IEEE Transactions on Power Systems, Vol. PWRS-2, No. 1, February 1987

LOW FREQUENCY OSCILLATIONS IN LONGITUDINAL POWER SYSTEMS:EXPERIENCE WITH DYNAMIC STABILITY OF TAIWAN POWER SYSTEM

Yuan- Yih Hsu, Member Sheng-Wehn ShyueDepartment of Electrical Engineering

National Taiwan UniversityTaipei, Taiwan

Republic of China

ABSTRACTSustained low frequency oscillations have been observed in

Taiwan power system which is of longitudinal structure. It is thepurpose of this paper to examine the various factors affecting thedamping characteristics of these oscillations which caused dynamicinstability problem in the operation of Taiwan power system. It isobserved that the amount of power flow on the EHV transmissionline and the characteristics of load have a significant effect on thedamping of the system while the speed-governing system and the gainof automatic voltage regulator have only a minor one. Detailedinvestigation using both the frequency domain and time domainapproaches also reveals that power system stabilizers can be employedas an effective means for improving dynamic stability of Taiwanpower system.

1. INTRODUCTIONAccording to a recent CIGRE report issued in 1979 [1],

spontaneous low frequency electromechanical oscillations in a

multimachine power system, which would cause system dynamicinstability, can be divided into two categories:(1) inter-area oscillations which occur when two areas are connected

by a long distance weak transmission line,(2) longitudinal system oscillations which are usually observed in a

system with a longitudinal structure.The oscillations of the first category have been reported in many

power systems in North America [ 2-1 1 ] and other parts of the world[12-17] while those of the second category were observed only inEurope [ 1 8-21 ] and Japan [ 22-23].

The power system in Taiwan is longitudinal in nature (see Fig. 1)and low frequency oscillations of the second category occurred on

February 28, March 1, 3 and 7 of 1984 [24]. These oscillationshappened during off-peak periods when there were great amount ofpower flow on the EHV transmission lines. Fig. 2 gives the recordingof megawatt output of second nuclear unit #1 in the evening ofMarch 3, 1984. The maximum amplitude of oscillation in the realpower output of the unit with 950 MW nominal output was found tobe 70 MW. The oscillations remained at constant amplitude for about15 minutes. The evidence of dynamic instability in the system was

clear and a research project sponsored by Taiwan Power Company wasthen conducted by the authors to investigate these low frequencyoscillations in Taiwan power system [25 ]. In that research project, allthe eigenvalues associated with electromechanical oscillation modesof the system along with the normalized generator speeds andmomenta are computed by using a modified version of AESOPS(Analysis of Essentially Spontaneous Oscillations in Power Systems)program which was originally developed by Byerly, et al. [ 26, 27] andmodified by the authors to take the special features of the digitalcomputer in National Taiwan University Computing Center intoaccount. In the final report [25] of the project, it was pointed outthat dynamic instability would result from the fact that there exist a

pair of eigenvalues with poor damping.After the project was finished, the authors felt that it's necessary

to examine the various factors affecting the damping characteristicsof the poorly-damped oscillation mode. The factors of major concern

86 WM 070-7 A paper recommended and approvedby the IEEE Power System Engineering Committee of

the IEEE Power Engineering Society for presentationat the IEEE/PES 1986 Winter Meeting, New York, New

York, February 2 - 7, 1986. Manuscript submitted

August 21, 1985; made available for printingNovember 18, 1985.

are the amount of power flow on the transmission line, the speed-governing system and the gain of the voltage regulator [1-5] and thecharacteristics of load [28]. Moreover, application of power systemstabilizers, which have been extensively studied during the past twodecades [29-38 ], to damp out the sustained low frequency oscillationsis also examined in this paper.

The contents of the paper are arranged as follows. In the nextsection, after a brief description of Taiwan power system underconsideration, the principal results including system eigenvalues andnormalized speeds and momenta in [251 are summarized. In thesubsequent section, the effects of various factors such as line flows,load characteristics, speed governors and voltage regulators on systemdamping are examined. Finally, tuning of power system stabilizersto improve dynamic stability of Taiwan power system is elaboratelyperformed.

HYoRo STAnON

THERMAL STATION FIRSTOAOBO

(0 345KV SUBSTATION gu m345KV TRANSMISSION LINE WX0341

/ \~~~~~~~75 25XI

wHUN~~~~UGLIAO/

79=9001~ ~ ~ ~ ~

Fig. 1 Taiwan Power System

2. DESCRIPTION OF THE SYSTEM

There are 16 generating units including 2 synchronouscondensers in Taiwan power system as shown in Fig. 1. Thesegenerators are geographically located at three different areas on theisland of Taiwan with a distance of 400 Km from the north to thesouth. The three areas are designated as N (the northern area), C (thecentral area) and S (the southern area). The bus number, bus name,

0885-8950/87/0100-0092$01.00© 1987 IEEE

Chung-Ching Su

92

a- 0

act

12 l1o0M. P.M. P.E

M. P.M.

Fig. 2 Recording of Second Nuclear Unit #1

Megawatt Output

real and reactive power generation, voltage magnitude and angle for

each generator bus are listed in Table 1. In order to examine the real

power flows among the three areas, we summarize the power

generations and load demands in the three areas in Table 2.

Table Summary of Generator Bus Data

numsber bus name9 type I0are power9 po0wer ma9g0i0049 90919

3 FirstNuclearPlant#1 9nuclea N 582 122.9 0.990 17.0

4 First NuclearPlant #2 nuclear N 587 123.5 0.990 17.0

9 Seond0NucloearPlant#lI nucl9ea N 950 088.0 0.990 17.4

10 Second NuclearPlant #2 00009a9 N 853 176.7 0.990 06.725 Shnao #1 00990090 N 39 26.4 0.990 00.127 Shenao0#2 thermaol N 85 71.7 0.990 9.8

900 Taipei (synchronouscondenser) S.C. N 0 -20.0 0.999 4.4

902 Chinshan9 hydro C 92.8 39.3 0,990 0.0

000 Chuokungg hoydro C 22 00 0.970 -93

118 Takuano hydro C 33 50 0.969 10.8

219 Talin #1 theronal S 112 119.2 0.990 -13.1237 Hsinta #1 thermal9 S 220 102.5 0.990 - 7.3

230 Hsnta1#2 thermalo S 220 161.8 0.990 -7.3

257 Nanpu #1 &2 thermaol 5 40 30.0 0.990 - 15.4

250 Nanpuoo#3 thermaio 5 57 39.3 0.990 -15.3

300 Kaohsiung (synchonous con0499999) IS.C. S 0- 33 0.998 101.5

Table 2 Real Power Generation and Load Demandin the Three Areas

real power real power load demand load demandeeneration generation

area (MW) (% (MW) (%

North 3095 81% 1402.3 37%(N)

Center 147.8 2% 909.6 24%(C)

South 649 17% 1478.1 39%(5)

Total 3891.8 100%7 3790 100%

It can be concluded from Tables and 2 that there will be a

considerable amount of power flow southward since there are

76i1.8 MW and 829.1 MW power deficiencies in the Central and

Southern areas respectively. The maximum transmission angle is

35.90 between buses 9 and 300. In view of the longitudinal structure

of Talwan power system (see Fig. 1) and the great amount of power

flows on the EHV transmission lines, sustained low frequencyoscillations in the system can be expected [18-23 ].

Using the modified version of AESOPS program, we computedthe eigenvalue, oscillation frequency and normalized generator speeds

associated with each electromechanical oscillation mode as given in

Table 3. The normalized generator momenta (momentum is the

product of speed and inertia) for each mode are given in Table 4. The

blocked entries in Tables 3 and 4 correspond to those generators with

the normalized speeds or momenta greater than 0.1. The generators

will be significantly affected by the corresponding oscillation mode

and they are summarized in Table 5.

Table 3. Normalized Generator Speedsmode egnfreqf bUnS 4 9 88902207 99912119I92199 729 57 2 0

-FOoflOlfll9Frn 9~~~~~~~~~~a70.003

00 F o95 000 o9 00 00 9o

~~~~~~~~~~00000009

a ol [ 0002990.

119 090 000 009 0 0 902 0994 0094 90 90 0.09 90 90

t1 a,9 09 00 0 0 0.0 0.0 9010 0

1. ,7-0. 3 -0. 0902L 0L 06 00 090 009I 90-0 0.00 039i 0.09 01093002 0.09 .01 M0 1 00 1 0 0 10 .08 01

[INE _00 900 90 090 0- _O90 _09 -0-

~~~~~~~~~90.09 O739 01 001 F0O02 -01 102 0102 O. 000 0992.8 997 00 0.0 0

1. 2099 02 0 0 90 o00 [

~ ~ ~ ~~~000

0 0 9o 0 06 0 0 00 00

0 0909 00 9990 -0.5j198 009 -0.00

0

0 0 9l 9O- 9o u099 03 O0 .0

9.8 ,.0iL,0.JI,.,JL9003,9943,025

*The two values of each normalized speed denote the real andimaginary parts of the speed phasor.

Table 4. Normalized Generator Momenta

mode y-lu freq bo 9 9 93

0

00l 31 OO1T53 i11 09 0'03 0 FO 1104100FEOSM Fo1OQr0 1 181 rnrrvO09j 07.2 ,,O ,349 9,5 0.02 00JLAL,0 00 00 0 LoL.o

0309090 0.07 -009 95L.9 0109 0 309 -439 9991 900 0.0 -006 -0. 900 998.60009 0.02 00802 09 &009 000 009 0lOOFO190.01 00 0 _01F01

33020 99 09 00 0998 0.06 0 0.09 0 0.04 -0.0 00 00 00 0 09003900900 009 009 FT1F3341 099 9 0 9 9 9 009~~~~~~~~~~009 9 0

I0 8,70S0 09 09 0.09 0.09 -0096 0 0 09 00.00 002 919 9900999 9009009 009 099 000 990 0 099 0 009 099 090 09~~~~~~[MOM 009 0.09 0

9 15 9 (04 0 0 00 0 0 0 09 9902 00 0090 03 0.0 0.0 0.0

0 90000 0 090000000!-Ol 7 909 9 90 9 0 009 909 009 00 0 99 i992 0997 90 90 990 090 00 09 9 90 9 00 00 90 00 0 0 9

9 9009000 903 090 090 9 909 0 ~~~~ ~~~~~~~099 0-L020 905 0 0.09 0.0 90. 086 09 090 9990 00 0 9 9 0 09 900 0 0 00 09 90 09

09999 F71409 009 090 9 0 0 9 0

0099 90 00299796 900 9110 0F 1 051 10.02 81 10.01 0.09 90 0090 099C 9909 0000 0 0 0.09 L,,9JL .57 0.01 0994 9.3, 0 00 0

0990 0.0 00 9. OLO 9 0.0 0 -0. 9 T 13409j- 99.44941.9 2 90 0.0 _90 _0 9 9 9 0 [,,,,9,J3RE,9,J09tj1790 900 00 0 09 000 . 00 9 - 00 l 0011~ [55lf 03 0j5 009 0090

0 09900099 1.900 0 0 09 999 000 00 9 0.09 9 -0004 1z.01,03L9.11..9 J 0.09 -009 0.009000887 9090 990 09- 9 0090 0 0906 'M 9F0l0TF0 0.02

090998- 0 0 9 9 9093,49930 90999 9899 9 9 9 09 0111 050

-1.6427099 0.99 0.0 900 900 900 9 -003 9 9 0 9 ,9 99,999355,3,,,9, 3,0,99[02 ,90999931 0.01 0F 1 -()T3 0.02 0 0.0 0002 09 99 900000 0 909 0.09,09939094 9009 0.0Li 0 OL,OJL,, .J .012 9 9090 90 9 0

Table 5. Summary of Generators which are Affecedby the Oscillation Modes

mode eigenvalue freqi. driven generators(Hz) generator affected

1 001051±j7.2443 1.153 238 3,4,9,10,112,116,118,219,237,236,257,278, 39002 -3.7566±j8.4680 1.348 100 9, 10, 100

3 -3.3027±j8.7405 1.391 300 219, 237, 238, 258, 300

4 01 5681±j9.0454 1.519 112 9, 10, 102, 219, 237, 23685 -0.3550±j9.9025 1.576 9 9, 10

6 -0.35160jlO 7243 1.707 10 3, 4, 9, 10, 259 277 -0.27860990.9945 1.750 27 3, 4, 9, 10, 20, 27

8 -0.1641+jll 4497 1.822 219 116,118,219,237,238,257,258,3009 0.5142±jl1.6759 1.058 3 3, 4

19 -2.28480j11.8871 1.892 116 1 16, 118, 219, 237, 238

11 -0.1060±431 9314 1.899 237 23 7, 238

12 -1.6427ojl2.2313 1.947 118 116, 118,219,237, 238

13 -0 1704+992.4558 1.982 257 219, 237, 238, 257, 20814 -0.2749±jl13.1039 2.886 258 219, 237, 238, 207, 258, 300

05 -0.3625,tjl9.3075 3.073 20 3, 4, 9, 10, 25, 27

In order to demonstrate the exact locations of the eigenvalues

associated with the fifteen oscillation modes of the system, we plotthe fifteen eigenvalues with positive imaginary parts in Fig. 3. The

other fifteen eigenvalues are simply complex conjugates of those

eigenvalues shown in Fig. 3. It can be observed from Table 3 that the

damping for the oscillation mode with lowest frequency (L1.153 Hz) is

very poor. The reason for the poorly-damped low-frequencyoscillation is that a great amount of power flow on the EHV transmis-

sion line is very likely to excite an electromechanical mode with poor

damping. It can also be observed from Table 5 that all the generators

93

-0-0151tJ 7.2443

-3.7566.t &4690

-3.3027:tj 8.7405

-1.5681:tj9.5454-Q3550

:d 9.9025

-03516:tjlO.7243

-0.2796JilO.994S

-0 1641til 1.4497

-&SI 2ti 1.6759

-2.2948*II 1.9871

-0.1960.Ij 1.9314

-1.642.tIZ2313

-o' 1704:wIl4SS8

-0. 2749till)(139

-0.3625IJ19.307S

94

except generators #25, #27 and #100 which are not directly incidentwith the EHV lines will be covered by the mode with lowestfrequency.

Another operating condition will be considered in this paper isthe one with one of the two circuits between Lungtan and Tienlunbeing tripped out. The eigenvalues are illustrated in Fig. 4. Theeigenvalue with the lowest oscillation frequency is found to be0.0561±i6.7333. Therefore, dynamic instability would result fromthe negative damping characteristics for this oscillation mode. Thisoperating condition will be employed in the following discussions.

- 3.5 -3 - 2.5 - 2 -1.5 -1 05

-2 0

-1 5

3. ANALYSIS OF FACTORS AFFECTING THE DAMPINGOF LOW-FREQUENCY OSCILLATIONS

The effects of line loading, load characteristics, speed-governingsystem and voltage regulator on the damping of low frequencyoscillations will be examined in this seciton.

3.1 Effect of line loadingThe effect of line loading on transient stability of Taiwan power

system has been extensively investigated [241. In a study that wasperformed by Taiwan Power Company, a three-phase fault lasting forfour cycles on the EHV transmission line was assumed. The systemwill be unstable unless the line flow is reduced from 1700 MW to1324 MW. In this paper, dynamic stability limit for Taiwan powersystem will be examined by computing the eigenvalues for fivedifferent values of power flows on the transmission lines. Fig. 5 givesthe real parts of the three pairs of eigenvalues (mode #1, #8 and #1 1)which are significantly affected by the line flows. It is found that,when the line flow is reduced from 1700MW to 1524MW, the systemwould become dynamically stable.

0.1

-0.1-1 0

-0.2 _

-0.3 -

-5-04

-0.5

0 05 C

Fig. 3 Eigenvalues for the Normal Operating Condition

1200 1300 1400 1500 1600ti --f-

01700

LINE FLOW(MW)

.

AAL

AAL

U

U

UU

Aa

LEGEND: * MODE * 1A MODE#8A MODE 11

Fig. 5 Effect of Line Loading on the Dominant Eigenvaluesof Taiwan Power System

-1 5

-1 0

-5

0 0.5 o-

Fig. 4 Eigenvalues for the Operating Condition with OneCircuit Tripped

3.2 Effect of load characteristicsIt has been pointed out [28] that load characteristics will affect

the dynamic stability of power system. In order to examine the effectof nonlinear load, the real and reactive power loads are expressed asfunctions of voltage:

-2 0

P= Po (A+BV+CV2)Q= QO(D+EV+FV2)

(1)(2)

where PO and QO are the real and reactive power load demands atrated voltage and the values of the six constants A, B, C, D, E and Fdepend on the load characteristics of the study system and are usuallydetermined by field tests. The exact values of these constants forTaiwan power system are not yet available at the present time.However, a research project regarding the determination of loadcharacteristics is to be conducted in the near future. In this paper, weshall consider the following three special cases:

Case 1: constant impedance load (C = F = 1),Case 2: constant current load (B = E = 1),Case 3: constant MVA load (A = D = 1).

The real load characteristics will be between two of these cases.Table 6 gives the computed eigenvalues for these three cases.

It can be concluded from Table 6 that load characteristics hasa significant effect on systefn damping. Nonlinear load will make thedamping of low frequency oscillation even poorer.

3.3 Effect ofspeed-governing systemSeveral reports in the literature [ 1-5] mentioned that automatic

generation controller (AGC) in the speed-governing system of agenerator may change the damping of low frequency oscillations. Inthe system considered in this paper, only three generating units

-3.5 -3 -25 -2 -15 -1 05

- lfvE~~~~~~~~~~ I - -i

0-

x

x

x xx

xx

x

0

X

:j

x

x

xx

xxx

XI

95

Table 6. Effect of Nonlinear Load on System Eigenvalues

mode driven constant inpedance constant current constant MVAnumber generator C= F= 1 B= E= 1 A= D= 1

1 238 0.0561±j6.7333 0.1864±j6.3999 0.4971±jS.83742 100 -3.7700±j8.5042 -3.7686±j8.5044 3.7664±j8.50443 300 -3.2918±j8.7048 -3.2929+j8.7108 -3.2977+j8.72014 112 -1.4724±j9.6617 - 1.4703±j9.661 2 - 1.4673±j9.66065 9 -0.3415±j9.9479 -0.3415±j9.9477 -0.3415*j9.94746 10 -0.3167+jlO.7423 -0.3087±jO.7434 -0.2992±jlO.74677 27 -0.2995±jlO.9998 -0.3074±jlO.9933 -0.3220±jlO.98598 219 -0.1572±jll.4659 -0.1622±jll.4371 -0.1719±jll.39669 3 -0.4918+jl 1.7421 -0.4918tjl 1.7421 -0.491 8±jl 1.7421

10 116 -2.2849±jll.8902 -2.2761±jll.8939 -2.2625+jl 1.902211 237 -0.1697±j11.9957 -0. 1697j1 1.9957 -0. 1697±jl 1.99571 2 118 -1.6422±jl2.2257 - 1.63 70jl 2.2045 -1.6287±j12.17261 3 257 -0. 1 706+j12.4506 - 0. 16 78±jl2.4427 -0.1655±jl 2.431114 258 -0.2743±jl3.1009 -0.2707±jl3.1002 -0.2670±j13.098115 25 -0.3692±.j19.3110 -0.3688±jl9.3057 -0.3686±j19.2992

(#112, #116 and #118) are equipped with AGC. As shown in Table7, only minor changes in system damping can be observed as the AGCin these three units are removed. This might be due to the factthat the capacities of these hydro units are small compared with otherunits in the system.

Table 7. Effect of AGC on System Eigenvalues

mode driven with AGC without AGCnumber generator

1 238 0.0561+j6.7333 0.0540±j6.73734 112 - 1.4724±j9.6617 - 1.4808±j9.74958 219 -0. 1572±j1 1.4659 -0. 1570±jl1.465710 116 - 2.2849±j11.8902 - 2.2509j 1 2.145 212 118 - 1.6422S 1 2.2257 - 1.6256±j12.2742

3.4 Effect of voltage regulatorFinally, let's take a look at the effect of regulator gain in Hsinta

plant on system damping. Table 8 gives the eigenvalues for fourdifferent values of the gain KA. Only three pairs of eigenvalues willbe affected by KA and they are listed in Table 8. It is found thatreducing the value of KA will deteriorate system damping.

Table 8 Effect of Regulator Gain on System Eigenvalues(without AGC)

mode driven K.=40 KKA20Onwnber generator KA4 KA= 200 A= 100 KA = 0

1 238 0.0540±j6.7373 0.067±j6.7394 0.0764±j6.7338 0.079_j6.7283

8 219 -0.1570±jl l.4657 -0.1608±jl 1.4715 -0.1608±411.4757 -0.1601±j1 1.4775

11 237 -0.16975±11.9957 -0.1730±jl 2.0017 -0.1728±jl 2.0058 -0.1720±+jl2.0078

4. APPLICATION OF POWER SYSTEM STABILIZER

In view of the poor damping for the oscillation mode withlowest frequency, a decision is made to employ power systemstabilizer (PSS), which has been widely used by the utilities, to dampout the low frequency oscillations. The power system stabilizer isboth effective and inexpensive for dynamic stability enhancement.Two problems will arise as one tries to design a proper power systemstabilizer for a multimachine power system [29-38]. The firstquestion is where we should place a power system stabilizer. Con-siderable efforts have been placed on finding the best site for PSS[34, 35, 361. In this paper, PSS is installed in the second nuclearplant (generators #9 and #10) and Hsinta plant (generators #237 and#238) based on the following reasonings:(1) The oscillation mode with poorest damping (and lowest

frequency) is excited by the great amount of power flow on theEHV transmission line connecting the second nuclear plant andHsinta plant (see Section 3). Therefore, power system stabilizersinstalled in these two plants will be most effective in dampingout this low frequency tie line oscillation.

(2) From the normalized generator momenta associated with mode 1in Table 4, it can also be concluded that generators #9, #10,#237 and #238 are suitable for PSS implementation. It shouldbe noted that generator #219 is not selected since it's notdirectly incident with EHV transmission line. This approach forselecting PSS location based on generator momenta is similar tothe one based on eigenvectors recommended by deMello et al.[34].The other problem in PSS design is the tuning of PSS constants.

Three types of signals, i.e., power, frequency and speed, are usuallyemployed as the input signals for PSS. In this paper, we employ thespeed as the input signal. The transfer function of a power systemstabilizer may be expressed as follows [31, 32 ]:

G TsK- Tws (1 +sT5)(l +sT3)G ( l TWS (1 +sT2) (l + sT4)

where Ks = stabilizer gainTw = washout time constantT5, T2, T3, T4 = time constants of the lead-lag pairs.

The washout term Tws/(1+Tw s) is employed to eliminate the steady-state offset of PSS and the washout time constant is chosen to be lOs[32]. It is our purpose to determine proper values of Ks, T,, T2, T3and T4 in order to have good damping for the low frequency oscillationmode. In this paper, root locus technique is employed for the tuningof stabilizer constants. Many root loci for various combinations oflead-lag time constants have been plotted with the stabilizer gain K, asparameter. Figure 6 shows three typical plots for different values oflead-lag time constants. Only the generators (#9 and #10) in secondnuclear plant are equipped with PSS. If the generators in both thesecond nuclear plant and Hsinta plant are equipped with PSS, the rootloci will be as shown in Fig. 7. It should be pointed out that thestabilizer gains and time constants for all the generators in each caseare assumed to be the same.

From the root loci in Fig. 6 and 7, the optimal stabilizerconstants can be determined based on the criterion of having greatestdamping (greatest absolute value of the real part of dominant eigen-value). They are summarized in Table 9.

Table 9 Summary of Stabilizer Constants

generators equipped with PSS Ks T1 T3 T2 T4

#9 and#10 5 0.5 0.5 0.05 0.05

#9,t10,#237and#238 18 0.225 0.225 0.015 0.015

In order to demonstrate the effectiveness of the proposed PSS,the dynamic responses of the rotor angle swings following a 10%small disturbance are given in Figures 8 and 9. The responses ofFigure 8 are obtained under the operating condition with 1700MWline flow and with one circuit between Lungtan and Tienlun trip. NoPSS is applied in this case. Fig. 9 shows the responses for the sameoperating condition as in Fig. 8 except that PSS is applied to generators#9 and #10. The stabilizer constants are given in Table 9. It can beconcluded from the root loci in Fig. 6 and the time-domain responsesin Figs. 8 and 9 that application of PSS to the second nuclear plantcan significantly improve the damping characteristics of the lowfrequency oscillations.

The rotor angle swings following a 4-cycle 30 fault in EHVtransmission line are plotted in Figs. 10, 11 and 12. As mentionedbefore, the line flow has to be reduced to 1324MW in order to ensuretransient stability. Fig. 10 shows the responses without any PSS inthe system. Oscillatory swings with very poor damping following30 fault have been observed. When power system stabilizers withthe settings given in Table 9 are applied to the second nuclear plant(generators #9 and #10), the damping is improved to a considerabledegree (Fig. 11). Further improvement in system damping can beachieved if generators #237 and #238 in the Hsinta plant are alsoequipped with power system stabilizers (Fig. 12).

5. CONCLUSIONSIn this paper, extensive studies have been made to investigate the

factors affecting the damping of the low frequency oscillations inTaiwan power system. Application of power system stabilizers to

(3)

Tj = T3 = 0.05

T2 = T4 = 0.005

10V0of

1%,Qo

-15

/XS.2S

-10

-3 -2 -I o

Ks2,/ J iI26'X

23j// T1 = T3 = 0.225

20.1T20t T2 = T4 0.015

17\

14

-

263r

-4 -3 -2 -1 0'

JPT1 = T3 = 0.5

T2 =T4=005KsS/

4/

2*s

_.5

-4 -3 -2 -1 01

Tr _ ¢1 -nAo1)I

IL)

-16

-15

-14Ks-1\

-13

-1 2

-1 1

-10

-9

T 13 = /

T2= T4 = 0.015

}5-'- ~~~~302t7it*7v-_' 1

12 i. 5 0

S-5--.I_

3 -_._

30

25

20f18~

1058

-7

-6

S5 -4 -3 -2 -1 0'

-10

5

U)c

15T1=T3 =0.5

3~~~~

T2 =T4=0.05 I-

./

/

{ s4i

55**

..

2

11._

"'-O

o8,N

-10

:ty.5

15

10

.5

-4 -3 -2 -1

Fig. 7 Root Loci for the System with PSS in Both the Second NuclearPlant and Hsinta Plant-MODE #1 --- MODE #8 MODE #5

96

j015

10

T1 =T3 0.05

T2 = T4 = 0.005

300

2010$-

019

1=3020100

'5

-4 - - -3-2 -1 u

Fig. 6 Root Loci for the System with PSS in Second Nuclear PowerPlant Only

MODE #1 ----MODE #5

II a

--I--=

iSu

^f28

\f.IL TT

1. 98bY 3.9S8980.9697 2.9881 5.9915

TIME

t

Fig. 8 Dynamic Responses for a 0.1 p.u. Small Disturbance(Without PSS)

Fig. 11 Rotor Angle Swings Following a 30 Fault(With PSS in Second Nuclear Plant)

S.9932 7.99b6 10.0004.9Y15 9.9999 6.9566TIME

ILI

Fig. 9 Dynamic Responses for a 0.1 p.u. Small Disturbance(With PSS in Second Nuclear Power Plant)

0o.1. 6. 6. 7 so .ooo0. 9Qs7

9 .b961 S

5S93

6.994 e. 0'TIME

Fig. 10 Rotor Angle Swings Following a 30 Fault(Without PSS)

XI

0.98Y7 2.9881 Y.9915 0.9999 6.9983TIME

Fig. 12 Rotor Angle Swings Following a 30 Fault (With PSS in BothSecond Nuclear Plant and Hsinta Plant)

improve dynamic stability of Taiwan power system was alsoexamined.

Specific conclusion arising from this work can be summarized asfollows:i) Low frequency oscillations with poor damping is expected to

occur during off-peak periods since the amount of power flow onthe transmission line is great. An effective means for enhancingthe damping is to reduce the power flow on the tie line. This islimited, however, by the constraint that the Megawatt outputof the first and second nuclear plants, which are located in thenorth of Taiwan, can not be reduced quite a lot for the sake ofeconomic and security reasons.

ii) With a proper selection of the location and constants for thepower system stabilizer, it has been demontrated that systemdamping can be significantly improved by the application of PSSto the second nuclear plant and Hsinta plant.

iii) The characteristics of load has a significant effect on the dynamicstability of the system.

iv) The gain of the voltage regulator has certain effect on systemdamping.

v) As the capacities of the generating units already equipped withAGC are small compared with other units, the effect of theseautomatic generation controller on system damping is verysmall.Further research works on the application of other stability

enhancement techniques such as static phase shifter (SPS), static varsystem (SVS) and HVDC modulation to improve the dynamic stability

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of Taiwan power system are being conducted by the authors.

6. ACKNOWLEDGEMENT

The authors would like to express their sincere gratitude toMessrs. C.J. Lin, T.F. Yang, C.Y. Chiou, C.L. Chang and Y.F. Jwangof the System Planning Department, Taiwan Power Company, forproviding the invaluable system data. Financial supports given to thisresearch work by the Taiwan Power Company and the NationalScience Council of R.O.C. are also appreciated.

7. REFERENCES

[1] C. Barbier, E. Ferrari and K.E. Johansson, "Questionnaire onelectromechanical oscillation damping in power systems:Report on answers", ELECTRA, vol. 64, pp. 59-90, 1979.

121 F.R. Schleif and J.H. White, "Damping for the Northwest-Southwest tieline oscillation-an analog study", IEEE Trans.PAS, vol. 85, pp. 1239-1247, 1966.

[3] F.R. Schleif, G.E. Martin and R.R. Angell, "Damping of systemoscillations with a hydrogenerating unit", IEEE Trans. PAS,vol. 86, pp. 438442, 1967.

[41 O.W. Hanson, C.J. Goodwin and P.L. Dandeno, "Influence ofexcitation and speed control parameters in stabilizing inter-system oscillations", IEEE Trans. PAS, Vol. 87, pp. 1306-1313, 1968.

[5] F.R. Schleif, H.D. Hunkins, G.E. Martin and E.E. Hatton,"Excitation control to improve powerline stability", IEEETrans. PAS, vol. 87, pp. 1426-1434, 1968.

[6] E.V. Larsen, "Field test and analytical experience with dynamicstability of a loosely interconnected power system", Paper A78519-1, presented at 1978 IEEE PES Summer Meeting.

[7] P.A. Rusche, D.L. Hackett, D.H. Baker, G.E. Gareis and P.C.Krause, "Investigation of the dynamic oscillations of theLudington pumped storage plant". IEEE Trans. PAS, vol. 95,pp. 1854-1 862, 1976.

[81 J.S. Czuba, L.N. Hannett and J.R. Willis, "Implementation ofpower system stabilizer at the Ludington pumped storageplant". Paper 85SM469-2, Presented at 1 985 IEEE PESSummer Meeting.

[91 P. Bingen, F.W. Keay, G.L. Landgren and C. Raczkowski,"Dynamic stability tests on a 733 MVA generator at Kincaidstation", IEEE Trans. PAS, vol. 93, pp. 1328-1334, 1974.

[10] J.E. Van Ness, F.M. Brasch, Jr., G. L. Landgran and S.T.Naumann, "Analytical investigation of dynamic instabilityoccurring in powerton statioi", IEEE Trans. PAS, vol. 99,pp. 1386-1395, 1980.

[11] A.B.R. Kumar and E.F. Richards, "An optimal control law byeigenvalue assignment for improved dynamic stability in powersystems", IEEE Trans. PAS, vol. 101, pp. 1570-1577, 1982.

[121 A. Olwegard, "Improvement of system stability in intercon-nected power systems". CIGRE Paper 32-17, 1970.

[13] T. Johansson, B. Wrang, L. Makela, Y. Laiho and T. Carlsen,"Stability problems in the Nordic power system". CIGREPaper 31-06, 1982.

[14] W. Fairney, A. Myles, T.M. Whitelegg and N.S. Murray, "Lowfrequency oscillations on the 275 KV interconnectors betweenScotland and England", CIGRE Paper 31-08, 1982.

[15] R.L. Bolden, P.J. Wallace and A.W. Grainger, "Considerationsin the improvement of system damping on the south eastAustralian interconnected system", CIGRE Paper 31-05, 1982.

[161 Z.G. Khvoschinskaia, I.V. Litkens, M.G. Portnoy, V.A. Stroev,Yu. A. Tikhonov and V.A. Venikov, "Damping of oscillationsin power systems". CIGRF, Paper 32-07. 1980.

[1 71 N. Martans and R. Baitelli, "Analysis of low-damped electro-mechanical oscillations in large power systems", CIGRE Paper31-02, 1982.

[181 V. Arcidiacono, E. Ferrari, R. Marconato and F. Saccomanno,"Analysis of factors affecting the damping of low-frequencyoscillations in multimachine systems", CIGRE Paper 32-19,1976.

[19] V. Arcidiacono, E. Ferrari, R. Marconato, T. Brkic, M. Niksicand M. Kajari, '"Studies and experimental results on electro-mechanical oscillation damping in Yugoslav power system",Paper A75 420-0, presented at 1975 IEEE PES SummerMeeting.

[201 V. Arcidiacono, E. Ferrari and F. Saccomanno, "Studies ondamping of electromechanical oscillations in multimachinesystems with longitudinal structure", IEEE Trans. PAS, vol. 95,pp. 450-460, 1976.

[21] V. Arcidiacono, E. Ferrari, R. Marconato and G. Manzoni,"Problems posed in power system planning by electro-mechanical oscillation damping and means for solution",CIGRE Paper 31-15, 1982.

[22] J. Toyoda and Y. Uriu, "Totalized stabilization of powerswing by multi-stabilizing apparatus", The Trans. of theInstitute of Electrical Engineers of Japan, vol. 98-B. pp. 1009-1015, 1978.

[231 H. Suzuki, S. Takeda and Y. Obata, "An efficient eigenvalueestimation technique for multimachine power system dynamicstability analysis". The Trans. of the Institute of ElectricalEngineers of Japan, vol. 100-B, pp. 525-532, 1980.

[24] Investigation of the Operational Problems During Off-peakPeriods, Internal Report of Taiwan Power Company, March1984

[25] Y. Y. Hsu, Frequency Domain Analysis of Power SystemDynamic Stability--Phase I, Research Report of Taiwan PowerCompany, May 1985.

[26] R. T. Byerly, D. E. Sherman and R. J. Bennon, FrequencyDomain Analysis of Low Frequency Oscillations in LargeElectric Power Systems, EPRI Research Project 744-1. vols. 1-5.1982.

127] R.T. Byerly. R.J. Bennon and D.E. Sherman, "Eigenvalueanalysis of synchronizing power flow oscillations in largeelectric power systems". IEEE Trans. PAS, vol. 101, np. 235-243, 1982.

[28] W. Mauricio and A. Sernlyen, "Effect of load characteristics onthe dynamic stability of power systems", IEEE Trans. PAS,vol. 91, pp. 2295-2304, 1972.

[29] P.M. Anderson and A.A. Fouad, Power System Control andStability, Iowa State University Press, Ames, Iowa, 1977.

[301 Y.N. Yu, Electric Power System Dynamics. Academic Press,New York, 1983.

[31] F.P. deMello and C. Concordia, "Concepts of svnchronousmachine stability as affected by excitation control", IEEETrans. PAS, vol. 88, pp. 316-329, 1969.

[32] E. V. Larsen and D. A. Swann, "Applying power systemstabilizers", IEEE Trans. PAS, vol. 100, pp. 301 7-3046, 1981.

[33] R.J. Fleming, M.A. Mohan and K. Parvatisam, "Selection ofparameters in moltimachine power systems", IEEE Trans.PAS, vol. 100, pp. 2329-2333, 1981

[34] F.P. deMello, P.J. Nolan, T.F. Laskowski and J.M. Undrill,"Coordinated application of stabilizers in multimachine powersystems", IEEE Trans. PAS, vol. 99, pp. 892-901, 1980.

[35] S. Abe and A. Doi, "A new power system stabilizer synthesisin multimachine power systems", IEEE Trans. PAS, vol. 102,pp. 3910-3918, 1983.

[36] C.M. Lim and S. Elangovan, "Design of stabilizers in multi-machine power systems", IEE Proc., Pt. C. vol. 132. pp. 146-153, 1985.

[371 W.C. Chan and Y.Y. Hsu, "An optimal variable structurestabilizer for power system stabilization", IEEE Trans, PAS,vol. 102, pp. 1738-1746, 1983.

[38] Y.Y. Hsu and C.Y. Hsu, "Design of a proportional-integralpower system stabilizer", Paper 85 SM 470-0, presented at1985 IEEE PES Summer Meeting, Vancouver, Canada.