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UBC Theses and Dissertations

A DSP based variable-speed induction motor drive for a revolving stage Zhang, Yong 2007

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A DSP BASED VARIABLE-SPEED INDUCTION MOTOR DRIVE FOR A REVOLVING STAGE   by YONG ZHANG B. A. Sc., Huazhong University of Science and Technology, WH, China, 1992   A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE  in  THE FACULTY OF GRADUATE STUDIES (Electrical and Computer Engineering)    THE UNIVERSITY OF BRITISH COLUMBIA December 2007  © Yong Zhang, 2007  ii Abstract Variable speed drive technology has advanced dramatically in the last 10 years with the advent of new power devices. In this study, a three phase induction motor drive using Insulated Gate Bipolar Transistors (IGBT) at the inverter power stage is introduced to implement speed and position control for the revolving stage in the Frederic Wood Theatre This thesis presents a solution to control a 3-phase induction motor using the Texas Instruments (TI™) Digital Signal Processor (DSP) TMS320F2407A. The use of this DSP yields enhanced operations, fewer system components, lower system cost and increased efficiency. The control algorithm is based on the constant volts-per-hertz principle because the exact speed control is not needed. Reflective object sensors which are mounted on concrete frame are used to detect accurate edge position of revolving stage. The sinusoidal voltage waveforms are generated by the DSP using the space vector modulation technique. In order to satisfy some operating conditions for safe and agreeable operation, a look-up table, which is used to give command voltage and speed signals in software, is applied to limit the maximum speed and acceleration of the revolving stage. Meanwhile, a boost voltage signal is added at the low frequency areas to make the motor produce maximum output torque when starting. A test prototype is then built to validate the performance. Several tests are implemented into the IGBT drive to explore the reason for unacceptable oscillations in IGBT’s gate control signals. Improvement methods in hardware layout are suggested for the final design.      iii Table of Contents  Abstract  ...........................................................................................................ii Table of Contents .............................................................................................iii List of Tables ....................................................................................................vi List of Figures .................................................................................................vii Acknowledgements .......................................................................................... X Chapter 1  Introduction.....................................................................................1 1.1 Overview of the Current System......................................................................................... 1 1.2 Advantages of an Induction Motor in Variable Speed Application ..................................... 2 1.3 Thesis Motivation and Objective ........................................................................................ 3 Chapter 2  Principles of Stage Mechanic System and V/Hz Control .............4 2.1 Elementary Principles of Mechanics................................................................................... 4 2.2 Safe Riding Conditions ....................................................................................................... 5 2.3 Induction Machines............................................................................................................. 8 2.3.1 Torque production ................................................................................................... 8 2.3.2 Equivalent circuit .................................................................................................... 9 2.3.3 Variable-voltage operation .................................................................................... 12 2.3.4 Variable-speed operation ....................................................................................... 13 2.3.5 Constant Volts/Hz operation.................................................................................. 13 2.4 Open Loop Volts/Hz Control with Voltage-Fed Inverter................................................... 15 Chapter 3  Hardware Implementation ............................................................17 3.1 Introduction of System...................................................................................................... 17 3.2 Three-Phase Rectifiers ...................................................................................................... 18 3.2.1 Thermistor ............................................................................................................. 18 3.2.2 The DC bus bulk capacitor.................................................................................... 19 3.3 Three-Phase Bridge Inverter ............................................................................................. 20  iv 3.3.1 The basic IGBT drive principle............................................................................. 21 3.3.2 Maintaining dv/dt noise immunity ........................................................................ 22 3.3.3 The applied IGBT drive ........................................................................................ 24 3.3.4 DC-DC converters................................................................................................. 25 3.3.5 Drive’s input resistors............................................................................................ 26 3.3.6 Gate resistors......................................................................................................... 26 3.3.6.1 Turn-on resistors............................................................................................. 26 3.3.6.2 Turn-off resistors ............................................................................................ 29 3.3.6.3 Minimal switching loss constraint.................................................................. 31 3.4 Energy Dissipation Subsystem.......................................................................................... 33 3.5 Over Current Protection .................................................................................................... 37 Chapter 4  Software Implementation .............................................................39 4.1 Approaches of SV_PWM Signals: .................................................................................... 39 4.2 Implementation-Open-Loop Speed Control for 3-Phase AC Induction Motor ................. 41 4.2.1 Overview............................................................................................................... 41 4.2.2 Initialization module description........................................................................... 43 4.2.3 Interrupt module description ................................................................................. 43 4.2.4 Generation of sine and cosine ............................................................................... 44 4.2.5 Space vector pulse width modulation.................................................................... 45 4.2.5.1 Expression of the 3 phase voltages (phase to neutral).................................... 46 4.2.5.2 Application to the static power bridge ........................................................... 47 4.2.5.3 Expression of the stator voltages in the (α, β) frame ..................................... 48 4.2.5.4 Projection of the stator reference voltage Vs ................................................. 50 4.2.5.5 Space vector algorithm................................................................................... 53 4.3 Voltage Per Hertz Algorithm ............................................................................................. 56 4.4 Frequency Command Module........................................................................................... 58 4.5 Deadtime Setting............................................................................................................... 59 4.6 Look-Up Tables................................................................................................................. 59  v 4.7 Execution Time ................................................................................................................. 60 Chapter 5  Experimental Results....................................................................62 5.1 Noise Studies of Gate Signals ........................................................................................... 62 5.2 Analysis of the Running Revolve...................................................................................... 63 5.3 Gate Resistor Studies with Different Drives ..................................................................... 67 5.3.1 Gate signal with flyback transformer as power supplies....................................... 69 5.3.2 Gate signals with battery as power supplies.......................................................... 71 5.3.3 IGBT’s gate signal with commercial drives .......................................................... 72 5.3.4 Improved drive circuits and corresponding gate signals ....................................... 74 5.4 Collector-Emitter Surge Voltage ....................................................................................... 75 5.5 Deadtime Analysis ............................................................................................................ 77 Chapter 6  Conclusion and Future Work .......................................................80 6.1 Conclusion ...................................................................................................................... 80 6.2 Future Work ...................................................................................................................... 81 References.........................................................................................................82 Appendix A: Estimation of Moment of Inertia of the Stage  ........................83 Appendix B: Induction Motor Parameter Estimation .....................................84 Appendix C: Clarke and Park Transformation................................................87        vi List of Tables  Table3.1 Features of the IGBT gate drive ............................................................................................. 25 Table3.2 Turn-on gate resistor sizing by tsw constraint ........................................................................ 28 Table3.3 Turn-on gate resistor sizing by dVout/dt constraint................................................................ 29 Table3.4 Turn-off gate resistor sizing.................................................................................................... 30 Table3.5 Gate voltage spike induced by high dv/dt .............................................................................. 32 Table3.6 Component list for the IGBT gate drive................................................................................. 32 Table 4.1 Power bridge output voltages (VAO, VBO, VCO)................................................................ 48 Table 4.2 Power bridge output voltages (VAN, VBN, VCN)................................................................ 49 Table 4.3 Stator voltages ....................................................................................................................... 50 Table 4.4 Relationship between sector and P ........................................................................................ 53 Table 4.5 Assigning the right duty cycle to the right motor phase ........................................................ 54 Table 4.6 State Sequence....................................................................................................................... 55 Table 4.7 Look-up tables used in the program ...................................................................................... 60 Table 5. 1 Features of the BG2B universal gate drive........................................................................... 74 Table a.1 Calculation of the moment of inertia of the stage.................................................................. 83 Table b.1 Nameplate data of the induction machine ............................................................................. 84           vii List of Figures  Figure 2. 1 Rotating object and its block diagram representation........................................................... 5 Figure 2. 2 Force analyses for variable speed revolution........................................................................ 6 Figure 2. 3 Angular acceleration versus angular speed........................................................................... 7 Figure 2. 4 Per phase equivalent circuit of induction motor ................................................................... 9 Figure 2. 5 Approximate Per phase equivalent circuit of induction motor ........................................... 10 Figure 2. 6 Torque-speed curves at variable frequency ........................................................................ 12 Figure 2. 7 Torque-speed curves with variable stator voltage............................................................... 13 Figure 2. 8 Torque-speed curves with constant voltage/frequency ratio............................................... 14 Figure 2. 9 Torque-speed curves with low-speed voltage boost, constant voltage/frequency ratio ...... 15 Figure 2. 10 Open loop volts/Hz speed control with voltage-fed inverter ............................................ 16 Figure 3. 1 Revolve system of the stage................................................................................................ 17 Figure 3. 2 Three-phase rectifiers ......................................................................................................... 18 Figure 3. 3 DC bus voltage curve.......................................................................................................... 19 Figure 3. 4 One leg of a three phase inverter ........................................................................................ 21 Figure 3. 5 Basic IGBT drive circuit..................................................................................................... 22 Figure 3. 6 Gate signal oscillation countermeasure .............................................................................. 23 Figure 3. 7 Noise shielding of opto-couplers ........................................................................................ 23 Figure 3. 8 Additional dv/dt immunity of negative bias turn-off voltage ............................................. 24 Figure 3. 9 IGBT turn-on sequence....................................................................................................... 27 Figure 3. 10 RGon sizing ...................................................................................................................... 27 Figure 3. 11 Current paths when Low Side is off and High Side turns on............................................ 30 Figure 3. 12 Separate gate current paths for turning-on and turning-off............................................... 31 Figure 3. 13 IGBT gate drive schematic ............................................................................................... 33 Figure 3. 14 Current paths for (a) Operation mode of motoring (b) Operation mode of generating..... 34 Figure 3. 15 Application speed, torque and power profiles .................................................................. 36 Figure 3. 16 over current censoring circuit ........................................................................................... 37  viii Figure 3. 17 Current scaling for short circuit protection....................................................................... 38 Figure 4. 1 Program flow chart ............................................................................................................. 42 Figure 4. 2 Software flowchart and timing ........................................................................................... 44 Figure 4. 3 Sin, Cos calculation using the sine look-up table ............................................................... 45 Figure 4. 4 Phase equilibrate system..................................................................................................... 46 Figure 4. 5 Power bridge....................................................................................................................... 47 Figure 4. 6 Stator voltages .................................................................................................................... 49 Figure 4. 7 Projection of the reference voltage vector .......................................................................... 51 Figure 4. 8 Sector 1 PWM patterns and duty cycles ............................................................................. 55 Figure 4. 9 Voltage versus frequency ................................................................................................... 56 Figure 4. 10 Speed waveform of accurate position control................................................................... 58 Figure 4. 11 Command frequency censoring hardware ........................................................................ 58 Figure 4. 12 Command frequency scale translation .............................................................................. 59 Figure 4. 13 Execution time of V/Hz control routine............................................................................ 60 Figure 5. 1 Gate signal, low side with different DC bus link voltage ................................................... 62 Figure 5. 2 Phase and line voltage reference waveforms with SVP...................................................... 63 Figure 5. 3 The tested stage with 1500kg unbalanced loads ................................................................. 64 Figure 5. 4 Motor current curves under different running conditions................................................... 65 Figure 5. 5 Gate signals......................................................................................................................... 67 Figure 5. 6 Basic gate charge waveforms ............................................................................................. 68 Figure 5. 7 The practical realization of the prototype ........................................................................... 69 Figure 5. 8 The schematic diagram of the flyback transformer ............................................................ 70 Figure 5. 9 Gate signal with flyback transformer as power source of the drive.................................... 71 Figure 5. 10 A group of batteries as power supply for IGBT drives..................................................... 71 Figure 5. 11 Gate signal with batteries as power source of the drive.................................................... 72 Figure 5. 12 The commercial drive ....................................................................................................... 72 Figure 5. 13 The gate signals with commercial drives.......................................................................... 73 Figure 5. 14 DSP embedded in PCB board with commercial drives .................................................... 74  ix Figure 5. 15 The gate signal curve with improved hardware layout ..................................................... 75 Figure 5. 16 Gate and Collector-emitter voltage curves ....................................................................... 76 Figure 5. 17 The layout of capacitors be mounted on bus bar .............................................................. 77 Figure 5. 18 The Collector-Emitter voltage curve with the new layout ................................................ 77 Figure 5. 19 Current waveforms with different command frequency, deadtime=2μs .......................... 78 Figure 5. 20 Current waveforms with different command frequency, deadtime=1.4μs ....................... 79 Figure 1 Stator current in the stationary reference frame and its relationship with a,b,and c stationary reference frame ....................................................................................................................... 87 Figure 2 Stator current in the d,q rotating reference frame and its relationship with,  stationary reference frame ....................................................................................................................... 89                 x Acknowledgements    I wish to express my deepest gratitude to my supervisor, Dr. William G. Dunford, for his support, advice and guidance throughout the course of my research. Numerous interactions with my colleges Weidong Xiao, Kenneth Wicks, Yan LI and Amir Rassuily have as well inspired me throughout my graduate study. In particular, I would like to express my thanks to Qiang Han who shared with me his experience and optimism in software and hardware setup. Thanks are extended to Mr. Jay Henrickson, the technical manager of the theatre, for providing necessary facilities and assistance throughout this process. Finally, I am expressing my sincerest gratitude to my parents and my wife for their love and support during my studies.   Chapter 1 Introduction  1 1. Chapter 1 Introduction 1.1 Overview of the Current System The Frederic Wood Theatre is located at the north end of The University of British Columbia (UBC). The original construction was built in 1963 and designed by Thompson, Berwick and Pratt. The building exterior is textured concrete with relief to the concrete walls coming from the landscape and the glazed entrance. This building is named after Frederic Wood, Founder of the UBC Players’ Club, as a tribute to his major contribution to the development of theatre in British Columbia. During the past 50 years, numerous shows, conferences and other actions have been held at the theatre. Nowadays, it is still busy to be a platform to operate various theatre programs, which make it possible to interact among students, scholars and guest artists. As the heart of a theatre, the stage serves as a space for actors. As is necessary in a drama, sceneries are required to be changed according to the mood, and rotary stage can serve a performance to the need of scenery change. There is a round revolver, with 27-feet diameter, in the Frederic Wood Theatre. This revolver is driven by a 3-hp Direct Current (DC) motor via a steel cable coupled the motor and the stage. The old control panel has three speed control option buttons and one bi-direction rotated knob to supply a coarse control approach. Position alignments in the scenery change are based on the operator’s experience. However, because the scenery setting differs from time to time, and so does the number of actors, this operation becomes complex and uncertain even to a veteran operator. Consequently, an automatic stage drive and control system is desirable. Chapter 1 Introduction  2 1.2 Advantages of an Induction Motor in Variable Speed Application Judged in terms of fitness for purpose coupled with simplicity, the induction motor must rank alongside the screw thread as one of mankind’s best inversions [1]. The induction motor (IM) has dominated a number of fixed-speed applications because of its reliability and low maintenance operation compared to DC motors. But, speed control had been one of the obvious shortcomings which impeded IM applications in some industrial fields, such as hydraulics. On the contrary, controlling the speed of a brushed DC motor is simple. The higher the armature voltage, the faster the rotation. This relationship is linear to the motor's maximum speed. In addition, most industrial DC motors will operate reliably over a speed range of about 20:1 -- down to about 5-7% of base speed. This is much better performance than comparable AC motors. However, in the last two decades, with the evolution of power semiconductor devices and power electronic converters, the IM is also well established in the controlled-speed arena. High performance Digital Signal Processor (DSP)’s introduction makes complicated control algorithms, such as flux vector control, available, which means that Alternating Current (AC) motors can be applied to accurate motor speed control as DC motor. Meanwhile, an AC induction motor, compared with a DC motor, is relatively inexpensive, since the windings consist of metal bars which are cast into steel laminations that make up the remainder of the rotor and the stator windings can easily be inserted in slots in stator laminations. An induction motor, at least the cage variety, has no brushes, no moving parts other than the rotor, and virtually no maintenance. As a result, AC motors are progressively replacing DC machines in variable-speed applications.     Chapter 1 Introduction  3 1.3 Thesis Motivation and Objective The objective of this thesis is to clarify the practical approaches needed to set up a Digital Signal Processor (DSP)-based variable-speed drive to realize accurate speed and position control. The specific objectives include: ˆ To find safe operation areas for the stage ˆ To build a three phase rectifier ˆ To develop a variable-speed drive ˆ To generate a DSP program with the assembly language ˆ To test the prototype to determine characteristics related to above theoretical analysis The thesis is organized into six chapters. Chapter 1 gives a brief introduction of the current stage system and outlines the objectives of this thesis. In Chapter 2, some basic principles of mechanics and IM variable-speed control are reviewed and a safe operation area for the stage is proposed. Chapter 3 is focused on hardware setup for a variable- speed IM drive. Chapter 4 will be dealing with software implementation. Some design illustration concerning software is presented. Selective experimental results are included in Chapter 5. The last chapter concludes the design and the implementation and proposes some work needed to be done in the future. Chapter 2 Principles of the Stage Mechanic System and V/Hz Control  4 2. Chapter 2 Principles of Stage Mechanic System and V/Hz Control 2.1 Elementary Principles of Mechanics In the stage and its drive system, both mechanical and electromagnetic energies exist and there is the exchange between the two types of energies. Since the whole system involves mechanical and electrical engineering, it is necessary to recall some basic concepts and laws related to mechanics. The most general equation to describe rotational motion is: M L dT T J dt ω− =   (2-1) where . )MT N m(  is the electrical torque and . )LT N m(  the load torque, ( / )rad sω is the angular speed, 2. )J kg m(  is the overall moment of inertia of the rotating mass about the axis of rotation. As speed is the derivative of the shaft positionθ , we have 2 2M L d dT T J J dt dt ω θ− = =   (2-2) where 2 2 d d dt dt ω θα = =   (2-3) 2( / )rad s  is the angular acceleration. The rotational system can be considered as a second-order differential equation, with the input as the driving torque and the load torque and the output as speed and position [2]. The following diagram, Figure 2. 1 describes such a mechanical system with a lumped mass. Chapter 2 Principles of the Stage Mechanic System and V/Hz Control  5 θ ω LM TT −  Figure 2. 1 Rotating object and its block diagram representation 2.2 Safe Riding Conditions Before proceeding to the system design, we have to find a way to decide what the maximum angular speed maxω  and maximum angular acceleration maxα  should be since they associate with the safety for actors on-board. We can divide the safety problem into two levels, mechanically safe and physiologically safe. For mechanical safety, the maximum angular speed maxω  and maximum angular acceleration maxα  should be within the range such that motors and the stage can stand. In addition, slippage in the cable coupled gear box and the stage should be taken into account while the maximum angular acceleration maxα  is chosen. For physiological safety, maxω  and maxα  should be within the range that those on-board can stand and have no dizziness or fear caused by the motion of the stage. Rotating along the shaft is a typical movement for the stage. The angular speed of the stage can be changed in the acceleration/deceleration period. So does the angular acceleration/deceleration. Therefore the motion of the stage is a varying-speed varying-acceleration revolution. If an object is rotating with a varying speed, its acceleration can be divided into two components, a radial/centripetal acceleration that changes the direction of the angular speed, and a tangential acceleration that changes the magnitude of the angular speed. Figure 2. 2 [3]shows the forces and accelerations applied to a person standing on a stage. Chapter 2 Principles of the Stage Mechanic System and V/Hz Control  6 TTF α, CCF α, ffF α, LL αω ,  Figure 2. 2 Force analyses for variable speed revolution Assume the stage is rotating at an angular speed Lω  and an angular acceleration Lα . fF  and fα represent the force applied to the person and the actual acceleration for the person respectively. fF  (the same to fα ) can be divided into two components, cF  in the normal direction and tF  in the tangential direction. Recall 2 C C LF ma m rω= =   (2-4) T T LF ma m rα= =   (2-5) with m  being the mass of the person and r  being the rotational radius of the person. From (2.4) and (2.5) we have 2 2 4 2 f C T L LF F F mr ω α= + = +   (2-6) fF , subscripted with f  referring to friction, is actually a friction acting as the force to keep the person moving with the stage simultaneously. The maximum of the friction is given by ,maxf sF mgμ=   (2-7) where sμ  is the coefficient of static friction between the stage and person’s shoes and Chapter 2 Principles of the Stage Mechanic System and V/Hz Control  7 g  is the acceleration due to gravity. For safety reasons, the inequality ,maxf fF F≥   (2-8) must be satisfied to prevent slip from happening. Substitute (2.6) and (2.7) into (2.8) and eliminate m results in 4 2 s L Lg rμ ω α≥ +   (2-9) or  4 2 sL L g r μω α+ ≤   (2-10) the most serious case, in terms of r, happens when people stand at the edge of the stage, thus /s g rμ  reaches its minimum /s g Rμ  with R  (13.5fts) the radius of the stage. Under this condition, Figure 2. 3 [3]shows the relationship of maximum angular acceleration versus speed with different friction coefficients. Safe operation states are those points bordered by the curves and the y  axis. 0 0.2 0.4 0.6 0.8 1 1.2 -1 -0.5 0 0.5 1 ωL (rad/s) α L  (r ad /s 2 ) μs=0.1 μs=0.2 μs=0.3 μs=0.4 μs=0.5  Figure 2. 3 Safe angular acceleration versus angular speed, radius is R From the figure it can be concluded that in low to medium speed area, acceleration/deceleration can be chosen in a relative big area under safe operation Chapter 2 Principles of the Stage Mechanic System and V/Hz Control  8 condition. However, as speed increases, allowable acceleration/deceleration decreases dramatically. In the following practical design, it is desirable to maintain the operation area of the stage in the middle left area shown in Figure 2. 3. According experience from the old system, the comfortable speed maxω  is limited at 1.42 rpm  (0.1495 /rad s ) and maxα  should be less than 0.05 2( / )rad s 2.3 Induction Machines Among all types of ac machines, the induction machine, particularly the cage type, is most commonly used in industry. These machines are very economical, rugged, and reliable, and are available in the ranges of fractional horse power (FHP) to multi-megawatt capacity [4]. In the following two sections, the principle of torque production is introduced and per phase equivalent circuits are used to figure out the expression of relationship between IM’s torque and speed. 2.3.1 Torque production If a IM’s rotor is initially stationary, its conductor will be subjected to a sweeping magnetic field, produced by stator’s current, inducing current in the short-circuit rotor with same frequency. The interaction of air gap flux and rotor Magnetomotive force (mmf) produces torque. At synchronous speed, the rotor can not have any induced currents and; therefore, torque can not be produced. At any other speed, there will be a difference between the rotating field (synchronous) speed and the shaft speed, which is called slip speed. The slip speed will induce current and torque in the rotor. The rotor will move in the same diction as that of the rotating magnetic field to reduce the induced current. We define slip as: e r e r sl e e e N Ns N ω ω ω ω ω − −= = =   (2-11) where eω =  stator supply frequency / )r s( , rω =  rotor electrical speed / )r s( , and Chapter 2 Principles of the Stage Mechanic System and V/Hz Control  9 slω =  slip frequency / )r s( . The rotor mechanical speed is (2 / ) ( / )m rP r sω ω= , where P =  number of poles of the machine. The rotor current is induced at slip frequency. Since the rotor is moving at speed rω  and it current wave is moving at speed slω relative to the rotor, the rotor mmf wave moves at the same speed as that of the air gap flux wave the torque expression [4] can be derived as sin 2e p p PT lrB Fπ δ⎛ ⎞= ⎜ ⎟⎝ ⎠   (2-12) where P =  number of poles, l =  axial length of the machine, r =  machine radius, PB = peak value of air gap flux density, PF = peak value of rotor mmf , and δ  is defined as the torque angle 2.3.2 Equivalent circuit A simple per phase equivalent circuit model of an induction motor is a very important tool for analysis and performance prediction under steady-state conditions. Figure 2. 4 shows the development of a per phase transformer-like equivalent circuit.  Figure 2. 4 Per phase equivalent circuit of induction motor  The various power expressions can be written form the equivalent circuit of Figure 2. 4 as follows: Input power: sin 2e p p PT lrB Fπ δ⎛ ⎞= ⎜ ⎟⎝ ⎠  (2-13) Chapter 2 Principles of the Stage Mechanic System and V/Hz Control  10 Stator copper loss: 23ls s sP I R=   (2-14) Core loss: 23 m lc m VP R =   (2-15) Power across air gap: 23 rg r RP I S =   (2-16) Rotor copper loss: 23lr r rP I R=   (2-17) Output power: 2 13o g lr r r sP P P I R S −= − =  (2-18) Since the output power is the produce of developed torque Te and speed ωm, Te can be expressed as 0 2 23 1 3 2 r e r r r m m e P RS pT I R I S sω ω ω − ⎛ ⎞= = = ⎜ ⎟⎝ ⎠  (2-19) The equivalent circuit of Figure 2. 4 can be simplified to that shown in Figure 2. 5 , where the core loss resistor mR  has been dropped and the magnetizing inductance mL has been shifted to the input. This approximation is easily justified for an integral horsepower machine, where ( )s e ls e mR j L Lω ω+ <<   (2-20) The performance prediction by the simplified circuit typically varies within 5 percent from that of the actual machine [4].  Figure 2. 5 Approximate Per phase equivalent circuit of induction motor In Figure 2. 5 , the current rI  is figured out by: Chapter 2 Principles of the Stage Mechanic System and V/Hz Control  11 ( ) ( )2 22/ s r s r e ls lr VI R R S L Lω = + + +   (2-21) substituting Equation (2-21) in (2-19) yields ( ) ( ) 2 2 22 3 2 / sr e e s r e ls lr VRPT S R R S L Lω ω ⎛ ⎞= ⎜ ⎟⎝ ⎠ + + +  (2-22) A further simplification of the equivalent circuit of Figure 2.6 can be made by neglecting the stator parameters sR  and lsL . This assumption is not unreasonable for an integral horsepower machine, particularly if the speed is typically above 10 percent [4]. Then, the equation (2-22) can be simplified as 2 2 2 23 2 s sl r e e r sl lr VP RT R L ω ω ω ⎛ ⎞⎛ ⎞= ⎜ ⎟⎜ ⎟ +⎝ ⎠⎝ ⎠   (2-23) where sl esω ω= . The air gap flux can be given by s m e Vψ ω=   (2-24) in a low-slip region, (2-23) can be approximated as ( )213 2e m slr PT R ψ ω⎛ ⎞= ⎜ ⎟⎝ ⎠   (2-25) where 2 2 2r sl lrR Lω>> . Equation (2-25) is critical for following analysis because it indicated that at constant flux, the torque is proportional to slip frequency, or at constant slip frequency, torque is proportional to flux. Chapter 2 Principles of the Stage Mechanic System and V/Hz Control  12 0.2 0.4 0.6 0.8 1 0 0.25 0.5 0.75 1 Speed (ωr/ωe) pu To rq ue  (T e/ T e m ) pu 1.0Vs 100% stator  voltage 0.25Vs 0.5Vs 0.75Vs  Figure 2. 6 Torque-speed curves at variable frequency 2.3.3 Variable-voltage operation A very simple and economical way to control speed in a cage-type induction machine is to adjust stator voltage at constant supply frequency. Figure 2. 6 illustrate the torque-speed waveforms with variable stator voltage which have been drawn from Equation (2-22).In this study, we used a 3-HP, 4-pole, 1760-rpm, 230V (line to line, rms) machine with the parameters 0.5sr = Ω , 4.7lsl mH= , 81.8ML mH= , 4.7lrl mH′ = , 0.42rr′ = Ω  This type of circuit has been used extensively as “soft starter” for constant speed IM, where the stator voltage is applied gradually to limit the stator current. Since the air gap flux is reduced at lower supply voltage, the stator current tends to be excessive at low speeds, which leads to high copper loss. Therefore, this type of drive is often used for speed control under the situation where the efficiency is not an important consideration. Chapter 2 Principles of the Stage Mechanic System and V/Hz Control  13 2.3.4 Variable-speed operation If the stator frequency of a machine is increased beyond the rated value, but the voltage is constant, the torque-speed cures derived from Equation (2-22) can be plotted as shown in Figure 2. 7. The air gap flux and rotor current decrease while the frequency increases and corresponding developed torque also decreases. The breakdown torque as a function of slip (at constant frequency) can be derived by differentiating Equation (2-23) as 2 2 2 23 2 s slm r em e r slm lr VP RT R L ω ω ω ⎛ ⎞⎛ ⎞= ⎜ ⎟⎜ ⎟ +⎝ ⎠⎝ ⎠   (2-26) where /slm r lrR Lω =  is the slip frequency at maximum torque. The equation show that 2 em eT ω =  constant 0  1  2 3 0.5 1 Frequency (ωe/ωb) pu To rq ue  ( T e /T em ) pu Temωe2=constant Rated cruve Tem  Figure 2. 7 Torque-speed curves with variable stator voltage 2.3.5 Constant Volts/Hz operation If an attempt is made to reduce the supply frequency at the rated supply voltage, the air gap flux mψ  will tend to saturate, causing excessive stator current. Therefore, the region below the rated frequency should be accompanied by the proportional reduction of Chapter 2 Principles of the Stage Mechanic System and V/Hz Control  14 stator voltage so as to maintain the air gap flux constant. This relationship can be expressed by Equation (2-24) as well. Figure 2. 8 shows the plot of torque-speed curves at /Volt Hz = constant. Note that the breakdown torque emT  given by Equation (2-26) remains approximately valid, except in the low frequency region where the effect of stator resistance in reducing the flux becomes very pronounced. It is clear from Figure 2. 8 that the starting torque at the minimum frequency is much less than the breakdown torque at higher frequencies, and this could be a problem for loads which require a high starting torque. For example, the starting torque for the stage’s revolve is quite high. The additional stator voltage can be compensated to restore emT  value, as shown in Figure 2. 9. 0.5 1 0 0.5 1 Frequency (ωe/ωb) pu To rq ue  (T e/ T e m ) p u Vs/ωe=constant Rated cruve Maximum torque  Figure 2. 8 Torque-speed curves with constant voltage/frequency ratio If the air gap flux of the machine is kept constant in the constant torque region, as indicated in Figure 2. 9, it can be shown that the torque sensitivity per ampere of stator current is high, permitting fast transient response of the drive with stator current control. In variable-frequency, variable-voltage operation of a drive system, the machine usually has low slip characteristics, giving high efficiency. With low-frequency voltage boosting, the machine can always be started at maximum torque, as shown in Figure 2. 9. The Chapter 2 Principles of the Stage Mechanic System and V/Hz Control  15 absence of high starting current in a direct-start drive reduces stress and therefore improves the effective life of the machine. 0.5 1 0 0.5 1 Frequency (ωe/ωb) pu To rq ue  (T e/ T e m ) p u Vs/ωe=constant Rated cruve Maximum torque  Figure 2. 9 Torque-speed curves with low-speed voltage boost, constant voltage/frequency ratio 2.4 Open Loop Volts/Hz Control with Voltage-Fed Inverter The open loop volts/Hz control of an induction motor is by far the most popular method of speed control because of its simplicity, and there types of motors are widely used in industry [4]. Traditionally, the induction motors have been used with power supplies at constant frequency for constant speed applications. For adjustable speed applications, variable voltage and variable frequency is prevalent. The simple principle is to keep state flux ( /s s eVψ ω= ) constant by changing voltage with proportional to frequency. Figure 2. 10 shows the block diagram of the /Volt Hz  speed control method. The power circuit consists of a diode rectifier with three phase AC supply, LC filter, and PWM voltage-fed inverter. The frequency command *eω  is the control signal because it is approximately equal to speed rω , neglecting the small slip frequency slω  of the machine. Based on /Volt Hz  control theory which has been motioned in the above Chapter 2 Principles of the Stage Mechanic System and V/Hz Control  16 section, the phase voltage command *sV  can be generated from frequency command be the gain factor G, as shown, So that the flux  sψ  remains constant. If the stator resistance and leakage inductance of the machine are neglected, the flux will also correspond to the air gap flux mψ  or rotor flux rψ . At low speed areas, the stator resistance become significant and absorbs the major amount of the stator voltage, thus weakening the flux. Therefore, the boost voltage boostV  is added to compensate flux to keep it equal to rated flux and corresponding full torque become available at low frequency. The *eω  signal is integrated to generate the angle signal *eθ , and the corresponding sinusoidal phase voltages ( *aV , *bV , *cV ) are generated by the expressions shown in the figure. Then PWM controllers which is embedded in DSP can generate control signals to drive the inverter. Detailed description of hardware and software for this control topology will be given in chapter3 and chapter 4 respectively. * 2 sina s eV V θ= * 22 sin 3c s e V V πθ⎛ ⎞= +⎜ ⎟⎝ ⎠ * 22 sin 3b s e V V πθ⎛ ⎞= −⎜ ⎟⎝ ⎠ ∫ Figure 2. 10 Open loop volts/Hz speed control with voltage-fed inverter Chapter 3 Hardware Implementation  17 3. Chapter 3 Hardware Implementation Based on the theory has been discussed in chapter 2, a practical variable-speed drive will be built for experimental result. In this chapter, emphasis will be given on how to choose components and put them together to form a prototype of IM variable-speed drive. 3.1 Introduction of System The drive system of the stage can be depicted in Figure 3. 1. It includes an AC-DC rectifier, a DC-AC inverter, a DSP, an induction motor and other accessorial components. It works based on popular AC-DC-AC topology. Following discussion will one by one explain above components.   Figure 3. 1 Revolve system of the stage  Chapter 3 Hardware Implementation  18 3.2 Three-Phase Rectifiers In order to obtain the essential DC bus voltage for the inverter, a three-phase diode bridge rectifier (Figure 3. 2) was applied in this application. A six pulse full bridge rectifier will produce 325V DC bus voltage while input AC line to line voltage is 230V.  Figure 3. 2Three-phase rectifiers 3.2.1 Thermistor A thermistor is installed to avoid high inrush current and voltage ringing when connecting the capacitors to the input network. When current begins to flow through resistor and charge capacitors, the voltage difference between the power source and capacitor is almost equal to 325V, which will produce big current in the circuit loop. This current could be so high that it is in excess of capacitor’s rating current and damage capacitors permanently. The thermistor has biggest resistance value of 5 ohms at 25 degree centigrade. It will be helpful in limiting starting charge current to 65A in a short time. With the process of charging capacitors, thermistor’s resistance will drop dramatically with the increase of its temperature. Finally, it reaches 0.082ohms, which brings very small power dissipation in the steady state. In other words, the thermistor can be considered as a short circuit and without any voltage drop on it in the steady state. Chapter 3 Hardware Implementation  19 3.2.2 The DC bus bulk capacitor Sizing of the capacitor represents a tradeoff. For a given load, a larger capacitor will reduce ripple but will cost more and will create higher peak currents in the supply feeding it. In Figure 3. 3, the voltage waveform of capacitors is depicted to calculate corresponding capacitance value. Electrolytic capacitors are used to smooth the dc bus voltage. Its capacitance can be found from the formula: min 2 2 max min 2 ( ) in rect PC V V f = −   (3-1) where Pin is the load power in watts, rectf  is the ripple frequency, maxV  is the maximum dc voltage and minV  is the minimum dc voltage [5].  Figure 3. 3 DC bus voltage curve In practical realization, a three phase 230V AC input is connected to the input of the rectifier. The peak voltage value of input is as follows: max 2 325LLV V V= = assume min max96% 312V V V= = ; WPin 2235745*3 == ; for three phase rectifier 6 60 360rectf Hz= × = . Then Chapter 3 Hardware Implementation  20 min 2 2 2 2 max min 2 2 2235 1499 ( ) (325 312 ) 360 in rect PC F V V f μ×= = =− − ⋅ tc, the charging time, can be calculated as 1 min 1 max cos ( ) cos (0.96) 753 2 2 60c in V Vt S f μπ π − − = = =⋅  (3-2) and discharging time tDC is 1 1 753 2 360DC crect t t mS f μ= − = − =   (3-3) the average charging current is given by max min 325 3121499 26 753C c c V VVI C C A t t −Δ −= = = =  (3-4) According to the calculation, at least a 1500μF capacitor should be employed to maintain the dc bus ripple within 4% or less. The capacitor should also can stand 26A charging current. 3.3 Three-Phase Bridge Inverter Figure 3. 4 shows a leg which includes high side and low side IGBT modules, drivers and DC-DC converters of the three-phase bridge inverter. In the following paragraphs, the detailed discussion will be focused on all components of this inverter. Chapter 3 Hardware Implementation  21 N/C1 ANODE2 CATHODE3 N/C4 Vcc 8 V0 7 V0 6 VEE 5 HCPL-1 R3 180R 3.8K R6 3.8K R5 10uF C5 10uF C2 +5 R1 180R Vin-1 Q1 IGBT-N R9 1.0K VCC 10uF C1 N/C1 ANODE2 CATHODE3 N/C4 Vcc 8 V0 7 V0 6 VEE 5 HCPL-2 R2 180R Vin-2 Q2 IGBT-N +Vin 1 -Vout 4 +Vout 6 -Vin 2 COM 5 *1 VASD1-S5-D15-SIP R4 180R 3.8K R8 3.8K R7 10uF C6 10uF C4 +5 R10 1.0K 10uF C3 +Vin 1 -Vout 4 +Vout 6 -Vin 2 COM 5 *2 VASD1-S5-D15-SIP Phase A Negative side of DC bus link  Figure 3. 4 One leg of a three phase inverter 3.3.1 The basic IGBT drive principle Figure 3. 5 illustrates a basic IGBT gate drive circuit, which converts logic level control signals into appropriate voltage and current that can drive the IGBT power Chapter 3 Hardware Implementation  22 module reliably and efficiently [6]. The conversion is performed by a pair of bipolar transistors alternately connecting the IGBT’s gate to the appropriate on (Von) and off (Voff) voltages. The gate resistor is selected to generate a proper peak current charging or discharging the IGBT’s gate. The optocoupler provides isolation between the high power component and control signal to avoid potential damage to the digital controller. 3.3.2 Maintaining dv/dt noise immunity The IGBT gate drive circuits are subjected to high common mode /dv dt  noise produced by the fast switching, high voltage and high current IGBT power modules. To maintain the immunity to the high /dv dt  noise is critical for the drive circuit to function normally in an offensive environment.    Figure 3. 5 Basic IGBT drive circuit  If the wiring between the drive circuit and the IGBT is long, the IGBT may be in a malfunction due to gate signal oscillation or induced noise. A countermeasure for this is shown in Figure 3. 6 . In order to avoid this situation, some points should be taken into account as follows: a) Make the drive circuit wiring as short as possible and finely twist the gate and emitter wiring. b) Increase RG. However, pay attention to switching time and switching loss c) Separate the gate wiring and IGBT control circuit wiring as much as possible, Chapter 3 Hardware Implementation  23 and set the layout so that they cross each other d) Do not bundle together the gate wiring or other phases Drive circuit Stray inductance RG RGE LS  Figure 3. 6 Gate signal oscillation countermeasure In this circuit, RGE is installed to prevent IGBT from being destroyed if gate circuit is bad or if the gate circuit is not operating and a voltage is applied to the power circuit  Figure 3. 7 Noise shielding of opto-couplers Furthermore, an optocoupler which is built in IGBT’s drive is used to prevent high common mode /dv dt . The immunity is normally achieved by adding shields between the “primary” and “secondary” side of the opto-coupler (Figure 3. 7). In addition, a larger series gate resistance is desirable to help reduce transient voltage during turn-off switching. Unfortunately, in most cases the series gate resistance must be increased substantially to have any significant impact on the turn-off fall time. Usually, such an increase in series gate resistance will result in poor /dv dt  noise immunity and excessive switching losses. It is usually better to reduce transient voltages with improved power circuit layout or snubber designs. There are detailed discussions about how to find a right way to build /dv dt  noise immunity in this application circuit in Chapter 5. Chapter 3 Hardware Implementation  24    Figure 3. 8 Additional dv/dt immunity of negative bias turn-off voltage Finally, a substantial negative bias is used for IGBT drive, which provides additional /dv dt  immunity and reduces turn-off losses. The additional margin to absorb "real" collector-gate capacitance coupled reverse transfer charge during high /dv dt , with respect to the gate-emitter "turn-on" threshold voltage, is a significant reliability improvement, particularly when switching peak (fault) current, coincident with a high dc-bus voltage (Figure 3. 8). 3.3.3 The applied IGBT drive The gate drive used in the prototype, HCPL-3120, is a high-current output IGBT gate drive with built-in opto-coupler. Its main parameters are given in Table 3.1. The current and voltage supplied by HCPL-3120 make it ideally suited for directly driving IGBTs with ratings up to 1200V/100A. In this drive, IR’s IGBTs (IRG40C50UD) are used as power switches. Their rating current is 27A at 100 oC and rating voltage is 600V. The switching frequency is 10 kHz. From HCPL-3120 datasheet, it is easy to draw a conclusion that this drive is suitable for designated IGBTs. The HCPL-3120 contains an under-voltage lockout (UVLO) feature that is designed to protect the IGBT under fault conditions which cause the HCPL-3120 supply voltage (equivalent to the fully- charged IGBT gate voltage) to drop below a level necessary to keep the IGBT in a low resistance state. When the HCPL-3120 output is in the high state and the supply voltage drops Chapter 3 Hardware Implementation  25 below the VUVLO- threshold, the opto-coupler output will go into the low state with a typical delay. When the HCPL-3120 output is in the low state and the supply voltage rises above the HCPL-3120 V UVLO+ threshold, the opto-coupler output will go into the high state with a typical delay.  Feature Specification Description Peak output current 2.0 A Common-mode rejection 15 kV/μs Vcm = 1.5 kV Input voltage Vcc 15 – 30 V UVLO Threshold Vuvlo+ 11-13.5 V UVLO Threshold Vuvlo- 9.5 – 12 V Hysteresis Maximum switch frequency 2 MHz Isolation 630 V peak  Table3.1 Features of the IGBT gate drive 3.3.4 DC-DC converters A dc-dc converter (VASD1-SIP-S5-D15-SIP) is chosen to provide the isolated ±15V power to the IGBT drive. The converter can provide 1kV dc voltage isolation across its input and output that is high enough in this application. The output isolated power is 1 w. A resistor has to be connected to the output of the converter which needs a minimum of 10% loading to maintain a reliable and fully-performed output. In order to confirm that converter can provide enough power to drive, a 3.8kΩ resistor is chosen as the load resistor. The corresponding power dissipation is: 2 230 0.12 2 7600 VP W R = = ≈   (3-5) Approximate 0.9W output power could be used by IGBT’s drive.  Chapter 3 Hardware Implementation  26 3.3.5 Drive’s input resistors To provide enough current to drive LED in HCPL-3120, a appropriate resistor has to be installed between output of DSP and input of HCPL. The operating condition of this LED diode is: Current: 7~16mA Voltage: 0.8V the following equation is employed to calculate essential resistance 3 3.3 0.8 178 180 14 10IN R x − −= = ≈ Ω   (3-6) 3.3.6 Gate resistors There are numerous methods to size IGBT’s gate resistors. Here some of them which are applied by industries will be illustrated. More accurate resistance values can be found by practical tests depending on the different emphasis of switching loss, switching time and slope of /dv dt . 3.3.6.1 Turn-on resistors By properly sizing the gate resistors the switching speed of the output IGBT can be controlled [7]. Some basic rules are given below for sizing the gate resistors to obtain desired switching time. The switching time swt  is defined as the time spent to reach the end of the plateau voltage, as shown in Figure 3. 9. *GEV  indicates the plateau voltage; GCQ  and GEQ  indicate the gate to collector and gate to emitter charge respectively. Chapter 3 Hardware Implementation  27  Figure 3. 9 IGBT turn-on sequence Depending on Figure 3. 10, to obtain the desired switching time, the gate resistance can be sized by: GC GE avg sw Q QI t +=   (3-7) and -CC GE TOT avg V VR I =   (3-8) where PTOT DR Gon R R R= +  GonR = gate on-resistor  PDR R = driver equivalent on-resistance  Figure 3. 10 RGon sizing Table3.2 shows the calculation process to size the turn-on gate resistor driven by Chapter 3 Hardware Implementation  28 swt  constraint. Reference Description IRG4PC50UD GEQ  Gate Emitter charge (turn-on) 25 nC GCQ  Gate Collector Charge (turn-on) 61 nC swt  Switching Time 500 ns sw GEGC avg t QQ I +=  Average Charging Current 172 mA * GEV  Gate Plateau Voltage 6 V avg GECC TOT I VVR *−=  Equivalent Output Resistance of the Gate Driver 52 Ω DRpR  Driver Equivalent on-resistance 0 Ω DRpTOTGon RRR −=  Gate On-resistance 52 Ω  Table3.2 Turn-on gate resistor sizing by tsw constraint Turn-on gate resistor can also be sized to control output slope /outdV dt . Although the output voltage has a non-linear behavior, the maximum output slope can be approximated by avgout RESoff IdV dt C =   (3-9) inserting the expression yielding Iavg and rearranging: -CC GE TOT out RESoff V VR dVC dt =   (3-10) The calculation of this kind of constraint is given in Table 3.3.   Chapter 3 Hardware Implementation  29 Reference Description IRG4PC50UD dt dVout  Output Voltage Slope 5 V/ns RESoffC Reverse Transfer Capacitance (off-state) 52 pF RESoff out avg Cdt dVI =  Average Charging Current 260 mA * geV  Gate Plateau Voltage 6 V avg geCC TOT I VV R *−=  Equivalent Output Resistance of the Gate Driver 34 Ω DRpR  Driver Equivalent on-resistance 0 Ω DRpTOTGon RRR −=  Gate On-resistance 34Ω  Table3.3 Turn-on gate resistor sizing by dVout/dt constraint 3.3.6.2 Turn-off resistors The worst condition in calculating the turn-off resistor is when the collector of the IGBT in the off state is forced to commutate by the turn-on of the companion IGBT [7]. In that case, a parasitic current through RESoffC  will be induced by the high /dv dt of the output node. If the voltage drop at the gate exceeds the threshold voltage of the IGBT, the device may be turned on by itself, which will cause cross conduction for the whole leg. If no negative bias voltage is used, condition ( ) outth ge Goff DRn RESoff dVV V R R C dt > = + ⋅ ⋅   (3-11) must be verified to avoid spurious turn-on. Rearrange (3-11) th Goff DRn RESoff VR RdVC dt < − ⋅   (3-12) Chapter 3 Hardware Implementation  30   Figure 3. 11 Current paths when Low Side is off and High Side turns on Figure 3. 12 shows the current induced by the high /dv dt  of the output node, where IESC  is the input capacitance, and RESoffC  is the reverse transfer capacitance. An example of calculating the turn-off gate resistor is given in Table 3.4  Reference Description IRG4PC50UD dt dVout  Output Voltage Slop 5 V/ns RESoffC Reverse Transfer Capacitance (off-state) 52 pF thV  Gate Threshold Voltage 6 V TOTR Equivalent Output Resistance of the Gate Driver 23 Ω DRnR  Driver Equivalent off-resistance 0Ω DRnTOTGoff RRR −=  Gate Off-resistance 23 Ω  Table3.4 Turn-off gate resistor sizing Apart from the methods mentioned above, another way to avoid the spurious turn-on is to use negative bias voltage for the off state. For the negative bias voltage of -15V, the actual gate voltage under the extreme condition will be -11V as maximum Chapter 3 Hardware Implementation  31 during the ‘off’ state, which is quite far from the threshold voltage of the IGBT. In the prototype, a -15V negative bias voltage is connected to VEE, which provide enough margin to avoid spurious turn-on by the parasitic current. 3.3.6.3 Minimal switching loss constraint There is a dilemma of how to choose proper resistance for gate resistor from turn-on and turn-off gate resistors. Figure 3. 13 shows a way to resolve this problem by employing a diode, which enables the gate resistor to be a different resistance depending on “on” or “off” state; however, another simple and practical way is introduced by calculating the gate resistor from drive side to minimize IGBT Switching Losses.  Figure 3. 13 Separate gate current paths for turning-on and turning-off From equation (3.12) [8], a new value of gate resistance is obtained. ( ) 15 ( 15) 2 11 2.5 CC EE OL OLPEAK V V VRg I A − − − − −≥ = = Ω  (3-13) where VOL is low level output voltage at the peak current of 2.5A. Table 4.7 gives the verification for the IGBT used in the prototype. The above-described methods for sizing gate resistors are intended to approximate phenomena of turn-on and turn-off switching time and switching losses of power IGBTs. More accurate sizing may rely on more precise IGBT modeling and parasitic components dependant on the layout and connection of the circuit. In the prototype, thanks to a big error from stray inductance of wires which are used to connect drives and IGBTs, an 180Ω resistor has been installed to avoid dramatic oscillation in VGE. In chapter 5, a detailed experimental study related to the gate resistor will be made. Chapter 3 Hardware Implementation  32 Reference Description IRG4PC50UD RESoffC Reverse Transfer Capacitance (off-state) 52 pF IESC  Input Capacitance 4000 pF ceV  Collector Voltage 300 V geV  Gate Voltage 3.9 V thV  Gate Threshold Voltage 3 - 6 V  Table3.5 Gate voltage spike induced by high dv/dt Other components used in the gate drive are listed in Table 3.6.  Reference Name Type Description U1 Dc/dc power supply VASD1-S5-D15 5V/±15V U2 Gate drive IC HCPL3120 With built-in opto-coupler RIN Resistor 180 Ω RG Gate resistor 180Ω R1 Resistor 1kΩ R2,R3 Resistor 3.8kΩ C1,C2,C3 Capacitor 10 μF electrolytic  Table3.6 Component list for the IGBT gate drive The per-phase IGBT drive schematic is shown in Figure 3. 14. Chapter 3 Hardware Implementation  33  Figure 3. 14 IGBT gate drive schematic 3.4 Energy Dissipation Subsystem When an induction motor’s rotor is turning slower than the synchronous speed set by the drive’s output power, the motor is transforming electrical energy obtained from the drive into mechanical energy available at the drive shaft of the motor. This process is referred to as motoring. When the rotor is turning faster than the synchronous speed set by the drive’s output power, the motor is transforming mechanical energy available at the drive shaft of the motor into electrical energy that can be transferred back to the drive. This process is referred to as regeneration Most AC PWM drives convert AC power from the fixed frequency utility grid into DC power by means of a diode rectifier bridge or controlled SCR bridge before it is inverted into variable frequency AC power. Diode and SCR bridges are cost effective, but can only handle power in the motoring direction. Therefore, if the motor is regenerating, the bridge cannot conduct the necessary negative DC current; the DC bus voltage will Chapter 3 Hardware Implementation  34 increase and cause an over-voltage fault at the drive. More complex bridge configurations use SCRs or transistors that can transform DC regenerative electrical power into fixed frequency utility electrical energy. This process is known as line regeneration. A more cost effective solution can be provided by allowing the drive to feed the regenerated electrical power to a resistor which transforms it into thermal energy. This process is referred to as dynamic braking. In the prototype, a braking resistor is applied to avoid high voltage in DC bus link during the regeneration of motor. The detailed method on how to calculate resistance of this resistor is explained as follows. During the braking period, the kinetic energy of the stage system will be reverted to electric energy through the induction machine, which is shown in Figure 3. 15[3]. The braking branch includes a voltage-controlled IGBT and a power resistor connected in series to the dc bus. The IGBT switch will be closed and connect the braking resistor to the dc bus when the dc voltage exceeds a threshold. The control circuit disconnects the braking resistor when the dc voltage drops back to normal level.  Figure 3. 15 Current paths for (a) Operation mode of motoring (b) Operation mode of generating In order to find the resistance, following information should be gathered: Chapter 3 Hardware Implementation  35 a) Required decelerate time b) Motor inertial and load inertia in kg-m2 c) Gear ratio d) Motor shaft speed, torque and power profile of the drive application Figure 3. 16 shows typical application profiles for speed, torque and power. The following variables are defined for Figure 3. 15 ( )W t =  Motor shaft speed in radians per second (rps) N =   Motor shaft speed in Revolutions Per Minute (RPM) ( )T t =  Motor shaft torque in Newton-meters ( )P t =  Motor shaft power in watts bω =   Rated angular rotational speed (rad/s) 0ω =   Angular rotational speed less than bω  (can equal 0) (rad/s) bP− =   Motor shaft peak regenerative power in watts Determine value of equation variables [9] Step 1 Total Inertia 2( )T m LJ J GR J= + ×   (3-14) where: TJ =  Total inertial reflected to the motor shaft (kg.m2) mJ =  Motor inertia (kg.m2) GR =  Gear ratio for any gear between motor and load LJ =  Load inertia (kg.m2) 2 20.14950.011 34000 0.107 . 89T J kg m⎛ ⎞= + × =⎜ ⎟⎝ ⎠ Chapter 3 Hardware Implementation  36  Figure 3. 16 Application speed, torque and power profiles Step 2 Peak Braking Power 2 ( 3 2) T b b JP t t ω×= −   (3-15) where bω =  Maximum rotor speed (89 /rad s ), the corresponding maximum speed of the revolving stage is 0.1495 ( /rad s ) 3 2t t− = Deceleration time from bω  to 0 20.107 89 28 30b P w×= = Step 3 Brake Resistance Value 2 d db b VR P =   (3-16) where: Chapter 3 Hardware Implementation  37 dV = DC bus voltage (150V) 2150 804 28db R = = Ω From above calculation, it is obvious that the regenerating power is small. Consequently, the braking resistor becomes large under designated voltage condition. The reason for this is that it takes 30 second to decelerate maximum speed to zero. In order to keep actors feel comfortable, the stage runs at a low speed (maximum 42 seconds per revolution). Limited acceleration/deceleration speed is applied to avoid jerks for the sake of riding safety and convertibility. The total deceleration time from permitted maximum to zero is 30 seconds. Under this condition, most power is dissipated as IGBT switching loss and stage friction loss. Some power is regenerated to charge the bus bulk capacitors to make their voltage increase; however, the voltage rise is still in the inverter’s rating area in this prototype. In the practical measurement, the maximum voltage rise is 5 Volts at DC bus 150V and fast drop to 150V with the completion of deceleration. Therefore, no braking resistors are installed in the prototype. In the future, a braking resistor could be mounted next to motor to ensure the inverter to work stably in deceleration of the motor. 3.5 Over Current Protection  port1 GND R10 5.6K R9 10k C7 104 C6 104 +15V -15V R11 10K I_protection C8 102 A3.3V 3 2 1 8 4 U17A OP284_1Ia_IN 13 2 D2 A3.3V R8 15K 5 6 7 U17B Comment: OP284_1 R13 10K R12 12K  Figure 3. 17 over current censoring circuit In Figure 3. 17, two operational amplifiers (Op amp) are employed to implement Chapter 3 Hardware Implementation  38 two tasks. The first one is used to scale input voltage to -1.5V~1.5V by a coefficient of 0.25. The second one will bring 1.5v offset, which scale output voltage to 0~3.3V. Depending on input signal from current voltage transducer and anticipating trip current, the coefficient could be modified by change R9 and R10 resistance. Figure 3. 18 gives detailed explanation for current scaling. Anticipating fault current Input of censoring circuit First Op-amp Current sensor 60A(pk) -6V 6V coefficient 1.5V 0 -1.5V offset 3.0V 0 Second Op-amp DSP 931 0 A/D x0.25x0.1 +1.5V  Figure 3. 18 Current scaling for short circuit protection After A/D conversion, a digital offset should be added in the program. Its value is -931/2., herein the number 931 corresponds to 3V where 1024 corresponds to 3.3V in DSP’s A/D conversion. The next step is to figure out absolute value of this signal and compare with threshold 450, which corresponds to 58A. If the input signal is larger than threshold, it means that the short circuit happens in the main circuit and DSP will disable all PWM outputs to shut down the inverter right away. In a commercial IGBT module, a fault signal pin will produce fault signal when IGBT’s internal circuit is exposed to abnormalities such as over-voltage and over-current. This pin can be connected to DSP PdpintA or Pdpint B pin. When fault signal pin carry a falling edge signal, Pdpint will be enabled and put PWM output pins in the high-impedance state, which prevents IGBT module from being damaged by over current and voltage. Chapter 4 Software Implementation  39 4. Chapter 4 Software Implementation Related hardware such as the inverter, driving circuits and DC link has been described in chapter 3. Here, a software setup to implement control algorithm will be posted. All description and discussion of the software are based on TI’s (Texas Instruments) DSP 320F-2407A CPU. A program flow chart will be presented with a detailed explanation of crucial points to achieve the design objective. 4.1 Approaches of SV_PWM Signals: In order to control a three-phase AC induction motor, one needs a three phase inverter with the required DC link and driving circuits, and a digital processor that supplies the PWM signals based on a selected control algorithm. In this chapter, we focus on algorithm and software implementation issues. ˆ A 3-phase AC induction motor control algorithm based on the discussed constant /V Hz  principle and the space vector PWM technique generally contains the following steps: ˆ Configure the timers and compare units to generate symmetric PWM outputs; ˆ Input desired speed, use it as the command speed; ˆ Obtain the magnitude of reference voltage vector outU  (command voltage) based on /V Hz  profile; ˆ Obtain the phase of outU based on command frequency; ˆ Determine which sector outU  is in; ˆ Decompose outU  to obtain T1, T2 and T0; Chapter 4 Software Implementation  40 ˆ Determine the switching pattern or sequence to be used and load the calculated compare values into the corresponding compare registers. The above procedure assumes that the digital signal processor has all the needed timers and compare units with associated PWM outputs. This is true in the case of TMS320F -2407A. The major features of the TMS320F2407A include: ˆ TMS320F-2407A CPU core with 25nS instruction cycle time; ˆ 544 words of on-chip data/program memory, 32K words of on-chip program ROM or Flash EEPROM, 64K words of program, 64Kwords of data and 64K words of I/O space of address reach; ˆ Sixteen multiplexed analog inputs 10-bit ADC core with built-in Sample and Hold (S/H) and fast conversion time (S/H + Conversion): 375 ns ˆ PLL, Watchdog Timer, SCI, SPI, and 41 multiplexed I/O pins; ˆ Event Manager featuring Two general-purpose (GP) timers; a) Three general-purpose up and up/down timers, each with a 16-bit compare unit capable of generating one independent PWM output; b) Pulse-width modulation (PWM) circuits that include space vector PWM circuits, dead-band generation units, and output logic; c) Three 16-bit simple compare units capable of generating 4 independent PWM outputs; d) Three capture units e) Quadrature encoder pulse (QEP) circuit; TMS320F2407A has the necessary features to allow easy implementation of different motor control algorithms and PWM techniques. For the application here, the following set up is needed for the generation of PWM outputs: ˆ GP Timer 1 is configured in continuous-up/down mode to generate symmetric PWM. The three full compare units are configured in PWM mode to generate six complementary PWM outputs. Chapter 4 Software Implementation  41 ˆ Once the above items are completed, all that is needed to generate the required PWM outputs is for the application code to update the compare values based on the discussed principle and PWM techniques. 4.2 Implementation-Open-Loop Speed Control for 3-Phase AC Induction Motor There are two major issues that must be resolved to implement the discussed principle and PWM technique. One is how to generate or represent the revolving reference voltage vector Uout given the command frequency and magnitude of the reference voltage vector. The other is the determination of the switching pattern based on this reference voltage vector. 4.2.1 Overview The major features of this implementation are 16-bit integration to obtain the frequency of the reference voltage vector, frequency-based table look-up magnitude of the reference voltage, frequency-based table look-up SIN and COS functions, projection of the reference voltage from _d q  to _α β axis, update of compare units for PWM channel toggling sequence. GP Timer 1 is used as the time base for PWM output generation with the Full Compare Units. The flow chart of this implementation is illustrated in Figure 4. 1  An ADC channel is used to input the speed command. In this application, the accuracy of speed response is not a concern. Therefore, open-loop speed control is implemented. ˆ The major steps involved in this implementation are: ˆ Integrate the command speed to get the phase, theta, of the reference vector; ˆ Determine theta, and use theta based look-up table to obtain SIN(theta) and COS(theta) and theα and β components of the reference voltage vector; Chapter 4 Software Implementation  42 ˆ Find out the Va, Vb and Vc by Clarke-1 transformation ˆ Calculate commutation duration for every sector ˆ Determine the sector s based on Va, Vb and Vc ˆ Determine the T1 and T2 based on sector and commutation duration ˆ Use table to load the compare registers with appropriate values. The assumptions here is that the timers and compare units and associated compare/PWM outputs have been properly configured to generate the right PWM outputs based on on-line determined compare values. The following explains the details of these steps. Step by Step Explanation  Figure 4. 1 Program flow chart Chapter 4 Software Implementation  43 4.2.2 Initialization module description After a processor reset, the initialization module performs the following tasks: ˆ DSP setup : core, watchdog, clocks, ADC, SCI, general purpose IO, event manager ˆ Variables initializations : default values ˆ Interrupt source selection and enable ˆ Waiting loop The waiting loop implemented corresponds to an interruptible communication between the DSP and a Graphical User Interface. The DSP communicates via its asynchronous serial port to the COM port of a PC. The user can send commands via this RS232 link and update variables and flags from the computer. 4.2.3 Interrupt module description The interrupt module handles the whole V/F algorithm. It is periodically computed according to a fixed PWM (pulse width modulation) period value. The choice of the PWM frequency depends on the motor electrical constant L/R. If the PWM frequency is too low, audible noise can be heard from the motor. Usually, PWM frequencies are in the range of 20 kHz. In this project, a PWM frequency of 10 kHz has been chosen. In Figure 4. 2 , the sampling period T of 100 μs (10kHz) is established by setting the timer period T1PER to 2000 (PWMPRD=2000). This timer is set in up-down count mode and generates a periodical interrupt on T1 underflow event. The goal of the interrupt module is to update the stator voltage reference and to ensure the regulation of rotor mechanical speed. Chapter 4 Software Implementation  44  Figure 4. 2 Software flowchart and timing 4.2.4 Generation of sine and cosine The Park-1 uses the value of the rotor electrical position in order to handle a rotating frame _d q  axis projection in a rotating frame _α β  axis. The electrical position is not directly used in this transforms but the sine and cosine values of this electrical position. To obtain both sine and cosine from the electrical angle, a sine look-up table has been implemented. The table contains 256 words to represent sine values of electrical angles in the range [0;360°]. As a result, the resolution on eθ  is limited to 360 / 256 1.40625o= . eθ = electrical angle / 360° (with eθ  in the range [0;1FFFh]) eθ  varies from 0 to 8191. As only 256 words are available to represent this range, eθ  is divided by 32 and stored into the variable index that will be used to address the lookup table. Chapter 4 Software Implementation  45 The content of the table row pointed by the index is fetched in indirect addressing mode via AR5 auxiliary register (Figure 4. 3). This content coded in Q12 is stored in the variable sin  that will be used in the Park-1 transforms. Note that to get the cosine value of the electrical angle, 90° is added to eθ . This operation corresponds to add 64 (256/4) to the value of index. The result is stored in the variablecos .  Figure 4. 3 Sin, Cos calculation using the sine look-up table 4.2.5 Space vector pulse width modulation The Space Vector Modulation is used to generate the voltages applied to the stator phases. It uses a special scheme to switch the power transistors to generate sinusoidal currents in the stator phases [10]. This switching scheme comes from the translation of the ( , )α β  voltage reference vector into an amount of time of commutation (on/off) for each power transistors. In order to understand some of the assumptions made in the case of the rectified voltage, a brief description of three phase systems is described in the following section. . Chapter 4 Software Implementation  46 4.2.5.1 Expression of the 3 phase voltages (phase to neutral) Previously, the method used to generate a rotating magnetic field was to use three independent voltage sources that were dephased from 120 degrees from one another.   Figure 4. 4 3-phase equilibrium system  In this standard three-phased system (Figure 4. 4), 3 sinusoidal voltages are applied to each of the motor phases to generate the sinusoidal currents. These voltages can be expressed as follows: 2 cos( * )oa eV V tω=   (4-1) ) 3 2*cos(2 πω −= tVV eob   (4-2) 42 cos( * ) 3oc e V V t πω= −   (4-3) In order to calculate the phase to neutral voltages(respectively Van, Vbn, Bcn) from the applied source voltages( respectively Voa, Vob, Voc), the assumption is made that the system is equilibrated is made. This leads to the following equations: 1*on oaV V Z I= +   (4-4) 2*on obV V Z I= +   (4-5) 3*on ocV V Z I= +   (4-6) Chapter 4 Software Implementation  47 then )(**3 321 IIIZVVVV ocoboaon +++++= ; where 0321 =++ III As Von is now expressed by a combination of )*cos(2 tVV eoa ω=  the source voltages the phase to neutral voltage for phase A can be calculated as: ocoboaoaocoboaoaon VVVVVVVVVVan 3/13/13/2))(3/1( ++−=−++=−= the same calculation is made for the three phases leading to: 1/ 3(2 )an ao bo coV V V V= − −   (4-7) 1/ 3(2 )bn bo co aoV V V V= − −   (4-8) 1/ 3(2 )cn co ao boV V V V= − −   (4-9) 4.2.5.2 Application to the static power bridge In the case of a static power bridge, sinusoidal voltage sources are not used. They are replaced by 6 power transistors that act as on/off switches to the rectified DC bus voltage. The goal is to recreate a sinusoidal current in the coils to generate the rotating field. Owing to the inductive nature of the phases, a pseudo sinusoidal current is created by modulating the duty cycle of the power switches. In Figure 4. 5, the power transistors are activated by the signals (a,b,c) and their complemented values.  Figure 4. 5 Power bridge Chapter 4 Software Implementation  48 Only eight combinations of the switches are possible with this configuration (Table 4.1). The applied voltages are referenced to the virtual middle point of rectified voltage.  A B C VAO VBO VCO 0 0 0 -VDC/2 - VDC/2 - VDC/2 0 0 1 - VDC/2 - VDC/2 +VDC/2 0 1 0 -VDC/2 +VDC/2 -VDC/2 0 1 1 -VDC/2 +VDC/2 +VDC/2 1 0 0 +VDC/2 -VDC/2 -VDC/2 1 0 1 +VDC/2 -VDC/2 +VDC/2 1 1 0 +VDC/2 +VDC/2 -VDC/2 1 1 1 +VDC/2 +VDC/2 +VDC/2  Table 4.1 Power bridge output voltages (VAO, VBO, VCO) Because of the equations: )2(3/1 coboaoan VVVV −−= )2(3/1 aocobobn VVVV −−= )2(3/1 boaococn VVVV −−= It is possible to express each phase to neutral voltages, for every combination of the power transistors as listed in Table 4.2. 4.2.5.3 Expression of the stator voltages in the ( ),α β  frame This voltage reference is expressed in the ( ),α β  frame. To make the relationship between the 3 phase voltages (VAN, VBN and VCN) and the voltage reference vector, the 3 phase voltages are also projected in the ( ),α β  frame.   Chapter 4 Software Implementation  49 A B C VAN VBN VCN 0 0 0 0 0 0 0 0 1 - VDC/3 - VDC/3 2VDC/3 0 1 0 - VDC/3 2VDC/3 - VDC/3 0 1 1 -2VDC/3 VDC/3 VDC/3 1 0 0 2VDC/3 - VDC/3 - VDC/3 1 0 1 VDC/3 -2VDC/3 VDC/3 1 1 0 VDC/3 VDC/3 -2VDC/3 1 1 1 0 0 0 Table 4.2 Power bridge output voltages (VAN, VBN, VCN) The expression of the 3 phase voltages in the ( ),α β frame is given by the general Clarke transform equation: 1 11 2 2 2 3 3 30 2 2 AN s BN s CN V V V V V α β ⎡ ⎤ ⎡ ⎤− −⎢ ⎥⎡ ⎤ ⎢ ⎥⎢ ⎥=⎢ ⎥ ⎢ ⎥⎢ ⎥⎣ ⎦ ⎢ ⎥− ⎣ ⎦⎢ ⎥⎣ ⎦   (4-10) Since only 8 combinations are possible for the power switches (Table 4.3), SV α and SV β  can also take only a finite number of values in the ( ),α β frame according to the status of the transistor command signals ( ), ,a b c . )010(2V )101(5V )100(4V)011(3V )001(1V )000(0V)111(7V )110(6V 02 06 01 03 04 05  Figure 4. 6 Stator voltages Chapter 4 Software Implementation  50 The eight voltage vectors defined by the combination of the switches are represented in Figure 4. 6 .  A B C Vα  Vβ  0 0 0 0 0 0V 0 0 1 3 DCV− 3 DCV−  1V 0 1 0 3 DCV− 3 DCV  2V 0 1 1 DCV3 2− 0 3V 1 0 0 DCV3 2  0 4V 1 0 1 3 DCV 3 DCV−  5V 1 1 0 3 DCV 3 DCV  6V 1 1 1 0 0 7V  Table 4.3 Stator voltages Now, given a reference voltage, the following step is to use the 8 above defined vectors to approximate this reference voltage. 4.2.5.4 Projection of the stator reference voltage Vs The method used to approximate the desired stator reference voltage with only eight possible states of switches is to combine adjacent vectors of the reference voltage and to modulate the time of application of each adjacent vector. Chapter 4 Software Implementation  51 )110(6V 44 V T T 6 6 T V T 060 )100(4VX refsV α refsV β  Figure 4. 7 Projection of the reference voltage vector In Figure 4. 7, the reference voltage SrefV  is in the third sector and the application time of each adjacent vector is given by: 4 6 64 4 6 0 sref T T T T TTV V V T T = + +⎧⎪⎨ = +⎪⎩ JG JG JG   (4-11) The determination of the amount of times T4 and T6 is given by simple projections: 06 6 4 4 0 cos(30 ) (60 ) s ref s ref s ref TV V T TV V x T V x tg β α β ⎧ =⎪⎪⎪ = +⎨⎪⎪ =⎪⎩ JG JG   (4-12) Finally, with the ( ),α β  components values of the vectors given in the previous Chapter 4 Software Implementation  52 table, the amount of times of application of each adjacent vector is: 4 6 (3 3 ) 2 3 s ref s ref DC s ref DC TT V V V TT V V α β β ⎧ = −⎪⎪⎨⎪ =⎪⎩   (4-13) The rest of the period is spent in applying the null vector. The variable / DCT V  is named DCinvTV . T is the period of the PWM interrupt and DCV  is the rectified DC voltage. 2DCinvT DC DC T PWMPRDv V V = ⇔   (4-14) For every sector, the commutation duration is calculated. The amount of times of vector application can all be related to the following variables: 3 DCinvT s refX v V β=   (4-15) 3 3 2 2DCinvT s ref DCinvT s ref Y v V v Vβ α= +   (4-16) 3 3 2 2DCinvT s ref DCinvT s ref Z v V v Vβ α= −   (4-17) in the previous example for sector 1, T4 = -2Z and T6 =2X. In order to know which of the above variable apply, the knowledge of the sector in which the reference voltage vector is, is needed. To determine this sector, a simple approach is to calculate the projections Ra, Rb and Rc of the reference voltage vector in the ( , , )a b c plane. These projections are then compared to 0. The projections Ra, Rb and Rc are given by the Clarke-1 transform as follow: a s refR v β=   (4-18) 1 ( 3 ) 2b s ref s ref R v vα β= −   (4-19) 1 ( 3 ) 2c s ref s ref R v vα β= − −   (4-20) Chapter 4 Software Implementation  53 The complete algorithm performed by the Space Vector Module is given in the next section. 4.2.5.5 Space vector algorithm Now that the meaning of the variables has been given, the order in which the steps are processed during the PWM interrupt is given. The first step is to determine in which sector the voltage vector defined by Vs refα . Vs refβ is found. The following few code lines give the sector as output:    Sector determination    IF 0>aR   THEN A: =1,  ELSE A: =0    IF 0>bR   THEN B: =1,  ELSE B: =0    IF 0>cR   THEN C: =1,  ELSE C: =0    P = A+2B+4C Then, finding corresponding Sector number based on Table 4.4 P 1 2 3 4 5 6 Sector 2 6 1 4 3 5  Table 4.4 Relationship between sector and P The second step is to calculate and saturate the duration of the two P boundary vectors application as shown below: CASE P OF 1 1t  =Z  2t  =Y 2 1t  =Y  2t  =-X 3 1t  =-Z  2t  =X 4 1t  =-X  2t  =Z Chapter 4 Software Implementation  54 5 1t  =X  2t  =-Y 6 1t  =-Y  2t  =-Z    End times calculation Saturations, which means that the total time of vector1’s interval and vector2’s interval is larger than the PWM period IF PWMPRDtt >+ 21  then  1 1 1 2 SAT PWMPRDt t t t = +  (4-21)  2 2 1 2 SAT PWMPRDt t t t = +  (4-22) The third step is to compute the three necessary duty cycles. This is shown below: 1 2 1 2 2aon bon aon con bon PWMPRD t tt t t t t t t − −⎧ =⎪⎪ = +⎨⎪ = +⎪⎩   (4-23) The last step is to assign the right duty cycle (txon) to the right motor phase (in other words, to the right CMPRx) according to the sector. The table below depicts this determination.    Sector Phase 2 6 1 4 3 5 CMPR1 tbon taon taon tcon tcon tbon CMPR2 taon tcon tbon tbon taon tcon CMPR3 tcon tbon tcon taon tbon taon  Table 4.5 Assigning the right duty cycle to the right motor phase After the duty cycle has been determined, the state sequence has to be determined by Table 4.6[11].  Chapter 4 Software Implementation  55 Sector Initial State 2nd State 3rd State Final State 1 V7 V6 V2 V0 2 V7 V5 V4 V0 3 V7 V6 V4 V0 4 V7 V3 V1 V0 5 V7 V3 V2 V0 6 V7 V5 V1 V0 1 V0 V2 V6 V7 2 V0 V4 V5 V7 3 V0 V4 V6 V7 4 V0 V1 V3 V7 5 V0 V2 V3 V7 6 V0 V1 V5 V7  Table 4.6 State sequence Based on Table 4.5 and Table 4.6, the PWM patterns in Sector 1 are drawn in Figure 4. 8. The corresponding PWM output in other sectors can be figured out by the same method, but will be omitted here  Figure 4. 8 Sector 1 PWM patterns and duty cycles Chapter 4 Software Implementation  56 4.3 Voltage Per Hertz Algorithm In order to compensate the flux in the low speed period, the voltage applied to the stator needs to be modified based on Figure 4. 9. In the software realization, a look-up table is used to calculate the corresponding phase voltage of motor’s stator. The detailed method is depicted as follows. The output of a three phase diode bridge rectifier is 310V. The corresponding maximum output of connecting inverter is: V V V DCpkphase 2.1793 310 3_ ===  Figure 4. 9 Voltage versus frequency This value is equal to the motor’s phase rating voltage, which is 180V pk_pk. Under this condition, the motor stator phase voltage change in the electrical speed of 60HZ. As mentioned above, the number 8192 expresses electrical angle of 3600.Thanks to fix PWM period, the number, called θΔ ,  which is counted in this time span can be used to express corresponding electrical speed. 8192 8192 1 49.15 1/ 60 10000sw T X T θΔ = = =  (4-24) where T is the period of stator’s voltage at rating frequency of 60Hz and swT  is the period of PWM’s switching frequency. Chapter 4 Software Implementation  57 It is obvious that θΔ  of 49.15 will present 60Hz in the DSP’s program. For convenience, an integer number, 50, is applied to express 60Hz in the software. Resolution is 60/50=1.2Hz. It is convenient to achieve high resolution by enlarging times of 4096 to 3 or 4. The next step is to figure out V/Hz constant by following formula: _ 180tan 3.5 _ 50 Vphase rateCons t f rate = = =  (4-25) During the accelerating period, the stator’s phase voltage can be calculated by given frequency timing Constant derived above. In the starting period, V/H=constant is not valid. Compensation will be applied based on practical test. If the given frequency is larger than the rating frequency, stator’s phase voltage becomes saturated, and its valve keeps constant to rating voltage. Depending on the above analysis, a look-up table is built to figure out command voltage based on different input command frequency (speed) signal in the software application. The whole program is written by assembly language based on the TI’s user guide. The detailed parameters are chosen depending on the practical stage revolve. Figure 4. 10 illustrates voltage waveform in a complete process of locating target position. The technique which applied in the starting phase is the same as what have been discussed above. In decelerating period, a sensor which is mounted on the steel bracket is used to detect   reflection material attached on the bottom of revolve bottom. While a reflecting signal is detected by the sensor, a binary stop-code is read by DSP through its A/D conversion units. Then DSP forces the motor to decelerate to a slow speed by reducing the command frequency automatically. The corresponding slew-rate is easy to adjust in the software by requests. Meanwhile, revolve becomes creeping with a speed of Slow. No sooner is “Stop Index” signal caught by the sensor than the revolve stop. It is obvious that an overshot exists in open loop control. However, because the big friction of revolve, the total weight of revolve, scenery and actors is 4000kg, TΔ  is so small that Chapter 4 Software Implementation  58 the corresponding displacement error can be neglected in this application.  Figure 4. 10 Speed waveform of accurate position control 4.4 Frequency Command Module In order to obtain command frequency signal, the hardware interface which is drawn in Figure 4. 11 is built. The output of a potentiometer connects to a DSP’s A/D pin directly, which translates analog signals into digital signals which are standard in DSP’s programs. The Figure 4. 12 represents the correspondence between the command frequency signal and its binary representations. The 0-3.3v analog input presents relevant -50 to +50 digital values in DSP, which will infer -60 Hz to +60Hz command frequency in physical value.  Figure 4. 11 Command frequency sensing hardware Chapter 4 Software Implementation  59   Figure 4. 12 Command frequency scale translation 4.5 Deadtime Setting Because any real power electronic devices do not turn on or off instantaneously, it is necessary to include a protection time, called the deadtime, to avoid cross conduction when two switching devices are in the same leg. In the EVA of the LF2407 DSP, a programmable dead-band unit DBTCONA is built-in to add a deadtime into the PWM signals. It has been found that the deadtime causes a reduction in the fundamental component of the output voltage and introduces low order harmonics [12]. In variable frequency drive systems the magnitude drop of the voltage subsequently leads to a reduction of the output electromagnetic torque. Therefore the deadtime should not be set excessively long compared with the total turn-off time of the IGBT devices. There are numerous papers discussing how to make deadtime compensation. However, in this application, efficiency is not crucial consideration in a few operating requests. In the software, the deadtime is set to 1.7μs. 4.6 Look-Up Tables Look-up tables are widely used in the program which provides an easy way to implement functions such as sin and cos calculation. V_H_period table is used to modify Chapter 4 Software Implementation  60 slew-rate of acceleration and deceleration speed. V_H_vol contains voltage compensation in motor’s starting phase. This compensation value may need to adjust based on the different Load. A brief introduction for all the look-up tables used in the program is attached for reference.  Name No. of Entries Format Range Step size /entry Description sin_entry_ 256 Q12 0 – 360 º 1.44 º Sine(θ) Cos(θ) V_H_period_ 50 Unsigned integer 6-20 Sec Slew-rate setting The interval time To increase one unit freq. V_H_vol_ 50 Q12 0-180V V/Hz Desired voltage value  Table 4.7 Look-up tables used in the program 4.7 Execution Time  Figure 4. 13 Execution time of V/Hz control routine Figure 4. 13 illustrates the execution time of control routine. The Open loop V/Hz Chapter 4 Software Implementation  61 control routine takes an average of 80us for execution. The amount of program memory used for the whole program is lower than 1Kword. Chapter 5 Experimental Results  62 5. Chapter 5 Experimental Results 5.1 Noise Studies of Gate Signals As mentioned in Chapter 3, a clean and noise-free gate signal is vital to confirm that IGBTs can turn on and off as they are required. In this application, Space Vector PWM (SVP) technique is employed to generate gate signals for the inverter. The DC bus bar is supplied from a diode bridge rectifier, and a variable transformer is used to produce different AC voltage inputs to the rectifier. Thus variable DC bus voltages are attained. -2 -1 0 1 2 3 x 10-4 -20 -10 0 10 20 Gate signal, Vdc-bus=0V Time(s) V G E( v)  lo w  s id e -2 -1 0 1 2 3 x 10-4 -20 -10 0 10 20 Gate signal, Vdc-bus=70V Time(s) V G E( v)  lo w  s id e  Figure 5. 1 Gate signal, low side with different DC bus link voltage The motor which is coupled to stage revolve is connected as the load of the inverter. No obvious /dv dt  noise is observed from the gate signal GEV  (Figure 5. 1) while the DC bus voltage is 0 V. Then increasing bus voltage to 70V, the waveform is still smooth except small oscillation in the rising period from 0V to 12V. The reason to apply SVP is that this technique is efficient in removing harmonics at the high Chapter 5 Experimental Results  63 modulation index compared with the sinusoidal PWM technique. In Figure 5. 2, the phase voltage command contains the triple order harmonics that are generate by SVP However, the triple order harmonics do not appear in the line voltage and the reference voltage becomes a perfect sinusoidal waveform, which results in a perfect motor performance. -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 -2 -1 0 1 2 Phase voltage signal, DSP output Time(s) V Ph as e( V ) -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 -4 -2 0 2 4 Line voltage signal, DSP output Time(s) V Li ne (V )  Figure 5. 2 Phase and line voltage reference waveforms with SVP 5.2 Analysis of the Running Revolve In the final test, 1500kg scenery is located on the corner of the stage as the full unbalanced load and the total weight including revolve is 4000kg, as shown in Figure 5. 3. The gate resistor is 180ohms. Manual and automatic starting processes are separately tested on inverter prototype. The maximum speed is 42 seconds per revolution (1.4rpm), Chapter 5 Experimental Results  64 and the total acceleration time is 30 second. The maximum speed and acceleration satisfy the safety and comfortable requirements which are analyzed in chapter 2. The actor standing on stage does not have any uncomfortable feeling in the whole process. By a knob mounted on control box, the stage speed can be adjusted continuously and the revolving stage can be controlled to move in both clockwise/ counterclockwise direction. Based on the system tested, the current curves of the induction motor are drawn in Figure 5. 4. In the initial period, because the rotor stays in a standstill, the starting current jumps to 60 Amps (peak to peak value) which is approximately equal to the current value in the Blocked-rotor test. Then the current value decreases with the increase of rotor speed and reaches to rated value 8.6 Amps (RMS) when the rotor speeds to 1.4 rpm.  Figure 5. 3 The tested stage with 1500kg unbalanced loads  Chapter 5 Experimental Results  65 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 -30 -20 -10 0 10 20 30 Starting current, Variable freq=2.4Hz, VDC=150V, Load=1500kg Time(s) C ur re nt (A ) -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 -10 -5 0 5 10  Current, Variable freq=28Hz, VDC=150V, Load=1500kg Time(s) C ur re nt (A )  Figure 5. 4 Motor current curves under different running conditions From chapter 1, based on the induction motor’s equivalent circuit, the three phase power across air gap can be written as 23 rg r RP I s =   (5-1) the mechanical torque developed mechT  per phase is given by 2 2 2 (1 )mech mech mech RP T I s s ω= = −   (5-2) Chapter 5 Experimental Results  66 the mechanical speed mechω  is related to the synchronous speed by (1 )mech synsω ω= −   (5-3) from Equation (5-1), (5-2) and (5-3), for three phase induction motor, 2 2 23mech syn RT I s ω =   (5-4) equation (5-4) can be written as 2 2 23mech syn RT I sω=   (5-5) In Figure 5. 4, the starting current is equal to 2 25 / (2) 17.7I sqrt A= = ; 1s = ; 4* * /syn pi f pω = ; 4p =  and 2 0.422R =  ohms. Substituting these parameters into Equation (5-4), the starting torque is attained 2 0.422( ) 3 17.7 52.5 . =38.3 . 3.14*2.4mech T start N m Lb ft= × × = In the practical measurement, the starting torque is 9lb.ft. The difference between of calculation and measuring result comes from a couple of reasons. First, the measure instrument is a regular scale with a piece of 1ft long wood instead of a sophisticated meter, which will bring a big measuring error. Another reason is that it is hard to locate the suitable point to measure the biggest starting torque because the torque value decreases dramatically with motion of the rotor. Figure 5. 5 shows the gate signals, GEV , at 150 V and 34 V DC bus link respectively. There are not obvious spikes on both curves. Meanwhile, during the rising period from 0v to 10v, there is quite small voltage drop on the gate waveform. However, with the objection of the layout of the prototype, above results are attained with a big gate resistor (180Ω), which will bring remarkable switching loss and lead to low power efficiency in the inverter. A detailed discussion on reasons and improvement methods of this problem will be introduced in the next section. Chapter 5 Experimental Results  67 -3 -2 -1 0 1 2 3 x 10 -4 -20 -10 0 10 20 Gate signal, VDC=150V, Load=1500kg Time(s) V G E( v)  lo w  s id e -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 x 10-4 -20 -10 0 10 20  Gate signal, VDC=34V, Load=1500kg Time(s) V G E( v)  lo w  s id e  Figure 5. 5 Gate signals 5.3 Gate Resistor Studies with Different Drives An ideal gate-to-source voltage waveform in Figure 5. 6 determines the charge required for the gate-to-emitter capacitance, and the charge required for the gate-to-collector capacitance. Since a constant current is supplied to the gate, the horizontal time scale is directly proportional to the charge supplied to the gate. With a suitable scaling factor, therefore, this waveform is a plot of gate voltage versus charge. Form t0 to t1, the gate-to-emitter (GTE) capacitance is charging. From t1 to t2, the gate-to-collector (GTC) capacitance is charging. The collector voltage excursion during the period t1 to t1 is relatively large, and hence the total drive charge is typically higher for the GTC capacitance than for the GTE capacitance [13]. At t2, the collector voltage falls to a value equal to IC x RCE, and the IGBT now comes out of the “active” region of operation, which means it has reached “saturation”. The gate voltage is now no longer constrained by the transfer characteristic of the IGBT to relate to the collector current, and is free to increase. This it does, until time t3, when the gate voltage becomes equal to the voltage “behind” the gate circuit current source. The total charge at time t2 is the charge required to switch the given voltage VCC and current IC. The additional charge Chapter 5 Experimental Results  68 consumed after time t2 does not represent “switching” charge; it is simply the excess charge which be delivered by the drive circuit because the amplitude of the applied gate drive voltage normally will be higher than the bare minimum required to accomplish switching  Figure 5. 6 Basic gate charge waveforms However, in the practical test, a big voltage drop is observed from t1 to t2 with the calculated gate resistance from chapter 3. Under the condition that gate resistors are chosen as 15ohms, 23ohms and 51ohms, VGE waveforms show obvious oscillation when the GTC capacitors are charged. Meanwhile, motor give out a harsh sound. This oscillation becomes inconspicuous with increase of gate resistor. In the prototype, a 180 ohms resistor is used to be a gate resistor and motor work smoothly. Selecting the proper series gate resistor series gate resistor for IGBT gate drive is very important. The value of the gate resistor has a significant impact on the dynamic performance of the IGBT. During turn off of the free wheeling diode across an IGBT, the /dv dt  applied to the IGBT and its CTG capacitance can cause a current to flow in the gate circuit. If this current is large enough, the voltage developed across the gate resistor can cause the IGBT to turn on. Therefore, smaller gate resistances offer enhanced ruggedness(rejection of /dv dt  turn on)[14]. But, they also provide fewer margins for noise and lead to oscillation problems in conjunction with the GTE capacitance and any parasitic inductance in the gate drive wiring. The practical implementation of prototype is depicted in Figure 5. 7 . Because signals from drive output to IGBT’s gate are transferred Chapter 5 Experimental Results  69 by twisted pair, the parasitic stray inductance inevitably induces big voltage drop with high di/dt accompanying with small gate resistances. Thus the oscillation occurs.  Figure 5. 7 The practical realization of the prototype In order to make further research of oscillation in VGE, several methods are chosen to set up drive circuits. The corresponding gate-emitter voltage waveforms are drawn to analyze the reasons and solution for diminishing oscillation. 5.3.1 Gate signal with flyback transformer as power supplies As mentioned in chapter 3, a dc-dc converter (VASD1-SIP-S5-D15-SIP) is used to supply ±15V isolated DC source for the drive chip. From the datasheet of VASD1, note that the highest isolation voltage between input and output is 1kV. From theoretical calculation, this converter has enough abilities to prevent noise being produced from IGBT switching on and off state from coupling back to its input of a 5V DC source, which shares the same ground with DSP. However, 1kV isolation only has a small margin to get rid of possible coupling noise. In some serious situation, such as high dv/dt, the isolation might be impaired and noise goes back to the input power, thus inducing noise signal in DSP. This noise signal becomes significant after it is enlarged by drive circuit and makes oscillation in gate voltage more serious. To eliminate this possibility, a flyback transformer (Figure 5. 8) which has 2kV isolation voltage is used to replace the converter. Chapter 5 Experimental Results  70  Figure 5. 8 The schematic diagram of the flyback transformer The gate signal curves are drawn in Figure 5. 9. With a 15 Ω gate resistor, the oscillation is still obvious in the gate signal under both 30V and 38V DC bus voltage. In order to fully remove the coupling noise from drive’s power supply, a group of batteries, which has isolating floating ground, is used to provide necessary positive and negative voltage to the drive. Chapter 5 Experimental Results  71 4.8 4.9 5 5.1 5.2 5.3 5.4 x 10 -5 -20 -15 -10 -5 0 5 10 15 Gate signal, VDC=38V, RG=15Ω Time(s) V G E( v)  lo w  s id e 4.8 4.9 5 5.1 5.2 5.3 5.4 x 10-5 -15 -10 -5 0 5 10 15  Gate signal, VDC=30V, RG=15Ω Time(s) V G E( v)  lo w  s id e 4.8 4.9 5 5.1 5.2 5.3 5.4 x 10-5 -5 0 5 10 15 20 25 30 35 Collector-Emitter signal, VDC=30V, RG=15Ω Time(s) V C E( V )  Figure 5. 9 Gate signal with flyback transformer as power source of the drive 5.3.2 Gate signals with battery as power supplies   Figure 5. 10 A group of batteries as power supply for IGBT drives Three batteries are applied to supply positive 18V and negative 9V DC power to an Chapter 5 Experimental Results  72 IGBT drive chip (Figure 5. 10)Figure 5. 10. In this topology, the floating common point is absolutely isolated from other disturbance sources. With a 15 Ω gate resistor, distinct oscillation is still observed in the gate signal, shown in Figure 5. 11. There is no notable amelioration while the gate resistance is increased to 51Ω. -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 x 10-6 -20 0 20 Gate signal, RG=51Ω , VDC=0V, RL-Load Time(s) V G E( v)  lo w  s id e -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 x 10-6 -20 0 20  Gate signal, RG=15Ω , VDC=60V, RL-Load Time(s) V G E( v)  lo w  s id e -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 x 10-6 -20 0 20  Gate signal, RG=51Ω , VDC=100V, RL-Load Time(s) V G E( v)  lo w  s id e  Figure 5. 11 Gate signal with batteries as power source of the drive 5.3.3 IGBT’s gate signal with commercial drives   Figure 5. 12 The commercial drive Chapter 5 Experimental Results  73 In order to find precise reasons accounting for oscillation in gate signal, a commercial drive, shown in Figure 5. 12. Its relevant parameters are given in Table 5.1. This prototype board has 2500VRMS isolation for control power and signals. To confirm the drive has an enough current to drive IGBTS, two types of drives, 1.5A and 5A, are chosen to make a test. The testing results are drawn in Figure 5. 13. Here, internal gate resistance 23 Ω is chosen as gate resistance. One test adds a 17 W external resistor as total gate resistance. 150, 100, 70 V DC bus voltages are used as input of the inverter respectably. There is not heart-stirring improvement in oscillation issue of gate signal waveform. 5A drive has a very similar result. -3 -2 -1 0 1 2 3 x 10-6 -10 -5 0 5 10 15 Gate signal, RG=41Ω , VDC=150V, RL-Load Time(s) V G E( v)  h ig h si de -3 -2 -1 0 1 2 3 x 10 -6 -10 -5 0 5 10 15 20  Gate signal, RG=23Ω , VDC=150V, RL-Load Time(s) V G E( v)  h ig h si de -5 0 5 x 10-6 -10 -5 0 5 10 15  Gate signal, RG=23Ω , VDC=100V, RL-Load Time(s) V G E( v)  lo w  s id e -3 -2 -1 0 1 2 3 x 10 -6 -10 -5 0 5 10 15  Output of drive, RG=23Ω , VDC=70V,driver with 5A peak output current Time(s) V G E( v)  lo w  s id e  Figure 5. 13 The gate signals with commercial drives   Chapter 5 Experimental Results  74 Gate Driver Peak Drive current Minimum RG Typical Application DC/DC Converter M57159L-01 +/-1.5A 4.2Ω Up to 100A VLA106-15424 VLA503-01 +/-5A 2.0Ω Up to 400A VLA106-15424  Table 5. 1 Features of the BG2B universal gate drive 5.3.4 Improved drive circuits and corresponding gate signals From above tests, it is obvious that the DC-DC converters in original prototype can provide fully isolated control power for IGBT driving channels. Meanwhile, the drive’s output current is not a reason for gate signal oscillation. The possible cause may come from imperfect layout, especially the long wires. In Figure 5. 14, a PCB board includes six GB2B universal gate drives is connected to IGBT power module. A DSP board is embedded into this PCB board to prevent the ribbon cable, which is used to transfer PWM signals to drives, from being infected noise. This time a 10 Ω resistance is chosen as gate resistor. The gate signal (Figure 5. 15) has substantial improvement. Under the 180V DC bus voltage, the voltage drop in oscillation is not low than 7 volt, which is essential to make motors work without harsh noise.  Figure 5. 14 DSP embedded in PCB board with commercial drives Chapter 5 Experimental Results  75 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 x 10-5 -20 -15 -10 -5 0 5 10 15 20 Gate signal, Vdc-bus=180V, RG=10Ω Time(s) V G E( v)   Figure 5. 15 The gate signal curve with improved hardware layout 5.4 Collector-Emitter Surge Voltage Because of a layout defect of the prototype, there are wires between bulk capacitors and DC bus bar; herein the stray inductance induces very high surge voltages in the process of charging and discharging bulk capacitors. As seen in Figure 5. 16 In order to get rid of the effect of stray inductance which comes from the wire between DC bus bar and IGBT’s collector, a commercial power module is replaced the prototype power module. Other components keep as same as the former test. The result is drawn in Figure 5. 15Figure 5. 16 too. We find that the surge becomes bigger than former one. The reason is that commercial power module’s built-in capacitance might induce resonance in the circuit loop. Chapter 5 Experimental Results  76 -2 -1 0 1 2 3 4 x 10 -4 -15 -10 -5 0 5 10 15 Gate signal, Vdc-bus=34.5V, RG=180Ω , Prototype Time(s) V G E( v)  -2 -1 0 1 2 3 4 x 10-4 0 20 40 60 80 100 120 Collecter-emitter signal, Vdc-bus=34.5V, RG=180Ω , Prototype Time(s) V C E( v) -5 0 5 x 10 -4 -15 -10 -5 0 5 10 15 Gate signal, Vdc-bus=34.5V, RG=180Ω , Commercial IGBT Time(s) V G E( v)  -5 0 5 x 10-4 0 50 100 150 200 250 300 Collecter-emitter signal, Vdc-bus=34.5V, RG=180Ω , Commercial IGBT Time(s) V C E( v)  Figure 5. 16 Gate and Collector-emitter voltage curves To remove surge voltage and ensure that the IGBTs can run with the rating voltage under the condition that maximum input DC bus voltage is 300V, a new layout for bulk capacitors and DC bus bar is shown in Figure 5. 17. Capacitor’s positive and negative electrodes are directly mounted to DC bus bar’s positive and negative sides correspondingly. There are not extra wires between them. The collector-emitter voltage of an IGBT in new layout is shown in Figure 5. 18. Surge voltages disappear in the VCE curve. Chapter 5 Experimental Results  77   Figure 5. 17 The layout of capacitors be mounted on bus bar -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 x 10-4 -50 0 50 100 150 200 Collector-emitter signal, Vdc-bus=180, RG=10Ω Time(s) V C E( v)  Figure 5. 18 The Collector-Emitter voltage curve with the new layout 5.5 Deadtime Analysis  As mentioned in chapter 4, deadtime is helpful in avoiding a cross conduction of two switching devices which are in the same leg; However, the introduction of the dead time causes a reduction in the fundamental component of the output voltage and introduces low order harmonics which are not intrinsically present in the ideal modulated Chapter 5 Experimental Results  78 waveforms. In variable speed drive, the reduction of fundamental voltage causes a reduction in output torque. There are a lot of papers discussing how to compensate the negative effect of deadtime in some sophisticated variable speed motor drive applications. In the prototype, because of the stage’s running specialties which are less than five minutes ruining time and   little power consumption, no special compensation methods are used except for limiting deadtime in a small value to make its negative effect as obscure as possible. Although there is reduction in torque output, drive can provide enough starting torque for the stage revolve. Figure 5. 19 and Figure 5. 20 show current waveforms at different deadtime settings. It is easy to conclude that the current distortion vanish at lower frequency with deadtime 1.4μs compared with another setting with 2μs deadtime. At the same time, one cross conduction between two switching devices which are in the same leg has been avoided. The reason for obvious current distortion at low frequency is that the ratio of deadtime to IGBT’s Ton time is big at low frequency, which corresponds to low voltage and small duty of PWM, and becomes small at high frequency, which corresponds to high voltage and big duty of PWM in V/F control. -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 -10 0 10 Current waveform @18.1Hz, Load=1750pounds, deadtime=2μs Time(s) C ur re nt (A ) -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 -10 0 10 Current waveform @15Hz, Load=1750pounds, deadtime=2μs Time(s) C ur re nt (A ) -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 -10 0 10 Current waveform @14Hz, Load=1750pounds, deadtime=2μs Time(s) C ur re nt (A ) -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 -10 0 10 Current waveform @9.8Hz, Load=1750pounds, deadtime=2μs Time(s) C ur re nt (A )  Figure 5. 19 Current waveforms with different command frequency, deadtime=2μs Chapter 5 Experimental Results  79 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 -10 0 10 Current waveform @14Hz, Load=1750pounds, deadtime=1.4μs Time(s) C ur re nt (A ) -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 -10 0 10 Current waveform @9.8Hz, Load=1750pounds, deadtime=1.4μs Time(s) C ur re nt (A ) -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 -20 0 20 Current waveform @6Hz, Load=1750pounds, deadtime=1.4μs Time(s) C ur re nt (A )  Figure 5. 20 Current waveforms with different command frequency, deadtime=1.4μs  Chapter 6 Conclusion and Future Work  80 6. Chapter 6 Conclusion and Future Work 6.1 Conclusion In this thesis, the development of a DSP-controlled variable-speed drive has been considered. A number of issues regarding the implementation of machine drive have been investigated. A brief conclusion opens in this section by summarizing the major concluding remarks obtained in the early chapters. In chapter 2, a safety area of stage revolve’s speed and acceleration is presented after a theoretical analysis of mechanical system. After thorough studies control requests from operators, the open-loop voltage per Hz topology is chosen as the implementation method for the variable speed. Meanwhile, a summary introduction of induction motor’s equivalent circuit and torque-speed characteristics are addressed. The next chapter introduces the method to choose main components for the motor drive. Numerous discussions have been addressed on how to figure out the suitable gate resistance for IGBT module, which is the key factor to make this drive work efficiently and reliably. Then the current detection circuit is introduced for over current protection of the IGBT power module and upgrading Volt/Hz to other sophisticated control methods, such as vector control, in the future. In chapter 4, a detailed description of realization of Space Vector PWM technique and volt/Hz control principles of induction motor drives on Ti’s DSP 320F-2407A. In order to limit the highest acceleration and speed of stage revolve, a look-up table is introduced in the software, and so does the low frequency voltage compensation. Although the greatest efforts have been made in components selection and schematic diagram design of the drive, a lot of deficiency still exists in the practical Chapter 6 Conclusion and Future Work  81 implementation. Much of this comes from layout of the hardware. In chapter 5, numerous pages are devoted to the oscillation problems in gate control signals. After a series of tests, we have concluded that the gate drive layout is critical to avoid potential oscillations, slow rise of gate voltage, loss of noise immunity, or reduction in efficiency of the gate protection circuitry. If we did not take discrete components to set up our own inverter, the above problems would have not been found with commercial products. Meanwhile, the experience from this implementation will give some guidelines to future work of IGBT related motor drives. 6.2 Future Work Due to the special operating schedule of the theatre, a wealth of options of future practical work exists. One consideration is to implement position sensor circuits because it is crucial in open loop accurate position control. According to analysis in chapter 4, in practical realization, the open loop control with a number of position sensors could satisfy requests of accurate position control with more simple/reliable software and hardware, affordable cost being compared with complicated close-loop position control. An additional contemplation is the improvement of layout by introduction of a PCB board. Based on the similar layout of commercial product drive (BG2B), a big PCB board includes six IGBT drives of the inverter; one IGBT drive of the breaker and I/O interface to connect with DSP’s I/O output directly. In addition, the drive’s output I/O interface which can be connected to power module directly should have enough ampere capacity of 2A. An interesting subject for future work encompasses connection of bulk capacitors and the DC bus bar. A pair of copper bus bar is an option for surge voltage removal. A further solution is to embed the DC bus bar into the big PCB board. Finally, a USB interface of the control box will be helpful in simplifying operation of position control. Operators input new position command through a laptop USB interface conveniently. References  82 References [1] Austin Hughes, Electric Motors and Drives, second edition, Nwenes, An imprint of Butterworth-Heinemann Ltd, Oxford, 1993, pp. 52 [2] H. B. Ertan, M. Y. Uctug, R. Colyer, and A. Consoli, Modern Electrical Drives, Kluwer Academic Publishers, Boston, 2000 [3] Y. Li, “Designing and Implementing A DSP Based Variable-Speed Drive for Theatre Stage System”, M. Sc. Thesis, Electrical & Computer Engineering Department, The University of British Columbia, BC, Canada, 2007 [4] Bimal K. Bose, Modern Power Electronics and AC Drives, Prentice-Hall, Inc.2003 [5] P. Wood, M. Battello, N. Keskar, and A. Guerra, Plug N Drive Application Overview, International Rectifier, 2002. [6] E. R. Motto, Hybrid Circuits Simplify IGBT Module Gate Drive, Powerex Inc., 1999. [7] Data Sheet, PD60232, IR22381Q/IR21381Q, International Rectifier, 2005. [8] Data Sheet, 2.0 Amp Output Current IGBT Gate Drive Optocoupler, Agilent Technologies, Inc., 2003 [9] Power flex, Dynamic Braking Resistor Calculator, Rockwell Automation, 2003 [10] Erwan Simon, Application report, Implementation of a Speed Field Oriented Control of 3-phase PMSM Motor using TMS320F240, Texas Instruments Incorporated, 1999 [11] Paul C, Krause, Oleg Wasynczuk, Scott D. Sudhoff , Analysis of Electric Machinery and Drive Systems, IEEE PRESS, 2002 [12] V. M. Cardenas, S. Horta, R. Echavarria, "Elimination of dead time effects in three phase inverters," in Proc. IEEE International Power Electronics Congress, vol. , no. , Oct. 1996, pp.258-262. [13] Application Note, Use Gate Charge to Design the Gate Drive Circuit for Power MOSFETs and IGBTs, International rectifier, see ttp://www.irf.com/technical-info/appnotes/an-944.pdf [14] Application Note, How to use IGBT Modules, Powerex Inc, 1999 Appendix A Estimation of Moment of Inertia of the Stage  83 Appendix A Estimation of Moment of Inertia of the Stage The moment of inertia of a complex structure, such as the stage, containing steel frame and wood surface can in practice only be determined by approximation. Here an estimation of the moment of inertia of the stage is given for simulation. The moment of inertia of the stage can be calculated as J=MR2/2; with M being the mass of the stage, R being the radius of the stage. The stage is a steel-framed wood-covered structure. The estimation is given by the table below. Item Calculation Note Radius of the stage mR 115.4 2 23.8 ==  diameter of the stage is 27-foot. Mass of the wood 1500M kg= Mass of the steel frame, scene setup and actors on the stage 2500kg Total mass of the stage 4000kg Total moment of inertia of the stage 234000kg m⋅ Table a.1 Calculation of the moment of inertia of the stage  Appendix B Induction Motor Parameter Estimation  84 Appendix B Induction Motor Parameter Estimation Parameters on the nameplate of the machine are given in Table b.1. Variable Value Rated output 3 hp (2.24kW) Voltage 230 V Full load current  8.2 A Frequency 60 Hz Speed 1760 rpm Power factor 0.77 Efficiency 89.5% Table b.1 Nameplate data of the induction machine Some tests have been carried out to estimate the detailed parameters of the machine. Tests include dc test, no load test and block rotor test. Testing results and parameter derivation are given below: 1) DC Test: Ω== 5.02/1sr  2) No-load Test V V V NLllas 47.1183 2.205 3 , === − , AI NL 577.3=  VAS NL 66.1257= , WPNL 108= ,  VARQNL 1253= ,  Pf = 0.086  Ω=×== 64.32577.33 1253 3 22NL NL NL I QX 3) Blocked-rotor Test Appendix B Induction Motor Parameter Estimation  85 3.1) V V V NLllas 37.163 35.28 3 , === − , AI BR 0015.4=  Ω=×== 166.143 56 3 22BR BR BR I PR  Ω=−=−= 92.3166.1)0015.4/37.16()/( 2222 BRBRasBR RIVX  Ω=== 96.1 2 ' BR lrls XXX 3.2) V V V NLllas 31.223 65.38 3 , === − , AI BR 995.5=  Ω=×== 196.1995.53 129 3 22BR BR BR I PR   Ω=−=−= 524.3196.1)995.5/31.22()/( 2222 BRBRasBR RIVX  Ω=== 762.1 2 ' BR lrls XXX 3.3) V V V NLllas 15.283 75.48 3 , === − , AI BR 0295.8=  Ω=×== 189.10295.83 230 3 22BR BR BR I PR  Ω=−=−= 298.3189.1)0295.8/15.28()/( 2222 BRBRasBR RIVX  Ω=== 649.1 2 ' BR lrls XXX  3.4) Average value:  Ω== 79.1'lrls XX  Ω=−=−= 85.3079.164.32lsNLM XXX Appendix B Induction Motor Parameter Estimation  86  4) Estimate 'rr  from the torque-speed curve VV XXr XV as Mlss M thas 5.1258.132945.03 230 64.325.0 85.30 )( 2222 , =×=+ = ++ = 6987.14466.0 )( )( ,, jXXjr jXrjXjXr Mlss lssM thlsths +=++ +=+ 19.12 )()/( /3 2' , 2' , '2 , =+++= lrthlsrths r syn thas e XXsrr srVT ω , find Ω= 422.0 ' rr Appendix C Clarke and Park Transformation  87 Appendix C Clarke and Park Transformation Clarke and Park transforms are used in high performance drive architectures related to variable speed motor control Functions to implement Clarke and Park transforms will be explored as follows. Through the use of the Clarke transform, the real (Ids) and imaginary (Iqs) currents can be identified. The Park transform can be used to realize the transformation of the Ids and the Iqs currents from the stationary to the moving reference frame and control the spatial relationship between the stator vector current and rotor flux vector. Clarke transformation  Figure 1 Stator current in the stationary reference frame and its relationship with a,b,and c stationary reference frame The Clarke transform uses three-phase currents ia, ib and ic to calculate currents in the two-phase orthogonal stator axis: iα and iβ. From Figure.1, the mathematical Clarke transform can be written as 2 1 ( ) 3 3a b c i i i iα = − − 2 ( ) 3 b c i i iβ = − Appendix C Clarke and Park Transformation  88 2 ( ) 3o a b c i i i i= + + with iα   and iβ components in an orthogonal reference frame and io the homopolar component of the system. In many applications, the homopolar component is absent or is less important. In this way, in absence of homopolar component the space vector u = uα + juβ represents the original three-phase input signal. Consider now a particular case with iα superposed with ia and ia + ib + ic is zero, in this condition ia, ib and ic can be transformed to iα and iβ with following mathematical transformation: ai iα = 1 2 3 3a b i i iβ = + 0a b ci i i+ + = The modification from a two-phase orthogonal α, β frame to a three-phase system is done by the following equations: ai iα= 1 3 2 2b i i iα β= − + 1 3 2 2c i i iα β= − − Park transformation The two phases α, β frame representation calculated with the Clarke transform is then fed to a vector rotation block where it is rotated over an angle θ to follow the frame d,q attached to the rotor flux. Appendix C Clarke and Park Transformation  89  Figure 2 Stator current in the d,q rotating reference frame and its relationship with ,  stationary reference frame The rotation over an angle θ is done according to the formulas: cos( ) sin( )di i iα βθ θ= + sin( ) cos( )qi i iα βθ θ= − + The vector in the d, q frame is transformed from d, q frame to the two phases α, β frame representation calculated with a rotation over an angle θ according to the formulas: cos( ) sin( )d qi i iα θ θ= − sin( ) cos( )d qi i iβ θ θ= +

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