Download Damping of Power System Oscillations using Unified Power Flow

INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR 721302, DECEMBER 27-29, 2002
427
Damping of Power System Oscillations using
Unified Power Flow Controller (UPFC)
Neelima Tambey
Abstract--This paper presents a systematic approach for
designing Unified Power Flow Controller (UPFC) based
damping controllers for damping low frequency oscillations in a
power system. Detailed investigations have been carried out
considering four alternative UPFC based damping controllers.
The investigations reveal that the damping controllers based on
UPFC control parameters δE and δB provide robust
performance to variations in system loading and equivalent
reactance Xe.
Keywords-- Power system Stability, Damping of power system
oscillations, UPFC, FACTS controllers.
I. INTRODUCTION
The power transfer in an integrated power system is
constrained by transient stability, voltage stability and small
signal stability. These constraints limit a full utilization of
available transmission corridors. Flexible AC Transmission
System (FACTS) is the technology that provides the needed
corrections of the transmission functionality in order to fully
utilize the existing transmission facilities and hence,
minimizing the gap between the stability limit and thermal
limit.
Unified Power Flow Controller (UPFC) is one of the
FACTS devices, which can control power system parameters
such as terminal voltage, line impedance and phase angle. It
can also be used for damping power system oscillations.
Recently researchers have presented dynamic models of
UPFC in order to design power flow, voltage and damping
controllers [4-10]. Wang [8-10], has presented a modified
linearised Heffron-Phillips model of a power system installed
with UPFC. He has addressed the basic issues pertaining to
the design of UPFC damping controller, i.e., selection of
robust operating condition for designing damping controller;
and the choice of parameters of UPFC (such as mB, mE, δB
and δE) to be modulated for achieving desired damping.
No effort seems to have been made to identify the most
suitable UPFC control parameter, to be modulated for
achieving robust dynamic performance of the system
following wide variations in loading condition.
In view of the above, the main objectives of the research
work presented in the paper are,
1.
To present a systematic approach for designing UPFC
based damping controllers.
Neelima Tambey is persuing her Ph.D at Indian Institute of Technology,
Delhi,India (e-mail: [email protected])
Prof. M.L. Kothari is with Electrical Engineering Deptt, Indian Institute of
Technology, Delhi, India.(e-mail : [email protected])
M. L. Kothari
2.
3.
To examine the relative effectiveness of modulating
alternative UPFC control parameters (i.e. mB, mE, δB and
δE), for damping power system oscillations.
To investigate the performance of the alternative
damping controllers, considering wide variations in
loading conditions and system parameters in order to
arrive at most effective damping controller.
II. SYSTEM INVESTIGATED
A single-machine-infinite-bus (SMIB) system installed
with UPFC is considered (Fig. 1). A static excitation system
model type IEEE-ST1A has been considered. The UPFC
considered here is assumed to be based on pulse width
modulation (PWM) converters. The nominal loading
condition and system parameters are given in Appendix-1.
VB
It
Vo
IB
XBV
X tE
IE
VSC - E
VSC - B
Vb
V0′
BT
Vdc
XE
ET
mE
δE
mB
δB
UPFC
Fig. 1. UPFC installed in a SMIB system.
III. UNIFIED POWER FLOW CONTROLLER
Unified power flow controller (UPFC) is a combination
of static synchronous compensator (STATCOM) and a static
synchronous series compensator (SSSC) which are coupled
via a common dc link, to allow bi-directional flow of real
power between the series output terminals of the SSSC and
the shunt output terminals of the STATCOM and are
controlled to provide concurrent real and reactive series line
compensation without an external electric energy source. The
UPFC, by means of angularly unconstrained series voltage
injection, is able to control, concurrently or selectively, the
transmission line voltage, impedance and angle or
alternatively, the real and reactive power flow in the line.
The UPFC may also provide independently controllable
shunt reactive compensation. Viewing the operation of
UPFC from the standpoint of conventional power
transmission based on reactive shunt compensation, series
compensation and phase shifting, the UPFC can fulfill all
these functions and therby meet multiple control objectives.
NATIONAL POWER SYSTEMS CONFERENCE, NPSC 2002
428
IV. MODIFIED HEFFRON-PHILLIPS SMALL
PERTURBATION TRANSFER FUNCTION
MODEL OF A SMIB SYSTEM INCLUDING
UPFC
link voltage. This model has been developed by Wang
[8], by modifying the basic Heffron-Phillips model
including UPFC. This linear model has been developed
by linearising the nonlinear model around a nominal
operating point.
The constants of the model depend on the system
parameters and the operating condition.
Fig. 2 shows the small perturbation transfer Function
block diagram of a machine-infinite bus system
including UPFC relating the pertinent variables of
electric torque, speed, angle, terminal voltage, field
voltage, flux linkages, UPFC control parameters, and dc
K1
+
+
∑
∆T m
+
∆Te
−
∑
∆ω
1
Ms + D
+
∆δ
ω0
s
+
K4
[K pu ]
K2
K5
K pd
K6
1
∆Eq'
K 3 +sT do '
K8
+
∑
[K qu ]
Ka
∑
1 + sTa
−
−
−
−
−
K qd
∆V ref
+
−
−
[K vu ]
K vd
+
[K cu ]
+
∑
1
∆V dc
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 ,
[Kvu] = [Kve Kvδe Kvb Kvδb]
[Kpu] = [Kpe Kpδe Kpb Kpδb],
[Kcu] = [Kce Kcδe Kcb Kcδb]
The control parameters of the UPFC are :
1. mB – pulse width modulation index of series
inverter. By controlling mB, the magnitude of series
injected voltage can be controlled.
2. δB – Phase angle of series inverter which when
controlled results in the real power exchange.
3. mE – pulse width modulation index of shunt inverter. By
controlling mE, the voltage at a bus where UPFC is
installed, is controlled through reactive power
compensation.
4. δE – Phase angle of the shunt inverter, which regulates
the dc voltage at dc link.
[Kqu] = [Kqe Kqδe Kqb Kqδb]
V. ANALYSIS
1) Computation of Constants of the Model
The initial d-q axes voltage and current components and
torque angle for the nominal operating condition needed for
computing constants of the model are calculated and are
given below:
Q
edo
eqo
δo
= 0.1670 pu
= 0.3999 pu
= 0.9166 pu
= 47.13 °
Ebdo = 0.7331 pu
Ebqo = 0.6801 pu
ido = 0.4729 pu
iqo = 0.6665 pu
INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR 721302, DECEMBER 27-29, 2002
The constants of the model computed for nominal
operating condition and system parameters are,
K1 = 0.3561
K2 = 0.4567
K3 = 1.6250
K4 = 0.0916
K5 = -0.0027
K6 = 0.0834
K7 = 0.6854
K8 = 0.1135
K9 = -0.0183
Kpb = 0.1333
Kqb = 0.1224
Kvb = - 0.0219
Kpe = 0.2964
Kqe = 0.4984
Kve = - 0.1025
Kpδb = 0.0924
Kqδb = - 0.0050
Kvδb = 0.0061
Kpδe = 1.9315
Kqδe = - 0.0404
Kvδe = 0.1128
Kcb = 0.1763
Kce = 0.0018
Kcδb = - 0.2047
Kcδe = 2.4937
Kpd = 0.1618
Kqd = 0.2621
Kvd = - 0.0536
2). Design of Damping Controllers
For this operating condition, the eigen-values of the
system are obtained (Table 1) and it is clearly seen that the
system is unstable.
The damping controllers are designed to produce an
electrical torque in phase with speed deviation.The four
control parameters of the UPFC (i.e. mB, mE, δB and δE) can
be modulated in order to produce the damping torque. The
speed deviation ∆ω is considered as the input to the damping
controllers. The four alternative UPFC based damping
controllers are examined in the present work.
Damping controller based on UPFC control parameter
mB shall henceforth be denoted as Damping controller (mB).
Similarly damping controllers based on mE, δB and δE shall
henceforth be denoted as Damping controller (mE), Damping
controller (δB), and Damping controller (δE) respectively.
Kdc
s Tw
1 + s Tw
∆ω
Gain
Signal Washout
Gc(s) =
1 + s T1
1 + s T2
∆u
Phase compensator
Fig. 3. Structure of UPFC based damping controller.
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
429
denoted as GEPA. The time constants of the phase
compensator are chosen so that the phase lag/lead of the
system is fully compensated. For the nominal operating
condition, the natural frequency of oscillation ωn = 4.0974
rad./sec. The transfer function relating ∆Te and ∆mB is
denoted as GEPA. For the nominal operating condition,
phase angle of GEPA i.e. ∠GEPA = 12.03° lagging. The
magnitude of GEPA i.e. GEPA = 0.1348. To compensate
the phase lag, the time constants of the lead compensator are
computed [11] and are obtained as T1 = 0.3016 sec. and T2 =
0.1975 sec.
Following the same procedure, the phase angle to be
compensated by the other three damping controllers are
computed and are given in Table 2. The critical examination
of Table 2 reveals that the phase angle of the system i.e.
∠GEPA, is negative for control parameter mB and mE
However, it is positive for δB and δE. Hence the phase
compensator for the Damping controller (mB) and Damping
controller (mE) is a lead compensator while for Damping
controller (δB) and Damping controller (δE) is a lag
compensator. The gain settings (Kdc) of the controllers are
computed assuming a damping ratio ξ = 0.5.
Table
2.
Gain and
GEPA.
phase
angle
of
the
GEPA
GEPA
∠GEPA (degrees)
∆Te / ∆mE
0.3168
- 18.4017
∆Te / ∆δE
1.8919
0.6357
∆Te / ∆mB
0.1348
- 12.0273
∆Te / ∆δB
0.0958
8.8143
System without any damping controller
function
Table 3 shows the parameters (Gain and Time constants) of
the four alternative damping controllers. Table 3 clearly
shows that the gain setting of the Damping controller (mB)
and Damping controller (δB) are much higher as compared to
gain setting of Damping controller (δE) and Damping
controller (mE).
Table 1. Eigen-values of the closed loop system.
Eigen-values
- 19. 1186
0. 171 ± 4. 06i
- 0. 765 ± 0.407i
transfer
ωn of the oscillatory mode
4. 06 rad/sec
0. 866 rad / sec
ς of the oscillatory modes
- 0. 0421
0.883
NATIONAL POWER SYSTEMS CONFERENCE, NPSC 2002
430
wide variation in loading conditions and line reactance Xe.
Table 3. Parameters of the UPFC based Damping controllers.
Damping
Controller (mE)
Damping
Controller (δE)
Damping
Controller (mB)
Damping
Controller (δB )
Kdc
T1 (seconds)
T2 (seconds)
74.6089
0. 3384
0. 1760
17.5203
0. 2214
0. 2468
196.7449
0. 3016
0. 1975
399.3160
0. 2091
0. 2848
Table 4. Eigenvalues of the system with UPFC Damping controllers.
Damping
Controller (mE)
Damping
Controller (δE)
Damping
Controller (mB)
Damping
Controller (δB )
Eigenvalues
Damping
ratio
Natural frequency
of oscillation (ωn)
-1.61 ± 3.46i
0.421
3.82
-1.92 ± 3.23i
0.511
3.76
-1.60 ± 3.37i
0. 429
3.74
-2.27 ± 3.68i
0. 524
4.33
Table 4 shows eigenvalues of the system at nominal
operating condition with the above alternative damping
controllers. Table 4 clearly shows that damping ratios
obtained with Damping controllers (δE) and (δB) are higher
than those obtained with Damping controllers (mE) and (mB).
4). Effect of Variation of loading condition and system
parameters on the dynamic performance of the system
In any power system, the operating load varies over a wide
range. It is extremely important to investigate the effect of
variation of the loading condition on the dynamic
performance of the system.
In order to examine the robustness of the damping
controllers to wide variation in the loading condition, loading
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
the loading condition considering parameters of the damping
controllers computed at nominal operating condition for the
step load perturbation in mechanical torque (i.e. ∆Tm = 0.01
p.u.)
Figs. 5 and 6 show the dynamic responses of ∆ω with
nominal optimum Damping controller (mB) and Damping
controller (mE) at different loading conditions. It is clearly
seen that the dynamic performance of the system is degraded
significantly as the system loading is reduced from the
nominal loading. Further it is seen that system becomes
unstable
2.5
x 10
-4
a
2
1.5
3). Dynamic Performance of the system with Damping
Controllers
Fig. 4 shows the dynamic responses for ∆ω obtained
considering a step load perturbation ∆Tm = 0.01 p.u. with the
four alternative damping controllers (Table 3)
Fig. 4 clearly shows that the dynamic responses of the
system obtained with the four alternative damping controllers
are virtually identical. At this stage it can be inferred that any
of the UPFC based damping controllers provide satisfactory
dynamic performance at the nominal operating condition.
2
x 10
-4
a
a-Damping controller(δB)
b-Damping controller(δE)
c-Damping controller(mE)
d-Damping controller(mB)
b
1.5
1
c
1
∆ω
a - Pe = 0.2p.u. Qe = 0.01 p.u.
b - Pe = 0.8p.u. Qe = 0.167p.u.
c - Pe = 1.2p.u. Qe = 0.4 p.u.
b
0.5
0
-0.5
-1
-1.5
-2
0
1
2
3
4
5
Time (Seconds)
Fig. 5.Dynamic responses for ∆ω with Damping controller (mB)
for different loading conditions.
2.5
x 10
-4
a
2
a - Pe = 0.2p.u. Qe = 0.01p.u.
b - Pe = 0.8p.u. Qe = 0.167p.u.
c - Pe = 1.2p.u. Qe = 0.4 p.u.
b
1.5
c
∆ω 0.5
1
d
c
0
∆ω 0.5
0
-0.5
-1
-0.5
-1
0
1
2
3
4
5
Time (Seconds)
Fig. 4.
Dynamic responses for ∆ω with four alternative Damping
controllers.
Further investigations are carried out to assess the
robustness of these four alternative damping controllers to
-1.5
-2
0
1
2
3
4
5
Time (Seconds)
Fig. 6. Dynamic responses for ∆ω with damping controller (mE) for
different loading conditions.
INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR 721302, DECEMBER 27-29, 2002
2.5
x 10
-4
2.5
a - Pe = 0.8p.u. Q e = -0.1p.u.
b - Pe = 0.8p.u. Q e = 0.167p.u.
c - Pe = 1.2p.u. Qe = 0.4 p.u.
c
2
1.5
1.5
a - Xe = 0.3 p.u.
b - Xe = 0.5 p.u.
c - Xe = 0.65 p.u.
a
1
b
0
∆ω
0.5
0
a
-0.5
-0.5
-1
-1
0
1
2
3
Time (Seconds)
4
x 10
-1.5
5
Fig. 7. Dynamic responses for ∆ω with damping controller (δB) for different
loading conditions.
2
c
b
0.5
-1.5
-4
2
1
∆ω
x 10
431
Fig. 9.
-4
a
b
c
d
c
1.5
1
-
Pe
Pe
Pe
Pe
= 0.8p.u. Qe
= 0.8p.u. Qe
= 1.2p.u. Qe
= 0.2p.u. Qe
= -0.1p.u.
= 0.167p.u.
= 0.4 p.u.
= 0.01 p.u.
0
1
2
Time (Seconds)
4
5
Dynamic responses for ∆ω with Damping controller (δB) for
different values of Xe.
2
x 10
-4
a
1.5
d
3
a - Xe = 0.65 p.u.
b - Xe = 0.50 p.u.
c - Xe = 0.30 p.u.
b
c
1
0.5
∆ω
b
a
0.5
∆ω
0
0
-0.5
-0.5
-1
-1
-1.5
0
1
2
3
4
5
-1.5
Time (Seconds)
Fig. 8. Dynamic responses for ∆ω with damping controller(δE) for different
loading conditions.
for typical leading power factor condition (i.e. Pe = 0.8 p.u.,
Qe = -0.1 p.u.).
Figs. 7 and 8 show the dynamic responses of ∆ω with
nominal optimum Damping controller (δB) and Damping
controller (δE) respectively. It is clearly seen that the
responses are hardly affected in terms of settling time
following wide variations in loading condition. Both the
controllers perform well for the leading power factor loading
condition also.
From the above studies, it can be concluded that the
Damping Controller (δB) and Damping controller (δE)
exhibit robust dynamic performance as compared to that
obtained with Damping controller (mB) or
Damping controller (mE).
In view of the above, the performance of damping
Controller (δB) and Damping controller (δE) are further
studied with variation in equivalent reactance, Xe of
the system. Figs. 9 and 10 show the dynamic
performance of the system with Damping controller
(δB) and Damping controller (δE) respectively for wide
variation in Xe.
0
1
2
3
4
5
Time (Seconds)
Fig. 10. Dynamic responses for ∆ω with damping controller (δE) for
different values of Xe.
Examining Figs. 10 and 11, it can be inferred that
Damping controller (δB) and Damping controller (δE)
are quite robust to variations in Xe also.
It may thus be concluded that Damping controller (δB)
and Damping controller (δE) are quite robust to wide
variation in loading condition and system parameters.The
reason for the superior performance of Damping controller
(δB) and Damping controller (δE) may be attributed to the
fact that modulation of δB and δE results in exchange of real
power.
VI. CONCLUSIONS
The significant contributions of the research work presented
in this paper are as follows:
1.
2.
A systematic approach for designing UPFC based
controllers for damping power system oscillations has
been presented.
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.
NATIONAL POWER SYSTEMS CONFERENCE, NPSC 2002
432
3.
Investigations reveal that the Damping controller (δE)
and Damping controller (δB) provide robust performance
to wide variation in loading conditions and line reactance
Xe. It may thus be recommended that the damping
controllers based on UPFC control parameters δE and δB
may be preferred over the damping controllers based on
control parameters mB or mE.
APPENDIX 1
The nominal parameters and the operating condition of the
system are given below.
Generator
:
Excitation system
Transformer
:
:
Transmission line
:
Operating condition :
UPFC Parameters
:
DC Link Parameters :
M = 2H = 8.0MJ / MVA
D = 0.0 Tdo′ = 5.044 sec.
Xd = 1.0 p.u. Xq = 0.6 p.u.
X′d = 0.3 p.u.
Ka = 10.0
Ta = 0.01 sec.
XtE = 0.1 p.u.
XE = XB = 0.1 p.u.
XBv = 0.3 p.u. Xe = 0.5 p.u.
Pe = 0.8 p.u. Vt = 1.0 p.u.
Vb = 1.0 p.u. f = 60 Hz
mE = 0.4013 mB = 0.0789
δE = -85.3478° δB = -78.2174°
Vdc = 2 p.u.
Cdc = 1 p.u.
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