2009 COMPATIBILITY AND POWER ELECTRONICS 196 On Control … · On Control of Gate Controlled Series Capacitor for SSR and Power Oscillation Damping ... (GCSC) are presented. The ...

On Control of Gate Controlled Series Capacitor for SSR and Power Oscillation Damping

Hossein Ali Mohammadpour1, Mohammad Reza Alizadeh Pahlavani1, Abbas Shoulaie1

1 Power Electronic Research Lab (PERL), Iran University of Science and Technology (Tehran, Iran) [email protected], [email protected], [email protected]

Abstract- The subsynchronous resonance (SSR) phenomenon

may occur when a steam turbine-generator is connected to a long transmission line with series compensation. In this paper, to mitigate SSR, two control methodologies for turn-off angle control of the gate-controlled series capacitor (GCSC) are presented. The first methodology is an open-loop control that uses the line current frequency oscillations to generate proper turn-ff angle for the GCSC. The second one is a closed loop control that is based on the Takagi-Sugeno (TS) fuzzy logic controller. The study system was modified from the IEEE First Benchmark Model by changing a part of the fixed series capacitor to the GCSC. The MATLAB® program was used to verify the effectiveness of each control methodology. Three different GCSC ratings were analyzed. It is shown that using an open-loop control methodology, in some GCSC ratings, the SSR can be properly damped. It is also shown that using TS fuzzy control methodology, not only SSR but also electromechanical power oscillation can be effectively damped.

I. INTRODUCTION

ERIES capacitive compensation is a useful and economical technique to improve the power transfer capability of

transmission lines. However, when this technique is applied together with a steam turbine-generator, it may lead to subsyn-chronous resonance (SSR) phenomenon. SSR problems result from the interaction between an electrical mode of the series compensated network and a mechanical shaft mode of a turbine-generator group that this may generate oscillating torsi-onal torques.

In general, if series flexible ac transmission system (FACTS) devices be used, it would be possible to say that the advantages of the series compensation can be guaranteed without risks of SSR phenomenon.The gate-controlled series capacitor (GCSC) is a new series FACTS device proposed initially for series co-mpensation of transmission line to control power flow [1], [2]. In [3], it was shown that the GCSC, when compared to the TCSC, presents a series of advantages. Naturally, when it is compared to the more sophisticated and expensive SSSC, the GCSC has less flexibility. On the other hand, it has the key advantage of being a much simpler devise [4]. Turn-off angle control of the GCSC for the SSR damping was given in [4]-[6]. In these references, it was shown that if a proper controller be designed for the GCSC, this device can effectively mitigate the SSR and can properly stabilize the system.

Following the SSR in power systems, the line current frequency will oscillate. Considering this fact, in this paper, firstly, an open-loop control methodology is presented. This control methodology detects these oscillations and changes the

turn-off angle of the GCSC in such a way that makes the GCSC able to damp SSR. The advantage of this control meth-odology is its simplicity. It also shows the ability of GCSC in SSR mitigation even with an open-loop control methodology. But in this control methodology, larger ratings of GCSC should be used to mitigate SSR, resulting in a high cost configuration for the GCSC.

Recently, fuzzy logic controllers have generated a great deal of interest in various applications and have been introduced in the power electronics field [7]–[10]. The advantages of fuzzy logic controllers over the conventional PI controller are that they do not need an accurate mathematical model; they can work with imprecise inputs, can handle nonlinearity, and may be more robust than the conventional PI controller. The TS fuzzy controller may have an edge over the Mamdani-type fuzzy controller given in the following that persuaded the authors to use this kind of fuzzy controller to control the GCSC turn-off angle [11]:

1) Numbers of fuzzy sets used for input fuzzification; 2) Number of rules to be used; 3) Number of coefficients to be optimized; 4) Computation time. Consequently, considering these views, as a second work in

this paper, a Takagi-Sugeno (TS) fuzzy logic controller is pre-sented to control the turn-off angle of the GCSC. As per the author’s knowledge, no significant work has been reported where the Takagi–Sugeno (TS) fuzzy control scheme has been used for GCSC. It is shown that using this control methodolo-gy, the SSR as well as power oscillation can be properly dam-ped in all GCSC ratings. Note that for the analysis presented in this paper, three GCSCs with different ratings were considered. Also, the IEEE First Benchmark Model [12] for the analysis of the SSR phenomenon was adopted, including a GCSC device, and the electrical and mechanical systems were modeled using MATLAB®/SIMULINK. The parameters used for simulation are given in this reference [12].

II. INVESTIGATED SYSTEM

For SSR analysis, the IEEE First Benchmark Model is adopted, depicted in Fig. 1. An 892.4 MVA synchronous generator is connected to infinite bus via a 500 kV compen-sated transmission line. The mechanical system consists of a four-stage steam turbine, the generator and a rotating exciter. In this model, the generator consists of two damper windings in the q axis and one damper and a field winding in the d axis. The mechanical system was represented by a multi-mass tand-

S long

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Fig. 1. IEEE First Benchmark Model.

Fig. 2. Decrement factors of the studied system as a function of the series compensation level.

em-compound system, with six lumped masses coupled by shaft sections. The transmission line was represented by a resistance, a reactance and a series fixed capacitive compensa-tion Xfc . The complete mechanical and electrical data for the studied system are presented in [12].

III. EIGENVALUE ANALYSIS

For dynamic characteristics assessment of the system, the eigenvalues are obtained by M-file in MATLAB® as follows:

oscjωσλ += (1)

whereσ is decrement factor and oscπfosc 2=ϖ is the frequency of oscillation.

Fig. 2 depicts the decrement factor of SSR modes of the system as a function of the series compensation level. As seen in this figure, the system has four unstable torsional modes. Whenever the subsynchronous electrical mode nears or coincides with one of the unstable mechanical modes, a torsional interaction between the mechanical and electrical system occurs. Above a certain level of compensation, the system experiences an electrical self excitation. The results in Table I show the torsional mode of oscillation of the system with the corresponding frequencies and also the value of the series capacitive reactance that, if used, would excite the corresponding mode.

IV. FIXED SERIES COMPENSATION

The system was tuned to the torsional mode 1, based on Table I, and then was simulated using MATLAB®/ SIMULINK. To excite the torsional modes of the system, a three phase fault was applied at point B (see in Fig.1) at t=2 s.

TABLE I FREQUENCY OF OSCILLATION AND CAPACITIVE REACTANCE FOR THE MAXIMUM

TORSIONAL INTERACTIONS

)( puXfc Frequency (Hz) Mode

0.472 15.72 Torsional 1 0.378 20.41 Torsional 2 0.285 25.55 Torsional 3 0.164 32.29 Torsional 4 0.609 9.70 Self excitation

- 0.5-2.5 Electromechanical

Fig. 3. Electric torque response with fixed series compensation.

Fig. 4. Shaft Torque on HP-IP.

Fig. 3 shows the unstable electric torque of the system. The zoom of the electric torque response shows that the main oscillation occurs at around 15.75 Hz that is the frequency of oscillation of the torsional mode 1, as given in Table I. In fact, this is the pulsating torque that excites significant torsional oscillations of the rotor. Hence, the induced voltages and currents will grow with the growing rotor oscillations. This ultimately will result in excessive mechanical shaft torques that one of them is depicted in Fig. 4.

V. THE GATE CONTROLLED SERIES CAPACITOR

The GCSC is composed of two anti-parallel gate-controlled switches and a capacitor bank in series with the transmission line as shown by the single line diagram in Fig. 5. The principle of operation of the GCSC [1]-[3] is based on the variation of the turn-off angle ( γ ) of the gate-controlled switches. By controlling the turn-off angle ( γ ), the voltage on the capacitor is controlled; as a result, the series compensation level of the transmission line can be controlled.

POWER ELECTRONICS CONTROLLERS FOR POWER SYSTEMS 197


Fig. 5. Basic configuration of the GCSC. Fig. 6 shows typical current and voltage waveforms for the

GCSC of Fig. 5, for a given turn-off angle ( γ ). The turn-off angle ( γ ) is measured from the zero crossing of the line current and the compensation level of the GCSC is determined by the fundamental component of the voltage Cv on the GCSC. The relationship between equivalent capacitive reacta-nce

and turn-off angle ( γ ) is given by [6]:

(2) ( ) ( )( )γπγ

πγ 2sin22 −−= CXX

where CX is the reactance of the GCSC capacitor, in Fig. 5.

Fig. 7 shows the nonlinear relationship between the equiva-lent capacitive reactance ( )(γX ) and turn-off angle ( γ ). At the fundamental frequency, the GCSC is equivalent to a continuo-usly variable series capacitor, where its reactance varies from its maximum value (1p.u) for 90=γ to minimum value (0 p.u) for 180=γ .This continuous reactance control of GCSC is one of the advantages of this device over the TCSC [3].

VI. SERIES COMPENSATION WITH GCSC

A GCSC device was substituted for a portion of the fixed series compensation in the IEEE First benchmark model in Fig. 1. Three cases for the proportion of GCSC equivalent reactance ( )(γX ) and fixed capacitor reactance ( fcX ) were considered equal to 1:2 ( CG21 ), 1:1 ( CG11 ), and 2:1 ( CG12 ), as given in Table II. The goal of considering these three cases was to probe the effects of the size of the GCSC on the SSR damping. Two control methodologies for turn-off angle control of the GCSC with the aforementioned cases were conducted, namely:

1) Open loop control of the GCSC based on the line current frequency detection;

2) Closed loop control of the GCSC based on the TS fuzzy controller.

For this study, the total capacitive series compensation was made equal to 0.472 p.u. to excite the SSR at mode 1, as given in Table I, and efficiency of each control methodology with several small and large disturbance test were investigated.

To determine the steady state GCSC equivalent reactance based on Table II, depending on the size of it’s capacitive reac-tance ( CX ) and the turn-off angle ( γ ) as can be verified in (2), there are many different cases. In this study, to increase the maneuverability of the GCSC equivalent reactance, the steady

Fig. 6. GCSC voltage, current, and switch control.

Fig. 7. Equivalent reactance of the GCSC as a function of turn-off angle.

TABLE II COMPANSATION CASES WITH GCSC

)(γX (p.u) Xfc (p.u) Case

0.152 0.318 1G2C 0.236 0.236 1G1C

0.318 0.152 2G1C

state turn-off angle ( γ ) was chosen in such a way that, )(γX is

in the middle of the entire variation range between )90(X and

)180(X as seen in Fig. 7. By this way, the steady state turn-

off angle ( γ ) was calculated 5.113 and then the GCSC equiv-alent reactance can be verified in (2) by setting CX .

VII. OPEN LOOP CONTROL OF THE GCSC BASED ON THE LINE CURRENT FREQUENCY DETECTION

This method is an open loop control system that uses the line current frequency variation for turn-off angle control of the GCSC. Indeed, this method uses the fact that following the SSR, the line current frequency will oscillate. Fig. 8 shows the schematic diagram of the GCSC turn-off angle control based on the line frequency detection. As seen in this figure, this controller includes four blocks, namely, frequency detection block, turn-off angle estimator block, pulse generator block, and decision block. This controller is described at the following.

A. Design of the Controller As seen in Fig. 8 , this controller composed by a “Sign”

block, a “Comparator”, an “Edge” detector, an “Integrator”, a “S/H” block for sampling and holding of the data in the speci-fic times and a “Counter”. In frequency detection block, the

γ



Fig. 8. Turn-off angle generator based on the line current frequency detection.

phase current is fed to the “Sign” block producing a square wave signal B as shown in Fig. 8. Then this square wave is compared with zero to produce signals C and 'C . The signals C and 'C are used to generate pulses G1 and G2, respectively. Here, the pulse generation for G1 is described and for G2 and other gates the way is the same. The “Edge” detector block generates the reset pulse for the integrator that is integrating signal C . Using the S/H block, the maximum value of the integrator output is obtained giving the half period of the line current iT .

In turn-off angle estimator block, for producing turn-off angle from iT , the reverse of this time is related with the turn-off angle by constant parameter M, as given by (3).

.i

i TM=γ

(3)

The constant parameter M for the steady state turn-off angle

( 5.113 ) is obtained by:

( )( ) 120

11801205.113** ×

×=⇒×= MTM γ

(4)

where *γ is the steady state turn-off angle and *T is the half

period of the steady state line current. Finally, to generate final pulse for G1, the produced turn-off

angle is compared with the output of the ‘‘Integrator’’ (E), and when the value of E is greater than the turn-off angle, a signal

Fig. 9. Electric torque in case 1G2C using open-loop control.

Fig. 10. Line current for a very intensive large disturbance for 2G1C.

is produced to reset the counter in pulse generator block, which had been activated by the signal C . The output of the counter is transmitted through a limiter that limits the turn-off angle

between 90 and180 , and then is applied to the switch G1.

Also, in Fig. 8 there is a decision block in which an operation mode selector prepares the ability of putting manual constant turn-off angle.

B. Simulation Results and Discussion The simulation of the system in Fig. 1 with the GCSC and

the aforementioned control method was started with an ideal voltage source and at t=17 ms, the ideal voltage source was substituted by the synchronous generator driven by the turbine. This can be considered as a small disturbance. Then at t=7.5 s, a very intensive short circuit was created by connecting a reactor at point B in Fig. 1 with 75 ms time duration, based on [12]. Fig. 9 shows the electric torque response for the case 1G2C. This figure shows that with this proportion of the GCSC equivalent reactance ( )(γX ) and fixed capacitor reactance ( Xfc ), this method can not damp SSR.

Fig. 10 shows the line current for the case 2G1C for a very large disturbance increasing the line current to about 3 p.u. Also, in Fig. 11, the applied turn-off angle by the open-loop control method to the GCSC for the case 2G1C is shown. This figure shows that ultimately the turn-off angle after fault reaches to its steady state situation ( 5.113 as mentioned before). Fig. 12 shows the electric torque response for the case 1G1C. Also, in Fig. 13, the eclectic torque response is compared for both cases 1G1C and 2G1C. As seen in these figures, the subsynchronous resonance is present at the first 0.35 s; however, the proposed open-loop control method is able



Fig. 11. Applied turn-off angle to the GCSC for a very large disturbance in the case 2G1C using open-loop control.

Fig. 12. Electric torque in case 1G1C using open-loop control.

Fig. 13. Electric torque for both cases 1G1C and 2G1C using open-loop control.

to stabilize the system, damping out this oscillation in the electric torque even for series compensation tuned to excite SSR at mode 1. This result shows how effective is the simple open-loop control methodology proposed here, making stable a system that was otherwise unstable and also shows the ability of the GCSC in SSR damping even without a closed-loop controller. This figure also shows that an electromechanical power oscillation appears in the system at a frequency around 1.25 Hz, as given in Table I, which is also damped; however, damping time of this kind of oscillation is long using this method and takes for about 6.5 s.

From the above discussion, it is concluded that although this method shows the ability of damping SSR by GCSC using open-loop control, this method is not able to damp the SSR in the case 1G2C. However, it would be better if a smaller GCSC could stabilize the system, resulting in a lower-cost config-uration. Besides, although this method is able to damp the SSR in the cases 1G1C and 2G1C, but the time duration of the

electromechanical power oscillation is long and it lasts for about 6.5 s, as seen in Fig 13. At the following, in order to damp the SSR in the case 1G2C and also improvement of the dynamic response of the system for the cases 2G1C and 1G1C, a new closed-loop TS fuzzy controller will be presented.

VIII. PROPOSED CLOSED LOOP CONTROL OF THE GCSC BASED ON THE TS FUZZY CONTROLLER

The fuzzy logic, unlike the crispy logic in the Boolean theory, that uses only two logic levels (0 or 1), is a branch of logic that admits infinite logic levels (from 0 to 1), to solve a problem that has uncertainties or imprecise situations [13].

Fig. 14 shows the schematic diagram of the GCSC turn-off angle control based on the TS fuzzy controller. The power calculation block diagram performs an βα − transformation of the measured ac voltages and currents and calculates the line real power. This measured power is then transmitted through a first order low-pass filter (LPF) and a band-pass filter (BPF). The LPF with cutoff frequency of 3 Hz is for diagnosing of the electromechanical power oscillation in the line real power. Also, the BPF allows only the transmission of electrical power oscillations with frequencies between 3 and 20 Hz, that the torsional mode 1 (15.75 Hz) is in this interval. The diagnosis of SSR in the line power is the duty of this filter. The outputs of these two filters are compared with a power order, and then are used as TS fuzzy logic controller inputs, namely,

SSRPX Δ=1 and hElectromecPX Δ=2 , respectively. The output of TS fuzzy controller is the GCSC turn-off angle

( γ ), that after transmitting through a limiter, is fed to a pulse generator block synchronized with the line current zero crossing to get the GCSC input final pulse. Also, in Fig. 14 there is an operation mode selector to prepare ability of setting manual constant turn-off angle. Through above operations, the

1G pulse is produced. 2G to 6G pulses are produced at the same way. The design of the proposed TS fuzzy logic contro-ller (FLC) for 1G2C is described at the following.

A. Fuzzification Fuzzification is the process of finding appropriate membe-

rship functions to describe crisp data. To determine appropriate

Fig. 14. Proposed TS fuzzy controller for the GCSC.

1X

2Xγ



Fig. 15. Block diagram for determination of fuzzy sets and ( nn ba , ).

Fig. 16. Membership function for (a) 1X (b) 2X .

fuzzy sets, the results of the GCSC closed-loop simulation based on proportional controller, according to the Fig. 15 containing turn-off angle ( γ ), SSRPΔ and hElectromecPΔ , were used. This was performed in such a way that according to the behavior of these three waveforms in different situations before and after fault, the appropriate fuzzy sets for fuzzy controller were defined. The membership functions for inputs of fuzzy controller are shown in Fig. 16.

The equation of the Gaussian membership used to determine the grade of membership values is as follows [13]:

))2/()(exp(),,( 2ji

jii

ji

jiij

iACXCX σσμ −−=

(5)

where j

iAμ is the value of grade of membership, iX is the TS fuzzy controller input, j

iC is the mean and jiσ is the variance

of the Gaussian membership function.

B. Fuzzy Rule Base The rule base is the heart of a fuzzy controller since the

control strategy used to control the closed-loop system is stored as a collection of control rules. The controller has two inputs,

1X and 2X represented by nine and six membership functions, respectively. Therefore, the TS fuzzy controller uses 54 rules as follows:

(6) If jAX 11 = and jAX 22 = then

where jA1 and jA2 are related to input fuzzy sets 1X and 2X , respectively, KZ is the thK output membership function of

thK “If-Then” rule and *γ is the reference turn-off angle and in this study was considered 5.113 . The proper values of ( nn ba , ) were chosen from different values of ( SSRPX Δ=1 ,

hElectromecPX Δ=2 ), and the latter pair were obtained by simulation of the system with proportional controller for differ-rent values of ( nn ba , ) as depicted in Fig. 15.

C. Fuzzy Inference The basic operation of the inference engine is that it infers,

i.e., it deduces from evidence or data a logical conclusion. In fact, the inference engine is a program which uses the rule base and the input data of the controller to draw the conclusion. The conclusion of the inference engine is the fuzzy output of the controller, which subsequently becomes the input to the defuz-zification interface. Here Zadeh’s rule for ‘‘And’’ operation is used.

D. Defuzzification In this part, the fuzzy conclusion of the inference engine is

defuzzified, i.e., it is converted into a crisp signal. The mentioned signal is the final product of the FLC which is the crisp control signal to the process. The output level KZ of each rule is weighted by the firing strength KW of the rule as follows:

(7) ))(),(( 2211 XXAndMethodW jA

jAK μμ= ;

The final output of the system is the weighted average of all rule outputs, computed by (8) [13].

(8)

Final Output .54

1

54

1

∑

∑= =

K

KKK

W

ZW

3D diagram of ( SSRPX Δ=1 , hElectromecPX Δ=2 , =Z γ ) as

the TS fuzzy controller process is shown in Fig. 17.

E. Simulation Results and Discussion The designed TS fuzzy controller for generating the GCSC

turn-off angle was implemented by using the MATLAB® program. To examine the efficiency of this controller in differ-rent types of disturbance, two cases of faults were considered. In the first case, at t=17 ms, the ideal voltage source was substituted by the synchronous generator driven the turbine, and at t=7.5 s, a relatively strong transient was created by connecting a small resistor at bus B in Fig. 1 and disconn-ecting it at t=7.6 s. In the second case, at t = 17 ms, the applied fault to the system was identical, but at t=7.5 s, a very intensive three phase short circuit was created by connecting a reactor at point B with 75 ms time duration, based on [12]. Fig. 18 shows the line current response for the second fault type where the line current increases to about 3.8 p. u.

In Figs. 19 and 20 the electric torque responses for the both fault types are depicted. The response of 1G2C without TS fuzzy controller was unstable, as shown in Fig. 9, but as seen in these figures, although the subsynchronous resonance is present at the first 0.3 s, the proposed TS fuzzy controller is able to stabilize the system, damping out this oscillation in the electric torque even for series compensated line tuned to excite

.54,...,2,1=K

*21 γ++= XbXaZ nnK ; 54,...,2,1=K

SSRPΔ

hElectromecPΔ γ

*γ

11A 2

1A 31A 4

1A 51A 6

1A 71A 8

1A 91A

12A 2

2A 32A 4

2A 52A 6

2A



Fig. 17. 3D diagram of fuzzy controller process.

SSR at mode 1. These figures also show that an electromech-anical power oscillation appears in the system at a frequency around 1.25 Hz, as given in Table I; however, the existence of LPF block with cutoff frequency of 3 Hz, makes the GCSC able to mitigate this oscillation in less than 2.5 s.

In Fig. 21 the electric torque response with TS fuzzy controller, presented in this paper, is compared with the electric torque responses presented in [6], which was controlled with proportional controller and specific controller, with the same fault condition (a relatively strong fault). This figure clearly shows that power oscillation damping time as well as oscillation magnitude with TS fuzzy controller is much smaller than the response presented in [6].

These good responses can be described using the simulation results shown in Fig. 22. In Fig. 22(A), the electric power resp-onse of the system and in Fig. 22(B) the corresponding turn-off angle are shown corresponding to the Fig. 19. As seen in these figures, when the electric power is increased, the turn-off angle is also increased, and consequently, the compensation level is decreased and vice versa. As a result, the turn-off angle of GCSC as the TS fuzzy controller’s output alters in such a way that makes the GCSC able to damp both SSR and electrome-chanical power oscillations, properly.

IX. DESIGN OF THE TS FUZZY CONTROLLER FOR THE CASES 1G1C AND 2G1C

The design of the TS fuzzy controller for the cases 1G1C and 2G1C with the aforementioned method was performed. Fig. 23 shows turn-off angle applied by TS fuzzy controller to the GCSC for the case 2G1C. As seen in this figure, the TS fuzzy controller’s output, i.e. turn-off angle, becomes conver-gence and reaches to its steady state that is 113.5 degree. This convergence results in stabilizing the power system. In Fig. 24, the electric torque is compared for control methods, open-loop and TS fuzzy, for the case 2G1C. As seen in this figure, for the case with the frequency detection based control, the SSR is totally damped; however, the low-frequency oscillation lasts for about 6.5 s. With the TS fuzzy logic controller presented in this paper, the SSR is also damped and the electromechanical power oscillation is much smaller than in the previous control method and lasts for about 1 s. These results show the dramatic effectiveness of the proposed TS fuzzy controller to enhance the GCSC ability to damp out not only subsynchronous resona-

Fig. 18. Line current for a very intensive large disturbance for 1G2C.

Fig. 19. Electric torque for a relatively large disturbance for 1G2C.

Fig. 20. Electric torque for a very intensive disturbance for 1G2C.

ance but also low-frequency oscillation. The comparison of these results with the results available in the literature [4]-[6] and [14], confirms the correctness of the developed controller.

X. CONCLUSION

This paper has shown some results of the performance of the GCSC in SSR and power oscillation damping in a highly unstable power system through simulation with MATLAB® program. In order to make the GCSC able to mitigate the SSR and power oscillation, two control methods were presented. The first control method is an open-loop control strategy that works based on the line current frequency detection. Simul-ation results show that in some cases (1G1C, 2G1C) the GCSC is able to damp the SSR using this simple open-loop controller. This result is very important and shows that the GCSC has potential ability in SSR damping; however, in this control method, the GCSC equivalent reactance has to be equal or larger than the fixed capacitor. Also, the electromechanical power oscillation time duration in cases that this controller is able to damp SSR (1G1C and 2G1C) is long.

To overcome these problems, a TS-type fuzzy logic contr-oller was presented. It was shown that a smaller GCSC (1G2C) with this controller is also able to properly damp both SSR and



Fig. 21. Comparison between the torque response with TS fuzzy controller presented in this paper and torque responses presented in [6].

Fig. 22. A. Electric power, B. Turn-off angle (γ ) of 1G2C, corresponding to Fig. 19.

Fig. 23. Applied turn-off angle to the GCSC by TS fuzzy controller for the case 2G1C corresponding to Fig. 24.

power oscillation, which results in a lower cost configuration. Besides, in other cases, this controller is able to damp not only SSR but also low-frequency electromechanical power oscilla-tion showing that GCSC can effectively damp this kind of oscillation with this controller. Moreover, the electric torque response of the system with TS fuzzy controlled GCSC presented in this paper was compared with the torque response presented in [6], which was performed with proportional controller, for the same fault condition. It was shown that power oscillation damping time as well as oscillation magnit-ude with the TS fuzzy controller is much smaller than the response presented in [6], even when case 1G2C in this paper is compared with 2G1C in [6]. So, the proposed TS fuzzy controller for the GCSC is able to guarantee SSR and power oscillation damping and increase the operating range of the sy-

Fig. 24. Electric torque for a very large disturbance with and without TS fuzzy controller for 2G1C. stem. Hence, the TS-type fuzzy controller is a good candidate to control the turn-off angle of the GCSC.

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Closed loop control response for 2G1C in Ref [6] with proportional controller. Closed loop control response for 2G1C in Ref [6] with specific controller. Closed loop control response for 1G2C in this paper with TS fuzzy controller.



2009 COMPATIBILITY AND POWER ELECTRONICS 196 On Control … · On Control of Gate Controlled Series Capacitor for SSR and Power Oscillation Damping ... (GCSC) are presented. The ...

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