Estimation of Sensitive Equipment Disruptions Due

Disruptions Due to V oltage Sags

Chan-Nan Lu,Senior Member,IEEE,and Cheng-Chieh Shen,Student Member,IEEE

Abstract—This paper presents a method for predicting the number of equipment disruptions due to voltage sags in a unit of time based on a concept described in IEC61000-3-7.The proposed method uses the probabilistic distributions of system disturbance and equipment immunity indices obtained from a unified fuzzy inference engine to represent the disturbance severity and equip-ment susceptibility of voltage sags.It takes stochastic behavior of service performance into account in the estimation of equipment disruption.The proposed framework is also applicable if other power-quality indices,such as the voltage sag energy index and voltage sag severity index,are adopted.It can be used as an alternative for performing voltage sag coordination andfinancial analysis.

Index Terms—Disturbance level,equipment disruption,fuzzy index,immunity level,power quality(PQ),voltage sag.

I.I NTRODUCTION

I N THE voltage sag coordination efforts,two databases are

needed.First,the voltage sag characteristics of a site should either be known from recorded events data or from predictive techniques.Second,the equipment’s response to voltage sags should be known either from the manufacturer’s specifications or from voltage sag immunity tests.One useful approach to obtain the voltage tolerance curve of a device is through tests based on IEC61000-4-11[1].This document provides a standard procedure to test equipment susceptibility to specific voltage sag durations and magnitudes.With an estimate of the annual number of compatibility-related process disruptions and an estimate of the cost of disruption,alternatives may be evaluated to minimize the overall costs.The alternatives include buying less-sensitive equipment,contracting for better service,or adding mitigating equipment.

A standard methodology for technical andfinancial analyses of voltage sag compatibility between process equipment and electric power systems is recommended in IEEE Std.1346-1998 [2].Coordination charts of voltage sags events are used to re-port and display site service information.The scatter diagram displays voltage sags in a two-dimensional grid of voltage mag-nitude and sag duration.Based on data shown in the scatter di-agram,site sag characteristics can be represented by some con-tours representing the number of sags in a unit of time[3].The sag coordination chart,as shown in Fig.1,combines the sag

Manuscript received September6,2005;revised November28,2005.Paper no.TPWRD-00524-2005.

The authors are with the Department of Electrical Engineering,National Sun Yat-Sen University,Kaohsiung804,Taiwan,R.O.C.(e-mail:cnl@ee.nsysu.edu. tw;d31811@student.nsysu.edu.tw).

Color versions of one or more of thefigures in this paper are available online at http://ieeexplore.ieee.org.

Digital Object Identifier

10.1109/TPWRD.2007.3433

Fig.1.Supply sag performance contours and equipment sensitivity[3].

number contours and an equipment tolerance curve on the same

chart to show equipment sensitivity to the sag events.In the past,

due to the test equipment used,sensitivity curves were typically

rectangular or approximated with several rectangles.The area

below and to the right of the sensitivity line shows the disrup-

tion region,while the area above and to the left corresponds to

sags that will not disrupt the equipment.The penetration of the

sensitivity curve knee into the supply contours determines the

number of disruption events from sags.The sag contour lines

work well with rectangular-sensitive curves.

The scatter diagram is useful for visualizing the annual voltage

sag events distribution,but a single voltage sag event index would

make the service performance comparison easy[4].If the single-

event index approach were used,the system disturbance level of

a site can be obtained from the indices of all events recorded.The

system disturbance level and equipment immunity level using

single-event index concepts were mentioned in IEC61000-3-7

[5]but without clear definitions.Using this concept,for a spe-

cific location,there might be an overlap between the distributions

of the system disturbance level and equipment immunity level as

shown in Fig.2.At most locations where most equipment oper-

ates satisfactorily,there is no overlap or only a small overlap.

Currently,there is no standard on how to determine the dis-

tributions and assign compatibility and planning levels of IEC

61000-3-7to the T&D interfaces[6].

An application of the fuzzy-logic technique to quantify the

voltage sag disturbance level and equipment immunity level

based on the single-event approach was presented by the authors

in[7]and[8].The framework takes network and equipment vul-

nerability,and uncertainties in voltage sag classification into ac-

count,therefore providing useful information for both the utility 0885-77/$25.00©2007IEEEFig.2.Illustration of basic voltage quality concepts with time/location statis-tics[5].

and customers.V oltage magnitude and the duration of sag events are used as the inputs to a fuzzy inference engine that provides fuzzy indices indicating the relative disturbance levels of the studied events.

In this paper,a new procedure for predicting the number of equipment disruptions due to voltage sags in a unit of time is proposed.Using the single-event index approach,the proba-bility density distributions of system disturbances and the equip-ment(or production line)immunity level are obtained based on the power-quality(PQ)measurements and the equipment voltage tolerance curves,respectively.It should be noted that although we use a fuzzy voltage sag index in this study,other PQ indices,such as the voltage sag energy index and voltage sag severity index[4],[6],could also be adopted to provide the distributions shown in Fig.2.The area of overlapping and the estimated number of interruptions are calculated by using the unreliability concepts in the interference theory and reliability computations[9].The proposed framework realizes the concept shown in Fig.2and can be used as an alternative for performing voltage sag coordination andfinancial analyses.

II.Q UANTIFYING S YSTEM D ISTURBANCE L EVEL

AND E QUIPMENT I MMUNITY L EVEL

An energy-based fuzzy index,which represents the relative severity of a voltage sag event,is used in this study.In order to be self-contained,the fuzzy voltage sag index is briefly described in the following.Interested readers should refer to[7]and[8] for further details.

A.Membership Functions of the Input Variables Fuzzy Sets The voltage sag attributes used to calculate the fuzzy index are the retained voltage magnitudes in percentage of the nom-inal voltage and the logarithm of the measured duration in seconds.In order to derive a meaningful index,viewpoints to the problem from the supply,equipment manufacturer,and customer sides are considered.Fig.3exhibits the definitions of the input variables fuzzy sets.These membership functions are based on the empirical information embedded in the ITIC and SEMI F47voltage-tolerance standard curves[4]repre-senting the users and manufacturers’viewpoints,and on the NRS-048-2:2003voltage sag window,an approach that is

used Fig.3.Fuzzy membership functions of input variables.

by a utility company to categorize the voltage sag events[6].

The trapezoidal functions are used to deal with the ambiguity

of a severity definition and they are also suitable for dealing

with the measurement uncertainties.

B.Fuzzy Reasoning Process[10],[11]

In the fuzzy-logic reasoning,IF–THEN inference rules are used

to combine membership values of fuzzy variables to perform

the reasoning.All of the consequences for each defined rule

are aggregated to give afinal value indicating the closest to the

knowledge being modeled.For crisp input variable data using

the rules,outputs are generated.In this study,the implication

is by“product”which scales the output fuzzy set.All of the IF–THEN rules used have the same weight,and the aggregation method is“sum,”which is simply the sum of each rule’s output

set.After aggregation,defuzzification is performed to obtain the

final crisp result.The defuzzification method used in this study

is the centroid calculation,which returns a value representing

the center of the area under the curve obtained.

C.Membership Functions of the Output Variable Fuzzy Sets Corresponding to each of the25magnitude-duration class combinations shown in Fig.3,an output variable fuzzy set membership function that represents the lost energy of each voltage sag severity category(window)is defined.As shown in Fig.4,for the top-left and bottom-right corners of a window, two voltage sag energies are calculated.The shape of each triangular membership function of the output variable fuzzy set is defined by the individual and average values of logarithms of the two calculated sag energies.

The calculated fuzzy index contours corresponding to all

combinations in the voltage magnitude and sag duration grid

are shown in Fig.5.As can be seen,the contours lean toward

the ITIC and the SEMI F47curves,and the gradients of the

LU AND SHEN:ESTIMATION OF SENSITIVE EQUIPMENT DISRUPTIONS DUE TO VOLTAGE SAGS

3

Fig.4.Example of building an output variable membership

function.

Fig.5.Contours of indices calculated by the proposed method.

contours are different at different windows of the plane de-pending on the fuzzy classi fications of the input variables.Using the approach,site performance indicators or disturbance level distribution can be obtained from the single-event indices of all recorded events.

Several equipment voltage sag immunity tests conducted by the authors have shown that equipment has different shapes of the tolerance curves and some show nonrectangular curves.Ex-amples of equipment with smooth tolerance curves can be found in the literature.Figs.6and 12show some examples of equip-ment with rectangular and nonrectangular tolerance curves.

In

Fig.6.V oltage sag susceptibility

curves.

Fig.7.Distributions of system disturbance level and equipment immunity levels.

the proposed method,in order to obtain a distribution of the equipment immunity level resembling that shown in Fig.2,var-ious voltage magnitude and sag duration combinations on the tolerance curve are used as inputs to the fuzzy inference process described in Section II.The indices corresponding to those com-binations are calculated and the distributions are plotted.Fig.7shows the fitted normal distributions of the calculated indices of the studied equipment.As can be seen,the distribution of de-vice A is to the right of those of devices B and C,indicating a better capability of tolerating voltage sag events as compared to devices B and C.This result agrees with the information shown in Fig.6(i.e.,equipment with tolerance curves to the lower right portion of the plane would have better capability in dealing with the voltage sag problems).The “system ”curve shown in Fig.7indicates a distribution of the disturbance level calculated for a location.These distributions can be used to compare the perfor-mance of different service areas and products alternatives.

4

IEEE TRANSACTIONS ON POWER

DELIVERY

Fig.8.Unreliability of interferences.

III.S TOCHASTIC P REDICTION OF E QUIPMENT D ISRUPTIONS In [3],the coordination chart shown in Fig.1was recom-mended to estimate the number of disruptions in a unit of time.This technique works well with rectangular sensitivity curves,but for nonrectangular curves,such as curve C in Fig.6and other smooth curves (e.g.,Fig.12),more effort would be required to obtain the estimates.

In the proposed approach,the number of disruptions is com-puted using the unreliability concept shown in Fig.8.The area of overlapping is calculated based on interference theory and re-liability computations [9].Let the density function for the dis-turbance level

()be denoted

by

,and that for immunity level (I)

by

,then,by de finition

Reliability

(1)

The overlap in Fig.8shows the interference area,which is indicative of the probability of disruptions.The probability of a

disturbance level lying in a small interval of

width

is equal to the area of the

element ;that

is

(2)

The probability that the immunity level

is greater than a

certain disturbance

level

is given

by (3)

The probability of the disturbance level lying in the small

interval

and the immunity level exceeding the disturbance level given by this small

interval

under the assumption that the disturbance level and the immunity level random variables are independent is given by

[9]

(4)

Fig.9.Flow diagram of the proposed method.

The reliability of the component is the probability that the

immunity level is greater than the disturbance

level for all possible value of the disturbance

level ,which is given

by

(5)

The unreliability is de fined

as

probability of

failure

(6)

(7)

where

is the cumulative distribution function of the equip-ment immunity level.The number of equipment

disruptions

the number of sag events recorded in the studied period.The flow diagram of the proposed method is shown in Fig.9.

IV .N UMERICAL E XAMPLES AND D ISCUSSIONS

In this study,the Fuzzy Logic Toolbox of M ATLAB is used to develop the fuzzy inference procedure and calculate the fuzzy disturbance and immunity indices.The Statistics Toolbox is used to estimate the statistical distribution parameters.When a lognormal distribution is a better choice for representing the distribution,the command “logn fit (data)”in the toolbox returns the parameters of the expected value and the standard deviation

LU AND SHEN:ESTIMATION OF SENSITIVE EQUIPMENT DISRUPTIONS DUE TO VOLTAGE SAGS

5

Fig.10.V oltage sag events recorded at a 161-kV bus of the Lung –Sung sub-

station.

Fig.11.Supply sag performance contours and equipment sensitivity.

of a lognormal distribution function.Simpson ’s one-third rule [14]can be used to calculate the integration in (7).

Fig.10shows a scatter diagram of the actual voltage sag events recorded in four years at a substation close to a high-tech industrial park in Taiwan.Based on this scatter diagram,Fig.11shows the voltage sag coordination chart.Using the technique recommended in [3],it will be easy to estimate the number of disruptions for devices A and B;they are six and fourteen,re-spectively.The number of disruptions of equipment C would be close to fourteen because the tolerance curve is between the contour line for thirteen events and the line for fifteen events.The “system ”curve shown in Fig.7was obtained based on the voltage sag data shown in Fig.10.Since the disturbance level and equipment immunity level are based on a uni fied infer-ence engine,therefore,using the curves shown in Fig.7and

the

Fig.12.V oltage –tolerance curve of a contactor and voltage sag events recorded at a 161-kV bus of the Lung –Sung

substation.

Fig.13.Fuzzy indices of system disturbances and equipment immunity levels.

method described in Section III,the estimated disruptions of de-vices A –C are 5.96,13.19,and 14.43,respectively.These num-bers match quite well with those sag events located at the lower-and right-hand side of the tolerance curves shown in Fig.10.Fig.12shows the tolerance curve of an ac contactor [12]in conjunction with the sag events recorded.It would be dif ficult to predict the number of disruptions for this device by using the voltage sag coordination chart method.Fig.13shows the proba-bility density distributions of the voltage sag severity indices and the equipment immunity indices.Fig.14shows the distributions fitted by a lognormal distribution and a normal distribution,re-spectively.The estimated number of disruptions of the contactor is 16.11in four years,which is again fairly close to the informa-tion shown in Fig.12.Other smooth tolerance curves were also tested,and experiences have shown that the choice of the fitting distributions will affect the accuracy of the estimation results and the best fits of the indices are dependent on the site service characteristics and equipment susceptibility.

DELIVERY

Fig.14.Fitted distributions of system disturbance and equipment immunity levels.

V.C ONCLUSION

A new framework for estimating the number of equipment disruptions at a supply service in a unit of time is presented. Using the fuzzy indices,stochastic distributions of system dis-turbances and equipment susceptibilities are obtained and the number of disruptions can be estimated.Note that the proposed framework could also be based on other single-event indices if they could better represent the system and equipment character-istics under study.The presented methodology is intended to be used as a planning tool to quantify the voltage sag environment and equipment sensitivity,and can be used to performfinan-cial analysis of the compatibility of equipment with an electric power system.

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Chan-Nan Lu(M’82–SM’92)received the Ph.D.degree from Purdue Univer-sity,West Lafayette,IN.

He was with the General Electric Company,Pittsfield,MA,and the Control Division,Harris Corporation,Melbourne,FL.Currently,he is with the Depart-ment of Electrical Engineering,National Sun Yat-Sen University,Kaohsiung, Taiwan,R.O.C.His current interests are in power system operations and power quality.

Cheng-Chieh Shen(S’05)received the M.S.degree from National Sun Yat-Sen University,Kaohsiung,Taiwan,R.O.C.,where he is currently pursuing the Ph.D. degree.