I
IEEETransactions on En-
'
I
,
1
Conversion, Vol. 6, No.4, December 1991.
573
APPLICATION OF SUPERCONDUCTING MAGNETIC ENERGY STORAGE UNIT TO IMPROVE
THE DAMPING OF SYNCHRONOUS GENERATOR
Qli-Jui Wu, Member IEEE
YuanpShung Lee
National Taiwan Institute of Technology
Taipei, Taiwan
Fu Jm University
Taipei, Taiwan
ABSTRACT
A systematic approach is presented to design a controller for
superconducting magnetic energy storage (SMES) unit to improve the
dynamic stability of a power system. The developed scheme employs
a proportional-integral @'I) controller to enhance the damping of the
electromechanical mode oscillation of synchronous generators. The
parameters of the proposed PI controller are determined by pole
assignment method based on modal control theory. Eigenvalues
analysis and nonlinear computer simulations show that SMES with
the PI controller can greatly improve the damping of system under
various operating conditions.
(b) The superconducting coil can draw or release the power during
the dynamic period. The energy stored in the coil is always
under its rating.
(c) Althoub the PI controller is designed at a special load condition,
it can also provide good damping effect at other load conditions.
(d) The stability margin can be expanded by the PI controller.
(e) The PI controller is very simple in structure and easy to be
implemented.
Key words: SMES, PI controller, pole assignment, computer simulation
Fig. 1 shows the studied system with a synchronous generator
connected to the infinite bus through a transmission line and a superconducting magnetic energy storage (SMES) unit. Although the
example system is a simple one, it is sufficient to demonstrate the
damping effect of SMES [ 181. The unit with thyristor controller is
located at the generator bus terminal. The nonlinear dynamic behavior
of the synchronous generator is described by two axis model [ 11,
where the armature transient voltage of direct axis and quadrature
axis are described by
1.
INTRODUCTION
Power system oscillations will occur if there are system disturbances such as load change or system fault. The damping of the
system must be enough such that the synchronous generators can
return to steady state after disturbances 1 11. Many countermeasures
have been suggested in the literatures to increase the damping such
as power system stabilizers P S S ) 12-61, governor and turbine system
[7], static Var compensator (SVC) [8-91, and phase shifter [ 101.
Due to the rapid development in the technique of high
temperature superconducting material, the application of the superconducting conductcv becomes an important h u e in the electrical
engineering [11-15]. The superconducting magnetic energy storage
(SMES) unit is designed to store electric power in the low loss superconducting magnetic coil [ 11-121. Power can be absorbed by or
released from the coil according to system requirement. The SMES
unit can also be applied to be a load frequency controller [ 161 and
transmission line stabilizer [ 111, or increase the stability of power
system [17-181.
In this paper, a systematic approach is used to design a SMES
unit with proportional-integra1 (PI) controller for increasing the
damping of synchronous generators. The PI controller is very simple
in structure and had been successfully used as a power system
stabilizer [SI. The paraqeters of the PI controller are determined
using modal control theory [ 191 by assigning the eigenvalues of
the electromechanical mode at the prespecified position.
The main results obtained in this paper are:
(a) Eigenvalues analysis and computer simulation results show that
the SMES unit with the proposed 'PI controller can greatly
enhance the damping of Ye synchronous generator. Rotor
oscillation can be qyiddy repressed down under system dis
turbances.
A paper recommended and approved
91 WM 132-1 EC
by t h e I E E E Energy Development and Power Generation
Committee of t h e IEEE Power Engineering Society f o r
p r e s e n t a t i o n a t t h e IEEE/PES 1991 Winter Meeting,
New York, New York, February 3-7, 1991. Manuscript
submitted June 1 8 , 1990: made a v a i l a b l e f o r
p r i n t i n g January 1 6 , 1991.
2. DESCRIPTION OF SYSTEM MODEL
EFD is the field excitation voltage, and Tdo and Tho represent d-axis
and q-mh transient time constant, respectively. The swing and
rotor
equations can be written as
LI = (P, - Dgu - Pe - P ~ M ) / M ~
(3)
6 = wo(u-l)
(4)
where Pm, De,and M are the output power of the reheat steam
turbine, damping c o e f h e n t , and moment constant. Pe = EA Id +
E&Iq is the electromagnetic pow& transfered in the air gap. PSM
is the stored power into the SMES. The terminal voltages which
describe the relation between transmission line and generator are
Eh - Ra Id -
vd'
= - v, sin (6-
rq
U) +
Reid + WLeIq
v q ' Eq - Ra Iq + x d Id
=VmC0S(6-a)+ R e I d - W L e I d
where Vt and V, represent terminal voltage of generator and infinite
bus voltage, respectively.
The static excitation control system is showh in Fig. 2, and
the governor and reheat turbine is also shown in Fig. 3. They are all
represented by the transfer functions in the S domain. Combining
generator, exciter, and governor-turbine system, we can obtain a set
of 10th order nonlinear differential equations, At the initial operating
point the nonlinear differential equations can be linearized to get
the linear differential equations [ 1I .
0885-8~/91$01.W1991 IEEE
Ti'-
574
!
i
i
,
Fig. 1
Single machine connected to infinite bus power system
with SMES unit
j
i
Y-h/Y-Y
CONNECTED
TRANSFORMER
i
'
Fig. 4
1
12-PULSE
CONVERTER
conduct I n g
I n d u c t0 r
The schematic diagram of the superconducting
magnetic energy storage unit
stabilizing
transformer
Fig. 2
1
2
2 Ld ISM^ is the initial energy in the inductor.
where w x o = -
Static excitation system
To use the SMES as a stabilizing control unit, the terminal
voltage VSM across the inductor is controlled continuousely depending
on the measured speed deviation of the generator rotor. That is
governor
10
Fig. 3
-eheat
turbine
Steam turbine and governor system
All eigenvalues of the open loop system, that is without SMES,
are shown in the first column of Table 1. From Table 1, the real
part of the electromechanical mode is -0.073, which means that the
damping of the synchronous generator is very bad. A SMES unit is
used in this paper to improve the damping under system disturbances.
Fig. 4 shows the configuration of the SMES unit, containing an
Y-A/Y-Y connected transformer, a 12-pulse converter and a DC
superconducting inductor. The converter unit is forced commutated
and a is the firing angle of SCR. If a < 90", the converter works as a
converter mode (charging mode). If a > 90", the converter then
works as an inverter mode (discharging mode) [ 171. Real power
can be absorbed from or delivered to the power system by controlling
the sequential firing angle of thyristors [ 151. In order t o effectly
control the power balance of the synchronous generator during
dynamic period, the SMES is located at generator terminal bus [ 171.
The current and voltage of superconducting inductor are related
by
where ISM^ is the initial current of inductor.
absorbed or delivered by the SMES unit then is
pSM = VSM ISM
The real power
(9)
If VSM is positive, power is transfered from the power system to the
SMES unit. While if the VSM is negative, power is released from
the SMES unit. The energy stored in the superconducting inductor is
where Kc is the gain of control loop, and Tdc is the delay time
constant of the control device. Because of constraint of hardward
implementation the voltage and current of the inductor all have
upper limit and lower limit. Since the converter operates in
continuous mode. the umer
_ _ limit of the inductor current is set in
1.38 ISM^ (p.u.),and the lower limit is 0.31 ISM^ (p.u.).The limit of
terminal voltage is i0.438 (P.u.). All the system datas of generator,
exciter, governor system, and SMES unit are given in Appendix.
3. DESIGN OF A PI SMES CONTROLLER USING
MODAL CONTROL THEORY [ 191
In order to enhance the electromechanical mode damping of
synchronous generator, a PI SMES controller is used to control the
inductor terminal voltage as shown in Fig. 5. Although many controllers can be used, the PI controller is sufficient and simplest to provide
two degrees of freedom to control the electromechanical mode in
Table 1 for damping the low frequency oscillation. The parameters of
the PI controller can be determined by using the modal control theory.
At the initial operation point, the linearized differential equations
can be expressed as
X=AX+BU
(12)
where X = [Aw, A 6 , AEFD, AVs , AEA, AE;, M r , Aph, APc,
APm , AVSM 1 T is the state vector, Y = Aw is the output signal, and
U = USM is the control signal. A, B, and C are all constant matrixes.
Pr ,Ph ,and Pc are states of the governor and reheat turbine.
Taking the Laplace transformation of eqs. (1 2) and (13), we have
sX(s) = AX(s)
Y(s) =
c X(s)
+
B U(s)
575
Table 1.
lo
Controller
I
Superconductingmagnetic energy storage unit
control system
I
The control signal from Fig. 5 can be represented by
STW
1+sTw
-217.8
- 41.9
-19.94
-10.23
-0.073+j9.35*
-1.966
-1.742
-4.885
-0.1249
1
U(s) = H(s) Y(s)
=
with SMES but
without PI controiier
with SMES and
PI controller
-217.8
- 41.9
-19.94
-10.23
-0.1929ij9.38*
-1.957
-1.750
-4.884
-0.1249
-38.21
-217.8
- 42.0
-18.28
-11.14
-9.1 ij9.35*
-1.809*j0.3121
-4.74 1
-0.1249
-21.62
-7.642
')Isno
SMES
Fig. 5
System eigenvaluesat Po = 1.O, PF = 0.85
1
I
I
I
* electromechanical mode
(Kp
+ .KI
.- ) Y(s)
S
where Tw is the washout time constant and Kp and KI are the
controller gains to be determined.
It is easy to see that the characteristic equation of the closed
loop control system is [ 191
1 - C (SI - A)-l B H(s) = 0
(17)
In order to examine the control ability of the PI controller at
any other load conditions, the real part of the eigenvalues of the
electromechanical mode is plotted in Fig. 6 for three control schemes.
The stability margins of the system without SMES and with SMES
but without PI controller are Po = 1.05 p.u. and Po = 1.14 p.u.
respectively. While the stability margin of the system with PI
controller is above Po = 1.6 P.u.. The system stability margin is
greatly enlarged by the PI controller.
For any closed loop system eigenvalue A ,
I - C (AI - A)-l B H(A) = 0
or
H(A) = [ C (AI - AT1 Bl-1
-1.1)
X1 ,A2
0-7
0.5
0.3
If AI and A2 are the pair of prespecified eigenvalues for electromechanical mode, we can substitute A1 and A2 into eq. (18) and
obtain a pair of linear algebra equations of Kp and KI. By solving
this pair of linear algebra equations, we can easily obtam the desired
values for Kp and KI.
In this paper, the eigenvalues of the electromechanical mode is
assigned at
0.9
1.1
1.5
1.3
a c t i v e power ( p . ~ )
II
-
,
-6
= -9.1tj9.35
From eq. (18), the PI controller parameters can be determined. They
are
-184 , ,
0.1
0.3
Kp = 45.99
-
,
0.5
,
, , , , , , ,
0.7
0.9
1.1
1.3
,
,
,
1.5
a c t i v e power (p.u)
KI = 376.4
a
It is noted that the prespecified eigenvalues are chosen arbitrarily
according to the expection of the damping of the synchronous
generator. If the parameter values of the PI controller is out of a
suitable range, the assigned eigenvalues must be adjusted until that
the parameter values are located in the suitable range.
4.
,
b
-
t
C
Fig. 6
+
t
s
without SMES
with SMES but without PI controller
with SMES and PI controller
Real part of electromechanical mode eigenvalueunder
various load conditions
EIGENVALUE ANALYSIS
At the initial operation condition, the system eigenvalues are
given in Table 1. When the system is with SMES but without PI
controller, there is little improvement in the damping of the electromechanical mode. The system with SMES but without PI controller
means that the controller is replaced by an unity gain. Of course, the
controller can be other types [ 161. If the PI controller designed in
section 3 is presented, there is great improvement in the damping of
the electromechanical mode as shown in the third column of Table 1.
It is noted that the eigenvalues of this mode are actually the prespecified values. The dynamic performance of the synchronous generator
can be greatly improved by the proposed PI controller.
5. COMPUTER SIMULATION
In order to demostrate the damping effect of the proposed PI
controller, computer simulations based on the nonlinear differential
equations are taken at various load conditions. All the nonlinearities
such as exciter ceiling voltage limit and voltage limit of the inductor
must be considered. Two types of system disturbances are tested.
Fig. 7 shows the system responses when there is a 0.01 p.u. 4
cycles load change. That is a small disturbance, and so the speed
oscillation curves certify the damping characteristics of the electromechanical mode as given in Table 1. Next we examine the dynamic
performances when there is a large disturbance. A 4 cycles three phase
576
7 1.0001
4
-
2 1.0001
1.0
4
1.0
Y
0.9999
30.9999
.
0.999sl
.
0
.
0.9998'
2
4
time (sec)
'
___
1.0002
.
- -?
-
,-_____-
1.0
-
&n - 0 . 0 1
a
r
0.01
0.0
-0.018
0.98
4
2
0
4
2
0
time (sec)
7(b) with SMES but
without PI controller
- 7
0 . 0 1 8 ~ - - - - -
0.99
time (sec)
7(a) without SMES
?
-
1.02
1.01
4
time (sec)
9(a) Po = 1.0, p.f = 0.85
- -~
1.02-
1.0001
b
Fig. 7 Dynamic responses
l.o~-~
0.9999
0.9998
0
2
under small
disturbance
4
0.98
1-L
2
0
time (sec)
7(c) with SMES and PI controller
1.02
1 1.01
4
1.0
3
0.99
0.98
2
4
1.0
3
0.99
0.98
4
time (sec)
0
2
4
1
time (sec)
8(a) Po = 1.O, P.f = 0.85
8(b) Po = 1.2, p.f= 0.85
-
1.02
I
o
.
0
1
,
8
j
v
0.98
1 - - d
0
-0.018i-
a
d,
1.02 7-
Fig. 9
Dynamic respanses under three phase short circuit with SMES but without PI controller
6 . CONCLUSION
In this paper, the superconducting magnetic energy storage
(SMES) unit with a proportional-integral (PI) controller is proposed
to enchance the damping of the synchronous generator. A systematic
approach based on the modal control theory is used to determine the
gain values of the PI controller by shifting the electromechanical mode
to the prespecified position. Eigenvalues analysis and computer
simulation results show that the damping effect of the SMES with PI
controller is excellent. The dynamic performance of the generator
can be greatly improved and the stability margin can be expanded.
Although the PI controller is design at a special load condition, it
can also provide good damping effect at other load conditions.
Application of the SMES t o increase the damping of the multimachine power system can be suggested for later study. The effect
of reactive power input/output of the SMES can also be considered.
But this needs a different system model and is currently under study.
Although the BPA has built a 30 MJ unit, the commercial devices
are still not currently available. The cost of a practical SMES unit is
unknown, but would more expensive than other damping devices,
such as PSS and SVC. The stability improvement must be an
additional benefit from the SMES but not the only one, since the
unit should be used for load leveling and load management.
6
Y
1.0
3
0.99
I
0.98j---
time (sec)
8(c) Po = 0.8, P.f = 0.85
Fig. 8 Dynamic responses
under three phase
short circuit-without
SMES
time (sec)
9(c) Po = 0.8, p.f = 0.85
w
I
1.01
-----A
4
2
time (sec)
7.
-
4
9(b) Po = 1.2, p.f = 0.85
fault is occurred at the transmission line near the infinite bus. The
system responses when there is no SMES are plotted in Fig. 8 for
three different load conditions. There is almost no damping at the
initial load condition P = 1. At Po = 1.2, the system is unstable.
Also the damping at Po"= 0.8 is not good enough. Fig. 9 shows the
system responses when there is with SMES but without PI controller.
The damping of the generator system is only a little improved, but
at Po = 1.2, the system is still unstable. The system responses when
there is with SMES and the proposed PI controller designed in the
previous section are shown in Fig. 10. Several observations can be
obtained from Fig. 10:
The damping of the synchronous generator can be greatly
improved by the SMES with PI controller.
From Fig. 10(b), the stability margin is expanded by the PI
controller.
During the dynamic period, the SMES unit draws power from
the generator output bus or releasesit to the bus. The power
delivery limit is constrained by the converter voltage rating, and
the size of the SMES unit. The SMES may allow the power
delivery to saturate during the transient period as shown in Fig.
10, but still provide excellent damping for dynamic period. The
power rating is chosen according to the size of generator and
types of disturbance [201.
The energy stored in the coil is always less than 6 MJ, the
energy rating of the superconducting inductor.
Although the PI controller is designed at a special operation
point, it also can provide good damping effect at other load
conditions. The controller is low sensitive to the system load.
-
2
0
4
time (sec)
E'
E&
VS
USM
V-k
d'
Vq
NOMENCLATURE
angular speed
torque angle
d-axis transient voltage
q-axis transient voltage
field voltage
stabilizing transformer output voltage
SMES controller output
infinite bus voltage
d-axis terminal voltage
q-axis terminal voltage
0.99
,--
0.98
-
r
2
0
6
0.0
-0.2
-0.3
0
2
-0.5
-1
2
0
4
time (sec)
time (sec)
3.99
4
1
0
time (sec)
--
2
---
’
___..
-I
4
time (sec)
a
::::k------i
3
0.99
1O(a) Po = 1.0, p.f= 0.85
a
-
f
z!k------]
1.0
transient reactance of d-axis stator winding
synchronous reactance of d-axis stator winding
synchronous reactance of q-axis stator winding
d-axis transient open circuit time constant
q-axis transient open circuit time constant
stator resistance
moment constant
damping constant
regulator gain
regulator time constant
stabilizing transformer gain
stabilizingtransformer time constant
current of superconducting inductor
voltage of superconducting inductor
power transfered to SMES
energy storage in SMES
gain of SMES control loop
time constant of control loop
washout time constant
8.
REFERENCES
(1) P.M. Anderson and A.A. Fouad, Power System Control and
Stability, Iowa State University Press, Ames, Iowa, 1977.
(2) E.V. Larsen and D.A. Swann, “Applying Power System
0.98
._-,
.
.
-0.3
- . _ - - ~
Stabilizers”, IEEE Transactions on Power Apparatus and
0
2
0
2
4
4
time (sec)
time (sec)
Systems, Vol. PAS-100, pp. 3017-3046, 1981.
(3) O.P. Malik, G.S. Hope, S . J. Cheng, and G. Hancock, “A multiMicro-Computer Based Dud-rate Self-tuning Stabilizer”, Paper
0.5,
4.01 r
86JPGC 652-2, Presented at the IEEEPES 1986 Joint Power
Generation Conference, Portland, Oregon.
(4) F.P. DeMello and C. Concordia, “Concepts of Synchronous
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Transactions on Power Apparatus and System, Vol. PAS-88,
pp. 316329,1969.
0
2
4
0
2
4
(5) Y.Y. Hsu and C.Y. Hsu, “Design of A Proportional-Integral
time (sec)
time (sec)
Power System Stabilizer’: IEEE Transactionson Power Systems,
PWRS, Vol. 1, NO. 2, pp. 46-53.
10(b) Po= 1.2, p.f= 0.85
(6) D.C. Lee, R.E. Beaulieu and J.R.R. Sewice, “A Power System
Stabilizer Using Speed and Electrical Power InputsiDesign and
Field Experience”, IEEE Transactions on Power Apparatus
and Systems, Vol. PAS-100, No. 9, pp. 41514157, 1981.
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Data Automatic Generation Control Analysis with Reheat
Steam Turbines and Governor Dead-Band Effect,” IEEE
Transaction on Power Apparatus and System, Vol. PAS-103,
~.gal
*
*
1
- 0 . 3 1 -______pp. 1045-1051, 1984.
0
2
4
0
2
4
(8) A.J. Ramos and H. Tyll, “Dynamic Performance of A Radial
time (sec)
time (sec)
Weak Power System with Multiple Static VAR Compensator”,
89 WM 183-5, PWRS.
(9) M. O’Briem and G. Ledwich, “Static Reactive Power Compensation Controls for Improved System Stability,” IEE Proceeding,
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(10) H. Stemmeler and G. Guth, “The Thyristor Controlled Static
Phase-Shifter-A New Tool for Power Flow Control in AC
3.99 1
Transmission System,” Brown Boveri Review, Vol. 69, pp. 730
2
4
2
i 1
78, 1982.
time (sec)
time (sec)
(1 1) J.D. Rogers, R.I. Schermer, B.L. Miller, and J.F. Hauer, “30
MJ Super-conducting Magnetic Energy Storage System for
1O(c) po = 0.8, p.f = 0 85
Electric Utility Transmission Stabilization”, Proceeding of
IEEE, Vol. 71, NO. 9, pp. 1099-1107,1983.
Fig. 10 Dynamic responses under three phase short circuit(12) H.J. Boening and J.F. Hauer, “Commissioning Tests of The
with SMES and PI controller
Bnneville Power Administration 30 MJ Superconducting
Magnetic Energy Storage Unit”, IEEE Transactions on Power
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(13) T. Ise, Y. Murakami and K. Tsuji, “Simutaneous Active and
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terminal voltage
Vt
Storage Using GTO Converter”, IEEE Transaction on PD,
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PO
Vol. PWRD-1, NO. 1, Pp. 143-150,1986.
power factor
P. f
(14) J.E.C. Williams, “Super-conducting Magnets and Their ApplicaWO
rated angular speed
tions’’, Proceeding of IEEE, Vol. 77, No. 8, pp. 1132-1141,
Le
line reactance
1989.
Re
line resistance
(1 5) L. H. Walker, “Forced-Commutated Reactive-Power Compensator”, IEEE Transactions on Industry Applications, Vol. IA-
-
a
-0.2
---- .
~
.- -.
r
----
22, NO. 6, pp. 1091-1104, 1986.
S. Banerjee, J.K. Chatterjee, and S.C. Tripathy, “Application of
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APPENDIX
SYSTEM PARAMETERS [ 1,161
Generator and transmission line
Rated 160 MVA
Excitation Voltage 375 V
Power 1 .O p.u.
Rated Voltage 15 KV
Field Current 926 A
Power Factor 0.85
Xi
Mg
Dg
T;o
Ra
xd
Xq
TAo
=
=
=
=
0.001096
1.70
1.64
5.9 s
Le
=
0.400
=
=
=
=
0.245
4.74
0
0.075 s
Re = 0.020
exciter
KAE = 400
KF = 0.025s
TAE = 0.05s
TF = 1.0s
governor
KG = 3.5
TRH = 8 s
TSM = 0 2 s
TCH = 0.05s
TSR = 0.1 s
KRH = 0.3
SMES unit
ISM^ =
Ld
Kc
Tw
0.6495
= OS H
= 1.83
= 0.125s
Chi-Jui Wu (M39) received the B.S.,
M.S., and Ph.D. degree in electrical engineering from National Taiwan University in 1983,
1985, and 1988 respectively. Now he is
an associated professor in Department of
Electrical Engineering, National Taiwan Institute of Technology. His current research
interests lie m dynamic control of synchronous
generator, static Var compensator, power
system simulator, and direct load control.
‘SMo
Tdc
=
= 0.026s
Yuang-Shung Lee was born in Taiwan,
Republic of China, on January 2, 1950. He
received his B.Sc. and M.Sc. degrees from the
National Taiwan Normal University and
National Taiwan Institute of Technology, in
1974 and 1983, respectively. Since 1986,
he has been with the Department of Electronic
Engineering, Fu Jen University, Taipei, Taiwan,
Presently he is pursuing the Ph.D. degree.
His current research interest is on the
dynamic stability analysis and control of
electrical power systems.