return to library mod-2 wind turbine farm stability study

DOE/NASA/0134-1NASACR-165156

RETURN TO LIBRARY

MOD-2 Wind Turbine FarmStability Study

E. N. Hinrichsen and P. J. NolanPower Technologies, Inc.

June 1980

11 D'EC1980Af'CD^N.vUL L uolAS

RESEARCH & EN .NLIRING LIBRARY£T LOJIS

Prepared forNATIONAL AERONAUTICS AND SPACE ADMINISTRATIONLewis Research CenterUnder Contract DEN 3-134

forU.S. DEPARTMENT OF ENERGYConservation and Solar EnergyDivision of Solar Thermal Energy Systems

N/I y n~

NOTICE

This report was prepared to document work sponsored by the United StalesGovernment Neither the United States nor its agent the United States Department ofEnergy nor any Federal employees, nor any of their contractors, subcontractors or theiremployees, makes any warranty express or implied or assumes any legal liability orresponsibility for the accuracy, completeness, or usefulness of any informationapparatus, product or process disclosed or represents that its use would not infringeprivately owned rights

DOE/NASA/0134-1NASACR-165156

MOD-2 Wind Turbine FarmStability Study

E. N. Hinrichsen and P. J. NolanPower Technologies, Inc.Schenectady, New York 12301

June 1980

Prepared forNational Aeronautics and Space AdministrationLewis Research CenterCleveland, Ohio 44135Under Contract DEN 3-134

forU.S. DEPARTMENT OF ENERGYConservation and Solar EnergyDivision of Solar Thermal Energy SystemsWashington, D.C. 20545Under Interagency Agreement DE-AI01-79ET20305

PAGE MISSING FROM AVAILABLE VERSION

TABLE OF CONTENTS

Page No.

1. SUMMARY 1

2. INTRODUCTION 2

3. PURPOSE, DIRECTION AND STRUCTURE 3

3.1 Background 3

3.2 Objective 3

3.3 Areas of Concern 3

3. 4 Scope 4

3.5 Orientation and Direction 4

3.6 Organization of Report 5

4. APPROACH 6

5. GENERAL CHARACTERISTICS OF WIND TURBINE GENERATORS 9

6. NATURAL FREQUENCIES AND MODE SHAPES 11

7. INTERACTIONS BETWEEN ADJACENT WIND TURBINE GENERATORS 16

8. TURBINE CONTROL 17

9. GENERATOR CONTROL 21

10. MECHANICAL AND ELECTRICAL DISTURBANCES 23

11. SMALL DISTURBANCE DYNAMICS - SINGLE MOD-2 SYSTEM 25

11.1 Preamble 25

11.2 Control Requirements 25

11.3 Modeling Detail 26

11.4 Simulation Results - Variation of Controland Electrical Transmission System 27

i i i

TABLE OF CONTENTS(Continued)

Page No.

11.5 Correlation of Time Response and Eigenvalue Results 27

11.6 Simulation Results - Goodnoe Hills System 28

12. SMALL DISTURBANCE DYNAMICS - MULTIPLE MOD-2 SYSTEM 30

12.1 Preamble 30

12.2 Two Identical Wind Turbines 30

12.3 General Number of Identical Wind Turbine Generators 32

12.4 General Number of Nonidentical Wind Turbines 35

12.5 Application to the Goodnoe Hills System—. 38

12.6 Discussion 38

13. ELECTRICAL SYSTEM DESIGN 40

13.1 Protection 40

13.2 Location and Number of Circuit Breakers 40

14. UTILITY NETWORK AT GOODNOE HILLS SITE 42

15. START-UP, SYNCHRONIZATION, LOADING, SHUTDOWN 47

16. ON SITE TESTING 48

16.1 Generator Excitation Control 48

16.2 Turbine Control 48

16.3 Shutdown Freouency 49

17. DISPATCH AND DATA ACQUISITION 50

18. SIMULATION RESULTS 51

18.1 Single Machine Simulation Results fromPower System Simulator (PSS/E) 51

Iv

TABLE OF CONTENTS(Continued)

Page No.

18.2 Multi-Machine Simulation Results fromPower System Simulator (PSS/E) 97

18.3 Simulation Results from MachineNetwork Transient Simulator (MNT/E) 121

18.4 Simulation Results from InteractiveDynamic Analysis Program (IDAP) 125

19. CONCLUSIONS AND RECOMMENDATIONS 157

20. MODELS AND DATA 158

20.1 Turbine Generator Drive Train 158

20.2 Turbine Control 158

20.3 Wind Turbine 158

20.4 Generator 158

20.5 Generator Excitation Control 161

20.6 Simulation System 161

21. REFERENCES 164

1. SUMMARY

The development of large wind turbine generators (WTGs) for operation inutility power systems is accelerating. This report contains the results of aninvestigation of the dynamics of single and multiple 2.5 MW, Boeing MOD-2 WTGsconnected to utility power systems, including the first three-machine clusterconnected to the grid of the Bonneville Power Administration.

The analysis is based on digital simulation of the complete electromechanicalsystem of single and multiple WTGs, including wind turbine, wind turbinecontrol, drive train, generator, generator excitation control, electricalnetwork and equivalent utility source. Both time response and frequencyresponse methods were used.

The results show that the dynamics of WTGs are characterized by two torsionalmodes, the lightly damped shaft mode at frequencies well below 1 Hz, and theelectrical mode at 3-5 Hz. The former is primarily excited by wind speeddisturbances, the latter by electrical disturbances. Since the shaft modefalls within the bandwidth of blade pitch control, additional damping for thismode is a prerequisite for good turbine control.

The variability of energy supply and the desire to deliver constant power haveled to the design of very fast acting blade angle control based on electricalpower. This type of control is contrary to normal power generation practice.Conventional turbine generators have fast turbine speed control and slow powercontrol which prevents turbine control responses to power variations caused byelectrical disturbances.

Multi-machine dynamics differ very little from single machine dynamics. Theshaft modes are essentially inaependent of electrical system parameters. Theyappear as repeated modes, i.e., they have the same frequency as single machineshaft modes. The additional modes created by interaction between WTGs aresimilar to single machine electrical modes except for higher frequencies andmore damping. They generally have little significance.

The Goodnoe Hills installation of three MOD-2 WTGs presents no electricalsystem problems. Relative to the power rating of the wind turbine farm,Goodnoe Hills is a strong utility tie point.

2. INTRODUCTION

The dynamics of wind turbine generators (WTGs) connected to electrical powersystems are primarily determined by five characteristics:

o Energy Supply

Contrary to other generation eouipment used by utilities, theenergy supply of WTGs cannot be controlled.

o Turbine Generator Drive Train

Large blade diameter and low turbine speed are required for maximumenergy capture. When referred to generator speed, WTG turbineinertia is very high and shaft stiffness between turbine andgenerator is very low compared to conventional steam and hydroturbine generators.

o Turbine Control

During on-line operation above rated wind speed the prime movercontrol of a MOD-2 WTG manipulates turbine blade angle to maintainpower and speed. Below rated wind speed, turbine control isinactive.

o Generator Control

Reactive power is varied by generator excitation. The controlvariable is either voltage, reactive power or power factor.

o Electrical System

The two key electrical properties affecting the dynamics of WTGsare stiffness and damping between the generator and the powersystem.

While the last three characteristics are identical or similar to conventionalturbine generators, the first two are idiosyncracies of wind turbinegenerators. All significant differences between the dynamic behavior of WTGsand other utility turbine generators can be related to variability of theenergy supply and the heavy turbine rotor connected to the light generatorrotor through a very soft torsional spring.

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3. PURPOSE, DIRECTION AND STRUCTURE

3.1 Background

The United States Department of Energy has undertaken a program toaccelerate the commercialization of large (>0.1 MW) wind turbinegenerators for electric power production. The effectiveness of a single0.2 MW machine paralleled to a utility has been demonstrated and severalfacilities are in operation. However, the connection of a farm of WTGs toan electric utility system has not been demonstrated.

The Wind Systems Branch, Division of Solar Technology, of the Departmentof Energy has funded the development of three MOD-2, 2.5 MW WTGs to beerected sufficiently close to each other to constitute a cluster or farm.This farm will produce a-c power with synchronous generators and will beconnected to an electric utility system.

3.2 Ob.lective

The objective of this contract was to perform a dynamic analysis of singleana multiple MOD-2 WTGs, paralleled to each other and to the utilitynetwork. The results of the dynamic analysis were used to determinewhether any unsatisfactory or undesirable performance can be expected.This determination included the eauipment in the WTG station, the powersystem to which the station is connected and the procedures to be usedduring operation.

3.3 Areas of Concern

The work done under this contract was directed at several areas whereconcerns had been expressed:

o Wind turbines operate with random variations in energy supply.What are the conseauences of a variable energy supply in terms ofsystems dynamics, e.g., excitation of torsional modes by windgusts, turbine control response, output power fluctuations,interactions between adjacent machines, loss of synchronism andvoltage fluctuations?

o Wind turbines have a lightly damped low freouency torsional modebelow 1 Hz. How is this mode excited, how is it damped, does itinterfere with blade angle control of the turbine, can adjacentmachines stimulate each others' torsional mode?

o Wind turbine generators are connected to power systems with a range ofimpedances at the tie point. Does system impedance have a significantimpact on WTG characteristics and what is the impact?

Wind turbine generators are subject to electrical faults. How doelectrical faults affect a WTG station, which modes of the WTG areexcited and what are the consequences? Is it better to shut downor to ride through a fault? Is there any conflict between utilitypractices relating to faults, e.g., circuit breaker reclosing, andwind turbine generator operation?

The design of turbine control in a WTG built for cluster operationin electric power systems is influenced by mechanicalconsiderations, such as drive train characteristics and wind speedvariations, but also by electrical considerations, such as loadsharing between machines and response to faults. What is the bestcompromise between all design requirements?

This investigation was specifically directed at the first multimachineapplication of the Boeing MOD-2 wind turbine generator in an electricutility network. The investigation deals with small and large disturbancedynamics and their effect on WTG equipment, the utility network and WTGoperating procedures.

3.5 Orientation and Direction

Since this report will probably be read by people with very differenttechnical backgrounds, it seems useful to describe the orientation of theauthors and to indicate what the authors expect from the reader.

The authors are accustomed to electric power systems dynamics andcontrol. Their orientation throughout this study has been: How does thisnew form of electric power generation fit into existing utility systems?What is similar and what is peculiar? Do the peculiarities requirechanges in current utility practices? The reader should realize that thisorientation implies that only those phenomena that are different fromnormal power system dynamics deserve attention. It cannot be the purposeof a small specialized investigation such as this one to provide acomplete background to a reader uninitiated in power system dynamics.Such a reader must look elsewhere for proof that the point of departuretaken by the authors is reasonable. The report is written for technicalspecialists in the areas of dynamics and control. The summary and theconclusions have been structured so-that both technical and nontechnicalreaders can acquaint themselves quickly witn the most importantconsequences of wind turbine generator dynamics.

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3.6 Organization of Report

The body of the report begins with a discussion of the approach (Section4), i.e., the models used in the computer simulation and the principalsimulation methods. This section also describes the reasons for choosingspecific simulation methods and presents the major assumptions.

Sections 5 through 10 contain a detailed review of wind turbine generatorcharacteristics as they affect system dynamics. Sections 5 through 10should be read as an introduction directed at the control and dynamicsspecialist. In Sections 11 and 12 the small disturbance dynamics ofsingle and multiple WTGs are analyzed in detail. Sections 11 and 12corroborate and reinforce the material presented in Sections 5 through10. Careful reading of Sections 11 and 12 will give the reader a greatamount of insight. This will help him understand the results of thesimulation runs showing dynamic responses to large disturbances.

Sections 13 and 14 discuss the electrical design of the WTG station andthe characteristics of the utility network at the location chosen for thefirst MOD-2 farm. Sections 15 through 17 deal with startup and operatingprocedures. Section 18 contains all simulation results. Nomenclature,units and conventions are explained and a narrative is provided for eachcase. Section 19 presents the conclusions. Section 20 contains the dataused during simulation.

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4. APPROACH

Digital simulation is the means chosen to develop insight into wind turbinegenerator dynamics. The simulation includes models of the turbines, drivetrain, turbine blade angle control, generator, generator excitation control,electrical network and equivalent utility source. For multi-machinesimulation, several sets of equipment models are connected to the electricalnetwork model at the appropriate points. Block diagrams of the individualequipment models and an overall block diagram of a two machine simulation areincluded in Section 20.

It is usually not economical to use the same degree of simulation detail forall investigations that are made in the course of a study. If, for example,the major interest is in the low frequency torsional mode of the MOD-2 (0.137Hz), it does not make sense to include the 60 Hz components of electricalparameters in the generator and the network in the simulation. An algebraicsolution at fundamental frequency is adequate. Furthermore, simplifiedrepresentations can reveal important relationships which are not obvious whenthe full simulation is used. A case in point is the relationship between modeshapes of the drive train and the distribution of inertias and stiffnesses.In summary, the choice of analysis tool is influenced both by the economics ofcomputation and by the effectiveness with which--the results assist theanalysis.

Three different analysis tools are used in this study:

o Machine Network Transient Simulation (MNT/E)

This system is based on a nonlinear representation of theelectromechanical WTG system including generator stator andelectrical network transients. All three phases are represented indifferential equation form so that balanced as well as unbalancedelectrical disturbances can be simulated. This tool is used wheninteraction between generator, drive train and electrical networkelements is the prime area of interest. Integration time step is0.0001 seconds. The small time step is necessary to allowintegration of the differential equations for the electricalnetwork. The post disturbance interval simulated is generally lessthan one second. Since the effect of turbine blade control in thisshort interval is generally negligible, this simulation system doesnot include models for wind power input to the turbine and windturbine control. Constant torque is applied to the blade inertiaof the drive train.

o Power System Simulation (P5S/E)

This system uses a nonlinear representation of theelectromechanical WTG system, including generator rotortransients. The generator stator and the electrical network aresolved algebraically for fundamental frequency, voltages and

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currents. In this system, the network reactances are madefrequency dependent. This tool is used when internal andinter-machine phenomena are at a freauency where interaction'withnetwork elements is negligible. Integration time step is 0.01seconds. The post disturbance interval simulated is typically 10to 20 seconds. The PSS/E simulation for wind turbine generatorsincludes the full representation of nonlinear turbinecharacteristics, wind turbine blade control and a filter tosuppress the 'two per rev1 (2P) excitation frequency.

o Interactive Dynamic Analysis Program (IDAP)

This program can be used for both linear and nonlinear systemrepresentations. In this application, the WTG system is describedby a set of linearized equations. In the case of nonlinear systemssuch as a WTG, perturbation techniques may be used to infer thelinearized system representation. Alternatively, the state spacematrix representation may be explicitly defined. The latterapproach was used in the IDAP simulation of WTGs. IDAP does nothave the network solving ability of MNT/E and PSS/E but comprisesanalysis capabilities for general dynamic systems in both time andfrequency domains. The electrical system between generatorterminals and infinite bus is represented by electrical 'stiffness'(synchronizing torque coefficient) (K£ in Fig. 1 - Pg. 8) andelectrical damping (D£ in Fig. 1 - Pg. 8).

The IDAP simulation of WTGs is used primarily for analysis in thefrequency domain, in particular parametric studies of the frequencyand damping of natural modes in relation to control characteristics,control tuning, drive train characteristics, synchronizing torquecoefficient (electrical 'stiffness'), and electrical damping.

The reader will notice that reference is made frequently to Fig. 1- Pg. 8, the basic block diagram of a single MOD-2 WTG, no matterwhich of the three analysis tools is used. He should keep in mindthat NWT/E and PSS/E are nonlinear representations which are usedto study small and large disturbance dynamics. When MNT/E or PSS/Eare used, Fig. 1 - Pg. 8 is only a linearized approximation of thereal simulation system.

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5. GENERAL CHARACTERISTICS OF WIND TURBINE GENERATORS

The torsional dynamics of present WTGs differ very much from those of otherutility turbine generators. Fig.2 - Pg 10 is a comparison of inertia/stiffnessrepresentations for typical steam, hydro and diesel turbine generators with aMOD-2 WTG. All Quantities are referred to generator speed. Turbine inertiain a WTG is very high. This is a result of the large rotor diameter requiredfor energy capture. It is an inherent feature. Shaft stiffness in a WTG isextremely low. This is not so much a result of deliberately designing windturbines with soft shafts, e.g., the quill shaft in the MOD-2, as of the speedratio between turbine and generator. In all other types of utility turbinegenerators, turbine and generator are directly coupled. The dynamicconsequences of the gearbox in a WTG drive train is not so much theintroduction of another concentrated inertia but the effective reduction ofstiffness. The frequency of the first torsional mode of the MOD-2 drive trainis 0.14 Hz, significantly lower than the so called system or electrical mode,which is 3-5 Hz in WTGs and 1-3 Hz in other turbine generators. In a typicalsteam turbine generator, the first torsional mode might lie at 15 Hz, muchhigher than the electrical mode. The first torsional mode not only has a verylow frequency, but it also has a very low damping ratio. Since it fallswithin the bandwidth of turbine blade angle control, the first torsional modebecomes the major design problem for pitch control.

Energy supply variations are another unique characteristic of WTGs. In otherturbine generators energy supply is controllable and energy supply dynamicsare slow compared to prime mover dynamics. Energy supply variations lead tothe design of very fast blade angle controllers. If blade angle control isbased on the difference between desired and actual power, tight blade anglecontrol also responds to electrical disturbances. This is an unoesirableconsequence of making blade angle control fast enough to respond to wind speedvariations.

Energy supply varies not only with wind speed, but also with blade position.With the usual two-bladed rotor, this effect creates torque variations at 'twoper rev1 frequency. The 2P frequency of the MOD-2 is 0.585 Hz, 4.28 times thefirst torsional frequency. The wind turbine model used in this study hasprovisions for periodic torque changes as a function of rotor position. Thisincludes sinusoidal functions to simulate rotor teetering and wind shear aswell as ramp functions to simulate tower shadow. It was found that the 2Pdisturbances do not play a major role in the system dynamics of the MOD-2connected to utility systems. 2P excitation of the electrical mode isunlikely because the mode shape of this torsional frequency has a node at theturbine location. Response of the blade angle controller to power variationsat 2P frequency is suppressed by a notch filter (Fig. 1 - Pg. 8).

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- 10 -

TYPICAL STEAM TURBINE-GENERATOR

Kp = 2.0

Generator

K,, = 70.0

H] =0.89 V

LP1Turbi ne

\2 = 0.88

K2, = 50.0

LP2Turbine

K^ = 30.0

H3 = 0.86

HPTurbine

H4 = 0-25

TYPICAL HYDRO TURBINE-GENERATOR

Generator

K£ = 2.0i

1

K , 2 - U . O

Turbine Inertia H in Secondson Machine Base.

Stiffness K in PU Torque/Radon Machine Base.

H, = 3.6 Q.k

TYPICAL DIESEL TURBINE-GENERATOR

(

KE = 2.0

Generator

HI = o.'i

K12 = 10.0

Engine

H2 = Q.k

MOD-2 WIND TURBINE-GENERATOR

KE = 2.0

Generato

H, = 0.5

r

K|2 = 0.065

f

Turbine

^2 = 15.7

FIGURE 2

COMPARISON OF DRIVE TRAINS OF TURBINEGENERATORS IN UTILITY SYSTEMS

6. NATURAL FREQUENCIES AND MODE SHAPES

One of the most important considerations during this study was the number ofsignificant natural modes. If the number selected is too low, potentiallysignificant effects go unnoticed. If the number is too high, engineering andcomputational effort are wasted. It is our conclusion that for interactionsbetween wind turbines and electrical networks four modes should be considered:

o Low Speed Shaft Mode - In the MOD-2 this is the first mode. Itrepresents torsional oscillation of hub and blades through the softlow speed shaft against the electrical system.

o Electrical Mode - In the MOD-2 this is the second mode. It representstorsional oscillation of the generator rotor through the eouivalentelectrical stiffness against the synchronous power system. Inconventional turbine generators this is generally the lowest mode and,therefore, the only one considered.

o Blade Mode - In the MOD-2 this is the third mode. It representsedgewise movement of blade tip inertias through blade stiffnessagainst the hub.

o High Speed Shaft Mode - This is the fourth mode. It representstorsional oscillation of the rotating part of the gearbox through thehigh speed shaft against the generator rotor.

The importance of each mode depends on the purpose of a particularinvestigation:

o The high speed shaft mode is of interest if gearbox inertia isappreciable with respect to generator inertia (0.1 or higher) and highspeed shaft stiffness exceeds low speed shaft stiffness by a widemargin (10.0 or higher, referred to same speed). Under theseconditions, toroue amplification in the high speed shaft can besignificant during electrical faults. Fig. 3 - Pg. 12 shows thatgearbox inertia in the MOD-2 is 0.064 of generator inertia. The highspeed shaft mode, therefore, is not an important consideration.

o The blade mode is a minor contributor to electromechanicalinteractions. It has the highest natural damping of the four modes.

o The electrical mode is of great importance. It dominates the dynamicresponse of the WTG system to electrical disturbances. In a WTG, theelectrical mode has a higher frequency (3-5 Hz) than in other utilityturbine generators (1-3 Hz). This is caused by the soft shaft, whichessentially eliminates the influence of turbine inertia on thefrequency of the electrical mode.

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FIGURE 3

MOD-2 DRIVE TRAIN REPRESENTATION

Infinite Generator Gearbox Hub BladesBus

KE

DE

Hl

K12

D12

H2

°23

H,

1

K34

D34

"k

i

Values Referred to High Speed Shaft

Values in Per Unit on Machine Base (3.125 MVA)

°3 °4

INERTIA[SECONDSJ

H = 0.528

H- = 0.034

H. = 0.384

= 15.34

STIFFNESS[PU TORQUE/EL RAO]

K]2 = 52.68

K23 = 0.06A6

K,,, = 3.656

DAMPINGLPUJ

Dj = 0.029

DZ = 0.020

D = 0.009

D^ = 0.007

D = 1.500

= 46.94

o The low speed shaft mode is the most important of the four modes. Itdominates the dynamic response of the WTG system to mechanicaldisturbances. Since it is excited by wind speed and blade anglechanges, it is a major factor in the design of blade angle control.

A model of a WTG drive train should have at least two degrees of freedom (twoinertias) to represent low speed shaft and electrical modes (Fig. 2 - Pg. 10).Addition of the blade mode by separating hub and blade inertias usuallyprovides little change due to high aerodynamic damping of blade edgewisebending. Addition of the high speed shaft mode by separating generator andgearbox inertia is only advisable if there is a possibility of high torquelevels during electrical faults.

In the MNT/E simulation described in Section 4 all four modes are represented(Fig. 3 - Pg. 12). Since this simulation includes generator stator andnetwork transients, the drive train is stimulated by electrical as well asmechanical frequencies. The higher electrical frequencies produced byelectrical faults can excite the high speed shaft mode. In the PSS/E and IDAPsimulations described in Section 4, low speed shaft, electrical and blademodes are represented. The high speed shaft mode has been omitted becausethere are no excitation frequencies high enough to stimulate this mode.

Fig. 4 - Pg. 14 shows modal frequencies and mode shapes of the first fourmodes for the MOD-2 drive train. This figure is valid for an open loop,undamped system. Blade pitch control raises the frequency of the low speedshaft mode, but the band width of pitch control is too narrow to affect theother three modes. The damped natural frequencies do not differ significantlyfrom the undamped natural frequencies because damping ratios for all modes areless than 0.4. Undamped, open loop mode shapes are a valuable analysis toolbecause they give insight into inherent characteristics of the drive train:

o It is not possible to stimulate or dampen a mode to any appreciableextent if the excitation or damping torque is applied close to a node.

o Points on the shaft which have small displacements at a particulartorsional frequency generally are poor sensor locations for that mode.

o The hub and blade locations are essentially nodes of the electricaland high speed shaft modes. Significant excitation of these two modesby wind gusts is, therefore, not possible.

o The high speed shaft between generator and gearbox is essentially anode in the low speed shaft and blade modes. In WTG torsional systemswith low shaft stiffness the low speed shaft and blade modes cannot bestimulated or damped easily from locations on the high speed shaft.As a result, it is quite unlikely that electrical disturbances canprovide excitation for these modes.

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- 14 -

FIGURE *t

MOD-2 DRIVE TRAINMODE SHAPES AND MODAL FREQUENCIES

ASSUMED ELECTRICAL STIFFNESSFREQUENCIES IN RAD/SECNO DAMPINGPITCH CONTROL INACTIVE

= 2.0 PU TORQUE/EL RAD

InfiniteBus

Generator Gearbox Hub Blades

LOW SPEED SHAFT - 0.859

ELECTRICAL - 26-30

BLADE - 1»3.26

HIGH SPEED SHAFT - 555-9

When analyzing the excitation of torsional modes by an electricalevent, one must differentiate between a disturbance and a change inequilibrium. A change in electrical system reactance caused byswitching a transmission line creates a disturbance at nearby WTGswithout creating a new equilibrium condition for the torsionalsystem. Low speed shaft and blade modes are not stimulatedappreciably. If, however, the WTG circuit breaker opens suddenly, thetorsional system must seek a new equilibrium in a free body mode. Afault is similar to a circuit breaker trip, i.e., load is lostabruptly. When the torsional system is forced to seek a newequilibrium, all modes are stimulated.

It is therefore, not correct to state that electrical events cannotstimulate the first torsional mode.

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7. INTERACTIONS BETWEEN ADJACENT WIND TURBINE GENERATORS

The dynamics of closely coupled WTGs generally represent a mixture of twoextreme cases:

o Machines interacting with the electrical system but not with eachother, e.g., two identical WTGs reacting to wind speed disturbances ofequal magnitude and direction.

o Machines interacting with each other but not with the electricalsystem, e.g., two identical WTGs reacting to wind speed disturbancesof equal magnitude but opposite direction.

Only the second case differs dynamically from the single WTG connected to anelectrical system. The second case creates an additional electrical modewhich usually has a higher frequency than the electrical mode for the singlemachine case. This mode is not particularly important as it is generallydifficult to stimulate and also well damped by the effective electricaldamping at the higher frequency.

Frequency and damping of the first torsional mode are essentially independentof electrical system configuration. If frequency and damping of the firsttorsional mode are satisfactory in a single WTG application, they will also besatisfactory in multi-WTG applications.

Another possible form of interaction between adjacent WTGs is coupling betweenblade angle controllers. The likelihood of this type of interaction ishighest when primary blade angle control is based on electrical power, andexcitation control of the generator is based on power factor. The bestpossible decoupling between turbine controls of adjacent WTGs is achieved whenthe primary turbine control variable is turbine speed and the control variablefor generator excitation is terminal voltage.

A third possible form of interaction between adjacent WTGs is coupling betweengenerator excitation controllers. This possibility is eliminated by thecommon practice of reactive droop compensation.

Adjacent WTGs connected to the same electric power system do not create newstability problems. The interactions that do occur are stable and well damped.

- 16 -

8. TURBINE CONTROL

Fig. 1 - Pg. 8 is a block diagram of the Mod-2 turbine control system validfor small perturbations from a steady state operating point above rated windspeed. Below rated wind speed, the control system is not in operation and theopen loop response of the system shown in Fig. 1 - Pg. 8 governs. Thetransfer function of the wind turbine, relating power change to blade anglechange, is shown in Fig. 5 - Pg. 18.

Primary control of a turbine generator refers to the first level of control ofthe turbine. In the case of WTGs, primary control manipulates turbine bladeangle. Its purpose is to control turbine power output or turbine speed. Itis instructive to compare the primary controls of WTGs and steam turbinegenerators (STGs). It should be possible to explain all differences with thetwo peculiarities of wind turbines:

o Variability of energy supply.

o Heavy turbine rotor connected to light generator rotor through a softtorsional spring.

The STG governor is a speed controller with proportional characteristics. Theoutput of the governor controls the position of steam valves. Since aproportional controller operates with a steady state error, there is a smalldifference between no load and full load speed. This is the speed droop.Power control of the STG is provided by a slow acting integral controller.The integral power controller provides the setpoint for the proportional speedcontroller. In this manner, a fast inner (primary) loop controls speed and aslow outer (secondary) loop controls power. The speed droop provides loadsharing capability independent of the slow acting power controller. If, forexample, all STGs in a system have the same speed droop from no load to fullload, a change in load is proportioned between all sets in relation to theirratings.

Primary control of wind turbines is not based on turbine speed, but ongenerator power (Fig. 1 - Pg. 8). The power controller of the Mod-2 hasintegral as well as proportional characteristics. The use of power in theprimary turbine control loop has several disadvantages:

o Electrical power output of the generator is affected not only by theprime mover but also by electrical disturbances. The power controllercannot differentiate between power changes caused by prime movertransients and those caused by electrical system transients.

o Transients caused by the prime mover appear first as speed changes.They do not become power changes until they have been integrated inthe drive train into changes of generator power angle. Prime movercontrol based on generator power is, therefore, inherently slower thancontrol based on speed.

- 17 -

- 18 -

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QQ.

tr\

ozu.ocLUU.

CO

fr\OL

3

CM

QO

cnCM

CTl•

CM

O

dCM

O

OCM

LTVO

SOCM

OI

OI

o Power control of WTGs is only active above rated power. When poweroscillates above and below rated power due to excitation of the lowspeed shaft mode, the control is active during parts of the positivehalf wave and inactive during parts of the negative half wave of thepower oscillation. This constraint can further stimulate the lowspeed shaft mode.

o Wind turbine generators with primary turbine control based on powercannot share load 'naturally', i.e. by features inherent in thecontrol at the primary level. It has been argued that WTGs do notrequire load sharing ability because they always represent a smallpart of the electric power systems. We believe that this imposes anunnecessary restriction on the application of WTGs. There are small,isolated power systems where a single WTG would be a significant partof total generation.

This difference in primary (turbine) control between STGs and WTGs is probablya result of the variability of energy supply to the WTG. Since turbine powerin a WTG changes more than linearly with wind speed, and wind speed changesare the major disturbance, wind turbine designers consider power the mostimportant control variable. It is likely that this view has been influencedby so-called 'power Quality' considerations, i.e., it has been the goal todeliver power to the utility at a constant level, independent of energy supplyvariations. In view of the disadvantages of primary turbine control based onpower, and the relatively mild conseauences of power variations, we believethat the tradeoff between good wind turbine control and 'power quality'deserves more attention. There is no reason to believe that fast proportionalprime mover control based on speed and slow integral control based on powerwould not protect the WTG against excessive torque levels. The MOD-2 is thefirst WTG in the federal wind energy program that uses on-line turbine speedcontrol as well as power control. Speed control is used to provide dampingfor the first torsional mode. MOD-2 prime mover control, therefore, isstructurally very similar to prime mover control of a steam turbine. Thedifference lies in the gain settings of the controller. We have experimentedwith a modified MOD-2 turbine control system with fast proportional controlbased on speed and slow integral control based on power, and have foundacceptable control performance without the disadvantages listed above.

In conventional turbine generator drive trains, the torsional modes are ofsuch high frequency that they are not a factor in the design of primaryturbine control. Their damping is low but is unaffected by control. They canonly be stimulated by severe electrical disturbances, not by variations ofenergy supply at the prime mover. In wind turbine generator drive trains, thefirst torsional mode is well within the bandwidth of turbine blade anglecontrol. The damping of this mode is an important aspect of the controlproblem.

- 19 -

In the MOD-2 a signal proportional and in phase with turbine speed is added tothe input of the blade angle controller. This method of damping isfunctionally equivalent to proportional speed control in an STG. Since theturbine blade angle is set at the maximum power position when operating belowrated power, this methoo of damping cannot be active at less than rated power.

Wind turbine generators are presently dimensioned to operate below rated windspeed more often than above. At a typical 14 mph mean wind site, the MOD-2 isexpected to be idle for 23%, to operate with less than rated wind speed for59% and produce rated power for 18% of a representative interval. At the samesite, approximately 60% of the energy will be captured below and 40% aboverated wind speed.

Do these present design conditions weaken or invalidate the precedingdiscussion of turbine control? In our opinion, they do not. An operatingregime between cut-in and the onset of blade angle control is unavoidable.The size of this regime, however, is not fixed. It is determined by atradeoff between several requirements, one of which is the most suitableturbine control for operation within a utility network. It is conceivablethat conditions will arise where a temporary reduction in energy capture dueto a less than optimum blade angle is well worth the gain in load sharingability or in damping of the first torsional mode.

- 20 -

9. GENERATOR CONTROL

The control variable of a synchronous generator in a WTG is field excitation.This variable can be used to control one of three parameters:

o Terminal voltage

o Reactive power

o Power factor

It is normal practice in electrical power systems to use generator excitationfor voltage control. Each generator participates directly in the control ofthis important system parameter. Since system var requirements and generatorvar capabilities generally do not coincide, generator excitation control isconstrained by limits in both lagging (overexcited) and leading (underexcited)directions. The overexcitation limiter provides thermal protection of thegenerator field when system voltage is low; the underexcitation limiterprevents operation at high power angles and marginal transient stability whensystem voltage is high. Full use is made of the reactive power capability ofeach generator. The utility company's task of maintaining acceptable systemvoltage by other means, such as tap changers and switched capacitors, isminimized.

Control of reactive power often produces results similar to voltage control.Since the largest part of voltage variations in electrical power systemsoccurs in reactive circuit elements, control of reactive power exchangedbetween a generator and a power system will often keep generator voltagenearly constant. However, reactive power control cannot hold system voltageat the desired level, unless the reactive power controllers are individuallyadjusted to the existing system condition. Reactive power control, therefore,is not a desirable substitute for voltage control in multi-unit power systems.

Control of generator power factor leads to results notably different fromeither voltage or reactive power control. Since power factor establishes theratio of real and reactive power, reactive power must now follow real power.This constraint creates variations in reactive power which produce new voltagevariations. The advantage of power factor control is a reduction of powerangle variations.

Since the MOD-2 is designed for power factor control, we have tried todetermine whether the smaller power angle variations have any measurablebenefit in terms of transient stability. The steady state full load powerangle for the Goodnoe Hill application of 3 MOD-2 machines in the SPA systemis expected to be near 28°. The reduction in power angle variations duringsevere disturbances, which can be attributed to power factor control, istypically 5-8°. This improvement of transient stability margin cannot beconsidered significant.

It is our opinion that large wind turbines with ratings of several megawattswill have sufficient impact on power system operation that participation insystem voltage control will be required. Voltage limits are especiallyimportant at distribution levels (up to 69 kV). In the forseeable future,most WTG installations will be at voltage levels of 69 kV or less. Anadequate transient stability margin will be available without power factorcontrol. We also believe that reactive power control will be foundimpractical because controller references would be system dependent.

- 22 -

10. MECHANICAL AND ELECTRICAL DISTURBANCES

In wind turbine generators, the torsional modes of the drive train can bestimulated from both ends, mechanically from the turbine and electrically fromthe generator. While all the possible electrical disturbances are of the samenature for conventional turbine generators and WTGs, the consequences ofparticular disturbances are different because the torsional system isdifferent. Mechanical disturbances of the drive train from the turbine endare a peculiarity of WTGs.

The two important mechanical disturbances are changes in turbine torque causedby wind speed changes and by blade position. The first is unpredictable andnot periodic, the second is predictable and occurs once for each blade foreach revolution. Torque changes caused by wind speed changes stimulate thelow speed shaft mode. Control response and damping for this disturbance havebeen discussed in other sections. The 2P excitation created by torque changeswith blade position must be far removed from the frequency of the low speedshaft mode.

The two most severe electrical disturbances are short circuits in the vicinityof the generator terminal and complete loss of load with subsequentrestoration of load. There are two differences in the response of WTGs andconventional turbine generators to these disturbances. Both are related tothe peculiar torsional dynamics of WTG drive trains:

o Transient torque levels in wind turbine generator shafts are verylow. Since mechanical stiffness is much lower than electricalstiffness (synchronizing toroue coefficient), shaft torques are muchlower than air gap torques. The mechanical limitation of a WTG duringa severe electrical disturbance is bracing of generator windings. Itshould be noted that the bracing required does not exceed normal,conventional levels.

o When a WTG loses load, the generator rotor very quickly moves awayfrom the synchronous reference position, unwinding the soft shaft andstarting an oscillation with respect to the turbine. In the MOD-2,for example, the shaft unwinds in 0.31 seconds, i.e., the frequency ofthis oscillation is approximately 5 rad/sec. The deviation ofgenerator speed is -13% and the variation in generator angle is-1300°. While this oscillation is taking place, the turbine beginsto accelerate because it has lost its load. Turbine acceleration ismuch slower. When the shaft has unwound for the first time andgenerator speed deviation is -13%, turbine speed deviation is +2%.

Since the turbine continues to operate close to synchronous speed,resynchronization is theoretically possible at almost any reclosingangle. The nearly synchronous turbine rotor and the soft shaftprovide a restoring toraue to the generator rotor that does not existin conventional turbine generators. If this behavior is utilized forresynchronization, the generator locks in at a rotor position otherthan the original. This results in large electrical transients aswell as high air gap torques and high forces on the generatorwindings. It has been shown before that shaft torques are not high.WTGs designed to take advantage of this unusual characteristic musthave generators that can withstand high transient air gap torquelevels (5-7 times rated).

The behavior of WTGs after loss of load must be reconciled with reclosingpractices in electric utility networks. There are two types of reclosingapplications in power systems: Low speed reclosing of radial (branch)circuits and high speed reclosing of circuits interconnecting parts of thenetwork. When reclosing is used in radial circuits and synchronous machinesare connected to such a circuit, it is possible to perform dead line orsynchronism checks prior to reclosing. If the dead line check determines thatthe synchronous machine is still on line or the synchronism check determinesthat the machine has moved "away from synchronism, reclosing does not takeplace. Most WTGs will be connected to radial circuits and can be protected inthis manner.

High speed reclosing applies to transmission lines between areas containinggeneration as well as loads. In this case, the generator rotor does notnecessarily change its angle quickly because a large part of the system ismoving in unison, i.e., the WTG characteristics alone do not determine theresponse. During the reclosing interval, the electrical tie between affectedareas changes. The consequences depend on the number of circuits betweenareas, the mix of generation and the type of load. Whether the unusual drivetrain characteristics of WTGs will have an influence on reclosingconsiderations will depend on a number of factors:

o Nurrber of WTGs in an area

o Characteristics of load

o Number of circuits between areas

o System reactance between generation and reclosing circuit breaker

- 24 -

11. SMALL DISTURBANCE DYNAMICS - SINGLE MOD-2 SYSTEM

11.1 Prearrble

In this and the next section the dynamics of MOD-2 Wind TurbineGenerators subjected to small disturbances are considered. The objectiveis to investigate the dynamic stability properties of a group of MOD-2wind turbines in general and specifically to analyze the Goodnoe Hillsconfiguration for satisfactory dynamic response. This section deals withthe situation of a single WTG installation or the lumped eouivalent for agroup of identical WTGs. In order to evaluate the overall dynamicproperties of MOD-2 WTG systems, a variety of different electricaltransmission systems and control settings are considered. The effect ofreduced proportional power and increased speed control is evaluated. Theproperties of the Goodnoe Hills system are evaluated for different loadconditions. It should be emphasized that this section focuses on smalldisturbance dynamics. The conclusions drawn must be reconciled with thecomplete nonlinear system (transient stability) results.

11.2 Control Requirements

The general reguirements for wind turbine control are:

o Regulation of power to the rated value.

o Introduction of adequate damping in the torsional system and inthe power swings between the generator and the remainder of theelectrical system.

Wind turbine design in the presently planned sizes is an evolvingtechnology and consequently there is not a wealth of operating andsimulation test results to support specific control designs. Wheneverappropriate, the inherent dynamics and control of WTGs will be comparedwith those of steam and hydraulic turbines.

The control problem for wind turbines is significantly different fromthose of hydraulic and steam turbines:

o Wind speed and hence prime mover power may be subject to rapidchanges. By contrast, the input to the drive train of steam andhydraulic turbines is controllable.

o The torsional system for wind turbines is radically different fromthat of steam and hydraulic units. Specifically the torsionalstiffness between the generator and hub is smaller than the'electrical stiffness1 holding the generator in synchronism. Bycontrast, the torsional stiffnesses in conventional turbines areconsiderably higher than the electrical stiffnesses.Consequently, low frequency torsional oscillations may occur inwind turbines. The relatively low value of shaft to electricalstiffness limits the interaction between the torsional andelectrical modes.

- 25 -

The rationale for setting reference power is different in wind turbinegenerators from that in steam and hydraulic turbines. In the case ofwind turbines operating at wind speeds above the design value, the powerset point is fixed at rated power. For wind speed increases withcorresponding increase in blade power, the blade pitch is adjusted sothat rated output power is maintained. By contrast, in thermal andhydraulic turbines the reference setting is varied either manually or bya slow acting automatic generation control.

In the case of a conventional turbine generator drive train it is notnecessary to introduce additional damping. The torsional modes are ofhigher frequencies (>10 Hertz) and are only stimulated by severeelectrical disturbances such as short circuits and poor synchronization.The torsional modes are not stimulated by the slower changes in primemover power. The damping in the torsional modes is low but is generallyunaffected by turbine control. In the case of wind turbines,disturbances can be applied at the prime mover end of the drive train aswell as the generator end. Drive train oscillations due to wind speedchanges occur frequently. The damping of these oscillations is animportant aspect of the control problem.

The MOD-2 control design includes proportional and integral control basedon electrical power, and damping is introduced by proportional control ofblade angle based on hub speed. As mentioned earlier in this report, ahigh value of proportional gain can result in undesirable responses ofthe power controller to electrical disturbances.

11.3 Modeling Detail

Fig. 1 - Pg 8 shows a block diagram representing the dynamics of a single(or lumped equivalent) MOD-2 WTG tied to an infinite bus. This modelcomprises:

o A three rotating mass torsional system representation.

o General proportional and integral power controller including hubrate damping.

o 2P torsional filter.

o Transfer function 9P$B representing the incremental wind powerchange for blade angle change. As shown in Fig. 5 - Pg 18, thisquantity varies approximately linearly with wind speed( 9P/ 86= - .05 MW/DEG at 26.4 MPH and - .25 MW/DEG at 45 MPHapproximately).

- 26 -

o The rotor dynamics of the synchronous machine are represented byeauivalent synchronizing and damping terms which are assumedfrequency independent in this application. Variation in electricaltransmission system strength, loading conditions, damper windings,etc. may be considered by proper adjustment of KE and D£.While it is possible to calculate these coefficients from machine,loading and excitation system data (Ref. 1), it is more practicalto infer these quantities from a full scale simulation setup (e.g.PSS/E) including detailed machine and excitation system modeling.

The state space 'A1 matrix is shown in Fig. 6 - Pg. 28. The elements of thismatrix are evaluated for a range of parameter variation and the eigenvalues ofthe system are presented in root locus plots.

11.4 Simulation Results - Variation of Control and Electrical TransmissionSystem

Section 18.4 contains the simulation results. Specifically, eigenvalueplots for the following cases are presented:

o Variation of Kp, Kj and Kp around the settings selected byBoeing and the base case electrical transmission system (Cases 14,15, 16).

o Variation of 9P/93 to investigate varying wind speed (Case 19).

o Variation of KE and D£ for fixed controller settings includingproportional action on electric power (Cases 17, 18).

o Variation of Kp with Kp = 0 for base case electricaltransmission system (Case 20).

11.5 Correlation of Time Response and Eigenvalue Results

Sample time response plots for the linearized system model are includedin Section 18.4. These results aid in the interpretation of theeigenvalue plots. Specifically, the responses for the followingdisturbances are considered:

o Initial displacement in hub and blade angles. This disturbancestimulates only the shaft mode (Case 21).

o Initial displacement in generator rotor angle with and withoutpower controller (Case 22). This disturbance stimulates only theelectrical mode and it is evident that the mode is notsignificantly affected by the power controller loop.

o Step change in wind power with and without power controller (Case23). This disturbance stimulates only the low frequency shaftmode.

- 27 -

11.6 Simulation Results - Goodnoe Hills System

A lumped equivalent was used for the three machines of the Goodnoe Hillsinstallation. The detailed system representation used in the PSS/Esimulation was used to provide the appropriate values for K£ and Dg.The frequency response plot for these coefficients, presented in Section18.4, shows that constant values may be used over the range offrequencies of interest.

Section 18.A contains the eigenvalue plots for light and heavy loads at0.9 overexcited and unity power factor.

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12. SMALL DISTURBANCE DYNAMICS - MULTIPLE MOD-2 SYSTEM

12.1 Preamble

The analysis of the previous section was based on the assumption of asingle WTG. It was tacitly assumed that multiple WTGs comprising a windfarm were identical and could be lumped into one.

The dynamic responses considered so far are valid for common disturbancesaffecting all WTGs to the same extent. Examples of such commondisturbances are equal wind speed changes on all machines or disturbanceson the common electrical network. All WTGs move coherently under theseconditions.

There is another type of disturbance which affects individual machines ina group of WTGs differently. An example is wind gusts of differentintensities impinging on the blades of individual WTGs in a group. Theresponse in this case has components in anti-phase (machines swingingagainst each other) as well as the in-phase modes previously considered.

The Question arises whether undesirable dynamic interaction between windturbines could occur for normal control setting and the normal range ofelectrical transmission system configurations.

This section shows that for a general group of identical wind turbinegenerators we may directly extend the results of the single WTG case andthat for a properly tuned controller (based on the design of a single WTGapproach) no adverse interactions between adjacent machines are expected.

This_ section first presents the results for two identical WTGs. Theresults are then extended to the general case and applied to the threemachine installation at Goodnoe Hills. Sample time responses arepresented to complement the eigenvalue results.

12.2 Two Identical Wind Turbines

Fig. 7 - Pg. 31 shows the case of two identical wind turbines feedinginto a stiff system. It is intuitively obvious that the dynamics consistof two sets of modes:

o Wind turbine generators move coherently with each other. Thesemodes would be stimulated by wind speed disturbances of the samemagnitude and sign applied to each machine. Electricaldisturbances on the common transmission system would also excitethese modes.

o Wind turbine generators move against each other with equal andopposite magnitudes. It is not possible to excite these modes bydisturbances on the common electrical transmission. The bus atwhich the machines are synchronized represents a node for allanti-phase modes.

- 30 -

(a) In-phase modes. Corresponding variables in each WT move in phase.

Node

(b) Anti-phase modes. Corresponding variables in each WT move in anti-phase.

FIGURE 7

IN-PHASE AND ANTI-PHASE MOOES

- 31 -

The dynamics of the above system can thus be analyzed in terms of twoequivalents:

o A lumped equivalent machine swinging against the receiving endinfinite bus.

o A single machine swinging against the bus at which the machinesare synchronized.

The results of the previous chapter can be applied to predict thedynamics. The mode shapes are shown in Fig. 8 - Pg. 33.

It was concluded from the results of the previous section that the firsttorsional mode is practically unaffected by the transmission systemstrength. Consequently, the natural frequency and damping of the firsttorsional mode is approximately the same for the single system and inter-system modes. A good design for the first torsional mode also satisfiesdamping requirements for the inter machine first torsional modes. Theinter-machine electrical mode has a higher frequency and is betterdamped.

12.3 General Nunter of Identical Wind Turbine Generators

It is possible to extend the results of the previous chapter to thegeneral case of 'N1 identical WTGs.

Consider the case where all generators are synchronized on a common busas shown in Fig. 9 - Pg. 34. Because of the symmetry of the situation itcan be argued that the state space matrix has the form:

A

B

B

A

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I I

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- 32 -

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1st torsional(anti phase)

'electrical' mode(in phase)

'electrical' mode(anti phase)

blade mode(in phase)

blade mode(anti phase)

FIGURE 8

MODE SHAPES FOR TWO MACHINE SYSTEM

- 33 -

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Base 3-125 MV

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FIGURE 9

EQUIVALENT REACTANCE FOR SINGLE MACHINE EQUIVALENT OF WTG FARM

- 34 -

where Xj_, X2 and /3 are the states of each WTG representation.

Matrix A defines the Dynamics of each WTG while the states of all othermachines are kept fixed. Matrix B defines the coupling hetween theWTGs. It can be seen by substitution that the eigenvalues of the overallsystem are given by the eigenvalues of the matrices:

A + (N-l)B

and

A - B (12.2)

The eigenvalues of the first matrix represent modes where correspondingvariables in each WTG move coherently. The eigenvalues of the secondmatrix (multiplicity N-l) represent modes where the average displacementfor each state is zero. For example, if we had a 3 WTG system, (such asthe Goodnoe Hills cluster) these modes would be excited if two rotorsmoved together with half the amplitude and opposite sense as the thirdrotor.

A typical mode shape for such a system is shown in Fig. 10 - Pg. 36. Itis seen that the two matrices required represent the dynamics of a singlemachine against the infinite system and the dynamics of one machineagainst an infinite bus at the point where the individual WTGs areconnected. Consequently, the natural frequencies and mode shapes can beinferred from an equivalent single WTG infinite bus system. Fig. 9 - Pg.34 gives the value of XJQJ for various numbers of generators andvarying transmission strengths.

Alternative busing schemes which have symmetry may also readily betreated. Consider the network shown in Fig. 11 - Pg. 37. The dynamicsconsist of modes in which

o All six WTGs swing coherently.

o Machines A, B and C as a group swing against C, D and E as a group.

o Machines swing against the other machines in the same group.There will be four such modes. These modes will correspond torepeated eigenvalues just as in the example in Fig. 7 - Pg. 31.

12.4 General Number of Nonidentical Wind Turbines

Cases involving nonidentical wind turbines have to be analyzed on anindividual basis. Engineering judgment must be used in extending theresults of the previous subsection to the situation of similar butnonidentical units.

A specific example of different WTGs is the case where one unit isuncontrolled. Results for this situation are presented in Section 18.4for the Goodnoe Hills installation.

- 35 -

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- 37 -

12.5 Application to the Goodnoe Hills System

The state space matrix for the three WTG system was evaluated and theeigenvalues determined for a variety of loading conditions (Section18.4). The data used is taken from the PSS/E simulation setup describedin Section 14. Although this system results in repeated eigenvalues andcan be analyzed using equivalents as discussed previously, we shallanalyze the entire system matrix. This will illustrate the phenomenonand also analysis of situations with nonidentical WTGs.

Section 18.4 contains the following cases:

o Frequency response for the linearized PSS/E system to yield theappropriate synchronizing and damping coefficients for thein-phase and anti-phase modes (Case 24).

o Frequency response for light and heavy loads at different powerfactors (Case 25).

o Time response illustrating in-phase and anti-phase motion (Cases26, 2-7).

o Eigenvalue plots for the three machine system including thesituation where the blade angle of a machine is uncontrolled(Cases 28, 29).

12.6 Discussion

A nulti-machine system with identical WTGs, all synchronized to the samebus, has

o Very closely spaced torsional modes comprised of one setcorresponding to the in-phase WTG movements (all WTGs movingcoherently) and N-l repeated sets of torsional modes correspondingto the anti-phase WTG movements (WTGs moving against each other);

o Less closely spaced electrical modes comprised of lower frequency,lightly damped system modes and N-l repeated inter-machine modesof higher frequency and damping.

A multi-machine system with identical WTGs where machines aresynchronized in groups has

o Very closely spaced torsional modes comprising system, inter-groupand inter-machine oscillation;

o Less closely spaced electrical modes comprising system, inter-group and inter-machine oscillation.

- 38 -

All natural modes can be derived using a single machine and appropriatetransmission to an infinite bus. Since the electrical transmissiongenerally has an insignificant effect on the torsional modes and thepower controller, we may draw the following conclusion:

o A good power controller design which adequately dampens torsionaloscillation in a single machine situation will also behaveadequately in a multi-machine situation.

The inter-machine electrical modes will be less closely spaced. For thefollowing reasons they are not particularly significant:

o These modes are not stimulated appreciably by wind speeddisturbances.

o They are adequately damped due to increased effectiveness ofdamper windings at the higher frequencies of inter-machineoscillation.

Both electrical and torsional modes of the Goodnoe Hills system areclosely spaced. This is due to the relative strength of the outgoingtransmission system. The small disturbance dynamic behavior of theGoodnoe Hills wind turbine cluster is satisfactory over the expectedrange of loading.

- 39 -

13. ELECTRICAL SYSTEM DESIGN

13.1 Protection

Figure 12 - Pg. 41 is the Boeing one-line diagram of the MOD-2 electricalsystem. The selection of protective relays for the MOD-2 electricalsystem is reasonable. Instantaneous overcurrent, time over-current, reverse power, ground fault, loss of field current, loss ofexcitation, loss of synchronism and differential current operate thegenerator circuit breaker in the nacelle through a tripping relay. Thisrelay must be manually reset. A second power interrupting device, thebus tie contactor, is located on the ground. The bus tie contactor isthe normal power interrupting device, i.e., it is operated during startupand shutdown sequences. Overfreauency, underfrequency and under voltageinitiate a shutdown sequence.

13.2 Location and Number of Circuit Breakers

The MOD-2 electrical system has two power interrupting devices, one inthe nacelle near the generator for fault clearing and one near thetransformer for normal startup and shutdown. In our opinion, it wouldhave been adequate to have one power interrupting device near thetransformer. Fault contribution from the utility network is generallyhigher than that from the generator, so that fault currents in the WTGstation are minimized when the circuit breaker is placed as close to theentrance as possible. Furthermore, fault currents from the generatordecay more rapidly than fault currents from the utility system. Ideally,the circuit breaker would be on the high side of the transformer. Thiswould result in the conventional unit arrangement: circuit breaker,transformer, turbine-generator. Unfortunately, the high number ofoperations required from a WTG power interrupting device necessitates theuse of contactors instead of circuit breakers. Contactors are notavailable at typical utility interconnection voltages (34.5 - 69 kV).

- 40 -

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The first installation of MOD-2 WTGs will be a three-machine cluster atGoodnoe Hills in Klickitat County in Southern^Washington. The 3 MOD-2 WTGswill be connected to the transmission system of the Bonneville PowerAdministration (BPA). Fig. 13 - Pg. 43 is a one-line diagram showing voltages(kV), impedances (per unit on 100 MVA base), as well as real power (MW) andreactive power (MVAR) for a heavy load condition with the WTGs at unity powerfactor. Figure 14 - Pg. 44 shows the same load condition with the WTGs at apower factor of 0.9 lagging (overexcited). Fig. 15 - Pg. 45 depicts a lightload condition with the WTGs at unity power factor.

Fig. 16 - Pg. 46 is a simplified electrical system diagram. The loads havebeen neglected and the BPA system has been replaced by an infinite sourcebehind a single equivalent reactance. The single reactance includes the 12/69kV setup transformer at the WTG station. Contrary to the other-one-linediagrams, the reactances are expressed in per unit on machine base (3.125MVA). The short circuit rating corresponding to the"equivalent systemreactance is 63.8 MVA or approximately 7 times the combined rating of the 3MOD-2 WTGs. This is a resonably 'stiff system. 2 times rating would beconsidered 'soft'; 20 times rating and higher would be considered 'infinitelystiff.

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WTG#1 0.05

4.2kV

0.003

12.OkV

WTG#2 0.05 0.0017

k.2M 12.OkV

WTG#3 0.05 0 0027

BPA SYSTEM

12.OkV 12.OkV

FIGURE 16

SIMPLIFIED ELECTRICAL SYSTEM - 3-125 MVA BASE

GOODNOE HILLS INSTALLATION - 3 MOD-2 WTGs

- 46 -

15. STARTUP, SYNCHRONIZATION, LOADING. SHUTDOWN

The turbine rotor accelerates from standstill to rated speed (17.55 rpm) ifwind speed is higher than cut-in. The blade angle during acceleration iscontrolled by a series of algorithms (described in Reference 3) that are basedon table lookup and proportional speed control. Speed control near ratedspeed prior to synchronization has integral characteristics. When the turbinespeed exceeds 17.5 rpm for the first time, generator field control is turnedon and the synchronizer is enabled. The bus tie breaker is closed whenvoltage and phase angle are within limits. The limits to be used at GoodnoeHills have not yet been set.

In the case of wind turbine generators there is room for tradeoff between theneed to match voltage and phase and the desire to have as many opportunitiesfor closing the breaker as possible. A soft shaft WTG such as the MOD-2 has amuch greater tolerance for synchronizing with moderate voltage and phasemismatch than conventional turbine generators. This characteristic should beexploited to minimize synchronization time.

After the breaker has been closed, the pitch control system switches fromspeed control to power control. This switch causes a load increase from 0 to2.5 MW. The rate of change of the blade angle is limited to l°/second.With a blade angle of 20° at zero power and -1° at rated power for ratedwind speed, the transition from 0 to 2.5 MW will take 21 seconds. This slowtransition will avoid significant excitation of the first torsional mode.

Reference 3 describes two shutdown modes, normal and fast. In both cases, theshutdown sequence ends when the turbine rotor has stopped. We believe thatunder certain conditions it would be desirable not to enter a shutdownsequence but to return to the last phase of speed control prior tosynchronization. The conditions are

o Bus tie contractor has opened;

o Power reasonableness test has failed.

These two conditions are likely to occur when there is an electrical systemdisturbance, such as a short circuit or the tripping of a circuit breaker.Since these disturbances are usually very brief, it would be preferable if thewind turbine generator system entered a standby mode instead of shuttingdown. If resynchronization did not occur within a specified interval (severalminutes) shutdown should be initiated.

A review of the electrical system of the MOD-2 (Fig. 12 - Pg. 41) and thesoftware specification (Reference 3) indicates that the MOD-2 will restartautomatically when utility voltage returns. If, for example, a utilitycircuit breaker in the transmission line to the WTG station opened and thenreclosed after 30 minutes, the MOD-2 would shut down at the beginning of theinterval and restart automatically at the end. This is a desirable feature.

- 47 -

16. ON SITE TESTING

We recommend that operational testing at the Goodnoe Hills site include threeinvestigations relating to interactions between the WTGs and the power system.

16.1 Generator Excitation Control

We support the step by step procedure recommended by BPA at the Boeing/NASA/BPA coordination meeting in Seattle on November 27, 1979:

A. Use power factor control during initial startup and test period.

B. Implement voltage control in lagging (overexcited) region. Allowpower factor to vary between 0.8 lagging and 1.0. Observe and gatherdata.

C. Extend voltage control to leading (underexcited) region by adjustingreactive power limit or power factor limit. A power factor limit of0.95 or 0.9 leading is suggested. Observe and gather data.

It will be necessary to record the following electrical parameters:

o Real power

o Reactive power

o Terminal voltage

This test will determine whether WTGs require special forms of excitationcontrol or can use the same procedures that have evolved for otherutility turbine generators.

16.2 Turbine Control

Since turbine control in the MOD-2 uses both turbine speed and electricalpower as control inputs during power generation, the system is very wellsuited to test different combinations of gains of speed control (damping)and power control. A reduction or elimination of the proportional gainof the power controller and an increase in the proportional gain of thespeed controller (damping) would bring the primary (turbine) control ofthe MOD-2 closer to utility practice and would, in our opinion, make theMOD-2 system less susceptible to electrical disturbances and the controltransition from above to below rated wind speed. The tests would includewind speed transients and planned electrical disturbances such as lineswitching and synchronization.

- 48 -

16.3 Shutdown Frequency

Shutdowns are undesirable; they reduce energy capture and impose a burdenon the utility company and its customers. Shutdown frequency is afunction of turbine control strategy, wind speed transients andelectrical disturbances. This is an area where a reasonable tradeoff hasto be found between protection of the WTG system and continuity of powergeneration. Since large WTGs on utility systems represent a newtechnology, it is likely that some experimentation and design evolutionis required. The on site test program would determine the correlationbetween shutdown frequency, control settings, wind speed transients andelectrical disturbances.

- 49 -

17. DISPATCH AND DATA ACQUISITION

Utility companies use a highly structured approach to communication betweenpower generation/distribution stations and central control facilities. Thiscommunication system is called Supervisory Control and Data Acouisition(SCADA). Typical functions are

o Analog input from remote location

o Digital input from remote location

o Accumulator at remote location (e.g. MWH accumulator), queried bymaster at regular intervals

o Momentary digital output to remote location

o Timed digital output to remote location.

Typical scan rates are 2-5 seconds. While the functions are the same, thehardware and the communication protocols vary from utility company to utilitycompany.

There are a number of manufacturers of electronic equipment which provideRemote Terminal Units (RTUs) compatible with the SCADA protocol of the largeutility companies. As wind turbine stations are integrated into a utilitynetwork, either the wind turbine manufacturer or the utility company shouldprovide an RTU equipped with the proper number of inputs and outputs anddesigned for the proper SCADA protocol. Dispatch and monitoring equipmentwhich cannot be integrated into the SCADA system will not be useful to theutility company.

- 50 -

18. SIMULATION RESULTS

The simulation results included in this report are divided into three groups.Each group contains results obtained with one of the three major analyticaltools used, PSS/E, MNT/E and IDAP (Section 4). There are twelve simulationcases using PSS/E, one using MNT/E and sixteen using IDAP. The twelve PSS/Ecases are further divided into ten single machine cases and two multi-machinecases. The results of each simulation case are accompanied by a description.

18.1 Single Machine Simulation Results from Power SystemSimulator (PSS/E)

Cases 1-10 comprise this group. Per unit power refers to the machinebase, which is 3.125 MVA for the MOD-2. Rated power is 2.5 MW. At ratedpower of 2.5 MW, per unit power is 0.8. The quantities plotted for Cases1-10 are:

Field Voltage

Generator Terminal Voltage

Turbine Power Coefficient

Turbine Blade Angle

Wind Speed

Power Angle

Electric Power at Generator Terminals

Mechanical Power at Blades

Blade Torque

Shaft Torque

Blade Speed Deviation

Generator Speed Deviation

Hub Speed Deviation

Output of Reactive Power Controller

Power Factor

Reactive Power at Generator Terminals

PU

PU

-

DEC

MPH

DEC

PU

PU

PU

PU

PU

PU

PU

PU

-

PU

EFD 1

VOLT 1

CP 1

BETA 1

WIND 1

ANGLE 1

PELEC 1

PMECH 1

TORQ IB

TORQ IS

SPEED IB

SPEED IG

SPEED 1H

QCTRL 1

PF 1

QELEC 1

- 51 -

The normal control settings used for Cases 1, 2, 4 and 6 are

o Proportional power gain 15°/MW = 46.9°/3.125 MVA

o Integral power gain 4°/MW SEC = 12.5°/3.125 MVA SEC

o Proportional speed gain 37CP/RAD/SEC = 680°/1.84 RAD/SEC

The modified control settings used for Cases 3, 5, and 7 are

o Proportional power gain 0

o Integral power gain 12.5°/3.125 MVA SEC

o Proportional speed gain 1360°/1.84 RAD/SEC

Case 1 - This is a single MOD-2 at rated condition. This case wasselected to show that the response of the turbine control system isdependent on wind speed. The gain of the AP/A3 transfer function (Fig.1 - Pg. 8) increases as wind speed increases. The increase is shown inFig. 5 - Pg. 18. This change in the wind turbine transfer function iscaused by the wind turbine characteristic cp = f( X,B). In thissimulation case wind speed is increased every 10 seconds in steps at 4MPH, starting at t = 5 seconds. The increase in gain and damping in theprimary (turbine) control loop is very evident.

- 52 -

NflSfl - WIND TURBINE PYNf lMICS - SINGLE WTGMOD 2WIND SPEED INCREflSE FROM RflTED TO CUTOUT IN STEPS OF 4 MPHCflSE 1

F000 WIND 1 10 0.0

100.00 RNGLE 1 0.0r r1.5000

IPMECH 1 -0.500

I

1.5000 PELEC 1 -0.500\

f

r

oin

ao

in

eao

inCO

oo

o ujo z:in !"""«\j I—

oooo(\J

oootn

ooo

oooin

oo

- 53 -

NflSfl - WIND TURBINE DTNflMICS - SINGLE WTGMOD 2WIND SPEED INCREflSE FROM RflTED TO CUTOUT IN STEPS OF 4 MPHCflSE 1

5.0000 EFD 1 0.0

1.1000

I T

VOLT 1

1

1.0000r I0.5000

I

CP 1

I0.0

-2.000

\f>

- 54 -

NfTSfl - WIND TURBINE DYNflMlCS - SINGLE WTGMOD 2WIND SPEED INCREflSE FROM flflTED TO CUTOUT IN STEPS OF 4 MPHCflSE 1

1.5000 TORO IB 17 -0.5001 I

l.SCuJ TORQ IS 12 -0.500I I

0.0500

I

SPEED IB 16

I

-0.050I T

0.0500

1

SPEED 1C 14

I

-0.050I 1

0.0500

I

SPEED 1H 15

1

-0.050I 1 1

-*-I

It

/X

i

oooin3"

0ooinm

gUJo z:

ooo

oo

- 55 -

*

NflSfl - WIND TURBINE OTNf lMICS - SINGLE WTGMOO 2WIND SPEED INCREflSE FROM RflTED TO CUTOUT IN STEPS OF 4 MPHCflSE 1

0.2500 OCTRL 1 20 -0.250I I I )1.0000 PF 11 1 1 1

.0000 OELEC 11 1 1

It

\

1

— f1

\

~ I/

XV

Ii/

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f'

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I I I ,

1 1 1 1 1 1

19 « « 0.50001 I I I

18 B B 0.01 1 1 1 1 1

i{

i —1

i, i

i:

i

i -

) jI

1 i1

\ !) 1f i\ !) j*x !/ I

i —I

i l l

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0aoin

o0o0a*

ooo•

inCO

0o0

oo0

inC\l

oo0CM

eooin

o0ao

oooin

oo

- 56 -

Case 2 - Case 3 - These cases were selected to demonstrate the responseof a single MOD-2 system to a design gust, starting at rated condition.A design gust is a 1-cos excursion of wind speed of 28%. For Case 2 thenormal control settings are used, for Case 3 the modified settings. Theelimination of proportional power gain in Case 3 has increased theexcursions of electrical power and shaft toraue. It should be noted,however, that no attempt was made to select the best possible speedcontrol for Case 3.

- 57 -

NflSfl - WIND TURBINE DYNRMICS - SINGLE WTGMOD 2DESIGN GUST (POSITIVE) INITIflTED flT T=1.0 SECONDCflSE 2 (NORMAL CONTROL)

1.000 HIND 1 10 0.0

100.00 HNGLE 1 0.0

I.5000 PMECH 1 -0.500

.5000 PEL EC 1

I

-0.500

i

oo0

arg

oo

I

(M

§UJo Z

oo

f oooo

li

aaa

oooo

- 58 -

NflSfl - »JINO TURBINE DTNflMICS - SINGLE WTGMOD 2DESIGN GUST ( P O S I T I V E ) INITIflTED flT T=1.0 SECONDCflSE 2 (NORMAL CONTROL)

5.0000 EFO 1 0.0I

1.1000

\

VOLT 1

I I

1.0000[ I

0.5000

I

CP 1

I I

0.0

- 59 -

NflSfl - WIND TURBINE OYNflMICS - SINGLE WTGMOD 2DESIGN GUST (POSITIVE) INITIflTED flT T=1.0 SECONDCflSE 2 (NORMAL CONTROL)

1.5000 TORQ IB 171 1 1 I 1

1.5000 TflRQ IS 121 1 1 1 1

fncnn coccn 10 i c.U3UU SrEEU IB lot i l l

Oncmn oocpn t c* 1 11. U3IJU 5PEEO lo 14r i i i i0.0500 SPEED 1H 15r i i i i

• 1/11

*_ 1 I

1 /*\ 1

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1t!

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1i1

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1 1 1 1

1 1 1 1

a Q -0.0501 1 1 1

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- 60 -

NflSfl - WIND TURBINE DTNflMICS - SINGLE WTOMOO 2DESIGN GUST (POSITIVE) INITIRTEO flT T=1.0 SECONDCflSE 2 (NORMAL CONTROL)

.2500 OCTRL 1 -0.250I

1.0000I T

.0000

I

PF 1I

QELEC 1 18

T I

0.5000I I

0.0

oo

org

\! oo

I

UJ

oo

oaa

ooo

ru

oa

- 61 -

NflSfl - WIND TURBINE DYNflMICS - SINGLE WTGMOO 2DESIGN GUST (POSITIVE) INITIflTED flT T=1.0 SECONDCflSE 3 (MODIFIED CONTROL)

50.000 H I N D 1 10 0.0I

100.00 RNGLE 1 0.0

1.5000

I

PHECH1

I

-0.500

.5000

I I

PELEC 1

I

-0.500I I

\

f

ooo

eoo

giuo z:

oooo

oooeg

- 62 -

NflSfl - WIND TURBINE DYNF1ICS - SINGLE WTGMOD 2D E S I G N GUST ( P O S I T I V E ) I N I T I R T E D R T T = 1 . 0 S E C O N DCflSE 3 (MODIFIED CONTROL)

S.OOOO EFD 1 0.0I I

1.1000

rVOLT 1 1.0000

I I0.5000

I

CP 1

I

0.0I IIB.000 BETR 1 13

I I

-2.000

- 63 -

NflSfl - HIND TURBINE DTNflMICS - SINGLE WTGMOD 2DESIGN GUST (POSITIVE) INITIflTED flT T=1.0 SECONDCflSE 3 (MODIFIED CONTROL)

1.5000 lunu JOI 1 1 1 1

1.5000 TORQ ISI 1 1 1 1

0.0500 SPEED 181 1 1 1 1

0.0500 SPEED 1G1 1 1 1 1

0.0500 SPEED 1H1 1 1 1

t

t\\\

\\

__ \\

— ,

1f

t

/'f

9f

9t

^^ 99

9t

t

91

1

t

\

X~— \

V

\

\_ \

\

\

\

\

!II

1 1 i l l

I / X -X -U.3UU1 1 1 1 1

1 1 1 1 1

16 «- « -0.0501 1 1 1 1

14 « 4 -0.0501 1 1 1 1

15 B a -0.0501 1 1 1

f1

: __\\\\

1 -

'

'

\ -1 1 1 1 1

1

1

1

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0

0

<o

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eo0

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o0

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oaoo

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- 64 -

- HIND TURBINE DYNflMICS - SINGLE HTGMOO 2DESIGN GUST [ P O S I T I V E ) INITIRTED f lT T=!.0 SECONDCflSE 3 (MODIFIED CONTROL)

F2500 QCTRL 1 -0.250

1.0000

I

PF 1

I \

0,5000

- 65 -

Case 4 - Case 5 - These two cases show the response of single MOO-2systems to a negative design gust starting at rated condition. Case 4has normal control; Case 5 has modified control. A comparison of thesetwo cases demonstrates the advantages of eliminating proportional controlfrom the power controller. In Case 4 the blade angle is constantlyrestricted by the blade angle rate limit of 8°/sec or by the minimumblade angle. This makes the control ineffective, causes increasingamplitudes of power and speed oscillation and prevents normal recovery.In Case 5 blade angle excursions and power oscillations are much smallerbecause the response of the blade angle controller to power variations ispurely integral. Power and speed oscillations decay rapidly and recoveryis normal.

- 66 -

NflSR - WIND TURBINE DYNF1MICS - SINGLE WTGMOO 2DESIGN GUST INEGflTIVE) INITIflTED RT T=1.0 SECONDCflSE 4 - NORMflL CONTROL

1.000 M I N D 1 10 0.0

100.00

I

flNGLE 1 0.0

1.5000

1

PHECH 1

I

-0.500I I 1

-0.500

- 67 -

NflSfl - WIND TURBINE OYNflMICS - SINGLE WTGMOO 2DESIGN GUST (NEGflTIVE) INITIflTED flT T=1.0 SECONDCflSE 4 - NORMRL CONTROL

5.0000 EFD 1f 0.0I I1.1000 VOLT 1

1 I

1.0000r r0.5000 CP 1

1 I

0.0

- 68 -

NflSfl - WIND TURBINE OYNf lMICS - SINGLE WTCMOO 2DESIGN GUST (NEGflTIVE) INITIflTED flT T=1.0 SECONDCflSE 4 - NORMflL CONTROL

1.5000 TORQ IB 17 ^0.500

1.5000

I I

TBRQ IS 12

1

^0.500I

0.0500

I I

SPEED IB 16

I

-0.050I

0.0500 SPEED 1C 14

I

^0.050

-0.050

- 69 -

NflSfl - W I N D TURBINE DYNHMICS - SINGLE WTCMOD 2DESIGN GUST JNEGf lTIVE) INITIflTED f lT T=1.0 SECONDCflSE 4 - NORMflL CONTROL

0^2500 OCTRL 1 -0.250

1.0000

I T

PF 1 19

I I 1 I

0.5000I I

.0000 r

iQELEC 1

I18

I I

EJI I

I

0.0

ooo•o

(M

OOo

V

oo

oo(M

Oooo

OO

oooo

oo

oo

- 70 -

•men - WIND ri lRBINE DTNflMlCS - SINGLE WTGMOD 2DESIGN GUST (NEGRTIVE) INITIRTED flT T=1.0 SECONDCflSE 5 - MODIFIED CONTROL

50.000 HINDI 10 0.0I

100.00 ANGLE 1 0.0

.5000

I

PHECH 1

I

-0.500

1.5000

1

PELEC 1 -0.500

- 71 -

NflSfl - W I N D TURBINE DTNflMICS - SINGLE WTGMOD 2DESIGN GUST INEGRTIVE) INITIflTED flT T=1.0 SECONDCflSE 5 - MODIFIED CONTROL

P.uuuuI

1.1000f 1

. 5LHJU

tr u j1 1 1

VOLT 11 1 1

Cr I

O

1

51

1 1 1

f^j H i l l 11 Q

1 1 1

u. u1 1

1.00001 1

O n. U

18.000 B E T R 1 13

I

-2.000f 1

I

X \

iiiiiii

i l

oo

CM

or:

eoo

oo

- 72 -

NPSfl - "INO TURBINE OYNHMICS - SINGLE WTGriC2 <;DESIGN GUST (NEGflTIVE) INITIflTEO flT T=1.0 SECONDCflSE 5 - MODIFIED CONTROL

1.5000 TORO IB 17 -0.500I

1.5000

I I

TORO IS 12

I I

-0.500I T

0.0500

I

SPEED IB 16

I I

-0.050

0.0500

I I I

SPEED 1C 14

I I

-0.050r0.0500

I I

SPEED 1HI

15

I I

-0.050I I

oao

aoo

oO I

ooo

oo

ooa

oo(VJ

oa

- 73 -

NflSfl - W I N D T I I R P T N F H Y N R M T r s - SINGLE WTGMOD 2DESIGN GUST (NEGflTIVEl INITIflTED flT T=1.0 SECONDCflSE 5 - MODIFIED CONTROL

0.2500 QCTRL 1 20 -0.250

1.0000

I

PF 1

I 1 T I I

0.5000

.0000

I I

QELEC 1 18

I I

0

T I

0.0I I

1

o00

§!

ooo

ooo

- 74 -

Case 6 - Case 7 - These two cases were selected to demonstrate thedifferences in response between turbine control with proportional powergain and without. Case 6 has normal control settings; Case 7 hasmodified control settings. Wind speed is 33 MPH, and the machine isproducing rated power. At t = 1 second, electrical load is lost. Theload is restored at t = 1.2 seconds. A comparison of the results showsthat in Case 7 the excursions during the recovery from this very severetransient are much smaller because blade angle activity has been reduced.

- 75 -

NflSfl - WIND TURBINE DTNf lMICS - SINGLE WTCMOD 2LOSS OF LORD FOR 0.2 SEC - 33 MPH WIND - NORMflL CONTROLCflSE &

1.000 HIND 1 10 0.0

1000.0 flNGLE 1 0.0

1.5000

I I

PHECH 1

1

-0.500I I

1.5000

I

PELEC 1 -0.500

- 76 -

NflSfl - HIND TURBINP nv f jnMi rs - SINGLE WTCMOD 2LOSS OF LOflO FOR 0.2 SEC - 33 MPH WIND - NORMflL CONTROLCflSE 6

5.0000 EFD 1 0.0

1.1000

I I

VOLT 1

I

1.0000I I0.5000

I I

CP 1

\

0.0

18.000

I I I

BETH 1 13

I I

-2.000

- 77 -

NflSfl - HIND TURBINE DTNflMICS - SINGLE WTGMOD 2LOSS OF LORD FOR 0.2 SEC - 33 MPH WIND - NORMflL CONTROLCRSE 6

L5000 TORQ IB 17 -0.500I

K5000

I

TORQ IS 12

T I

-0.500I I

0.0500

I

SPEED IB 16

I I

-0.050I

0.0500

I

SPEED 1G

T1 14

1

-0.050I

0.0500

I T

SPEED 1H 15

I

-0.050

- 78 -

NflSfl - WIND TURBINE DTNflMICS - SINGLE WTGHOD 2LOSS OF LORD FOR 0.2 SEC - 33 MPH WIND - NORMflL CONTROLCflSE 6

.250D QCTRL 1 -0.250

1.0000

I

PF 1

I

0.5000I

- 79 -

NflSfl - WIND TURBINE DYNf lMICS - SINGLE WTGHOD 2LOSS OF LORD FOR 0.2 SEC - 33 MPH WIND - MODIFIED CONTROLCflSE 7

1.000 HJND 1 10 0.0

1000.0

T I I

flNGLE 1

I I

0.0I I

1.5000

I

PMECH 1

I 1

-o.sao

- 80 -

NflSfl - WIND TURBINE H f ' I P n r C S - S T N ^ L F WTGMOD 2LOSS OF LORD FOR 0.2 SEC - 33 MPH WIND - MODIFIED CONTROLCflSE 7

5.0000 EFD 1 0.0I I

1.1000

1

VOLT 1

I - I

1.0000I I

0.5000

I

CP 1

I I

0.0

- 81 -

- WI'IO TURBINE 01TNRMICS - SINGLE WTGHOD 2LOSS OF LORD FOR 0.2 SEC - 33 MPH WIND - MODIFIED CONTROLCflSE 7

L.5000 TORQ IB 17 -0.500

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Case 8, Case 9, Case 10 - These three cases have been included to showthe differences between the three possible methods of generatorexcitation control:

o Voltage control - Case 8

o Power factor control - Case 9

o VAR control - Case 10

A single MOD-2 at rated condition is perturbed by a 4 MPH wind speedincrease. Initial power factor is 0.8 lagging. Primary (turbine)control has been deactivated so that it is easier to interpret theresults. A comparison shows the characteristics of the three controlmethods:

o Voltage Control

Excursions of generator terminal voltage are small, power angleexcursions are normal, and an increase in real power isaccompanied by a decrease in reactive power and an increase inpower factor.

o Power Factor Control

Excursions of generator voltage are large, excursions of powerangle are small, and an increase in real power is accompanied byan increase in reactive power and a nearly constant power factor.

o VAR Control

Excursions of generator voltage are small, power angle excursionsare normal, and an increase in real power is accomplished by anincrease in power factor and nearly constant reactive power.

These three cases are also representative of MOD-2 operation at less thanrated wind speed when blade angle control is inactive. It will be notedthat there is very little damping of the first torsional mode.

- 84 -

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18.2 Multi-Machine Simulation Results from Power SystemSimulator (PSS/E)

Cases 12 and 13 comprise this group. Both are simulations of the threemachine MOD-2 farm at Goodnoe Hills. Per unit power refers to the systembase which is arbitrarily set at 100 MVA. At rated power of 2.5 MW, perunit power is 0.025. The quantities plotted for Cases 12 and 13 are

Hub Speed PU SPD-TUR

Shaft Torque PU TRQ-SFT

Reactive Power PU Q

Real Power PU P

Turbine Blade Angle DEC BETA

Wind Speed MPH WIND

Field Voltage PU EFD

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Bus Voltage at Specified Bus PU V

Case 12 - This case illustrates interaction between machines during anelectrical fault. Prior to the fault, all three machines are operatingat rated load. Wind speed is 30 MPH. The power factor is 0.9 lagging.Generator excitation is in voltage control mode. The initial load flowcondition for this case is shown in Fig. 14 - Pg. 44. At t = 1 second,WTG #3 loses its electrical load for 0.1 second. This is a very severedisturbance which affects all three machines. The machine recoverswell. The prevailing oscillation has a frequency of approximately 30rad/sec. It is caused by the electrical mode.

- 97 -

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Case 13 - This case demonstrates interaction between the three MOD-2 WTGsat Goodnoe Hills during a disturbance induced at the turbine. Prior tothe disturbance, all three machines are operating at rated load. Windspeed is 26.5 MPH, the minimum wind speed to produce rated power. Thepower factor is 0.9 lagging. Generator excitation is in voltage controlmode. The initial load flow condition for this case is shown in Fig. 14 -Pg. 44. At t = 1 second, wind speed at WTG #1 is abruptly increased by 7MPH to 33.5 MPH. WTG #1 makes a stable transition from a pitch angle of-1° to +9°. The prevailing oscillation has a frequency ofapproximately 1.7 rad/sec. It is caused by the first torsional mode.Note that the closed loop frequency of the first torsional mode isconsiderably higher than the open loop frequency. WTG #2 and WTG #3 arehardly affected by the severe wind speed change at WTG #1.

- 109 -

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,1 |[ INTERRCTION BETWEEN RDJflCENT WIND TURBINES *UP VOLTflGE CONTROL - WIND SPEED INCREASE 7 hPH (WTG#1)

CASE 13 ^

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CASE 13

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.1500 Q-CHENOHIT 11 0.0

0.3000 P-CHENOHIT 0.0I

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- 113 -

GOODN3E HILLS WIND TURBINE STRTION (NRSR-BOEING-BPfl)HERVT SYSTEM LORD - W T G S RT RRTED LORD - 0.9 PF LRGGINGINTERRCTION BETWEEN RDJRCENT WIND TURBINESVOLTflGE CONTROL - WIND SPEED INCREASE 7 MPH (WTG#1)CASE 13 LU

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- 114 -

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GCODNOE HILLS W I N D TURBINE S T R T I O N (NflSfl-BOEING-BPfl)HERVY S Y S T E M LORD - WTGS RT RflTED LORD - 0.9 PF LflGGINGINTERflCTION BETWEEN RDJRCENT WIND TURBINESVOLTRGE CONTROL - WIND SPEED INCREASE 7 MPH (WTG#1)CASE 13

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GOOCWOE HILLS WIND TURBINE S T R T I O N (NRSR-BOEING-BPfl)HEflVT S Y S T E M LORD - W T G S flT RRTEO LORD - 0.9 PF LflGGINGINTERflCTION BETWEEN f lDJRCENT WIND TURBINESVOLTRGE CONTROL - WIND SPEED INCREASE 7 MPH (WTG#1)CASE 13

COLUOCE

l.£UUU

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m ^nnnl.cUUUi i. cUUU

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CJODi IE H I I L S HIND TURBINE S T R T I O N WRSfl-BOEING-BPR)HEflVT SYSTEM LORD - WTGS RT RflTEO LORD - 0.9 PF LflGGINGINTERRCTION BETWEEN ROJRCENT WIND TURBINESVOLTRGE CONTROL - WIND SPEED INCREASE 7 MPH (WTG#1)CASE 13

ft

UJ

fDCC

1.5000 TRQ-SFT «1 40 0.5000r0.0250

I

SPD-TUR »1 37

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- 118 -

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CASE 13

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0.0250

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- 120 -

18.3 Simulation Results from Machine Network TransientSimulator (MNT/E)

Case 11 is the only case in this group. This simulation was performed todetermine whether the high speed shaft mode of the drive train can beexcited by electrical frequencies. This requires a four inertiarepresentation of the drive train. Per unit power refers to the machinebase, which is 3.125 MVA for the MOD-2. At rated power of 2.5 MW, perunit power is 0.8. The quantities plotted for Case 11 are

High Speed Shaft Torque RJ TORQUE HSH

Blade Torque PU TORQUE BL

Low Speed Shaft Torque PU TORQUE LSH

Air Gap Torque ' PU TORQUE AG

Electric Power at Generator Terminals PU PELEC

Mechanical Power at Blades PU PMECH

Power Angle DEC ANGLE

Gearbox Speed Deviation PU SPEED GB

Blade Speed Deviation PU SPEED BL

Hub Speed Deviation PU SPEED HB

Generator Speed Deviation PU SPEED GN

Case 11 - This is a single MOD-2 system at rated condition. At t = 0.05second, a three-phase fault of 0.1 second duration is applied at the highside of the WTG step-up transformer. The 60 Hz air gap torque componentand the initial air gap torque level of nearly 6.0 PU should be noted.The torque in the high speed shaft follows the 60 Hz excitation andreaches peaks of 1.0 PU. The torque in the low speed shaft hardlydeviates from the rated value of 0.8. The plots for speed show that thegearbox inertia generally follows the generator inertia, but alsooscillates with respect to generator inertia at a 60 Hz rate. Theprevailing frequency, other than the 60 Hz excitation, is caused by theelectrical mode.

- 121 -

WIND TURBINE SHflFT TORQUE 5TUCY - MOD 2NORMRL SYSTEM RERCTRNCE0.1 SEC THREE PHRSE FRULT NERR WTG - 4 INERTIR DRIVE TRRINCRSE 11

O0=O

6.0000 TORQUE HSH 20 -4.000i r6.0000

I

TORQUE BL

T

18

I 1

-4.000I I

6.0000

I I

TORQUE LSH 17

I 1

-4.000I

6.0000

\ I

TORQUE flG 10

I I

-4.000

- 122 -

HI MO TURBINE SHflFT TORQUE STUDY - MOD 2NORMflL SYSTEM RERCTRNCE0.1 SEC THREE PHRSE FflULT NERR WTC - 4 INERTIR DRIVE TRRINCRSE 11

7 conn pen. DUUU tru

ccL±J

j«j ^. ...... --_..+ _ g^ sou A

6.0000

I

PELEC 13

I »-4.000 UJ

I

6.0000

I

PHECH 12

I

-4.000CD

I I

200.00

I

HNGLE 11

I

0.0

- 123 -

WIND TURBINE SHRFT TORQUE STUDY - MOO 2NORMflL SYSTEM RERCTflNCE0.1 SEC THREE PHflSE FRULT NEflR WTG - 4 INERTIR DRIVE TRRINCRSE 11

CDLULUQ_

CO

0.0500 SPEED G8 21 -0.050

0.0500 SPEED BL 16 -0.050I

0.0500

\

SPEED HB 15 -0.050

- 124 -

18.4 Simulation Results from Interactive Dynamic AnalysisProgram (IDAP)

This group is comprised of Cases 14-29. Cases 14-23 are from singlemachine simulations; Cases 24-29 are from multi-machine .simulations.

Case 14 - This shows the movement of the eigenvalue locus as the gain ofthe proportional power control is varied. All other control settings arenormal (Section 18.1). The electrical, blade, filter and sha.ft modes areidentified. In particular, it can be seen that the proportional gainonly affects the shaft mode. A proportional gain of 45 gives maximumdamping.

- 125 -

NASA - WIND TURBINE DYNAMICS - SINGLE SYNCH. GEN - MOD 2EFFECT OF CHANGING KP (PROPORTIONAL GAIN)

KP • L75BZE+02 BASE CASE - LOT VINO SPEED (28 MPH)

KP • 0.62ZEE+32 BASE CASE - U» HND SPEED 28 WH>

KP - 2.452SE-H32 BASE CASE - LGS 'HMD SPEED (29 MPH)

KP « SL33raE+a2 BASE CASE - LOV VINO SPEED (28 WW

KP - a 150HE+a2 BASE CASE - LOV VWJ SPEED C2B WW

KP = a.0BaaE*0a BASE CASE - LOV VINO SPEED (28 MPH)

X

123.02

x :

blade m

electrical

i —

f i l ter

f 'x ;

A ^

shaft ' I^™"

l1

•

l

rw • A j v A vIfK fll » 1 A VTAi

ill 1 1 ! ' i I!1 ! M 1 i 1 II!! 1 1 i i ! I'' : l ! ' : I ' ' ; ' ' ';•-123.3 -12. C3 -1.2SS -S.1C3

10.223

1. S223

ju(rads/sei

U, 'iuuu

« • rtftf^Urn LtotiU

a (sec )

PROPORTIONALCase lA

- 126 -

Case 15 - This shows the movement of the locus as the hub damping term(proportional speed control) is varied. The shaft mode is unstable atzero value of K.

- 127 -

NASA - WIND TURBINE DYNAMICS - SINGLE SYNCH. GEN - MOD 2EFFECT OF CHANGING KD (HUB RATE DAMPING)

KD -B.15B2E+04 BASE CASE - LOT VINO SPEED (28 MPH)

KD • 8. 12BBE+84 BASE CASE - LOT VINO SPEED (28 KPH)

XD - ISSSaE+ffl BASE CASE - LW '*IND SPEED <Z8 MPH)

KD • a.6fflJlE+B3 BASE CASE - LOT VIND SPEED (28 MPH)

KD - &.38BZE+03 BASE CASE - LOT VINO SPEED (28 MPH)

KD • SLffi5B0E*ffiI BASE CASE - LOT VIND SPEED (28 MPH)

X

182. CO

*blade

electrical

f i Iter

* 0 X +X T

shaft

KR « ^W-

II! ! ! ! I ! |U! : ' : ; ! 1!" I I I : > 1 ! ! ' I I I i 1

«•

^

""

^

^

—

—

12.3Z3

4 **f*"<*4. MA)Uil

JO)

(rads/se

n «rt**^lita *wi-iJ

-13.23 -1.223 -4123

a(sec )

- 128 -

Case 15

Case 16 - This case shows the decrease in damping of the shaft moderesulting from an increase in integral power control. The shaft mode isthe only oscillatory mode significantly affected by this parameter. Thelocus of the monotonic mode indicates the increased effect of integralgain reset action.

- 129 -

NASA j: WIND TURBINE DYNAMICS - SINGLE SYNCH. GEN - MOD 2EFFECT OF CHANGING Kl (INTEGRAL GAIN)

KI - 0.2520E+02 BASE CAS - LOV VINO SPEED (28 MPH)

XI - B.2222E*fl2 BASE CAS - UW WND SPEED (28 ffH>

XI - 3.15SSE*fl2 SASE CASE - Ltt *IJ!3 SPEED (28 MrH)

KI - 3.lBfflE+82 BASE CASE - LOT WIND SPEED C28 MPH)

KI - 0LSBffi+fll BASE CASE - LOV VIND SPEED (28 WW

KI • imazE+ro BASE CASE - un WIND SPEED czs KPH>

o

X

i 51 -

*blade

electrical

* !f i l ter I -

AJKJ^Xshaft , ~

——

_

_—

iii

M> Tm ^ JK A. * / *Hi «r AT-V A ) ;

;; i ! i i i ! I::M i i I 1 l « : : I ! ! ! ! l it • i ! i • 1 • ; . , • •-isaa -11:3 -usaa _j -2.122

a (sec" )

13.233

!• ZUitZ

ju(rads/sec

« « rtn^u. >.t<4.b

1*-W*^• b*4.A*

INTEGRAL GAINCase 16

- 130 -

Case 17 - This shows the effect of varying KE, the electricalsynchronizing coefficient. The frequency of the electrical modeincreases but all other modes are nearly stationary. This reveals thatpower control is largely independent of electrical system properties.

- 131 -

NASA - WIND TURBINE DYNAMICS - SINGLE SYNCH. GEN - MOD 2EFFECT OF VARYING KE (ELECTRICAL STIFFNESS)

XE • 2.SXEE+01 BASE CASE - LC» HJBJ SFSED (29 MFH)

KE - 0. 15BflE«tt BASE CASE - UW HMJ SPEED <28 HW

KE -flumffi+fli BASE CASE - UM VIND SPESJ <28 »w

KE - a.52BZE+ea BASE CASE - un YIND SPEED as mo

9tf

blade ^

A

electrical

XIf i l ter

ashaft

III 1 1 1 1 1 III! I 1 1 1 1 Illl 1 1 1 1 1 III! 1 1 1 1 1

-

-

—

—

-

I 1 I 1 1 III

IBB. 38

-123,3 -13.23 -1.382a(sec"

-fl.100

L2228

(rads/st

2.1223

3.1323

ELEC. STIFFNESSCase I?

- 132 -

Case 18 - This shows the effect of varying DE, the electrical dampingcoefficient. Only the damping of the electrical mode is affected. Nodamping is introduced into the shaft system from the generator.

- 133 -

NASA - WIND TURBINE DYNAMICS - SINGLE SYNCH. GEN - MOD 2EFFECT OF VARYING DE (ELECTRICAL DAMPING)

OE -L1888E+fl2 BASE CASE - U» ¥DO SPES) (28 JffH)

DE - a.752ZE+fll BASE CAS - LCT KIND SPEED GB MPH)

OE • a.5B8ffi*ai BASE CASE - U» ¥DO SPEED (28

DE - a.23SE*il BASE CASE - U» ¥DO SFES (28

DE • a.mes-48 BASE CASE - un VINO SPSD <zs tno

X

*blade A

electr ical

*f i l ter

shaft

III 1 1 1 1 1 (III 1 1 1 1 1 (III 1 1 1 1 1 MM 1 1 1 1 1

-

=

-

-

1 1 1 | | III

1BB.BB

13.208

JO)

(rads/sec

0.1228

-120.0 -IB. 30 -LB20 -lira 8.1223

aCsec"1)

ELEC. DAMPINGCase 18

- 134 -

Case 19 - This shows the effect of wind speed change. As wind speedincreases, 3P/ 96 increases. This increases overall controller gain.Only the shaft mode is affected.

- 135 -

NASA - WIND TURBINE DYNAMICS - SINGLE SYNCH. GEN - MOD 2EFFECT OF VARYING WIND SPEEDS

OP/IB -B,5aB0£-01 BASE CASE VALUES

LP/Z3 -fl. 1SZZMS BASE CASE VALUES

DP/US -41502E+B8 BASE CASE VALUES

DP/EB ~0,208gE«ffl BASE CASE VALUES

DP/IB -a.25B8E+ffi BASE CASE VALUES

blade

electrical

f i l ter

shaft

III 1 1 1 1 1 till 1 1 1 1 1 HIM II 1 1 III! 1 | | 1 1

-

—

~

1 1 1 1 1 1 1!

-i0a.il -10.20 -L202 -i , -0.108a(sec )

108.28

12.820

_ L2222

JO)

[rads/se

a.

8.1200

WIND SPEED CHANGESCase 19

- 136 -

Case 20 - This case shows the effect of varying Kn, when Kp is zero.The shaft mode is unstable - as in Case 15 - for zero hub damping rate.The frequency is lower than in Case 15, and a higher Kn. must be used toachieve the same damping. At the high values of Kn, the filter mode isslightly less damped than in Case 15.

- 137 -

NASA - WIND TURBINE DYNAMICS - SINGLE SYNCH. GEN - MOD 2EFFECT OF VARYING KD (HUB TERM) WITH ZERO PROP. GAIN

KD - L2fflBE+04 KP - 0 .. KI - 5.

KD -0L16BeE*B4 K P - 8 . . KI-5.

KD - a.!2ZSE*B4 XP - 3 .. K I - 5 .

KD • BLffire+ffl KP - 0 .. KI -5 .

KD -a.48aE+83 K P - B . . KI-5 .

KD - flLffigfE+ffl KP - a.. KI - s

»blade

IHK-

; t

*e lec t r i ca l

f i l t e r

shaft

-ira.3 -12. S -1.SZ2a(sec~ l )

-3.123

122.30

13.223

(rads/se

HUB RATE - ZERO PP.CFCase 20

- 138 -

Case 21 - This time response was included to complement the eigenvalueplots. The linearized system model was used. An initial displacement inhub and blade angles stimulates the shaft mode. The strong decouplingbetween generator and blade motion is obvious. The freauency and dampingare consistent with the eigenvalue results for the base case design.

- 139 -

K

NASA - WIND TURBINE DYNAMICS - SINGLE VTGMOD 2SIMULATION OF 'SHAFT' MODE

EQUAL INITIAL DISPLACEMENTS IN HUB & BLADE ANGLES

U.<:xCO

0.1000 ANG-ROTOR -0.100I I0.1222I I

0.1000r T

I I

ANG-BLADET I

ANG-HUBT

I I

-0.100I I

-0.100

- 140 -

Case 22 - An initial displacement in generator angle was used. There isvery little motion of the blade and hub in this mode. The frequency anddamping are consistent with the eigenvalue plots.

- 141 -

If

NASA - WIND TURBINE DYNAMICS - SINGLE tfTGHOD 2SIMULATION OF 'ELECTRICAL1 MODE

INITIAL DISPLACEMENT IN 'ROTOR' ANGLE

LUCDCD

0.1000I

I Tfc 0,1000r

ANG-BLAOE 6

ANG-HUB

ANG-ROTOR Q-

-0,100I

-01122I I

-0.100

Ui—•o:h-CJUJ_iLU

Case 2

- >42 -

Case 23 - This case shows the varying effects of control and was includedto complement Cases 14 to 16. The base design (normal control settings)provides a good dynamic response. The system is unstable for zero hubrate damping.

- 143 -

p

.1

.

0.1

.

0.

:,

!

fli NflSR - UIND TURBINE DTNRMICS - E Q U I V R L E N T MOD 2 WTG

BRSE DESIGN VRLUES - LOW W I N D SPEED ( 28 MPH )COMPARISON OF CASES WITH 6 WITHOUT CONTROLLINEARIZED MODEL

.

onon - PCI cc* MI 13 ' __ ^CUUU rtLtL "1 13 T- r1 1 1 1 1 1 1 1

2000 PELEC «1 13 *- o1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1

9500 PM «1 l" B EJ1 1 1 1 1 1 1 1

/ \ • 'S 1 i/ i i

/ 1 .

c '/ "t J 1

/ ^* * '' *™~ I f ^^

1 "> / , c

/' "D f / CL

/ 4) / • TO

TO / /^I rt | > i^

6 — / / a' ° / / •=

£ ' 0c y / =-*-0 4

o / .'•'2 / *

_J0QCt—

0

0 *3 n n.200 -— ,1 0

-0.200 21

r\ onn ^^-U. cUU1

-0.0501 1

1 0o0oin

ooOin

3>

O0Q

O

3-

O

— oirs

O |

§!

ooo

oooin

Case 23

- 144 -

Case 24 - The PSS/E simulation setup and perturbation technique was usedto provide the frequency response shown in Case 24. This casedemonstrates that the synchronizing and damping coefficients arereasonably constant over the range of frequencies of the electricalsystem mode. The input Quantity is mechanical torque. The frequencyresponses of electrical torque, power angle, synchronizing coefficient

and electrical damping coefficient (ug) are shown.

- 145 -

GOODNOE HILLS WIND TURBINE STATION (NASA-BOEING-BPA)HEAVY SYSTEM LOAD - YTGS AT RATED LOAD - UNITY POWER FACTORUSE OF PSS/E SET UP TO PROVIDE VALUES FORSYNCHRONIZING 8 DAMPING IN LINEARIZED MODEL

100.80 ELECTRICAL DAMPING COEFFICIENT (DE)

\A UUUU t. ' "•~'™™~ U» Utttltl

r i

10.0001 1 1 i i i i10.000

i i iPOWER ANGLE (6)i i 1 1 1 i i iELECTRICAL TORQUE

1 1 1 1 1 1

0.01000II 1 1 1 1 1 I 1 1 1 1 1

^— ^_ fl fllflflfl

11 I I I I I I I I

Case

- 146 -

Case 25 - This shows how the appropriate synchronizing coefficients varywith loading. The inter-unit synchronizing coefficient is also shown.It is not appreciably stronger than the system synchronizing coefficientapparently because of the relatively strong tie to the BPA system atGoodnoe Hills. It is also evident that there is little change insynchronizing coefficient with change in load.

- 147 -

GOODNOE HILLS WIND TURBINE STATION (NASA-BOEING-BPA)HEAVY SYSTEM LOAD - VTGS AT RATED LOAD - .9PF LAGGINGUSE OF PSS/E SET UP TO PROVIDDE VALUES FORSYNCHRONIZING COEFFICIENTS AT DIFFERENT LOAD LEVELS

5.0800 SYNCH COEFF TO INF SYSTEM-HEAVY LD-1.0 PFI I I I I I I T

5.0000 SYNCH COEFF TO INF SYSTEM-LIGHT LD-1.0 PFI I

0.00Z0I I I I I I I I

SYNCH COEFF BETW UNITS-HEAVY LD-1.0 PF

T I

I I I I I I I

5.0000 SYNCH COEFF TO INF SYSTEM-HEAVY LD-0.9 PF

r i0.1

r i i i i r I o

LTV

O

Case 25

- 148 -

Case 26 - This case uses a time response simulation based on thelinearized model to illustrate the in-phase modes when all WTGs movecoherently.

- 149 -

D.450G

NflSR - WIND TURBINE DYNRMICS - THREE MOD 2 W T G SBflSE DESIGN VRLUES - LOW W I N D SPEED ( 28 MPH )ILLUSTRATION OF 'IN-PHASE1 MODESEQUAL DISTURBANCE IN WIND SPEEDS ON ALL UNITS

PELEC 151 1

0.35001 1

0.25001 1

0.30001 1

0.1500

1 1 1

PELEC » 21 1 1

PELEC «11 1 1

PM «21 1 1

PM «1

1

141

131

21

1

1

1

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1

1 1

1 1

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1 1

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-0.850

enoo_

0.050 CDLUOC

LUcnCEXQ_I

ooo

oooin

in i< \ j l

oooin

oooUJ

Case 26

- 150 -

Case 27 - This case is similar to Case 26 except that the anti-phasemodes are stimulated.

- 151 -

NRSfl - WIND TURBINE DTNflMICS - THREE MOD 2 WTGSBflSE DESIGN VRLUES - LOW WIND SPEED ( 28 MPH )ILLUSTRflTION OF 'flNTI-PHflSE' RESPONSEONE UNIT SWINGING RGfllNST OTHER TWO

Q_cn

0.45001 1

0.35001 1

0.2500

PELEC »31 1 1

PELEC » 21 1 1

PELEC »1

151

141

13

x x -0.0501 1 1 1 1

H H -0.1501 1 1 1 1

« o -0.250 -PH

RS

E

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0.3000 PH »2 -0.700I I

0.1500 PM

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o.

CO

CM O.=*fc

X ?OL (0

oooin

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oooin

oooin

Case 27

- 152 -

Case 28 - This shows the eigenvalues for the three-WTG system. Asexpected, the only difference between this and the single WTG case is thepresence of two repeated anti-phase electrical modes. There is verylittle difference at the loading conditions considered.

- 153 -

NASA - ¥IND TURBINE DYNAMICS - GOODNOE HILLS SYST.EIGENVALUES FOR 3 MACHINE SYSTEM AT DIFFERENT LOADS

ffiAYY SYSTEM LOAD - «TCS AT RATED LOAD - .9 F LAGGING

UQfT SYSTEM LOAD - VTQS AT RATED LOAD - UOTY POKER FACTOR

HEAVY SYSTEM LOAD - VTGS AT RATED LOAD - UNITY COVER FACTOR

USB. 88

^ — electrical anti-phase, R

* ^ electrical in-phaseIK XLjJ

blade

*f ilter mode, R

^ shaft mode, R

I

R = Repeated root

r-*r w ft

MM 1 1 1 1 HIM 1 1 1 1 HIM 1 1 1 1 HIM 1 1 1 1

_

—

-

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—

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1 1 1 1 III!

1B.B88

L0BB0

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11828

-IBS. 8 -l&BB -LB88 -0.188

-SIGMA

GOODNOE HILLS SYSTEMCase 28

- 154 -

Case 29 - This shows the situation with power control shut off on one WTG.All modes other than one shaft mode are unaffected. No adverseinteractions are evident.

- 155 -

NASA - «?B TURSINE DYNAMICS -GC^CE HILLS SYST.EIGENVALUES FOR 3 MACHINE SYSTEM

HEAVY LOAD -OC TO OFF CONTROL - LEV ¥DO SPffiJ OB

HEAVY SYSTEM LOAD - ¥TGS AT RATED LOU - UNITY POffi? FACTOR

18B.B8

shaft modepredominatelyassociated wi thuncontrolled WTG

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1B.C23

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SSO

2L123

-122L3 -12. C3 -1.ZZ3-SIGMA

8.1:23

OvT" li/^1^ PP""UiNt Aib .Grr

- 156 -

Case 29

19. CONCLUSIONS AND RECOMMENDATIONS

From an electric power system perspective, the MOD-2 wind turbine generatorhas several peculiarities, which affect its response to mechanical andelectrical disturbances. Some are inherent in WTGs: large turbine inertia,low shaft stiffness. Others are the result of engineering decisions: primary(turbine) control, generator excitation control. None of these idiosyncrasiescause interaction problems peculiar to WTGs. A well designed WTG will,therefore, perform equally well in single and multi-machine applications.

The same WTG design can be applied to a wide range of electrical systemconfigurations, i.e., WTGs do not have to be custom-tailored for particularapplications. This statement does not apply to data collection, dispatch andprotection systems. They must be coordinated for each utility application.

Wind turbine generators in general and the MOD-2 in particular do not havetransient stability problems, even though the energy supply to the turbine israndomly variable. The soft shaft effectively decouples turbine and generatortransiently.

Shaft torque amplification during electrical switching and faults is much lesssevere than in conventional turbine generators. The limitation in a WTGduring electrical disturbances is bracing of generator windings, not strengthof shafts.

The utility connection at the Goodnoe Hill site is electrically stiff relativeto the generating capacity of the three MOD-2 machines to be installed.Voltage variations caused by wind speed changes are not- expected to exceedacceptable levels.

Turbine blade angle control would be less sensitive to electrical disturbancesif the power controller had an integral characteristic only, not proportionaland integral, as is presently the case.

Generator excitation control based on voltage rather than power factor couldbe used without a significant loss in transient stability margin. This wouldreduce voltage variations near the WTG installation.

It would be desirable to have better damping of the first torsional mode whenthe MOD-2 operates below rated power and the present blade angle control isinactive.

The transient decoupling of turbine and generator through the soft shaftreduces the accuracy required for matching voltage, speed and phase angleduring synchronization. This characteristic should lead to simplersynchronization equipment.

- 157 -

20. MODELS AND DATA

20.1 Turbine Generator Drive Train

The torsional model of the MOD-2 including data for stiffnesses, inertiasand damping is shown in Fig. 3 - Pg. 12. The four inertia representationof Fig. 3 - Pg. 12 is valid for the MNT/E simulation. For the PSS/E andIDAP simulation, a three inertia representation was used. The fourinertia model can be reduced to a three inertia model by combininggenerator and gearbox-inertias. The stiffness K12 is so high relative toK23 that it can be neglected.

20.2 Turbine Control

The configuration of the turbine controller is shown in Fig. 1 - Pg. 8Gain settings are given in Section 18.1. KP is the proportional powergain, Kl the integral power gain and KD the proportional speed gain. Theconstants of the 2P notch filter are

Kl = 0.22

K2 = 1.1

K3 = 13.5

The pitch actuator time constant is

TS = 0.159 second

20.3 Wind Turbine

The characteristics of the wind turbine model are defined by thecharacteristic curves Cp = f(X,3] shown in Fig. 17 - Pg. 159 and theblade angle control logic of Figure 2.3.5 of Reference 4. The followingconstants were used:

Radius of turbine rotor 150 FT

Air density 0.0765 LB/FT^

Turbine speed 17.55 RPM

Pitch angle velocity limit 8.0 DEG/SEC

20.4 Generator

Fig. 18 - Pg. 160 is a block diagram of the generator model. Generatordata is also listed.

- 158 -

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20.5 Generator Excitation Control

Fig. 19 - Pg. 162 shows block diagrams of the excitation and the reactivepower controllers. The constants for both controllers are also listed.

20.6 Simulation System

Fig. 20 - Pg. 163 shows the interconnections between equipment and systemmodels for a two machine simulation system.

- 161 -

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- 163 -

21. REFERENCES

1. "Concepts of Synchronous Machine Stability as Affected by ExcitationControl," F. P. de Mello and C. Concordia, IEEE Transactions PAS-88, No.4, April 1969.

2. "Shaft Dynamics in Closely Coupled Identical Generators," T. H. Alden,P. J. Nolan, J. P. Boyne, IEEE PES Summer Meeting, July 1976.

3. MOD-2 Control Subsystem Software Requirements, Boeing DocumentD277-10125-1, dated 11/9/78.

4. MOD-2-107 Preliminary Design Blade Pitch Control System SimulationReport. Boeing Document D277-10131-1, dated 12/18/78.

- 164 -

1 Report No 2 Government Accession No

NASA CR-1651564 Title and Subtitle

MOD-2 WIND TURBINE FARM STABILITY STUDY

7 Author(s)

E. N. Hinrichsen and P. J. Nolan

9 Performing Organization Name and Address

Power Technologies, Inc.P.O. Box 1058Schenectady, New York 12301

12 Sponsoring Agency Name and AddressU.S. Department of EnergyDivision of Solar Thermal Energy SystemsWashington, D.C. 20545

3 Recipient's Catalog No

5 Report Date

June 19806 Performing Organization Code

8 Performing Organization Report No

R35-8010 Work Unit No

11 Contract or Grant No

DEN 3-13413 Type of Report and Period Covered

Contractor Report14 Sponsoring Agency 6»* Report No.

DOE/NASA/0134-115 Supplementary Notes

Final report. Prepared under Interagency Agreement DE-AI01-79ET20305. Project Manager,L. J. Gilbert, Wind and Stationary Power Division, NASA Lewis Research Center, Cleveland,Ohio 44135.

16 Abstract

This is an investigation of the dynamics of single and multiple 2.5 MW, Boeing MOD-2 windturbine generators (WTGs) connected to utility power systems, including the first three machinecluster connected to the grid of the Bonneville Power Administration. The analysis was basedon digital simulation. Both time response and frequency response methods were used. Resultsshow that the dynamics of this type of WTG are characterized by two torsional modes, a lowfrequency 'shaft' mode below 1 Hz and an 'electrical' mode at 3-5 Hz. High turbine inertia andlow torsional stiffness between turbine and generator are inherent features. Turbine control isbased on electrical power, not turbine speed as in conventional utility turbine generators.Multi-machine dynamics differ very little from single machine dynamics.

17 Key Words (Suggested by Author(s| )

Wind turbine dynamicsControl of turbine generatorsElectric power systemsDigital simulation

19 Security Classif (of this report)

Unclassified

18 Distribution StatementUnclassified - unlimitedSTAR Category 44DOE Category UC-60

20 Security Classif (of this page) 21 No of Pages 22 Price*

Unclassified 169

* For sale by the National Technical Information Service, Springfield, V i rg in i a 22161

OUSGPO 1980 — 657-145/408

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