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7/27/2019 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
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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)
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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
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460 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 23, NO. 1, JANUARY 2008
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
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VASQUEZ-ARNEZ AND ZANETTA : NOVEL APPROACH FOR MODELING THE STEADY-STATE CONTROLLERS 461
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
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462 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 23, NO. 1, JANUARY 2008
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.
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VASQUEZ-ARNEZ AND ZANETTA : NOVEL APPROACH FOR MODELING THE STEADY-STATE CONTROLLERS 463
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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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.