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Nazrul Islam, Rizvy Ahmed

Factors influencing the development of women entrepreneurship in Bangladesh

M. G. Rabbani, R. I. Sheikh

  Damping of Power System Subsynchronous  Oscillation Using 
Superconducting Magnetic Energy Storage Unit 
 
M. G. Rabbani         R. I. Sheikh  
Department of Electrical & Electronic Engineering 
B.I.T. Rajshahi,   Bangladesh - 6204 
 
Abstarct - A novel strategy to damp the torsional 
oscillations due to subsynchronous resonance (SSR) of a 
capacitor compensated power system through control of 
firing angles of Superconducting Magnetic Energy Storage 
(SMES) unit is presented in this paper.  The gain of the 
SMES controller is generated on-line depending on the 
operating conditions and the type of the disturbance. The 
proposed method of control of SMES unit for power 
system stabilization has been tested on the IEEE first 
benchmark model for subsynchronous resonance studies. 
Dynamic simulations are performed using the non-linear 
system model. It has been found that the SMES unit is 
very effective to eliminate the slowly growing transients 
resulting from the unstable modes. 
 
Keywords: SSR, Energy Storage, SMES                                                                                                                                                                                                                                                                           
 
1. INTRODUCTION 
 
     Series capacitor compensation is a commonly used 
technique to raise the power transfer capability of high 
voltage long transmission lines of a power system, to 
economically acceptable levels. This also has the added 
advantage of keeping the line regulation within tolerable 
margins. However, one major drawback of such capacitor 
compensation is that such systems are prone to 
Subsynchronous Resonance(SSR). This occurs when the 
subsynchronous frequency of the electrical components  
(such as transmission lines, series capacitors, transformers 
and generators) are close to the one of the natural torsional 
frequencies of the mechanical components of the 
turbogenerators. During any system disturbance, such as 
line switching or load change, transient currents of sub-
harmonic frequency are excited and this eventually leads 
to large electromechanical oscillations which often result 
in generator tripping, system separation and in some cases, 
mechanical failure of the machine shafts. Even in cases 
where there is no mechanical failure, the severe stresses 
induced by the excessively large torques of high frequency 
invariably reduces shaft life due to mechanical fatigue [1]. 
     Ever since the two shaft failures in the Mojave 
generating station in 1970 and 1971, the subsynchronous 
resonance problem has received much attention and the 
IEEE (SSR) working group has proposed countermeasures  
such as static and dynamic filters and special excitation 
system dampers, to prevent or alleviate the problems 
caused by SSR [2-4]. Since the torsional oscillations are 
caused by the undesirable component of exchange of 
energy between the electromechanical turbogenerator 
system and the electrodynamic  power system, energy 
storage devices are good candidates for the solution of this 
problem. Recent developments in Superconductive 
technology have resulted in the use of large 
Superconducting electromagnets as a competitive alternate 
means for storage of electrical energy, comparable to that 
of storage batteries, fly wheels and fuel cells. In addition 
to load leveling, such systems can be used for power 
system stabilization as well. Since the successful 
commissioning of a SMES unit of substantial size in 1985, 
the application of SMES unit for SSR elimination has 
generated much interest in recent years.  
     Superconducting magnetic energy storage systems have 
the capability of storing energy in their low resistance 
coils. The energy can be transferred to or /from the system 
according to the system requirements. The amount of 
energy supplied or received by it can be controlled by 
controlling the firing angles of the converters in the SMES 
unit. A number of articles have been reported 
demonstrating the use of SMES unit for power system 
transient stability, dynamic stability, load frequency 
control and stabilizing transmission lines [5,6].
Applications of SMES to damp SSR have been reported 
recently to the IEEE first and second benchmark 
models[7-9]. 
     In this paper, a novel idea of controlling the SMES 
compensating power to damp subsynchronous oscillation 
in power system is presented. The gain of the SMES 
controller is decided on-line depending on the type of the 
disturbance and the rating of the SMES unit. The required 
SMES voltage is derived from the power and once the 
SMES voltage is determined, the corresponding  firing 
angles of the converters can be calculated  by using the 
sensed SMES current. Direct generation of the 
compensating power from the SMES unit makes the 
control strategy very effective in controlling the 
uncontrolled subsynchronous modes.  
  
2. SYSTEM MODELLING 
 
     The studied system considered in this paper is the IEEE 
first benchmark model [3], which consists of a 
turbogenerator connected to the infinite bus through a 
capacitor compensated transmission line as shown in 
Fig.1. The superconducting magnetic energy storage unit 
is located at the generator bus terminal to  increase the 
damping of the SSR modes. The dynamic behavior of the 
generator is described by the non-linear full current model 
[1,2]. Combining the mass-spring system, armature and 
field windings, excitation system, governor system, and 
the capacitor compensated transmission line, a set of 27 
order non-linear differential equations for the system 
without SMES can be obtained.  All the state equations 
can be found in [1] The mass-spring system contains six 
bodies such as the high-pressure turbine (HP), the 
medium-pressure-turbine (IP), the two low-pressure 
turbines (LPA and LPB), the generator (GEN), and the 
exciter(EXC), are all coupled on the same shaft. 
     Fig. 2 shows the configuration of SMES unit. It 
consists of a dc superconducting inductor, a 12-pulse 
cascaded bridge type AC/DC converter and an Y-D / Y-Y 
 
Second International Conference on Electrical and Computer Engineering 
ICECE 2002, 26-28 December 2002, Dhaka, Bangladesh 
ISBN 984-32-0328-3 32
                              itd,itq 
          R11=0.02    X11=0.5 
         id , iq               Y-          FILTER        A    R10=0.5      X10=1.5           B                   V 
                                                                           XC 
            
               gap 
          GEN.                XT,RT                                                                                                 X11=0.06 
X11=0.06 
                Psm  
                                          Qsm                      XF                              XF 
                                 SMES 
 
                                        Fig. 1    IEEE First Benchmark Model for SSR 
 
step down transformer. Control of the converter firing 
angle enables the dc voltage Vsm appearing across the 
inductor to be continuously varied between a wide range 
of positive and negative values. Gate turn off thyristors 
(GTO) allow us to design such type of converter. The 
converter output current Ism being unidirectional, the 
control for the direction of the inductor power flow Psm, is 
achieved by continuously regulating the firing angle a. 
     For initial charging of the SMES unit, the bridge 
voltage Vsm is held constant at a suitable positive value 
depending on the desired charging period. The inductor 
current Ism rises exponentially and magnetic energy Wsm is 
stored in the inductor. When the inductor current reaches 
its rated value Ism0 , it is maintained by lowering the voltage 
across the inductor to zero. The SMES unit is then ready to 
be coupled with the power system for torsional oscillation 
stabilization. 
     Due to sudden application or rejection of load, the 
generator speed fluctuates. When the system load 
increases, the speed falls at the first instant, but due to the 
governor action, the speed oscillates around the reference 
value. The converter works as an inverter (90°<a<180°) 
when the actual speed is less than the reference speed and 
energy is withdrawn from the SMES unit (Psm negative). 
However the energy is recovered  when the speed swings 
to the other side. The converter then works as a rectifier 
(0°<a<90°) and the power Psm becomes positive [6]. The 
current and voltage of superconducting inductor are related  
as 
            ò t=
t
0t
sm0sm
sm
sm I+dV
L
1
I                                                 
where Ism0  is the initial current of the inductor. The real 
power absorbed or delivered by the SMES unit is 
           Psm = Vsm Ism             
                                 
 
 
 
 
 
                                                                             Vsm 
 
 
 
 
Fig. 2    SMES configuration 
 
If Vsm is positive, power is transferred from power system 
to the SMES unit. Whereas, if Vsm is negative, power is 
released from the SMES unit. The energy stored in the 
superconducting inductor is  
          ò t+=
t
0t
smsm0sm dPWW  
  where 2smsmsm0 IL2
1
W =  is the initial energy in the 
inductor. 
Because of the constraint of  hardware implementation, the 
current of the inductor has upper and lower limits. As the 
converter operates in continuous mode, the upper limit of 
the inductor is 1.38Ism0 , and the lower limit is 0.3Ism0 . The 
limits of the terminal voltage are ± 0.2532(p.u.) [7]. 
 
3. THE PROPOSED CONTROL SCHEME FOR 
THE SMES UNIT  
 
     The basic structure of the proposed SMES controller 
used in this study is shown in Fig. 2. Using the knowledge 
gained fro m experience, generator speed deviation (Dw) is 
considered as the input signal to the SMES controller. The 
required SMES power Psm can be determined as 
  wD
+
=
dc
sm
sm sT1
K
P                                                                
where Ksm is the gain of the controller and Tdc is the delay 
time. The SMES voltage Vsm is then calculated from Psm 
and the sensed current Ism. If the magnitude of Vsm  lies 
beyond Vsm,max in the rectifier mode or in the inverter 
mode, the actual Vsm  is set equal to the corresponding 
limiting value. In such a case, the Vsm settling signal along 
with this sensed Ism signal gives the active power required 
to flow through the converter. To determine gain of the 
controller, the following steps are performed. 
1. Bring the studied power system to the verge of 
instability by simulating it with a significantly large 
disturbance. Determine  the maximum deviations  
Dwmax  and maximum derivative maxwD &   in the 
presence of  SMES unit. Obtain the ratio 
maxmaxb /K wDwD= & . In the present analysis, the  
value of the constant  Kb  is found to be 0.034  and it 
has to be determined once off-line 
2. From the first few samples of Dw, calculate the 
derivative wD &  on-line for a particular operating 
condition. and then update the value of wD & , if  and 
only if  | wD &  | > maxwD & .  It is necessary because the
33
  
                                                                                                                      Ism0  
                                                                                                                               + 
              w  +                                          P¢sm                       Vsm                           +             Ism                 Psm 
 
 
                    wref 
 
                                                       Fig. 3  SMES Controller       
 
free responses of the system to a transient disturbance may 
converge to steady state  through mixed modes of 
behavior, i.e. damped and. undamped. Once the system 
enters into a consistent damped mode wD &  becomes fixed. 
3. Determine the gain of the SMES controller as follows: 
    
maxb
max,smmaxsm,
sm K
IV
K
wD
=
&
   
where Vsm,max and Ism,max are the maximum limits of 
converter dc voltage and inductor current for a particular 
SMES unit. The value of Ksm is not fixed but is adapted 
depending on the operating condition and disturbance 
 
4.    COMPUTER SIMULATION AND  PERFORM - 
       ANCE EVALUATION 
 
     Digital simulations on the non-linear dynamic model of 
the system are performed under the MATLAB 
environment in order to highlight  the damping effect of 
the SMES unit with the proposed controller. All the 
nonlinearities such as exciter  voltage limit and the current 
limit of the superconducting inductor are also included. To 
show the performance of the SMES unit a 100 ms,  0.15 
p.u. step change in torque with initial operating condition, 
P0 = 1.0 p.u. and  XC/XL = 0.5  is considered  as the 
disturbance. Table 1 lists the eigenvalues of different 
modes of torsional oscillations without SMES unit. It can 
be observed that in mode 3 and mode 4, positive real parts 
of the eigenvalues appear which pose a threat to the 
stability of the system without SMES unit. This point can 
be further proved from the dynamic analysis of the system. 
Fig. 4 clearly indicates that the system without the SMES 
unit is unstable as expected. However the addition of the 
SMES unit has improved the situation. It  is worthwhile to 
mentioned that the SMES unit with the proposed controller 
damps out subsynchronous oscillations. 
 
Eigenvalues of different modes of torsional oscillations 
P0 =1.0 p.u.  XC /XL = 0.5 
Modes Eigenvalues 
mode 5: - 0.1817 ± 298.180 
mode 4:   0.3798 ±  202.796 
mode 3:   0.8380 ±  162.509 
mode 2:   0.7432 ±  127.093 
mode 1: - 0.7633 ±  99.581 
mode 0:  - 0.8752 ±  10.441 
 
      Fig. 4 shows the system performance with and without 
the SMES unit following the disturbance. The system 
oscillations are growing up and after 5 secs., the system
 
            Without SMES                                With SMES 
Fig. 4  System performances with and without  SMES unit 
dc
sm
sT1
K
+ smI
1
smsL
1
34
 becomes unstable.  These growing oscillations may lead 
to series shaft failure. A well controlled SMES unit can 
easily counter these problems. It is observed in the figure 
that the SMES unit suppresses all such oscillations and 
the system stabilizes within 0.6sec. The maximum 
deviation of the speed and rotor angles also decreases. It 
is also evident from the figure that the third peak has 
almost diminished with the addition of SMES unit. It is 
also evident from the figure that the third peak has 
almost diminished with the addition of SMES unit. These 
improved responses are achieved due to the following 
reasons: 
 
1. The compensating power is obtained  directly which 
makes the controller more sensitive to the 
disturbance. 
2.  The gain of  the controller is adapted according to 
the  grade of the disturbance. 
     In the present paper, reactive power modulation is  not 
utilized which is an additional benefit for stabilization. 
This is currently under investigation. 
 
6. CONCLUSIONS 
 
     A method of controlling the unstable modes arising 
from the subsynchronous resonance phenomenon 
through control of the power of the SMES unit is 
presented. The control strategy is derived from a simple 
principle that the SMES unit should receive or deliver 
power according to the degree of disturbance. The gain 
of the controller is therefore adapted that makes the 
controller more effective. The unstable synchronous 
modes due to series capacitor compensation are 
cancelled by the appropriate transfer of compensating 
power as is evidenced in the results. The proposed 
controller for the SMES unit is equally effective for any 
degree of disturbance. Transient responses show that the 
subsynchronous oscillations are removed in less than one 
second. This indicates that long transmission links with 
series capacitor  compensation can be reliably operated if 
equipped with proper SMES control circuitry. 
 
 
REFERENCES 
 
[1] Y. N. Yu, “Electric Power System dynamics”,  
[2] IEEE SSR Working Group, “Third Supplement to a 
Biography for the Study of Subsynchronous 
Resonance between the Rotating Machines and 
Power Systems”, IEEE Trans. on Power Systems, 
Vol. PWRS-6 pp. 830-834, 1991. 
[3] IEEE committee, “ First Benchmark Model for 
Computer Simulation of Subsynchronous 
Resonance” IEEE Trans. on Power Apparatus and 
Systems, Vol. PAS-96, pp. 1565-1572, 1977. 
[4] Li Wang and Y. Hsu, “ Damping of Subsynchronous 
Oscillations Using Excitation Controllers and Static 
Var Compensators”, IEEE Trans. on Energy 
conversion, Vol. 3, pp. 6-13, 1988. 
[5] C. J. Wu and Y. S. Lee, “ Application of 
Superconducting Magnetic Energy Storage Unit to 
improve damping of Synchronous Generator”, IEEE 
Trans. on Energy Conversion, Vol. 6, pp. 573-578, 
1991. 
[6] S. Banerjee, J. K. Chatterjee and S.C. Tripathy, “ 
Application of Magnetic energy Storage Unit as 
Load Frequency Stabilizer”, IEEE Trans. on Energy 
Conversion, Vol. 5, pp. 46-51, 1990. 
[7] Y. S. Lee and C. J. Wu, “Application of 
Superconducting Magnetic Energy Storage Unit on 
Damping of Turbogenerator Subsynchronous 
Oscillation”, IEE Proceedings-C, Vol. 138, pp. 419-
426, 1991. 
[8] L. Wang, S. Lee and C. Huang, “Damping 
Subsynchronous Resonance Using Superconducting 
Magnetic Energy storage Unit”, IEEE Trans on 
Energy Conversion, Vol. 9, pp. 770-777, 1994. 
[9] A. H. Rahim, A.M. Mohammad and M. R. Khan, 
“Control of Subsynchronous Resonant Modes in a 
Series Compensated System Through 
Superconducting Magnetic Energy Storage Units”, 
IEEE Trans. on Energy Conversion, Vol. 11, pp. 
175-180, March 1996. 
 
 
APPENDIX 
 
The system data used are as follows [1,6,7] 
 
Mass-spring system:  
MH = 0.185794 sec.    DH = 0.1 p.u.          KHI = 19.303 
MI = 0.311178 sec.     DI = 0.1 p.u.           KIA = 34.929 
MA = 0.185794 sec.    DA = 0.1 p.u.          KAB = 19.303 
MB = 0.185794 sec.    DB = 0.1 p.u.          KBG = 19.303 
MG = 0.185794 sec.    DG = 0.1 p.u.          KGX = 19.303 
MX = 0.185794 sec.    DX = 0.1 p.u.                             
 
Turbine and governor 
FH = 0.30          TCH = 0.3 sec.                 KG = 25 
FI = 0.26           TRH = 7.0 sec.                 TSR = 0.2 sec. 
FA = 0.22          TCO = 0.2 sec.                            
FB = 0.22          TSM = 0.3 sec 
 
Transformer and transmission line 
RT  = 0.01 p.u.            RL = 0.02 p.u.  
XT = 0.14 p.u.            XL = 0.56 p.u 
 
Synchronous generator (p.u.) 
Xd = 1.790   Xq = 1.710       Xfd = 1.700 
Xkd = 1.666   Xfq = 1.695      Xkq = 1.825 
Xad = 1.660   Xaq = 1.580       Ra  =  0.0015 
Rfd  =  0.001                    Rkd  =  0.0037 
Rkq  =  0.00182                Rfq  =  0.0053 
 
Exciter and voltage regulator 
KAE = 50                    TAE = 0.01 sec 
KF   = 0.5                    TF   =  0.5 sec. 
 
SMES unit 
Ismo  = 0.2018 p.u.    Vsmo  = 0.2532 p.u.  
Lsm = 0.5 H              Tdc = 0.026 sec.       Wsmo =  4.0 MJ 
 
The initial operating conditions 
Po = 1.0 p.u.       Vt = 1.05 p.u.               P.F. = 0.9 lag       
 
 
 35


Damping of power system sub synchronous oscillation using superconducting magnetic energy storage unit

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