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FLEXIBLE AC TRANSMISSION SYSTEMS
3.1 INTRODUCTION:
In its most general expression, the FACTS concept is based on
the substantial incorporation of power electronic devices and methods
into the high-voltage side of the network, to make it electronically
controllable (IEEE/CIGRE, 1995).
Many of the ideas upon which the foundation of FACTS rests
evolved over a period of many decades. Nevertheless, FACTS, an
integrated philosophy, is a novel concept that was brought to fruition
during the 1980‘s at the Electric Power Research Institute (EPRI), the
utility arm of North American utilities [39]. FACTS looks at the ways of
capitalizing on many breakthroughs taking place in the area of high-
voltage and high current power electronics, aiming at increasing the
control of power flows in the high voltage side of the network during
both steady-state and transient conditions.
Power electronic devices have had a revolutionary impact on the
electric power systems around the world. The availability and
application of thyristors has resulted in a new breed of thyristor-based
fast operating devices devised for control and switching operations.
This chapter deals with basic operating principles of FACTS devices
and provides detailed discussions about the structure, operation, and
modeling of the SVC, TCSC, STATCOM and the UPFC.
32
3.2 TYPES OF FACTS CONTROLLERS:
FACTS controllers can be broadly divided into four categories,
which include series controllers, shunt controllers, combined series-
series controllers, and combined series-shunt controllers. Their
operation and usage are discussed below.
3.2.1 PRINCIPLE OF THE SERIES CONTROLLERS:
A series controller may be regarded as variable reactive or
capacitive impedance whose value is adjusted to damp various
oscillations that can take place in the system. This is achieved by
injecting an appropriate voltage phasor in series with the line and this
voltage phasor can be viewed as the voltage across an impedance in
series with the line. If the line voltage is in phase quadrature with the
line current, the series controller absorbs or produces reactive power,
while if it is not, the controllers absorb or generate real and reactive
power. Examples of such controllers are Static Synchronous Series
Compensator (SSSC), Thyristor-Switched Series Capacitor (TSSC),
Thyristor-Controlled Series Reactor (TCSR), to cite a few. They can be
effectively used to control current and power flow in the system and to
damp oscillations of the system.
3.2.2 PRINCIPLE OF THE SHUNT CONTROLLERS:
Shunt controllers are similar to the series controllers the
difference being that they inject current into the system at the point
where they are connected. A variable shunt impedance connected to a
line causes a variable current flow by injecting a current into the
system. If the injected current is in phase quadrature with the line
33
voltage, the controller adjusts reactive power while if the current is not
in phase quadrature, the controller adjusts real power. Examples of
such systems are Static Synchronous Generator (SSG), Static Var
Compensator (SVC). They can be used as a good way to control the
voltage in and around the point of connection by injecting active or
reactive current into the system.
3.2.3 PRINCIPLE OF THE COMBINED SERIES – SERIES
CONTROLLERS:
A combined series-series controller may have two
configurations. One configuration consists of series controllers
operating in a coordinated manner in a multi line transmission
system. The other configuration provides independent reactive power
control for each line of a multi line transmission system and, at the
same time, facilitates real power transfer through the power link. An
example of this type of controller is the Interline Power Flow Controller
(IPFC), which helps in balancing both the real and reactive power
flows on the lines.
3.2.4 PRINCIPLE OF THE COMBINED SERIES – SHUNT
CONTROLLERS:
A combined series-shunt controller may have two
configurations, one being two separate series and shunt controllers
that operate in a coordinated manner and the other one being an
interconnected series and shunt component. In each configuration,
the shunt component injects a current into the system while the
series component injects a series voltage. When these two elements
34
are unified, a real power can be exchanged between them via the
power link. Examples of such controllers are UPFC and Thyristor-
Controlled Phase-Shifting Transformer (TCPST). These make use of
the advantages of both series and shunt controllers and, hence,
facilitate effective and independent power/current flow and line
voltage control.
3.3 STATIC VAR COMPENSATOR (SVC):
The IEEE definition of the SVC [40] is as follows: ―A shunt
connected static var generator or absorber whose output is adjusted to
exchange capacitive or inductive current so as to maintain or control
specific parameters of the electrical power system (typically bus
voltage).”
In other words, an SVC is a static var generator whose output is
varied in order to maintain or control the specific parameters of an
electric power system. Svcs are primarily used in power systems for
voltage control or for improving system stability.
Static var compensators (svcs) are used primarily in power
systems for voltage control as either an end in itself or a means of
achieving other objectives, such as system stabilization [39-42].
3.3.1 V-I CHARACTERISTICS OF SVC:
As shown in Fig 3.1., the dynamic characteristics of an SVC are
the plots of bus voltages versus current or reactive power. In Fig 3.1.,
the voltage Vref is the voltage at the terminals of the SVC when it is
neither absorbing nor generating any reactive power. The reference
voltage value can be varied between the maximum and minimum
35
limits, Vref max and Vref min, using the SVC control system. The
linear range of the SVC control passing through Vref is the control
range over which the voltage varies linearly with the current or
reactive power. In this range, the power is varied from capacitive to
inductive.
The slope or droop of the V-I characteristic is the ratio of change in
voltage magnitude to the change in current magnitude over the linear
control range. This slope is given by
I
VK sl (3.1)
Where ΔV denotes the change in voltage magnitude (V) and ΔI denotes
the change in current magnitude (I).
The slope Ksl can be changed by the control system. Ideally, for voltage
regulation it is required to maintain a flat voltage profile with a slope
equal to zero. In practice, it is desirable to incorporate a finite slope of
about 3-5% for the following reasons:
ILr Inductive Capacitive
Linear Range of Control
Over load
Range
VSVC
ISVC ICr
Vref
Bmax
Fig 3.1 Voltage – Current characteristics of SVC
36
1. It reduces the reactive power rating of the SVC substantially for
achieving similar control objectives;
2. It prevents the SVC from reaching its reactive-power limits too
frequently;
3. It facilitates the sharing of reactive power among multiple
compensators connected or operating in parallel.
Once the SVC‘s operating point crosses the linear controllable
range, it enters the overload zone where it behaves like a fixed
inductor or capacitor.
3.3.2 MODELING OF SVC IN POWER FLOW STUDIES:
In its simplest form, the SVC consists of a TCR in parallel with a
bank of capacitors. From the operational point of view, the SVC
behaves like a shunt-connected variable reactance, which either
generates or absorbs reactive power in order to regulate the voltage
magnitude at the point of connection to the AC network. It is used
extensively to provide fast reactive power and voltage regulation
support. The firing angle control of the thyristor enables the SVC to
have almost instantaneous speed of response. Conventional and
advanced power flow models of svcs are presented in this section. The
advanced models depart from the conventional generator-type
representation of the SVC and are based instead on the variable shunt
susceptance concept..
3.3.3.SHUNT VARIABLE SUSCEPTANCE MODEL:
In practice the SVC can be seen as an adjustable reactance with
either firing-angle limits or reactance limits [32]. The equivalent circuit
37
shown in Fig. 3.2 is used to derive the SVC nonlinear power equations
and the linearised equations required by Newton‘s method.
With reference to Figure 3.2, the current drawn by the SVC is
kSVCSVC VjBI (3.2)
And the reactive power drawn by the SVC, which is also the reactive
power injected at bus k, is
SVCkkSVC BVQQ 2 (3.3)
The linearised equation is given by Equation (3.4), where the
equivalent susceptance BSVC is taken to be the state variable
i
svcsvc
k
i
k
i
k
k
BBQQ
P
/0
00 (3.4)
At the end of iteration (i), the variable shunt susceptance BSVC is
updated according to
i
svc
i
svcsvc
i
svc
i
svc BBBBB /1 (3.5)
The changing susceptance represents the total SVC susceptance
necessary to maintain the nodal voltage magnitude at the specified
value. Once the level of compensation has been computed then the
thyristor firing angle can be calculated. However, the additional
Fig 3.2 Variable Shunt Succeptance Model
VK
BSVC
ISVC
38
calculation requires an iterative solution because the SVC
susceptance and thyristor firing angle are nonlinearly related.
3.3.4.FIRING ANGLE MODEL:
An alternative SVC model, which circumvents the additional
iterative process, consists in handling the thyristor-controlled reactor
(TCR) firing angle α as a state variable in the power flow formulation
[43]. The variable α will be designated here as αsvc.
From Eqn No. 3.3, the positive sequence susceptance of the SVC is
given by
SVCSVCC
L
LC
kk
XX
XX
VQ
2sin2
2
(3.6)
From Eqn No. 3.6, the linearised SVC equation is given as
i
svc
k
i
SVC
L
k
i
k
k
X
VQ
P
12cos2
0
002
(3.7)
At the end of iteration (i), the variable firing angle αsvc is updated
according to
111
i
SVC
i
SVC
iSVC (3.8)
3.4. THYRISTOR – CONTROLLED SERIES COMPENSATOR
(TCSC):
The basic conceptual TCSC module comprises a series
capacitor, C, in parallel with a thyristor-controlled reactor, LS, as
shown in Fig. 3.3. However, a practical TCSC module also includes
protective equipment normally installed with series capacitors. A
metal-oxide varistor (MOV), essentially a nonlinear resistor, is
39
connected across the series capacitor to prevent the occurrence of
high-capacitor over- voltages. Not only does the MOV limit the voltage
across the capacitor, but it allows the capacitor to remain in circuit
even during fault conditions and helps improve the transient stability.
Also installed across the capacitor is a circuit breaker, CB, for
controlling its insertion in the line. In addition, the CB bypasses the
capacitor if severe fault or equipment-malfunction events occur. A
current-limiting inductor, Ld, is incorporated in the circuit to restrict
both the magnitude and the frequency of the capacitor current during
the capacitor-bypass operation.
An actual TCSC system usually comprises a cascaded
combination of many such TCSC modules, together with a fixed-series
capacitor, CF. This fixed series capacitor is provided primarily to
minimize costs.
3.4.1 OPERATION OF THE TCSC:
A TCSC is a series-controlled capacitive reactance that can
provide continuous control of power on the ac line over a wide range.
From the system viewpoint, the principle of variable-series
Fig 3.3 A TCSC Basic Module
T2
T1
IT
IC
LS
Iline ILOOP
+
C
40
compensation is simply to increase the fundamental-frequency voltage
across a fixed capacitor (FC) in a series compensated line through
appropriate variation of the firing angle, α [44]. This enhanced voltage
changes the effective value of the series-capacitive reactance.
A simple understanding of TCSC functioning can be obtained by
analyzing the behavior of a variable inductor connected in parallel
with an FC, as shown in Fig. 3.4
The equivalent impedance, Zeq, of this LC combination is expressed as
LC
jZeq
1
1
(3.9)
The impedance of the FC alone, however, is given by
Cj
1
There are essentially three modes of TCSC operation. They are
(i) By-passed Thyristor Mode
(ii) Blocked thyristor Mode
(iii)Partially Conducting thyristor Mode
Two alternative power flow models to assess the impact of TCSC
equipment in network wide applications are presented in this section
[45]. The simpler TCSC model exploits the concept of a variable series
reactance. The series reactance is adjusted automatically, within
limits, to satisfy a specified amount of active power flows through it.
Fig 3.4 A variable Inductor connected in shunt with an FC
L
C
+
41
The more advanced model uses directly the TCSC reactance–firing-
angle characteristic, given in the form of a nonlinear relation. The
TCSC firing angle is chosen to be the state variable in the Newton–
Raphson power flow solution.
3.4.2 VARIABLE SERIES IMPEDANCE POWER FLOW MODEL:
The TCSC Variable Impedance Power Flow model presented in
this section is based on the simple concept of a variable series
reactance, the value of which is adjusted automatically to constrain
the power flow across the branch to a specified value. The amount of
reactance is determined efficiently using Newton‘s method. The
changing reactance XTCSC, shown in Figure 3.5, represents the
equivalent reactance of all the series-connected modules making up
the TCSC, when operating in either the inductive or the capacitive
regions.
The transfer admittance matrix of the variable series
compensator shown in Figure 3.5 is given by
m
k
mmkm
kmkk
m
k
V
V
jBjB
jBjB
I
I (3.10)
For inductive operation, we have
Bkm=Bmk=TCSCX
1
reg
kmP
m k reg
kmP
m k
Fig 3.5 TCSC Equivalent Circuit (a) Inductive (b) Capacitive operating
Regions
42
Bmm=Bkk=-TCSCX
1 (3.11)
And for capacitive operation the signs are reversed.
The active and reactive power equations at bus k are:
)sin( mkkmmkk BVVP (3.12)
)cos(2
mkkmmkkkkk BVVBVQ (3.13)
For the power equations at bus m, the subscripts k and m are
exchanged in Equations (3.12) and (3.13).
In Newton–Raphson solutions these equations are linearised
with respect to the series reactance. For the condition shown in Figure
3.5, where the series reactance regulates the amount of active power
flowing from bus k to bus m at a value reg
kmP , the set of linearised power
flow equations is:
TCSC
TCSC
m
m
k
k
m
k
TCSC
TCSC
X
kmm
m
X
kmk
k
X
km
m
X
km
k
X
km
TCSCm
m
m
mk
k
m
m
m
k
m
TCSCk
m
m
kk
k
k
m
k
k
k
TCSCm
m
m
mk
k
m
m
m
k
m
TCSCk
m
m
kk
k
k
m
k
k
k
i
X
km
m
k
m
k
X
X
V
V
V
V
XX
PV
V
PV
V
PPP
XQ
VV
QV
V
QQQ
XQ
VV
QV
V
QQQ
XP
VV
PV
V
PPP
XP
VV
PV
V
PPP
P
Q
Q
P
P
TCSCTCSCTCSCTCSCTCSC
TCSC
--
(3.14)
Where
calTCSCTCSCX
km
reg
km
X
km PPP , (3.15)
is the active power mismatch for the series reactance and calTCSCX
kmP , is
the calculated power as per equation 3.12 The state variable XTCSC of
43
the series controller is updated at the end of each iterative step
according to
11
i
TCSC
i
TCSC
TCSCi
TCSC
i
TCSC XX
XXX (3.16)
3.4.3 FIRING ANGLE POWER FLOW MODEL:
The model presented in Section 3.4.2 uses the concept of an
equivalent series reactance to represent the TCSC. Once the value of
reactance is determined using Newton‘s method then the associated
firing angle αtcsc can be calculated. Of course, this makes engineering
sense only in cases when all the modules making up the TCSC have
identical design characteristics and are made to operate at equal firing
angles. If this is the case, the computation of the firing angle is carried
out. However, such calculation involves an iterative solution since the
TCSC reactance and firing angle are nonlinearly related. One way to
avoid the additional iterative process is to use the alternative TCSC
Variable Impedance Power Flow model presented in this section.
The fundamental frequency equivalent reactance XTCSC(1) of the TCSC
module [45] shown in Figure 3.8 is
tantancos2sin2 2
21)1( CCXX CTCSC
(3.17)
Fig 3.6 TCSC Firing Angle Power Flow Model
XL
XC
Im Ik
Vm Vk
m k
ILOOP
44
Where
LCC XX
C 1 (3.18)
L
LC
X
XC
2
2
4 (3.19)
LC
LCLC
XX
XXX
(3.20)
2
1
L
C
X
X (3.21)
The equivalent reactance XTCSC(1) in Equation (3.17) replaces XTCSC in
Equations (3.11) and (3.10), and the TCSC active and reactive power
equations at bus k are
)sin( mkkmmkk BVVP (3.22)
)cos(2
mkkmmkkkkk BVVBVQ (3.23)
Where
)1(TCSCkmkk BBB (3.24)
For equations at bus m, exchange subscripts k and m in Equations
(3.22) and (3.23). For the case when the TCSC controls active power
flowing from bus k to bus m, at a specified value, the set of linearised
power flow equations is:
45
TCSC
m
m
k
k
m
k
TCSC
kmm
m
kmk
k
km
m
km
k
km
TCSC
mm
m
mk
k
m
m
m
k
m
TCSC
km
m
kk
k
k
m
k
k
k
TCSC
mm
m
mk
k
m
m
m
k
m
TCSC
km
m
kk
k
k
m
k
k
k
km
m
k
m
k
V
V
V
V
PV
V
PV
V
PPP
QV
V
QV
V
QQQ
QV
V
QV
V
QQQ
PV
V
PV
V
PPP
PV
V
PV
V
PPP
P
Q
Q
P
P
TCSCTCSCTCSCTCSCTCSC
TCSC
(3.25)
Where calTCSCTCSC
km
reg
kmkm PPP , is the active power mismatch for the TCSC
module. TCSC is the incremental change in the TCSC firing angle.
3.5 STATIC SYNCHRONOUS COMPENSATOR (STATCOM):
The STATCOM (or SSC) is a shunt-connected reactive-power
compensation device that is capable of generating and/ or absorbing
reactive power and in which the output can be varied to control the
specific parameters of an electric power system. It is in general a solid-
state switching converter capable of generating or absorbing
independently controllable real and reactive power at its output
terminals when it is fed from an energy source or energy-storage
device at its input terminals. Specifically, the STATCOM considered in
this chapter is a voltage-source converter that, from a given input of
dc voltage, produces a set of 3-phase ac-output voltages, each in
phase with and coupled to the corresponding ac system voltage
through a relatively small reactance (which is provided by either an
interface reactor or the leakage inductance of a coupling transformer).
The dc voltage is provided by an energy-storage capacitor.
46
3.5.1 PRINCIPLE OF OPERATION:
A STATCOM is a controlled reactive-power source. It provides
the desired reactive-power generation and absorption entirely by
means of electronic processing of the voltage and current waveforms
in a voltage-source converter (VSC).
In Fig. 3.7 a STATCOM is seen as an adjustable voltage source
behind a reactance—meaning that capacitor banks and shunt
reactors are not needed for reactive-power generation and absorption,
thereby giving a STATCOM a compact design, or small footprint, as
well as low noise and low magnetic impact.
Fig 3.7 Functional model of a STATCOM
Vac 0
Coupling
Transformer
AC System
Iac
Idc
Vdc
Vout=kVdc
Voltage-Sourced
Converter
47
The exchange of reactive power between the converter and the
ac system can be controlled by varying the amplitude of the 3-phase
output voltage, Es, of the converter. That is, if the amplitude of the
output voltage is increased above that of the utility bus voltage, Et,
then a current flows through the reactance from the converter to the
ac system and the converter generates capacitive-reactive power for
the ac system. If the amplitude of the output voltage is decreased
below the utility bus voltage, then the current flows from the ac
system to the converter and the converter absorbs inductive-reactive
power from the ac system.
If the output voltage equals the ac system voltage, the reactive-
power exchange becomes zero, in which case the STATCOM is said to
be in a floating state. Adjusting the phase shift between the converter-
output voltage and the ac system voltage can similarly control real-
power exchange between the converter and the ac system. In other
words, the converter can supply real power to the ac system from its
dc energy storage if the converter-output voltage is made to lead the
ac-system voltage. On the other hand, it can absorb real power from
the ac system for the dc system if its voltage lags behind the ac-
system voltage.
3.5.2 V-I CHARACTERISTICS OF STATCOM:
A typical V-I characteristic of a STATCOM is depicted in Fig. 3.8.
As can be seen, the STATCOM can supply both the capacitive and the
inductive compensation and is able to independently control its
output current over the rated maximum capacitive or inductive range
48
irrespective of the amount of ac-system voltage. That is, the STATCOM
can provide full capacitive-reactive power at any system voltage—even
as low as 0.15 pu.
The characteristic of a STATCOM reveals another strength of
this technology: that it is capable of yielding the full output of
capacitive generation almost independently of the system voltage
(constant-current output at lower voltages).
3.5.3 MODELING OF STATCOM FOR POWER FLOW STUDIES:
Following on the discussion of the STATCOM operational
characteristics, it is reasonable to expect that for the purpose of
positive sequence power flow analysis the STATCOM will be well
represented by a synchronous voltage source with maximum and
1.0
0.75
0.50
0.25
Transient
Rating
Vt
ILmax IL ICmax IC Inductive Capacitive
Transient
Rating (t<1 s)
Fig 3.8 V-I Characteristics of the STATCOM
49
minimum voltage magnitude limits. The synchronous voltage source
represents the fundamental Fourier series component of the switched
voltage waveform at the AC converter terminal of the STATCOM [40-
41].
The bus at which the STATCOM is connected is represented as
a PVS bus, which may change to a PQ bus in the event of limits being
violated. In such a case, the generated or absorbed reactive power
would correspond to the violated limit. Unlike the SVC, the STATCOM
is represented as a voltage source for the full range of operation,
enabling a more robust voltage support mechanism. The STATCOM
equivalent circuit shown in Figure 3.9 is used to derive the
mathematical model of the controller for inclusion in power flow
The power flow equations for the STATCOM are derived below
from first principles and assuming the following voltage source
representation:
vrvrvrvr jVE sincos (3.26)
Based on the shunt connection shown in Figure 3.9, the following may
be written:
****
kvrvrvrvrvrvr VVYVIVS (3.27)
Fig 3.9 STATCOM Equivalent circuit
Bus k
Z VR
kkV
IVR
Ik
VRVRV
50
After performing some complex operations, the following active and
reactive power equations are obtained for the converter and bus k,
respectively:
kvrvrkvrvrkvrvrvrvr BGVVGVP sincos2 (3.28)
kvrvrkvrvrkvrvrvrvr BGVVBVQ cossin2 (3.29)
vrkvrvrkvrkvrvrkk BGVVGVP sincos2 (3.30a)
vrkvrvrkvrkvrvrkk BGVVBVQ cossin2 (3.30b)
Using these power equations, the linearized STATCOM model is
given below, where the voltage magnitude Vvr and phase angle vr are
taken to be the state variables:
m
m
vr
k
k
k
vr
vr
vr
vr
vr
k
k
vr
k
vr
vr
vr
vr
vr
vrk
k
vr
k
vr
vr
vr
k
vr
k
k
k
k
k
k
vr
vr
k
vr
k
k
k
k
k
k
vr
vr
k
k
V
V
V
V
VV
QQV
V
VV
PPV
V
PP
VV
QQV
V
VV
PPV
V
PP
Q
P
Q
P
(3.31)
3.6 UNIFIED POWER FLOW CONTROLLER (UPFC):
The UPFC is the most versatile FACTS controller with
capabilities of voltage regulation, series compensation, and phase
shifting. The UPFC is a member of the family of compensators and
power flow controllers. The latter utilize the synchronous voltage
source (SVS) concept to provide a unique comprehensive capability of
transmission system control [46]. The UPFC is able to control
simultaneously or selectively all the parameters affecting power flow
51
patterns in a transmission network, including voltage magnitudes and
phases, and real and reactive powers. These basic capabilities make
the UPFC the most powerful device in the present day transmission
and control systems.
3.6.1 BASIC OPERATING PRINCIPLES OF UPFC:
As illustrated in Fig 3.10, the UPFC is a generalized SVS
represented at the fundamental frequency by controllable voltage
phasor of magnitude Vpq and angle injected in series with the
transmission line. Note that the angle ρ can be controlled over the full
range from 0 to 2π. For the system shown in Fig 3.10, the SVS
exchanges both real and reactive power with the transmission system.
Fig 3.10 Representation of UPFC in a two-machine power system
Ppq
Qp
q
Vp
q P
I VX
X
VSeff=VS+Vp
q
VR VS
Vpq
VX
VSeff VS
VR
52
In the UPFC, the real power supplied to or absorbed from the
system is provided by one of the end buses to which it is connected.
This meets the objective of the UPFC to control power flow rather than
increasing the generation capacity of the system.
As shown in Fig 3.11, the UPFC consists of two voltage-sourced
converters, one in series and one in shunt, both using Gate Turn-Off
(GTO) thyristor valves and operated from a common dc storage
capacitor. This configuration facilitates free flow of real power between
the ac terminals of the two converters in either direction while
enabling each converter to independently generate or absorb reactive
power at its own ac terminal.
Series
Transformer
Fig 3.11 UPFC Implemented by two back-to-back voltage source converters
ac ac
Vpq V V+Vpq i
Converter-2
Supply Transformer
Transmission Line
Z
ref
Vdc
Parameter
Settings
Measured
Variables
Qref
Vref
Control
Vpq
V V+Vpq
σref
Converter-1
53
The series converter, referred to as Converter 2, injects a voltage
with controllable magnitude Vpq and phase ρ in series with the line
via an insertion transformer, thereby providing the main function of
the UPFC. This injected voltage phasor acts as a synchronous ac
voltage source that provides real and reactive power exchange between
the line and the ac systems.
The reactive power exchanged at the terminal of series insertion
transformer is generated internally while the real power exchanged is
converted into dc power and appears on the dc link as a positive or
negative real power demand. By contrast, the shunt converter,
referred to as Converter 1, supplies or absorbs the real power
demanded by Converter 2 on the common dc link and supports the
real power exchange resulting from the series voltage injection. It
converts the dc power demand of Converter 2 into ac and couples it to
the transmission line via a shunt connected transformer.
Converter 1 can also generate or absorb reactive power in
addition to catering to the real power needs of Converter 2;
consequently, it provides independent shunt reactive compensation
for the line. It is to be noted that the reactive power exchanged is
generated locally and hence, does not have to be transmitted by the
line. On the other hand, there exists a closed path for the real power
exchanged by the series voltage that is injected through the converters
back to the line. Thus, there can be a reactive power exchange
between Converter 1 and the line by controlled or unity power factor
54
operation. This exchange is independent of the reactive power
exchanged by Converter 2.
3.6.2 TRANSMISSION CONTROL CAPABILITIES:
The UPFC can fulfill the functions of reactive shunt
compensation, series compensation, and phase angle regulation.
Hence it can meet multiple control objectives by injecting a voltage
phasor with appropriate amplitude and phase angle to the terminal
voltage. The basic UPFC power flow control functions are
Voltage regulation with continuously variable in-phase/out of
phase voltage injection;
Line-impedance compensation or series reactive compensation
by the series injected voltage. This injected voltage phasor can
be kept constant over a broad range of the line current while the
voltage across the compensating impedance varies with the line
current;
Phase-shifting control that is achieved by injecting a voltage
phasor with any particular angular relation with the terminal
voltage. In other words the desired phase shift can be obtained
without any change in the voltage magnitude;
Simultaneous multifunction power flow control by an adequate
adjustment of the terminal voltage, series impedance
compensation, and phase shifting. This functional capability is
unique to the UPFC; no other single conventional equipment
has similar multifunction capability.
55
3.6.3 MODELING OF UPFC FOR POWER FLOW STUDIES:
It follows from that discussion that an equivalent circuit
consisting of two coordinated synchronous voltage sources should
represent the UPFC adequately for the purpose of fundamental
frequency steady-state analysis. Such an equivalent circuit [47,48] is
shown in Figure 3.12. The synchronous voltage sources represent the
fundamental Fourier series component of the switched voltage
waveforms at the AC converter terminals of the UPFC [40, 41].
The UPFC voltage sources are:
vrvrvrvr jVE sincos (3.32)
crcrcrcr jVE sincos (3.33)
Where Vvr and vr are the controllable magnitude (Vvr min Vvr Vvr
max) and phase angle (0 vr 2) of the voltage source representing
the shunt converter. The magnitude Vcr and phase angle cr of the
voltage source representing the series converter are controlled
between limits (Vcr minVcr Vcr max) and (0 cr 2), respectively.
Fig 3.12 UPFC Equivalent circuit
mmV
Im
Bus m Bus k
VRVRV
IVR
Z VR
Z CR
kkV
ICR
Ik
CRCRV
+
+
Re( **
mCRVRVR IVIV )=0
56
The phase angle of the series-injected voltage determines the
mode of power flow control. If cr is in phase with the nodal voltage
angle θk, the UPFC regulates the terminal voltage. If cr is in
quadrature with respect to θk, it controls active power flow, acting as
a phase shifter. If cr is in quadrature with the line current angle then
it controls active power flow, acting as a variable series compensator.
At any other value of cr, the UPFC operates as a combination of
voltage regulator, variable series compensator, and phase shifter. The
magnitude of the series-injected voltage determines the amount of
power flow to be controlled. Based on the equivalent circuit shown in
Figure 3.12 and Equations (3.32) and (3.33), the active and reactive
power equations are
At bus k:
vrkvrvrkvrvrk
crkkmcrkkmcrk
BGVV
BGVV
mkkmB
mkkmG
mV
kV
kkG
kV
kP
sincos
sincos
sincos2
(3.34a)
vrkvrvrkvrvrk
crkkmcrkkmcrk
BGVV
BGVV
mkkmB
mkkmG
mV
kV
kkB
kV
kQ
cossin
cossin
cossin2
(3.34b)
At bus ‗m‘:
)sin()cos(
)sin()cos(2
crmmmcrmmmcrm BGVV
kmmkB
kmmkG
kV
mV
mmG
mV
mP
(3.35)
)cos()sin(
)cos()sin(2
crmmmcrmmmcrm BGVV
kmmkB
kmmkG
kV
mV
mmB
mV
mQ
(3.36)
57
At Series Converter:
)sin()cos(
)sin()cos(2
mcrmmmcrmmmcr BGVV
kcrkmB
kcrkmG
kV
crV
mmG
crV
crP
(3.37)
)cos()sin(
)cos()sin(2
mcrmmmcrmmmcr BGVV
kcrkmB
kcrkmG
kV
crV
mmB
crV
crQ
(3.38)
At Shunt Converter:
)sin()cos(2kvrvr
Bkvrvr
Gk
Vvr
Vvr
Gvr
Vvr
P (3.39)
)cos()sin(2kvrvr
Bkvrvr
Gk
Vvr
Vvr
Bvr
Vvr
Q (3.40)
Assuming loss-less converter valves, the active power supplied to the
shunt converter, Pvr, equals the active power demanded by the series
converter, Pcr; that is,
0vr
Pcr
P (3.41)
Furthermore, if the coupling transformers are assumed to contain no
resistance then the active power at bus k matches the active power at
bus m. Accordingly,
0m
Pk
Pvr
Pcr
P (3.42)
The UPFC power equations, in linearized form, are combined
with those of the AC network. For the case when the UPFC controls
the following parameters: (1) voltage magnitude at the shunt converter
terminal (bus k), (2) active power flow from bus m to bus k, and (3)
reactive power injected at bus m, and taking bus m to be a PQ bus,
the linearized system of equations is given by equation 3.52, where
Pbb is the power mismatch given by Equation (3.58)
58
If voltage control at bus k is deactivated, the third column of
Equation (5.60) is replaced by partial derivatives of the bus and UPFC
mismatch powers with respect to the bus voltage magnitude Vk.
Moreover, the voltage magnitude increment of the shunt source,
Vvr/Vvr is replaced by the voltage magnitude increment at bus k,
Vk/Vk. If both buses, k and m, are PQ the linearised system of
equations is given by equation 3.53
vr
cr
cr
cr
m
m
k
k
m
k
vr
bbcr
cr
bb
cr
bbm
m
bbk
k
bb
m
bb
k
bb
vr
mkcr
cr
mk
cr
mkm
m
mkk
k
mk
m
mk
k
mk
vr
mkcr
cr
mk
cr
mkm
m
mkk
k
mk
m
mk
k
mk
vr
mcr
cr
m
cr
mm
m
mk
k
m
m
m
k
m
vr
kcr
cr
k
cr
km
m
kk
k
k
m
k
k
k
vr
mcr
cr
m
cr
mm
m
mk
k
m
m
m
k
m
vr
kcr
cr
k
cr
km
m
kk
k
k
m
k
k
k
bb
mk
mk
m
k
m
k
V
V
V
V
V
V
PV
V
PPV
V
PV
V
PPP
QV
V
QQV
V
QV
V
QQQ
PV
V
PPV
V
PV
V
PPP
QV
V
QQV
V
QV
V
QQQ
QV
V
QQV
V
QV
V
QQQ
PV
V
PPV
V
PV
V
PPP
PV
V
PPV
V
PV
V
PPP
P
Q
P
Q
Q
P
P
(3.43)
vr
cr
cr
cr
m
m
vr
vr
m
k
vr
bbcr
cr
bb
cr
bbm
m
bbvr
vr
bb
m
bb
k
bb
vr
mkcr
cr
mk
cr
mkm
m
mkvr
vr
mk
m
mk
k
mk
vr
mkcr
cr
mk
cr
mkm
m
mkvr
vr
mk
m
mk
k
mk
vr
mcr
cr
m
cr
mm
m
mvr
vr
m
m
m
k
m
vr
kcr
cr
k
cr
km
m
kvr
vr
k
m
k
k
k
vr
mcr
cr
m
cr
mm
m
mvr
vr
m
m
m
k
m
vr
kcr
cr
k
cr
km
m
kvr
vr
k
m
k
k
k
bb
mk
mk
m
k
m
k
V
V
V
V
V
V
PV
V
PPV
V
PV
V
PPP
QV
V
QQV
V
QV
V
QQQ
PV
V
PPV
V
PV
V
PPP
QV
V
QQV
V
QV
V
QQQ
QV
V
QQV
V
QV
V
QQQ
PV
V
PPV
V
PV
V
PPP
PV
V
PPV
V
PV
V
PPP
P
Q
P
Q
Q
P
P
(3.44)
59
Different FACTS devices modeling is discussed in this chapter.
In the next chapter power flow studies with FACTS devices for well
conditioned system is presented.
