suppress torsional vibrations on turbine shafts by high temperature superconductive fault current...

Electric Power Systems Research 55 (2000) 65–72

Suppress torsional vibrations on turbine shafts by hightemperature superconductive fault current limiter

Ta-Peng Tsao a,*, Chi-Hshiung Lin a, Wen-Chang Tsai b

a Department of Electrical Engineering, National Sun Yat-Sen Uni6ersity, Kaohsiung 80424, Taiwanb Department of Electrical Engineering, Far East College, Hsinshih 74404, Tainan, Taiwan

Received 20 January 1999; accepted 29 April 1999

Abstract

In this paper, the effectiveness of a high temperature superconductive fault current limiter (HTS FCL) bank is verified from theviewpoints of suppressing torsional vibrations on turbine shafts. The bank, composed by successfully tested HTS FCL units inseries and parallel connections, is installed between the generator and the step-up transformer. Normally, the HTS FCL bankoperates in superconductive state without interrupting to the power system. Only in the event of a fault, the normal-stateresistance of the HTS FCL bank is introduced into the system to restrict the variation of generator delivering power and theunsymmetrical fault current. As a result, the unidirectional and the system-frequency components of transient E/M torque can berestricted. Depending on the response characteristics of the turbine system, great degree of vibrations on turbine shafts aresuppressed accordingly. Moreover, it is shown from simulation analysis that only low normal-state resistance is adequate for thestudied purpose. Also, the recovery time and the thermal rating of the HTS FCL bank are not critical with the aid of a by-passpower switch. Therefore, it is easier to realize the required characteristics of the HTS FCL bank. Furthermore, the effects ofdifferent fault type, fault clearing time and circuit breaker reclosing time are studied in this paper. The results show that the HTSFCL bank is effective on all the simulated conditions. © 2000 Published by Elsevier Science S.A. All rights reserved.

Keywords: Torsional vibration; High temperature superconductive fault current limiter; Normal-state resistance; Electromagnetic torque

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1. Introduction

Recently, expansion in power system capacities led todevelopment of larger-scale generating units. Therefore,a fault on the power system may abnormally inducelarge fault current and cause over-stress problems ongenerators, transformers, breakers and transmissionlines etc. Especially, a network fault would result inconsiderably large torsional vibrations on stem turbineshafts [1–3]. To alleviate these vibrations, many coun-termeasures have been proposed such as power systemstabilizer (PSS) [4], static VAR compensator (SVC) [5],thyristor controlled series capacitor (TCSC) [6], fastphase shifter [7], braking resistor [8], superconductiveenergy storage system [9] and HVDC [10] etc. Almostall of them are based on the modulation of the effective

and reactive powers to bring supplementary dampinginto the system. However, little has been discussedabout suppressing shaft vibrations by restricting theirinitial vibration magnitudes instead of augmenting sys-tem damping. Herein, with the aid of high temperaturesuperconductive fault current limiter (HTS FCL) bank,the initial vibration magnitude of shafts due to powersystem faults can be suppressed. As compared to othermethods, the proposed method has the advantage ofalleviating the impact of both turbine systems and otherutilities.

Fault current limiter using high temperature super-conductor is a newly developing technology to controlthe fault current levels on distribution and transmissionnetwork in the utility [11–13]. Several kinds of HTSFCL units have been successfully tested and applied atsome distribution systems [14]. Two types of them arelisted in Appendix B. The prototype for applying at 500kV-transmission level is expected to emerge in year2000. The switching time of a HTS FCL unit from one

* Corresponding author.E-mail addresses: [email protected] (T.-P. Tsao),

[email protected] (W.-C. Tsai)

0378-7796/00/$ - see front matter © 2000 Published by Elsevier Science S.A. All rights reserved.PII: S 0 3 7 8 -7796 (99 )00096 -6

T.-P. Tsao et al. / Electric Power Systems Research 55 (2000) 65–7266

state to the other state is within several tens microsec-onds. Due to the fast response, a HTS FCL unit can beused to suppress the peak fault current and improve thevibration behavior of the turbine-generator.

2. Studied system

The practical steam turbine unit, including a high-pressure stage and two low-pressure stages steam tur-bines, analyzed in this study is a close-coupled andcross-compound reheat unit that operates at a rota-tional speed of 1800 rpm. The rated capacity of thegenerator, which was installed in 1984, is 951 MW.Each of low-pressure steam turbines has A and Bspindles and uses the shrunk-on rotor with 11 stages ofeach spindle, including rotary and stationary bladestages.

The turbine-generator electromechanical system usedto present the model is shown schematically in Fig. 1a.The complexity of turbine-generator arrangement isalso seen in Fig. 1a. It can be modeled numericallyusing finite elements to represent the inertias, dampings,and stiffnesses of the electrical machines, turbine stages,shafts and couplings. Fig. 1b shows the mechanicalmodel of the simulated turbine-generator. Their electri-cal and mechanical data are given in Appendix A. Allthe parameters of the system are in the per unit system,based on generator ratings.

The proposed approach to suppress the torsionalvibrations on turbine shafts is to install a HTS FCL

bank, via a current transformer, between the generatorand the step-up transformer, as shown in Fig. 2a. Thiskind of series and parallel configuration has been testedsuccessfully in Japan using the unit listed in AppendixB. Fig. 2b shows the equivalent circuit model of a singlecrystal superconductor, including a parallel connectionof a pure Josephson tunnel junction and a semi-conduc-tive shunt resistor. Fig. 2c demonstrates its current–voltage characteristics. Accordingly, the HTS FCL unitoperates as a nonlinear resistance that is a function ofthe current flowing through it. The simplified circuitmodel of the HTS FCL bank, including current trans-former, then can be obtained as in Fig. 2d.

3. Using the HTS FCL bank to restrict the E/Mdisturbing torque

It is well known that the E/M disturbing torqueinduced by three-phase short circuit fault will consist ofa unidirectional component and a system-frequencycomponent, which correspond to the generator deliver-ing power and the unsymmetrical fault current respec-tively. For unsymmetrical types of faults, an additionalsecond harmonic of the E/M disturbing torque will beinduced due to unbalanced armature currents. Overall,there are three components to be present in E/M dis-turbing torque due to power system faults. All the typesof E/M disturbing torques are the main sources tostress turbine mechanism.

Fig. 1. System studied and the turbine model.

T.-P. Tsao et al. / Electric Power Systems Research 55 (2000) 65–72 67

Fig. 2. The proposed HTS FCL bank and the equivalent circuitmodel.

The unidirectional component of E/M torque is gov-erned by the power delivered from generator to thesystem. With a fault of short circuit, the main busvoltage drops to nearly zero and the generator is nolonger able to deliver power to the system. Then,considerable amount of E/M torque variations wouldoccur in step changing way. Now, if an additionalresistance provided by the HTS FCL bank is broughtinto the system to dissipate some of generator outputpower during fault period. The variation of the genera-tor delivering power will be reduced, which leads toreduction in the step-changing component of E/Mtorque. Because the HTS FCL bank consumes nopower during normal operation but dissipates the oscil-lation power during the fault condition, the transientE/M torque can be restricted without interrupting thenormal operation.

The system-frequency component of E/M torque isinduced by the dc component of fault current. Thisunsymmetrical fault current decays away with a timeconstant governed by the generator armature resis-tance. Usually, it takes many cycles to decay away. If asupplementary HTS FCL resistance is externally addedinto the system to substantially increase the systemdamping effect, the peak unsymmetrical fault currentwill be limited and sustained for only one or two cycles.Thus, the system-frequency component of E/M torquecan be restricted.

For common application of fault current limiter, thefault current-limiting resistance is used to limit thesymmetrical fault current such that the resistance oughtto be designed far larger than the system impedance.Herein, it is not intended to limit the symmetrical faultcurrent but to restrict the transient E/M torque, hencethe normal-state resistance of the HTS FCL bank canbe relatively small.

4. Torsional response of turbine shafts

Because the E/M disturbing torque consists of threecomponents with different frequency, the response ofthe turbine system to the three kinds of excitationdominates the behaviors of the shaft vibrations. Thispaper analyzes the torque responses of turbine genera-tor shafts by frequency-scanning method. Suppose thatthe terminal of generator rotor is a shaker with one perunit excitation, the frequency-scanning inspects the nat-ural frequencies of steam turbines from 0.01 to 140 Hzwith an interval of 0.01 Hz.

The scanning results of the 951 MW generator set areshown in Fig. 3. Fig. 3a shows the frequency responseson GEN-LP2R shaft section. Eight vibration modes arepresent in the turbine system, which are summarized inFig. 3b. The vibration modes have been avoided fromthe forbidden frequency bands defined as 60 Hz95%

3.1. The effects of the HTS FCL bank

The severity of a vibration is characterized by twofactors as initial vibration magnitude and system damp-ing. The initial vibration magnitude corresponds di-rectly to the magnitude of disturbing source, thetransient E/M torque in this study. For the HTS FCLbank, there are two effects to restrict the transient E/Mtorque. One is to decrease the variation of the generatordelivering power. The other is to increase the decay rateof the unsymmetrical fault current.


Fig. 3. Results of frequency scanning for 951 MW turbine-generatorunit.

5. Simulation results

To illustrate the suppressing effect of the HTS FCLbank to torsional torques on the turbine-generatorshafts, two types of more severe faults such as three-phase to ground and line-to-line faults have been stud-ied. For each type of fault, the fault is arbitrarilyapplied at 0.1 s and is cleared at 0.22 s, which is theworst clearing case as shown in later studies. It isassumed that fault is applied to one of the doubletransmission lines and at the transformer-side terminalof the line. In the case of line-to-line fault, fault isapplied between phase b and c. Moreover, it is assumedthat the resistance of the HTS FCL bank at the super-conducting state is so small as to be neglected. Theresistance of the HTS FCL bank at the normal state isdesigned to be 0.19 pu. Critical current for quenchesoccurrence of the HTS FCL bank is designed at 2.0 pu.Recovery time of HTS FCL bank is not critical becausea by-pass power switch is used to control the bank foroperation only for a short time, 0.4 s in the simulations.

5.1. Fault current and E/M torque

The generator phase-B current for three-phase toground fault is illustrated in Fig. 4 to show the differ-ence between two cases without and with the HTS FCLbank in service. In the figures, the unsymmetrical com-ponent of fault currents is significantly reduced whilesymmetrical component is kept unchanged. Therefore,stress imposed on facilities will be reduced withoutdisturbing the operation of circuit breakers. Fig. 5illustrates the E/M torques for the same fault. Owing tothe reduction in fault currents, both system-frequency

and 120 Hz95%. Fig. 3c depicts the torque responseson various shaft sections excited by the three types ofE/M disturbing torque. It is clear that the torsionalresponses of turbine shafts are dominated by the unidi-rectional E/M disturbing torque. Therefore, most of theshaft torsional vibrations are excited by the step-chang-ing E/M disturbing torque component, but little vibra-tions by the system-frequency one.

Fig. 4. Phase B current of generator armature for three-phase to ground fault (a) without; (b) with the HTS FCL bank in service.

Fig. 5. E/M torque for three-phase to ground fault (a) without; (b) with the HTS FCL bank in service.


Fig. 6. E/M torque for double-phase fault (a) without; (b) with the HTS FCL bank in service.

and step-changing components of the E/M torques aresignificantly suppressed during the fault being sustainedand cleared. Nevertheless, it is worthwhile to note thatwhen the line-to-line fault occurs, the HTS FCL bankson the two faulty phases have been switched to thenormal-state while that on the healthy phase remainedin its superconductive state. Considerable amount ofE/M torques with double system frequency would beproduced due to system unbalance as shown in Fig. 6.Therefore, it is necessary to make sure that the resonantfrequencies of the turbine system are avoided awayfrom double system frequency, otherwise electrome-chanical resonance would occur. This limitation is also

considered for other unsymmetrical faults. Besides, it isfound from response curves of E/M torques that in-stalling the HTS FCL bank enhances the transientstability of the system. The reason is that the generatorrotor obtains a less acceleration because some of theelectric power of the turbine-generator is dissipated bythe HTS FCL bank during the fault. Furthermore,there is another disturbance in E/M torque at theswitch-out instant of the HTS FCL bank, which arisesby the resistance variation of the switching. Therefore,the normal-state resistance of the HTS FCL bankcannot be designed too large, otherwise severe switch-out disturbance will occur.

Fig. 7. Torsional torques of shafts due to the excitation of three-phase to ground fault (a) without; (b) with the HTS FCL bank in service.


Fig. 8. Influence of the normal-state resistance of HTS FCL on torsional torques of shafts for (a) three-phase to ground fault; (b) double-phasefault.

5.2. Time beha6ior of shaft torsional torque

For the case of three-phase to ground fault, thesuppressing effect of the proposed HTS FCL bank ontorsional torques of turbine-generator is demonstratedin Fig. 7. Clearly, remarkable reductions of the tor-sional torques are found in various turbine-generatorshafts. The amplitude between maximum and minimumtorsional torques is defined as the peak-to-peak torque.The reduced percentages of the peak-to-peak torques inthe HP-LP1F, LP1R-LP2F and LP2R-GEN shaft sec-tions are 50.6, 53.5, and 55.3%, respectively. Similarly,they are 47.9, 51.6 and 54.6% for the case of line-to-linefault, which are not shown in figures due to spacelimitation.

Moreover, the suppressing effect of the normal-stateresistance of HTS FCL bank to the torsional torqueson each shaft section has been studied. Resistanceranging from 0.038 to 0.19 pu is adopted for simula-tions. The results for three-phase to ground and line-to-line faults are demonstrated in Fig. 8a and b,respectively. It is shown that the relationship betweenthe resistance and the peak-to-peak torque for each ofshaft sections is nonlinear. Consequently, it is unneces-sary to bring too much fault current-limiting resistanceinto the system because the effectiveness is limited. It isrecommended for study purpose that the fault current-limiting resistance be designed only to adequately re-strict the peak unsymmetrical fault current, such that

only lower thermal rating is required for the HTS FCLbank.

5.3. Effect of clearing tune

It is assumed that clearance of a fault is initiated attime interval after fault inception. The time intervalaccounts for the operating time of protection and cir-cuit breaker. Fault is actually cleared at the instant ofcurrent zero crossing. The effect of the fault clearingtime on the torsional torques of turbine-generatorshafts for three-phase to ground fault is examined andthe results are illustrated in Fig. 9. In these figures, thepeak-to-peak shaft torsional torques are plotted asfunctions of the fault clearing time. On the average, it isabout 50% reductions in peak-to-peak torsional torqueswhen the HTS FCL bank with 0.19 pu normal-stateresistance is in service.

5.4. Effect of auto-reclosing

To illustrate the operation of the HTS FCL bank atauto-reclosing, the following fault and switching se-quence is studied. A three-phase to ground fault occursat one of the transmission lines at 0.1 s. Clearance offault is initiated 0.12 s after fault inception. After aninterval of time, which accounts for the recovery timeand the reclosing time of the circuit breaker, the line isreclosed onto the same fault. After an additional time

Fig. 9. Relationship between clearing time and torsional torques of shaft for three-phase to ground fault (a) without; (b) with the HTS FCL bankin service.


Fig. 10. Relationship between reclosing time and torsional torques of shafts for three-phase to ground fault (a) without; (b) with the HTS FCLbank in service.

interval of 0.12 s, the line is again cleared withoutsubsequent reclosing.

The relationship between the reclosing time and thepeak-to-peak torque on each of the shaft sections areshown in Fig. 10. Again, there are about 50% reduc-tions in peak-to-peak torques.

6. Conclusions

The technical feasibility of using a HTS FCL bank tosuppress the torsional vibrations in large steam turbineshafts has been examined. From the results of thesestudies, the following conclusions can be summarized.

For the application of the studied purpose, it isunnecessary to introduce a HTS FCL bank with highnormal-state resistance into the system because only thetransient E/M disturbing torque is to be restricted.Neither, the recovery time nor the thermal rating of the

HTS FCL bank are critical due to the assistance of aby-pass power switch. Therefore, it is easier to realizethe required characteristics for the HTS FCL bank.

Due to considerable reductions in peak fault currentsand in maximum torsional torque induced on turbineshafts, benefits may be obtained from both reductionsin utility capacities and extension in operating life ofthe turbine unit, though the HTS FCL bank is expen-sive. Also, it is possible in the planning and designingstage of a turbine-generator system the utilities and theturbine shafts be designed, based on smaller strength.

Furthermore, it has been shown that the effectivenessof the proposed method does not depend either on thefault clearing time or on the reclosing time. This meansthat the method can be readily applied to any turbine-generator system with different protection scheme. Par-ticularly, high-speed auto-reclosing of the transmissionline circuit breaker is permissible. Finally, the transientstability of the system will be enhanced when the HTSFCL bank is brought into the system.

Appendix A. 951 MW turbine-generator systemparameters

Generator Mechanical dataInertia DampingMass Stiffness1057 MVA/23.75 kV r=0.00359 X1d=0.110

0.0018060 Hz/four poles Xl=0.190 X1q=0.490 H.P. 0.1787144.15Xd=1.574 Rfd=0.00070 R1d=0.02571

LP1F 0.6546 0.00023Xq=1.490 Xfdl=0.168 R1q=0.025711595.0Transformer

0.6486 0.000211057 MVA LP1R23.75/345 kV Xt=0.14304 Rt=0.00192206.0Transmission line

0.000211057 MVA 345 kV LP2F 0.65751584.9XA=0.1088 XB=0.1088 XC=0.1088

LP2R 0.6676 0.00012RA=0.0073 RB=0.0073 RC=0.0073325.28Initial operating conditions

GEN 1.1616 0.00012P0=0.90 Q0=0.10 Vt=1.03


Torque distribution 117.160.0HP 0.31 LP1F 0.1445 B1F 0.028 REC 0.00334

LP1R 0.1445 B1R 0.028 1.610.0LP2F 0.1445 B2F 0.028 EXE 0.002360.000040.0344Blade 36.2B2R 0.028LP2R 0.1445

Appendix B. List of two types of HTS FCL units

Continuous current (rms) Resistive/coil Resistive/coilManufacturer Europe Japan

6.6 kV40 kVVoltage (rms)1000 AContinuous current (rms) 2000 A

Reaction time 10–100ms :100 msSuperconductor NbTi NbTiType Resistive/coil Resistive/coil

65 V 3.8 VNormal-state resistanceNext step plan 6.6 kV/? kA40 kV/5 kAFuture plan 500 kV/8 kA225 kV/?kA

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