Assessment of Two Methods to Select Wide-Area

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572 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 23, NO. 2, MAY 2008

Assessment of Two Methods to Select Wide-AreaSignals for Power System Damping Control

Annissa Heniche , Member, IEEE , and Innocent Kamwa , Fellow, IEEE

Abstract—In this paper, two different approaches are applied tothe Hydro-Québec network in order to select the most effectivesignals to damp inter-area oscillations. The damping is obtainedby static var compensator (SVC) and synchronous condenser (SC)modulation. The robustness analysis, the simulations, and statis-tical results show, unambiguously, that in the case of wide-area sig-nals, the geometric approach is more reliable and useful than theresidues approach.In fact, this study shows that thebest robustnessand performances are always obtained with the stabilizer configu-ration using the signals recommended by the geometric approach.In addition, the results confirm that wide-area control is more ef-fective than local control for damping inter-area oscillations.

Index Terms—Compensator, control loop selection, geometricmeasures, inter-area oscillations, power system stabilizer, residues,

wide-area control.

I. INTRODUCTION

INTER-AREA oscillations have been observed in electrical

networks for many years [1]. Many power systems in the

world are affected by these oscillations [2]–[4] whose frequency

varies between 0.1 and 1 Hz. Currently, inter-area oscillation

damping is done with devices that use local signals. The basic

question we are asking here is: are these signals really the most

efficient?

In practice, the choice of measurement and control signals isa problem regularly faced by designers. In fact, to obtain the

desired performances and robustness, we have to select signals

that allow good observability and controllability of the system

modes. To quantify the observability and controllability of the

modes, measures have been defined in [5] and [6]. These mea-

sures, which are deduced from the Popov Belevich Hautus test

[7] and from residues, respectively, indicate how the th mode

is observable from available measurements and how it is con-

trollable from the system inputs. Thus, it is possible to select,

for each mode, the most efficient control loop.

By scientific curiosity, we wanted to know if the two methods

always lead at the same conclusion. Rapidly, we noted that it wasnot the case. The results of a first work were published [21], but

those associated with the 9 areas–23 generators test system [14]

were not. As Hydro-Québec is currently considering a project on

wide-area control, we thought that it was important to test the

two approaches on its network rigorously. In addition, even if

Manuscript received May 11, 2007; revised November 9, 2007. Paper no.TPWRS-00346-2007.

The authors are with IREQ, Hydro-Québec, Varennes, QC J3X 1S1, Canada(e-mail: [email protected]; [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/TPWRS.2008.919240

the results concern only the Hydro-Québec network, it is impor-

tant to notice that a statistical analysis was realized. This anal-

ysis allowed the test of the two approaches using 1140 different

configurations of the network.

The aims of this paper are on one hand to show that the two

measures do not provide the same conclusion in terms of con-

trol loop selection and on the other hand to demonstrate the effi-

ciency and reliability of one measure in comparison to the other.

To do that, the two measures were applied in order to select the

most effective control loops for damping the 0.6-Hz inter-area

mode of Hydro-Québec network. Local and global angle shiftswere considered. The inter-area damping is obtained by com-

pensators modulation. The modulation signal is produced by a

multi-band power system stabilizer (MBPSS) which uses only

intermediate frequency band [8]. The description and the pa-

rameters of this stabilizer are given in the Appendix.

This paper is organized as follows. Section II is devoted to

system modeling, while Section III presents a brief review of the

controllability-observability measures used in this work. Sec-

tion IV describes the application. Section V contains the re-

sults. Sections VI is devoted to the discussion of the results, and

Section VII is the conclusion.

II. SYSTEM MODELING

An electrical network is a nonlinear system which can be de-

scribed by the following nonlinear state equation:

(1)

where , and are the state,

input and output vectors, respectively. n is the dimension of

the system, m is the number of inputs, and p is the number of

outputs.

f: and g: are functions.

For measurement and control signals selection, a linear model

of the network is used. The latter is obtained using the modal

analysis tool developed at Hydro-Québec’s Research Institute

(IREQ) [9]. The linear state representation (A,B,C,D) of the net-

work is obtained using the identification eigensystem realization

algorithm (ERA) which was originally introduced in [10]. In the

context of electrical power systems, this approach was first ap-

plied in [2], [11] and then in [12], [13], [14], and [15]. The first

stage consists in exciting the nonlinear system by means of a

pulse of duration 0.4 s and amplitude of 1%. Thereafter, the ex-

citation u and associated outputs y are used by the ERA identi-

0885-8950/$25.00 © 2008 IEEE



HENICHE AND KAMWA: ASSESSMENT OF TWO METHODS TO SELECT WIDE-AREA SIGNALS 573

fication algorithm which provides the linear state representation

of the system given by

(2)

where and are the state, inputand output vectors, respectively. and

are state, input, and output matrices, respectively.

III. SIGNALS SELECTION

For measurement and control signals selection, two dif-

ferent approaches were used: the geometric and the residues

approaches.

Let us consider the identified linear model of the network

given by (2). An eigenanalysis of matrix A produces the eigen-

values (assumed distinct for ) and corresponding

matrices of the right and left eigenvectors ] and, respectively. The eigenvectors and cor-

responding to are orthogonal and normalized, which implies

that ( is the complex conjugate transpose

of G, and I is the identity matrix of size n).

A. Geometric Approach

The geometric measures of controllability and observ-

ability associated with mode ‘i’ are defined as follows [5]:

(3)

(4)

In (3) and (4), is the th column of is the th row of

is the acute angle between the input vector and the left

eigenvector is the acute angle between the output

vector and the right eigenvector and are, respec-

tively, the modulus and the Euclidien norm of z. Using (3) and

(4), the joint controllability/observability measure is expressed

by

(5)

B. Residues Approach

The interconnected system transfer function associated with

the state (2) is expressed by

(6)

where is the residues matrix associated with mode

(7)

As shown in (7), the residues matrix depends on matrices

B and C and the right and left eigenvectors. Note that is

the complex conjugate transpose of . For and

, the elements ) of matrix are given by

(8)

Using the residues matrix, the joint controllability/observ-

ability measure is given by [6]

(9)

In [6], the controllability measure and observability mea-

sure are deduced from (9) by setting and ,

respectively

(10)

(11)

From (3), (4), (10), and (11), we can say that if is orthog-

onal to , then pole is uncontrollable from input . If is

orthogonal to , then pole is unobservable from output .

The signals and for which and are maximum are

the most ef ficient for damping mode ‘i’. Equation (9) shows that

the joint measure associated with mode ‘i’ is proportional to the

norm of the associated residues matrix. According to [16], this

means that, if the maximal value of the residues associated with

mode ‘i’ is obtained with input k and output l, then andare the most ef ficient signals to damp mode ‘i’.

C. Remarks

The two approaches show that the modal observability and

controllability is related to the orthogonality between the eigen-

vectors and the output and input vectors, respectively. Contrary

to the geometric approach, residues are independent of any

scaling of , and . Indeed, as shown in (9) –(11), for

observability and controllability analysis, the residues use the

magnitudes of and as measures without scaling. That

means that we are free to scale the left and right eigenvectors

arbitrarily. For example, we can increase the observability of

mode “i” in output l by increasing the magnitude of as

one wants by multiplying the right eigenvector with a positive

constant. In this case, the magnitude of decreases since

is required. In addition, using the geometric approach,

the magnitudes of and can be written as

(12)

(13)

In (12), represents the amount of information in the output

l. A higher norm means that the mode “i” is clearly present in

output l, which means more observability. On the other hand, in(13), represents the power injected into the system by the




Fig. 1. The 2001 Hydro-Québec Network.

input k. A higher norm means more power injected by the input

and then more controllability.

On the basis of these considerations, we can say that the re-

sults of modal analysis for input and output selection depend

critically on the scaling of the variables. This is the way to ex-press the relative contribution of each signal and then to rigor-

ously select and classify control and measurement signals.

IV. APPLICATION

A. Power System Description

The power system used in this study is represented in Fig. 1.

This is the 2001 Hydro-Québec peak load network, which is

characterized by its very good robustness and well-damped

inter-area modes. In order to obtain more oscillations, the line

between Micoua and Saguenay was removed. The network was

divided into nine electrically coherent areas [17].In Fig. 1, the numbers inside the little circles and squares

represent the number of SCs and static var compensators (SVCs)

connected at the associated substation. In addition, the numbers

and the associated words located in the lower left corner refer

to the substations located in the southern part of the system and

identified, in Fig. 1, by 1-2-3.

As shown in Fig. 1, the network includes six SVCs and four

synchronous condensers (SC). Table I describes the nomencla-

ture and the characteristics of the SVCs and SCs used in this

work.

Even if the network presents several inter-area modes [15],

we will devote our study to the 0.6-Hz mode which is considered

as the most dominant mode during major events. The two zonesaffected by this mode are James Bay and Churchill Falls.

TABLE I

SVC AND SC DESCRIPTION

Fig. 2. Control system configuration.

B. Power System Linear Model

The identified linear model of the Hydro-Québec network

represented in Fig. 1 is described by the linear state (2) with

the input vector u and output vector y given by the following

relations:

(14)

(15)

In (14), is the voltage reference of the compensator

) as represented in Fig. 2.

The output vector y corresponding to the 49 available mea-

surement signals includes 29 wide-area signals and 20 local sig-

nals. In (15), the subscripts G and L indicate wide-area refer-

enced and local measurements, respectively. Consequently, the

measurements coi, , and are global referenced

angle shifts whereas angle shifts and are local mea-

surements calculated by a line model which uses the voltage and

current phasors at bus k [18]. The definition of measurementsignals is given in Table II. For the global angle shift , the




TABLE II

AVAILABLE MEASUREMENTS DEFINITION

reference bus is equal to the Churchill bus, except if refers

to the Churchill plant. In this case, the reference bus is equal to

the Robert–Bourassa (LG2) bus.

The tools presented in Section III were applied to select the

most effective measurement and control signals to damp the

0.6-Hz inter-area mode of the Hydro-Québec network. As rep-

resented in Fig. 2, the damping is obtained by modulating the

reference voltage of the compensator with the stabiliza-

tion signal VPSS. The latter is produced by an MBPSS stabilizer

which uses a global or a local angle shift. Indeed, as shown in

Fig. 2, if the control system is in global mode, the input of the

PSS is , which represents the angle shift between two remote

buses. On the other hand, if the control system is in local mode,

the input of the PSS is equal to the angle shift between the com-

pensator bus (bus k) and a neighboring bus (bus nk or bus sk in

our case).

V. RESULTS

A. Residues Approach

For all compensators, the joint measures obtained using the

residues are given in Table IV. Taking into account the large

number of available measurements, for each control signal, we

chose to select only the measurements which exhibit the larger

residues. More precisely, for each compensator and for each cat-

egory of measurement signals as defined by lines of Table II, we

choose those which present the larger residues. The physical in-

terpretation of these measurements is given in Table III.

If we consider only the global measurement signals, the re-sults of Table IV show for each column and each row decreasing

value from top to bottom and from left to right, respectively.

That means that if we consider only one global measurement

signal as input for the PSS (one column in Table IV), then the

damping of the 0.6-Hz inter-area mode obtained in closed loop

depends on the modulation of the input of a given compensator.

More precisely, in closed loop, the damping obtained is larger if

the control site is SVC LVD or in other words if the modulation

concerns the voltage reference of SVC LVD. On the other hand,

the damping decreases if another compensator than SVC LVD

is selected. The diminution of the damping is observed from

top to the button, i.e., according to compensator controllability

classification given in the first column of Table IV. The samereasoning can be used to explain the decreasing value of each

TABLE III

SELECTED MEASUREMENTS SIGNALS

TABLE IV

JOINT MEASURES OBTAINED WITH RESIDUES APPROACH

row. In this case, if we consider one compensator, the damping

of the 0.6-Hz mode in closed loop depends on how observable

it is from the measurements.

Table IV shows that for damping the 0.6-Hz inter-area mode,

the best control strategy is to modulate the input of the SVC

LVD with a stabilization signal obtained by using the angle shift

between LA1 and Churchill. The results show that the

second choice corresponds to a joint measure equal to 0.8. In

this case, the control loops (y-u) are ( -SVC LVD) and

( -SC MAN). The third choice corresponds to a joint mea-sure equal to 0.7. It can be performed using the measurement

and by voltage reference modulation of compensators

NEM, ALB, and CHI.

B. Geometric Approach

Table V shows the joint measures obtained using the geo-

metric approach. As for the residues approach, only the signal

associated to the larger measures are listed. One notes that

the results obtained are different from those obtained with

the residues. Indeed, contrary to the residues, the geometric

approach recommends the angles shifts between CHI and

Churchill , ALB and Churchill , and LG2 and

Churchill . In addition, except for SC MAN and SVCLTD, the geometric approach leads to the conclusion that the




TABLE V

JOINT MEASURES OBTAINED WITH GEOMETRIC APPROACH

Fig. 3. Wide-area signal r coi.

best measurement is the angle shift between LG1 and Churchill.

At this stage, the question that remains to be answered is:

which is the most effective method? The answer to this question

is given by the comparative analysis.

C. Comparative Study

To compare the two approaches, we chose to consider the

control and measurement signals recommended by the residues.

Consequently, in what follows, the global measurement signals

are those which represent the columns of Table IV. Concerning

the control sites, only those with a controllability greater than

or equal to 0.7 (SVC LVD, SC MAN, SVC NEM, SVC ALB,and SVC CHI) will be considered.

1) Identification Results: Fig. 3 compares the output signal

coi of the network with that of the identified system. In this

case, the excitation is applied to the voltage reference of SVC

LVD.

As expected, the results obtained show that the system

remains stable even if the transmission line from Micoua to

Saguenay were removed. In addition, one observes a very good

superposition between the identified signal and the real signal

which is the output of the nonlinear simulation model obtained

using ST600 software. Note that the same results were observed

for all compensators and all measurements, which implies that

the identified linear models used for the signals selection andanalysis are good and reliable.

Fig. 4. Joint measures.

2) Control Loops Selection Results: Fig. 4 represents the

joint measures obtained with the two approaches. For each com-

pensator and for each method, the joint measures were divided

by the associated maximum measure.

The results show that the joint measures obtained with the

residues and the geometric approaches are different. As global

measurements are different from those given in Table V and

knowing that the geometric measures are scaling dependent, in

Fig. 4, it is normal that the conclusions concerning coi are

different from those in Table V.

For all compensators, as showed in Fig. 4, the results obtained

with the residues reveal that the observability of the 0.6-Hz

mode is maximum with the global angle shift between LA1 andChurchill . On the other hand, with the geometric ap-

proach, maximum observability is obtained with global angle

shift between NEM and Churchill buses in case of SVC

LVD and with global angle shift between LG1 and

Churchill for the other compensators. For all compensators, the

residues, contrary to the geometric approach, allow us to con-

clude that the worst wide-area measurement is coi. In ad-

dition, the results show that the conclusions concerning local

signals are the same with the two methods. Indeed, for the local

measurements, even if the values of the geometric measures are

higher than those obtained with the residues, for each compen-

sator, the two approaches recommend the same signals. For thefive selected compensators, in case of local measurement, ex-

cept for compensator MAN, the two methods reveal that the

best observability is obtained with local measurement .

On the other hand, in case of compensator MAN, the two ap-

proaches recommend the local measurement . Finally, the

results show that the joint measure associated to wide-area mea-

surements are greater than those related to local signals what

implies that global control is more effective than local control

to damp the 0.6-Hz inter-area mode.

3) Small-Signal Study Results: In this section, we compare

the performances and robustness of three PSSs: PSS RES,

which uses the global angle shift ( - )

recommended by the residues approach; PSS GEO, which,depending on the case, uses the measurement (




Fig. 5. Global measurement in open loop.

Fig. 6. Step at LG2, angle shift between Churchill plant, and LG2 plant buses.

Fig. 7. Step at LG2, angle shift between Churchill plant, and LG2 plant buseswith optimized PSS.

- ) or ( - ) recommended by

the geometric approach; and PSS LOC, based on local

measurements.

a) Performances: Figs. 6 and 7 show the responses of the

closed-loop system in the case of a step applied to the voltage

reference of plant LG2 (Robert Bourassa). For each compen-

sator, the angles in per unit in Figs. 5 and 6 are the angles shiftsbetween Churchill plant bus and LG2 plant bus.

Fig. 8. Step at LG2, delay of 200 ms.

Fig. 6 reveals that the performances obtained with the

PSS GEO are better than those obtained with PSS RES. As

shown in Fig. 5, this is due to the fact that, contrary to the

geometric approach, the signal classification obtained with

residues is based only on signals amplitude. In this case, if

the gain of the stabilizer is too large, the risk of closed-loop

instability is higher.

As the closed-loop performances depend on the PSS parame-

ters and the measurements used, the stabilizers were optimized.

The optimized parameters are given in the Appendix.

As shown in Fig. 7, the optimization was performed in order

to obtain similar small-signal performances for the three PSSs.

This approach was adopted to allow a fair comparison between

the two control-loop selection methods and between globaland local control. This methodology is used to compare the

three PSSs in terms of a compromise between robustness and

performances.

b) Robustness: The gain MG, phase MP, modulus MM,

and delay MR margins as well as the sensitivity S and the com-

plementary sensitivity T functions [19], [20] were used to eval-

uate the robustness of the closed-loop system.

The results of Table VI show that the highest gain margin is

obtained with stabilizer PSS GEO. For compensators LVD and

CHI, compared to PSS RES, the gain margins obtained with

the local PSS are higher. The opposite effect is observed with

compensators MAN, NEM, and ALB. In addition, except forcompensator MAN with local control, the modulus margins are

satisfactory. For all compensators, the highest modulus margin

is obtained with PSS GEO. Except for compensator MAN, the

phase margin obtained with all compensators and all PSS is in-

finite. As shown in Table VI, for SC MAN, the highest phase

MP and delay MR margins are obtained with PSS GEO, which

means that this stabilizer tolerates the most important delay.

This result is confirmed by the simulation results illustrated in

Fig. 8.

For compensators ALB and LVD, Figs. 9 and 10 illustrate

the sensitivity functions associated with the three PSSs. The

sensitivity function T is always less than 1, which means that

the stabilizers have a good robustness with respect to modeluncertainties. Between 0.1 and 10 Hz, global control guarantees




TABLE VI

ROBUSTNESS MARGINS

Fig. 9. Sensitivity functions S and T, SVC ALB.

a better robustness than local control and stabilizer PSS GEO is

more robust than PSS RES. Note that, except for compensator

MAN with local control, these results have been observed with

all PSSs and compensators. In addition, between 0.1 and 10

Hz, the sensitivity function S associated with PSS GEO does

not present a peak. This result, observed with all compensators,

implies that PSS GEO provides better performances than

PSS RES and PSS LOC.

4) Large-Signal Results: The behavior of the three PSSs was

tested on the 2003 Hydro-Québec network using the transient

stability program ST600. Three contingencies were considered.

The first, 3SVC19c, is a fault at Micoua with a the loss of the linebetween Micoua and Saguenay. The second, 3SVCnem, and the

Fig. 10. Sensitivity functions S and T, SVC LVD.

Fig. 11. Contingency m0100-3SVC19c.

third, 3SVCalb, are successive line losses in Robert Bourassa

(LG2) and LG4 corridors, respectively.

The results, illustrated in Fig. 11, show that the two global

PSSs have similar performances, both better than those obtained

with the local PSS. The oscillation frequency is around 0.32 and

0.27 Hz with the global and the local PSS, respectively. This

result is in accordance with the associated sensitivity function S

given in Fig. 9.As shown in Fig. 12, in the case of successive line losses

in corridor LG4, the best performances are obtained with the

global stabilizer PSS GEO. With the stabilizer based on the

residues approach, oscillations around 0.84 Hz are observed.

This result was foreseeable because, as shown in Fig. 10, the

sensitivity function S associated with SVC LVD and PSS RES

has a peak at this frequency.

Fig. 13 confirms that the best performances are obtained with

the stabilizer based on the geometric approach. In addition, the

frequency of the oscillations obtained with the PSS RES corre-

sponds to the resonance peaks observed on the associated sen-

sitivity functions.

5) Statistical Analysis Results: A total of 1140 contingen-cies were simulated for the statistical analysis. Among them,




Fig. 12. Contingency p0100-3SVCalb.

Fig. 13. Contingency p0100-3SVCnem.

780 associated with 60 load flows and 13 faults were applied to

the peak load network. The others, associated with 30 load flows

and 22 faults, were applied to the summer network, which cor-

responds to a load equal to 17 500 MW.

In the statistical analysis, to evaluate the impact of SVC andSC control on the damping of the 0.6-Hz inter-are mode, the

results in closed loop were compared with those obtained in

open loop, i.e., without PSS connected to the compensators. In

this paper, the open loop is considered as the reference case. In

addition, to compare local and global controls, two scenarios

were considered. In the first, only SVC NEM, SVC LVD, and

SVC ALB were equipped with local and global stabilizers. In

the second, in addition to these SVCs, the SC MAN was also

equipped with a PSS. The behavior of the stabilizers was com-

pared using four indicators. The first is the number of stable

cases obtained. The second is the number of voltage and/or

frequency criteria-violation cases. The third is the number of

loss-of-synchronism cases observed, and the last is the numberof cases of unstable before 2 s obtained.

Fig. 14. Statistical analysis in the case of three SVCs.

Fig. 15. Statistical analysis in the case of three SVCs and one SC.

In Figs. 14–16, for the open loop and the closed loop associ-

ated to each stabilizer, the bars represent the value of the four in-

dicators. The numbers from which these figures were obtained

are given in the Appendix. As shown in Figs. 14 and 15, the

two global PSSs are more ef ficient than the local PSS. Com-

pared to local PSS, the global stabilizers allow an increase in the

number of stable cases and a larger reduction of the number of

voltage and frequency criteria violations, loss-of-synchronism

cases, and unstable before 2 s cases. To be more precise, the

global stabilizers allow an increase around 3.5% of the numberof stable cases with respect to the reference case. Concerning the

number of criterion violation cases, with local PSS, the results

reveal an augmentation of 15% and 4% in the case of three and

for compensators, respectively, whereas with the global PSS,

one observes a diminution of 22% and 34%. Concerning the

increase in stable cases and the reduction of criteria-violation

cases, Figs. 14 and 15 show that the two global stabilizers are

equivalent. On the other hand, the results show that the reduc-

tion in the number of loss-of-synchronism and unstable before

2 s cases is more significant with the PSSbased on the geometric

approach.

Fig. 16 shows the statistical results obtained when a 200-ms

delay is added in the global control loops. In this case, only theSC MAN, SVC LVD, and SVC ALB are equipped with global




Fig. 16. Statistical analysis: Global PSS with 200-ms delay.

stabilizers. The results obtained show that the stabilizer based

on the geometric approach is more robust with respect to thedelay than that based on the residues approach.

In fact, with respect to the reference case, the number

of losses of synchronism increases by 15% with PSS RES,

whereas it increases by only 5% with PSS GEO. In addition,

the number of stable cases is lower with PSS RES and the per-

centage of reduction of criteria-violation and unstable before

2 s cases is the same with the two stabilizers.

VI. DISCUSSION OF THE RESULTS

In the statistical study, the time delay was increased from 0 to

200 ms. The results highlighted similar behavior of the global

stabilizers until 100 ms. Even if the technology today allows toobtain delays of around 50 ms, we chose to consider a longer

delay for two reasons. The first was, to evaluate the robustness

of the closed-loop with respect to the delay and neglected dy-

namics, while the second relates directly to the implementa-

tion solution cost. Indeed, as a future work, Hydro-Québec is

currently considering a project to test wide-area control on its

network.

VII. CONCLUSION

The geometric measures and the residues were used to

select the most effective control loops to damp the 0.6-Hzinter-area mode of the Hydro-Québec network. The damping is

obtained by compensators voltage reference modulation. Two

control scenarios were studied: global and local control. The

results showed that the two selection methods produce different

control loops. The analysis of open-loop signals reveals that,

contrary to the geometric approach, the residues recommend

high-amplitude signals independently of the phase. For all

compensators, the robustness analysis reveals that the PSS

based on the geometric approach is the more robust. On the

other hand, in terms of robustness, it is not possible to clearly

discriminate between the PSS based on residues and the local

PSS. All these observations were confirmed by small-signal

simulations which allowed the validation of the theoreticallycalculated robustness margins. In addition, in the case of severe

Fig. 17. MBPSS description.

TABLE VIICASE OF THREE SVCS EQUIPPED WITH PSS

TABLE VIIICASE OF THREE SVCS AND ONE SC E QUIPPED WITH PSS

TABLE IXDELAY OF 200 MS

TABLE XMBPSS PARAMETERS

TABLE XIMBPSS OPTIMIZED GAIN KI

contingencies produced with the transient stability program

ST600, for all compensators, the best performances were ob-

tained with the PSS based on the geometric approach. For all

contingencies, the link between the frequency oscillations and

the peaks observed on the sensitivity functions was established.

On the basis of the statistical study, we can conclude that global

control is more effective than local control to damp the 0.6-Hz

inter-area mode of the Hydro-Québec network. In addition,

concerning the control-loop selection, the results showed un-

ambiguously that the geometric approach is more reliable than

the residues approach, which is the one usually used in severalstudies. This last result confirms those presented in [21].




APPENDIX

Fig. 17 describes MBPSS. Table VII shows the case of three

SVCs equipped with PSS, Table VIII shows the case of three

SVCs and one SC equipped with PSS, Table IX shows a delay

of 200 ms, Table X shows the MBPSS parameters, and Table XI

shows the MBPSS optimized gain ki.

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Annissa Heniche (M’02) received the B.Eng. degree in electrical engineeringfrom Ecole Nationale des Ingénieurs et Techniciens d’Algérie in 1985 and theMaster’s and Ph.D. degrees from Paris 11 University, Paris, France, 1992 and1995, respectively.

She joined the Hydro-Québec Research Institute, Varennes, QC, Canada, in2001, where she is involved as a researcher in the Power System Analysis, Op-eration, and Control Department.

Dr. Heniche is a member of the Québec Order of Engineers.

Innocent Kamwa (S’83–M’88–SM’98–F’05) received the graduating degreeand Ph.D. degree in electrical engineering from Laval University, Qu ébec City,

QC, Canada, in 1988 and 1984, respectively.Since then, he has been with the Hydro-Québec Research Institute, Varennes,

QC, where he is at present a Principal Researcher with interests broadly in bulk system dynamic performance. Since 1990, he has held an Associate Professor’sposition in electrical engineering at Laval University, where five students havecompleted their Ph.D. under his supervision.

Dr. Kamwa is a recipient of the 1998and 2003IEEE PES Prize Paper Awardsand is currently serving on the System Dynamic Performance Committee,AdCom. He is a member of CIGRé

Assessment of Two Methods to Select Wide-Area

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