INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR 721302, DECEMBER 27-29, 2002 427

Damping of Power System Oscillations using

Unified Power Flow Controller (UPFC)
Neelima Tambey M. L. Kothari

Abstract--This paper presents a systematic approach for 2. To examine the relative effectiveness of modulating
designing Unified Power Flow Controller (UPFC) based alternative UPFC control parameters (i.e. mB, mE, δB and
damping controllers for damping low frequency oscillations in a
δE), for damping power system oscillations.
power system. Detailed investigations have been carried out
considering four alternative UPFC based damping controllers.
3. To investigate the performance of the alternative
The investigations reveal that the damping controllers based on damping controllers, considering wide variations in
UPFC control parameters δE and δB provide robust loading conditions and system parameters in order to
performance to variations in system loading and equivalent arrive at most effective damping controller.
reactance Xe.
II. SYSTEM INVESTIGATED
Keywords-- Power system Stability, Damping of power system
oscillations, UPFC, FACTS controllers. A single-machine-infinite-bus (SMIB) system installed
with UPFC is considered (Fig. 1). A static excitation system
I. INTRODUCTION model type IEEE-ST1A has been considered. The UPFC
considered here is assumed to be based on pulse width
The power transfer in an integrated power system is modulation (PWM) converters. The nominal loading
constrained by transient stability, voltage stability and small condition and system parameters are given in Appendix-1.
signal stability. These constraints limit a full utilization of
available transmission corridors. Flexible AC Transmission VB
System (FACTS) is the technology that provides the needed It Vo
IB Vb
XBV
corrections of the transmission functionality in order to fully
utilize the existing transmission facilities and hence, X tE V0′
minimizing the gap between the stability limit and thermal IE VSC - E VSC - B
BT
limit. Vdc
Unified Power Flow Controller (UPFC) is one of the
FACTS devices, which can control power system parameters
XE
such as terminal voltage, line impedance and phase angle. It ET
can also be used for damping power system oscillations.
Recently researchers have presented dynamic models of mE δE mB δB UPFC
UPFC in order to design power flow, voltage and damping
controllers [4-10]. Wang [8-10], has presented a modified
Fig. 1. UPFC installed in a SMIB system.
linearised Heffron-Phillips model of a power system installed
III. UNIFIED POWER FLOW CONTROLLER
with UPFC. He has addressed the basic issues pertaining to
the design of UPFC damping controller, i.e., selection of
Unified power flow controller (UPFC) is a combination
robust operating condition for designing damping controller;
of static synchronous compensator (STATCOM) and a static
and the choice of parameters of UPFC (such as mB, mE, δB
synchronous series compensator (SSSC) which are coupled
and δE) to be modulated for achieving desired damping. via a common dc link, to allow bi-directional flow of real
No effort seems to have been made to identify the most power between the series output terminals of the SSSC and
suitable UPFC control parameter, to be modulated for the shunt output terminals of the STATCOM and are
achieving robust dynamic performance of the system controlled to provide concurrent real and reactive series line
following wide variations in loading condition. compensation without an external electric energy source. The
In view of the above, the main objectives of the research UPFC, by means of angularly unconstrained series voltage
work presented in the paper are, injection, is able to control, concurrently or selectively, the
transmission line voltage, impedance and angle or
1. To present a systematic approach for designing UPFC alternatively, the real and reactive power flow in the line.
based damping controllers. The UPFC may also provide independently controllable
shunt reactive compensation. Viewing the operation of
Neelima Tambey is persuing her Ph.D at Indian Institute of Technology,
UPFC from the standpoint of conventional power
Delhi,India (e-mail: neelu_tambey@yahoo.com) transmission based on reactive shunt compensation, series
Prof. M.L. Kothari is with Electrical Engineering Deptt, Indian Institute of compensation and phase shifting, the UPFC can fulfill all
Technology, Delhi, India.(e-mail : mohankothari@hotmail.com) these functions and therby meet multiple control objectives.
428 NATIONAL POWER SYSTEMS CONFERENCE, NPSC 2002

IV. MODIFIED HEFFRON-PHILLIPS SMALL link voltage. This model has been developed by Wang
PERTURBATION TRANSFER FUNCTION [8], by modifying the basic Heffron-Phillips model
MODEL OF A SMIB SYSTEM INCLUDING including UPFC. This linear model has been developed
UPFC by linearising the nonlinear model around a nominal
operating point.
Fig. 2 shows the small perturbation transfer Function The constants of the model depend on the system
block diagram of a machine-infinite bus system parameters and the operating condition.
including UPFC relating the pertinent variables of
electric torque, speed, angle, terminal voltage, field
voltage, flux linkages, UPFC control parameters, and dc

K1

+ + ∆Te ∆T m
− + ∆ω ∆δ
1 ω0
∑ ∑
Ms + D s
+
+

K4 K5 K pd
[K pu ] K2
K6

− − −
∆V ref
1 Ka +
+ ∑
∆Eq' ∑
K 3 +sT do ' 1 + sTa
− −
− −

K8
[K qu ] K qd [K vu ] K vd

+ 1 ∆V dc
[K cu ] ∑
s + K9

[∆u] +

K7

Fig. 2. Modified Heffron-Phillips model of SMIB System with UPFC.

In the above transfer function model [∆u] is the column vector while [Kpu], [Kqu], [Kvu] and [Kcu] are the row vectors as defined below,

[∆u] = [∆mE ∆δE ∆mB ∆δB]T , [Kpu] = [Kpe Kpδe Kpb Kpδb], [Kqu] = [Kqe Kqδe Kqb Kqδb]
[Kvu] = [Kve Kvδe Kvb Kvδb] [Kcu] = [Kce Kcδe Kcb Kcδb]

The control parameters of the UPFC are : V. ANALYSIS

1. mB – pulse width modulation index of series
inverter. By controlling mB, the magnitude of series 1) Computation of Constants of the Model
injected voltage can be controlled.
2. δB – Phase angle of series inverter which when The initial d-q axes voltage and current components and
controlled results in the real power exchange. torque angle for the nominal operating condition needed for
3. mE – pulse width modulation index of shunt inverter. By computing constants of the model are calculated and are
controlling mE, the voltage at a bus where UPFC is given below:
installed, is controlled through reactive power
compensation. Q = 0.1670 pu Ebdo = 0.7331 pu
4. δE – Phase angle of the shunt inverter, which regulates edo = 0.3999 pu Ebqo = 0.6801 pu
the dc voltage at dc link. eqo = 0.9166 pu ido = 0.4729 pu
δo = 47.13 ° iqo = 0.6665 pu
INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR 721302, DECEMBER 27-29, 2002 429

The constants of the model computed for nominal denoted as GEPA. The time constants of the phase
operating condition and system parameters are, compensator are chosen so that the phase lag/lead of the
system is fully compensated. For the nominal operating
K1 = 0.3561 Kpb = 0.1333 Kpδe = 1.9315 condition, the natural frequency of oscillation ωn = 4.0974
K2 = 0.4567 Kqb = 0.1224 Kqδe = - 0.0404 rad./sec. The transfer function relating ∆Te and ∆mB is
K3 = 1.6250 Kvb = - 0.0219 Kvδe = 0.1128 denoted as GEPA. For the nominal operating condition,
K4 = 0.0916 Kpe = 0.2964 Kcb = 0.1763
phase angle of GEPA i.e. ∠GEPA = 12.03° lagging. The
K5 = -0.0027 Kqe = 0.4984 Kce = 0.0018
K6 = 0.0834 Kve = - 0.1025 Kcδb = - 0.2047 magnitude of GEPA i.e. GEPA = 0.1348. To compensate
K7 = 0.6854 Kpδb = 0.0924 Kcδe = 2.4937 the phase lag, the time constants of the lead compensator are
K8 = 0.1135 Kqδb = - 0.0050 Kpd = 0.1618 computed [11] and are obtained as T1 = 0.3016 sec. and T2 =
K9 = -0.0183 Kvδb = 0.0061 Kqd = 0.2621 0.1975 sec.
Kvd = - 0.0536 Following the same procedure, the phase angle to be
compensated by the other three damping controllers are
2). Design of Damping Controllers computed and are given in Table 2. The critical examination
of Table 2 reveals that the phase angle of the system i.e.
For this operating condition, the eigen-values of the ∠GEPA, is negative for control parameter mB and mE
system are obtained (Table 1) and it is clearly seen that the However, it is positive for δB and δE. Hence the phase
system is unstable. compensator for the Damping controller (mB) and Damping
The damping controllers are designed to produce an controller (mE) is a lead compensator while for Damping
electrical torque in phase with speed deviation.The four controller (δB) and Damping controller (δE) is a lag
control parameters of the UPFC (i.e. mB, mE, δB and δE) can compensator. The gain settings (Kdc) of the controllers are
be modulated in order to produce the damping torque. The computed assuming a damping ratio ξ = 0.5.
speed deviation ∆ω is considered as the input to the damping
Table 2. Gain and phase angle of the transfer function
controllers. The four alternative UPFC based damping GEPA.
controllers are examined in the present work.
GEPA GEPA ∠GEPA (degrees)

Damping controller based on UPFC control parameter ∆Te / ∆mE 0.3168 - 18.4017
mB shall henceforth be denoted as Damping controller (mB).
Similarly damping controllers based on mE, δB and δE shall ∆Te / ∆δE 1.8919 0.6357
henceforth be denoted as Damping controller (mE), Damping ∆Te / ∆mB 0.1348 - 12.0273
controller (δB), and Damping controller (δE) respectively.
∆Te / ∆δB 0.0958 8.8143

1 + s T1
Kdc
s Tw
Gc(s) = Table 3 shows the parameters (Gain and Time constants) of
1 + s Tw 1 + s T2
∆u
the four alternative damping controllers. Table 3 clearly
∆ω
Gain
shows that the gain setting of the Damping controller (mB)
Signal Washout Phase compensator and Damping controller (δB) are much higher as compared to
gain setting of Damping controller (δE) and Damping
Fig. 3. Structure of UPFC based damping controller. controller (mE).
The structure of UPFC based damping controller is
shown in Fig. 3. It consists of gain, signal washout and phase
compensator blocks. The signal washout is the high pass
filter that prevents steady changes in the speed from
modifying the UPFC input parameter. The value of the
washout time constant Tw should be high enough to allow
signals associated with oscillations in rotor speed to pass
unchanged. From the viewpoint of the washout function, the
value of Tw is not critical and may be in the range of 1 to 20
seconds. Tw equal to 10 seconds is chosen in the present
studies. The parameters of the damping controller are
obtained using the phase compensation technique [11].
The transfer function of the system relating the electrical
component of torque (∆Te) and UPFC control parameter is
Table 1. Eigen-values of the closed loop system.

Eigen-values ωn of the oscillatory mode ς of the oscillatory modes

- 19. 1186
System without any damping controller 0. 171 ± 4. 06i 4. 06 rad/sec - 0. 0421
- 0. 765 ± 0.407i 0. 866 rad / sec 0.883
430 NATIONAL POWER SYSTEMS CONFERENCE, NPSC 2002

wide variation in loading conditions and line reactance Xe.

Table 3. Parameters of the UPFC based Damping controllers.
4). Effect of Variation of loading condition and system
Kdc T1 (seconds) T2 (seconds)
Damping
parameters on the dynamic performance of the system
74.6089 0. 3384 0. 1760
Controller (mE)
Damping In any power system, the operating load varies over a wide
17.5203 0. 2214 0. 2468
Controller (δE) range. It is extremely important to investigate the effect of
Damping variation of the loading condition on the dynamic
196.7449 0. 3016 0. 1975
Controller (mB)
Damping performance of the system.
399.3160 0. 2091 0. 2848 In order to examine the robustness of the damping
Controller (δB )
controllers to wide variation in the loading condition, loading
Table 4. Eigenvalues of the system with UPFC Damping controllers. of the system is varied over a wide range (Pe = 0.2 to Pe =
1.2 p.u.) and the dynamic responses are obtained for each of
Damping Natural frequency the loading condition considering parameters of the damping
Eigenvalues
ratio of oscillation (ωn)
controllers computed at nominal operating condition for the
Damping
Controller (mE)
-1.61 ± 3.46i 0.421 3.82 step load perturbation in mechanical torque (i.e. ∆Tm = 0.01
Damping p.u.)
-1.92 ± 3.23i 0.511 3.76
Controller (δE) Figs. 5 and 6 show the dynamic responses of ∆ω with
Damping
Controller (mB)
-1.60 ± 3.37i 0. 429 3.74 nominal optimum Damping controller (mB) and Damping
Damping controller (mE) at different loading conditions. It is clearly
-2.27 ± 3.68i 0. 524 4.33 seen that the dynamic performance of the system is degraded
Controller (δB )
significantly as the system loading is reduced from the
Table 4 shows eigenvalues of the system at nominal nominal loading. Further it is seen that system becomes
operating condition with the above alternative damping unstable
-4
controllers. Table 4 clearly shows that damping ratios 2.5
x 10

obtained with Damping controllers (δE) and (δB) are higher a a - Pe = 0.2p.u. Qe = 0.01 p.u.
2
than those obtained with Damping controllers (mE) and (mB). b
b - Pe = 0.8p.u. Qe = 0.167p.u.
c - Pe = 1.2p.u. Qe = 0.4 p.u.
1.5

3). Dynamic Performance of the system with Damping 1

c

Controllers 0.5
∆ω
Fig. 4 shows the dynamic responses for ∆ω obtained 0

considering a step load perturbation ∆Tm = 0.01 p.u. with the -0.5

four alternative damping controllers (Table 3) -1

Fig. 4 clearly shows that the dynamic responses of the
-1.5
system obtained with the four alternative damping controllers
are virtually identical. At this stage it can be inferred that any -2
0 1 2 3 4 5
of the UPFC based damping controllers provide satisfactory Time (Seconds)
dynamic performance at the nominal operating condition.
x 10
-4 Fig. 5.Dynamic responses for ∆ω with Damping controller (mB)
2 for different loading conditions.
a
b a-Damping controller(δB) -4
1.5 b-Damping controller(δE) x 10
2.5
c-Damping controller(mE)
a a - Pe = 0.2p.u. Qe = 0.01p.u.
1 d-Damping controller(mB) 2
b b - Pe = 0.8p.u. Qe = 0.167p.u.
c - Pe = 1.2p.u. Qe = 0.4 p.u.
1.5
c
∆ω 0.5 d 1
c
0 ∆ω 0.5
0
-0.5
-0.5

-1 -1
0 1 2 3 4 5
-1.5
Time (Seconds)
-2
Fig. 4. Dynamic responses for ∆ω with four alternative Damping 0 1 2 3 4 5
controllers. Time (Seconds)

Further investigations are carried out to assess the Fig. 6. Dynamic responses for ∆ω with damping controller (mE) for
different loading conditions.
robustness of these four alternative damping controllers to
INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR 721302, DECEMBER 27-29, 2002 431

-4 -4
x 10 x 10
2.5 2.5

c
2 c a - Pe = 0.8p.u. Q e = -0.1p.u. 2 a - Xe = 0.3 p.u.
b - Pe = 0.8p.u. Q e = 0.167p.u. b b - Xe = 0.5 p.u.
c - Pe = 1.2p.u. Qe = 0.4 p.u.
1.5 1.5 c - Xe = 0.65 p.u.
a
1 1
b
0.5 ∆ω 0.5

∆ω 0 0
a

-0.5 -0.5

-1 -1

-1.5 -1.5
0 1 2 3 4 5 0 1 2 3 4 5
Time (Seconds) Time (Seconds)
Fig. 7. Dynamic responses for ∆ω with damping controller (δB) for different
loading conditions. Fig. 9. Dynamic responses for ∆ω with Damping controller (δB) for
x 10
-4
different values of Xe.
2 -4
a - Pe = 0.8p.u. Qe = -0.1p.u. x 10
c 2
b - Pe = 0.8p.u. Qe = 0.167p.u.
1.5 c - Pe = 1.2p.u. Qe = 0.4 p.u. a a - Xe = 0.65 p.u.
d - Pe = 0.2p.u. Qe = 0.01 p.u. 1.5 b - Xe = 0.50 p.u.
b
1 c - Xe = 0.30 p.u.
d
1 c
0.5
a 0.5
b
∆ω 0
∆ω
0
-0.5
-0.5
-1
-1
-1.5
0 1 2 3 4 5
-1.5
0 1 2 3 4 5
Time (Seconds)
Time (Seconds)
Fig. 8. Dynamic responses for ∆ω with damping controller(δE) for different
loading conditions. Fig. 10. Dynamic responses for ∆ω with damping controller (δE) for
different values of Xe.
for typical leading power factor condition (i.e. Pe = 0.8 p.u.,
Qe = -0.1 p.u.). Examining Figs. 10 and 11, it can be inferred that
Figs. 7 and 8 show the dynamic responses of ∆ω with Damping controller (δB) and Damping controller (δE)
nominal optimum Damping controller (δB) and Damping are quite robust to variations in Xe also.
controller (δE) respectively. It is clearly seen that the It may thus be concluded that Damping controller (δB)
responses are hardly affected in terms of settling time and Damping controller (δE) are quite robust to wide
following wide variations in loading condition. Both the variation in loading condition and system parameters.The
controllers perform well for the leading power factor loading reason for the superior performance of Damping controller
condition also. (δB) and Damping controller (δE) may be attributed to the
From the above studies, it can be concluded that the fact that modulation of δB and δE results in exchange of real
Damping Controller (δB) and Damping controller (δE) power.
exhibit robust dynamic performance as compared to that
obtained with Damping controller (mB) or VI. CONCLUSIONS
Damping controller (mE).
In view of the above, the performance of damping The significant contributions of the research work presented
Controller (δB) and Damping controller (δE) are further in this paper are as follows:
studied with variation in equivalent reactance, Xe of
the system. Figs. 9 and 10 show the dynamic 1. A systematic approach for designing UPFC based
performance of the system with Damping controller controllers for damping power system oscillations has
(δB) and Damping controller (δE) respectively for wide been presented.
variation in Xe. 2. The performance of the four alternative damping
controllers, (i.e. Damping controller (mE), Damping
controller (δE), Damping controller (mB), and Damping
controller (δB) ) has been examined considering wide
variation in the loading conditions and line reactance Xe.
432 NATIONAL POWER SYSTEMS CONFERENCE, NPSC 2002

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