Testing Small Wind Turbine Generators - Renewable and ...

Testing Small Wind Turbine Generators: Design of a Driving DynamometerbyStephen Rehmeyer PepeSc.B. (Brown University) 2005A report submitted in partial satisfactionof the requirements for the degree ofMasters of Science, Plan IIinMechanical Engineeringin theGRADUATE DIVISIONof theUNIVERSITY OF CALIFORNIA, BERKELEYCommittee in charge:Professor Daniel Kammen, ChairProfessor Dennis LieuSpring 2007

The report of Stephen Rehmeyer Pepe is approved.ChairDateDateUniversity of California, BerkeleySpring 2007

Testing Small Wind Turbine Generators: Design of a Driving DynamometerCopyright c○ 2007byStephen Rehmeyer Pepe

AbstractTesting Small Wind Turbine Generators: Design of a Driving DynamometerbyStephen Rehmeyer PepeMasters of Science, Plan II in Mechanical EngineeringUniversity of California, BerkeleyProfessor Daniel Kammen, ChairTo design an effective wind turbine, it is essential to understand the characteristics of itselectrical generator. While the generator itself does not interact with the wind directly, itsproperties determine how the turbine’s rotor will respond to the wind. In this way, thegenerator effects the turbine performance profoundly, and must be designed in tandem withits intended rotor. To enable small wind turbine generators to be tested in the laboratory, adriving dynamometer is designed and built. This test platform is designed to run generatorsat variable speed and load resistance, up to 240 rpm and 1.0 kW. The dynamometer is testedto establish its own performance characteristics, and is used to test and evaluate a small windturbine generator. Improvements are proposed that would facilitate its future use testingother small wind turbine generators.Professor Daniel KammenCommittee Chair1

“And now,” cried Max, “let the wild rumpus start!”– Maurice SendakWhere the Wild Things Arei

ContentsContentsList of FiguresList of TablesAcknowledgementsiiviiixx1 Introduction 12 System Design 52.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2 Mounting Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2.1 Building System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.2 Basic Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2.3 Additional Design Considerations . . . . . . . . . . . . . . . . . . . . 102.3 Drivetrain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3.2 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3.3 Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4 Power Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.4.1 Motor Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.4.2 Transistor Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.4.3 NPN Transistor Control . . . . . . . . . . . . . . . . . . . . . . . . . 192.4.4 PNP Transistor Control . . . . . . . . . . . . . . . . . . . . . . . . . 202.4.5 Additional Circuit Design . . . . . . . . . . . . . . . . . . . . . . . . 21iii

2.5 Control System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.5.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.5.2 Control Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.5.3 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.5.4 Motor Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.5.5 Speed Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.5.6 Frequency Considerations . . . . . . . . . . . . . . . . . . . . . . . . 272.5.7 Encoder Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.5.8 Digital Signal Processor Properties . . . . . . . . . . . . . . . . . . . 292.6 Dump Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.6.1 Resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.6.2 Electrical System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.6.3 Mounting Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.7 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 Testing 353.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.2 Test Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.3 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.4 Test Round 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.5 Test Round 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.6 Raw Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414 Analysis 434.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.2 Basic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.2.1 Energy Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.2.2 Characterization of Losses . . . . . . . . . . . . . . . . . . . . . . . . 474.2.3 Physical Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . 494.2.4 Reality Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.3 Dynamometer Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.3.1 Torque Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.3.2 Power Electronics Performance . . . . . . . . . . . . . . . . . . . . . 534.4 Generator Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55iv

4.4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.4.2 Motor Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.4.3 Generator Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.4.4 Model Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.4.5 Evaluation of Generator Ratings . . . . . . . . . . . . . . . . . . . . 615 Summary and Conclusions 675.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69Bibliography 71A Component Specifications 73B Complete Control Program: Dynamic C Code 83C Raw Test Data 91v

List of Figures1.1 California Energy and Power (CE&P) 1 kW generator. . . . . . . . . . . . . 32.1 Subsystems comprising the driving dynamometer. . . . . . . . . . . . . . . . 72.2 Completed driving dynamometer, labeled to show main subsystems. . . . . 82.3 Comparison of electrical machine orientation options. . . . . . . . . . . . . . 92.4 One of two roller platforms on which the generator rests. . . . . . . . . . . . 112.5 Dynamometer mounting structure. . . . . . . . . . . . . . . . . . . . . . . . 112.6 Sprocket mounted on the shaft of a CE&P generator. . . . . . . . . . . . . . 132.7 Sprocket mounted on the shaft of the optical encoder. . . . . . . . . . . . . 132.8 Encoder sprocket positioning in relation to drivetrain motion and torques. . 142.9 Relationships between motor phases and torque output. . . . . . . . . . . . 162.10 Active motor phases for constant maximum torque. . . . . . . . . . . . . . . 172.11 Switches connecting each motor lead to each DC power line. . . . . . . . . . 172.12 PNP and NPN transistors connecting each motor lead to the positive voltageand to ground. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.13 Control circuit for each NPN transistor. . . . . . . . . . . . . . . . . . . . . 192.14 Control circuit for each PNP transistor. . . . . . . . . . . . . . . . . . . . . 202.15 Complete transistor configuration, including flyback diodes. . . . . . . . . . 222.16 Assembled power switching circuitry. . . . . . . . . . . . . . . . . . . . . . . 222.17 Assembled control circuitry. . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.18 Locations where phase switching should occur associated with encoder counts. 252.19 Control system timing, showing processes as scheduled and as performed. . 282.20 Three-phase bridge rectifier connected to the generator leads and dump load. 312.21 Resistor connection assemblies on the dump load. . . . . . . . . . . . . . . . 312.22 Mounted resistor and exposed resistor-mounting structure on the dump load. 32vii

2.23 Complete dump load, including resistors, bridge rectifier, and shunt resistor. 332.24 Complete system with main electrical measurement locations. . . . . . . . . 344.1 Flow of power within the dynamometer-generator system. . . . . . . . . . . 444.2 Power flows during each test run. . . . . . . . . . . . . . . . . . . . . . . . . 464.3 Generator frictional torque; data versus model. . . . . . . . . . . . . . . . . 484.4 Generator frictional losses; data versus model. . . . . . . . . . . . . . . . . . 494.5 Difference between modeled and measured frictional torque. . . . . . . . . . 504.6 Frictional power difference as a percentage of non-resistive power losses. . . 504.7 Generator phase current: modeled versus measured. . . . . . . . . . . . . . 614.8 Generator line voltage: modeled versus measured. . . . . . . . . . . . . . . . 624.9 Generator output power: modeled versus measured. . . . . . . . . . . . . . 624.10 Generator efficiency: modeled versus measured. . . . . . . . . . . . . . . . . 634.11 Generator applied torque: modeled versus measured. . . . . . . . . . . . . . 634.12 Nameplate of the CE&P generator. . . . . . . . . . . . . . . . . . . . . . . . 64A.1 Primary transistor specifications. . . . . . . . . . . . . . . . . . . . . . . . . 74A.2 Secondary transistor specifications. . . . . . . . . . . . . . . . . . . . . . . . 75A.3 Quadrature optical encoder specifications, page 1 of 2. . . . . . . . . . . . . 76A.4 Quadrature optical encoder specifications, page 2 of 2. . . . . . . . . . . . . 77A.5 Digital signal processor specifications, page 1 of 2. . . . . . . . . . . . . . . 78A.6 Digital signal processor specifications, page 2 of 2. . . . . . . . . . . . . . . 79A.7 Three-phase bridge rectifier specifications. . . . . . . . . . . . . . . . . . . . 80A.8 Shunt resistor specifications. . . . . . . . . . . . . . . . . . . . . . . . . . . . 81A.9 Operational amplifier specifications. . . . . . . . . . . . . . . . . . . . . . . 82B.1 Dynamic C code, page 1 of 6. . . . . . . . . . . . . . . . . . . . . . . . . . . 84B.2 Dynamic C code, page 2 of 6. . . . . . . . . . . . . . . . . . . . . . . . . . . 85B.3 Dynamic C code, page 3 of 6. . . . . . . . . . . . . . . . . . . . . . . . . . . 86B.4 Dynamic C code, page 4 of 6. . . . . . . . . . . . . . . . . . . . . . . . . . . 87B.5 Dynamic C code, page 5 of 6. . . . . . . . . . . . . . . . . . . . . . . . . . . 88B.6 Dynamic C code, page 6 of 6. . . . . . . . . . . . . . . . . . . . . . . . . . . 89C.1 Raw data, page 1 of 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91C.2 Raw data, page 2 of 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92viii

List of Tables2.1 Phase names and associated motor power connections. . . . . . . . . . . . . 152.2 DSP pins and their uses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.1 Test plan in data sheet format. . . . . . . . . . . . . . . . . . . . . . . . . . 384.1 Frictional torque curve fit options . . . . . . . . . . . . . . . . . . . . . . . . 484.2 Dynamometer torque equation . . . . . . . . . . . . . . . . . . . . . . . . . 544.3 Generator current equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.4 Generator applied torque equation . . . . . . . . . . . . . . . . . . . . . . . 594.5 Generator line voltage equation . . . . . . . . . . . . . . . . . . . . . . . . . 594.6 Generator power output equation . . . . . . . . . . . . . . . . . . . . . . . . 594.7 Generator efficiency equation . . . . . . . . . . . . . . . . . . . . . . . . . . 604.8 Generator modeled versus measured variables . . . . . . . . . . . . . . . . . 61ix

AcknowledgementsTo everyone who helped make this project work, helped maintain my sanity when it didn’t,and shared my excitement when it did: I give you my sincere thanks, and I owe you a beer.‡ Thanks especially to Dan Kammen, for his part in creating such a wonderful communityof people who care about making energy renewable and appropriate ‡ Dennis Lieu,for infecting me with his passion for electromechanical devices ‡ Mike, Scott, and Pete,for making Hesse Hall the most welcoming building on campus ‡ David Auslander, for hispatience during a time of microcontroller crisis ‡ David, the Rabbit Semiconductor guy, forgenerously giving me $230 worth of assistance on a $215 purchase ‡ Tim, for his inspirationand guidance in the realm of quotations ‡ Mick, for bringing the student shop to life withlearning and laughter ‡ Christian and Nate, for managing to always seem excited by myprogress ‡ Pete Schwartz, whose 6-o’clock poems brought a rare beam of sunlight into thelab ‡ Jude, for keeping my ego in check on the tennis court ‡ and a very special thanks toDan Prull, for his companionship and guidance from start to finish–as well as a thanks inadvance for hiring me when he becomes a hot-shot professor. ‡x

Chapter 1IntroductionHorizontal boosters. Alluvial dampers. Ow. That’s not it, bring me the Hydrospanner.I don’t know how we’re going to get out of this one.– Han Solo1

Wind turbines are comprised of to two main subsystems: one, the rotor, captures windpower and converts it to mechanical power. The second subsystem is the generator, whichconverts that mechanical power into electricity. Of the two, rotor design is by far the sexierpursuit: the rotor is the most visible part of the turbine and the part that interacts directlywith the wind, making its design essential for effective operation and aesthetic acceptance.Proof of this is the number of rotor designs in existence.One design–the three-bladedhorizontal axis rotor–has become extremely popular, but it is by no means ubiquitous, noris every such rotor designed in the same way. But no less important to the effectivenessof a wind turbine is the design of its generator. For one, the generator determines howefficiently mechanical power produced by the rotor is converted to electrical power. Evenmore importantly, the generator determines how the rotor interacts with the wind, byaffecting how a specific electrical loading translates into mechanical loading of the rotor.One generator might require a rotor to rotate quickly to reach a specific voltage, while adifferent generator could reach that same voltage at low speed. Depending on the designof the rotor, either case could be ideal. It is crucial, then, that the generator and rotor bedesigned in tandem, so they can work together most effectively.Of course, it is impossible to design around a generator when that generator’s propertiesare not well understood. This is especially true when a new generator is developed. A novelgenerator must be characterized though testing; not just to guide its improvement, butalso to inform the design of the entire wind turbine it will be a part of. But even whenan off-the-shelf generator is utilized, it is sometimes necessary to independently test thegenerator’s performance, verifying that the generator behaves exactly as its manufacturerclaims.Such was the case for California Energy and Power (CE&P), a startup company developingsmall vertical axis wind turbines. For their 1 kW prototype wind turbine, CE&Pobtained a set of generators from a manufacturer in China: Fēng Huá Generators Ltd. ofShĕn-Yéng. The Renewable and Appropriate Energy Laboratory (RAEL) was asked to testthese generators in November 2006, as part of a larger contract to test CE&P’s prototypewind turbine. This need became even more critical in January 2007, when the prototype2

Figure 1.1. California Energy and Power (CE&P) 1 kW generator.turbine was tested at a facility in Texas and failed to operate as expected. The wind turbinewould begin to rotate only in high winds, and even then would move slowly and produceminimal power. The nature of the problem was elusive, however, because there was no wayto measure the torque transferred from the turbine’s modified Savonius rotor to its generator.There were simply too many variables: the rotor’s torque output as a function of windspeed and tip speed ratio had yet to be determined. Similarly, the generator’s relationshipbetween applied torque and electrical output had not be characterized. Thus by independentlytesting the generator, RAEL would verify the machine’s ratings and characterize itsbehavior. With a thorough understanding of their generator, CE&P would be better able tounderstand their unexpected test results, and redesign their turbine to suit the generator.To bench-test a generator, it is necessary to do two things: drive the generator mechanically,and load it electrically. Loading the generator would not be difficult: the three-phasemachine could be loaded easily with a three-phase rectifier and set of power resistors. Mechanicallydriving the generator would be more difficult, as variable-speed motors powerful3

enough to drive a 1 kW generator are very expensive.Using a different driving motorwould also create a paradox: how would this new motor be accurately characterized? Forthese reasons, it was determined that the CE&P generator should be driven with a secondidentical CE&P generator. One machine would be supplied power and driven as motor,providing mechanical power to the second. The first advantage to this strategy is economic:since two generators were available from CE&P, it was unnecessary to invest in anotherelectrical machine. The second advantage is technical: using two identical electrical machineswould allow analysis of both machines to be performed simultaneously. The fact thatboth machines should have the same properties–specifically motor constants and frictionallosses–would allow for a more accurate analysis.The design challenge, then, was to build a system capable of driving a 3-phase, permanentmagnet CE&P generator as a variable-speed motor; transmitting its torque to a secondCE&P generator; and electrically loading the generator output with a variable resistance.This system is referred to as a driving dynamometer, and its design is presented in Chapter2. Once the dynamometer was complete, it was used to perform preliminary testing ina process described in Chapter 3. Next, Chapter 4 presents the analysis of the test data:the theory behind it, the analysis itself, and its results. Lastly, Chapter 5 summarizes theproject, presents specific conclusions, and outlines future work.4

Chapter 2System DesignI had invested $14 and approximately an hour for research, development, andinstallation. In the collision the beer cans collapsed (as they were intended to);both my car and the Senate office building remained splendidly unscathed.– Victor PapanekDesign For the Real World5

2.1 OverviewThe purpose of the dynamometer system is to drive the CE&P permanent magnetelectrical generator at various speeds and various resistive loads, while electrical currents,voltages, and rotational speed are measured.To accomplish this, an identical electricalgenerator is operated as a motor, supplying mechanical power to the generator being tested.Several subsystems make this possible, each of which is discussed in detail.• Mounting Structure: A rigid platform holds both electrical machines steady duringtesting. The platform is designed for high static and vibrational loads.• Drivetrain: A chain drive conveys mechanical power from the motor to the generator.• DC Power Supply: To reach adequate voltage, the system is powered by two DCpower supplies. These are connected in series and operated simultaneously.• Power Electronics: A custom power electronics package is required to allow thepermanent magnet generator to operate as a motor.• Control System: Continuous control of the motor is achieved through the use of anoptical encoder and a digital signal processor running Dynamic C code.• Dump Load: The generator output is rectified and loaded with up to five powerresistors. A mounting structure holds the resistors securely in place.• Measurement System: To adequately analyze the system, the system speed, inputand output voltage, and input and output currents must be measured.Figure 2.1 shows these systems and the flow of power and information between them.Electrical power is supplied by the DC power supplies.The power electronics packagecontrols the flow of this power to phases of the motor, where the motor converts it tomechanical power. The drivetrain transfers mechanical power to the generator, where itis turned back into electricity and is dissipated in the dump load.To keep the motorrunning smoothly, an optical encoder tracks the angular position of its shaft. Based on the6

instantaneous shaft position, a digital signal processor determines which motor phases toactivate, and signals the power electronics package accordingly.Figure 2.1. Subsystems comprising the driving dynamometer.Figure 2.2 shows the entire system, as set up in the student laboratory. While the testarea is cluttered due to the limited bench space in the student laboratory, all the majorsubsystems are visible and labeled.2.2 Mounting StructureThe first system needed to begin development of the dynamometer is a mouting structure:a platform to which the motor and generator can be bolted securely. The structure isrequired to handle the high static loads present during high-torque operation as well as thevibrations characteristic of high-speed operation. It must also be flexible in terms of designand construction: the dynamometer may have to be disassembled and moved, it may needto be redesigned for improved functionality, and it may be used to test different generatorswith different (and as yet unknown) dimensions.7

Figure 2.2. Completed driving dynamometer, labeled to show main subsystems.2.2.1 Building SystemTwo building systems were found to possess the required combination of strength, easeof construction, and ease of redesign. The first, “80/20,” consists of extruded aluminumbeams and a wide range of fasteners, connectors, and accessories. One key feature of thisbuilding system is the fact that connectors can be affixed to any side of a given aluminumbeam, providing maximum flexibility for design and redesign. On the other hand, the 80/20building system often requires drilling to allow the attachment of fasteners. This systemwas also found to cost significantly more than the alternative.The second building system considered, “Unistrut,” is based on extruded steel beamsand related fasteners, connecting brackets, and accessories. Unlike 80/20, unistrut beams8

consist of only one deep channel, so connections can be made on one side of a beam only.However, that limitation does not pose a significant problem for this application, due to thesimplicity of the mounting structure and the variety of connecting brackets available. Inaddition, Unistrut members require no machining to make connections. The system is alsosignificantly more economical than the 80/20 building system. For these reasons, Unistrutwas selected over 80/20 for construction of the mounting structure.2.2.2 Basic DesignThe design of the mounting structure was complicated by the fact that the permanentmagnet generators obtained from CE&P are designed for use in vertical-axis wind turbines.When mounted on a horizontal surface, their shafts extend up vertically, rather than extendingout horizontally. Thus the simplest solution–mounting the generators on a horizontalsurfact and connecting their shafts directly–was not an option. With this limitation in mind,two mounting options were considered. First, the shafts chould be connected directly witha shaft coupling if the generators were mounted to extend horizontally, facing each otheron parallel upright surfaces. On the other hand, the generators could be mounted on thesame horizontal surface, extending vertically. In this case, the shafts cannot be connecteddirectly, and require a drivetrain to link the two shafts. Both configurations are illustratedin Figure 2.3.Figure 2.3. Comparison of electrical machine orientation options.The direct-drive, horizontal configuration has the advantage that if a rigid coupling9

is used, frictional losses between the two machines are entirely eliminated. The verticalconfiguration, however, has even more important advantages. For one, it requires a muchsimpler mounting structure, since the 75-lb motors rest directly on the platform rather thanbeing cantilevered out towards each other. Similarly, the vertical configuration simplifiesassembly: while mounting or dismounting an electrical machine, it is not necessary to fightgravity while getting the machine into position. While the introduction of a chain driveis an additional system and expense, it confers two more advantages. First, it simplifiesalignment. Since the shafts are not connected directly, they need not be perfectly aligned.Second, it introduces an opportunity for easy and effective position sensing.While thechain drive keeps the motor and generator turning in unison, it can also turn a sprocketmountedoptical encoder. In the horizontal configuration, an additional drivetrain would berequired to link the shafts to the optical encoder–thus making it no simpler than the verticalconfiguration. For these reasons, the vertical configuration is selected for the dynamometer.2.2.3 Additional Design ConsiderationsTo ensure proper tensioning of the roller chain, and to allow easy disassembly of thesystem, the generator mount is designed to rest on rolling trolleys that move within the mainhorizontal channels. Thus during disassembly, the generator’s mount can be untightenedand rolled towards the motor to create slack in the drive chain. For reassembly, the generatoris pulled away from motor to lightly preload the chain while the mount is tighened securelydown for testing. The rolling trolleys must withstand the compressive force of the generator,as well as an additional compressive force introduced when the generator mount is tighteneddown.Distributed among four trolleys, the total force on generator mount can safelyreach 400 lbs, or over five times the weight of the generator alone. Figure 2.4 shows oneroller assembly, consisting of two roller trolleys supporting a Unistrut beam. The completegenerator mount consists of two such assemblies: the generator rests on two parallel Unistrutbeams, each of which is supported by a roller trolley on each end. This complete setup isvisible in Figure 2.5 Unlike the generator mount, the motor mount is connected rigidly tothe rest of the mounting structure without rollers.10

Figure 2.4. One of two roller platforms on which the generator rests.The optical encoder needs a mounting platform of its own, raising it up to the level ofthe electrical machine shafts, where it can engage the drive chain that connects them. Likethe rest of the mounting platform, this structure is built from Unistrut beams. Becauseit should not be subject to any appreciable forces, it is connected with 90 ◦ angle bracketsonly, and no diagonal braces. Figure 2.5 shows the completed mounting structure, includingindividual component mounts and the range of motion of the rolling generator mount.Figure 2.5. Dynamometer mounting structure.Connecting brackets, roller units, and the electical machines themselves are attachedto the Unistrut channels with bolts and special nuts that grip the lip of the strut channel.11

To ensure that connections remain secure throughout potentially vibration-prone testing,split-ring lock washers are used with every fastener.2.3 Drivetrain2.3.1 TheoryWhen the dynamometer is running, It is essential for both electrical machines andthe encoder to rotate exactly synchronously.If the generator alone turns at a differentdifferent angular velocity, the speed measurement developed by the encoder and digitalsignal processor will inaccurately reflect the true speed of the generator. Worse still, if theencoder and motor get out of sync the motor will stop turning smoothly, jerk to a halt, ormove erratically with potentially dangerous torque and current.Thus a belt and pully system would be inadequate. Belts can have a tendency to slip(suddenly losing traction) and creep (slowly advancing one pulley faster than another).Chain drive systems, however, guarantee sychronous motion by engaging discrete chainlinks on the teeth of a sprocket. As long as each sprocket has the same number of teeth andthe chain does not fail, the motion of each component will remain synchronous indefinitely.2.3.2 DesignThe generator shafts are designed for an attachment to be bolted on, compressed betweenthe thick main shaft and a nut on the thinner, threaded end of the shaft. The threadis an unusual metric size: 20 mm in diameter, with a 1.5 mm pitch. Thus to fit the shafts,flat sprockets with a 5/8” (15.9 mm) bore were machined on a lathe to have the required20 mm bore. Figure 2.6 shows a sprocket mounted on the generator shaft.The shaft of the optical encoder is 1/4”, far too small for any standard sprocket. Thisproblem was solved by increasing the diameter of the shaft with aluminum shaft couplings.These inexpensive units attach with set screws, and are adequate for the low torque appliedto the encoder. One coupling has an inside diameter of 1/4” and and outside diamter of12

1/2”. The next has an inside diameter of 1/2” and an outside diameter of 1”. Finally, asprocket with an inside diameter of 1” and the required 21 teeth is attached to this effective1” shaft. Unlike the flat sprockets mounted on the electrical machines, this sprocket has athick hub with set screws to secure it to the shaft. Figure 2.7 shows the sprocket mountedto the optical encoder.Figure 2.6. Sprocket mounted on theshaft of a CE&P generator.Figure 2.7. Sprocket mounted on theshaft of the optical encoder.Because a chain failure during testing could be very dangerous, a roller chain is selectedthat can handle much higher loads than are expected. The dynamometer is designed totest the CE&P generator up to its rated specifications: 1 kW at 300 rpm and 48 voltsDC. To produce this rated power at rated speed, a torque of about 32 Nm is expected.Similarly, 1 kW of power output at 48 volts requires about 21 amps. A design limit of 30amps is selected based on the availability of power transistors, as is discussed in the powerelectronics section. Thus when maximum amperage is supplied to the motor, it is expectedto produce no more than 46 Nm of torque. A 21-tooth sprocket for ANSI-40 roller chainhas a minimum diameter of about 3.5”. The maximum expected tension in the chain isabout 1040 N, or 234 lbs. Steel ANSI-40 roller chain has a rated working load of 810 lbs,or about three and a half times the expected working load. It has a rated breaking pointof 4,300 lbs, or about 18 times the expected working load. Based on this analysis, steelANSI-40 roller chain is considered a very safe choice for this application.13

2.3.3 AssemblyUnlike a belt drive, the chain drive does not require any appreciable tensioning. Thegenerator is simply pulled away from the motor until the chain connecting the two is taut.The encoder sprocket is located between the two electrical machines.To keep it firmlyengaged on the roller chain, it is not collinear with their shafts–rather, it is pushed outto the side, so that it deflects one side of the chain and does not contact the other. Thisarrangement is illustrated in Figure 2.8. Note that when the system operates at high torque,the motor pulls very strongly on the generator, developing great tension in one side of theroller chain. It is essential that the encoder not engage this taut side of the chain, but ratherthe opposite slack side. If it does engage (and thus deflect) the taut side, the encoder shaftwill be subject to extreme bending forces as that length of chain experiences more tensionand tends to straighten out. (This was discovered the hard way, during testing.) On theother hand, if it engages the slack side of the chain, the encoder sprocket will remain firmlyengaged–but not subject to these dangerous bending forces.Figure 2.8. Encoder sprocket positioning in relation to drivetrain motion and torques.14

Motor ConnectionsPhase Name DC Positive DC NegativePhase A-B Line A Line BA-C A CB-C B CB-A B AC-A C AC-B C BTable 2.1. Phase names and associated motor power connections.2.4 Power Electronics2.4.1 Motor TheoryThe CE&P permanent magnet generators are designed to operate only as generators.When driven, they produce a three-phase variable-speed AC output. This output intendedto be passively rectified through a three-phase bridge rectifier, giving a variable DC output.To run the machine as a motor, this process effectively proceeds backwards: DC power issupplied, it is actively switched to the three motor phases, and the motor turns as functionof the DC voltage applied and the frequency of switching.The function of the power electronics package is to perform that DC power switching.It allows the DC supply voltage to be applied across any two motor leads. For the threemotor leads A, B, and C, there are six possible ways to apply a DC voltage to them: thesesix combinations are called “phases”, and are listed in Table 2.1. For easy reference, eachphase is given a distinct and easily-identifiable phase name. For example, if the positiveDC line is connected to motor lead C and the negative DC line is connected to motor leadB, “phase C-B” is said to be active.The torque produced by the motor at any instant depends upon two things: the phasethat is active and the current position of the shaft.Figure 2.9 shows this relationship.Depending on the active phase and the shaft position, the motor may produce positivetorque (torque in one direction), negative torque (torque in the opposite direction) or notorque at all.15

Figure 2.9. Relationships between motor phases and torque output.Note that the torque profile of every phase is identical. In fact, the three unique phasesA-B, B-C, and C-A are simply offset from each other by 120 ◦ . The three remaining phasesB-A, C-B, and A-C are simply mirror images of the first three. For example, phase B-Ais equivalent to phase A-B with the poles reversed–thus the torque output of phase B-Ais simply the opposite of phase A-B. This relationship is shown in Figure 2.9: each pairof related phases shares a color. Solid lines represent the main phases, and dotted linesrepresent their mirror images.To keep the motor running continuously, the motor must always produce a positivetorque. That is, it must always “push” in the direction that the shaft is moving. To maintainmaximum positive torque, then, it is necessary to continuously switch which phase is active.This is illustrated in Figure 2.10. By switching to each new phase in the correct sequence,the torque output of the motor is kept positive and relatively constant, as represented bythe heavy black curve.The purpose of the power electronics package is to allow this switching of phases. Itenables the DC supply voltage to be applied across any two motor leads. This is accomplished,quite simply, by the use of six switches. For each of the three motor leads, oneswitch connects it to the positive DC terminal, and a second switch connects it to the neg-16

Figure 2.10. Active motor phases for constant maximum torque.ative DC terminal. Figure 2.11 shows this setup. By controlling which two switches areFigure 2.11. Switches connecting each motor lead to each DC power line.open, it is possible to apply the DC voltage in any of the six permutations listed in Table2.1. For example, to activate phase C-B, switches 3 and 5 are opened while switches 1, 2,4, and 6 are left closed. In this case, power would flow from the positive supply voltageterminal through switch 3 to line C. After passing through the motor, it would exit motorline B through switch 5, returning to the negative supply voltage terminal.17

2.4.2 Transistor SelectionRather than use mechanical switches, power transistors are used.Like mechanicalrelays, transistors switch on and conduct electricity when a small activation current isapplied. Transistors, however, are smaller, cheaper, quicker, more reliable, and quieter thanmechanical relays. There are two types of transistors–NPN and PNP–each of which has adifferent arrangement of P-type and N-type doped semiconductor material. For this design,it is important to understand the functional differences between each type of transistor, butnot the theory behind their operation. The crucial difference, then, is that NPN transistorsare generally used to switch ground to a load, while PNP transistors work best switchingthe positive voltage to a load. In this case the load is the motor, so a PNP transistor isused to connect the positive DC line to each phase, while an NPN transistor connects eachphase to the negative DC line. Figure 2.12 shows this arrangement: the six switches inFigure 2.11 are replaced by three PNP and three NPN transistors. Unlike the switches theyreplaced, these transistors have a third lead. That third contact, the transistor’s “base”,allows a controlling current to flow into or out of the transistor, controlling the switchingaction. Each base is marked with a star, to indicate where it connects to the supplementalcontrolling circuitry discussed later.Figure 2.12. PNP and NPN transistors connecting each motor lead to the positive voltageand to ground.As discussed in the drivetrain design section, the CE&P generators will be operatedup to their rated specifications, which are expected to be 48 volts and 21 amps. To givea safety margin, design limits of 60 volts and 30 amps are set. The transistors selected to18

meet these requirements are ON Semiconductors High Current Complementary DarlingtonTransistorsrated to 120 volts and 30 amps. The transistor specifications are provided inAppendix A, Figure A.1.2.4.3 NPN Transistor ControlTo allow the transistors to be controlled by the 0-3.5 volt output of the digital signalprocessor (DSP), some additional circuitry is required, and this circuitry is different foreach type of transistor. Figure 2.13 illustrates the control circuit associated with each NPNtransistor.Figure 2.13. Control circuit for each NPN transistor.First, the DSP output is tied to ground with a pull-down resistor: this prevents theDSP output from floating high when it is not actively running. Next, the DSP signal isbuffered with an operational amplifier (op-amp) wired as a voltage follower. This simplyensures that the DSPthe most expensive and sensitive device in the setupis isolated fromthe rest of the circuit and potentially dangerous voltages and currents. The voltage followeroutput, like the DSP output, is “on” at 3.5 volts and “off” at 0 volts.The transistor,however, operates on a current input, rather than a voltage input. The current allowed toflow between the collector (C) and the emitter (E) is proportional to the current that flowsfrom the base (B) to the emitter. Specifically, these power transistors have a minimum DCcurrent gain of 1000: for every milliamp flowing into the base, at least one amp will beallowed to flow from the motor. Thus to allow all 30 potential amps to flow from the motor19

to ground–that is, to make sure the transistor is 100% “on”–at least 30 milliamps shouldflow to the transistor base. On the other hand, it is also necessary to limit current thatenters the base: the power transistors have a maximum base current of 1.0 amps. To fulfillthese requirements, a 22ω resistor is placed between the voltage follower and the transistorbase. When the transistor is switched on with 3.5 volts, the base current is limited to 160mA: well above the minimum 30 mA required, yet below the 1 amp maximum.2.4.4 PNP Transistor ControlThe PNP transistors require a slightly more complex circuit to operate. It is illustratedin Figure 2.13.Figure 2.14. Control circuit for each PNP transistor.PNP transistors operate in essentially the opposite way as NPN transistors. They allowcurrent to flow from the emitter (E) to the collector (C) when current flows out of the base(B) to ground. This poses a problem: how can the 0-3.5 volt output of the DSP control thesinking of current from up to 50 volts at the base of the PNP transistor? The answer is touse another transistor. The base of the main PNP transistor is connected to ground througha smaller “secondary” NPN transistor. This transistor also has a voltage rating of 60 volts,but a current rating of only 1 amp. It is controlled by the DSP the same way the mainNPN transistors are controlled: through a pull-down resistor, voltage follower, and currentlimitingresistor. When this secondary NPN transistor is turned on, it allows current toflow out the base of the main PNP transistor, through another current-limiting resistor,20

and to ground. This current flow allows the PNP transistor to open, sending the positiveDC voltage to that motor lead. When the DSP signal drops to zero, the NPN resistor shutsoff: current cannot flow from the PNP transistor’s base, so the PNP transistor shuts off aswell. The secondary NPN transistor specifications are given in Appendix A, Figure A.2.2.4.5 Additional Circuit DesignTo facilitate development and troubleshooting, the DSP outputs are also fed to an LEDarray. This array consists of two rows of three LEDs, representing the six switches thatcontrol the motor. Whenever a switch is activated, the corresponding LED is illuminated.Because the amount of current supplied by each op-amp is limited, each LED is bufferedthrough its own voltage follower.In this way, the lighting circuit is guaranteed not tointerfere with the current requirements of the switching circuit.Because the motor windings consist of many turns of wire around a steel core, theyhave a considerable amount of inductance. This could pose a serious problem for the maintransistors: when a transistor shuts off, the current flowing in its motor phase will wantto continue to flow, potentially building up a temporary but dangerous amount of reversevoltage across the transistor. To avoid this problem, “flyback diodes” are used to dissipatevoltage spikes. These are simply diodes placed in parallel with each main transistor: if alarge reverse voltage builds across a transistor, it will simply flow through a flyback diode inthe direction opposite normal current flow. This complete configuration is shown in Figure2.15.Figure 2.16 shows the assembled switching electronics package, with the major componentslabeled. Similarly, Figure 2.17 shows the assembled control circuitry with majorcomponents labeled.21

Figure 2.15. Complete transistor configuration, including flyback diodes.Figure 2.16. Assembled power switching circuitry.22

Figure 2.17. Assembled control circuitry.2.5 Control System2.5.1 TheoryThe power electronics package allows the switching of DC power to any two motorterminals, but another system is required to control that switching. As the motors shaftrotates, this control system must power the correct motor leads with the correct polarityat the correct times. If it succeeds, the motor will continue to turn smoothly; if it fails, themotor will jerk, apply variable torque, or operate erratically. The overall control strategy isto sense the position of the motors shaft, and to activate the appropriate motor leads basedon that position.23

2.5.2 Control StrategyA high-resolution quadrature encoder is used to track the position of the motor shaft.As it turns, the encoder produces two square-wave pulses–offset by 90 ◦ –that correspond toits movement. A decoder within the DSP interprets that signal, and converts it to an integercount. As the encoder moves in one direction, the count increments every 0.35 degrees–or 1024 times per revolution. If the encoder moves in the opposite direction, the countdecreases. Thus the encoder does not report absolute position, only the relative positionof the shaft. It also does not reset its count to zero each revolution. Instead, it countscontinuously up.An absolute shaft position must be determined, however, because power must beswitched to various motor phases at fixed angular positions of the motor shaft. To producean absolute position, the encoder is first initialized at a known position, in a processthat is outlined in section 2.5.3 below. Next, the true encoder count is modulated to 1024,the number of encoder counts in one revolution. Thus even as the encoder completes multiplerevolutions and the count far exceeds 1024, the absolute shaft position is always trackedas a number between zero and 1024.Thus a number is obtained that corresponds to the instantaneous position of the motorshaft. To make use of this number, the locations where phase switching should take placemust also be associated with a number. These locations are dubbed “switch points,” becausethey are the shaft positions where phase switching should occur. Once the switch pointsare associated with integers, the DSP can determine which motor phase to activate simplyby comparing two integers.Figure 2.18 illustrates this control strategy. Say the encoder returns a current position38. This value is between 35 and 76, so phase A-C is activated: the DSP signals thetransistors associated with phase A-C to open, connecting motor line A to the positive DCterminal and motor line C to the negative DC terminal. Later, the encoder may returna value of 95:again this value is compared to the values associated with each switchpoint. Since it is between 76 and 104, phase B-C should be activated. This process repeats24

indefinitely to continuously keep track of the motor shaft position. For this control processto work, however, it is first necessary to determine what integers should be associated witheach switch point.Figure 2.18. Locations where phase switching should occur associated with encoder counts.2.5.3 InitializationThis control strategy depends on determining the location of each switch point.Inother words, the system must be able to determine what motor shaft positions correspondto phase switching events. In the example above, it had to have been determined somehowthat the relevant switch points occurred at locations 35, 76, and 104, as opposed to any otherlocations. To determine the integer counts associated with each switch point, a process of“mapping” takes place before the control system attempts to operate the motor smoothly.The mapping process exploits the fact that at each switch point, the torque producedby some phase falls to zero. This can be seen in Figure 2.18. For example, power should beswitched from phase A-B to phase A-C at the location where the solid blue curve intersectsthe dashed green curve (at location 35). At this exact position, the dashed red line intersectsthe abscissa, indicating that the torque output of phase C-B becomes zero. So this switchpoint can be located by simply applying power to phase C-B, and letting the shaft turn25

until it stops. When the shafts stops, the encoder is sampled and its reading–in this case35–is stored. The next switch point is located in the same way: the next phase, phase A-B,is powered. Again the motor shaft will turn, and eventually stop. This new location isassociated with switching from phase A-C to phase B-C. The process of stepping, waiting,encoder sampling, and storing is repeated for an entire revolution.The CE&P generator is a 10-pole machine. For each pair of poles, the machine experiencesone full electrical cycle, where one cycle consists of all six phase transitions as shownin Figure 2.18 above. Thus for each revolution of the motor shaft, the motor must effect fivesets of six transitions, or 30 phase transitions. The process of mapping, then, continues forone full revolution, logging thirty switch point locations, each of which is a number betweenzero and 1024.Once the motor completes this initialization sequence, it immediately enters the normalrunning mode. In this mode, the DSP constantly compares the encoder position to themapped positions, changing phase when necessary to maintain smooth operation.2.5.4 Motor SpeedNowhere in the control strategy is the motor speed addressed, because the motor speedis not determined by the control system.Instead, the motor speed is controlled by thevoltage of the DC power supply. If the DC input is low, the motor will advance from oneswitch point to the next slowly (but still smoothly). If a higher voltage is applied, the motorwill turn more quickly. Because the control system makes phase switches as a function ofshaft position (as opposed to a timed schedule), it automatically adjusts the frequency ofphase switching to match any motor speed, as determined by the voltage input.2.5.5 Speed MeasurementBecause the motor speed is not directly controlled, it must be measured. This is doneby reusing the information provided by the encoder.Once a second, the encoder countcount N is logged and compared to the encoder count one second before, count N−1 . The26

difference is divided by the one second time interval, and scaled to give a speed reading inrevolutions per minute, as shown in Equation 2.1.ω rpm =60 sec/min count N − count N−11024 counts/rev 1 sec(2.1)The motor speed reading must be noted in real time during testing, so it is output fromthe DSP to a PC serial port. By using the program Hyperterminal on the PC, the speed isread from the serial port and displayed on-screen in real time.2.5.6 Frequency ConsiderationsTo operate smoothly at all speeds, the control system must be able to keep up with therequired motor switching frequency. Specifically, the control system should always run atleast two cycles for each switching operation, where one cycle consists of reading the encoderand activating the corresponding phase. The CE&P generators have a rated speed of 300rpm. Given 30 switch points per revolution, the motor will require 150 switching operationsper second at that speed. For the control system to operate at twice that frequency, it mustrun at at least 300 Hz, sampling at least once every 3.3 milliseconds.The first solution to this challenge was to run the control system with a timer and atight loop. That is, sampling events would be scheduled every, say, 2 ms. An empty while() loop would simply idle until a scheduled time, at which point the encoder-sampling andphase-switching process would take place. As long as this sequence finished in less than2 ms, the scheduled timing would be maintained. Unfortunately, one essential commandtakes the DSP more than 2 ms to complete, disrupting the timing. This is the puts( )(literally, “put string”) command that enables the speed to be communicated to the PCand displayed in real time. That command alone was found to take about 3.5 to 4 ms tocomplete, making impossible to maintain the 3.3 ms minimum sampling frequency.A new solution was devised using the slice( ) command available in the Dynamic Cprogramming language used by the DSP. This function allows long processes like the puts() command to be paused while other commands run, and re-started when there is anotheropportunity. It is based on the idea that segments of code can be separated into “slices,”27

each of which has a precisely-timed beginning and end. Figure 2.19 illustrates timing withthe slice technique. One process, called moveSlice, is responsible for running the motor: itchecks the encoder and switches the motor phases when appropriate. It runs once every 2ms, and has 1 ms to complete. It runs very quickly, so it is always done before its allotted1 ms time interval has expired. The second process, called speedSlice, is responsible forcalculating and displaying the motor speed. It is initiated only once per second. It too isgiven only 1 ms to complete, because if it took longer, it would delay the more essentialmoveSlice process. Of course, speedSlice cannot finish its job in just 1 ms, so it continuesto operate in the vacant 1 ms time periods after each subsequent moveSlice operation.Figure 2.19. Control system timing, showing processes as scheduled and as performed.The full Dynamic C code, covering initialization and steady-state motor control, isprovided in Appendix B, Figures B.1 through B.6. It is heavily commented, describing indetail how the program runs the scheme oulined here.2.5.7 Encoder PropertiesAs calculated in Section 2.5.3, the motor must effect five sets of six phase transitions–or30 total phase transitions–for each revolution of the motor shaft. The resolution of theoptical encoder (1024 pulses per revolution) is about 34 times as great, so it has more thanadequate resolution for the application.The encoder outputs are sent through voltage followers before reaching the DSP, againfor the purpose of ensuring isolation and protection of the DSP. The encoder is poweredwith 5 volts DC, provided by a small DC power supply. This supplemental power supply28

is independent from the main DC power supplies, and also powers the op-amp chips thatfunction as voltage followers. The encoder specifications sheet is provided in Appendix A,Figures A.3 and A.4.2.5.8 Digital Signal Processor PropertiesThe digital signal processor is part of a Rabbit Semiconductor RCM4100 RabitCoreDevelopment Kit. It was selected because it is the least expensive product found to containboth the functionality needed for this project, and the standard functionality that wouldbe helpful for future DSP-based projects undertaken at RAEL. These capabilities include aquadrature decoder, digital inputs and outputs, analog inputs, and pulse-width modulators.The DSP runs the control program provided in Appendix B, and communicates to the restof the system though a set of input and output pins. These I/O pins and their specific usesare listed in Table 2.2. The DSPs specifications are provided in Appendix A, Figures A.5and A.6.2.6 Dump LoadIn order to fully characterize the performance of a generator, it is necessary to vary bothits speed and the electrical load it powers. Once the motor is up and running, changingthe generator speed is a simple matter of changing the voltage input to the motor.Tovary the electrical load on the generator, it is necessary to develop a variable resistive loadcompatible with the generators three phase output.2.6.1 ResistorsThe dump load is designed to utilize power resistors already available in RAEL. Theseresistors can each dissipate up to 300 watts of power, and come in three resistances: 1.2 Ω,8 Ω, and 15 Ω. By combining these resistances in different series and parallel arrangements,it is possible to create loads between 1.2 Ω and 46 Ω that can dissipate up to 1.5 kW.29

Pin Name Use Pin Name Use+3.3VGNDRST OUTIORDIOWRRST INVBAT EXTPA0PA1 Digital output - PNP PA2PA3 Digital output - PNP PA4PA5 Digital output - PNP PA6PA7PB0PB1 Digital output - NPN PB2PB3 Digital output - NPN PB4PB5 Pin broken PB6PB7 Digital output - NPN PC0PC1PC2PC3PC4PC5PC6PC7 PE0 Encoder output APE1 Encoder output B PE2PE3PE4PE5PE6PE7PN0 LN0PN1 LN1PN2 LN2PN3 LN3PN4 LN4PD5 LN5PD6 LN6PD7 LN7CVTVREF System ground AGNDTable 2.2. DSP pins and their uses.30

2.6.2 Electrical SystemTo load the three-phase AC generator with resistors, it is first necessary to rectify itsoutput. This is done with a three-phase bridge rectifier rated to 35 amps and 800 volts. Therectifier is shown in Figure 2.20, and its specifications are given in Appendix A, Figure A.7.The rectifier is mounted directly to one of the Unistrut support beams. To facilitate heattransfer from the rectifier without the use of additional cooling fins, this support beam ismade from aluminum rather than steel. In addition, heat-transfer grease is applied betweenthe metal rectifier face and the aluminum beam. The DC output of the bridge rectifieris fed directly into the resistors. Depending on the type of load required for a given test,these resistors may be connected in series, in parallel, or in some combination of series andparallel.To facilitate making inter-resistor connections quickly and securely, each terminal ofeach resistor is fitted with a bolt and wing nut. Short lengths of wire, fitted on each endwith a spade terminal, can be easily secured onto the resistor tab with the wing nut, asshown in Figure 2.21.Figure 2.20. Three-phase bridge rectifierconnected to the generator leads anddump load.Figure 2.21. Resistor connection assemblieson the dump load.2.6.3 Mounting StructureIt is necessary to keep the resistors elevated, so they do not overheat, and separate,so they do not accidentally short each other out. For these reasons, a mounting system is31

developed to hold the resistors in place. Like the dynamometer platform, it is constructedfrom Unistrut components. Each resistor is supported by a long bolt through its hollowaxis, which compresses the resistor between L-brackets on each end. This structure is shownin Figure 2.22, where one resistor is mounted and one resistor has been removed to exposeits supporting hardware. The entire dump load structure is shown in Figure 2.23. Alsovisible in this photograph is a shunt resistor, which is discussed in Section 2.7.To test the CE&P generator up to 1.0 kW, at least four of these 300 watt resistors areneeded at a time. The mounting structure, however, is sized to hold up to five resistors,allowing additional permutations of resistor connections.Figure 2.22. Mounted resistor and exposed resistor-mounting structure on the dump load.2.7 MeasurementTo adequately characterize the generator’s performance during testing, five key measurementsmust be taken:1. Motor/generator rotational speed2. Motor input voltage3. Motor input current32

Figure 2.23. Complete dump load, including resistors, bridge rectifier, and shunt resistor.4. Generator output voltage5. Generator output currentSpeed measurement is built into the control system, as is discussed in detail in Section 2.5.4.The current and voltage measurements are all taken at the leads of the electrical machines,where 3-phase AC power is flowing. This permits a direct and accurate measurementof each machines electrical behavior. If, on the other hand, DC currents and voltages weremeasured, it would be unclear exactly what power was lost in the transition to or from AC–that is, what voltage drops or leakage currents were taking place in the motor controllerand rectifier.The motor input and generator output voltages, then, are measured between two phases:as RMS phase-to-phase voltage (aka “line-to-line” or simply “line voltage”). Similarly, thecurrent is measured through one AC phase: as RMS line current.The current is notmeasured directly with a current meter: these were deemed unnecessary and expensive.Rather, a shunt resistor is used to allow the current to be measured as a voltage. The shunt33

esistors employed develop a voltage drop of 50 mV at 25 amps. Their specifications areprovided in Appendix A, Figure A.8. Figure 2.24 illustrates the final system setup with themain electrical measurements shown.Figure 2.24. Complete system with main electrical measurement locations.It is also helpful to measure the DC supply voltage and current, so that the lossesacross the power electronics package can be determined. These losses may include leakagecurrents and voltage drops, resulting in some overall power dissipation. Obtaining thesemeasurements is trivial, since the DC power supplies provide a digital readout of the voltageand current they supply.34

Chapter 3TestingThe perception of electric shock can be different depending on the voltage,duration, current, path taken, frequency, etc. Current entering the hand hasa threshold of perception of about 5 to 10 mA (milliampere) for DC and about1 to 10 mA for AC at 60 Hz.– wikipedia35

3.1 OverviewOnce the dynamometer’s subsystems are complete and assembled, testing can begin.The goals of this first round of testing are twofold:1. Assess the performance of the dynamometer. Ensure that it works as designed, andcharacterize its operation as a function of measured quantities.2. Assess the performance of the CE&P generator.Based on the analytical methods developed in Chapter 4, these two goals are performedsimultaneously, using the simplifying fact that the generator and motor are identical. Ofconcern here is the problem of fulfilling these dual objectives within a very limited timeframe.It is entirely possible that the dynamometer could not work as designed; it could,say, fail at some current below the 30 amp design current. Such a failure would be a showstopper:testing could not continue without a functioning system, and diagnosing and fixinga fault could take a considerable amount of time.To address this concern, a testing sequence is chosen that begins by loading the systemas lightly as possible. By beginning with a high dump load resistance, both the electricalcurrents and mechanical torque are minimized. As testing proceeds the dump load resistanceis decreased, and the system experiences higher currents and torques. This strategy hastwo advantages. First, since currents and torques increase gradually, potential problemslike mechanical deflections, vibrations, overheating, or excess current draw can be identifiedbefore they cause damage. Second, even if a system failure does occur, a set of data upto the failure point will have been collected. This partial data set could help diagnose thefailure (or near-failure) and could even be sufficient to allow preliminary analysis of thedynamometer and generator.3.2 Test PlanWith this strategy in mind, the following test plan is developed:36

1. Begin with no dump load resistors connected (open circuit: infinite resistance).2. Begin with a DC supply voltage of 10V.3. Collect system speed, input line voltage, input shunt voltage, output line voltage,output shunt voltage, and DC supply current.4. Increase DC supply voltage by 5V, and repeat data collection.5. After the DC supply voltage reaches 50V, return to 10V and decrease dump loadresistance to the next increment.Table 3.1 shows this test outline graphically, in the form of a data collection sheet usedduring testing. Towards the end of the test plan, some data points must be skipped. Incertain instances where dump load resistance is very low and DC supply voltage is high,the expected power output exceeds the dump load resistor ratings. Specifically, at dumpload resistances of 2.4 Ω and 1.2 Ω, the DC supply voltage should not be increased beyond30 volts. This detail is not represented in Figure 3.1, but is noted on the real data sheetsprovided in Appendix C, Figures C.1 and C.2.3.3 SetupThe student lab in Etcheverry Hall was selected to be the testing location because ithoused the largest DC power supplies available, but these power supplies were permanentlylocked down at their workstations. The dynamometer, then, had to be disassembled, transportedfrom the RAEL lab on the fourth floor to the student lab on the first floor, andreassembled. Testing was performed over two days, Wednesday March 28 and ThursdayMarch 29, 2007. While this timing was determined by the design and debugging process(testing began immediately after the dynamometer was complete), it was fortunate thatthe system was ready for testing during spring break, when student lab was not crowded.Testing was performed with the assistance of Daniel Prull and Peter Schwartz of the RAELlab.37

Test Nominal Dump DC Supply Rotational Input Line Input Shunt Output Line Output Shunt DC SupplyNumber Load Resistance Voltage Speed Voltage Voltage Voltage Voltage Current1 ∞ 10 V2 ∞ 15 V3 ∞ 20 V..8 ∞ 45 V9 ∞ 50 V10 46 Ω 10 V....19 30 Ω 10 V...28 19 Ω 10 V...37 11.5 Ω 10 V...46 7.5 Ω 10 V...55 4.8 Ω 10 V...64 3.6 Ω 10 V...73 2.4 Ω 10 V...82 1.2 Ω 10 V...Table 3.1. Test plan in data sheet format.38

The dynamometer frame was slightly larger than the narrow desktops in the studentlab, but once secured down with clamps, was quite stable. Two power supplies were usedin series to supply the DC supply power. Each power supply had a rated output of 35 voltsand 25 amps, giving a total possible output of 70 volts and 25 amps. Because of the seriesconfiguration, the DC current output could be read from either power supply, and the DCvoltage was obtained by adding the output voltages of each.While relocating to the student lab was not ideal, it had the additional advantage ofproviding an abundance of voltage meters.Each voltage output was connected to onevoltage meter, making data collection much easier than if one meter had been used tosample every output.3.4 Test Round 1The first day of testing began well, and data at all voltage levels was obtained for thefirst two dump load resistance values. However, as testing progressed and the dump loadresistances were decreased, two problems began to develop. First, the supply current beganto increase more quickly than expected, indicating that either (a) there was a considerableamount of leakage current passing through the power electronics, or (b) something wasputting an extra load on the system, forcing the motor to draw more power. Second, a“grinding” sound began to emanate from the encoder, which could be seen visibly bendingat its shaft. For fear of destroying the encoder, testing was immediately halted for the day.Eventually, with the help of the student shop staff, it was determined that the problemlay in the positioning of the encoder. The encoder sprocket was incorrectly engaging thetaut side of the drive chain. As the dump load resistance decreased, the electrical machinesdeveloped greater torque. This created more tension in the taut side of the chain, increasingthe force on the encoder sprocket. The encoder shaft was unable to handle this bendingforce, causing the shaft to deflect and make the observed grinding sound. The extra loadingthis grinding placed on the system may have also explained the increase in current drawnby the system.39

A solution proved rather simple: the encoder was simply repositioned to the slack sideof the chain. Luckily, the encoder was not damaged, and the system was up and runningonce again. Data from this first day of testing was thrown out, to be repeated with theimproved test setup.3.5 Test Round 2The second day of testing proceeded much more smoothly, and the system performedwell enough to gather data at all planned resistance values. Another strange phenomenonwas observed, however: at low resistances and high voltages, a new grinding sound washeard, but could not be located. The sound was accompanied by unsteady voltage readings.It could be eliminated by resetting and restarting the dynamometer, but would eventuallyreturn. But no cause was immediately evident–it seemed that the problem might be internalto the electrical machines themselves–so once data was gathered at each resistance value,testing was stopped and the test setup broken down.The underlying problem was eventually discovered: at high torques, the generator’sdrive sprocket was actually slipping with respect to the generator shaft.This was ablehappen because the generator sprocket was pulled counter-clockwise by the motor (as viewedfrom above) while the generator tried to resist this motion, creating a clockwise torque. Withthe torques arrayed in this manner, the nut holding the generator sprocket in place wouldtend to loosen, gripping the sprocket less firmly. The motor sprocket, however, experiencedforces in the opposite directions, properly causing the nut holding its sprocket to tightenas torques increased. The deep grinding sounds, then, were caused by the steel sprocketmoving against the generator shaft. This also produced a fine black dust that settled onthe generator, as the sprocket was slightly worn by the grinding action. The fact that thesystem ran unsteadily could be due to the fact that the grinding was not perfectly constant,but rather a cycle of sticking and slipping that became more intense as the nut loosenedfurther.Unfortunately there was simply was not sufficient time to redesign the dynamometer40

to address this problem.While a solution is absolutely necessary for future use of thedynamometer, it was not immediately necessary.Even though the problem affected asignificant amount of data, enough valid data remained to begin preliminary analysis of thedynamometer and generator.3.6 Raw DataThe raw data obtained during the second day of testing is provided in Appendix C,Figures C.1 and C.2. In these figures, data points shaded grey are those that are deemedquestionable (due to unsteady readings or other observations), and are not used in analysisof the system. While the majority of the questionable data is due to the sprocket slippageproblem, it was also observed that low-voltage operation produced consistently unsteadyresults. There are two possibilities for this unsteadiness: either the dynamometer does notoperate smoothly as slow speeds, or the voltage meters were unable to give a steady RMSreadings as slow electrical frequencies. In either case, this is not considered problematic.The unsteady low-voltage data is discarded, and future tests should start at an input voltageof 20 volts rather than 10 volts.After purging all remotely questionable data points, 33 remain. They range over inputvoltages of 20 to 50 volts, and dump loads from open circuit to 11.5 Ω. This is sufficient tobegin preliminary analysis of the dynamometer and the CE&P generator.41

Chapter 4AnalysisHeisenberg Something you’re always accusing me of. ‘If it works it works.’Never mind what it means.Bohr Of course I mind what it means.Heisenberg What it means in plain language.Bohr In plain language, yes.– Michael FraynCopenhagen43

4.1 OverviewOnce testing has been performed, the resultant data is analyzed with two goals in mind:assess the performance of the dynamometer, and assess the performance of the CE&Pgenerator. First, the entire dynamometer-generator system is addressed in Section 4.2.1. Inthis section the overall energy flows within the system are characterized. This enables thedynamometer’s characteristics to be quantified in Section 4.3. Finally, the CE&P machineis assessed as a generator in Section 4.4.4.2 Basic Analysis4.2.1 Energy BalanceThe analysis of the dynamometer-generator system begins with an energy balance. Theflow of power through the system is illustrated in Figure 4.1. Electrical power P M entersFigure 4.1. Flow of power within the dynamometer-generator system.the system through the motor. Within the motor, there are “I 2 R” losses: as currentflows through the motor windings, power P RM is lost to resistive heating. There are also avariety of other losses within the motor that are not as easily quantified. These could include44

viscous, Coulomb friction, eddy-current, or hysteresis losses, and are lumped together asP F M . The remaining power P T is transmitted to the generator mechanically through thedrivetrain. The generator, like the motor, experiences resistive and miscellaneous losses P RGand P F G . The remainder exits the generator as electrical power. Equation 4.1 representsthis energy balance mathematically.P M = P RM + P F M + P T= P RM + P F M + P RG + P F G + P G (4.1)The voltage input to the motor, V LM , is measured as an RMS line-to-line voltage. Thevoltage output of the generator is also an RMS line-to-line voltage, V LG . They are relatedto the voltages over a single phase, V P M and V P G by equations 4.2 and 4.3.V LM = √ 3V P M (4.2)V LG = √ 3V P G (4.3)The RMS line current to the motor, I LM , and from the generator, I LG , are also measured.The current through one phase is the same as the line current.I LM = I P M = I M (4.4)I LG = I P G = I G (4.5)The power input to the motor is the product of voltage and current over one phase timesthe number of phases. The power output of the generator is defined in the same way.P M = 3V P M I M = √ 3V LM I M (4.6)P G = 3V P G I G = √ 3V LG I G (4.7)Before testing, the resistance of each motor and generator phase is measured with a multimeter.Since the phases are balanced and the electrical machines are identical, the resistance45

is the same for all phases: R P = 0.50 Ω. Given the phase resistance, the phase current, andthe number of phases, it is possible to calculate the resistive losses in each machine.P RM = 3I M 2 R P (4.8)P GM = 3I G 2 R P (4.9)These power flows are illustrated in Figure 4.2. Each column represents the total inputpower to the motor, P M , for each test run. The bars are broken up to show the ultimatedestination of the input power: either electrical output from the generator (P G ), resistiveheating in the motor (P RM ), resistive heating in the generator (P RG ), or other losses(P F M + P F G ). Clearly, a large portion of of the power supplied during each run is claimedby these yet-to-be-classified miscellaneous losses. Thus, characterizing them accurately isof great importance.Figure 4.2. Power flows during each test run.46

4.2.2 Characterization of LossesNext it is assumed that the non-resistive losses within each electrical machine are dominatedby frictional losses: either viscous or Coulombic. This is a reasonable assumption, aswell-designed generators generally lose little power to eddy currents and hysteresis. If thisis indeed the case, then P F M and P F G will be a function of the system speed ω (if viscous)and transmitted torque T T (if Coulombic). Since speed and transmitted torque are alwaysthe same for both the motor and generator, the two miscellaneous losses should be equal.P F M = P F G = P F = f(ω, T T ) (4.10)Now every term in Equation 4.1 is defined except P F , so it is possible to solve for P F interms of measured quantities. The frictional torque developed in each machine can then becalculated as the frictional power loss divided by the angular velocity in radians per second.P M = 2P F + P RM + P RG + P GP F = 1 2 (P M − P G − P RM − P RG )= 1 (√3VLM I M − √ )3V LG I G − 3I 2 M R P − 3I 2 G R P2T F = 1 (√3VLM I M − √ )3V LG I G − 3I 2 M R P − 3I 2 G R P2ω(4.11)(4.12)To investigate and later extrapolate these losses, a variety of curves are fit to the frictionaltorque T F . Each is fit to the data by using the least squares method to determinethe constants A, B, C, and D. Then the best-fitting curve is selected by inspecting the fitof each curve visually and calculating its R-squared value. Table 4.1 lists the seven curveequations that are attempted.After comparing each curve’s best approximation of the data, it is determined thatcurve number one gives the best fit. That is, according to the limited set of data available,it is believed that the frictional torque in each electrical machine is best characterized byEquation 4.13:T F [Nm] = 0.965[Nm] + 0.0126[ ] Nmω[rpm] (4.13)rpmThe R-squared value for this curve is 0.75, indicating that the given equation explains 75%of the observed variation in T Fvalues. Many of the other curves yielded slightly higher47

Curve Number Basis Equation1 T F = f(ω) T F = A + Bω2 T F = f(ω 2 ) T F = A + Bω 23 T F = f(T T ) T F = A + BT T4 T F = f(ω, ω 2 ) T F = A + Bω + Cω 25 T F = f(ω, T T ) T F = A + Bω + CT T6 T F = f(ω 2 , T T ) T F = A + Bω 2 + CT T7 T F = f(ω, ω 2 , T T ) T F = A + Bω + Cω 2 + DT TTable 4.1. Frictional torque curve fit optionsR-squared values, but the differences were rather insignificant–on the order of 1 to 3%.Thus it is unlikely these more-complicated equations actually capture any more informationabout the behavior of T F . Figure 4.3 shows the calculated frictional torque over a range ofspeeds and dump load resistances as compared to this best-fit model. Figure 4.4 shows theassociated frictional power losses, both as measured and as predicted by the model.Figure 4.3. Generator frictional torque; data versus model.Both plots indicate that the fit is a reasonable one.To see more clearly how closethe fit it is, the difference between the modeled and measured values (the “remainder”)48

Figure 4.4. Generator frictional losses; data versus model.is plotted. Figure 4.5 shows the remainder in terms of Newton-meters of torque. For amore intuitively accessible measure, Figure 4.6 shows the remainder as a percentage: thedifference in measured versus modeled power loss, divided by the total non-resistive powerloss.Figure 4.6 indicates that the selected frictional torque model predicts power losses within-2% to +6% of the actual non-resistive power losses. Furthermore, there is no clear trend inFigure 4.5 or Figure 4.6, suggesting that the remaining variation in power loss is a functionof measurement error or small system perturbations, rather than some un-accounted-fortrend. Further testing would help to either confirm this theory, or help elicit a more subtletrend occurring alongside the frictional trends already observed.4.2.3 Physical InterpretationThe selected equation demands some explanation, because it is rather unexpected. Oneinteresting observation is that the frictional torque seems to scale with ω rather than ω 2 :49

Figure 4.5. Difference between modeled and measured frictional torque.Figure 4.6. Frictional power difference as a percentage of non-resistive power losses.50

generally, viscous losses are proportional to the square of the speed. However, viscous lossesare linearly proportional to speed at low speeds. Thus this portion of the frictional lossesmay be physically located towards the center of the machine–perhaps around its bearings–which move relatively slowly even at high angular velocities.The second interesting fact is that the frictional torque over the entire tested range isrelatively constant, as reflected in the large constant A and the small constant B in theselected curve fit equation 4.13. Why is the friction torque largely constant over a widerange of speeds? This could be because a normal force, which results in a Coulomb frictionforce, is built into the generator–for example, in the pre-loading of the bearings. A Coulombfriction force was expected to scale with the applied torque T T , indicating that it increasedwith increasing lateral loading of the shaft. However, the large constant term indicates thata built-in Coulomb friction force outweighs such an external effect.4.2.4 Reality ChecksIt is worthwhile to revisit the initial assumption: is it still believable that the nonresistivelosses are dominated by friction? If hysteresis losses were present, some portionof the non-resistive losses (either their bulk or their difference from the frictional model)would scale with the machine currents. Similarly, eddy current losses would be expected toscale with the square of the machine currents. Neither of these situations seems to be thecase, so the assumption that the non-resistive losses are dominated by friction is consideredvalid.Finally, one piece of data obtained during testing has not yet been employed:themeasured dump load resistance. The output current and voltage, as well as the analyticalmethods used to manipulate them, can be verified by comparing the “apparent” resistancewith this “nominal” resistance. That is, how well does the relationship between generatorcurrent and voltage jibe with the sum of the dump load resistor values? To find out, themeasured RMS voltage and current must be converted to DC voltage and current andvoltage, as they would be over the three-phase rectifier. The three-phase line voltage is51

elated to the DC output voltage by Equation 4.14, where V B is the voltage drop across thebridge rectifier: about 1.3 volts for a silicon rectifier operating in this current range.V DC = 3√ 2π V LG − V B (4.14)Next, the DC output current must be determined from the RMS phase current. The currentoutput of each phase is a form of square wave, determined by the sequence in which therectifier diodes conduct. The phase current is I max for 120 ◦ , zero for 60 ◦ , −I max for 120 ◦ ,and again zero for 60 ◦ . These square waves nest together such that I max = I DC : the DCcurrent is equal to the maximum phase current. Therefore to determine I DC , it is necessaryto determine I max as a function of I RMS given the shape of the square wave. Using thedefinition of the RMS (root-mean-square) value,√√360I DC = I max =◦3(1) 2 120 ◦ + (−1) 2 120 ◦ + 0 2 120 ◦ I RMS =2 I RMS (4.15)Now the apparent resistance can be calculated.R apparent = V DC= 2√ 3I DC π(V LG − √ )2/3V BI RMS(4.16)Calculated as such, the apparent resistances are very close to the measured resistances:within +/- 1 Ω, or +/- 4%.The calculated resistances vary slightly, but nearly alwaysincrease from one test to the next. This is to be expected: as testing continues the resistorsheat up, causing their resistance values to increase slightly. This similarity between apparentand nominal resistance values is very encouraging.4.3 Dynamometer ResultsHaving quantified the various power flows within the dynamometer-generator systemand characterized the remaining power loss, it is possible to begin analyzing thedynamometer–that is, the motor and the power electronics that drive it.The primarygoal of this analysis is to determine the driving torque produced by the motor, becausethe assessment of the CE&P generator depends on it.Furthermore, a torque equationwill enable the dynamometer to be employed usefully in the future: the dynamometer’s52

applied torque will be determined from experimental data and used to asses any generator’sresponse to such torque. A secondary goal of the dynamometer analysis is to quantifythe losses across the power electronics package. While it is not necessary that the powerelectronics be efficient per se, it is worthwhile to ensure that they do not experience largevoltage drops, leakage currents, or power losses–any of which could signal a potentiallydamaging problem within the power electronics package.4.3.1 Torque OutputApplying equation 4.1 over the motor alone, the mechanical power transmitted by themotor is determined as a function of the motor’s input power, resistive power losses, andfrictional power losses.P T = P M − P RM − P F (4.17)The transmitted torque, then, is determined by dividing the transmitted power by theangular velocity. The expression is then simplified and put in terms of measured quantitiesalone.T T = 1 ω [P M − P RM − P F ]= 1 ω [P M − P RM ] − T F= 1 [√ ]3VLM I M − I 2 M R P − A + Bω (4.18)ωTable 4.2 shows the final dynamometer torque equation and all the information required touse it.4.3.2 Power Electronics PerformanceTo asses the leakage current, voltage drop, and power loss within the power electronicspackage, its DC electrical input is compared to its AC output (the AC input to the motor).The DC input voltage, V IN−DC is shown on the power supply displays. To enable a directcomparison, the RMS motor line voltage is converted to a DC voltage. This is done exactlyas it was in Section 4.2.4, where the RMS output of the generator was converted to DC53

T T = 1 (√ω 3VLM I M − I 2 )M R P − A + BωSymbol Value and Units MeaningT T Nm Torque applied to generatorradωsRotational speed of motorV LM V RMS RMS line voltage to motorI M A RMS RMS line current to motorR P 0.50 Ω Measured phase resistance of motorA 0.965 Nm Experimentally-derived constantB 0.0126 NmrpmExperimentally-derived constantTable 4.2. Dynamometer torque equationover the bridge rectifier. In this case, the opposite conversion takes place–DC to AC–butthe voltage transformation is the same.V OUT −DC = 3√ 2π V LM (4.19)Comparing V IN−DC to V OUT −DC , a voltage drop of between 1.5 and 2.1 volts is observedover the range of tests. About 1.3 volts of that drop is attributable to the power transistors,while the remainder represents the voltage drop over the 12-guage wire within the powerelectronics package and connecting it to the power supplies. This voltage drop is a reasonableand safe value.Similarly, the AC current is transformed as it was in Section 4.2.4, and compared to theDC current obtained from the digital power supply displays.I OUT −DC =√32 I M−RMS (4.20)This comparison yields leakage currents of between 0 and 0.25 amps, with no apparentrelationship to overall current or voltage. Thus the leakage current is expected to remainwithin this low range for all test conditions.Finally, the power loss within the power electronics package is determined by comparingthe DC supply power and the AC motor input power.P DC = V DC I DC (4.21)54

P AC = √ 3V LM I M (4.22)The power loss is found to range between 0.7 and 11 watts, giving an efficiency of 80% to99%. This amount of power dissipation is low enough that is not cause for concern–11 wattsshould be easily dissipated by the transistors and other components. The power loss doesnot seem to track well with overall current or voltage, however, so it is difficult to predicthow much power the package will have to dissipate at higher currents. Thus, testing athigher currents should proceed with caution.4.4 Generator Results4.4.1 OverviewAt last, using the results of the overall and dynamometer analyses, the generator’sproperties can be evaluated. One way to evaluate a generator is to simply run it at thepoints of interest and measure what happens. If the generator is expected to operate atspeeds (ω 1 , ω 2 , ..., ω n ) and load resistances (R 1 , R 2 , ..., R n ), it may be possible to runtests at each of those specific combinations. To predict the behavior of the generator insituations between these discrete data points, interpolation might give adequate results.However, a more powerful tactic would be to develop a model of the generator.Inthis case, data from dynamometer testing is used to inform and check the model. Such atechnique should give more accurate results than simply interpolating between data points.Furthermore, modeling is crucial when the data gathered does not span the generator’s entirepotential range of operation–which, unfortunately, was the case with the first round ofCE&P generator testing. The analysis of the CE&P generator (or any other future generator)proceeds as follows: first, the generator’s motor constants are derived from test data.Second, the energy methods used previously are employed once again to model the generator’sbehavior based on only measured quantities, its speed, and its derived motor constant.55

The resultant model is then checked against the data gathered during dynamometer testing.Lastly, the model is used to assess the generator’s claimed specifications.4.4.2 Motor ConstantThe motor constant has two incarnations: the voltage constant relates the generator’sopen-circuit voltage to its speed, while the torque constant relates the back torque of thegenerator to the current that flows through it. Under certain conditions both constantsshould be equal, so as a check both constants are evaluated and compared.First, thevoltage constant is determined. This is done by fitting a line to the generator’s open circuitvoltage-versus-speed data. The slope of this line is the voltage constant, presented in threedifferent units.K v = 0.184 V RMS line−to−linerpm= 1.76 V RMS line−to−linerad/s= 1.01 V RMS line−to−neutrad/s(4.23)(4.24)(4.25)Next, the torque constant is determined: in theory, it should be equal to the value of K vgiven in Equation 4.25. The effective torque constant can be found at each data point.These values vary only very slightly, and are averaged to give an overall torque constant.K t = T T − T F3I G(4.26)NmK t = 1.02A RMS total(4.27)Indeed, the K v and K t values match up extremely closely–they differ by only 0.6%.4.4.3 Generator ModelingCurrent EquationNow it is possible to develop relations for the generator current, voltage, torque, efficiency,and power output, given any generator speed and dump load resistance. The analysis56

egins with an energy balance over the generator, which is expressed in terms of torquesby dividing through by the rotational speed. Next, the torque terms are combined and thepower terms are expanded.P T = P G + P RG + P F (4.28)T T = P G + P R G+ T F (4.29)√ω3IG V LG + 3I 2 G R PT T − T F =(4.30)ωThis equation contains four variables: the applied torque T T , the phase current I G , the linevoltage V LG , and the rotational speed ω. Since the first three of these variables must beisolated and related to ω and the dump load resistance alone, two more relations are neededto unravel Equation 4.30. The first is torque constant identity of Equation 4.27. Pluggingthis in puts the torque variables in terms of the phase current.√3IG V LG + 3I 2 G R P3K t I G =ω(4.31)3K t ω = √ 3V LG + 3I G R P (4.32)The line voltage can also be related to the phase current. First, Ohm’s law is used to relatethe DC current and voltage over the dump load resistance R D . The DC current and voltageare then replaced by their AC equivalents, as defined in Section 4.2.4.V DC = I DC R D (4.33)3 √ √23π V LG − V D =2 I GR D (4.34)V LG =π2 √ 3 I GR D + π3 √ 2 V D (4.35)Now V LG is plugged into Equation 4.32, so that the phase current alone is related to thetwo variables: rotational speed and dump load resistance. The equation is solved for thephase current I G , and constitutes the first useful equation of the generator model.3K t ω = √ [ π32 √ 3 I GR D + π3 √ 2 V D3K t ω − π √6V D = I G( π2 R D + 3R P)]+ 3I G R P (4.36)(4.37)I G = 3K tω − π √6V Dπ2 R D + 3R P(4.38)57

Table 4.3 shows the final generator current equation and the information required to use it.I G =[3K t ω − π √6V D] [ π2 R D + 3R P] −1Symbol Value and Units MeaningI G Nm RMS phase current through generatorradωsRotational speed of motorK t Nm/A RMS total Derived generator torque constantR D Ω Variable dump load resistanceR P 0.50 Ω Measured phase resistance of motorV D 1.3 V Bridge rectifier voltage dropTable 4.3. Generator current equationTorque EquationWith the generator’s phase current modeled, the torque applied to the generator iseasily determined. Once again, the equation for the torque constant K t is employed. Thisassumes that the generator’s frictional torque has already been modeled. In the case of theCE&P generator, it has been. For future generator testing, it can be determined with thesame energy balances and curve fitting, as described in Sections 4.2.1 and 4.2.2.K t = T T − T F3I G(4.39)T T = 3K t I G + T F (4.40)T T = 3K t I G + A + Bω (4.41)Table 4.4 shows the final applied torque equation and definitions of its variables.Voltage EquationLikewise, the generator output line voltage, V LG , is found simply by plugging the modeledline current I G into the relationship derived from Ohm’s law, Equation 4.35. Table 4.5gives the final line voltage equation.58

T T = 3K t I G + A + BωSymbol Value and Units MeaningT T Nm Torque applied to generatorradωsRotational speed of motorI G Nm RMS phase current (Table 4.3)A 0.965 Nm Experimentally-derived constantB 0.0126 NmrpmExperimentally-derived constantTable 4.4. Generator applied torque equationV LG =π2 √ 3 I GR D + π3 √ 2 V DSymbol Value and Units MeaningV LM V RMS RMS line voltage developed by generatorI G A RMS RMS phase current (Table 4.3)R D Ω Variable dump load resistanceV D 1.3 V Bridge rectifier voltage dropTable 4.5. Generator line voltage equationPower Output EquationThe electrical power output of the generator is modeled by plugging the output linevoltage V LG and the line current I G into Equation 4.7. Table 4.6 outlines the power outputequation.P G = √ 3V LG I GSymbol Value and Units MeaningP G W Electrical power output of generatorV LM V RMS RMS line voltage (Table 4.5)I G A RMS RMS phase current (Table 4.3)Table 4.6. Generator power output equation59

Efficiency EquationLastly, the generator efficiency is modeled by dividing the predicted electrical poweroutput by the predicted torque input times the rotational speed. Table 4.7 presents thegenerator efficiency equation.η G = P GT T ωSymbol Value and Units Meaningη G % Efficiency of generatorP G W Electrical power output of generatorT T Nm Torque applied to generatorωradsRotational speed of motorTable 4.7. Generator efficiency equation4.4.4 Model EvaluationThe CE&P generator model consists of equations for the output current, output voltage,output power, efficiency, and applied torque of the generator. Each of these quantities canbe predicted given the generator speed and dump load resistance, in addition to somegenerator characteristics derived through dynamometer testing. To evaluate the model, itis compared to the data points actually measured during the first round of dynamometertesting. This comparison indicates that model accurately represents the CE&P generator’soperation in the range that was tested. The model may be used to predict its performanceoutside the tested range, then, with a good degree of confidence.The observed and modeled current are compared in Figures 4.7 through 4.11. Table4.8 lists each modeled variable, its maximum deviation from the observed data, and theR-squared value that quantifies the quality of the fit.60

Variable Max Deviation R 2 Value ComparisonPhase current 1.4% 0.9999 Figure 4.7Line voltage 1.0% 0.9998 Figure 4.8Output Power 1.6% 0.9997 Figure 4.9Efficiency 1.6% 0.9999 Figure 4.10Applied Torque 5.9% 0.9994 Figure 4.11Table 4.8. Generator modeled versus measured variablesFigure 4.7. Generator phase current: modeled versus measured.4.4.5 Evaluation of Generator RatingsThe generator model developed in Section 4.4 can be employed to predict the CE&Pgenerator’s behavior at any speed and load resistance. This ability will be extremely usefulfor the design and deployment of wind turbines using the generator. More immediately, themodel can be put to use validating the generator’s rated characteristics.The generator nameplate is shown in Figure 4.12. As the nameplate attests, the generatoris rated 1 kW at 48 volts DC and 300 rpm. Literature on the generator gives two61

Figure 4.8. Generator line voltage: modeled versus measured.Figure 4.9. Generator output power: modeled versus measured.62

Figure 4.10. Generator efficiency: modeled versus measured.Figure 4.11. Generator applied torque: modeled versus measured.63

more bits of information: the rated efficiency is 77.7%, and the supposed voltage constantis 0.193 volts RMS line-to-line.Figure 4.12. Nameplate of the CE&P generator.First, the generator voltage constants are compared. Dynamometer testing indicatedthat the generator has a voltage constant of 0.184 volts RMS line-to-line, differing from therated value by 4.7%. While it would be tempting to chalk up the difference to error in thedynamometer test, this is unlikely. As discussed in Section 4.4.2, the voltage constant wasfound directly with great accuracy, and also verified by an independent formulation of thetorque constant to within 0.6%.Next, the generator’s rated operating point is evaluated. The generator speed is set to300 rpm, the rated speed. The load resistance is then varied until the generator voltage–asdetermined by the model–is equal to the rated voltage, 48 volts. This load resistance isfound to be 1.8 Ω. Now that the load resistance and speed are fixed, the model outputsthe predicted power output and efficiency. The power output is predicted to be 1384 watts,38% more than anticipated. The efficiency at this operating point is predicted to be 65%,16% lower than expected. Neither of these values match up well to the rated operatingpoint, so the model is run again. This time, the load resistance is varied until the the poweroutput, not the voltage, matches up to the rating. At 300 rpm, the generator is predicted64

to output 1000 watts when the load resistance is 3.6 Ω. At this operating point the voltageis expected to be 58 volts–21% greater than expected. The efficiency, however, is predictedto be 77.0%, which matches up quite well with the rated 77.7% efficiency.Given these results, it is hard to assess exactly how much the model and the generatorratings differ, because it is unclear what specific operating points should be compared. Inany case, the model predicts behavior quite different from that indicated by the machine’snominal ratings. There are three possibilities for this significant discrepancy:1. The model may not be valid over the generator’s entire range of operation. At highertorques and currents, the generator may exhibit behavior not observed during the firstround of testing.2. The generators obtained by CE&P may not behave consistently. That is, each individualelectrical machine may exhibit different qualities, due to manufacturing imprecisionor lack of quality control.3. The data provided by the generator manufacturer could be incorrect.To determine what is truly taking place, it is crucial to retest the CE&P generator athigher torques and currents, as was originally intended. This will either validate the model,or inform a more accurate model.It would also be helpful to swap the two electricalmachines: use the generator as the dynamometer motor, and test the motor as a generator.This would help address item number 2, and ensure that each machine behaves just like itstwin.Lastly, the generator’s maximum efficiency is evaluated, as predicted by the model.Limiting the generator speed to 450 rpm, or 50% greater than its rated speed, the maximumefficiency is found to be 86% at 450 rpm and 13 Ω. At this operating point, the power outputis 873 watts.65

Chapter 5Summary and ConclusionsThis matter is a pot of sweet potatoes.The words of all men point in one direction: agreement.– Zulu proverb67

5.1 SummaryThe Renewable and Appropriate Energy Laboratory was contracted by California Energyand Power to test a 1 kW permanent magnet generator for use in small, vertical axiswind turbines. To enable testing of the generator, as well as to facilitate accurate analysis ofthe test data, a driving dynamometer was developed using a second identical generator. Thedynamometer was comprised of several subsystems. A custom power electronics package,optical encoder, and digital signal processor allowed one generator be driven as a motor,providing the dynamometer’s motive force.A chain drive transferred mechanical powerfrom the motor to the generator, which was electrically loaded with a variable-resistancedump load.Testing was performed over two days. While an unresolved sprocket-mounting problemprohibited testing their full range operation, enough data was collected to permit preliminaryanalysis of both the dynamometer and the generator. Analysis began by determiningthe machines’ motor constants, as well as characterizing their non-resistive power losses.With this information, the dynamometer’s torque output was determined as a function ofmeasured quantities. Then the generator itself was evaluated: using test results and generatortheory, a model of the generator’s performance was developed. The model was found tocorrelate extremely well to measured data points, and was used to evaluate the generator’smanufacturer-specified ratings.5.2 ConclusionsThrough the process of designing, fabricating, and using the driving dynamometer,several major conclusions have been reached.68

Dynamometer1. The dynamometer is a promising tool for testing small wind turbine generators. Withsome improvements to the drivetrain, it should be able to test generators up to amaximum of 240 rpm, 800 volts DC, 35 amps, 1 kW, and 40 Nm of applied torque.2. The dynamometer should be run with a DC voltage input of 20 volts and above. Thiswill allow the test operator to bypass the range of unsteady operation observed below20 volts.CE&P Generator1. The California Energy and Power 1 kW permanent magnet generator can be accuratelymodeled in the low-power range that was tested.While it must be verifiedthrough testing, the model is expected to hold up at higher power levels.2. The CE&P generator experiences non-resistive power losses from what can be representedas a frictional torque. The frictional torque is approximated as the sum of aconstant value and a term proportional to the generator speed. This characterizationof the generator’s non-resistive power losses forms the basis of the generator model.3. The model suggests that the CE&P generator’s motor constant and operating pointratings are inaccurate, or vary considerably between supposedly-identical machines.Again, this claim must be verified by testing at higher torque, current, and powerlevels.5.3 Future WorkThrough preliminary testing and analysis, the dynamometer has proven that it canfunction effectively and produce high-quality results. Further work is needed, however, tocomplete the analysis of the CE&P generator, and enable the testing of other generators inthe future.69

First and foremost, the problem outlined in Section 3.5 must be addressed: the chaindrive or generator shaft-to-sprocket connection must be redesigned, so that the connectiondoes not naturally loosen at high torques. This will enable the dynamometer to run testsin the high torque, high current, and high power regime it was designed for. Once thatredesign takes place, the CE&P generator can be retested through a larger range of operatingconditions. Retesting will serve as a check on the conclusions developed here: doesthe generator actually perform as predicted by the model? Retesting should also involveswapping the two CE&P generators, so each is run as both a motor and generator. Bycomparing the results from two such tests, the consistency of individual generator unitsproduced by this manufacturer can be evaluated.Beyond testing the CE&P generator, the dynamometer setup could use some improvementsif it is to continue testing generators for the RAEL laboratory. More than anything,the dynamometer needs a home–specifically, a home with an adequately-sized DC powersupply. If it must be shipped to the student lab in Etcheverry for every test, it is unlikelythat the dynamometer will be used. Since RAEL is relocating to the Richmond Field Station,this will may necessitate the purchase of a power supply for the lab. In the samevein, at least one voltage meter should be obtained for use with the dynamometer. Thiswill enable the accurate voltage measurements necessary for high-quality results withoutrelying on those in the student lab, or a lower-resolution multimeter. Lastly, future testingand analysis would be simplified if a tool were developed to automatically process test results.This could take the form of a spreadsheet that embodies the calculations outlined inthis report. Test operators would enter readings into such a spreadsheet directly, and getimmediate results. As well as facilitating analysis of the generator, it would enable the testprocess to be tuned in real time–for example, by warning the user when the chain tensionor resistor power dissipation was approaching a limit to safe operation.70

BibliographyLieu, P. D. K., Design of Basic Electro-mechanical Devices (Course Packet), 2005.Shigley, J. E., Mechanical Engineering Design, McGraw-Hill Higher Education, 2004.Wildi, T., Electrical Machines, Drives, and Power Systems, Sixth Edition, Prentice Hall,2006.71

Appendix AComponent Specifications73

Figure A.1. Primary transistor specifications.74

Figure A.2. Secondary transistor specifications.75

Figure A.3. Quadrature optical encoder specifications, page 1 of 2.76

Figure A.4. Quadrature optical encoder specifications, page 2 of 2.77

Figure A.5. Digital signal processor specifications, page 1 of 2.78

Figure A.6. Digital signal processor specifications, page 2 of 2.79

Figure A.7. Three-phase bridge rectifier specifications.80

Figure A.8. Shunt resistor specifications.81

Figure A.9. Operational amplifier specifications.82

Appendix BComplete Control Program:Dynamic C Code83

Figure B.1. Dynamic C code, page 1 of 6.84

Figure B.2. Dynamic C code, page 2 of 6.85

Figure B.3. Dynamic C code, page 3 of 6.86

Figure B.4. Dynamic C code, page 4 of 6.87

Figure B.5. Dynamic C code, page 5 of 6.88

Figure B.6. Dynamic C code, page 6 of 6.89

Appendix CRaw Test DataFigure C.1. Raw data, page 1 of 2.91

Figure C.2. Raw data, page 2 of 2.92