Dynamic equivalents of power systems with onlinemeasurements. Part 2: applications

P. Ju, F. Wu, N.G. Yang, X.M. Li and N.Q. He

Abstract: Final validation of a dynamic equivalent (DE) has been used to obtain the equivalentparameters from field tests and apply them to practical stability studies. Microcomputer-basedequipment was developed for online measurement and identification, from which several valuablefield results were captured. The results were then applied to dynamic response simulation andstability limit calculation.

1 Introduction

Online identification is an important application fordynamic equivalents. A previous paper [1] studied thetheoretical aspects and this paper gives the field test resultscaptured in Henan Power Company (HNPC), People’sRepublic of China. The results were applied to dynamicresponse simulations and stability limit calculations. To theauthors’ knowledge, such online measurements and appli-cations have not previously been reported elsewhere.HNPC has a generator capacity of 9692MW and

maximum load 8341MW. The network consists mainly of220kV transmission lines. There are two 500kV lines, one isan intra-line from Zhengzhou to Yaomen, and the other is atie line from Yaomen (in the area of interest, i.e. HNPC) toShuanghe (in the neigbouring area, i.e. Hubei PowerCompanyFHBPC). HNPC consists of only one waterpower plant with capacity of 400MW, and the neighbour-ing system consists of a large number of water power plants.As a result, the power flow between HNPC and HBPCvaries with seasons.At the end of 1998, a microcomputer-based equipment

was developed and installed at Yaomen Power Plant ofHNPC for online measurement and identification. Theequipment monitors the bus voltage and power flow of tieline periodically. If the variation of bus voltage exceeds apreset value, the equipment automatically records the three-phase voltage and current and then identifies the equivalentparameters. During the past two years, several valuablelarge disturbances have been captured. With the dynamicresponses, the equivalent parameters were estimated andthen applied to dynamic response simulations and stabilitylimit calculations.

2 Measurements

Four of the recorded disturbances are reported here, asdescribed in Table 1, in which, PG¼ total generation powerin Henan, PL¼ total load power in Henan, PT¼ totaltransmitted power through the tie line from Yaomen toShuanghe, and negative power means the power fromShuanghe to Yaomen.The dynamic curves recorded during four disturbances

are shown in Figs. 1–4, numbered 1. With them, theequivalent parameters are identified as given in Table 2.Using the measured voltage as input to the equivalentmodel, the identified parameters led to the dynamicresponses in Figs. 1–4, numbered 2. The results show that:

(a) The dynamic curves from the equivalent model are closeto those recorded in the field, which means that theequivalent model is able to represent the main dynamics ofthe external system with respect to the studied system.

(b) At different times and faults, the main equivalentgenerator parameters vary slightly and the equivalent loadparameters vary greatly. This may be explained by the factthat the service states of the generators (in or out) varyslightly; however, loads change very much from time totime.

3 Applications

3.1 Dynamic simulationsTwo system models are studied:

(i) Model A: All the generators in the whole system arerepresented by the fifth-order transient model and standardparameters, which are not necessary accurate. Load modelsare composed of half constant impedance and halfinduction motors.

(ii) Model B: The generators in Henan Power System(studied system) are represented by the fifth-order transientmodel and standard parameters. The left neighbouringsystem (external system) is described by the third-orderelectromechanical model with measured parameters.

Under fault 1, the simulation results with models A and Bare given in Figs. 5 and 6, respectively. The power base inFigs. 5 and 6 is 100MVA and the power base in Fig. 1 is theinitial steady power. As a result, multiplying by 0.32 foractive power and by 0.55 for reactive power gives the valueson the base 100MVA.

P. Ju is with the President’s Office, Hohai University, 1 Xikang Road, Nanjing210098, People’s Republic of China

N.G. Yang and N.Q. He are with the Dispatching Institute, Henan PowerCompany, 7 Songsan Road, Zhengzhou 450052, People’s Republic of China

X.M. Li and F. Wu are with the College of Electrical Engineering, HohaiUniversity, 1 Xikang Road, Nanjing 210098, People’s Republic of China

r IEE, 2004

IEE Proceedings online no. 20040075

doi:10.1049/ip-gtd:20040075

Paper received 13th June 2001

IEE Proc.-Gener. Transm. Distrib., Vol. 151, No. 2, March 2004 179

It can be seen from the Figures that the results of thetwo simulations are close to each other. The simulationresults are similar to the recorded ones, but, with smallerperiod.

3.2 Transient stabilityTransient stability is indicated by the index of maximumclearing time (MCT). Using two system models defined

above, MCTs are computed under several supposed faultsas listed in Table 3. It is clearly seen that, in most of thecases, there is only a little difference between theMCTs withtwo system models.The CPU times taken for the two system models are

compared in Table 4. It is clearly that system model B,which uses the simplified equivalent model to represent thestudied system, saves much computation effort.

1.21.11.00.90.8U

, tP,

tQ

, t

t, s

0.70.6

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

0.5

1.0

1.5

2.0

0

0.6

1.2

1.8

2.4

0

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

uo=548.3KV, PO=31.73MW, QO=54.79MVA

(i)

(ii)

Fig. 1 Dynamic responses under fault 1(i) Measured(ii) Dynamic equivalent

1.21.11.00.90.8U

, tP,

tQ

, t

t, s

0.70.6

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

0.5

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2.0

0

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0

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

uo=100KV, PO=100MW, QO=1MVA

(i)

(ii)

Fig. 2 Dynamic responses under fault 2(i) Measured(ii) Dynamic equivalent

Table 1: Four of the recorded disturbances

Fault 1 Fault 2 Fault 3 Fault 4

Time 22:52, 28 Dec, 1998 17:51, 8 Sept, 1999 21:49, 30 July, 1999 11:47, 4 Aug, 1999

Fault type One phase to ground,reswitching with success

One phase to ground,reswitching with success

Generator out of service Unknown

Fault Location 28km at the line from Yaomento Yahekou, 220kV

98km at the line from Yaomento Zhengzhou, 500kV

#2, Danhe plant Unknown

Operation state PG¼ 4728MW PG¼ 6753MW PG¼7465MW PG¼ 7130MW

PL¼4812MW PL¼ 6874MW PL¼7570MW PL¼ 7165MW

PT¼ 32MW PT¼58MW PT¼ 47MW PT¼�41MW

180 IEE Proc.-Gener. Transm. Distrib., Vol. 151, No. 2, March 2004

1.21.11.00.90.8U

, tP,

tQ

, t

t, s

0.70.6

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

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2.4

0

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

uo=100KV, PO=100MW, QO=1MVA

(i)

(ii)

(i)

(ii)

Fig. 3 Dynamic responses under fault 3(i) Measured(ii) Dynamic equivalent

1.21.11.00.90.8U

, tP,

tQ

, t

t, s

0.70.6

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

0.5

1.0

1.5

2.0

0

0.6

1.2

1.8

2.4

0

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

uo=548.3KV, PO=31.73MW, QO=54.79MVA

(i)

(ii)

(i)

(ii)

Fig. 4 Dynamic responses under fault 4(i) Measured(ii) Dynamic equivalent

Table 2: Equivalent parameters measured at Henan, China

Fault 1 Fault 2 Fault 3 Fault 4

Error index 3.167 13.725 4.16 3.224

Pv 1.311 0.487 0.016 1.025

Qv 1.049 5.091 1.06 0.047

Pso 20.162 20.02 20.006 20.049

Qso 11.151 2.991 4.34 9.672

M 1162.398 1347.849 1246.48 1281.958

T 0d 25.517 8.205 77.373 75.063

X 0.196 0.128 0.238 0.178

X 0 0.073 0.048 0.089 0.066

D 47.689 48.338 17.314 48.142

Kv 3.225 22.746 29.217 7.742

−1.0

−0.5

0

1.0 2.0 3.0 4.0 5.0

time, s

0.5

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2.0

AC

YY

S50

0-Y

YM

500

0

VI (I side V)P (I side P)Q (I side Q)

0

V

Q

P

Fig. 5 Dynamic responses under fault 1Whole system with full model and standard parameters

IEE Proc.-Gener. Transm. Distrib., Vol. 151, No. 2, March 2004 181

3.3 Sensitivity of stability limit toequivalent parametersMCTs, which indicate the stability, are repeatedlycalculated under several faults with changing equivalentparameters. It is clear from Table 5 that the effects

of equivalent parameters are related to fault locations,but, not necessarily proportional to the distancebetween equivalent point and fault location. In theTable, Tangyin Station is the farthest from the equivalentpoint and Yaomen Plant is the closest. However, neithercases has much effect. When a fault appears at Souyang-shan Station, the MCTs vary obviously. The stability caseshave been carefully analysed, and it was found that theinstability mode under the fault at Souyangshan Stationwas inter-area (between Henan and Huazhong) instabilityand other two cases were intra-area (inside Henan)instability.

4 Conclusions

Several field measurements have been captured at HenanPower Company, China. Equivalent parameters wereidentified and then applied in dynamic simulations and

stability analysis. Conclusions reached are: (i) the dynamicresponses with equivalent model and full model are close toeach other, and also similar to the recorded ones; (ii) theMCTs obtained with the equivalent model and the fullmodel show no obvious difference, and (iii) equivalentparameters have larger effect on inter-area stability and lesseffect on intra-area stability. The equivalent model takes lessthan half the CPU time as the full model.

5 Acknowledgments

The project is supported by China National ScienceFoundation.

6 References

1 Ju, P., Ni, L.Q., and Wu, F.: ‘Dynamic equivalents of power systemswith online measurements. Part 1: theory’, IEE Proc., Gener. Transm.Distrib., 2004, 151, pp. 175–178

2 EPRI Report EL-456:‘Development of dynamic equivalents fortransient stability studies’. Research Project 763, 1977

3 Yu, Y.N.: ‘Dynamic power systems’ (Pergamon Press, Canada, 1986)4 Chang, A., and Adibi, M.M.: ‘Power system dynamic equivalents’,

IEEE Trans. Power Appar. Syst., 1970, 89, (4), pp. 157–1615 DeMello, R.W., Podmore, R., and Stanton, K.N.: ‘Coherency-based

dynamic equivalents: applications in transient stability studies’. Proc.USA Power Industry Computer Applications Conf. (PICA), 1975,pp. 212–215

6 Dommel, H.W., and Sato, N.: ‘Fast transient stability solutions’, IEEETrans. Power Appar. Syst., 1972, 91, (4), pp. 185–190

−1.0

0

0

V

Q

P

1.0 2.0 3.0 4.0 5.0time, s

1.0

3.0

2.0A

C Y

YS

500-

YY

M50

0 0

VI (I side V)P (I side P)Q (I side Q)

Fig. 6 Dynamic responses under fault 1Studied system with full model and stand parameters, external systemwith equivalent model and measured parameters

Table 3: Comparison on the maximum clearing time

Location State 1 State 2 State 3 State 4

B A B A B A B A

Jiaozuo plant 0.22 0.23 0.24 0.23 0.16 0.17 0.21 0.21

Tangyin station 0.27 0.28 0.23 0.25 0.13 0.15 0.20 0.23

Zhengzhou station 0.33 0.30 0.31 0.29 0.21 0.20 0.30 0.28

Yaomen plant 0.22 0.21 0.24 0.24 0.20 0.18 0.22 0.23

Shouyangshan plant 0.28 0.27 0.22 0.21 0.16 0.16 0.22 0.21

Table 4: Comparison on the CPU time

Location Model A Model B

Jiaozuo plant 20 8

Tangyin station 18 7

Zhengzhou station 20 7

Yaomen plant 17 8

Shouyangshan plant 19 9

Table 5: Effect of equivalent parameters on maximumclearing time

Location Tangyinstation

Yaomenplant

Shouyangshanplant

Measured values 0.27 0.22 0.28

M� 2 0.26 0.22 0.27

MC2 0.28 0.22 0.33

X� 10 0.27 0.22 0.27

XC10 0.27 0.22 0.28

X 0 �10 0.26 0.21 0.22

X 0C10 0.27 0.22 0.28

PSO�10 0.28 0.20 0.29

PSOC10 0.28 0.23 0.32

182 IEE Proc.-Gener. Transm. Distrib., Vol. 151, No. 2, March 2004