A Novel Approach for Modeling the Steady-state Vsc-based Multiline Facts Controllers and Their Operational Constraints

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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 23, NO. 1, JANUARY 2008 457

A Novel Approach for Modeling the Steady-StateVSC-Based Multiline FACTS Controllers and

Their Operational ConstraintsR. Leon Vasquez-Arnez and Luiz Cera Zanetta, Jr. , Senior Member, IEEE

Abstract—A new, simple approach for modeling and assessingthe operation and response of the multiline voltage-source con-troller (VSC)-based flexible ac transmission system controllers,namely the generalized interline power-flow controller (GIPFC)and the interline power-flow controller (IPFC), is presented inthis paper. The model and the analysis developed are based on theconverters’ power balance method which makes use of the –orthogonal coordinates to thereafter present a direct solution forthese controllers through a quadratic equation. The main con-straints and limitations that such devices present while controlling

the two independent ac systems considered, will also be evaluated.In order to examine and validate the steady-state model initiallyproposed, a phase-shift VSC-based GIPFC was also built in theAlternate Transients Program program whose results are also in-cluded in this paper. Where applicable, a comparative evaluationbetween the GIPFC and the IPFC is also presented.

Index Terms—Generalized interline power-flow controller(GIPFC), interline power-flow controller (IPFC), power-flowcontrol, voltage-source controller (VSC).

I. INTRODUCTION

THE significant progress in the unified power-flow con-troller (UPFC) investigation [1]–[3] has opened new

opportunities for other multifunctional devices. It is the case

of the generalized interline power-flow controller (GIPFC)

and the interline power-flow controller (IPFC) depicted in

Fig. 1. In a joint effort to consolidate these emerging flexible

ac transmission controllers (FACTS) systems, the New York

Power Authority (NYPA) and Electric Power Research Institute

(EPRI) [4] have recently installed the first convertible static

compensator (CSC) which can work under various FACTS

configurations, namely static synchronous series compensator

(SSSC), static compensator (STATCOM), UPFC, and IPFC.

Power systems can present an inadequate line-flow control

which may result in some overloaded lines, while other partsof the system, even in the case of some neighboring lines, could

operate under an idle-like state. By utilizing these devices, an in-

dependent controllability over each compensated line of a mul-

tiline system can be achieved. The basis of the IPFC function-

ality was introduced almost a decade ago [5]. Since then, very

few in-depth researches have been conducted, exploring and

Manuscript received January 10, 2006; revised October 25, 2006. Paper no.TPWRD-00763-2005.

The authors are with the Electric Power and Automation Engineering De-partment, University of São Paulo, São Paulo 05508-900, Brazil (e-mail: [email protected]; [email protected]).

Digital Object Identifier 10.1109/TPWRD.2007.905564

Fig. 1. Generic representation of a GIPFC (S W = O N ). When S W =

O F F , there is independent operation of a STATCOM and an IPFC.

showing the potential benefits and drawbacks of such multiline

controllers.

Despite the existence of some references on this subject

[6]–[9], the control ability that these devices present alsocomes accompanied with a certain degree of complexity in its

structure, control system, and the possible indirect effects that

they may cause upon the network.

In [10], a method for optimal dimensioning, sizing, and

steady-state performance directed to single and multicon-

verter VSC-based FACTS controllers, applied to a particular

real-world reduced system, is presented. In [11], the possibility

of a generalized unified power-flow controller (GUPFC) appli-

cation to an existing grid is also investigated. In [12] and [13],

mathematical models for multiterminal VSC-based HVDC

schemes and for the GUPFC addressing optimal power-flow

methods are presented. Steady-state models for the UPFC

and their extensions to the GUPFC, using either the powerinjection model or the voltage source model, have also been

addressed in [10]–[15]. Nonlinear solutions applied to such

models regarding the converters’ power balance are presented

in [16]–[19].

This paper’s main concern is to present a practical and di-

rect method to asses the steady-state response of the GIPFC and

IPFC controllers as well as investigate the main constraints ap-

pearing after their installation to the network.

Notice that there is a small topological difference between

the GUPFC addressed by [10] and the GIPFC addressed in

this paper. In the former, as well as in [11] and [13], buses

(Fig. 1) are all connected. One advantage of

0885-8977/$25.00 © 2007 IEEE



458 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 23, NO. 1, JANUARY 2008

Fig. 2. Elementary GIPFC system used in the analysis.

the GIPFC configuration is its ability to control lines that are

physically close but operate at different voltage levels.

The steady-state operation of the GIPFC, as will be the case

of other similar multiconverter controllers, also requires that

the sum of the active power, exchanged by the total number of converters, be zero. In both configurations (GIPFC and IPFC),

the primary converter(s) or assisted line(s), will have priority

over the secondary converter in achieving their set-point re-

quirements.

II. GIPFC AND IPFC MODELING AND ANALYSIS

The analysis developed in this section considers a GIPFC that

is connected to two balanced independent ac systems (Fig. 2).

The equivalent sending and receiving-end sources in both sys-

tems were regarded as stiff ac sources (infinite buses). It was

also assumed that systems 1 and 2 (hereinafter also referred toas primary and secondary systems, respectively) have identical

line parameters, although, in practice, they would usually be dif-

ferent.

To accurately analyze the response of large power systems,

the load-flow formulation has been shown to be the most ad-

equate. However, it is also very common to reduce and repre-

sent the load, circuit, and sources through their Thevenin equiv-

alents, thus greatly reducing the complexity of the analyzed net-

work. In this model, each converter will be seen as a shunt or

series source operating with fundamental frequency and char-

acterized by ideal sinusoidal waveforms [16], [17]. Also, the

steady-state model developed makes use of the – orthogonalcoordinates [17] which facilitates the control of the direct and

quadrature components of the ideal sources representing the

converters. As will be shown later, the proposed approach is

simple and practical since it only depends upon a quadratic

equation and its solution to thereafter compute the receiving-end

power flow or any other variable needed. Systems 1 and 2 shown

in Fig. 2 will be used for this purpose.

It should be noted that the ON or OFF state of the switch circuit

breaker (CB) (Fig. 2) will not affect the analysis developed at all.

The closed condition of CB (i.e., ) will represent the

case of a substation from which power is dispatched to different

receiving ends. Basically, the forthcoming equations result from

the independent effect of the series and shunt sources over eachsystem (superposition theorem).

So, the total current at the receiving-end of System 1 can be

written as

(1)

where

line current with ,(uncompensated case);

real and imaginary current components due to

the effect of .

For ease of analysis, each line resistance has been neglected.

Likewise, it was regarded to be more appropriate to work using

only the equivalent reactance in each system

and . Thus, for the uncompensated case of

System 1, it can be established that

(2a)

Similarly, the – orthogonal components of will be

(2b)

Substituting (2b) into (1) and further separating the resulting

expression in its – orthogonal components, yields

(3)

Thus, the receiving-end power expressed in terms of the –

orthogonal current components will be

(4a)

(4b)

The and terms correspond to the uncompensated

power flow in System 1.

The secondary system can also be analyzed in a similar way,

except for the presence of the shunt current , whose contri-

bution to System 2 can be represented as shown in Fig. 3.

Therefore, using the current divider shown in Fig. 3 and fur-

ther separating each contribution in their – orthogonal com-

ponents as well as adding them to and will result in

(5a)

(5b)

(6a)

(6b)

The bus voltage projected into the – orthogonal axis,

will be

(7)



VASQUEZ-ARNEZ AND ZANETTA : NOVEL APPROACH FOR MODELING THE STEADY-STATE CONTROLLERS 459

Fig. 3. Shunt converter current contribution within System 2.

with and already obtained, it can be written

(8a)

(8b)

The voltages and currents so far obtained will then be used to

calculate (series VSC-1) in their – components

(9)

Similarly, for System 2

(10a)

Equation (10a) can also be expressed as

(10b)similarly for (shunt VSC)

(11a)

substituting (8a) and (8b) into (11a) yields

(11b)

If the inverter losses are neglected, then the equality between

the shunt and the total series power in the dc link must be

complied

(12)

where represents the number of series converters connected

to the dc link.

The substitution of (3), (9), (10b), and (11b) into (12) yields

(13)

Thus, in a simple way, (13) can be written as

(14)

The reactive power supplied or absorbed by the shunt con-

verter from bus will be

(15)

Substituting (8) into (15) as well as regarding the and

terms yields

(16a)

where , , and .

The and components in both (14) and (16a) are to

be calculated. Note that (16a) can be further reduced to a simple

quadratic equation either using or from (14). Should

be substituted into (16a), the resulting equation will be

(16b)

whose , , and terms are

The use of this simple quadratic equation provides a more

direct solution to analyze the system depicted in Fig. 2; thus,

avoiding the establishment of the set of nonlinear equations and

their iterative solution presented in [18] and [19]. In this new

model, the reactive power ( ) also has to be specified. Once

the and current c omponents a re computed, can

be calculated using (6). Finally, the power flow in the receiving

end of this line can be computed through (17)

(17a)

(17b)

The and terms correspond to the uncompensated stateof the power flow in System 2. The – plane results obtained

through this approach are identical to those presented in [19].

Furthermore, it is fully valid for the case of an IPFC too.

In this case (IPFC mode), the shunt converter will no longer

be present in the arrangement, so some of the variables in the

equations just shown will have to be zeroed, namely ,

, and ; thus simplifying the analysis for this

device. Recall that in this case, System 1 will have two indepen-

dently controlled variables( , ), whereas System 2 will only

have one variable ( ) to be independently controlled. The

component in System 2 will depend on the variation of and

can be obtained from (13).

The inclusion of the series transformers’ coupling reactanceswithin impedances and , was only done to shorten




the system equations. Once the line current is computed, the

voltage can be calculated through (18).

(18)

The line voltage (System 2) can be similarly obtained.

III. GIPFC GENERIC MODEL FOR A MULTILINE SYSTEM

The GIPFC model developed in Section II, can well be gen-

eralized for the case of a GIPFC, compensating an number

of primary lines in a multiline system, such as the one shown in

Fig. 1. The procedure will basically follow the steps presented in

the referred section. A more complete model of the transmission

lines, if needed, can also be included in the method without dif fi-

culty. As the number of compensated lines increases, the power

availability in the system termed as secondary should be bigger

so as to not significantly degrade the original characteristics of

this system.

Basically, (11b) and (15) that were previously given

will be kept unaltered; however, the total series power( ) will become a function of the number

of series converters. So regarding the steady-state power

equality given in (12), a generic expression for the series

voltage-source controllers (VSCs) can be written

(19)

The and terms presented in (13) will also remain unal-

tered. Thus, (13) in its generic form will turn into

(20)

Notice that the term in (13) will now be renamed as

as it will depend on the series voltages and their line currents

(uncompensated state) in the number of lines assisted by the

GIPFC or IPFC

Note that the term (series voltage) is specified; thus, (20)

can be written as

(21)

Once is computed, the shunt current components ( ,

) can be calculated similar to the procedure given in

Section II. The effect of the series converter(s) upon System

2 can be computed through (17). Likewise, the receiving-end

power flow over System 1, or in the th system, can be calcu-

lated similar to (4).

IV. RESULTS

The – plane results shown in Fig. 4 were obtained using

the mathematical model developed in Section II in which both

series angles were simultaneously varied from 0 through360 . The region inside the ideal circle and inside the ellipse

Fig. 4.P –Q

plane at the receiving end of systems 1 and 2.. (a) GIPFC withV = 0 : 2 p.u. and V = 0 : 1 5 p.u. (b) IPFC with V = 0 : 2 p.u., V = 0 ,and

V = f ( V )

.

correspond to the controlled area provided by and ,respectively. The ellipse obtained in Fig. 4(a) is due to the

real-power demand imposed by the primary system over the

secondary system. For this condition, no shunt reactive power

( ) was applied to bus . During the uncompensated

condition, the receiving-end active and reactive power were

equal to p.u. and p.u.,

respectively.

Should the shunt VSC be connected to a different line, both

systems with series compensation would present, ideally, a cir-

cular-controlled region as none of them would affect the voltage

or power characteristics of either line. A similar result will be

obtained when , as in this case, voltagesand (stiff sources) will take over from voltages and .

Fig. 4(b) shows the power-flow behavior corresponding to a

two-converter IPFC having identical line parameters as that de-

picted in Fig. 2. As approaches the quadrature position with

respect to the line current (in our case, , 255 ), both

and in System 2 return to the uncompensated condition

(i.e., and ). This is due to the less (eventually null) de-

mand in the exchanged power ( ) between the series-con-

nected VSCs.

Notice that, while the power flow in System 1 ( ) can be

set to operate in an uncompensated mode at p.u.,

with solely System 2 being compensated through , the oppo-

site operative condition (i.e., System 1 being compensated andSystem 2 kept unaltered) will present a drawback. That is, it is




Fig. 5. Power-flow control on System 1 and its effect over System 2 (uncom-pensated), when V = 0 ! 0 : 2 p.u. (IPFC configuration).

not possible to maintain the unaltered power flow over System 2

(at p.u.) when solely System 1 is being compensated.

Despite , the bus voltage and, consequently, the

power flow ( ), will slightly vary (Figs. 4 and 5). This pattern

was observed to occur in both FACTS devices.The referred vari-

ation will be proportional to the level of compensation applied toSystem 1 (i.e., high values of will cause relatively significant

variations over System 2) as can be observed in Fig. 5 (IPFC

scheme). This fact shows the small degradation that System 2

experiences on account of helping to control the power flow in

System 1.

Still, in the GIPFC configuration, the voltage variation that

bus experiences, while helping to manipulate the series

voltage of System 1, can be largely controlled through the

shunt converter’s action. Also, the referred effect may become

less significant when, say, an independent or a high power line

provides the real power required by a low capacity line in order

to improve its power transmission. In this way, the former willonly be slightly affected in its own transmission features.

Fig. 6, obtained using the generic model presented in

Section III, shows the – plane behavior when a third line

is included in the model. As in this case , the term

will become (21). Once and the rest of the variables are

computed, the – behavior of each system can be plotted.

Notice how the ellipse characterizing the response of System

2 becomes even more reduced at its sides. The addition of,

say, two more lines with heavy series demand, might virtually

leave no real power availability in the shunt VSC to fulfill the

demand of its own series converter. As a consequence, this

series converter will only be able to control (System 2) through

its available reactive compensation, unless the shunt converteris resized.

Fig. 6. GIPFCP –Q

plane at the receiving end of Systems 1, 2, and 3 for the

full 360 of , V = 0 : 2 p.u., V = 0 : 1 2 p.u., and V = 0 : 1 5 p.u.

Fig. 7. Twelve-pulse GIPFC scheme implemented in ATP.

Fig. 8. GIPFC power-flow control over Systems 1 and 2V = 0 : 1 0 6 0

att = 0 : 1 s , V = 0 : 2 0 6 0 at t = 0 : 2 s , V = 0 : 1 0 2 4 0 at t = 0 : 1 s ,and

V = 0 : 0 5 2 4 0

att = 0 : 3 s

.

On the other hand, the results shown in Figs. 8–10 have beenobtained using the Alternate Transients Program (ATP) pro-

gram, in which a GIPFC, also controlling two lines (Fig. 7),

was implemented. As this paper’s main goal is to address the

steady-state power flow control in a multiline system, the re-

ferred results were chiefly included to observe what the response

would be like when a more detailed GIPFC scheme is built.

In this ATP program, which was based upon the phase-shift

control technique [20] using a 12-pulse three-level inverter con-

figuration and gate turnoff thyristors (GTOs) as switching de-

vices, both equivalent ac systems were assumed to operate at

a rated voltage of 230 kV. The shunt converter rated power is

equal to MVA through which the real power demand can

be fulfilled from both series VSCs (each having 100-MVA ratedpower) and to compensate, through its shunt reactive power, the




Fig. 9. Series voltages (V

,V

) characterizing the power-flow control pro-vided to Systems 1 and 2.

Fig. 10. Power-flow control over System 1:V = 0 : 1 0 6 0

att = 0 : 1 s

,

V = 0 : 2 0 6 0

att = 0 : 2 s

,V = 0

.

terminal voltage (Fig. 2). The coupling transformers were

chosen regarding: 1) the rated power of each converter and 2) the

dc-link rated voltage which, in our case, was equal to 25 kV.

The power-flow control sequence applied over both systems

(Fig. 8) can be summed up as follows: due to system require-

ments, at . is reduced whereas (System 1) is in-

creased. Subsequently, the power-flow reduction effect of is

cancelled out ( ) whereas , on account of a hypothet-

ical greater demand, is increased even more. The final control

action occurs at when is, due to a system require-

ment too, once again forced to reduce its transmitted power.

The series voltage waveforms ( , ) characterizing the ef-fect of the power-flow control shown in Fig. 8 can be observed

in Fig. 9. On the other hand, Fig. 10 shows the slight power-flow

degradation ( ) experienced by System 2 (despite )

on account of helping to manipulate the series voltage spec-

ified in System 1.

Generally speaking, the GIPFC implemented provided a high

degree of controllability for each line as the transmitted power

was almost instantaneously and simultaneously reduced or in-

creased according to the operative needs of each line.

V. OPERATIONAL CONSTRAINTS

Despite the benefits introduced by the series-connected VSC-based FACTS controllers studied herein, there are also a number

Fig. 11. GIPFC nonoperative areas (NOA) of theseriesvoltages correspondingto: (a) System 1. (b) System 2 with

Q = 0 : 1

p.u.

of operative constraints and limitations that should be accounted

for, such as those to be described.

A. Bus Voltage Limitations

During steady state, certain system restrictions can cause lim-

itations in the operative areas of the series voltages in both mul-tiline controllers. The nonoperative areas (NOAs) depicted in

Fig. 11 are due to the boundaries imposed on buses , ,

, and which should not be violated (i.e., and

p.u.) and on the assisting converter’s rating restric-

tions (nominal apparent power).

Although in our case, voltages and are internal

voltages, in classical schemes, they might represent the sub-

station voltage. The smaller NOAs were obtained for System

2 [Fig. 11(b)] because the bus voltage was compensated

through , from the shunt VSC.

As the magnitude of (or ) is increased, according to

the behavior of the NOA curves and if no other parameter in thesystem is altered, there will be a trend among the NOA parabolic

curves to cross each other, thus increasing the NOA areas even

more (e.g., p.u.). A similar effect (onset of NOAs)

will occur in cases when the assisting converter in the GIPFC

and IPFC controllers does not have enough capacity to meet the

demand imposed by the rest of the series VSCs. This condition,

along with the bus voltage limitation analyzed, will cause the

NOA curves to slide further downwards with respect to the po-

sitions shown in Fig. 11.

On the other hand, if voltages or (postseries voltages)

could be more flexible in their operative ranges, they could help

to reduce the NOAs. Of course, this must be in accordance with

the specifications of the line’s maximum voltage withstandingcapacity.




Fig. 12. Real-power limitation due to shunt converter rating (GIPFC).

B. Shunt Converter Rating Constraint

Another important restriction to be analyzed, as mentioned

earlier, is related to the shunt converter capacity (the converter

in the secondary system in an IPFC scheme). The few references

found addressing this topic [14], [21] are mainly directed to theUPFC concept.

Since the shunt VSC has limited capacity, it was established

that whenever the maximum (rated) real power was about to

be surpassed, the exceeding value should be limited to its max-

imum value (e.g., p.u.) as seen in the response of

Fig. 12. Of course, this limitation will impose a detrimental ef-

fect upon the active power of the series inverters, thus upon

and , creating nonoperative regions such as those presented

in Section V-A.

Note that the capacity of the shunt converter is determined

by the addition of the series converters real power and the re-

active power that it provides for shunt compensation. The same

effect is also applied for the IPFC and its assisting (secondary)

converter

(22)

C. Maximum Power Exchange Through the DC Link

The maximum real power transferred through the dc link by

the inverter in the secondary system can impose another restric-

tion to the operation of the GIPFC and IPFC. Therefore, it is

important to identify which will be the steady-state maximum

power that can be exchanged through the dc link for fulfilling thedemand of the series inverter(s). The real power entering each

series converter, regarding the dc-link currents shown in Fig. 7

can be written as

(23)

Also, the output power of each series converter can be ex-

pressed as

(24)

The line current over System 1 can be written as

(25)

If the losses within the inverters are neglected, then it can be

assumed that and . So, manipulating

(24) and (25) yields

(26)

Similarly for System 2

(27)

The derivative of (26) with respect to will allow us to cal-

culate and the maximum power ( ) corresponding to

VSC-1

(28)

(29)

Recalling the assumption made earlier on about the converter

losses, it can be stated that this will be the maximum power

transferred via the dc link to System 1. As for the GIPFC, a

similar procedure, regarding the derivative of with respect

to and the substitution of into (27), will have to be realized

for System 2. Finally, the total maximum power transferred by

the shunt VSC will result from the addition of the (in our case

two) series converters as stipulated in (30)

(30)

VI. CONCLUSION

A new, simple approach based upon a quadratic equation and

its solution to model and analyze the series-connected multi-

line VSC-based FACTS controllers, was presented in this paper.

Such a method can easily be extended and applied to systems

having more than only two transmission lines. The main con-

straints arising due to the GIPFC and IPFC insertion to the net-

work during steady state were also a matter of concern. It was

observed that the bus voltage boundaries can cause some nonop-

erative regions within the series voltage operative area which, inturn, will affect the control area of the receiving-end power flow.

The power-flow degradation experienced by the system termed

as secondary on account of fulfilling the control needs of the

primary system(s) was also shown. Finally, in order to validate

the steady-state model presented and to show the GIPFC capa-

bilities and its associated drawbacks, the results of a 12-pulse

VSC-based GIPFC elaborated in the ATP program were also

presented.

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[21] S.Arabi,P. Kundur, and R. Adapa, “Innovative techniques in modelingUPFC for power system analysis,” IEEE Trans. Power Syst., vol. 5, no.1, pp. 336–341, Feb. 2000.

R. Leon Vasquez-Arnez was born in Bolivia in 1966. He received the B.Sc.

degree in electrical engineering from the Technical University of Oruro, Oruro,Bolivia, in 1994; the M.Sc. degree from the University of Birmingham, Birm-ingham, U.K., in 1998; and the Ph.D. degree from the University of S ão Paulo,São Paulo, Brazil, in 2004.

In 2005, he was a Postdoctoral Fellow in the Department of Electrical Engi-neering at the University of São Paulo. His main areas of interest include powersystems and FACTS. Currently, he is with the Electric Power and AutomationEngineering Department, University of São Paulo.

Luiz Cera Zanetta, Jr. (SM’90) was born in Brazil in 1951. He received theB.Sc., M.Sc., and Ph.D. degrees from the University of São Paulo, São Paulo,

Brazil, in 1974, 1984, and 1989, respectively.From 1975 to 1989, he was with the Power Systems Group at THEMAG

Engineering Ltd., which developed power systems studies for most Brazilian

utilities. Currently, he is a Professor in the Electric Power and Automation En-gineering Department, Universityof São Paulo, working inthe fieldof electricalsystem dynamics, electromagnetic transients, and FACTS.

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