Field tests to validate hydro turbine-governor model ... - IEEE Xplore

IEEE Transactions on Power System, Vol. 9,No. 4,November 1994

1744

FIELD TESTS TO VALIDATE HYDRO TURBINE-GOVERNOR MODEL STRUCTURE AND PARAMETERS B. Fardanesh, Member

Louis N. Hannett, Senior Member James W.Feltes, Member

New York Power Authority New York,NY

Power Techobgm * ,Inc. Schenectady, NY Abstract - A test procedure was developed to obtain accurate govanor models for b y h l e c t r i c statious owned by tbe New York Power Authority to improve the accuracy of stability simulations of the New York State system. Tmts were performed on units at three stations and values fir paramem of previously available model structures were derived from the information obtained during these tests. However, it was found that the model structures were not adequate to repsent the entire range of operating conditions. Additional examination of test measuremeats and model structues indicated that the model structure needed to be refmed. This paper reports on the refinaneats made to the hydm turbine-governor models which enabled repmduction of the physical system responses. Simulation results indicate that the refined models with the correspondii identifii m e t e r s produce responses which on three hydro closely fit those recorded from the tesb perf& units.

KEY WORDS Hydro-governors, simulation models, testing. INTRODUCTION

A research project sponsoned by the New York Power Autnority and the Esnpire State Electric Research Company is being undertaken to conduct field testing of a number of hydm and thermal units throughout the state. ?he objective of this project is to update and validate the model parameters of g e n e r a m excitation systems, and governors used in A paper recommended and approved 94 WN 190-9 PWRS by the IEEE Power System Engineering Cornittee of the IEEE Power Engineerfng Society for presentationat the IEEE/PES 1994 Winter Meeting, New York, New York, January 30 - February 3, 1994. Manuscript submitted July 30, 1993; made available for printing January 14, 1994.

computer simulation stability studies. In parallel with identifying values for model parameters, the existing model structures are also examined and, whenever seeded, further refinements are made such that simulation results closely match the fEld recordings of the staged tests. In the spring of 1992 hydro units at Blenheim-Gilboa, St. Lawrence Power Project, and the Niagara Power Project were tested. The results of the initial simulation runs and model development revealed that the simulation model required some refinements in or&r to represent these hydro-governors for a wide range of applications. Selection of Model Structure

The technical literatwe [l-71 contains several articles in which model srructures are presented for diffmnt types of governors and for representing the hydraulic effects in the penstock. The governors of the three units wem of the mechanical-hydraulic type and the recommeoded transfer function is shown in Fig. 1, as presented in Reference 7 and in Fig. 9B of Reference 5. The results from the simulation runs to match the staged test recordings for the three units as presented in a later section reveal that the transfer function in Fig. 1 adequately represents tbe governor controls. The development of the model of the hydraulic dynamics in the penstock is presented in detail in Reference 4. The equations for a single penstock are

where

q is the turbine flow hs is the static head of the water column A is the penstock cross section area L is the length of the penstock g is the acceleration of gravity h is the head at the turbine admission hI is the head loss due to friction in the conduit

and

0885-8950~4/$04.000 1994 IEEE

1745 "elm Gate Position 1 ____

Tg(l

-"elm

i ST

-1 -

)

G

S

MIN

simulation studies, use of the linearized penstock model will require different values for Tw as the dispatch of the hydro units is changed in the initial condition load tlows. Using the model shown in Fig. 2 will avoid that problem, allowing for one data base to represent the dynamic models for the system independent of dispatch. The model in Fig. 2 is independent of dispatch provided that there are no common flow paths (e.g. shared penstocks) for more than one unit at the plant.

Perrnoneot Speed Droop

U

q NL

Temporary Spaad Droop

Fig. 1. Block Diagram for Mechanical Hydraulic Governor on a Hydro Unit

where

-

I

q is the per unit turbine flow E is the per unit gate position

-

h is the per unit head at the turbine admission (a bar over a variable denotes a per unit quantity) When equation (1) is converted to the per unit system, the terms for the physical design of the plant define the water time constant for rated conditions (see equation 1.4 of Appendix I). The turbine model is based on steady state measurements relating output power with water tlow. As cited in Reference 3, thls relationship is for the most part linear and can be exxnressed by (3) ,P A,(G - { m ) h where

-

,P is the mechanical power in per unit A, is the turbine gain -qm is the no load flow in per unit

Equations 2,3, and 1.4 of Appendix I can be combined to produce the block diagram for the penstock and turbine model as shown in Fig. 2. An additional term is subtracted from the output of this block diagram to represent speed deviation damping due to the water flow in the turbine. For small signal analysis, the equations 1.4,2 and 3 can be linearized to obtain the transfer function shown in Fig. 3. T h ~ stransfer function is commonly used to represent the penstock and turbine effects. However, as presented in Appendix 11, the time constant T, in the Fig. 3 transfer function is not the same as that in equation 1.4 of Appendix I. The value for Tw in equation 1.4 is obtained at rated conditions using rated head and rated flow as the bases. T, in the transfer function of Fig. 3 is calculated for the tlow and head at which the unit is presently operating. Thus for

I

Fig. 2. Block Diagram for Penstock and Turbine Model

I

7

7 Fig. 3. Linearized Penstock and Turbine Model Testing Procedure

One means to determine the values for the parameters in the turbine/govemor block diagram is to gather information from tests. These tests consist of load rejections to obtain the dynamic response of the governor and steady state measurements to obtain the turbine characteristics. The direct method to obtain the water time constant is by calculation using the physical data of the penstock and measured plant performance. The following quantities are measured for the load rejections and steady state tests: 1. Electrical power 2. Gate position 3. Turbine speed Generator frequency can be measured instead of turbine speed during the load rejection tests. Steadv State Measurements

The steady state measurements consist of setting the unit at a given load and recording the values of electrical power and gate position. The head should be noted and, if possible,

1746

recording of water flow would be desirable. A sufficient number of points should be recorded over the bpwating m g e with finer steps neat light load and full load. A sample plot of electrical power v e r s u ~lgjate position is shown in Fig. 4. Note that m points w o d have baen desirable is the rmge greater than 605%gate positim.

60

D o

3 % 40 I

-m

,g20 The dynamic response tests are load rejections which exercise the governor with small scale changes and large scale changes in load. In the normal test sequence, two load rejections are conducted, the first with the unit initially loaded at 10% of its MVA rating and a second with the unit at 25% of its M V A rating. With the larger load, the action of the gates will be limited at a fixed velocity rate and the initial response of turbine speed can be attributed to penstock and turbine dynamics as the gate position changes at a constant rate. The smaller load rejection will exercise governor action without the gate position reaching velocity limits, thus giving information concerning temporary droop and the governor time constant.

.

.

.

.

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. . . . .:.. . . .: . . . .:. .

30

....

v 10

, , ,

. . .

..

..

.

. .

./.

I.

. .. .. .. . . . . . . . . . . . . . .

/

.;.. . . . . i. . . . ./,

.

,

. . . . . . . . . . ,. . . . ... . . . . ... . .

.

. .

.

.

I

.

.

.

.

0 10 20 30 40 50 60 70 80 90 100

0

Gate Position (“A)

Fig. 4. St. Lawrence Unit 32, Electrical Power versus Gate Position 3/21/92 at Head = 80.38 Feet

Table 1. Water Time Constpatp (Seeoads) For Different Number of Units Dispatdred

Model Derivation After the tests are completed, the next step is to process the information to derive the models. The water time constant for rated conditions is calculated first from the plant drawings and measured flows. This task was straight forward for the units at St. Lawrence and Niagara, since each unit had its own penstock to conduct water from @e upper reservoir to the unit. For the pump-storage units at Blenheim-Gilboa, this calculation is not as simple since there is a common 2500 foot vertical pipe Erom the upper reservoir to the individual penstocks. The water time constant becomes a function of the number of units that are on-line. One approach is to develop a model in which a matrix of water time constants are used for the penstock dynamics, as presented in reference 4. Another approach is to use separate models for the penstock, but vary the water constant for the number of units that are on-line. This second approach was used and Table 1 summarizes the analysis for the number d units on-line to determine the water time constant. The water time constant varies from 0.54 ti0 1.7 seconds as the number of units on line varies from one to four. The relationships of some of the variables in Fig. 2 can be identified from the steady state measurements of electrical power versus gate position. The value for i is 1 pu for rated head conditions and in steady state operation the per unit value for gate position is equal to the per unit value for

TailRace

1 Total

I I

0.0489 0.5411

I I

00489

7

0.0489

0.9248

I

1.3085

I

1.692

1

flow. A plot of electrical power versus gate position is shown in Fig. 4. Based on rated hydraulic conditions and the machine MVA rating, the values for the gate position and electrical power are converted to per unit. After the conversion to the per unit system, the slope of AP/AG can be identified as the turbine gain 4 in Fig. 2 and q at Pe = 0 as 9NL The value for permanent droop can be identified from the load rejection test recordings. This is accomplished by measuring the final speed deviation after load rejection, and using the formula An a=-A, AP where

An is the difference between final speed and initial speed in per unit AI? is the change in load in per unit on unit MVA rating

1747

To determine the values for the other parameters requires simulation of the load rejections starting with typical values for those parameters that Cannot be directly calculated. Simulation results are compared with the recorded measurements and adjustments are made to the values of the parameters until reasonable matches are obtained. Experience with this process has provided the following insights to guide the selection of parameter values. 1. The value for the temporary droop will determine the initial peak speed excursion for small load rejections. 2. The value for the governor time constant T, will determine the rate of transition from temporary droop to permanent droop with smaller values producing a short transition. Examples of matches between recorded measurements and simulation results are shown in Figs. 5 and 6. These simulations included the model refinements discussed in the following section. The parameters which resulted in this close match with the measured responses are listed in Table 2.

small for light load conditions to the point that it contributes little to the model's response for a load rejection. The first load rejection simulations for Blenheim-Gilboa with an initial load of 70 MW (25%)revealed that the speed excursions produced by the model were much larger than those obtained from the tests.

I

Table 2. Values Cor Hydro Governor Models

St. Lawrence

BlenheimGilboa 3

Parameter

Niagdra 1

32

MVA Rating

2.72 0.03

0.225

0.15

8.0

3.5 sec

TR

4.0 sec

sec I

I

I

0.045 sec

0.5 sec

0.67 sec

0.1 sec

GENERATOR SPEED DEVIATION

0.020

GMlh

I

1.0 p11

1.0 pu

1.0 pu

0.0 pu

0.0 pu

0.0 pu

1.72 sec

0 2 9 sec

0.9 sec

SIMULATION MODEL

I .6S

0.010

l1.000

il

RECORDEDMEASUREMENTS

0.185

0.184

0.094

I

__ Fig. 5. Niagara-Moses 1, 14.77 MW Load Rejection, Speed Deviation Model Refinements

The model structure for the turbine as shown in Fig. 2 was found to not fully represent all effects seen in the staged tests and additional features were added to the model. The first refinement was to introduce damping for no load conditions. The term for turbine damping as shown in Fig. 2 depends on the load on the unit, and the damping becomes

During the time period between opening of the breaker and reaching peak speed, the gates were moving at a constant rate eliminating governor effects and allowing matching of the gate movement in the model to that seen in the measurements. Thus the differences must be due to the model of the turbine, leading to the conclusion that the damping effect as a function of speed was not accounted for properly at light loads. Since some of the no load losses are attributed to windage, a change in the model was made to introduce windage torques as a function of speed squared (power 01 n3). The revised formula for no load flow is qNL(n) = QNL*((~- P W N D ) + P W N D * " 3) where QNL is the no load turbine flow at rated speed

1748

P-

is the proportion of no load losses attributed

mwtodrge n is the tullbitle speed

0.20

I

GATE WSITKW

0.15

Fig. 4 for St. Lawrence Unit 32. ’Ihe data point at 57 M W and 77% gate p u n does not fit the straight line approximation of the standard model structure. Further inquiries were made and data from earlier tests was provided. Thii data is plotted in Fig. 7 and RV& that the turbine characteristics m not linear over the entire mge of gate position and tha block diagram in Fig. 2 needs to be cbanged to reflect that. A suggestad revision is shorn io Fig. 8. In cases whew data for water flow is not available but curves relating electrical power with sate position can be determined, the block diqgnun in Fig. 9 is suggested.

0,IO

0.05 TINE (CYCLES)

-

2nn.n

4nn.n

My1.n

wm,&m.o

i z n nI un

I

I

n

~

Fig. 6. Niagara Moses 1, 14.77 MW Load Rejection, Gate Position

I

Fig. 8. Revised Block Diagram for Penstock and Turbine Including Nonlinear Gate/Flow and Mechanical PowerflFlOw Relationships

ST. LAWRENCE UNlT 32 ELECTRCAL W W E R VS. GATE POSmON

60.0

c I

I1

40’0

I

I ~~

20.0

I

~

Fig. 9. Revised Block Diagram for Penstock and Turbine Including Mechanical Power/Gate Relationship

0,o

20.0

30.0

4n.n

5n.n

60,O

7n.n

M.n

w.n

Fig. 7. St. Lawrence 32, P, (MW) Versus Gate Position From Earlier Tests

The values for P as listed in Table 2 were applied in the above equation. The seoaod refmment was made after examining the curve for electrical power versus gate position as shown in

To illustrate the effects of these nonlinear turbine characteristics, two simulation cases were run in which the disturbance was a 5 MW drop in load on an isolated unit using the turbine characteristic as plotted in Fig. 7. The initial load on the unit for the two simulations was 35 MW and 55 MW respectively. The plot of speed deviation shown in Fig. 10 reveals a difference in the unit’s response to the change in load for the different initial loads. The governor is more sluggish in its response to load change when the unit is initially carrying the higher loading. Accounting for these nonlinearities allowed the matching of model response to the

measured response for different loading, an example of which is shown in Figs. 5 and 6.

I

gA by hbase We get qbase

0.04, Initial Power = 55 MW

2 0.03 c Q.- 0.02 Y

Initial Power = 35 MW

zi 0.01

-q is the per unit flow -

where

g o

h, is the per unit static head

v)

-0.01

4

is the per unit head at the turbine admission

I 5

0

10 15 Time (Seconds)

h I is the per unit head loss due to friction

20

Tw = -, Fig. 10. Comparison of Speed Deviation for Isolated System With 5 MW Load Drop with Initial Load of 35 MW and 55 MW

A testing procedure to obtain governor models for hydro units is presented along with steps to identify values for model parameters. The results from the program reveal that the current model structures with minor refinements for speed damping effects are reasonably adequate to produce matches with recorded measurements. Other refinements have been identified from the steady state measurements of the turbine characteristics and are shown to improve accuracy over the entire operating range. APPENDIX I. CONVERSION OF EQUATION 1 TO PER UNIT AND DEFINITION OF WATER TIME CONSTANT T,

The following derivation shows the development of the per unit equations from the general physical equations and the definition of the water time constant T,. Starting with equation (1) dt

(1.1)

Dividing equation 1.1 by qbase, i.e. rated flow for rated output and rated head hbasewe get

-

the water time constant

APPENDIX II. LINEARIZATION OF PENSTOCK MOOEL

CONCLUSION

dq = (h, - h - hI)gAL.

qbase

hbasegA

dq/qbase = dq = (hs - h - h ~ ) gA (1.2) dt dt qbase Dividing the term (h, - h - hI) by hbaseand multiplying

A linearized model of the penstock is commonly used in dynamic simulation models. However, as will be shown, this can lead to inaccuracies if not judiciously applied. Starting with equations 1.4 and 2

(2.1.)

i=$

(2.2)

We can then linearize equations 2.1 and 2.2 by substituting x = x, + Ax for each variable and dropping out any terms with higher order of Ax. In equation 2.1 h, and hKare fairly constant giving in LaPlace form - 1 Aqs = -Ahor Ah = -AqTws (2.3) TW For equation 2.2

The terms under the radical can be linearized by using a Taylor expansion of a polynomial raised to the 1/2 power: (xo

+

Ax)

Thus equation 2.4 becomes

-

qo

+

Ai =

(Go + AG)

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Dropping out the initial terns reduces 2.5 to

which corresponds to the unit's operating condition rather than the rated condition. Thus to accurately model the unit in stability shulations, it would be necessary to adjust the value of T, each time the dispatch of the hydroelectricunits was changed in the initial condition load flow. This problem can be avoided by use of the model of Fig. 2.

in 2.6 gives

Substituting 2.3 for

Solving for

(2.14)

-

gives

ACKNOWLEDGMENTS

L

The equation for mechanical power developed in the

turbine is

-

P,

= At@i

REFERENCES

(2.9)

1.

4 is the turbine gain

where

We would like to acknowledge the New York Power Authority and the Empire State Electric Research Company for the funding of this lesearch project and the staffs of the Blenheim-Gilboa, St. Lawrknce, and Niagara Power Projects for their assistance in the performance of the tests.

Linearizing equation 2.9 gives (2.10)

G m = A~G~ +) AJQC, E

2. Substituting equation 2.3 into 2.10 for AFm = At&, Substituting 2.8 for

gives (2.11)

- G0T+s)AC

3.

& into 2.11 gives 7

4.

Recognizing that

Go

5.

fi0is equal to io

equation 2.12

boUU?S

(2.13)

NotethatsinceT, =-andthatq, Lqbase

-h,

hbam&A

ho = -, hbase

the time constant in 2.13 is

-

6.

7. =-and 90 qbase

J. L. Woodward, "Hydraulic-Turbine Transfer Function far Use in Governing Studies", Proceedinns of the IEE, Vol. 115, March 1968, pp 424-426. R. Oldenburger and J. Donelson, "Dynamic Response of a Hydroelechric Plant", Transactionsof AIEE, Vol. 81, Pt.111, October 1962, pp. 403-418. J. M. Undrill and J. L. Woodward, "Non-Linear Hydro Governing Model and Improved Calculation for Determining Temporary Droop", Transactionson Power A ~ ~ a r aand tu~ Svstems, Vol. PAS-86, April 1967, pp. 443-453. EEE Committee Report, "Hydraulic Turbine and Turbine Control Models For System Dynamic Studies", IEEE T r a n ~'ons a on Power Svstems, Vol. 7, No. 1, February 1992, pp. 167-179. IEEE Committee Report, "Dynamic Models for Steam and Hydro Turbms in Power System Studies", IEEE, Transactions on Power A ~ ~ a r a u s and Svstems, Vol. PAS-92, No. 6, Nov./Dec. 1973, pp. 1904-1915. C. C. Young, "Equipment and System Modeling for Large Scale Stability Studies", IEEE Transactions on Power A ~ ~ a r aand t u ~Svstems, Vol. 91, January 1972, p ~ 99-109. . D. G. Ramey and J. W. Skooglun4 "Detailed Hydrogovemor Representation for System Stabiity Studies", IEEE Transactions on Power A D D ~ ~ ~ ~ u s and Systems, Vol PAS-89, No. 1, January 1970, pp. 106-112.

1751 James W. Feltes (M’79) received his BSEE degree with honors from Iowa State University in 1979 and his MSEE degree from Union College in 1990. He joined PTI in 1979 and is currently a senior engineer in the Utility System Performance unit. At €TI,he participated in many studies involving the analysis and design of transmission and distribution system. These studies have involved simulation of power systems including load flow, transient and dynamic stability, lightning and switching surges, and harmonics. He has authored or coauthored several IEEE papers. He is a member of the IEEE and its Power Engineering Society and Industry Applications Society. Louis N. Haunett graduated from Clarkson University in 1971 receiving a B.S. in Electrical Engineering with honors. Upon graduation, he joined Power Technologies, Inc. as an analytical engineer and was promoted to

senior engineer in 1982. He has contributed to the area of dynamic stability and model of electrical machines. Mr. Hannett is a senior member of the IEEE and is a registered professional engineer with the State of New Yak. Behruz (Bruce) Fardanesh m83) received his B.S. in Electrical Engineering from Sharif Technical University in Tehran, Iran. He also received his M.S. and Dodm of Engineering degrees both in Electrical Engineering from the University of Missouri-Rolla and Cleveland State University in 1981 and 1985, respectively. Since 1985 he has been teaching at Manhattan College where he holds the rank of Associate Professor of Electrical Engineering. Currently, he is working as a senior R&D Engineer at the New York Power Authority. His areas of interest are power systems operations, dynamics, and control.