1348 IEEE Transactions on Power Delivery, Vol. 13, No.

4, October 1998

na Power Flow
ntroller
K.R. Padiyar, Senior Member A.M. Kulkarni
Department of Electrical Engineering
Indian Institute of Science
Bangalore, India 560012

A b s t r a c t - T h e UPFC as a solzd state controller whzch power with the transmission line. However the UPFC as a

-
can be used to control actave and reactzve power flows an a whole cannot supply or absorb real power in steady state
transmzsszon 1zne.In thzs paper we propose a control strat- (except for the power drawn to compensate for the losses)
egy f o r UPFC an whzch we control real power flow through unless it has a power source at its DC terminals. Thus the
the lane, whzle regulatzng magnztvdes of the voltages at ats shunt branch is required to compensate (from the system)
two ports. We deszgn a controller for thzs purpose whzch
uses only local measurements. The control strategy 2s eval-
uated uszng dagztal samulataon for a case study. Transmission line

&
y n t Transformer Transformer

The Unified Power Flow Controller (UPFC) [l,2] is the

most versatile of the FACTS controllers envisaged so far.
It can not only perform the functions of the STATCON, control
TCSC, and the phase angle regulator but also provides
additional flexibility by combining some of the functions Figure 1: UPFC
of the above controllers. The main function of the UPFC
is to control the flow of real and reactive power by injec- for any real power drawn/ supplied by the series branch
tion of a voltage in series with the transmission line. Both and the losses. If the power balance is not maintained,
the magnitude and the phase angle of the voltage can be the capacitor cannot remain at a constant voltage.
varied independently. Real and reactive power flow con- The relationship can be expressed mathematically as (see
trol can allow for power flow in prescribed routes, loading Fig. 2):
of transmission lines closer to their thermal limits and can -- --
be utilized for improving transient and small signal sta- q V " 1 IT + vu2 I ; ) - Pi,,, = 0
bility of the power system. The schematic of the UPFC
is shown in Fig.1. The UPFC consists of 2 branches. The In addition to maintaining the real power balance, the
series branch consists of a voltage source converter which - r . _ . _ . . _ _ _ _ _ _ . _ . . . . . ~ ~-
~~~~.......-----.~.
___
injects a voltage in series through a transformer. Since
the series branch of the UPFC can inject a voltage with
variable magnitude and phase angle it can exchange real

PE-I 72-PWRD-0-12-1997 A paper recommended and approved by

the IEEE Transmission and Distribution Committee of the IEEE Power
Engineering Society for publication in the IEEE Transactions on Power
Delivery. Manuscript submitted June 5, 1997, made available for
printing December 12, 1997.

Figure 2: UPFC as a two port device

shunt branch can independently exchange reactive power

with the system.
The main advantage of the power electronics based
FACTS controllers over mechanical controllers is their
speed. Therefore the capabilities of the UPFC need to

0885-8977/98/$10.00 0 1997 IEEE

 1349
be exploited not only for steady state load flow control bility. In addition, reactive power can be controlled to
but also to improve stability. However it is not obvious as prevent dynamic over/undervoltages. In fact, instead of
to how to use the series voltage and shunt current (sub- having closed loop control of reactive power using the rea\
ject to the power balance constraint) for UPFC control. voltage, the voltage a t port 2 (see Fig. 2) of the UPFC
It is in this context that suitable control strategies and can be controlled readily by calculating the required real
controller design to acheive the same is of importance. voltage to be injected. We can control reactive power in-
A control strategy, in general, should preferably have the directly by changing the voltage reference for port 2.
following attributes :
1. Steady state objectives (ie. real and reactive power
flows) should be readily achievable by setting the refer- 2.2 Shunt Current Control
ences of the controllers. It is well known that shunt reactive power injection can be
2. Dynamic and transient stability improvement by ap- used to control bus voltage. Thus the shunt current is split
propriate modulation of the controller references. into real (in phase with bus voltage) and reactive current
While the application of UPFC for load flow control and components.The reference value for the real current is set
in stability improvement has been discussed in [3,4], a so that the capacitor voltage is regulated (which implies
detailed discussion on control strategies backed by perfor- power balance). The reactive current reference is set by a
mance evaluation is not yet reported in literature. In this bus voltage magnitude regulator (for port 1 of the UPFC).
paper we propose a control strategy for UPFC in which we The voltage reference of the voltage regulator itself can be
control real power flow through the line, while regulating varied (slowly) so as to meet steady state reactive power
magnitudes of the voltages a t its two ports. We design a requirements.
controller for this purpose which uses only local measure-
ments. The control strategy is evaluated using transient
digital simulation for a case study. 3 Controller Design
To simplify the design procedure we carry out the design
2 Control Strategy for the series and shunt branches separately. In each case,
the external system is represented by a simple equivalent.
The UPFC allows us three degrees of freedom The design has to be validated when the various subsys-
1. Magnitude and angle of series voltage tems are integrated.
2. Shunt reactive current. The design tasks are listed below:
The real and reactive power flow in the line can be con- 1. Series injected voltage control
trolled independently using the series injected voltage (see a. Power Flow control using reactive voltage.
[l]for an elaborate exposition). b. UPFC port 2 voltage control using real voltage.
It should be noted that the UPFC uses Voltage Source 2. Shunt converter voltage control
Converters (VSCs) for series voltage injection as well as a. Closed loop current (real and reactive) control.
shunt current control. The injection of series voltage can b. UPFC port I voltage control using reactive current.
respond almost instantaneously to an order. The shunt c. Capacitor voltage regulation using real current.
current, however, is controlled indirectly by varying the The basic design considerations are illustrated using sim-
shunt converter voltage (closed loop control of shunt cur- plified system models. The performance of all the con-
rent is required). trollers is subsequently evaluated using detailed simula-
tions for a case study.
2.1 Series injected voltage control
To achieve real and reactive power flow control we need 4 Series injected voltage controller
to inject series voltage of the appropriate magnitude and
angle. The injected voltage can be split into two compo- 4.1 Power flow control
nents which are in phase (real voltage) and in quadra-
ture (reactive voltage) with the line current. It is to be In this section we consider the control of real power using
noted that the line current measurement is locally avail- reactive voltage (real voltage injection is assumed to be
able. The real power can be effectively controlled by vary- zero). We carry out the analysis on the simplified system
ing the series reactance of the line. Reactive voltage in- shown below in Fig. 3. The differential equations for the
jection is like series insertion of reactance except that the current a t port 2 in the D-Q (synchronously rotating a t
injected voltage can be independent of the transmission system frequency U,) frame of reference [5] are given by:
line current. Thus we control active power flow using the
reactive voltage. It should be kept in mind that real and
reactive power references are obtained from (steady state)
power flow requirements. The real power reference can
also be modulated to improve damping and transient sta-
1350
DU2

Figure 3: Simplified system

where,

and, W b is the base frequency. The subscripts 'D' and 'Q' -180
denote the variables in the D-Q frame. (w,", w;), (WE',
w;') iop 10' 1O2 1o3
Freqwncy (radlsec)
10' io5

and (wE2]w;;") are the components of the voltages at the

receiving end bus, UPFC port 1 a n d p o K 2 respectively.
We assume in this section that V s = V u 1 = constant. Figure 4: Bode Plots of (a)without auxiliary feed-
Power at receiving bus PR is approximately equal to that back (b)with auxiliary feedback
at port 2 ( P u z )of the UPFC in the steady state; therefore
we control the power at port 2 since the feedback signal
is readily available. (w) with the auxiliary feedback has a vastly im-
proved phase margin. This allows larger gains to be used
pu2 = w;2;gr + vu2jser
Q Q (6) in the output feedback controller with a consequent speed-
ing up of the response.
Injected reactive and real voltages are written in terms of While the plots are shown for one operating point: egt =
injected voltages in the D-Q frame (eg', e$?') as, 0, the improvement is there for positive and negative eg;
egr = eDs e r cos(4') - eyrsin(ba)
(7)
also.

e y r = egrsin(4i) + eyrcos(bi) (8)

where 4i= tan-'$

sev
I
Q PU2
For the design of the control of power flow by reactive

function (w)
voltage using output feedback, we examine the transfer
of the linearized system at various op-
erating points. U(.) is the reactive voltage order obtained
Figure 5: Real Power Controller

from the output feedback controller. Since the injection of

voltage can respond almost instantaneously to an order, 4.2 Port 2 voltage control
we can assume e:",d' =..e: The voltage at port 2 of the UPFC is algebraically related
In Fig. 4 , we show the Bode plot of the tranfer function to that at port 1 and the reactive voltage injected (eg') for
for quiescent voltage injection =O. The main concern in power flow control. (For simplicity the series transformer
the design of an output feedback controller is the stability reactance is clubbed with the line impedance). The volt-
of the oscillatory mode (in the D-Q frame of reference: age relation is given by:
nearabout w, r a d s l s ) associated with the series induc-
tance.
To make the system more amenable to feedback control
we use an auxilliary feedback using the signal,
sTw
-k@(S)
+ sTw
~

1
as shown in Fig. 5. Note that the contribution of this aux-
illiary feedback is zero in steady state. An advantage of
using the auxiliary feedback instead of conventional cas- WR - WD
U1 - U1 COS(^^) - wz1sin(4i) (10)
cade compensators is that even if the output feedback con- U 1 - VUD1 sin(4i)
~p +w ; ' c ~ s ( ~ ~ ) (11)
trol of active power is not used, the auxiliary signal can
still be used to improve stability of network mode. Since all quantities are locally available, we can easily cal-
From the Bode plot it is seen that the transfer function culate real voltage ey' to be injected to obtain desired
 1351
magnitude of Vu2 (see Fig. 6 ). Note that there are two If we vary the inverter output voltages as follows,
solutions of eyr;the solution which has a lower magnitude
is chosen.

I di sh
ep
- sh W
- epord = - - X s h i k h + vU1+ -up
xsh
(22)
wb wb

the differential equations (16) and (17) get decoupled as

follows,

(23)

Figure 6: Port 2 Voltage Controller

(24)

Independent output feedback control of the currents is

5 Shunt Current Control achieved by varying U R ,u p as,

The shunt current is controlled by varying the magnitude

and angle of the shunt converter voltage (see Fig. 2). The
dynamical equations in the D-Q frame are given by,
G J h ( s ) is the transfer function of the controller (we have
used a PI controller).
The reactive current reference is set by a voltage regulator
A=--
dish .sh + woi$
rshWb zQ + -(e$
wb - ut1) (13) (PI type) for the UPFC bus (port 1).
dt 2sh xsh The dynamical equation for the capacitor voltage is given
by
where,
Tsh xsh=ShUnt transformer resistance and leakage reac-
tance respectively
ebb, e$=converter output voltage components
~ 2 ; ~ , v ~ ' - v o l t a gcomponents
e a t the bus into which cur- gcap, bcap are the conductance and susceptance of the
Q .-.
rent is injected (port 1 of the UPFC) capacitor respectively.
Reactive and Real current are defined as Any real power drawn/supplied by the series branch (due
to e F r ) or by the shunt branch (due to real current in-
iR
sh - i sDh C O S ( P ~ ) - i $ s i n ( P l )
(14) jection igh) manifests as DC side currents igg and i&
i;h =i;hsin(P) +i$cos(P1) (15) respectively. Since we allow variable real series voltage in-
jection, and due to the losses, the capacitor voltage tends
where, to change. To compensate this by igC,we set the real
,U1 = tan-& current reference ( i $ ! E F )as the output of a PI type ca-
U$
pacitor voltage regulator.
vu1 = JM The controller block diagram is shown in Fig. 7.
For control of shunt current we proceed in a way similar
to the one outlined by Schauder and Mehta[6]. We can
rewrite the differential equations as
Shunt

current

Figure 7: Shunt current controller

dBU1
w=wo+-
dt
1352

6.1 Simulation Results

Digital simulation has been carried out using SIMULINK
Generator Receiving
bus [8] dynamic system simulation software. The switchings
of the converters are modelled as switching functions (the
switches are assumed to be ideal) in the differential equa-
tions. The simulation method used is Runge-Kutta 4th
order method (this is an explicit integration method and is
recommended for systems with discontinuities) with vari-
able time step feature.
Figure 8: System under study

We consider the system shown in Fig. 8 .

Nominal System Data:
?'ieT= 0.0075, X/,,, = 0.075, x,h = 0.15, l",h = 0.01.
bcap = 2 . O , g , , , = 0 . 0 2 , ~ = 1 . O L 3 0 , F = 1.OLO
All quantities are on the UPFC MVA base which is as-
sumed to be (i)" of the transmission line MVA base.
Both the shunt and series branches of the UPFC consist
of two 12- pulse converters each. Magnitude control is
achieved by vector addztion of the output of the 2 twelve
pulse converters [7]. The magnitude ( E ) is varied by dis-
placing the output of one 12 pulse converter with respect
to the other while maintaining the required phase (4)of
the resultant voltage. This is done as shown in Fig. 9.
The resultant voltage is given by,

I I

Q
Figure 9: Magnitude control

Note that the factor relates the capacitor voltage

( U D C ) to the line to line rms inverter output voltage for a
12 pulse converter. With the knowledge of the capacitor Figure 10: Steady.state Waveforms
voltage and the inverter voltage order, 0 can be calculated.
While this scheme of magnitude control may not be opti-
mal from the point of view of equipment utilization and (a) STEADY ~ T A T EWAVEFORMS
harmonics, we use it to here only to validate the control In Fig.10 we show the steady state waveforms for 2 cases:
strategy. 1. V s = 0.975, PREF= 4.5, V,U$, = V,U& = 0.975
To allow for a power flow of 4.5 pu the UPFC injects a
 1353
"capacitive" voltage in series with the line. Also, to main- I
tain the voltage a t port1 the shunt branch injects reac-
tive power in addition to drawing real current to maintain
power balance.
2, V s = 1.0, PREF = 2.5, V&F = Vi&- = 0.975 Referenu, Power = 4.5pu
Here the UPFC injects an "inductive" voltage in order to
maintain a power flow of 2.5 pu. !!I 0,;s Ol2 O . k hms (seconds)
04 O.& 0'4 0.145 015

(b) RESPONSEFOR A PULSE DISTURBANCE I N POWER

REFERENCE
811
The UPFC can respond rapidly (order of one cycle) to %
w
a pulse change in power reference (4.5 to 2.5 to 4.5 pu) 0 1

(Fig. 11). At the same time it maintains its port voltages 2

B 09
constant. While reactive voltage is changed in order to
change the power flow, the real voltage injection and the '801 015 02 025 03 035 04 045 05
iime (seconds)
shunt reactive current maintain the port voltage magni-
tudes constant.
Figure 12: Response to pulse change in sending end volt-
age

The high frequency oscillations observed in steady state

in Figs. 11 and 12 are due to the presence of voltage
harmonics introduced by the converters.
21 " " " " ' 1
0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32

7 Modulation Controller [9]

N
I-
811- The fast response time of the UPFC can be utilised to im-
Q
prove damping and transient stability of the power system.
If we consider the case of a SMIB system where the gener-
8 ator rotor is oscillating sinusoidally, restoring torques are
1
0.9
08' " " " ' 1 ' 1
set up which oppose the motion. The component of the
012 014 016 018 02 022 024 026 028 03 032 torque in phase with the rotor angle is called the synchro-
iime
nising torque and the component in phase with the rotor
velocity is called the damping torque. Assuming the small
signal rotor oscillations are governed by a n approximate
second order equation

Mp2AS+ -PAS
TD + Ts AS = 0 (29)
0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 WB
where M is the inertia constant, p is the differential op-
2 02 erator d/dt and W B is the base speed, TS and TD are the
9 synchronising and damping torque coefficients, it is es-
-
'p 01
sential for the system to be stable that both Ts and To
P9 o be positive. Trying to maintain a constant power in the
p-0' line during contingencies prevents the flow of synchronis-
UL-02
ing and damping torques. To damp power oscillations it
012 014 016 018 02 022 024
ime (seconds)
026 028 03 032 is necessary to enhance damping torque and to improve
transient stability it is necessary to enhance the synchro-
Figure 11: Response to pulse change in PREF nising torque. Hence, during a contingency the real power
demand is changed to enhance both the damping and syn-
chronising torques.
(c) RESPONSE
FOR A PULSE DISTURBANCE I N SENDING - of Fig. 8, where one of the
We consider the system
END VOLTAGE! the voltage sources ( V s ) is replaced by a generator (1.1
The capability of the UPFC t o regulate both the power modelptator transients included). The generator rating is
and voltages a t both ports is clearly seen for a pulse dis- compatible with the transmission line rating.
turbance in sending end voltage magnitude (1.05 to 0.975 The modulation controller structure is shown in Fig. 13
to 1.05 pu) (see Fig. 12). The response time is of the which supplements the controller shown in Fig.5.
order of a cycle. Since we consider a single radial line exporting power from
1354

9 Acknowledgement
The financial support received from the Dept. of Science
and Technology, Govt. of India under the project titled
Flexible AC Transmission Systems (FACTS) controllers
Figure 13: Modulation controller
is gratefully acknowledeged.

the generator, power flow control is not meaningful; hence IO References

reactive voltage is modulated directly. The auxiliary con-
trol to damp network mode in the power flow controller 1. L.Gyugyi,C.D.Schauder ,S .L.Wil1ianqT.R .Rietman,
is retained. D and K are constants to provide damping D.R.Torgerson, A.Edris, The Unified Power Flow
and synchronising powers in the line. A washout circuit Controller : A new Approach to Power Transmission
is provided to eliminate any steady state bias in the con- Control,IEEE Trans. on Power Delivery, Vol. 10,
troller. No.2 April 1995, pp. 1085-1097.
The transient simulation results for a pulse in the input 2. L. Gyugyi, Unified power flow concept for flexi-
mechanical torque is shown in Fig. 14 While this distur- ble AC transmission systems IEE Proc-C, Vo1.139,
~

bance is not realistic, the improvement brought in the sys- No .4, July 1992, pp .323-332.
tem response is clearly seen both in maximum generator 3. D. Povh, R.Mihalic, LPapic, FACTS equipment for
angle deviation as well as damping. Load Flow Control in High Voltage Systems, Cz-
gre Symposzum, Power Electronics an Power Systems,
120 ,--- I
Tokyo, May 1995.
WiihoutUPFC , 1 I 4. R.Mihalic, P.Zunko, D.Povh, Modelling of Unified
Power Flow Controller and its impact on power oscil-
lation damping, Czgre Symposzum, Power Electron-
zcs zn Power Systems, Tokyo, May 1995.
, 5. K.R.Padiyar, Power System Dynamacs - Stabalaty and
I

05 1 15 2 25 3 Control, John Wiley and Sons (SEA) Pte Ltd, Singa-

pore, 1996.
0.5 6. C.Schauder and H.Mehta, Vector Analysis and Con-
trol of Advanced Static Var Compensator, IEE
Proc.-C, Vol. 140, No.4, July 1993., pp.299-306.
7. Loren H. Walker, 10-MW G T O Converter for Bat-
tery Peaking Service, IEEE Trans. on Industry Ap-
plzcatzons, Vol. 26, No. 1, Jan/Feb 1990, pp. 63-72.
-0 5
05 1 15 2 25
I
3
8. SIMULINK Users Guide, The Math Works Inc., Nat-
lime (seconds) ick, Mass., 1993.
9. K.R.Padiyar and M. Uma Rao, A Control Scheme
Figure 14: Response for pulse disturbance in input torque for Unified Power Flow Controller to improve Stabil-
ity of Power Systems , paper presented a t the Nznth
National Power Systems Conference, Kanpur, India
Dec. 1996.
Biographies
K.R.Padiyar: is Professor of Eletrical Engineering at Indian
In this paper we have proposed a control strategy for the Institute of Science, Bangalore, India. He obtained his BE de-
UPFC. The salient features are: gree in Electrical Engineering from Poona University in 1962,
1 Real power flow control by reactive voltage injection. ME degree from 1.1.S~.in 1964, and PhD degree from Univer-
2. Indirect reactive power flow control by control of volt- sity of Waterloo, Canada in 1972. He was with I.I.T, Kanpur
age at the two ports of the UPFC. from 1976-1987 prior to joining 1.I.Sc..
The controllers are designed independently and use locally His research interests are in the area of HVDC and FACTS,
available measurements. The simulation results for a case System Dynamics and Control. He has authored two books
study indicate that this is a viable control scheme. By and over 150 papers. He i s a Fellow of National Academy of
modulating the active power it is possible to bring a vast Engineering (India).
improvement in transient stability and damping. A.M.Kulkarni: received his B.E. degree from the University
While this paper gives the basic strategy and design con- of Roorkee and M.E. degree from Indian Institute of Science
siderations, further refinement is possible in the context of in Electrical Engineering in 1992 and 1994 respectively. He is
the recent advances in control theory. Also, performance currently working towards a PhD degree at the Indian Insti-
evaluation considering effect of torsional dynamics of the tute of Science. His research interests are in the area of FACTS
generator is another aspect to be studied. and power system dynamics.