Torsion a I1 fat i g u e of tu r b i ne- g en era t o r shafts owi n g to network faults

C.Chyn H.-C.Wu lr. - P. Tsa o

Indexinz iermr: Sqfity factor, Towional fktigue, Turbine gtnerator

Abstract: Many studies have been madle of the fatigue processes resulting from cyclic stress which metal for making turbine generator shafts has to bear. In the paper a modified dynamic program written on the basis of the theories is used to simulate the shaft torsional vibrations resulting from four types of network fault. The purpose is to s8tudy the influence of a safety factor, selected iin the first stage of design, on the damage accumulated following worst-case fault clearance and 1;ynchronising of the s,imulated machines.

II Introduction

The initial price of machines decreases with increase in rnachine unit capacity. Higher capacity gives higher heat efficiency. Turbine generators of higher capacity can be produced because of the improvements on design ancl production techniques and thlerefore the capacity of newly established machine units will keep increasing. In the past, the material strength of small rnachine units could be designed to be six times higher than the working stress. Vibration does not threaten the safe working of the turbine generator. The high rated power of new units is accompanied by larger machines. However, the material composition for mak- ing the rotating shafts (chrome steel) has been devel- oped to its, maximum. The vibration of machine units therefore needs to be researched. Particu1ar:ly large tur- bine generators are: arranged as multistages to obtain higher heat efficiency. A structure of this type results in the inevitable and obvious torsional vibration modes

The size of machines, the plurality of the constituting elements and the high expenditure certainly limit the experimental outcome. Only by setting up an accurate system model and programming complete simulation equations can the dynamic action of every constituent element of the machine units be clearly revealed. To

[I, 21.

0 IEE, 1996 IEE Proceedings online no. 19960598 Paper first received 15th January 1996 and in final revised form 14th May 1996 C. Chyn is with the Department of Electrical Engineering, Nan-Tai College, Yungkung, Tainan, Taiwan, Republic of China PLC. Wu and T.-P. Tsao are with the Department of Electrical Engineer- ing, National Sun Yat-Sen University, Kaohsiung, Taiwan, Republic of China

properly simulate the dynamic action of the turbine generator three subsystems (mechanical, electrical and control) need to be taken into consideration to estab- lish the state equations. The dynamic program of the turbine generator is written according to working prin- ciples [3-51.

A transmission-line fault can produce a large tran- sient current in the synchronous machine in the power system. In addition, this shock can also lead to a tem- porary and violent kimk of the turbine generator. The rotating shafts must bear hung stress and therefore the material fatigue life will be decreased and may result in a shaft crack and, even more serious, accidents once the fatigue accumulates to a certain degree [6]. The paper examines fault clearance and faulty synchronisa- tions for an operating 951MW unit. Similar results would appear to apply to a 666MW machine [7] and a 750MW machine [8]. The system parameters and simu- lation comparisons of the two machines are given in Section 9.

2 System studied1

Fig. 1 indicates the s:yiichronous generator and busbar or power offering network which are connected with a step-up transformer and two transmission lines. Once an accident occurs to any of the transmission lines, the circuit breakers at two ends will open and separate from the fault line in the time that has been set. The circuit breakers will close again at the appropriate time to resume working after the instantaneous accident dis- appears.

synchronous step-up transmission Line busbar and generator transformer network

A 0 fauC c Fig. 1 Sy.stc.m equivalent zrad by jault studied

Fig. 2 shows the rotoir spring-mass model and lumped parameter model of the simulated 951 MW tur- bine generator. The data for the unit is given in Section 9. The majority of tlie mechanical parameters associ- ated with a particular shaft system are not amenable to variation and change owing to the design specification and conditions under which the machine is to operate ~ 5 , 91.

419 IEE Pvoc -Genev Trunsm. Di.\trih , Vol. 143, No -5, Septm?her 1996

l b 11f LPlR LP2F

LP2R

Fig.2 Mechanical syytenz model

3 Fatigue theories and models

The analytical techniques presented in two previous papers can be used to predict the torques that will result in a shaft system following electrical system dis- turbances [lo, 111. Fatigue models for the most part are based on empirical data. This data usually takes the form of a stredlife curve.

The rotor materials used by the studied turbine gen- erator were tested. NiMoV is a generator field material, NiCrMoV is a low pressure rotor material, and CrMoV is a high-pressure rotor material within the scope of ASTM specification A469, A470 and A471. Typical softening between the monotonic and stable cyclic are represented mathematically with the follow- ing equations:

1

(1) ff e, = -2 + [2] E

where and 0, are strain and stress amplitude, E is the elastic modulus, and H and s are constants. A simi- lar expression for the torsional data is given by

The material fatigue properties in the form of strain- life diagram are presented as a function of total strain amplitude against cycles-to-failure Nr

where the constants A , a, B and fi are determined by the elastic and plastic components of strain. In the same manner, the data also may be represented by a universal slope-type equation

E , = A(2ivf), + B(2ivf)' ( 3 )

Y, = A'(21Vf)"' + B'(2Nf)'' (4) The results of a three-year programme to estimate the cumulative fatigue damage sustained by a turbine-gen- erator shaft system during a torsional transient is pre- sented. The numerical values are given in Table 1 [l 11.

Fig. 3 shows the torsional stress-strain curves for the three materials studied in this programme. The tor- sional strain--1ifc and stress-life diagrams are presented in Figs. 4 and 5 as the plots of shear strain and stress amplitude against cycles-to-failure.

Because fatigue damage is assessed on a closed hys- teresis loop basis, the rotor deformation history must be analysed to identify the reversals that form closed hysteresis loops or cycles. A cycle-counting technique, currently considered to be the best available and known as the rain-flow cycle counting technique, uses closed loops in the stress-strain plane. An example of a stress-time history can be seen in Fig. 6 with its accompanying stress-strain plot.

4x0

Table 1: Material stress-strain and strain-life constants

Materials

NiMoV NiCrMoV CrMoV (A 469) (A 470) (A 471)

E(MPa) 201,000 200,000 204,000

(psi) 29,200,000 29,000,000 29,600,000

H(MPa) 726.7 689.5 748.8

(psi) 105,400 100,000 108,600

S

A

U

B

B G(MPa)

(psi)

H'(MPa)

(psi)

0.075

0.0037

-0.55

1.34

-0.71

82,760

12,000,000

387

56,180

0.061

0.0034

-0.043

1.14

-0.69

80,670

11,700,000

426

61,750

0.060

0.004

-0.051

2.6

-0.79

82,760

12,000,000

45 1

65,430

S' 0.074 0.087 0.082

A' 0.0048 0.0055 0.0059

a' -0.043 -0.054 -0.052

B' 1.24 1.69 1.69

B' -0.59 -0.62 -0.64

materials

0 ASTM A469 D ASTM A470

ASTM A471

0 +,---: i ~ i

0 6 12 18 24 30 36 42 48 strain amplitude 10-3

Touionnl cyclic srress-srrain curves Fig. 3

75

? 60 0 DASTM A470 aJ 7 45 - - Q

5 30 c P I

15

0 15 2 5 35 45 5 5 6 5 7 5 8 5

logarithmic reversals to failure

Fig. 4 Tot w n a l wain-life i elation

The Palmgren-Miner rule states that the damage associated with each closed hysteresis loop found in a complex load history may be added together to obtain the cumulative damage This is known as linear

IEE Pioc -Gmm Tvirnim Dutith Vol 141 No 5 SeptenhJi 1996

damage cumulation theory and can be exprlessed math- ematically as [ 101

- n 2 I= fraction of life lost

where a, is the number of cycles at the ith stress level, and Nji is the number of cycles to failure at the ith stress level When the fraction of life expended equals one, linear damage cumulation predicts failure of the material.

(5) T ‘; Nf?.

~- - 500 ---- materials

I

C ASTM A469 o ASTM AL70 .ASTMA471

U

--z 2 180

1 2 3 4 5 6 7 8 9 logarithmic reversals to failure

Fig. 5 Toisional rtress-lde relation

I

l i

Fig.6 Samlde ojstress strain history

-11 I

I 4

Fig. 7 Stress-strain relation and Goodman line

Although the relation of Fig. 5 is derived for fully reversed stress cycles, the actual life history of interest most often occurs along with a mean stress. The most commonly used method for equating the values of alternating stress (ci,) and (U,) to an ‘equivalent stress’ is callcd the Goodman line and shown in Fig. 7. For example, say we have an alternating stress (5,4s and a mean stress G , ~ ~ ; if the ultimate tensile strength is S, (0, = O), from the Goodman line we obtain. the ‘equiv- alent stress,’ Sno.

IEE Proc.-Gener. Transm. Distrib , Vol. 143, No. 5 , September 1996

The maximum shear stress on stress at the outer radius [lo]

27 -

TR: gsnaax - -

the shaft is the shear

(6) where Ro is the radius of a uncorm shaft, and T is the net torque. Because {of the multimodal nature of fre- quencies of the shaft response, and the effects of stress concentrations and centrifugal stresses must be quanti- fied, it is important to recognise that the present state of the art of fatigue estimates may be imprecise. This purpose of this paper is to investigate the influence of safety factor, as alterled by the radius, on the cumula- tive damage of the shaft system.

4 Simulation procedures

Entering generator and transmission line data to the operating point and calculating the initial values of the states in the dynamic representation is the first step of this program. The next step concerns the control and mechanical systems, called the initial condition rou- tines.

After execution of lhese subroutines there is a corre- sponding program segment which assembles the first- order differential equations. A fourth-order Runge- Kutta numerical analysis method with Gill’s coefficient is applied to solve thesle differential equations including the shaft angular displacements, velocities and torques.

The torsional torque occurring from the network dis- turbance and due to itlie mechanical response oscillates in the material of this shaft system. These resonances consume the shaft lifk. The main theorem is the rain- flow counting methodl [12, 131.

5 Results of transient simulation

Most of power system accidents are (single) line-to- ground faults; others are line-to-line, double-line-to- ground, and three-philrje faults, inorder of frequency Qf occurrence. The fault under simulation is applied to the network at 0.1s and the circuit breakers must be able to open the short-circuit current at 0.2s. The effect of autoreclosure of shafts is considered. The circuit break- ers reclosed at 0.45s and reopened at 0.55s is examined.

The method of simulation uses a full representative three-phase turbine generator model to cover the asym- metric fault conditions. The three phases of the trans- mission line are modlelled as separate resistances and reactances. The exciter and governor control action are included. Information and data used for the 951MW machine set under consideration are given in Section 9.

The data from the shaft torque simulation was sam- pled at 1000 samples per second. For the time period of 0.1s to 7.1s, 7000 points may be obtained from the shaft torque oscillation output. This information gives an evaluation of the ,severity of the oscillations. The methods of predicting shaft loss of life based on shaft torque-time histories have been modified and improved. The worst perturbation occurred in the low pressure turbine stage, that is, 2R-GEN.

The effect of machine disconnection following four types of network faults is examined. Peak-to-peak torque at various shaft locations is computed as the function of the fault clearing time. Assume the fault applied at 0.1 s and autoreclosure sequence successful; Figs. 8 and 9 illustrate the comparison of perturbation of torsional oscillati’ons for each fault. Figs. 10-13

48 1

show, for example, the effect on the shaft section 1R- 2F performance for the 951 MW unit when subjected to each network fault. The line-to-line disturbance is the onerous case.

t !

160 168 176 184 192 200 208 216 224 time.sx10-3

Fig. 8 fault: 951 M W machine, LPIR-LP2F shaft

Comparison of perturbation of torsional oscillations for each

0.1 s fault applied, autoreclosure successful 0 L-E A L-L-L-E 0 L-L-E 0 L-L

I

160 168 176 184 192 200 208 216 224 time,sx 10-3

Fig. 9 fault: 951 M W machine, LP2R-GEN shaft 0.1 s fault applied, autoreclosure successful 0 L-E A L-L-L-E 0 L-L-E 0 L-L

Comparison of perturbation of torsional oscillations for each

2.5 I

1

_J & -0.51

100 200 300 400 500 600 700 800 900 time,s x

Fig. 10 Operational sequence: 0 I s fault applied; 0.2s circuit breaker opened, 0.45s breaker reclosed; 0.55 s breaker reopened

Example of comparison for 951MW machine: L-Ejault

-1.51 ~ ~ ! ! : ~ ! ! : : I : ~ ! ! I

time,s x 100 200 300 400 500 600 700 800 900

Example of comparison for 951MWmachine: L-L-E fault Fig. 11 Operational sequence: 0.1 s fault applied; 0.2s circuit breaker opened, 0.45s breaker reclosed; 0.55s breaker reopened

482

3 5 , 2 -1 I

V " I -1.5 . ~: ~ 1 : ~: ~ ~: I : ~ ~ I

100 200 300 400 500 600 700 800 900 time, s x 10-3

Fig. 12 Example of comparison for 95IMW machine: L-L fault Operational sequence: 0.1 s fault applied, 0.2s circuit breaker opened, 0.45s breaker reclosed, 0 5 5 s breaker reopened

100 200 300 400 500 600 700 800 900 time, sx IO-^

Example of comparison for 95lMW muchine: LL-L-Efuult Fig. 13 Operational sequence: 0.1 s fault applied; 0.2s circuit breaker opened, 0.45s breaker reclosed; 0.55s breaker reopened

6 Results of fatigue prediction

Torsional oscillations cause the extra stress the shafts have to bear; the constituent materials either rapidly wear because of violent oscillation or gradually waste the fatigue life through consistent and mild oscillation. Time-accumulated stress will eventually lead to crack lengthening and destruction. The fatigue processes due to the cyclic stress of the metal material for making the rotating shafts has been discussed and programmed.

How the selection of safety factor at the design stage impacts on cumulated deterioration is studied when different types of power system accidents occur to the 951 MW unit at the third nuclear plant of the Taiwan Power Company. The mechanical structure is mainly divided into three: turbines, generator and exciter. The following analyses focus on the concentration of the stresses.

It is useful to normalise the torque on each shaft sec- tion to the torque associated with that shaft under rated machine operating conditions [lo]. Making use of a transient simulation program, we obtained the nor- mal operating stresses for the rotating shaft. The stresses at HP-LPlF, LPlR-LP2F, LP2R-GEN and GEN-REC are 0.27958pq 0.59128pu, 0 . 9 0 2 8 3 ~ ~ and O.O208Opu, respectively.

The materials used by HP-LP1F is CrMoV, LPlR- LP2F and LP2R-GEN are NiCrMoV, and GEN-REC is NiMoV. The safety factor is defined as the stress times base on the material softening point (set the cycles to failure at 100,000). The curves shown in Fig. 14 illustrate the relationship, stress against number of cycles to failure, for the simulated unit asso- ciated with safety factor is 3.0 assigned to shafts.

Values quoted correspond to the fault clearing time or synchronising angle which gave rise to the highest

IEE ProcGener . Transm. Distrib , Vol. 143, No. 5, September 1996

peak torque at the tcoupling [9]. Fig. 15 relates to the 951 MW unit, produces time responses showing load angle for a synchroinous generator. Figs. 16-19 depict peak-to-peak torque at the turbine shafts and shaft torque following worst-case disturbance. Successful cir- cuit-breaker autoreclosure sequences often give rise to more onerous shaft torques than unsuccessful ones. Owing to tlhe practical condition of the 951 MW unit, the effect of autoreclosure on fatigue life expenditure of shafts is not considered.

shafts OH P-LP1F aLP1R- LP2F

LP2R -GEN

______ 0 1 6 7 - -- I -1

1 2 3 4 5 6 7 8 logairithmic reversals to failure

Fig. 14

U HP-LPIF A LPZR-GEN 0 LP1R-LPZF 0 GEN-REC

Stress-& expediture relation for 951MW m,zchine (Safety factor = 3 0 )

20t-+-T-T---: 1 ~ i -4

100 200 300 400 500 600 700 800 900 time,sx 10-3

Fig. 15 (I) L-L (111) L- L-E (ii) L-L-L-E (IV) L-E

Comparison of generator load angle for each fault

I I

-U

015-- --- c---ct-

100 110 120 130 140 150 160 170 180 Load angle

IFig. 16 tug, comparing malsyncJmisatm for each shaft section

Perturbation ollowig L-L-L-E fault clearance and synchronu-

Tables 2 and 3 list the results of worst-caae torsional fatigue for three-phase and line-to-line faults. The material fatigue daimage is done in l.Os, 3.0s, 5.0s, and '7.0 seconds after thLe accident happens.

I'EE Proc -Genm Trunrm Distrzh Vol 143 No 5 September 1996

aJ 3 * U c 6 3 6 -

-3.6 - -++e 0 0.'4 ~ 0 8 ~ 1.2 1.6 20 ~ 2(4 ' 2k-2

time,s Fig. 17 L-L-Efuult clearing at 0.277s

LPIR-LP2F shaft torque following worst-case disturbance; L-

3 P c

+ L

c 0. Q

zH.P.-LPlF o LPlR-LP2F A LP2R-GEN e GEN-REC I--- I

9 i

6

3

015=:- -1

0 4 : : : : : -- 100 110 120 130 140 150 160 170 180

load angle,deg Fig. 18 comparing mulsynchronisation for each shaft section

Perturbation following L-L fault clear ance and synchronising,

-36c--c-t-+-- ~ i i i : --i--t-~------l

0 0 4 0 8 1 2 16 20 24 28 3 2 time, s

Fig. 19 fault clearing at 0 279s

LPIR-LPZF shafi toque following worst-case duturbance, L-L

7 Discussion and conclusions

Torsional oscillations cause the shafts to bear extra stress and lead to crack lengthening and destruction owing to cumulative stresses. This thesis, having a focus on the 951MW nuclear unit, is on the basis of the material fatigue theory in the two-table analysis. The results show that: (i) Almost all of the rnaterial fatigue damage is done in the 3 s immediately after the accident happens; there- fore as far as the needs of fatigue analysis is concerned, time for dynamic simulation will not necessarily be very long. (ii) Malsynchronisation and fault clearance give rise to onerous shaft torques and ffatigue life expenditure. The agent that can cause the most violent vibration is a line- to-line or three-phase fault, double line-to-ground is the third and the single li ne-to-ground causes the least oscil- lation; therefore the material strength should be designed to be able to bear line-to-line and three-phase faults.

4x3

Table 2: Torsional fatigue due to worst-case L-L-L-E fault

Time

Shaft Safety factor 0.1-1 . Is , % 0.1-3.1 s, % 0.1-5.1 s, % 0.1-7.1 s, %

1.75 1.962114 2.046474 2.144871 2.147627

2.0 HP -LPIF (clearing at 0.277s, load anale at 107.5") 2.25

0.152078 0.159144 0.167630 0.167858

0.0171 12 0.017982 0.018932 0.018957

2.5 0.002356 0.002486 0.002629 0.002632

3.0 2.622693 15.666850 15.824230 15.824530

3.5 (clearing at 0.277s, load angle at 107.5") 4.0

LPIR-LP2F 0.152321 0.905903 0.915233 0.915250

0.013196 0.077894 0.078674 0.078676

4.5 0.00 146 1 0.008851 0.008945 0.008945

3.0 0.134019 4.376990 5.464202 5.464202

3.5 (clearing at 0.277s, load angle at 107.5") 4.0

LP2R-G E N 0.007915 0.252368 0.316248 0.316248

0.000669 0.021959 0.027489 0.027489

4.5 0.000080 0.002449 0.003060 0.003067

1.75 7.363626 7.381460 7.381460 7.381460

2.0 GEN-REC (clearing at 0.277s, load angle at 107.5") 2.25

0.332005 0.332539 0.332539 0.332539

0.017547 0.017554 0.017554 0.017554

2.5 0.000876 0.000876 0.000876 0.000876

0.1 s fault applied, machine malsynchronisation, autoreclosure sequence not successful

Table 3: Torsional fatigue due to worst-case L-L fault

Time

Shaft Safety factor 0.1-1 , Is , % 0.1-3.1 s, % 0.1-5.1 s, % 0.1-7.1 s, %

1.75 0.805885 5.626513 6.505370 6.564077

2.0 HP -LPIF (clearing at 0.279s, load angle at 112.5") 2.25

0.064358 0.440665 0.509897 0.514468

0.007268 0.049579 0.057223 0.057731

2.5 0.001 104 0.006966 0.008078 0.008145

LP1 R-LP2F (clearing at 0.279s, load angle at 112.5")

LP2R-GEN (clearing at 0.279s, load angle at 112.5")

G E N-REC (clearing at 0.331 s, load angle at 150")

3.0

3.5

4.0

4.5

3.0

3.5

4.0

4.5

2.0

2.25

2.5

3.0

17.151160

0.969947

0.081212

0.009425

2.885353

0.167660

0.0 14576

0.001618

44.132060

2.497299

0.210813

0.02440 1

6.643706

0.386734

0.033470

0.003764

49.622160

2.81 5381

0.237434

0.027424

7.667989

0.445393

0.038561

0.004334

49.622310

2.81 5389

0.237434

0.027424

7.668127

0.445401

0.038561

0.004334

6.791221

0.461 196

0.034652

0.000160

6.792237

0.461219

0.034652

0.000160

6.792237

0.461219

0.034652

0.000160

6.792237

0.461 21 9

0.034652

0.0001 60

0.1 s fault applied, machine rnalsynchronisation, autoreclosure sequence not successful

(iii) Since the exciting agent comes from the generator, consider the worst-case oscillation deterioration for structural reasons; it is suggested that a safety factor of no less than 3.5 should be adopted for shaft LPlR- LP2F and LP2R-GEN, no less than 2.25 for GEN- REC and no less than 2.0 for HP-LPlF.

This study is done on the basis of the nuclear unit; however, it is discovered that after a trial similar out- comes can be obtained from thermal power plant units (see Section 9). For all, 'almost all of the material fatigue damage is done in the three seconds immedi- ately after the accident happens', and 'the agent that can cause the most violent oscillation is line-to-line fault or three-phase fault' are general and common.

484

Because of the multimodal nature of frequencies of shaft response, and the effects of stress concentrations and centrifugal stresses must be quantified, the present state of the art of fatigue estimates is imprecise. The methodology presented in this paper is relatively simple and easy to use.

References

YANG, B., and CHEN, H.: 'Reduced-order shaft system models of turbogenerators', IEEE Trans., 1993, PWRS-8, (3), pp, 1366- 1374 KEARTON, W.J.: 'Steam turbine theory and practice' (Shin Yueh, Taipei, 1977 7th Edn.), pp. 471490 MASRUR, M.A., AYOUB, A.K., and TIELKING, J.T.: 'Stud- ies on asynchronous operation of synchronous machines and related shaft torsional stresses', IEE Proc. C, 1991, 138, (1). pp. 47-56

IEE Proc.-Gener. Transni. Distrib., Vol. 143, No. 5, September 1996

4 IEEE working group on Computer modelling of excitation systems: ‘Excitation system models for power system stability studies’, ZE.EE Trans., 1982, PAS-101, (2), pp. 2364--2374 CUDWORTH, C.J., and SMITH, J.R.: ‘Steam turbine generator shaft torque transients: A comparison of simulated and test results’, IEE Proc. C, 1990, 137, (9, pp. 327-334

6 JOYCE, J.S., KULIG, T., and LAMBRECHT, El.: ‘Torsional fatigue of turbogenerator shafts caused by different electrical sys- tem faults and switching operations’, ZEEE Trans., 1978, PAS-97,

7 HAMMONS, T.J.: ‘Suessing of large turbine-generators at shaft couplings and LP turbine final-stage blade roots following clear- ance of grid system faults and faulty synchronisation’, ZEEE Trans., 1980, PAS-99, (4), pp. 1652-1662 IEEE SSR task force o f the Dynamic system performance working group: ‘Fir:st benchmark model for computer simulation of sub- synchronous resonance’, ZEEE Trans., 1977, PAS-96, (5 ) , pp. 1565-1572 HAMMONS, T.J.: ‘Electrical damping and its effect on accumu- lative fatigue life expenditure of turbine-generator shafts follow- ing worse-case supply system disturbances’, ZEEE Trans., 1983,

10 JACKSON, M.C., and UMANS, S.D.: ‘Turbine-generator shaft torques and fatigue: Part I11 - refinements to fatigue model and test results’, ZEEE Trans., 1980, PAS-Y9, (3), pp. 1259-1268

11 WILLIAMS, R.A., PLDAMS, S.L., PLACEK, R.J., KLUFAS, O., GONYEA, D.C., and SHARMA, D.K.: ‘A methodology for predicting torsional fatigue crack initiation in large turbine-gener- ator shafts’, ZEEE Truns., 1986, EC-1, (3), pp. 80-86

12 TSAO, T.P., CHYN, C., and NIEN, H.H.: ‘PL large-scale mechanical filter - the application of turbine-generator flywheel coupling’, EPSR J., 1992, 25, (l), pp. 3 5 4 5

13 MARTINE:Z, J.A.: ‘Educational use of EMTP models for the study of rotating machine transients’, IEEE Trans., 1993, PWRS- 8, (4), pp. 1392-1399

14 IEEE committee report: ‘Dynamic models for steam and hydro turbines in power sys,tem studies’, ZEEE Trans., 1973, PAS-92, (6), pp. 19061915

5

( 5 ) , pp. 1865-1877

8

9

PAS-102, (6), pp. 1552-1563

9 Appendix

9. 1 System parameters of 951 MW machine

9. 1.1 Electrical system data Synchronous generator: (rating: 1057.5MVA, 23.75kV, 60Hz, four pole) Xd = 1.574 Xq 1.490 X , = 0.190 xfl = 0.168 x k , j 0.110 X/cq = 0.4901 R, = 0.00359 R k d 0.02571 R k q = 0.02571 Rf 0.000698 Step-up transformer (rating: 1057.5MVA, 23.751345 kV): X , = 0.14304 Transmissialn line (rating: 1057.5MVA, 345kV):

R, == 0.00192

Xi, = XI, == XI , = 0.1088 X 2 A = X . , == X 2 , = 0.1088

RI, = R I B = RI, = 0.0073 R,A = R 2 B = R 2 , = 0.0073

Initial operating conditions: Po = 0.90 QO = 0.10 V, = 1.03

9.1.2 Control system data

Table 4: AVR Data (modified type 1 AVR moddl [41

Lead time Lag t ime constant constant

- Gain

- Block 1 1 .ooo 0.0010 0.0010

Block 2 50.00 0.0000 0.0000

Block 3 -34.48 0.0000 -4.0300

&lock 4 1.000 0.0460 0.5780

Limit (pos., leg.) 1 .oooo -0.9500

Threshold volt. (1, 2) 3.7960 5.0620

SE (1,2,3) 0.0000 0.0750 0.2230 ~~~~

IEE Puoc.-GPnPr. Transm. B s t i i b , Vol. 143, No. 5, September I996

Table 5: Governor Data 1141

Lead t ime Lag t ime constant constant

Gain

Block 1 18.00 0.0000 0.0010

Block 2 1.000 0.0010 0.1000

Block 3 1.000 0.0000 0.7000

Block 4 0.690 0.0000 3.0000

Limit (pos. , neg.) ’I ,0400 0.0000

9.7.3 Mechanical s ystern data

Table 6: Rotor spring miass parameters

--

Inertia Damping Stiffness MMWsIMVA) D(MWs/MVA rad) K(MW/MVA rad)

Mass

HP

LP1 F

LP1 R

LP2F

LP2R

GEN

REC

EXC

0.1787

0.6538

0.6486

0.6575

0.6676

1.1616

0.00344

0.00236

0.00780

0.00230

0.00210

0.00210

0.00210

0.0

0.0

0.0

144.15

1595.0

206.0

1584.9

325.28

117.16

1.61

Relative torques: Th = 31% TI,= TI,= 7;,= TZr= 17.25%

9.2 System parameters of 666 and 750MW machines

9.2.1 Mechanical system data of 666 MW machine (see Figs. 20 and 2 1)

Table 7

Inertia Damping Stiffness Mass H(MWs/MVA) 1XMWs/MVA rad) K(MW/MVA rad)

HP 0.072 0.00088

IP 0.318 0.001 14

LPIF 0.575 0.00029

LPIR 0.539

LP2F 0.612

LP2R 0.573 0.00029

49.0

94.0

0.00029 2146.0

0.00029 85.7

2146.0

GEN 0.784 0.0

EXCI 0.014 0.0 EXC2 0.048 0.0

63.6

37.4

18.0

Relative torques: Th = 27.8% T; = 35.8% TI,= 9.2% TI,= 9.0% TZf= TZr= 9.1%

~

2 0 1 - t : i i 8 ’ , i I 100 200 300 400 ‘500 600 700 800 900

time, s x Fig.20 machine (1) L-L (111) L-L-E

Comparison of generator load angle for each fault, 666MW

jii) L-L-L-E (iv) L-E

485

OH P - I P 0 1 P-LPIF A LP2R-GEN a- I T

a I 21 a :-

0 0 c--I------c-I +T 100 110 120 130 140 150 160 170 180

load angle Fig. 21 i g (autoreclosure sequence not successful), 666M W machine 0 HP-lP 0 IP-LP1F A LPZR-GEN

Perturbation following L-L-L-Ejault clearance and synchronn-

9.2.2 Mechanical system data of 750 MW machine (see Figs. 22 and 23)

Table 8

Inertia Damping Stiffness H(MWs/MVA) D(MWs/MVA rad K(MW/MVA rad)

Mass

HP 0.0929 0.00002 1

IP 0.15559 0.000067 19.303

34.929

52.038

70.858

2.828

LPA 0.85867 0.000265

LPB 0.88422 0.000265

GEN 0.8685 0.000263

EXC 0.03422 0.000180

Relative torques: T h = 30% T, = 26% T, = Tb = 22%

486

201 i , ~ i : ~ : i ~ ~ i i i i i 1 time, s x

100 200 300 400 500 600 700 800 900

Fig.22 machine (i) L-L (iii) L-L-E (ii) L-L-L-E (iv) L-E

Comparison of generator load angle for each ,fault, 750MW

100 110 120 130 140 150 160 170 180 load angle

Fig. 23 (autoreclosure sequence not successful), 750M W machine 0 HP-IP 0 IP-LPA A LPB-GEN

Perturbation following L-L fault clearance and synchronising

IEE Proc.-Gene?. Trunsm. Distrib., Vol. 143, No. 5, September 1996