Helwan University
From the SelectedWorks of Omar H. Abdalla
Winter February 15, 2009
Steady State Analysis of Unified Power Flow
Controllers
Omar H. Abdalla
Mohamed A. E. Ghazy
Lotfy M. Lotfy
Nermeen A. M. Hassan
Available at: http://works.bepress.com/omar/9/
1
Steady State Analysis of Unified Power Flow
Controllers
O. H. Abdalla(1), Senior Member, IEEE, M. A. E. Ghazi(2), L. M. Lotfy(2), and N. A. M. Hasan(2)
(1) Oman Electricity Transmission Company, ohabdalla@ieee.org (2) University of Helwan, Egypt.
Abstract—The paper presents a tutorial review of the basic
operation, control functions and steady state performance of a
Unified Power Flow Controller (UPFC). A typical circuit
arrangement of a UPFC is given and principles of controlling
active and reactive powers are described. The main functions of
UPFC are analyzed; including voltage regulation, series reactive
compensation, phase compensation, and combined actions. A
simplified two-bus power system is considered to demonstrate the
main effects of the UPFC. Studies and results are presented to
show the wide range capabilities of the UPFC in controlling
transition active and reactive powers simultaneously and/or
independently.
higher the harmonic order present which is not required here,
Therefore, the UPFC with GTO is preferable than UPFC with
IGBT. The shunt converter and series converters are
connected to the transmission line through step down
transformers. They are operated from a common DC link
provided by a DC storage capacitor which has a capacitance
value specified for better dynamic performance but with cost
consideration. These back to back converters can
independently generate (or absorb) reactive power at its own
AC output terminal [1-3].
VS
Index Terms—Unified Power Flow Controller, Transmission
Systems, Control of Active and Reactive Powers.
IS
T
IS
I. INTRODUCTION
HE Unified Power Flow Controller (UPFC) concept was
proposed by Gyugyi in 1991 [1]. The UPFC is used for
the real time control and dynamic compensation for AC
transmission systems, providing more flexibility in power
system today [2-4]. Moreover, the UPFC has the unique
capability to control simultaneously and/or independently, all
the parameters affecting power flow in the transmission line
which are voltage, impedance, and phase angle [5, 6]. Also it
can independently control both the real and reactive power
flows in the line under transmission system constraints [7-9].
This paper demonstrates the UPFC main configuration with
the detailed operation for its series and shunt branches. Also
each branch control functions and the effect of the injected
voltage in the active and reactive power control are discussed
in more details.
II. CIRCUIT ARRANGEMENT
The UPFC circuit as illustrated in Fig. 1 consists of a shunt
and a series branches. Each branch is considered as a voltage
source converter using semiconductor devices of fully
controlled type, such as the Insulated-Gate Bipolar Transistors
(IGBT) and the Gate Turn-Off (GTO) thyristors. The GTO is
a more advanced version of the conventional thyristor, where
the GTO unlike Silicon-Controlled Rectifier (SCR), can be
turned off by applying negative gate signal. Also it has fast
turn off, lower cost, weight, volume and noise. The IGBT is a
faster switching device than the GTO which is limited to the
order of 1 kHz. But the higher the switching frequency the
Shunt
Series
Fig. 1. UPFC circuit arrangement.
III. OPERATION OF UNIFIED POWER FLOW CONTROLLERS
The shunt converter basic function is to provide the real
power demanded by the series converter from the AC power
system. It can also, if desired, generate or absorb reactive
power at the UPFC connected bus, which is independent of
the active power transfer to (or from) the DC terminal.
Therefore it can provide reactive power compensation for the
transmission line and thus provide indirect voltage regulation
at the input terminal of the UPFC [3].
The main function of the UPFC is provided by the series
converter by injected an AC voltage in series with the line
with controllable magnitude VSE (0 ≤ VSE ≤ VSEmax) and phase
angle α (0 ≤ α ≤ 360o), at the power frequency, through a
series connected transformer. The converter output voltage
injected in series with the line can be used for direct voltage
control, series compensation, phase shifter and their
combinations which will be discussed in details in the next
section. The real power exchanged at AC terminal of the
insertion transformer is converted by the series converter into
DC power which appears at the DC link as positive real power
2
demanded by the shunt converter. The reactive power
exchange at the AC terminal is generated internally by the
inverter.
IV. UPFC FUNCTIONS
Fig. 4 (a). With no series compensation, the function of the
shunt branch is to regulate the line voltage by injecting a shunt
reactive current into the transmission line. The compensation
type inductive or capacitive is depending on whether the shunt
voltage source VSH is higher or lower than the sending end
voltage VS as shown in Fig. 4 (b).
The operation of the UPFC from the standpoint of
conventional power transmission is based on reactive shunt
compensation, series compensation, and phase shifting [1-3].
The UPFC can fulfill these functions and thereby meet
multiple control objectives by adding the injected voltage VSE,
with appropriate amplitude and phase angle. The basic UPFC
XL
I
ISH
XSH
VR
VSH
XSE
I
VSE
XL
ISH
VSH
ISH
XSH
VS
VS
VR
VS
ISH
VSH
VSH
UPFC
VSH < VS
Inductive compensation
Fig. 4. Shunt compensation.
Fig. 2. UPFC schematic diagram.
power flow controller functions are illustrated in Fig. 2.
A. Uncompensated simple power system
A simple two machine system connected through a
transmission line whose reactance is xL with its voltages
phasors shown in Fig. 3 (a) and (b). The equation of power
transfer is given as follows:
PS =
V SV R
sin δ
XL
C. Series converter operation
The series branch provides the main function of the UPFC
by controlling the three parameters affect the power flow in a
transmission line simultaneously and independently. It is
represented by a series AC variable voltage source with
controllable magnitude VSE and phase angle α measured from
the reference voltage VR and connected to the sending end by
a reactance XSE as illustrated in Fig. 5.
(1)
I
XSE
VSE∟α
XL
V
V
VS
I
δ
(a)
VSH > VS
Capacitive compensation
VS1
VS
VR
(
Fig. 3. Uncompensated system.
(a) Circuit (b) Voltage phasors
B. Shunt converter operation
The shunt branch is represented as a variable voltage
source VSH with variable magnitude and phase angle and
connected to the sending end by a reactance XSH as shown in
Fig. 5. Series branch schematic diagram.
V S ∠ δ = − V SE ∠ (α
)+
jI ( X SE + X L ) + V R ∠ 0
(2)
3
I=
V S ∠ δ + V SE ∠ (α
jX
) − VR∠0
Therefore,
VS1(Inductive)
V . VR
V . V SE
P= S
Sin (δ ) + R
Sin (α )
X
X
Where,
(3)
VS1
VSE2
X = XL+XSE
The series converter has the following four operation modes:
VS1
I
(Capacitive)
• Voltage regulation
(a)
It is considered as a terminal voltage regulator similar to that
obtainable with a transformer tap-changer having infinitely
small steps [1, 2] and [9]. The phasor diagram is shown in Fig.
6 (a) and (b). When the series voltage VSE is injected in-phase
or out-of-phase (substituting angle α = ± δ in Equation (3)),
the voltage VS1 at bus S1 in Fig. 5 is increased (or decreased).
Fig. 6 (c) illustrates the effect of the injected series voltage on
the transmitted power.
• Series reactive compensation
It is used to control the current or power flow by regulating
the transmission line’s effective reactance by connecting the
series voltage VSE in quadrature with the line current as shown
in Fig. 7 (b), where the series voltage VSE may be replaced by
a reactance XCSE (0 ≤ XCSE ≤ X).
Therefore, Equation (1) can be written as follow:
V S .V R
P=
sin δ
( X ± X CSE )
VSE1
(a)
VS1
VS1
Fig. 7. Series reactive compensation
(a) Phasor diagram
(b) P- δ curves
(4)
Note: the equivalent reactance (X + XCSE) means inductive
compensation and the equivalent reactance (X – XCSE) means
capacitive compensation.
VS
(b)
(b)
•
Phase angle compensation
VS
This is used for regulating the phase angle of the line
voltage by a series connected compensating voltage VSE, in
quadrature with respect to the voltage, keeping the voltage
amplitude of the sending-end nearly constant as shown in
Figure 8.
VSE1
P=
V S .V R
. sin (δ ± θ )
X
(5)
Where, θ is the resultant phase shifting angle.
•
Combined compensation:
It can be achieved by simultaneous voltage regulation, series
compensation, and phase shifting, as shown at Fig. 9.
Where,
VT = VSE1 + VSE2 + VSE3
(c)
Fig. 6. Voltage regulation
(a) VS1= VS+ VSE
(b) VS1= VS- VSE
(c) P- δ curves when VSE varied
4
and the reactive powers Qs and QR against the transmitted
power P for (0 ≤ δ ≤ 90o), respectively.
Where;
VS+
+θ
V S .V R
(6)
. sin δ
X
V 2 V .V
(7)
Q S = S − S R . cos δ
X
X
⎛ V .V
V2 ⎞
(8)
Q R = − ⎜⎜ S R . cos δ − R ⎟⎟
X
X
⎝
⎠
Where, the negative sign for the opposite direction shown in
Fig. 8 (a), assuming that VS = VR= 1 pu and X = 1 pu.
P =
VS
-θ
VSE3
VS(a)
I
+ VX QS
p
QR
VS
VR
(a)
VS
VX
(b)
δ
Fig. 8. Phase angle compensation.
(a) Phasor diagram
(b) P- δ curves
(b)
VR
Fig. 10. (a) Simple two machine system
VS
VSE1
VT
I
VST
VSE2
Qs,QR
P
VSE3
Fig. 9. Combined compensation phasor diagram.
V. PRINCIPLES OF REAL AND REACTIVE POWER CONTROL
A. Basic two-bus system
The basic power system of Fig. 10 with the well known
transmission characteristics is introduced to provide a
guideline to establish the capability of the UPFC to control the
transmitted real power P and the reactive power demands, Qs
and Qr at the sending end and receiving end of the line,
respectively.
(a)
A simple two bus system with sending end voltage VS,
receiving-end voltage VR, line impedance X (assumed, for
simplicity inductive) and the phasor diagram with power angle
δ are shown in Fig. 10 (a) and (b).
Fig. 11 (a) and (b) show the relation of the transmitted
power P, and the reactive power QS and QR against angle δ,
(b)
(b) Voltage phasors
5
Fig. 11. (a) Angle δ versus P, QS and Qr
(d) P versus QS and Qr
B. Two-bus system with UPFC
The above system is expanded to include the UPFC, which
is represented by a controllable voltage source in series with
the line as shown in Fig. 12. The series branch provides the
main function of the UPFC. The phasor VSE has a magnitude
VSE (0 ≤ VSE ≤ VSEmax) and phase angle α measured from the
reference voltage VR (where α = δ - ρ). The phase angle ρ
(0≤ρ≤ 360o) is measured from the given position of phasor VS,
as illustrated in Fig.12 (a) and (b).
VSE∟α
I
+
VX -
VS
Fig. 12 shows that the transmission line VS + VSE as the
effective sending end voltage. Thus it is clear that the UPFC
affects the voltage magnitude and phase angle across the
transmission line. Therefore, by varying the magnitude and
angle of VSE, the transmitted real power as well as the reactive
power demand of the line can be controlled at any given
transmission angle between the sending-end and receiving-end
voltages.
VI. EFFECT OF INJECTED VOLTAGE ON P AND Q CONTROL
QR
QS
The UPFC shunt inverter is assumed to be operated at unity
power factor, as its reactive compensation capability of the
UPFC not utilized. Its main function is to transfer the real
power demand of the series inverter to the sending-end
generator. With these assumptions, the series voltage source,
together with the real power coupling to the sending end
generator is an accurate representation of the basic UPFC.
VR
To illustrate the effect of the series injected voltage of the
UPFC, the reactive power at sending and receiving ends QS,
and Qr are plotted separately against the transmitted power P
as a function of the power angle δ (0 ≤δ≤90o). The magnitude
of VSE = 0.5 pu and phase angle ρ which provides the
maximum transmitted power at:
dPR/dρ = 0, (ρ = ρP=Pmax., ρ= -tan-1 (cot δ))
(a)
The results are shown in Fig. 13. Also, the P-Q curve without
UPFC is included in the figure as a reference. Equations (6) to
(8) can be modified to include the UPFC as follow:
ρ
VSE
VS
P =
VS . VR
V . V SE
Sin ( δ ) + R
Sin ( δ − ρ )
X
X
QS =
V S2
V V
V V
+ S SE cos( ρ ) − S R cos (δ
X
X
X
VX
δ
(b)
VR
Fig. 12. Two bus system with UPFC.
(a) Schematic diagram
(b) Phasor diagram
In order to represent the UPFC properly, the series voltage
source is stipulated to generate only the reactive power QSE it
exchanges with the line. Thus the real power PSE exchanged
with the transmission line is assumed to be transferred to the
sending-end generators if a perfect coupling for real power
flow between it and the sending-end generator excited. The dc
link between the two converters establishes a bi-directional
coupling for real power flow between the injected series
voltage source and the sending-end bus.
)
(9)
(10)
⎛V V
V V
V2 ⎞
QR = − ⎜⎜ S R Cos (δ ) + R SE Cos (δ − ρ ) − R ⎟⎟ (11)
X
X ⎠
⎝ X
It can be observed from Fig. 13 that when the power angle
is zero (δ=0). With VSE = 0 (without UPFC), P, QS, and QR are
all zero. But when the UPFC is operated with VSE = 0.5, pu it
is possible to provide 0.5 pu power flow, without any reactive
power demand on either the sending-end or the receiving-end.
Also, at the same real power flow, the sending and receiving
end reactive power is lower.
For illustrating the wide boundaries of P and Q due to the
effect of the injected voltage magnitude VSE= 0.5 pu and the
variations in the angle ρ with full revolution (0≤ρ≤360°), the
6
same plots in Fig. 13 is repeated but with definite values of δ
(δ=0, 30°, 60º), as shown in Fig. 14.
In contrast, the control region boundary for P and QR in the
{QR, P} plane remains a circle at all transmission angles.
1.5
VII. CONCLUSIONS
s e n d in g re a c tiv e p o w e r (Q s )
Vpq=0
Vpq=0.5,Pmax.
The Unified Power Flow Controller (UPFC) can provide
simultaneous, real-time control of all or any combination of
the basic power system parameters (voltage, line impedance
and phase angle) which affect the power flow in transmission
networks.
1
0.5
0
0
0.5
1
1.5
Transmitted Real Power (P)
1.5
R e c ie v in g re a c tiv e p o w e r (Q r)
Vpq=0
Vpq=0.5, P=max.
1
0.5
0
0
0.5
1
1.5
Transmitted Real power (P)
The series converter provides the main operation of the
UPFC, thus the UPFC is represented by a controllable voltage
source in series with the line. The shunt converter is assumed
to be operated at unity power factor, when its reactive
compensation capability of the UPFC not utilized. In this case
the main function of the shunt converter is to provide the real
power demand of the series converter to the sending-end
generator.
The UPFC provides flexibility for ac power transmission
control that has been illustrated by representing the steadystate operation functions of the UPFC. The shunt converter
can regulate the bus voltage in which the UPFC is inserted,
and the series converter has the ability to provide voltage
regulation, series reactive compensation, phase angle
compensation and also combination of them. Therefore by
controlling the magnitude and phase angle of the series
voltage VSE, the power flows in the transmission line and
hence the magnitude of loading can be controlled.
The UPFC can be viewed as a generalized real and reactive
power flow controller that is able to maintain a prescribed P
and Q at a given point on the transmission line. Moreover, a
wide range of P and Q control is achievable with the UPFC.
Fig. 13. Reactive power at sending and receiving ends versus transmitted
real power with and without UPFC.
VIII. REFERENCES
[1]
In Fig. 14 (a), the circles in the {QS, P} and {QR, P} planes
define all P and QS and, respectively, P and QR values
achievable with the UPFC of a given rating. These circles
illustrate the wide range operational capability of the UPFC.
The UPFC with voltage rating of 0.5 pu is able to establish
0.5 pu power flow, in either direction, without demanding any
reactive power generator at either the sending-end or the
receiving-end. The UPFC can force the generator at one end
to supply reactive power for the generator at the other end.
In general at any given transmission angle δ, the transmitted
real power P, and the reactive power demands at the
transmission line ends, QS and QR, can be controlled freely by
the UPFC within the boundaries obtained in the {QS, P} and
{QR, P} planes by rotating the injected voltage phasor VSE
with its maximum magnitude a full revolution (0≤ ρ ≤ 360°).
Wherever the transmission angle δ is increased, the control
region in the {QS, P} plane in Fig. 14 (b) at δ=30° becomes an
ellipse. It becomes narrower at δ = 60° until it degenerates
into a straight line at δ = 90° as shown in Fig. 14 (c) and (d),
respectively.
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
L. Gyugyi, "A unified power flow control concept for flexible AC
transmission systems," International Conference on AC and DC Power
Transmission, 17-20 Sept. 1991
L. Gyugyi, T. R. Rjetmu, A. Edris, C. D. Schauder, D. R. Torgoan, and
S. L. Williams, “The unified power flow controller: A new approach
transmission control,” IEEE Trans. Power Delivery, Vol. 10 No. 2,
1995.
I. Papic, P. Zunko, D. Povh, and M. Weinhold, "Basic control of
unified power flow controllers," IEEE Trans. Power Systems,” Vol. 11,
No. 4, Nov. 1997.
E. Wirth, and A. Kara, “Innovative power flow management and
voltage control,” Power Engineering Journal, vol. 14, No. 3, June 2000.
K. R. Padiyar, and A. M. Kulkarni, “Control design and simulation of
unified power flow controller,” IEEE Trans. Power Delivery, Vol. 13
No. 4, Oct. 1998.
Z. Huaung, Y. Ni, C. M. Shen, F. F. Wu, S. Chen, and B. Zhag,
“Application of unified power flow controller in interconnected power
systems – Modelling, interface, control strategy, and case study,” IEEE
Trans. Power Delivery, Vol. 15 No. 2, April 2000.
C. D. Schaider, L. Gyugyi, M. R. Lund, D. M. Hamai, and A. Edris,
“Operation of the unified power flow controller (UPFC) under practical
constraints,” IEEE Trans. Power Delivery, Vol. 13 No. 4, Oct. 1998.
J. Y. Liu. Y. H. Sing, and P. A. Mehta, “Strategies for handling UPFC
constraints in steady-state power flow and voltage control,” IEEE
Trans. Power Delivery, Vol. 15 No. 2, April 2000.
S. An, J. Condern, and W. Gedra, “ An ideal transformer UPFC model,
OPF first-order sensitivities, and application to screening for optimal
UPFC locations,” IEEE Trans. Power Systems,” Vol. 22, No. 1, Feb.
2007.
7
(a) δ = 0o , VSE=0.5 pu
ρ
ρ
(b) δ = 30o, VSE=0.5 pu
ρ
ρ
(c) δ = 60o, VSE=0.5 pu
ρ
ρ
(d) δ = 90o, VSE=0.5
ρ
ρ
Fig. 14. Sending and receiving reactive power against the active power