Voltage Stability Considerations in Composite Power System Reliability Evaluation

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IEEE Transactions on Power Systems, Vol. 13,No. 2, May 1998

VOLTAG E STAB ILITY CONSIDERATIONS IN

COMPO SITE POWER SYSTEM RELIABILITY EVALUATION

Roy B illinton, Fellow, IEEE Saleh Aboreshaid, Student Member, IEEE

Power Systems Research GroupUniversity of Saskatchewan

Saskatoon, Canada

655

Abstract -This paper presents an approach wh ich includesvoltage stability considerations in the a dequ acy assessm ent

of a composite power system. A fast technique for the

probabilistic assessment of voltage stability is presented

which can be u sed in conjunction with detailed contingency

evaluation in a composite system adequacy assessment.

Voltage stability is quantified using an indicator that can be

easily included in the framew ork of an existing composite

power system adequacy program. The effect on the

adequacy indices (load point and system indices) of

incorporating voltage stability con straints is illustrated b y

application to the IEE E-Reliability Test S ystem.

I. INTRODUCTION

Voltage stability has been defined by the System DynamicPerformance Subcommittee of the IEEE Power EngineeringCommitteeasbeing the ability of a system to main tain voltageso that when load admittance is increased, load power willincrease, and both power and voltage are controllable [11. Avoltage collapse may be caused by a variety of single ormultiple contingencies such as a sudden removal of real orreactive power generation or a transmission element (a

transformer or a transmission line), an increase of load w ithout

an adequate increase of reactive power. The voltage stability ofa power system is greatly dependen t upon the amount, loca tionand type of reactive power sources available in the system. Ifthe reactive power support is insufficient in quantity orphysically far away then a rela tively normal contingency suchas a line outage or a sudden increase in load can trigger a largesystem voltage drop.

Voltage stability is a serious problem that power utilitiesusually explore in the planning stage. It is essential that

techniques to protect a pow er system fiom a voltage collapse be

investigated, taking into account all contingencies hat cause thesystem to lose voltage stability. Significant progress has beenmade in the last decade in the development of methods toanalyze and evaluate power system voltage stability [1-12].There is no consensus on whether the voltage collapse

PE-051-PWRS-2-06-1997 A paper recommended and approved bythe IEEE Power System Planning and Implementation Committee ofthe IEEE Power Engineering Society for publication in the IEEE

Transactions on Power Systems. Manuscript submitted January 31,1997; mad e available fo r printing June 9, 1997.

mechanism is a steady-state [2-51 or dynamic [6-81 phenomenaand therefore whether it should be analyzed by the relevant

methods. This is perhaps due to the fact that voltage instabilityis a dynamic phenomena that possibly lends itself nicely tostatic analytical approaches.

Most of the computational tools de velop ed so far are based ondeterministic criteria, i.e., on the analysis of a predetermined setof severe but credible situations. Deterministic techniquesusually result in effective designs, as they are based onengineering experience and on the analysts knowledge of thesystem. The essential wea kness of such techn iques is that they

do not and cannot account for the probabilistic or stochastic

nature of system behavior, of customer demands or ofcompo nent failures. In recent years, voltage collapse has beenconsidered recognizing he uncertainty associatedwthpracticalsystem operatio n [9-121.

Adequacy evaluation of a composite generation andtransmission system in a complete sense involves the simulationand load flow ana lysis of each possible outage c ondition in thesystem in order to determine the inability to supply load,voltage violations, line generator overloads, violations of

generator W a r , etc. and to quantitatively express the

deficiencies, f any, in terms of reliability indices. Reference 13

presents an approach to calcula te voltage collapse related bulkreliability indices as well as their impact on composite powersystem adequacy indices based on restoring system solvabilityby load shedding. This paper presents a fast technique toincorporate voltage stability considerations in the adequacyassessmentof a com posite power system. The voltage stabilityindicators developed in [3] are calculated for all possiblesystem contingencies. A bisection algorithm is then used todetermine the amount of load which m ust be shed to alleviate

all voltage stability violations. The impact of considering

voltage stability constraints on the adequacy indices isillustrated by application to the IEEE-RTS [141. The proposedtechnique can be easily included in an existing compositepower system adequacy program to monitor the effect on theadequacy indices of incorporating voltage stability constraints.

11. VOLTAGE STABILITY CONSIDERATIONS IN

COMPOSITE POWER SYSTEM RELWILIT Y

E VALUATION

There are two fundamental approaches to composite powersystem adequacy evaluation: analytical enumeration and MonteCarlo simulation. There is a wide ran ge of co mputer programs

0885-8950/98/$10.00 0 1997 IEEE



656

available for composite power system adequacy evaluation.These programs are briefly described in Reference 15,including a list of the calculated indices and the factorsinvolved in the assessment. The approach presented in this

paper is based on an analytical enumeration procedure for

composite system evaluation. It can be also incorporate d in a

Monte Carlo simulation program.

1 . C a ~ c u ~ a ~ i o nf voltage stab ility indicators

For a given system contingency, voltage stability indicatorscan be calculated using the AC load flow results as follows:

The hybrid representation of a transm ission system is given by

the following equation:

[ z [ GLL L y G G""1 [$where VL, IL are the vectors of voltage and currents at

customer nodes,VG,IG are the vectors of voltage and currents at

generator nodes,zLL,", KG",YGG ar e sub matrices of the hybridmatrix.

Reference 3 defines the indicator L , to assess the voltage

stability of load bus K under a given outage condition j as

follows:

K IThe indicator at each bus varies between zero (no load) and one

(voltage collapse). The superscript (B) or any of the submatrices' elements and the bus voltages represents the adjusted

value a fter modifying the hybrid matrix and the bus vo ltagesdue to outage j .

2. in corpora tin^ voltage stability considerations in

ower system adequacy evaluation

There is no consensus among pow er utilities regarding uniformfailure criteria and therefore all utilities do not use the samefimdamentalnetwork solution technique to calculate the systemadequ acy. The basic justification for these differences lies inthe intent behind the adequacy studies. This paper deals withthe problem of incorporating voltage stability conside rations in

composite power system reliability evaluation. The utilizationof AC load flow is therefore an integral part of the solutionprocess.

It should be noted that the occurrence of a system problem maybe itself recorded as a failure event. In many cases, however, itis possible to eliminate a system problem by taking approp riatecorrective action. It is, therefore, of interest to determine

whether it is possible to eliminate a system problem byemploying proper corrective actions such as generation

rescheduling, correction ofWar limit violations, allevia tion of

line overloads, the solution of ill-conditioned networksituations and or load curtailment.

The basic structure of the contingency enumeration approach&er incorporating voltage stability considerations is sho wn inFigure 1.In this figure, load is curtailed, if necessa ry, for somecontingency due to violating the operational constraints

(capacity deficiency in the system, bus isolation, networkislanding and line/transformeroverloads) or due to violating thevoltage stability constraints. Load curtailments due to violatingoperational constraints are discussed in detail in manycomposite power system reliability publication and are notrepeated in this paper. If the voltage stability constraints areviolated, load is curtailed to ensure that the voltage stabilityindicators at all system load buses are less than or equal anacceptable threshold value.

Select a contingency

1 Load flow with corrective action if necessary I

N o

L Jalculate adequacy indices

Figure 1: Basic structure of the contingency enumeration approach.

If the voltage stability constraints are violated, the load buswhich h as the hig hest voltage stability indicator is selected toca ny out load shedding using a bisection algorithm as shownin Figure 2. Load shedding at this bus is an efficient way toreduce the vo ltage stability indicators. In this case, the systemis initially operating at point 1 which has a voltage stability

indicator of L,. A bisection algorithm [16] can be used todetermine the minimum amount of load to be shed (AP) to

reduce the value of the voltage stability indicator at the selectedbus fiom L, to b,where L, is the minimum ac ceptable voltagestability indicator "threshold value". In itial load limits [PI,P2 ]

are defined for the selec ted bus load w here PI equals zero andP, equals the original load at the selected load bus (P,). Voltagestability violation is then checked at the mid point of theselimits, ,. If it is found that the voltage stab ility constraints are

satisfied, then the lower load limit of the interval is replaced bythe mid point value, P,. Otherwise, the upper value is rep laced



657

2, Effect on the loadpoint indices o f ncorDoratinp voltagestabilitv considera tions

by the mid-point value, P,. The procedure is repeated until the

required minimum load (AP=Po-P,) which must be she d at theselected bus to reduce the value of the voltage stabilityindicator at this bus from L, to L, is determined. The voltage

stability indicators are then recalculated for all the system loadbuses, using the procedure described in [3], and the bisectionprocess is repeated in the case of ano ther voltage violation untilall buses do no t are violate the voltage stability constraints.

The threshold value of the vo ltage stability indicator is less thanone and sho uld be selected for a given system in such a waythat the power system is far from a voltage instability point. Itis worthwhile noting that the threshold values are nearly thesame for every power system. Such a value can b e obtained inthe state where the voltage profile is higher than or eq ual to theminimum acceptable voltage and at the same time all thegenerators are operating within their reactive p ower limits [5].

The lo ad power factor is assumed to be constant at each loadbus after shedding a portion of the load.

Vo!tage stability indi cato r

i

/I Bisection algorithm /

4A PLoad

Figure 2: Functional description of the load-shedding calculationprocess using the bisection algorithm.

111. ADEQUACY INDICES FOR THE IEEE-RTS

CONSIDERING VOLTAGE STABILITY

CONSTRAINTS

The single line diagram of the 24-bus EEE -RT S is shown inFigure 3 [141. The system has 10 generator (PV) buses, 10 load(PQ) buses, 33 transmission lines and 5 transformers. The totalnumber of generating units is 32 with a minimum andmaximum rating of 12 MW and 400 MW respectively. Thesystem can be divided into two subsystems on the bases of

voltage levels. The north subsystem is at 230 KV and the southsubsystem is at 138 KV . The northern region has a surplus in

power while the southern region is a power deficient area. The

north subsystem load is 1518 MW while that of the southsubsystem is 1332 MW. The installed capacity in the northregion is 2721 MW and that of the south is 684 MW . In theanalysis conducted in this section, independent overlappingoutages up to the fourth level for generating units and up to thethird level for transmission lines and/or generating units areconsidered.

Table 1 lists the probability and frequency of failure for thedifferent buses in the IEEE-RTS. Two cases are presented:Ca se I is the traditional adequacy evaluation (without voltagestability considerations, i.e., only operational constraintsviolations are considered) and Case I1 presents the indices after

con side ring voltage stability constraints. It can be seen fromthis table that an increase in the failure probability andfrequency occurs when voltage stability constraints areconsidered. The highest percentage increase in the indiceswhen considering voltage stability constraints are for buses 3-6,8-10, which are located in the 1 38 KV portion of the networkand has inadequate MVar g eneration. On the other hand buses19 and 20 wh ich have the low est percentage increase in theindices are located in the 230 KV side of the network which

has 80% of the total system generation. It should be noted thatthe inclusion of voltage stability considerations do not affectthe indices of buses 1, 2, 7 and 15-18 since these buses arevoltage controlled buses.

2

I4- 3 0 K V buses 13 8 K V buses

Figure 3: Single line diagram of the IEEE-RTS.



658

Table 1: Effect on the basic load p

we probaI

ease il

0,022121

0.040691

0.039858

0.0324020.032648

0,032354

0,016587

0.025931

0.021908

0.022XTX

0.069587

0.009562

0.057700

0.025452

0.084624

0.0386980.048299

5"

b hmease

0

0

10.8

6.46.3

13.6

0

3.9

4.6

4.4

0

4.3

0

0

0

1o0.9

Int reliability indices for thep ooz1siderations.

lccc./year

I h m

0

0

10.5

6.45.3

13.4

0

3.1

4.2

4.2

0

3.9

0

0

0

0.50.5

Th e risk indices presented in Table 1 are based on the

theoretical fomidation that the point of collapse is reached when

the voltage shbility indicator equals or is greater than 1.0.Experiments show that a vo ltage instability Indicator of 0.2 to0.3 is a good criterion for safe operation [SI. When the 0.3

tiweshold is exceeded, the indicator increases rapidly with asmall increase in lo&ng or a change in the network topology.Table 2 shows the effect:of on the probability and 5equency offailure for different load buses (Case ID) using a voltage

stability iiidiclatorthreshold value of0.3. Table 2 shows that the

iisk indices for a given load bus ittcrease as the thresholdvdueof the indicator decreases.It cm be seen from this table that thesouthern region of th e IEEE-RTS Is more sensitive to the

change in the voltage stability threshold value . This is due to a

deficiency in M V a generation in this region. The northem

subsystem which contains 80% ofthe total system generationis less likely to exp erienc e voltage instability problems .

Table3 lists the avemge load and mer# curtailment: ndices fordifferent load buses of the EEE-RTS. Tw o cases arecompared: Case I (without considering voltage stability

constraints) and Case 111 (Considering a practical voltagestability itidicstlor threshold value o f0 .3 ) . It can e seen &om

this table that the incorporationof voltage stability constraintsincreases the a verage load and energy c.llrtailment indices. Itcitn also be seen that the southern subsystem which contains20% ofehetotal system generation and 47% ofthe total systemload violates the voltage stability eomtralnts more often t han

die northern subsystem.

The adequacy indices calculated for Case s I, II and 111do notconside r uncertainty in the forecast load, It was assumed that

loads iu he IEEE-RTS are ~io nna lly istributedwth a standard

devi&on of4%. Th e normal distribution can be approximatedby a discrete seven hterv al model. Table 4 lists the voltagestability indices €or diAFarmt EEE-RTS load buses. Tw o cases

arepresentd without including load forecast wr&inty Caseur>and when load forecast uncertainty is included (Case IV).It c m be stfen from Table 4 that the risk indices increase whenload forecast uncertainty sidered. This i s due to th e factthatthe v&ige stability s S Q I I X ~ ~ ~ ~ Sncrease rapidly

even wth only a small increase in the system load. Th erami" increasesare for buses 3-6, 8-10 which are located

in the 138 KV portion of the tietivork. Buses 14, 19, 20 are

h a t e d in th e 230 KV side ofthe network which has 80% of&e totaI system generatlion md therefore are less affected by the

load fore cast Uncel2&1ty.

Table2: Effect outhe basic loadpoint itldices for the IEEE-RTSof

9

10

14

19

20

Case1 CaseNI

0.035973 0.040974

0.030453 0.0334550.030713 0.033714

0.028481 0.033489

0.024958 0,026963

0.020945 0.023947

0.021914 0.023923

0.009168 0.009671

0.038315 0.038821

0.047868 0,04835'5

Table 3: Effect on the average laad atid energy curtailmentindicesfar the IEEE-RTS of voltage stability considerations.

Average load cuftailed,Mw

Average e m r e curtailed,

Bus

3

4

5

6

8

9

10

14

19

20

_.

-

Case I

20.8120

8.7120

8.2350

15.4250

21.1270

20.9380

23.9470

18.9800

22.9900

17,0320

Case ll

22.3120

9.2120

8.4850

16.9260

21.6270

21.4380

24.4470

19.2300

23.2400

17.2820

Case Iff311,609

118.705

109.532

218.107

277.26

297.537

339.772

228.034

342.579

238.586

9" Increase

6.6

5.7

2.7

9.5

1.5

2.1

1" 3

0.8

0.5

0.8

Figure 4 shows the e&ct on the basic load point ksk indices(probability and fjrequency of fdm)t buses 3 and 15 ofchanging the threshold value of th e voltage stability indicator.It can be seen from this figurethat, or a given load point, therisk itldices increase as the threshold value decmses. The loadpoint risk indices for buses 3 an d 19 respectively, when a

threshold value for the voltage stability indicator of 0. 3 is used,areapproximately 13% and 1%higher than the values obtained



, Bus CaseIII

3 0.040974

4 0.033455

5 0.033714

6 0.0334898 0.026963

9 0.022947

10 0.023923

14 0.009671

19 0.038821

20 0.048375

Case IV

0.04265

0.03443

0.03469

0.035230.0276

0.0236

0.02457

0.0098

0.03897

0.04854

Cake II I

27.2212

23.4437

23.6688

23.473118.7481

14.2977

14.9163

6.8351

23.2998

%Increase

4.1

2.9

2.9

5.22.4

2.8

2.7

1.6

0.4

0.3

CaseIV

28.2637

24.1145

24.3033

24.619919.1898

14.6985

15.2806

6.9258

23.3548

31.5502

for the load points without including any voltage stabilityconstraints. Figure 4 also sho ws that b us 3 which is located in

the southern subsystem is more sensitive to voltage stabilityconstraints than bus 19 which is located near the majorgenerating stations.

%Increase

3.8

2.9

2.7

4.92.4

2.8

2.4

1.3

0.2

0.3

0.043 1

0.035’ : : : : : : : : : : I0.2 0 .3 0.4 0.5 0.6 0.7 0.8 0.9 1

Threshold value of the indicator

- us3- US193

3 8

- us3- US193

3 8

$’26P)Y + 2 h L J+s24 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1


Figure4: Effect on the probability and frequency of failure of

changing the threshold value of the voltage stability

indicator.

Effect on the svstem indices o f incorporating voltagestabilih, consid erations

The load point indices are very useful in system design and incomparing alternative system configurations. The overallsystem indices indicate the adequacy of the compositegeneration and transmission system to meet its total loaddemand and energy requirements. It is important to appreciatethat the two sets of load point and system indices do not replace

each other but are complementary. Table 5 shows the effect onthe overall system indices of the IEEE -RTS of incorporating

659

voltage stability considerations. Table 5 shows that there is an

increase of more than 3% in the overall system indices byincorporating voltage stability considerations in the analysis(Case 111). It can be seen fkom this table that the maximumpercentage increases in the system indices due to incorporating

voltage stability considerations are low er than those obtainedfor the load points. This is due to the fact that the voltagestability constraints do not impact some of the PV controlled

load points (1,2, 7 and 15-18).

Table 5: Effect on the system indices for the EEE-RTS of voltage

stability considerations.

Index

Basic Values

Bulk Power Interruption Index

(MW/MW-Yr)

Bulk Power Energy Curtailment

Index (MWMW-Yr)

Bulk Power Supply Average MW

Curtailment Index (MW/Dist.)

Severity Index(System Minutes)

Modified Bulk Power Energy

Curtailment Index

Averave Values

Load CurtailmentLoad

Poinuyear

Energy CurtailmentLoad

PointlYear

Case I

3.52198

49.2961

160.521

2957.77

1.005637

590.450

8264.34

Case Ill

3.65289

50.8648

165.775

3050.89

1.005807

612.397

8527.35

b Increasc

3.7

3.2

3.3

3.2

3.0

3.7

3.2

Figure 5 shows the effect on the severity index (systemminutes) of chang ing the threshold value of the voltage stability

indicator when load forecast uncertainty is not included (Case111) and when the load forecast uncertainty is included (Case

IV). It can be seen fiom this figure that the severity indexincreases as he threshold value decreases. The severity index,when a threshold value for the voltage stability indicator of 0.3

is used, is 3% higher than the one obtained for the systemwithout including any voltage stability constraints (onlyoperational constraints are included) and 5% higher when loadforecast uncertainty is included. Similar curves can be draw nfor other system indices.

Voltage stability is a serious problem that m ust be considered

in the system planning stage. It is essential that techniques to

protect a power system from a voltage collapse, which tak e intoaccount all the contingencies that can cause the system to losevoltage stability, be investigated. This can be achieved byincluding acceptable voltage stability constraints in theevaluation of composite power system adequacy indices. Thestudies presented in this paper show that the inclusion ofvoltage stability considerations in composite generation and

transmission adequacy assessment can result in a significantincrease in both the load point and system adequacy indices.

This inc rease is further amplified by considering load forecastuncertainty in the analysis.



660

m

5 3150

8 3100

'050

$3000

3

.fla,c

a

.e I. -Case I V- Case III

6 2950 I IVI 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1


Figure 5: Effect of changing the threshold value of the voltage

stability indicator on the severity index.

IV.CONCLUSIONS

This paper presents an effective and fast technique to

incorporate voltage stability considerations in composite

generation an d transmission system adequacy evaluation. In

this technique, load shedding is performed in two stages. In the

first stage, load is curtailed, if necessary, to eliminate anyoperational constraint violations and in the second stage load is

curtailed, also if necessary, to restore the system to a voltage-

stable operating point using a s imple voltage stability indicator

derived from the AC load flow results. A fast bisectionalgorithm is used to calculate the amount of load to be shed in

the case of voltage stability violations.The proposed technique

can be easily incorporated in an existing composite power

system adequacy program. The numerical results show that the

proposed technique suitably reflects the effects of voltagestability constraints on the composite generation and

transmission system adequacy indices.

V. REFERENCESSystem Dynamic Performance Subcommittee of the IEEE

Power System Engineering Committee, "Voltage Stability of

Power Systems: Concepts, Analytical tools and Industry

Experience", IEEE Publication No. 90-THO358-2-PWR.

Y. Tamura, H. Mori and S. Iwamoto, "Relationship between

voltage instability and multiple load flow solutionsin electric

power systems", IEEE Trans. on Power Apparatus and

Systems, Vol. 102,No . 5, May 1983, pp. 1115-1125.

P. Kessel and H. Glavitch, "Estimating he Voltage Stability ofa Power System", IEEE Trans. on Power Delivery, Vol. 1,No.

3, Jul. 1986, pp. 346-354.

A. Tlranuchlt and R.J. Thomas, "A Posturmg Strategy Agamst

Voltage InstabilityinElectric Power Systems",EE E Trans. onPower Systems, Vol. 3, No. 1, Feb. 1988, pp. 87-93.

T. Quoc Tuan, J. Fandino, N. Hadjsaid, J.C., Sabonnadiere and

H. Vu, "Emergency Load Shedding to Avoid Risks of Voltage

Instability Using Indicators", IEEE Trans. on Power Systems,

Vol. 9, No . 1,Feb. 1994, pp. 341-351.

M.S. Calovic , "Modeling and Analysis of Under Load Tap

Changing Transformer Control Systems", IEEE Trans. on

Power Apparatus and Systems, Vol. 103, No . 7, Jul. 1984, pp.

1909-1915.

A.E. Hammad and W. Kuhn, "A Computation Algorithm for

Assessing Voltage Stability at ACDC Interconnections", E E E

Trans. on Power Systems, Vol. 1,No. 1, Feb. 1986, pp. 209-

216.

C.W. Taylor ,"Concepts of Undervoltage Load Shedding for

Voltage stability", IEEE Trans.on Power Delivev, Vol. 7, No.

2, Apr. 1992, pp. 480-488.

K.L. Loparo and G.L. Blankenship, "ProbabilisticMechanism

for Small DisturbancesInstabilities in Electric Power Systems",IEEE Trans. on Circuits and Systems, Vol. 32, No. 2, Feb.

1985, pp. 177-184.

C.L. DeMarco and A.R. Bergen, "A Security Measure for

Random Load Disturbances in Non Linear Power System

Models", EE E Trans. on Circuits and Systems, Vol. 34, No.

12, Dec. 1987, pp. 1546-1557.

C.O. Nwankpa, S.M. Shahidehpour and Z. Schuss "A

StochasticApproach to Small Disturbance Stability Analysis",

IEEE Trans. on Power Systems, Vol. 7, No. 4, Nov. 1992, pp.

1519-1528.

C.O. Nwankpa and R.M. Hassan "A StochasticBased Voltage

Collapse Indicator", IEEE Trans. on Power Systems, Vol. 8,

A.C.G. Melo, J.C.O. Mello and S. Granville, "The Effect of

Voltage Collapse Problems in the Reliability Evaluation ofComposite Systems", IEEEPES Winter Meeting, Paper # 96

IEEE Committee Report, "IEEE Reliability Test System", IEEE

Trans. on Power Apparatus and Systems, Vol. 98, Nov.iDec.

R. Billinton and E. Khan, "A Comparison of Existing Computer

Programs for Composite System Adequacy Evaluation",

Canadian Electrical Association Trans., Vol. 28, Part 3, Mar.

1989.

S. Aboreshaid, R. Billinton and M. Fotuhi-Firuzabad,

"Probabilistic Transient Stability Studies Using the Method ofBisection", IEEE Trans. on Power Systems, Vol 11, No. 4,

NO.3, Aug. 1993, pp. 1187-1193.

WM 316-0 PWRS, Jan 21-25, 1996.

1979, pp. 2047-2054.

NOV.1996, pp. 1990-1995.

VI. BIOGRAPHIES

RoyBillinton (F'78) came to Canada from England in 1952. Obtained

B.Sc. and M.Sc. Degrees from the University of Manitoba and Ph.D.

and D.Sc. Degrees from the University of Saskatchewan. Worked for

Manitoba Hydro in the System Planning and Production Divisions.

Joined the University of Saskatchewanin 1964. Formerly Head of the

ElectricalEngineeringDepartment. Presently C.J. Mackenzie Professor

of Engineering and Associate Dean, Graduate Studies, Research and

Extension of the College of Engineering.

Author of papers on Power System Analysis, Stability, Economic

System Operation and Reliability. Author or co-author of eight books

on reliability. Fellow of the IEEE, the EIC and the Royal Society of

Canada and a Professional Engineer in the Province of Saskatchewan.

SalehAboreshaid (S'92) was bom in Saudi Arabia. Received his BSc.

Degree from King Saud University in 1990. Obtained an M.Sc. Degree

fromthe University of Saskatchewan in 1993. He is currently working

towards a Ph.D. degree in the area of power system reliability

evaluation.

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Voltage Stability Considerations in Composite Power System Reliability Evaluation