEMENS (SIPROTEC7SA6) or ALSTOM (EPAC 3000, MiCOM P440). All those

protective relay system is of instantaneous tripping type that istypically less than 100ms. The switching devices are almostSIEMENS, SCHNEIDER or ABB products manufactured inEurope with typical breaking time of 40ms for 500kV to 60msfor 220kV circuit breakers. Besides the above mentionedoperating times of protective relays and circuit breakers,additional time delays are also included for auxiliary relaytrips and operating time of tele-protection with total additionaloperating 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

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