milanovic_2008E

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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 23, NO. 2, APRIL 2008 1063

The Influence of Induction Motors on Voltage SagPropagationPart I: Accounting for the Change in

Sag CharacteristicsJovica V. Milanovic, Senior Member, IEEE, Myo T. Aung, Member, IEEE, and Sarat C. Vegunta

AbstractThis paper presents an analytical approach to theanalysis of the interaction between induction motors (IMs) andvoltage sags. The presented methodology enables quick assess-ment of the influence of IM on sag characteristics and avoidstime-consuming transient simulations. The accuracy of the de-rived analytical formulae is verified through classical transientsimulations using the PSCAD/EMTDC package. This paper fur-ther proposes a simple, yet efficient transformation of resultingnonrectangular voltage sags, based on the loss of voltage index,into equivalent rectangular sags suitable for conventional voltagesag performance benchmarking.

Index TermsInduction motors (IMs), power quality (PQ),voltage sags.

I. INTRODUCTION

POWER-QUALITY (PQ) issues continue to receive signif-

icant attention due to their potentially huge economic im-

pact on the industry. Voltage sags, transients, and momentary

interruptions are among the most common PQ disturbances and,

by large, the most frequent cause of equipment malfunctions and

costly disruptions of industrial processes [1].

The IEC 61000-4-30 standard defines the voltage dip (sag)as a temporary reduction of the voltage at a point of the elec-

trical system below a threshold. This threshold is defined by

the IEEE 1159-1995 standard as 90% of the nominal voltage.

If the magnitude of the retained voltage drops below 10% of

the rated voltage, the disturbance is classified as an interrup-

tion. Most voltage sags and short interruptions recorded in ac-

tual power systems last from a few cycles to 1 min. Voltage

sag characteristics (i.e., magnitude, duration, phase-angle jump,

sag shape, etc.) change when sags propagate through power

system networks. The extent of this change depends on network

topology (mesh or radial), line and cable impedances, trans-

former winding connections, system protection and groundingpractices, load connections (star or delta), and load dynamics

(e.g., IMs) [2], [3]. The influence of all of these factors has been

Manuscript received October 18, 2006; revised June 5, 2007. This work wassupported in part by the EU Framework V Project Microgrids and in part by theEU Framework VI Project RISE under Contract FP6-INCO-CT-2004-509161.Paper no. TPWRD-00650-2006.

J. V. Milanovic and S. C. Vegunta are with the School of Electrical and Elec-tronic Engineering, The University of Manchester, Manchester, M601QD, U.K.(e-mail: [email protected]).

M. T. Aung is with the University of Bath, Bath, BA2 7AY, U.K. (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPWRD.2007.915846

studied in the past either by considering an individual effect or

through more inclusive studies that dealt with several influences

at the same time (typically not all of them). A large number of

published and easily accessible reports describe the results of

those studies.

One of the major deficiencies of the past studies remains as

the accounting for dynamic effects in large system sag prop-

agation studies. Typically, sag calculation and propagation in

large systems are studied by applying static fault calculations

based on system impedance (or admittance) matrix and equiva-lent positive-, negative-, and zero-sequence networks. It is fur-

ther assumed that voltage sags originate from faults (cleared by

primary protection) on transmission and/or distribution systems

and that they have a rectangular shape. The assumption about

the shape is based on neglecting the change in fault impedance

during the fault and the effect of load dynamics.

The shape of voltage sags, however, ceases to be rectangular

if there is an appreciable number of IMs in the network and the

faults last longer (e.g., distribution system faults or faults cleared

by secondary protection). In such cases, the shape of the sag

changes due to the IMs dynamic responses. When a voltage

sag appears at the terminals of an induction motor, the torqueand the speed of the motor decrease to levels below their nom-

inal values. Once the voltage sag is removed, the IM attempts

to reaccelerate, and starts drawing an excessive amount of cur-

rent from the power supply. The flow of such current through

the supply impedance prevents fast recovery of the voltage and

causes a prolonged sag duration and change in the shape of the

sag. This new resulting sag may cause sensitive equipment to

trip even though it might have been able to ride through the orig-

inal voltage sag.

Effectively, all existing, standard benchmarking approaches

(e.g., SARFI, DISDIP, ESKOM, and UNIPED sag tables, 3-D

cross tabulation of the rms variation, magnitude-duration bar-

charts, etc.) register voltage sags as rectangular events [4]. (Forexample, for a typical voltage sag, only the information about

phase-to-neutral or line-to-line voltage magnitude and sag dura-

tion is provided.) These tabulated results are then used for com-

paring the sag performance of different buses/systems and even

for the assessment of equipment/process sensitivity to voltage

sags.

A few past works (e.g., [3] and [5]) dealt with the influence

of IMs on voltage sags. They typically modeled IMs using dy-

namic models and, therefore, are not suitable for large system

applications. The results of that analysis could not be presented

using standardized, widely accepted voltage sag tables due to

nonrectangularity of the resulting voltage sags.

0885-8977/$25.00 2008 IEEE


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1064 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 23, NO. 2, APRIL 2008

Fig. 1. Simplified system impedance model.

To capture the IM behavior during the sag and its influence on

sag characteristics, a comprehensive analytical tool was devel-

oped and partially reported in [5]. The method presented there

described the general behavior of IMs when subjected to sym-

metrical and asymmetrical voltage sags using positive- and neg-

ative-sequence IM equivalent circuits. It did not discuss the in-

fluence of IM operating condition and parameters on the char-

acteristics of the resulting voltage sag.

This paper builds on and is an extension of the work presented

in [5]. It considers comprehensively the influence of IM on in-

dividual phase voltages and the conversion of resulting nonrect-

angular voltage sags into rectangular ones suitable for conven-

tional sag benchmarking purposes.

The results of developed analytical method (implemented in

Matlab [6] and based on static calculations) are verified using

classical transient simulations in PSCAD/EMTDC [7]. The

proposed methodology accounts for the influence of IM on

voltage sag characteristics and propagation, without performing

lengthy transient simulations, making it applicable for large,

practical system studies where hundreds of sags at numerous

bases have to be evaluated. It further enables studies of prop-

agation of voltage sags from the point of common coupling

(PCC) to the end-user equipment in an industrial plant with a

number of IMs or the propagation of voltage sags through the

electrical system of an industrial park to be built. The majoradvantage of the method is that it starts with conventionally

recorded/represented voltage sags and produces the output in

the same, universally adopted, format.

II. MODELLING OF AGGREGATE IM

FOR VOLTAGE SAG STUDIES

Voltage sagIM interaction is studied based on a group of

identical IMs connected at the PCC (as shown in Fig. 1) and

subjected to a typical, asymmetrical, three-phase, rectangular

voltage sag. IM and sag parameters are given in Appendix A.

The model is implemented in Matlab to facilitate static calcu-

lations. The integration step of 20 ms (to account for the delay

in rms calculation in PSCAD/EMTDC) is used in order to val-

idate the results by transient simulations in PSCAD/EMTDC.

The methodology is developed for the most general case of an

asymmetrical sag and a group of IMs, but it can be easily simpli-

fied and applied either to a single IM or a group of IMs subjected

to symmetrical voltage sags.

A. Sequence Components Voltages

For a given presag, during the sag and after sag voltages (see

Appendix C), corresponding sequence component voltages can

be calculated as follows:

(1)

Fig. 2. Simplified induction motor equivalent circuits. (a) Positive-sequencecircuit. (b) Negative-sequence circuit.

With , where is a com-

plex operator. It is assumed that at the end of the voltage re-covery, the voltages in all three phases reach their respective

nominal presag values, i.e.,

(2)

B. Aggregation of IMs

The aggregate model of a group of IMs retains the same form

as a model of an individual motor of the group. The aggregated

parameters of the equivalent IM representing a group ofniden-

tical (or different) IMs can be calculated as suggested in [8].

However, for simplicity, only identical IMs are chosen in thisstudy and could well extend to a group of nonidentical IMs.

For identical IMs, the aggregated parameters are obtained by

dividing electrical parameters of an individual motor by

(number of aggregated motors) and multiplying mechanical pa-

rameters by , e.g.,

(3)

(Note: The aggregated motor parameters are represented in

the paper with suffix agg.)

C. Electromagnetic Torque Variations

Fig. 2 shows the equivalent positive- and negative-sequence

circuits of the IM. Since the magnetizing impedance of the IM

is much larger than the stator and the rotor impedances, it is

neglected. The stator and the rotor currents are assumed equal.

The positive- and negative-sequence electromagnetic torques

are given in [9] as

(4)

(5)


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MILANOVIC et al.: INFLUENCE OF INDUCTION MOTORS ON VOLTAGE SAG PROPAGATIONPART I 1065

Fig. 3. Speed-torque curves under normal and voltage sag conditions [4].

where and

Under balanced supply conditions, only positive-sequence

components exist and they contribute to the development of

positive-sequence torque only. During unbalanced supply con-

ditions, however, negative-sequence components appear, giving

rise to negative-sequence torque, which opposes the existing

positive-sequence torque. The resulting electromagnetic torque,

or net torque, in the machine under unbalanced operating con-

ditions, is a vector sum of positive- and negative-sequence

torques

(6)

D. Machine Speed Variation During and After Voltage Sag

The presence of either balanced or unbalanced voltage sags at

the IM terminals will cause electrical and mechanical transients

in the IM. The dynamic performance of the IM during the sag

can be described by the following electromechanical equation:

(7)

Due to small time constants (fast response of electrical cir-

cuits of the IM), the electrical transients in the IM are mostly

finished before the onset of the mechanical transients [3], [5].

The electrical torque in the machine therefore will reduce in

proportion to the square of the rms value of the voltage sag

magnitude, while the mechanical torque will remain largely un-

changed. Due to the reduction in electrical torque, the motor

operates at a new operating point given by intersection of the

motor-speed curve during the voltage sag and load torque char-

acteristic, as shown in Fig. 3. The speed of motor reduces from

the nominal value at time to that at the end of the

sag at time along the load torque curve. Depending

on the duration of the voltage sag, the during voltage sag speedwill be between and .

Under balanced or unbalanced voltage sags, (6) can be trans-

formed to a first-order differential (8) which, when solved, gives

the expression (9) for or motor deceleration speed

(8)

(9)

where

At the end of the sag, the balanced nominal voltage supply is

restored, resulting in positive-sequence torque only. This now

causesthe motorto reacceleratefrom at time toat time . During this condition, (6) can be transformed to (10).

The solution of (10) gives the expression (11), which represents

voltage recovery speed or motor acceleration speed

(10)

(11)

where and

.The reacceleration time from to , at the end of

the sag, is given by

(12)

where .

E. Machine Current Variations During and After Voltage Sag

Positive- and negative-sequence currents during the sag are

given by

(13)

(14)

where ; and

At the onset of the voltage sag, the positive-sequence current

falls almost instantly with a drop in terminal positive-sequence

voltage. As the voltage sag magnitude stays constant during the

sag (for a sag duration ), the positive-sequence currentincreases gradually followed by a gradual increase in motor slip


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during the sag; hence, the motor slows down. How-

ever, in the case of unbalanced operation, the negative-sequence

current rises instantly with the appearance of voltage unbalance

and as negative-sequence voltage stays constant during the sag,

the current remains almost unchanged with little or a negligible

change in slip (as ).

Similarly, positive- and negative-sequence currents after thesag are given by

(15)

(16)

where .

At the start of voltage recovery, the voltage rises to nominal

balanced value and the slip is large (depending on the speed

drop seen at the end of the sag). These contribute to a large

positive-sequence inrush current (to build up the flux in the

air gap) which gradually decays as the motor accelerates (de-

creasing motor slip) to nominal speed. As the nominal and bal-

anced voltage is restored, the negative-sequence current dropsclose to zero.

III. INDUCTION MOTORVOLTAGE SAGS INTERACTION

A. Basic Change in Sag Shape Due to IM Dynamics

As a result of this continuous variation in the motor cur-

rents, the motor terminal voltages will not remain constant and a

change in terminal voltages occurs in accordance with the vari-

ation in currents. To describe this phenomenon, a simple test

system consisting of an aggregated IM connected to the infi-

nite (system) bus through a system impedance , as shown

in Fig. 1, is considered.

During the voltage sag, positive- and negative-sequence volt-

ages at the system bus are calculated using (1) and positive- and

negative-sequencecurrents at the end of voltage sag are obtained

from (13) and (14). Once the initial conditions ( and

) are established, the variation in IM terminal volt-

ages (i.e., voltages at the PCC) are calculated from

(17)

(18)

(19)

(20)

Similarly, positive- and negative-sequence (21), (22) voltages

at the system bus ( and ) after the sag can

be obtained. Finally, the variation in IM terminal voltages is

given by (23) and (24)

(21)

(22)

(23)

(24)

It can be seen from (23) and (24) that the change in IM ter-

minal voltage depends on the motor current, system voltage, and

impedance. The zero-sequence voltage during the sag is not in-fluenced by the motor dynamic behavior and, hence, remains

Fig. 4. IM dynamic responses following the asymmetrical three-phase voltagesag (sag parameters given in Appendix B) obtained with the Matlab model.

constant. Finally, the phase components of IM terminal voltages

during and after the sag are ob-

tained from

(25)

(26)

Responses of the aggregate IM to an asymmetrical voltage

sag obtained using (1)(26) are shown in Fig. 4. The top dia-

gram in this figure illustrates the original voltage sag applied,

and the subsequent diagrams present speed, voltage, and cur-

rent responses of the IM.

B. Model Validation

The developed IM model has been partially validated in [5]

by comparing the IM speed response (following a three-phase

symmetrical sag) with a previously published speed response

obtained with the more detailed model of the IM. A good agree-ment between the two sets of results was found and discussed in

detail in [5]. In order to validate the model further, in particular

responses of IM to asymmetrical sags, the test system of Fig. 1

is modeled in PSCAD/EMTDC as shown in Fig. 5.

The model consists of an aggregated IM of three identical

squirrel-cage induction motors (with the parameters similar to

those in Appendix A) connected to the PCC bus (as shown in

Fig. 5). A voltage sag generator originally developed in [10]

is also connected to a PCC bus via a system impedance de-

fined in Appendix A. Classical transient simulations with full

dynamic models of IMs are performed in PSCAD/EMTDC to

observe the motor transient response to voltage sags. In order to

initiate the PSCAD/EMTDC model smoothly, all motors werebegan with 0.07914-p.u. torque, and then when they reached full


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Fig. 5. IM connected to a voltage sag generator through system impedance.

Fig. 6. Comparison of Matlab (dashed lines) and PSCAD (solid lines) results.

speed, switched to a full load (0.7914 p.u.). Fig. 6 compares IM

terminal voltages following an asymmetrical three-phase sag,obtained with Matlab (dashed lines) and PSCAD (solid lines)

models. The top pair of curves represent Phase A voltages, the

middle pair is Phase B voltages, while the bottom pair repre-

sents Phase C voltages. It is evident from Fig. 6 that the re-

sults of Matlab and PSCAD/EMTDC agree well, not only qual-

itatively but also quantitatively, (both in terms of sag magni-

tude and duration) with a maximum difference occurring during

the sag voltage magnitudes at the beginning of the sag of less

than 10%. (Note: The sag magnitude that matters is the min-

imum value of the rms voltage during the sag, the value that is

usually recorded as the equivalent sag magnitude in commonly

used in sag representation tables. The difference in this valuebetween two sets of curves, as can be seen from Fig. 6, is far

less than 10%.) The observed difference can be attributed not

only to simplifications made in the development of the Matlab

model [based on (1)(26)] but also to the originally different IM

model used in PSCAD/EMTDC. Namely, the IM model avail-

able in the PSCAD/EMTDC library is based on double-cage IM.

A similar or better agreement between responses obtained with

Matlab and PSCAD/EMTDC models was observed for other

types of voltage sags. Therefore, it can be deduced that the sim-

plified IM model developed in Section II can be used to ade-

quately describe the IM behavior when subjected to any type of

single stage (constant sag magnitude for the whole duration of

the sag), rectangular voltage sag, and, consequently, the IM in-fluence on voltage sag shape.

Fig. 7. Comparison of the IM speed change with respect to symmetrical andasymmetrical sags (adopted from [4]).

Fig. 8. Comparison of the IM speed change with respect to asymmetrical sagswith a small and large amount of negative-sequence contents.

The results of the analysis obtained for different case studies

are presented in Sections III-C and D. All results are obtained

with the model developed in Section II.

C. Effects of Voltage Sags on IM

Fig. 7 (reproduced from [5] for the completeness of dis-

cussion) illustrates that the voltage sags of different types

and severity will result in different variations in motor speed.

For this specific case, a symmetrical voltage sag caused by

a single line-to-ground fault results in a slight drop in speed

compared to that caused by a symmetrical three-phase voltage

sag. According to the previous discussion, it can be concluded

that this particular asymmetrical voltage sag contributes only

to a small amount to the negative-sequence voltage component

while its positive-sequence component is much higher than thatdeveloped by the symmetrical sag. In the same cases, however,

unbalanced voltage sags might cause a significant drop in speed

as shown in Fig. 8. This is particularly the case when they are

associated with large negative-sequence voltage components.

Fig. 9 illustrates the influence of a combined inertia of motors

and loads on IM behavior during the sag. It can be seen that the

IM with a low inertia load decelerates rapidly during the sag

though it also restores the nominal speed soon after the voltage

sag is over. In contrast, a steady slow speed drop and a slow

speed recovery can be expected in the case of the motor with a

high inertia load.

As far as the influence of motor parameters on the change in

speed is concerned, Fig. 10 shows that different motor param-eters will cause different changes in motor speed. The greater


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Fig. 9. Comparison of the induction motor speed changes with respect to lowand high inertia loads.

Fig. 10. Comparison of the IM speed changes with respect to low and highrotor resistances.

Fig. 11. Effects of the dynamic response of 168 aggregated small IMs on sagswith different magnitude.

speed drop can be expected in case of motors with high rotor

resistance. Speed recovery time, however, is not affected signif-

icantly.

D. Effects of IM Dynamic Responses on Voltage Sags

It can be seen from Figs. 11 and 12 that the shape of voltage

sags is not rectangular when the effect of IMs is taken into ac-

count. Additionally, Fig. 13 shows that different groups of IMs

differently influence the shape of the resulting voltage sags.

(The effect of 168 aggregated small IMs is particularly pro-

nounced).

Table I shows that the output power produced by groups 3 and

5 is almost the same though group 5 needs a longer recovery

time (i.e., 1.38 s versus 0.48 s). Fig. 14, however, shows an al-most identical influence of individual (small and large) IMs on

Fig. 12. Effects of dynamic responses of 168 aggregated small IMs on sags

with different magnitude and duration.

Fig. 13. Different changes in the shape of voltage sags due to different groups

of IMs.

TABLE I

GROUPS OF IMS USED IN THE STUDY

Fig. 14. Effects of a single large or small induction motor on the change in theshape of the voltage sag.

voltage sag characteristics. The change in sag characteristics is

highly dependent on the number and type of motors involved in

the group.

Fig. 15 illustrates that different inertia of the group results in

a small change in sag shape even dough the difference in inertia

is significant. A motor driving a low inertia load will recover abit faster than the one driving a high inertia load.


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Fig. 15. Effects of inertia on the change in the shape of voltage sag.

Fig. 16. Effects of dynamics responses of IMs on voltage sags with a differentmagnitude.

Fig. 17. Effects of dynamics responses of IMs on voltage sags with differentduration.

By applying this methodology, voltage sag performance at

any given bus, with or without IMs, can be explored. For this

purpose, voltage sags can be conveniently arranged in three dif-

ferent categories: severe, with a magnitude of less then 0.5 p.u.;

medium with a magnitude in the range of 0.50.7 p.u.; and

shallow with a magnitude greater than 0.7 p.u. Figs. 16 and

17 show that IM dynamics do not change the characteristics

of every voltage sag. (Note: the original rectangular sags (sags

at the bus without the IMs) corresponding to those shown in

Figs. 16 and 17 are illustrated in Figs. 18 and 19, respectively).

This is particularly true for very shallow voltage sags, with a

magnitude of p.u., or for those lasting less than 0.08 s.(Note: The change in duration of sags with magnitudes

Fig. 18. Original rectangular sags for nonrectangular sags of Fig. 16.

Fig. 19. Original rectangular sags for nonrectangular sags of Fig. 17.

Fig. 20. Nonrectangular sag (solid line) originated by a rectangular0.6.-p.u./0.3-s sag and its respective equivalent rectangular sag (dashedline).

p.u. is not relevant anyway since their magnitude is above the

sag threshold of 0.9 p.u.) However, when the sag magnitude is

p.u., or when the duration is s, the IM dynamicsalter sag characteristics as shown by the solid line in Fig. 20.

As a result of this, the rectangular voltage sag becomes nonrect-

angular, and the methodology proposed in Section IV should

be applied to convert it back into the equivalent rectangular sag

(shown by the dashed line in Fig. 20) for benchmarking pur-

poses.

IV. NONRECTANGULAR TO RECTANGULAR SAG CONVERSION

A major consequence of the IM dynamics on voltage sag

characteristics is the change in sag shape from rectangular to

nonrectangular as illustrated in the previous section. The non-

rectangular part of the sag has basically a time-varying magni-tude [as illustrated in Fig. 21(a)] and, as such, is not suitable for


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Fig. 21. IMs connected to a voltage sag generator through system impedance.(a) Voltsseconds lost due to IM nonrectangular sag (shaded area). (b)Voltsseconds lost due to new IM rectangular sag (shaded area).

inclusion in existing magnitude-duration tables used for bench-

marking purposes.

Any conversion of nonrectangular to rectangular shape is as-

sociated with a certain level of simplification and the equivalent

rectangular sag becomes an approximation of the actual distur-

bance. Even though it is an approximation, it still represents the

actual voltage sags in low-voltage networks (in particular) more

accurately then current practices. The existing approaches al-

most completely ignore the presence and, consequently, the ef-

fects of IMs on voltage sags in the network. One possible way

for converting nonrectangular to rectangular voltage sags is to

use the loss of voltage concept/index [11] and (27). In thisway, the original nonrectangular and corresponding rectangular

voltage sags have the same loss of voltage (or voltseconds)

(27)

Fig. 21 illustrates the methodology for voltage sag conversion

based on the loss of voltage concept. Consider an IM exposed

to rectangular sag represented by the dashed curve abcefijm in

Fig. 21(a). Due to the effect of IM dynamics, this sag is changed

to a nonrectangular sag represented by the solid line abcfihm.

Using (27) and considering only the area below 0.9-p.u. voltage

threshold, the nonrectangular sag represented by the shaded areain Fig. 21(a) is converted to a rectangular sag represented by the

Fig. 22. Study procedure for sag conversion.

shaded area in Fig. 21(b). A new rectangular sag, represented by

the dashed curve abcdghk, is equivalent to the original nonrect-

angular sag in terms of volt-seconds lost. (Note: The original

integration step of 20 ms for determining the nonrectangular

voltage sags by procedure described in Section II is reduced in

this case to 1 ms to increase the accuracy of the conversion.)

The original nonrectangular sag is shown in Fig. 21(a) by a

solid line (only the part below 0.9-p.u. voltage threshold is used

for conversion). The curve bcefih is defined by a set of points

and it encompasses the area

(28)

with a sag duration given by

(29)

The new rectangular sag will have the same duration as the

original sag while its magnitude will be reduced and given by

(30)

Using (29) and (30), the original nonrectangular sag (bcefih)

is transformed into an equivalent rectangular sag with magni-

tude and duration , as shown in Fig. 21(b).

The consequence of this conversion is that the resulting rectan-

gular sags have a slightly higher (and constant) magnitude than

the original nonrectangular sags and the same duration (only the

part below 0.9-p.u. magnitude is considered in accordance with

the definition of voltage sags). Since this conversion is applied

to all three phases independently, the resulting rectangular sags

may have different sag durations as illustrated and discussed in

detail in the adjoining paper (Part II).

A. Study Procedure

The study procedure is divided into two parts (see Fig. 22):

IM dynamic response analyzer and nonrectangular to rectan-

gular sag converter.

1) Part 1: Induction Motor Dynamic Response Analyzer:

Using the input data (IM equivalent circuit data, original

rectangular sag parameters, number of motors connected at

the PCC and system impedance) and the model developed in

Section II, this part calculates the change in sag parameters at

IM terminals using the following algorithm.

Parameters of the equivalent aggregate IM connected at

PCC are calculated based on parameters of individual IMs.

The original (without the effect of IMs) pre, during, andafter sag voltages are calculated using (1)(3).


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The aggregate IM speed during the sag is calculated every

millisecond of the sag duration using (12) and aggregate

motor parameters.

Motor reacceleration time is computed using (15).

Motor speed after the sag is calculated every millisecond

during the reacceleration of the motor using (14).

The motor currents during and after the sag are determinedusing (1821).

Finally, the change in sag shape due to IM dynamics is

determined using (22), (23), and (26)(29)

2) Part 2: Nonrectangular to Rectangular Sag Converter:

This block uses the output from the part 1 (i.e., nonrectangular

voltage sag parameters) and converts them to parameters of

the equivalent rectangular voltage sag using the following

algorithm.

The voltseconds lost in each phase are calculated using

(30). Only the part of the voltage sag curve that falls below

the defined voltage sag threshold (90% of nominal voltage)

is considered in this calculation.

The sag duration in each phase is calculated using (34). The equivalent rectangular sag magnitude in each phase is

calculated using (35).

V. CONCLUSION

This paper presented an analytical tool to describe the influ-

ence of voltage sags on a group of IMs (aggregated model) and

the influence of IM dynamics on voltage sag characteristics.

The results show that the presence of IM(s) at a bus may

initially provide voltage support, however, during the voltage

recovery, the sag duration may increase due to the reaccelera-

tion of IM(s). The change in voltage sag shape due to IM dy-

namics depends on various parameters, such as number of mo-tors, motor electrical and mechanical parameters, number of

sagged phases, and severity of voltage sag.

To facilitate the assessment of the impact of IMs on voltage

sag performance of a bus using conventional benchmarking ta-

bles, an analytical nonrectangular to rectangular sag conversion

method is introduced. The method accounts for the effect of IMs

on sag characteristics and enables quick and convenient repre-

sentation of resulting voltage sags using conventional bench-

marking approaches. Further details about the sag conversion

method and practical application issues are discussed in detail

in the adjoining paper (Part II).

APPENDIX A

LARGE INDUCTION MOTOR AND SYSTEM PARAMETERS:

Eight poles V/ph, kW,

rad/s, rad/s, ,

, , ,

, , Nm,

, .

APPENDIX B

SMALL INDUCTION MOTOR PARAMETERS

Four poles V/ph, kW,

, , ,

, , ,Nm

APPENDIX C

THREE-PHASE TEST ASYMMETRICAL SAG PARAMETERS

Phase A presag p.u., ; during

the sag p.u., , ms.

Phase B presag p.u., ;

during the sag: p.u., ,

ms.Phase C presag p.u., ; during

the sag: p.u., , ms.

ACKNOWLEDGMENT

The authors would like to thank the Microgrids and RISE

partners for their contributions.

REFERENCES

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M. F. Mcgranaghan, Dynamic sag correctors: cost-effective industrialpower line conditioning, IEEE Trans. Ind. Appl., vol. 37, no. 1, pp.212217, Jan./Feb. 2001.

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Jovica V. Milanovic (M95SM98) received the Dipl.Ing. and M.Sc. degreesfrom the University of Belgrade, Belgrade, Yugoslavia, and the Ph.D. degree

from the University of Newcastle, Newcastle, Australia.Currently, he is a Professorof Electrical Power Engineering and DeputyHead

of School (Research) of Electrical and Electronic Engineering, The Universityof Manchester, Manchester, U.K.

Myo T. Aung (M05)receivedthe B.E.degree in electrical engineering from theYangon Technological University, Rangoon, Burma, the M.E. degree in electricpower system management from the Asian Institute of Technology, Bangkok,Thailand, and the Ph.D. degree from the University of Manchester (formerlyUMIST), Manchester, U.K.

Currently, he is a Lecturer with the Department of Electronic and ElectricalEngineering at the University of Bath, Bath, U.K.

Sarat C. Vegunta received the B.E. degree in power electronics from NagpurUniversity, Nagpur, India, and the M.Sc. degree from the University of Man-

chester Institute of Science and Technology (UMIST), Manchester, U.K.He is currently a Ph.D. student in the School of Electrical and Electronic

Engineering at The University of Manchester, Manchester.

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