Design, Control and Evaluation of a Prototype Three Phase Inverter …publications.lib.chalmers.se/records/fulltext/183933/183933.pdf · Drive System for an Ultra-Light Electric Vehicle

Design, Control and Evaluation of a Prototype ThreePhase Inverter in a BLDC Drive System for anUltra-Light Electric Vehicle

Master’s Thesis in Electric Power Engineering

PHILIP LARSSON

NICLAS RASMUSSEN

Department of Energy and EnvironmentDivision of Electric Power EngineeringCHALMERS UNIVERSITY OF TECHNOLOGYGothenburg, Sweden 2013Master’s Thesis 2013

MASTER’S THESIS IN ELECTRIC POWER ENGINEERING

Design, Control and Evaluation of a Prototype Three Phase

Inverter in a BLDC Drive System for an Ultra-Light

Electric Vehicle

Master’s Thesis in Electric Power EngineeringPHILIP LARSSON

NICLAS RASMUSSEN

Department of Energy and EnvironmentDivision of Electric Power Engineering

CHALMERS UNIVERSITY OF TECHNOLOGY

Gothenburg, Sweden 2013

Design, Control and Evaluation of a Prototype Three Phase Inverter in a BLDCDrive System for an Ultra-Light Electric Vehicle

PHILIP LARSSONNICLAS RASMUSSEN

c©PHILIP LARSSON, NICLAS RASMUSSEN, 2013

Master’s Thesis 2013ISSN 1652-8557Department of Energy and EnvironmentDivision of Electric Power EngineeringChalmers University of TechnologySE-412 96 GothenburgSwedenTelephone: + 46 (0)31-772 1000

Chalmers ReproserviceGothenburg, Sweden 2013

Design, Control and Evaluation of a Prototype Three Phase Inverter in a BLDCDrive System for an Ultra-Light Electric Vehicle

Master’s Thesis in Electric Power EngineeringPHILIP LARSSONNICLAS RASMUSSENDepartment of Energy and EnvironmentDivision of Electric Power EngineeringChalmers University of Technology

Abstract

With an evolving vehicle industry there has been an increase in thedemand for light electric vehicles. This thesis was conducted in order togain further knowledge within the field of sensorless BLDC motor controlfor light electric vehicles.

A three phase inverter was modeled and simulated in Simulink with sen-sorless BLDC motor control. A requirement specification for a three phaseinverter in a drive system for a light electric vehicle was made. From therequirement specification a three phase inverter with two different sensor-less control approaches was designed in Altium Designer. The PCB wasmanufactured and software control algorithms as well as drivers were imple-mented.

The three phase inverter and its control algorithms were tested and eval-uated. The three phase inverter operates successfully with sensorless controlat a motor speed above 300RPM and fits into a light electric vehicle.

Keywords: BLDC, Design, Drive System, Electric Vehicle,Light Electric Vehicle,Motor Control, PCB, Sensorless

I

II

Acknowledgements

We would like to express our appreciation to our supervisor Peter Dahlin atQRTECH AB and our examiner Prof. Torbjorn Thiringer at Chalmers for theirguidance and support throughout this thesis project.

Our coworkers at QRTECH AB also deserve our gratitude for all of their con-tribution and interest in the project. A special thanks to Dr. Andreas Magnussonfor his advice and expertise.

We would also like to sincerely thank QRTECH AB for believing in our projectand also for the necessary funds and equipment that were provided during theproject.

Lastly we would like to thank our girlfriends and family for their supportthroughout our five years at Chalmers University of Technology.

Gothenburg 2013Philip Larsson & Niclas Rasmussen

III

IV

Abbreviations

ADC Analog-to-Digital Converter

Back-EMF Back Electromotive Force

BLDC Brushless DC

CCS Code Composer Studio

DSP Digital Signal Processor

EMI Electromagnetic Interference

GPIO General Purpose Input/Output

IC Integrated circuit

JTAG Joint Test Action Group

LED Light-Emitting Diode

MOSFET Metal Oxide Semiconductor Field Effect Transistor

PCB Printed Circuit Board

PI Proportional-Integral

PMSM Permanent Magnet Synchronous Motor

PWM Pulse-Width Modulation

QEP Quadrature Encoder Pulse

V

VI

Contents

Abstract I

Acknowledgements III

Abbreviations V

Contents VII

1 Introduction 11.1 Problem Background . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Delimitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Technical Background 32.1 BLDC Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Motor Control with a Three Phase Inverter . . . . . . . . . . . . . . 6

2.2.1 Sensored Motor Control . . . . . . . . . . . . . . . . . . . . 72.2.2 Sensorless Motor Control . . . . . . . . . . . . . . . . . . . . 7

2.3 Gate Driver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3 Modeling and Simulation 113.1 BLDC Motor Model . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 Three Phase Inverter Model . . . . . . . . . . . . . . . . . . . . . . 133.3 Requirement Specification . . . . . . . . . . . . . . . . . . . . . . . 16

3.3.1 Longitudinal Vehicle Dynamic Model . . . . . . . . . . . . . 163.3.2 Drive System Requirement Specification . . . . . . . . . . . 17

4 Inverter Design 184.1 Control PCB Schematic . . . . . . . . . . . . . . . . . . . . . . . . 18

4.1.1 Voltage Regulators . . . . . . . . . . . . . . . . . . . . . . . 194.1.2 Radio Receiver . . . . . . . . . . . . . . . . . . . . . . . . . 194.1.3 Cell Protection . . . . . . . . . . . . . . . . . . . . . . . . . 194.1.4 LED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.1.5 Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.1.6 DSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.1.7 Back-EMF . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.1.8 Level Shifter . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.2 Power PCB Schematic . . . . . . . . . . . . . . . . . . . . . . . . . 224.2.1 Gate Driver . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.2.2 Half Bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.2.3 DC-Link Capacitors . . . . . . . . . . . . . . . . . . . . . . 244.2.4 Current Measurement . . . . . . . . . . . . . . . . . . . . . 244.2.5 Temperature Measurement . . . . . . . . . . . . . . . . . . . 24

4.3 PCB Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.3.1 Control PCB Layout . . . . . . . . . . . . . . . . . . . . . . 25

VII

4.3.2 Power PCB Layout . . . . . . . . . . . . . . . . . . . . . . . 26

5 Software Implementation 27

6 Verification and Evaluation of Results 336.1 Board Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336.2 Sensored and Sensorless Evaluation . . . . . . . . . . . . . . . . . . 376.3 Further evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

7 Closure 467.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

References 47

Appendix A Calculation of Inverter Output Voltage 49A.1 Case 60− 120◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49A.2 Case 120− 180◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51A.3 Case 180− 240◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53A.4 Case 240− 300◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55A.5 Case 300− 360◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Appendix B Control PCB Schematic 59

Appendix C Power PCB Schematic 71

VIII

1 Introduction

The vehicle industry is rapidly evolving. With many different aspects coincidingsuch as depletion of fossil fuels, global warming, air pollution, carbon emissionreduction legislation and new up and coming battery technologies there is a gradualincrease in demand for electric vehicles.

With new technology and a growing market, there are many new kinds ofelectric vehicle topologies developing. There are also many old vehicle topologiessuch as bicycles and scooters that are being electrified. The high efficiency ofelectric drive systems which on average is 85 % compared to the regular drivesystems with an internal combustion engine which has an average efficiency of 12-20 % , make it possible to design and build much lighter vehicles with the samepower ratings as the heavier vehicles with an internal combustion engine [1], [2].

There are many different electric motor types with different features available.For the application of driving light electric vehicles there are two very similarmotor types that stand out from the others because of their high power versussize and weight characteristics, those are the Brushless DC (BLDC) Motor andthe Permanent Magnet Synchronous Motor (PMSM).

The battery is only capable of supplying a DC voltage, while the BLDC- andthe PMSM- motors require a three phase voltage. In order to solve this probleman interweaving stage that converts the DC voltage to a three phase voltage isrequired. The conversion is made by a three phase inverter which also adds theability to control the motor by having the ability to adjust the voltage input tothe motor.

1.1 Problem Background

QRTECH is a consultancy firm within the field of hardware and software researchand development. With many customers within the automotive sector they havedeveloped a lot of embedded electronic solutions for vehicles. One such solution isa high end controller for a PMSM motor in a light electric vehicle. With alreadyhaving a solution for the PMSM motor they now want an equivalent solution fora BLDC motor. In order to improve reliability and reduce cost they also wantthe BLDC controller to be able to operate without a positioning sensor. Havingsolutions for both of the motor technologies will make it possible to evaluate andprovide the best solution depending on the customer needs.

1.2 Purpose

The thesis work was conducted with the purpose of developing a three phaseinverter in a BLDC-motor drive system for an ultra-light vehicle. This was donein order to have a prototype platform which can be evaluated and lay as a basisfor future decision making and quotation when offering customers new solutions.

Further the thesis was carried out in order to increase theoretical knowledgeabout BLDC-motor drive systems and in order for the authors to gain knowledgeand skill of how to realize the theoretical acquired knowledge into a constructionof a real working product.

1

The main focus of the conducted work was on the realization, constructionand software implementation of a three phase inverter which is able to control aBLDC-motor with both sensored- and different sensorlesscontrol strategies.

1.3 Delimitations

In order to be able to complete the project within a timeframe of 20 weeks afew delimitations have been made. Only one sensored and two different sensorlesscontrol approaches based on back-EMF measurement will be implemented. Onlya rather modest model for the motor simulation will be implemented, with themain purpose of evaluating the sensored and senorless control algorithms. Thethree phase inverter will only be built and tested in a lab environment duringthe period of the thesis. Support for a third party solution for wireless controlwill be implemented instead of adding an additional RF circuit to the three phaseinverter.

1.4 Outline

The project started with a theoretical study on previous work within the field. Thestudy kept on throughout the project. A Simulink model of a BLDC drive systemwas implemented which provided a platform that allowed for experimenting withdifferent sensorless control techniques. Power requirement simulations were alsomade in order to determine the requirement specifications of the inverter. Oncethis was done and finalized the work on the circuit layout started. When all com-ponents had been selected the design of the Printed Circuit Board (PCB) startedsimultaneously with the software development for the Digital Signal Processor(DSP). When the PCB had been manufactured and all of the components hadbeen mounted, short circuit tests and circuit functionality tests were conducted.Lastly motor control tests with the different control algorithms were carried out.The results were evaluated and compared to the simulated results.

2

2 Technical Background

This chapter introduces the BLDC motor and the three phase inverter. It alsopresents the inverter control techniques such as sensored and sensorless control.The chapter also give some technical background to the gate driver.

2.1 BLDC Motor

The BLDC motor seen in Figure 2.1 is a permanent magnet AC synchronous motor.It is characterized by ideally having a trapezoidal back Electromotive Force (back-EMF) which is presented in Figure 2.2 and that it is driven by square shapedcurrents. These are the major differences from the PMSM which has a sinusoidalshaped back-EMF and is driven with sinusoidal phase currents. The BLDC motoris usually constructed in single-phase, two-phase and three phase configurations,where the three phase configuration is the most common. Motors with more thanthree phases can be manufactured but are however uncommon since the numberof power electronic devices increases with the number of phases which increasesmanufacturing cost [3].

N

N

S

S

a

a

b

b

c

c

S

S

N

N

S

N

N

S

Vc

Vn

Va

Vb

ea

ebec

Figure 2.1: A three phase BLDC motor with its circuit diagram

3

0 60 120 180 240 300 360

ea

0 60 120 180 240 300 360

eb

0 60 120 180 240 300 360

ec

Degrees [°]

Figure 2.2: Ideal back-EMF voltages , ea, eb and ec of the BLDC motor

The stator is made out of stacked steel laminations and is constructed in a verysimilar way to that of the induction motor. The rotor is made out of permanentmagnet pairs with the north pole and south pole in consecutive order. Since it is asynchronous motor, the stator and rotor rotate at the same frequency. This meansthat there is no slip between the stator and rotor in the BLDC motor which is thecase for the induction motor. The three phase BLDC motor is driven by applying apositive current to one of the motor phases and a negative current to another whilehaving no current going through the third phase leaving it at floating potential.Since torque is produced by the interaction between the field generated in thestator and by the permanent magnets on the rotor, the motor starts to rotate. Tokeep the permanent magnets of the rotor from aligning with the stator in a staticcondition, the current through the stator which gives rise to the magnetic fieldneeds to be commutated in a specific way. The current commutation is controlledso that the rotor field keeps trying to align with the stator field and thereby themotor continues to rotate. The current is switched in six different commutationsteps for each electrical rotation. The BLDC-motor in comparison to a brushedDC motor has a lot of advantages which are presented in Table 2.1. The majordisadvantage of the BLDC motor is that it needs a more advanced controller inorder for it to operate [4].

4

Table 2.1: The BLDC Motor Compared to the Brushed DC Motor [4], [5]

Property BLDC Motor Brushed DC Motor

Maintenance Low rate of maintenance re-quired.

The brushes need consistentmaintenance.

Speed Range A very wide speed rangesince there are no mechan-ical brushes that limits thespeed at higher RPM.

Medium. This is mainly dueto that there is a mechanicallimitation which is causedby the increased wearing ofbrushes at higher speeds.

Power Versus Size Very high because of thevery good thermal charac-teristics. This is becausethe windings are located inthe stator, which is con-nected to the case, which inturn gives a better heat dis-sipation.

Moderate to Low. The ar-mature current will increasethe temperature in the airgap which limits the outputpower.

Rotor Inertia Low. The permanent mag-nets are lighter than regularrotor windings made out ofcopper.

Higher since the copperweigh more than permanentmagnets.

Efficiency Very high, since there areno copper losses in any ro-tor windings.

Lower because of the volt-age drop in the brushes.

Lifespan Very long. Shorter since the brusheswill wear out.

Torque Versus SpeedCharacteristics

Flat. Flat until reaching higherspeeds where friction willincrease due to the brushes.

ElectromagneticInterference

Low. The brushes will generatenoise.

Commutation Electrical commutation in-side an inverter.

Mechanical commutation inthe brushes.

Control Requires digital controlledinverter in order to run.

Simple control, can runat fixed speed without theneed of a controller, inex-pensive.

Manufacturing Cost Easy to manufacture, how-ever the material cost ishigh due to the high mate-rial cost of the permanentmagnets.

More complex to manufac-ture because of the mechan-ical brushes. Has a cheapermaterial cost, since no ex-pensive permanent magnetsare required.

5

2.2 Motor Control with a Three Phase Inverter

A three-phase inverter technically is three sections of half bridge inverters. Eachinverter stage is able to produce an output 120◦ displaced with respect to theother. The half-bridge sections are usually referred to as legs with a three phaseinverter consisting of three legs, one for each phase, see Figure 2.3.

BLDC Motor

Vd

Figure 2.3: Three phase inverter with a connected BLDC motor

Since the BLDC motor is characterized by only having two phases energized atthe same time, only three out of the six switches of the inverter will be active foreach switching sequence. One of the three phase inverter legs will be Pulse WidthModulated (PWM) with the lower transistor inversely switched with respect tothe upper transistor and in another leg the lower transistor will conduct. This isperformed in a periodical six-step commutation sequence, which can be seen inTable 2.2 [6], [7]. If reverse rotation is desired the sequences needs to be reversedas well.

Table 2.2: Switching sequences

Sequence Rotor position, θeSwitching Phase current

PWM ON A B C

1 0− 60◦ Q1,Q2 Q4 DC+ DC- OFF

2 60− 120◦ Q1,Q2 Q6 DC+ OFF DC-

3 120− 180◦ Q3,Q4 Q6 OFF DC+ DC-

4 180− 240◦ Q3,Q4 Q2 DC- DC+ OFF

5 240− 300◦ Q5,Q6 Q2 DC- OFF DC+

6 300− 360◦ Q5,Q6 Q4 OFF DC- DC+

Unlike brushed DC motors where a commutator and brushes are used to changecurrent polarity the BLDC motor usually use semiconductors with feedback fromthe rotor position to change current polarity. Hence to be able to know when to

6

commutate each phase of the BLDC motor the position needs to be known. Thiscould be done in many different ways, either by sensored or sensorless techniques.During the last decade many new sensorless methods have been developed. Thereare mainly two reasons for this, the high cost of positioning sensors and that ofincreased reliability since sensors can fail during operation. In certain applicationssuch as flooded compressors or pumps it is not even possible to use sensors. Thereare however also drawbacks to the different sensorless techniques, for example thatit is generally hard to control the motor at low speeds [4].

2.2.1 Sensored Motor Control

Hall effect sensors are normally used in order to determine the motor rotor position.They can either be mounted on the surface of the stator or be embedded into thestator. Typically three hall sensors are mounted with a 120◦ phase shift betweenthem. These make it possible to determine in which of the six sequences the rotorcurrently is in and when to commutate [8].

Other sensors such as encoders and resolvers could however also be used. Theencoder transmits two digital pulses and measures the distance and time betweenthem which makes it possible to calculate the speed and the angle of the rotor.Resolvers produce a sinusoidal and a cosinusoidal signal which both are used inorder to indicate the position within a 360◦ revolution [9].

2.2.2 Sensorless Motor Control

There are many different sensorless control techniques that can be implementedfor a BLDC motor. One method in order to estimate the rotor position is bymeasuring the back-EMF of the motor. This can effortlessly be done by measuringthe terminal voltages of the phases. The back-EMF voltage is generated in the non-driven winding by the permanent magnets when the motor rotate. The magnitudeof the voltage is proportional to the rotor speed and for this reason it is difficult tocontrol the motor at low speed. The back-EMF method can be implemented sinceone of the phases is not energized during each of the commutation sequences [6].For the case when phase C is the phase that is not fed by the inverter the phasevoltages will be

Va = Ria + Ldiadt

+ ea + Vn (2.1)

Vb = Rib + Ldibdt

+ eb + Vn (2.2)

Vc = ec + Vn (2.3)

where Vn is the motor neutral voltage with reference to ground. Since current onlyflows through the motor from phase A to phase B the current in those phases willbe equal but opposite. This gives

ia = −ib (2.4)

7

By adding (2.1)-(2.4) the following expression is obtained

Va + Vb + Vc = ea + eb + ec + 3Vn (2.5)

and from the back-EMF waveforms shown in Figure 2.4 it can realized that thesum of the back-EMFs at a zero crossing point is equal to zero. This reduces (2.5)to

Va + Vb + Vc3

= Vn (2.6)

and is used in order to determine when the back-EMF crosses the virtual groundof the motor in each phase.

The next step in the commutation sequence occurs 30◦ after the zero crossingpoint which also can be seen in Figure 2.4. So by measuring the phase potentialsand implementing an algorithm it is possible to estimate the rotor position andthe needed switching state in the sequence.

0 60 120 180 240 300 360 / 0 60 120 180 240

0 60 120 180 240 300 360 / 0 60 120 180 240

0 60 120 180 240 300 360 / 0 60 120 180 240

1 2 3 4 5 6 1 2 3 4

ea

eb

ec

Degrees [°]

Figure 2.4: Ideal back-EMF voltages

8

2.3 Gate Driver

The N-channel Metal Oxide Semiconductor Field Effect Transistor (MOSFET)needs a gate-source voltage in the magnitude of 10− 12 V in order to fully behavelike a switch. This imposes a problem for the upper switch in each of the halfbridge sections of the three phase inverter since the source potential will be equalto the input voltage. One way to solve this problem is by using a gate driver witha bootstrap capacitor. This method is quite simple and effective but it has certainlimitations [10]. One such limitation is that the duty cycle and the on-time ofthe MOSFET cannot be too large due to the fact that the bootstrap capacitorrecharges during the off-time of the MOSFET. If a very high duty cycle is requireda charge pump circuit which makes it possible to recharge the capacitor duringthe on-time of the transistor can be implemented [11].

The gate driver is used as a power amplifier between the Integrated Circuit(IC) which is acting as a controller, such as a DSP, and the power MOSFET. Itmakes sure that there is sufficient current in order to charge and recharge the gatecapacitance of the MOSFET. A typical connection of a gate driver IC can be seenin Figure 2.5, where CB is the bootstrap capacitor. A bootstrap circuit consistsof a capacitor and a diode. The capacitor is charged through the diode whenthe lower MOSFET is on, which means that Vs is connected to ground. Whenthe upper MOSFET should be turned on the lower MOSFET is turned off andthe negative side of the capacitor is then connected to Vs and the positive side isconnected to the gate, V OA, through the gate driver circuit. This will provide theneeded gate voltage to turn on the upper MOSFET [11].

VBAT

Vdriver,A

Vdriver,B

Figure 2.5: A typical connection of a high-side/low-side gate driver IC with abootstrap capacitance, CB

9

The value of the bootstrap capacitor is proposed to be

CBS,min =∆QBS,min

∆VBS,max(2.7)

where ∆QBS,min is the minimum charge the capacitor must supply to turn theMOSFET on and ∆VBS,max is the maximum allowed voltage dip in the capacitor.The minimum charge is calculated by

∆QBS,min = QG +QLS +IQBS,max

fs+ICBS,leak

fs(2.8)

where QG is the required gate charge of the MOSFET, QLS is the level shift chargerequired by the driver, IQBS,max is the maximum current that is required by thefloating section of the driver, ICBS,leak is the leakage current of the bootstrapcapacitor and fs is the switching frequency. The maximum allowed voltage dip iscalculated by

∆VBS,max =(VDD − Vf − VLS

)− VGS,min (2.9)

where VDD is the positive supply voltage, Vf is the voltage drop across the boot-strap diode, VLS is the voltage drop across the lower MOSFET and VGS,min is theminimum required gate-source voltage to turn the MOSFET on.

(VDD−Vf−VLS

)is the voltage which the capacitor will be charged to.

In order to have a safety margin from this worst case voltage drop the rule ofthumb is that the value obtained in (2.7) is multiplied by 15.

10

3 Modeling and Simulation

In this chapter the motor model and three phase inverter model are introduced.The models are used to simulate the three phase inverter with a BLDC motor inSimulink. In order to define the design framework a requirement specification wasformulated.

3.1 BLDC Motor Model

The mathematical model which was used in order to simulate the BLDC motorconsisted of an electrical- and a mechanical-part.

If the mutual inductance is assumed to be constant when the motor rotatesthe voltage in the stator windings can be expressed as

Va = Ria + Ldiadt

+ ea (3.1)

Vb = Rib + Ldibdt

+ eb (3.2)

Vc = Ric + Ldicdt

+ ec (3.3)

where Va, Vb, Vc is the terminal voltage, R is the stator resistance, ia, ib, ic is thestator phase current, L is the stator inductance and ea, eb, ec is the induced back-EMF in each phase.

The trapezoidal back-EMF in a 3-phase BLDC motor is related to a functionof rotor position where each phase is 120◦ phase shifted and given by

ea = KeωmF (θe) (3.4)

eb = KeωmF (θe +2π

3) (3.5)

ec = KeωmF (θe +4π

3) (3.6)

where Ke is the motor back-EMF constant, ωm is the rotor speed, θe is the electricalrotor angle and F is the trapezoidal shape reference function with respect to rotorposition, with boundaries between +1 and -1.

F (θe) =

1 0 ≤ θe <

2π3

1− 6π(θe − 2π

3) 2π

3≤ θe < π

−1 π ≤ θe <5π3

−1 + 6π(θe − 5π

3) 5π

3≤ θe < 2π

(3.7)

Since there is no wire connected to the motor’s neutral phase the phase-to-phase voltage equations are used in order to control the motor. The phase-to-phasevoltage equations are derived from (3.1)-(3.3) and turn into

Vab = R(ia − ib) + Ld

dt(ia − ib) + eab (3.8)

11

Vbc = R(ib − ic) + Ld

dt(ib − ic) + ebc. (3.9)

Only (3.8) and (3.9) will be needed since the third phase-to-phase voltage willbe a combination of the other two. In order to obtain the state space model (3.8)and (3.9) are combined together with the fact that the sum of all phase currentssimultaneously will be zero, ia + ib + ic = 0, which gives

diadt

= −RLia +

2

3L(Vab − eab) +

1

3L(Vbc − ebc) (3.10)

dibdt

= −RLib −

1

3L(Vab − eab) +

1

3L(Vbc − ebc) (3.11)

The last of the currents is given by the following equation

ic = −ia − ib (3.12)

The total electric torque produced by the BLCD motor is the summation ofthe electric torque produced in each phase.

Te = Ta + Tb + Tc =eaia + ebib + ecic

ωm(3.13)

The mechanical part is represented by the following equation

Te = βωm + Jdωmdt

+ TL (3.14)

where B is a constant of friction, J is the rotor and coupled shaft inertia and TLis the load torque.

The Simulink model of the ideal BLDC motor is then obtained by (3.10)-(3.12)together withs (3.13) and (3.14).

12

3.2 Three Phase Inverter Model

Simulating an inverter of a BLDC motor in Simulink has been proven to be a bitdifficult due to the complications in simulating the freewheeling diodes. Baldursson[12] proposed a method in order to solve this problem. It simulates the freewheelingdiodes as voltage sources in order to make sure that the freewheeling currents onlycan flow in one direction. The diode model is implemented into a Matlab function.This function is then implemented in Simulink which uses the phase currents, back-EMF, rotor position and dc-source voltage as inputs. For each of the differentposition intervals showed in Table 2.2 the function will output different voltagesto the motor.

eb

ec

VnVd

ic = 0

ic ≠ 0 +

ea

Figure 3.1: Current path through the three phase inverter for the interval 0−60◦

where the green path represents the current through the active phases and the redpath represents the commutating current from the previous switching sequence

Figure 3.1 represent the interval between 0−60◦ where the different output voltagescan be derived for the case when there is a current through the freewheeling diode,in this case D6. When the current through the freewheeling diode is zero, blocking,the diode will be represented by a voltage source, in this case Vbc, to make surethat the current only flows in one direction. A simplified case can be seen in Figure3.2 for the interval between 0− 60◦.

When ic 6= 0 the three phase-to-phase voltages can easily be derived from Figure3.1

Vab = Vd (3.15)

Vbc = 0 (3.16)

Vca = −Vd (3.17)

13

ia ic

eb

eceaL LR R

( )Vd

Vbc

D6

L

R

Vn

Figure 3.2: Circuit topology for the case 0−60◦, where Vbc represents the voltageover the reversed biased diode, D6

When ic = 0 Kirchhoff’s voltage law are applied around each mesh in Figure3.2 to obtain the three phase-to-phase voltages

Vd −Ria − Ldiadt− ea + eb − L

d(ia + ic)

dt−R(ia + ic) = 0 (3.18)

− Vbc −Ric − Ldicdt− ec + eb − L

d(ia + ic)

dt−R(ia + ic) = 0 (3.19)

when ic = 0

Vd − 2Ri− ea − 2Ldi

dt− ea + eb = 0 (3.20)

− Vbc − ec + eb − Ldi

dt−Ri = 0 (3.21)

(3.20) and (3.21) gives

Vbc =1

2(−Vd + ea + eb − 2ec) (3.22)

So the three phase-to-phase voltages will be

Vab = Vd (3.23)

Vbc =1

2(−Vd + ea + eb − 2ec) (3.24)

Vca =1

2(−Vd − ea − eb + 2ec) (3.25)

The same derivation is applied for the rest of the switching sequences and result inTable 3.1. The calculations for the five remaining cases are presented in AppendixA.

14

Table 3.1: Inverter output voltages

θe Diode current Vab Vbc Vca

0− 60◦ ic 6= 0 Vd 0 −Vdic = 0 Vd

12(−Vd + ea + eb − 2ec)

12(−Vd − ea − eb + 2ec)

60− 120◦ ib 6= 0 0 Vd −Vdib = 0 1

2(Vd + ec + ea − 2eb)

12(Vd − ec − ea + 2eb) −Vd

120− 180◦ ia 6= 0 −Vd Vd 0ia = 0 1

2(−Vd − eb − ec + 2ea) Vd

12(−Vd + eb + ec − 2ea)

180− 240◦ ic 6= 0 −Vd 0 Vdic = 0 −Vd 1

2(Vd + ea + eb − 2ec)

12(Vd − ea − eb + 2ec)

240− 300◦ ib 6= 0 0 −Vd Vdib = 0 1

2(−Vd + ec + ea − 2eb)

12(−Vd − ec − ea + 2eb) Vd

300− 360◦ ia 6= 0 Vd −Vd 0ia = 0 1

2(Vd − eb − ec + 2ea) −Vd 1

2(Vd + eb + ec − 2ea)

15

3.3 Requirement Specification

In order to be able to define a framework for the design criterias of the drive system,such as selection of motor, battery technology and the controller specifications,several models and simulations are required. This needs to be done in order to beable to determine the maximum power, speed, current and voltage as well as thetotal energy needed for the system. Vehicle dynamics can be modeled in intricateways, however a longitudinal vehicle road serves well for the purpose of determinethe maximum limits of a drive system [13].

3.3.1 Longitudinal Vehicle Dynamic Model

In the longitudinal vehicle dynamic model the vehicle and the forces acting uponit can be described with a free body diagram represented in Figure 3.3. In thismodel the vehicle’s center of mass where all of its weight is concentrated is usedas a reference point. The forces that will be taken into account for are the force ofgravity, the force of friction due to the rolling resistance exerted by the road andwheel interaction, the aerodynamic drag force and the propulsive force exerted bythe electric motor at the wheel. The sum of the forces in the system will determineacceleration or deceleration of the vehicle [13].

Vveh

Fd

Fp

Ff

Fg sin(α)

Fgα

Figure 3.3: Free body diagram

The system can be modeled as

Fp = mvehdvvehdt

+ Fd + Ff + Fgsin(α) (3.26)

where Fp is the force of propulsion exerted by the motor, Fd is the aerodynamicdrag force, Ff is the frictional force between the road and the wheels, Fg is thegravitational force α is the slope angle and mveh is the total vehicle mass. Thetractive power needed to be exerted by the motor is given by (3.27)

Pp = Fpvveh = mvehdvvehdt

vveh + Fdvveh + Ffvveh + Fgsin(α)vveh (3.27)

Pp = mvehdvvehdt

vveh + Pd + Pf + Pg (3.28)

where Pd is the power exerted on the vehicle due to the aerodynamic friction alsoknown as the drag power, which is described by (3.29), Pf is the frictional power

16

between the wheels and the road, which is shown in (3.30), and Pg is the powerexerted by gravitation which is described in (3.31).

Pd = Fdvveh =1

2CdAfρav

2effvveh (3.29)

where Cd is the drag coefficient, Af is the effective area of the vehicle perpendicularto the direction of motion, ρa is the density of air, veff is the velocity of the vehiclerelative to air and vveh + vair.

Pf = Ffvveh = CrrFNvveh (3.30)

where Crr is the coefficient of rolling resistance and FN is the normal force.

Pg = Fgvveh = mvehgsin(α)vveh (3.31)

where g is the acceleration due to gravity.

3.3.2 Drive System Requirement Specification

Several drive cycle models were made in order to calculate the current and thepower output needed in the different drive cycle scenarios. In order to determinethe maximum peak power and current needed, a worst case drive cycle was im-plemented. This was realized into a slope with a 15◦ incline where the vehicleaccelerated from stationary to full speed in five seconds. To determine the nec-essary current during regular driving condition, a drive cycle on flat surface wasimplemented. A worst case scenario was implemented in order to determine themaximum amount of power needed. It was calculated to approximately 2 kWwhen accelerating from stationary to full speed, 20 km/h, at an incline of 15◦ in 5seconds.

In addition the battery technology and battery voltage needs to be selected.The battery voltage is set in discrete steps by the number of battery cells chosenand by their nominal voltage. For the purpose of driving a light electric vehicleweight and size has to be minimized. To reduce the weight and the size, a highpower density is needed. In order to be economically viable the high power densitymust come at a low cost. From these design criteria’s a six cell lithium polymerbattery (LiPO) with a nominal cell voltage of 3.7 V and especially thin designand was chosen. With the nominal battery voltage set to 22.2 V it is possible todetermine the maximum current to 90 A and to select a BLDC motor which isable to handle the voltage and currents up to at least 90 A for a short period.

17

4 Inverter Design

The inverter layout was divided into two different PCBs, a Control PCB and aPower PCB. This was done in order to separate the high power components fromthe low power components. A four layer FR-4 PCB was used for the control circuitsand a one-layer aluminum PCB was used for the power circuits. The aluminumwas used in order obtain an improved cooling performance for the transistors.

Due to layout optimization and the component shape the current sensor andthe gate drives were placed on the Control PCB although they usually are placedon the Power PCB.

An electronic design software called Altium Designer from Altium where usedto draw both the schematics and PCBs.

4.1 Control PCB Schematic

The control PCB consists of low voltage logic components which are necessaryfor the control of the electronic commutation of the motor. An overview over thecontrol PCB can be seen in Figure 4.1 where every major circuit is divided into ablock. All of the circuit schematics for the Control PCB can be seen in AppendixB.

Figure 4.1: Overview of the different blocks in the PCB

18

All of the different blocks will be described in more detail in the followingsections.

4.1.1 Voltage Regulators

The voltage regulator block converts the battery voltage down into four differentvoltage levels. The voltage values were 10 V, 5.0 V, 3.3 V and 1.9 V where 3.3 Vand 1.9 V also were used as analog voltages.

To transform the battery voltage down to 10 V a buck converter was used.The 10 V was used in order to supply the high and the low side driver outputs ofthe gate drivers with power. The voltage was also used in a gate amplifying stagein order to maintain a good gate signal to the MOSFETs on the power PCB.

The 5.0 V voltage level was also acquired by using a buck converter. Thisvoltage level was used in order to supply, the radio receiver, the encoder, the levelshifter and the gate driver with power.

A buck regulator with dual outputs was used in order to attain the digital 3.3 Vand 1.9 V from the digital 5.0 V . Both of the voltages were used to supply theDSP and the 3.3 V was also used to supply two Light-Emitting Diodes (LEDs), thelevel shifter and the back-EMF circuits. The same analog voltages were obtainedby using linear power regulators with the 5.0 V as input. These voltages whereused to supply the DSP and the current sensor.

A supervision circuit with dual inputs was used in order to detect power failsof the voltages, which supply the DSP. This was implemented as a safety functionto protect the DSP and the critical components supplied by the same voltage.

4.1.2 Radio Receiver

The radio receiver block consists only of a connector for a radio receiver withthree analog inputs which are connected to the DSP and a 5.0 V output. Theradio receiver and the transmitter were third-party components which normallyare used for radio-controlled cars. The purpose of this circuit was to be able tocontrol the vehicle wirelessly in the future.

4.1.3 Cell Protection

Since a lithium polymer battery was used as power supply the voltages from eachof the cells needed to be monitored by the DSP. This was done to reduce the riskof damaging the cells under running operation. An input header for the balanceconnector of the battery was mounted along with six differential amplifiers toobtain the different cell voltages. The voltage protection circuit is limited to onlymeasuring six cells due to the design with six differential amplifiers. The nominalcell voltage is 3.7 V and the voltage of each cell should be in the range from 4.2Vto 2.7 V in order to protect the cell from taking any damaged because of an underor over voltage. This gives a nominal voltage of 22.2 V for the input supply voltageto the inverter. The gain of the differential amplifiers was set to 0.62 to be able tosample within the full signal range with the Analog-to-Digital Converter (ADC).

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4.1.4 LED

The LED block consists of two LEDs, one green and one red, and two MOSFETswhich are used to switch the LEDs on and off. The LEDs act as indicator lights forthe DSP to show if the controller is working and in order to make the debuggingprocess easier.

4.1.5 Encoder

A quadrature encoder was used for verification and comparison of the two differentsensorless methods. The outputs from the encoder were A, B and index pulse alongwith their inverted signals. All of these signals were used to obtain an accurateposition of the rotor and rotor direction. The A and A signals were filtered witha common mode choke and amplified in a differential amplifier to achieve a morestable and reliable A-signal. The B signals and the index signals where filteredand amplified in the same way. These three signals were then sent to the DSP inorder to calculate the position.

4.1.6 DSP

The DSP functions as a brain for the three phase inverter. It is here all of theinput and output signals are processed in order to make it possible to control theswitching sequences. All of the signals used by the three phase inverter can be seenin Table 5.1 and Table 5.2. Filters were connected to each of the DSP’s analoginputs to reduce signal noise. This improved the signal quality and made it easierto use the signals in the software. A Joint Test Action Group (JTAG) connectorwas also connected and used for programming and debugging the DSP.

4.1.7 Back-EMF

In the back-EMF block, the phase potentials were measured in order to be usedby the two sensorless methods. The signals were filtered to reduce noise fromthe PWM switching and scaled down to use the full range of the ADC conversion.Back-EMF A, back-EMF B and back-EMF C, were measured with the DSPs analoginputs which can be seen in Figure 4.2. Three resistors from each phase wereconnected in parallel in order to recreate the potential of the motor neutral. Themotors virtual neutral was also measured by the DSP ADC. These four analoginput signals along with a digital sensorless algorithm, were used for one of thesensorless methods.

The other sensorless method which was implemented used a similar approach,but instead of analog signals it used three digital signals as input to the DSP. Thesignals, Zero Cross A, Zero Cross B and Zero Cross C, was obtained from threecomparators, which also can be seen in Figure 4.2.

When the phase potential is higher than the virtual neutral the output of thecomparator will be high and when the phase potential is low, vice versa. Theshapes of these signals were very similar to the ones from a hall sensor. Analgorithm was also used in this case to estimate the next needed switching state.Both of the algorithms are based on the equations in Section 2.2.2.

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Back-EMF A

Zero Cross A

Back-EMF B

Zero Cross B

Back-EMF C

Zero Cross C

Neutral Voltage

Phase A

Phase B

Phase C

Figure 4.2: Schematic overview of the back-EMF block

4.1.8 Level Shifter

The level shifter was used to connect digital circuits which used different voltagelevels. For example the output signals from the encoder were shifted down from5.0 V to 3.3 V , which the DSP is able to measure. In the other direction, thePWM outputs from the DSP were shifted up from 3.3 V , to 5.0 V , which wasrequired for the gate driver.

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4.2 Power PCB Schematic

An overview over the power PCB with all of the major parts divided into differentblocks can be seen in Figure 4.3. All of the circuit schematics for the power PCBcan be seen in Appendix C.

Figure 4.3: Overview of the different blocks in the PCB

All the blocks will be described more detailed in the following subsections.

4.2.1 Gate Driver

The gate driver that was used had both a high-side and a low-side driver along witha bootstrap capacitor and a bootstrap diode at the upper MOSFET, which can beseen in Figure 4.4. In order to achieve independent control of the MOSFETs boththe low side and high side input were used with an individual PWM signal. ThePWM output signals from the DSP with a voltage level of 3.3 V goes through alevel shifter to adjust the voltage level to 5.0 V . The adjusted voltage is compatiblewith the gate driver inputs VIA and VIB.

The distances between the output signals of the gate driver and the inputsignals to the MOSFETs need to be as short as possible in order to reduce parasiticinductance in the traces. The inductance decrease the instantaneous current whichin turn decreases the speed of the switching [14]. This phenomenon lead to thatan amplifying stage was placed in front of the MOSFET gate.

22

.

Figure 4.4: The high-side/low-side gate driver IC with a bootstrap capacitance,CB

The bootstrap capacitor, CB was selected according to (2.7)-(2.9). A fastrecovery diode was chosen as the bootstrap diode in order to reduce the timeframein which the bootstrap capacitor can discharge into VDD.

4.2.2 Half Bridge

There are three half bridge blocks, Half Bridge 1, Half Bridge 2 and Half Bridge 3,which together compose the three phase inverter. Each block consist of two MOS-FETs, one upper and one lower MOSFET which are connected to one commongate driver IC.

The MOSFET switching scheme for BLDC motor control is presented in Table2.2 and from this table it can be seen that two switches always are on except forthe dead time between the PWM pulses. Dead time is used in order to avoid thatboth the upper switch and the lower switch are on at the same time. During thedead time, the current will freewheel through the body diode of the MOSFET. Sothe power dissipation of the MOSFETs in the three phase inverter will be

Ptotal = 2Pcond(1− Tdead

)+ 2Pswitch + 2Pcond,diodeTdead (4.1)

where Pcond and Pcond,diode are the conduction losses of the MOSFET and Pswitchare the switching losses of the MOSFETs. Which are

Pcond = I2onRds(on) (4.2)

23

Pswitch =VdsIonfs

2

(tr + tf

)(4.3)

Pcond,diode = VfIon (4.4)

where Rds(on) is the on state resistance of the MOSFET, Ion is the conductioncurrent, Vds is the drain to source voltage when the MOSFET is off, tr and tf isthe turn on and turn off times, fs is the switching frequency and Vf is the diodeforward voltage drop [15].

The power dissipation during a worst case scenario was calculated to be 32 W ,which correspond to a loss of 1.6 %. The current used in this worst case was90A, from Section 3.3.2, and the nominal battery voltage of 22.2 V . The selectedMOSFETs were specified to handle these parameters.

4.2.3 DC-Link Capacitors

A capacitor bank consisting of two electrolytic capacitors and four ceramic capac-itors were connected in parallel and placed between the battery and the three halfbridges in order to obtain a steady bus voltage. The two electrolytic capacitorsfilter the low frequency voltage ripple and the four ceramic capacitors filter thehigh frequency voltage ripple. The following expression was used to calculate theminimum value of the electrolytic capacitor

Cmin =Imotor,peak

∆V fs(4.5)

where Imotor,peak is the peak motor current, ∆V is the maximum allowed voltageripple and fs is the switching frequency [16].

4.2.4 Current Measurement

Current control was used in order to regulate the motor output power. This makesit necessary to measure the current continuously. Since the BLDC motor only hasone active current at the time, two phases conducting, there is no need to measureall three phase currents. Instead one current sensor was mounted between thebattery and the three phase inverter.

A hardware shutdown function consisting of two comparators where used asa safety function in case of a software or external failure. The two comparatorswere set to trigger on two different currents, one for maximum allowed positivecurrent and one for maximum allowed negative current with the analog currentsensor signal used as an input.

4.2.5 Temperature Measurement

Near one of the half bridges a negative temperature coefficient resistor was mountedto be able to measure temperatures. The temperature was monitored by the DSPas a software safety function and is able to trig a shutdown when the temperaturebecomes too high.

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4.3 PCB Layout

Circuit noise and disturbances are a common problem when realizing a schematiccircuit layout into a PCB layout. This is was mainly due to the fact that thecomponents are not ideal and that the signal traces cannot be made infinitely shortand thereby give rise to phenomena’s such as Electromagnetic Interference (EMI)because of unwanted coupling to other circuits caused by capacitive, inductive orconductive coupling. A first approach in order to reduce those unwanted effectswhen designing a PCB is to follow PCB design guidelines. Those help the designerto make general layout decisions without having to stop and analyze each andevery step and thereby speed up the design process significantly. This makes theguidelines a very cost efficient tool in order to reduce EMI instead of having to relyupon expensive containers such as metallic enclosures [17], [18]. There are howeveralmost as many guidelines as there are design engineers. It is therefore necessaryto be critical and investigate if the guidelines are up to date and in which specificcase each guideline apply [17].

4.3.1 Control PCB Layout

The Control PCB layout was influenced by a number of aspects of which the majorones will be discussed in this section. The first aspect was to determine the PCBdimensions. Since the application is light electric vehicles this is a crucial factorsince it needs to be able to fit and to be mounted in a good way. The two PCBs,the Control PCB and the Power PCB were placed beside each other, instead of ontop of each other, because of the definite height constraint of the application.

The control PCB was decided to be a multilayer PCB and to have four layersmade out of the regular glass epoxy panel FR-4 with copper foil laminated on eachlayer. The four layers made it possible to have a ground plane, a power plane andtwo signal layers. The four layer structure was a very cost effective approach inorder to reduce current loops and trace inductances that can cause EMI and signalnoise [17].

Circuits with similar noise characteristics were grouped together such as thedifferent switching voltage regulators and the encoder signal input interface. Theanalog circuits, the DSP’s analog inputs and the linear regulators, were put farfrom the switched regulators in order to reduce the risk of noise coupling with theanalog measurements. A separate ground for the analog circuits was also realizedwith the same intention.

The components within a block were placed close to each other with the mainfocus on minimizing the signal current loop area. Having a ground plane alsoreduce the signal current loop area since it provides the signals with a close andlow-impedance path [17].

The different power planes were placed on a single layer which prevents cou-pling between two different power buses. This also allows for an efficient designsince devices with same voltage rating could be grouped together. To further min-imize EMI, decoupling capacitors were placed as close to the power supply pins aspossible with direct via holes down to the ground plane.

All of the connectors onto and from the PCB were located at the edges of the

25

board in order to minimize the length of the connector cables. Connector headersleading to the Power PCB were aligned with the corresponding connector headersto allow for short wiring between the circuit boards.

4.3.2 Power PCB Layout

The Power PCB is a single layer PCB made out of aluminum which gives it sig-nificantly better thermal conductivity properties than a regular PCB such as FR4made out of glass epoxy panel. The aluminum PCB is composed of a three layerstructure of, a circuit layer made out of a copper foil, a dielectric insulation layerwith good thermal conductivity properties and a metal substrate [19]. The ther-mal conductivity of the aluminum PCB is 2.2 W/mK which is six times higherthan the thermal conductivity for the FR4 material [20].

The component placement became even more critical since only one circuitlayer was available and components needed to act as bridges for the traces inorder to be able to minimize the current loops effectively. The conduction traceswhere made into planes in order to support the high currents of up to 90 A.

26

5 Software Implementation

The DSP which was used to control the motor was a Texas Instruments TMS320F28335.It is a 32-bit floating-point processor with a clock rate of up to 150 MHz. It hasfloating-point capability which makes the processor well suited for motor controlin relation to fixed-point because of its capability of having a wider range of val-ues and more accurate measurements. The DSP is equipped with both on-boardRandom Access Memory (RAM) and internal flash memory for standalone control.There are 16 ADC inputs with a 12-bit resolution with an input range of 0−3.0 V .There are also 88 General Purpose Input/Output (GPIO) pins where some of themhave special features such as PWM and Encoder support. It is also possible tomake interrupts with different types of trigger signals. The different pins andsoftware functions that are being used are further explained in this section.

An overview over the system can be seen in Figure 5.1, where the differentfunctions are represented in different blocks.

Figure 5.1: DSP block layout overview

For the software implementation Code Composer StudioTM v5 (CCS) with li-braries from ControlSUITETM for C2000TM was used.

The DSP operation procedure starts with a hardware initialization where theprocessor first resets and then initialize functions like stack pointers, registers,clocks and watchdog [21]. After the hardware initialization is done the softwareinitialization starts and settings are loaded to the RAM. Examples of settings arethe PWM switching frequency, assigning the PWM outputs and other featuresfor the GPIO pins and the ADC channels. An overview of the pinouts can beseen in Table 5.1 and Table 5.2. The software goes into a waiting loop after theinitializations is done and wait for trigger signals for interrupts. The trigger signal

27

for the interrupt was set at the end of every PWM cycle, which has a switchingfrequency of 20 kHz. Flow chart for the startup can be seen in Figure 5.2.

Figure 5.2: Main procedure flow chart

The algorithms that need to be run in real time are placed in the interruptblock. The flow chart of the most necessary functions in the interrupt block canbe seen in Figure 5.3.

28

Figure 5.3: Interrupt procedure flow chart

29

All of the ADC channels were set to sample simultaneously with the PWMsignal as trigger. The input voltages were then attained with the following formula

D =4095

3.0Vin (5.1)

where D is the digital number converted from the ADC and Vin is the inputvoltage to the DSP. 4095 is the resolution of an ADC with 12-bits and 3.0 is therange of the input voltage. The digital numbers are then scaled with differentfactors, depending on the hardware, to determine the true voltages. The signalswhich are sampled by the ADC are represented in Table 5.1 together with a shortdescription.

Table 5.1: Input signals to the ADC moduleInput Name Description

ADC A0 I meas DC-link currentADC A1 Radio ref Torque reference from radio controlADC A2 Torque ref Torque reference wiredADC A3 Temp-NTC Temperature from the three phase inverterADC A4 Back-EMF A Voltage potential in phase AADC A5 Back-EMF B Voltage potential in phase BADC A6 Back-EMF C Voltage potential in phase CADC A7 Virtual n Virtual neutral point of the motorADC B0 Cell voltage 1 Voltage battery cell 1ADC B1 Cell voltage 2 Voltage battery cell 2ADC B2 Cell voltage 3 Voltage battery cell 3ADC B3 Cell voltage 4 Voltage battery cell 4ADC B4 Cell voltage 5 Voltage battery cell 5ADC B5 Cell voltage 6 Voltage battery cell 6ADC B6 Ch 1 ext Extra channel from radio control (Not in use)ADC B7 Ch 3 ext Extra channel from radio control (Not in use)

There are two different methods implemented to estimate the rotor position,one using ADC channels which samples the phase voltage potential and anotherusing the digital inputs with a comparator triggering on the zero crossing of theback-EMF. For the method using the ADC the signal value is continuously com-pared to the value of the virtual neutral point, which is obtained from a resistornetwork with three resistors connected in parallel with the motor, see Section 4.1.7.All the signals have digital filters implemented in order to reduce high-frequencyswitching noise. When the back-EMF value and the neutral point value are equal,the DSP indicates that a zero-cross event has occurred. The time difference com-pared to the previous zero-crossing event is also calculated. This time divided bytwo is then used to delay the output of the commutations sequence estimator with30◦. This is done because of the zero-cross event occuring 30◦ before the nextcommutation sequence should start, which can be seen in Figure 2.2. The motordirection is obtained by comparing in which order the zero-cross events occurs.

30

Six of the input signals to the ADC were used to measure the cell voltages ofthe battery pack. If one of these cells exceeds its upper or lower voltage limitsthe program will shut down the controller. The same will happen if the inputvoltage to the converter exceeds its upper or lower voltage limits. This is a safetyfunction for the battery to minimize the risk to damage the cells. Other safetyfunctions that were implemented were temperature measurement and over currentprotection, with both hardware and software.

The digital input and output pins that are being used are represented in Table5.2 together with a short description.

Table 5.2: Input and output signals of the DSPPin Input/Output Name Description

GPIO 0 Output PWM-1a PWM signal for S1GPIO 1 Output PWM-1b PWM signal for S2GPIO 2 Output PWM-2a PWM signal for S3GPIO 3 Output PWM-2b PWM signal for S4GPIO 4 Output PWM-3a PWM signal for S5GPIO 5 Output PWM-3b PWM signal for S6GPIO 10 Input PSC PFO Power fail inputGPIO 11 Output PSC WDI Watchdog timer output

GPIO 12 Input I trip Hardware current tripGPIO 20 Input QEP-A Encoder A pulseGPIO 21 Input QEP-B Encoder B pulseGPIO 23 Input QEP-I Encoder I pulseGPIO 26 Input ON/OFF On/Off button for the sensorGPIO 27 Output Disable Disable the gate drivers when highGPIO 29 Input Zero cross A Signal from back-EMF comparator, phase AGPIO 30 Input Zero cross B Signal from back-EMF comparator, phase BGPIO 31 Input Zero cross C Signal from back-EMF comparator, phase CGPIO 76 Output Led 1 Red LEDGPIO 77 Output Led 2 Green LED

The other method which is implemented to estimate the rotor position worksin a similar way to the one which is sampled by the ADC. The difference is thatthe zero-cross event is detected with comparators. So when the back-EMF voltageis higher than the neutral point, the comparator output will be high and when theback-EMF voltage is lower than the neutral point, the output will be low. In thisway the direction of the rotation and the commutation sequence can be calculated.

Encoder support was implemented to be able to evaluate the sensorless meth-ods. The enhanced Quadrature Encoder Pulse (QEP) register and special pinsreserved for this purpose where used to calculate the angle, the direction of therotation and the speed.

Another register which was used in the DSP was the register of the enhancedPWM. This register controls the PWM output signals, which is varied to changethe speed and the torque of the motor. The output depends on which of theswitching sequences the rotor is in and of the duty cycle. These two parameters

31

are the inputs to the PWM function. The switching sequence is received fromeither one of the two sensorless algorithms or the encoder and the duty cycleis received from the Proportional-Integral (PI) regulator, see Figure 5.1. Table5.3 represents the PWM switching of the transistors depending on the switchingsequence.

Table 5.3: Commutation states for the three phase inverterSequence S1 S2 S3 S4 S5 S6

1 PWM PWM OFF ON OFF OFF

2 PWM PWM OFF OFF OFF ON

3 OFF OFF PWM PWM OFF ON

4 OFF ON PWM PWM OFF OFF

5 OFF ON OFF OFF PWM PWM

6 OFF OFF OFF ON PWM PWM

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6 Verification and Evaluation of Results

In this section the simulation and laboratory measurement results will be presentedand evaluated.

6.1 Board Verification

A major part of the project was put into functionality verification. Already atan early stage of the inverter design process, jumper resistors were used in orderto simplify the validation and troubleshooting procedure. They also reduce thedamage of circuit errors and the short-circuit failures, since they isolate an errorwithin a specific circuit function, for example one of the switched power regulators.This made the troubleshooting process more structured and significantly reducedthe risk of damaging components. It also saved a lot of time since the error wasisolated within a smaller circuit and not the whole circuit board. The LED lightsalso proved to be very valuable for the purpose of troubleshooting. By receivingdirect visual feedback the process went much faster.

All the power levels were verified to their specified value. This was an importantand necessary result in order to have any functionality at all from any of thecomponents. The next major step was the validation of the onboard DSP, thisincluded; establishing a connection to the DSP, compiling to its flash memory andverifying the input and output signals. The PWM output signals were measuredin order to verify that the PWM control registers had been setup correctly. Themeasured PWM outputs of the switches S1, S2, S5 and S6 which corresponds tothe ones in Table 5.3 is illustrated in Figure 6.1.

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1 2 3 4 5 6 12 3 4 5 6

Figure 6.1: PWM outputs from the DSP with a 50 % duty cycle with motor inno load operation, blue S1, magenta S2, yellow S5 and green S6 at [5 V/div] and[1 ms/div]

The measured signals corresponds correctly to the desired state in Table 5.3.There is however also a dead time on the measured PWM outputs which is notvisible in Figure 6.1. The dead time is necessary in order to protect the threephase inverter from a shoot through in one of the half bridges.

The gate driver output signal was measured in order to validate that the am-plification of the PWM signal worked as intended. The signal for the same fourswitches after the gate driver amplification stage is presented in Figure 6.2.

34

1 2 3 4 5 6 13 4 5 62

Figure 6.2: PWM outputs from the gate driver with a 50 % duty cycle with motorin no load operation, blue S1, magenta S2, yellow S5 and green S6 at [10 V/div]and [1 ms/div]

The similarities of Figure 6.1 and Figure 6.2 shows that the gate driver properlyamplifies the PWM input signals. In this case 3.3 V is amplified to 5.0 V throughthe level shifter and then amplified to 10 V through the gate driver. The safetyshutdown functionality of the gate drivers was also tested and validated.

The output signals of the encoder, the A pulse and the A pulse, is presentedin Figure 6.3 along with output from the differential amplifier.

35

Figure 6.3: Encoder output signals, green differential amplifier, magenta A, blueA, [100 mV/div] and [20 µs/div]

The encoder signals from the measurement presented in Figure 6.3 has a verygood looking shape without any noise and would be able to function well withoutthe differential amplifying stage. The measurements were however conducted ina lab environment and not in a real field test with a lot of exterior noise. Ina case with a lot of external disturbances the differential stage can improve thereliability. The differential amplifiers chosen for this stage were a bit slow and ifreplaced, they could probably give a considerably faster response.

The current measurement signal presented in Figure 6.4 has some noise ontop of the actual signal. This was mainly caused by the necessary placement ofthe current sensor, close to battery connectors. This was however also close tothe switched power regulators which gives rise to a lot of noise. This signal is ofmajor importance in order for current control to be able to function as intended.The noise level was a lot higher than the current measurement sensitivity. Thisproblem was solved by using a digital filter.

36

Figure 6.4: Current sensor analog output voltage with circuit noise [100 mV/div]and [1 ms/div]

6.2 Sensored and Sensorless Evaluation

The Simulink motor model was used in order to be able to confirm that the sen-sorless control algorithms functioned as intended. To be able to have a referencemodel, a sensored control was first implemented. The back-EMF of the simulatedBLDC motor in sensored operation is shown in Figure 6.5 and the correspondingresult from the in lab BLDC motor is shown in Figure 6.7.

37

1 2 3 4 5 6 7 8

−8

−6

−4

−2

0

2

4

6

8

Time [ms]

Voltage [V]

Figure 6.5: Back-EMF of a simulated BLDC motor in sensored operation, yellowPhase A, magenta Phase B, green Phase C and blue virtual ground

Figure 6.6: Measured phase potential of a BLDC motor in sensored operationat a 100 % duty cycle, yellow Phase A, magenta Phase B and green Phase C,[2 V/div] and [500 µs/div]

38

1 2 3 4 5 6 1 3 4 52

Figure 6.7: Measured filtered phase potential of a BLDC motor in sensoredoperation at a 50 % duty cycle, yellow Phase A, magenta Phase B, green Phase Cand blue virtual ground, [200 mV/div] and [500 µs/div]

The unfiltered phase potential in Figure 6.6 and the voltage divided and filteredphase potential in Figure 6.7 are both very similar to the simulated back-EMF inFigure 6.5. This is because the phase potential is equal to the back-EMF in everythird switching sequence for each phase. For example in phase A in Figure 6.7the back-EMF is visible during switching sequence three and six. This is whenthe phase is not being driven. The filtered signal in Figure 6.7 has a trapezoidalshape, with a PWM noise of 20 kHz.

The simulated model controlled with the sensorless algorithm gave the sameresult as with the sensored operation presented in Figure 6.5. This was expectedbecause of the ideal characteristics of the model. The major difference was that thesimulated motor could not start in sensorless operation since it needs a back-EMFto estimate the position.

The phase potential of a BLDC motor was measured with the three phaseinverter operating in the two different sensorless modes. The measurements arepresented in Figure 6.8 and in Figure 6.9. The first one uses comparators fordetection of the zero crossing of the back-EMF and the later one uses the analoginputs of the DSP and digitally detects the zero crossing.

39

1 2 3 4 5 6 1 3 42

Figure 6.8: Measured filtered phase potential of a BLDC motor in sensorlessoperation using comparators at a 50 % duty cycle, yellow Phase A, magenta PhaseB, green Phase C and blue virtual ground, [200 mV/div] and [500 µs/div]

40

1 2 3 4 5 6 1 3 42

Figure 6.9: Measured filtered phase potential of a BLDC motor in sensorlessoperation using analog inputs at a 50 % duty cycle, yellow Phase A, magentaPhase B, green Phase C and blue virtual ground, [ 200mV/div] and [500 µs/div]

The sensorless methods are fully functional however they both require a min-imum motor RPM in order to be able to operate. The threshold RPM was mea-sured to approximately 600 RPM for the method with comparators and roughly300 RPM for the method which measures the phase potential and virtual mo-tor neutral with analog inputs. The difference between the results is due to thatthe hysteresis which is set to reduce the impact of noise is not adjustable for thecomparators. However the method which uses the ADCs is able to adjust thehysteresis depending on the motor speed which gives the increased performance.When the signal has been sampled it can be digitally filtered which also gives anincreased performance. The 300 RPM measurement is presented in Figure 6.10.For light electric vehicles the required initial speed usually is not a problem sinceit can be supplied by the driver.

41

Figure 6.10: Speed [200 RPM/div] versus Time [500 ms/div]

The simulated comparator output signal and the measured comparator outputsignal presented in Figure 6.11 and Figure 6.12 looks very similar.

1 2 3 4 5 6 7 8 9

−8

−6

−4

−2

0

2

4

6

8

Time [ms]

Voltage [V]

Figure 6.11: Simulated back-EMF in phase C, green, with the comparator outputsignal, yellow, and the virtual ground, blue

42

Figure 6.12: Measured phase potential in phase C, green [0.5 V/div], withthe comparator output signal, yellow [1 V/div], and the virtual ground, blue[0.5 V/div], at [500 µs/div]

The comparator triggers correctly when the back-EMF crosses the virtualground. The same also applies for the two other phases. The three compara-tor outputs give a similar signal sequence as corresponding hall sensors would.

43

6.3 Further evaluation

The phase A current during simulated motor operation and motor operation weremeasured and presented in Figure 6.13 and Figure 6.14. The simulated and themeasured current have similar looking shapes.

1 2 3 4 5 6 7 8 9 10

−1

0

1

Time [ms]

Current [A]

Figure 6.13: Simulated current in phase A

Figure 6.14: Measured current in phase A, 1 V corresponds to 10 A, [500 mV/div], [ ms/div]

44

The phase currents have a small dip at the top and bottom which is becauseof the current commutation due to the motor inductance when going from oneswitching sequence to the other in the three phase inverter. For phase A the posi-tive current dip occurs between switching sequence one and two and the negativecurrent dip occurs between switching sequence four and five from Table 5.3.

The implemented current regulator operates as expected and keeps the currentconstant when changing loads. Current control is especially well suited for electricvehicles since the current is proportional to the motor torque and thereby givesthe driver the same feedback experience as it would from a regular car throttle.

The battery cell protection circuit is verified to be operational with an emulatedbattery. However a test with a real lithium ion battery with its balance connectorconnected to the cell protection circuit needs to be conducted in order to fullyverify its functionality. A draw back with this circuit is that in its present state itcan only handle up to six cells. The circuit solution is also redundant since eachof the battery cells uses an analog input; these are usually few and expensive onDSPs. A better solution to this problem would be to use a battery cell monitoringsolution that only communicates with the DSP through digital inputs and outputs.If a low manufacturing cost is the prominent design factor then it is possible tomeasure only a few of the cell voltages which are more likely to suffer from anover- or under- voltage.

45

7 Closure

This section presents the conclusions as well as introducing some potential futurework.

7.1 Conclusion

The thesis purpose was to design and develop a three phase inverter for an ultra-light electric vehicle with sensorless BLDC motor control and to evaluate theresult. A three phase inverter has been simulated, designed, built and evaluated.The purpose has been fulfilled since the three phase inverter has been verified tofunction as intended.

The three phase inverter supports two different sensorless algorithms based onback-EMF measurement as well as support for sensored control. The two sensorlessalgorithms give similar results however they require different surrounding compo-nents as well as DSP inputs. The method using ADCs is preferred in this casesince the DSP had ADCs available and it required less surrounding componentscompared to the one using comparators.

The three phase inverter has been made small enough to fit in an ultra-lightvehicle in its present state and is able to independently control a BLDC drivesystem.

7.2 Future Work

From the knowledge acquired throughout the project there are a lot of designimprovements that can be made. One example is using fewer power levels whichwould make it possible to remove a lot of components and another is only usingone position feedback method which also would allow for a smaller design. A DSPwith only the necessary functionality and inputs and outputs would also allow foran improved and more efficient design.

Evaluation of the necessary cooling for the MOSFETs remains. Proper mea-surements could determine if the aluminum PCB is required or if the design couldbe fitted on only one PCB. This would make it possible to remove all connectorsbetween the two PCBs as well as the extra amplifying stages at the MOSFETgates.

In order to improve the drive system reliability a connector for motor tem-perature measurement should be implemented. Another cell protection circuitthat is able to protect more cells without using any of the ADC inputs should beimplemented.

46

References

[1] S.S Williamson el al., ”Comprehensive Drive Train Efficiency Analysis of Hy-brid Electric and Fuel Cell Vehicles Based on Motor-Controller Efficiency Mod-eling,” in Transactions on Power Electronics, 2006 , pp. 730-740.

[2] P. Waide and C.U. Brunner, ”Energy-Efficiency Policy Opportunities for Elec-tric Motor-Driven Systems,” International Energy Agency, France, 2011.

[3] D. Hanselman, Brushless Permanent Magnet Motor Design, 2 nd. Ohio:Magna Physics Publishing, 2006.

[4] AN885 - Brushless DC (BLDC) Motor Fundamentals, Microchip TechnologyInc., Chandler, AZ, 2003.

[5] A. Hughes, Electric Motors and Drives, 3 rd. Oxford, Great Britain: Elsevier,2006.

[6] AN1083 - Sensorless BLDC Control With Back-EMF Filtering, MicrochipTechnology Inc., Chandler, AZ, 2007.

[7] N. Mohan, T.M. Undeland, and W.P. Robbins, Power Electronics - Converters,Application and Design, 3 rd. Hoboken: John Wiley and Sons Inc., 2003.

[8] K.A. Coke and S.D. Sudhoff, ”A Hybrid Observer for High Preformance Brush-less DC Motor Drives,” in Transactions on Energy Conversion, 1996, pp. 318-323.

[9] M. Konghirum, ”Automatic Offset Calibration of Quadrature Encoder PulseSensor for Vector Controlled Drive of Permanent Magnet Synchronous Mo-tors,” in TENCON, Melbourne, 2005, pp.1-5.

[10] P. Dwane et al., ”A Resonant High Side Gate Driver for Low Voltage Appli-cations,” in Power Electronics Specialists Conference, Recife, 2005.

[11] Bootstrap Component Selection For Control IC’s, International Rectifier, ElSegundo, CA, 2001.

[12] S. Baldursson, ”BLDC Motor Modelling and Control - A Matlab R©/Simulink R©

Implementation,” M.S. thesis, Dept. Elect. Eng., Chalmers Univ., Gothenburg,Sweden, 2005.

[13] P. Suntharalingam el al., ”Gear Locking Mechanism to Extend the ConsistentPower Operating Region of the Electric Motor to Enhance Acceleration andRegenerative Braking Efficiency in Hybrid Electric Vehicles,” in Vehicle Powerand Propulsion Conference, Dearborn, MI, 2009, pp.103-108.

[14] L. Balogh, ”Design And Application Guide For High Speed MOSFET GateDrive Circuits,” Texas Instruments Inc., 2012.

47

[15] S.A Hossain and P. Reis, ”Effect of BLDC Motor Commutation Schemeson Inverter Power Loss,” in International Conference on Electrical Machines,Vilamoura, 2008, pp. 1-5.

[16] S.A Hossain and R. Pedro, ”Effect of BLDC Motor Commutation Schemes onInverter Capacitor Size Selection,” in International Conference on ElectricalMachines, Rome, 2010, pp. 34-36.

[17] T. Hubing, ”PCB EMC Design Guidelines: A Brief Annotated List,” inInternational Symposium on Electromagnetic Compatibility, 2003. 2003.

[18] S. Muralikrishna and S. Sathyamurthy, ”An Overview of Digital Circuit De-sign and PCB Design Guidelines - An EMC Perspective,” in ElectromagneticInterference and Compatibility, Bangalore, 2008, pp. 567-573.

[19] J.K Park et al., ”Formation of Through Aluminum Via for Noble MetalPCB and Packaging Substrate,” in Electronic Components and TechnologyConference, Lake Buena Vista, FL, 2011, pp. 1787-1790.

[20] Thermal Clad - HT-04503, The Bergquist Company, Chanhassen, MN, 2009.

[21] TMS320F28335 Digital Signal Controllers - Data Manual, Texas InstrumentsInc., 2012.

48

A Calculation of Inverter Output Voltage

A.1 Case 60− 120◦

eb

ec

VnVd

ea

ic = 0

ic ≠ 0 +

Figure A.1: Current path through the three phase inverter for the interval 60−120◦ where the green path represents the current through the active phases and thered path represents the commutating current from the previous switching sequence

ic ib

ea

ebecL LR R

( )

Vd

Vab

D3

L

R

Vn

Figure A.2: Circuit topology for the case 60 − 120◦, where Vbc represents thevoltage over a reversed biased diode

ib 6= 0

Vab = 0 (A.1)

Vbc = Vd (A.2)

Vca = −Vd (A.3)

When ib = 0 Kirchhoff’s voltage law are applied around each mesh in Figure A.2to obtain the three phase-to-phase voltages

− Vd −Ric − Ldicdt− ec + ea − L

d(ic + ib)

dt−R(ic + ib) = 0 (A.4)

− Vab −Rib − Ldibdt− eb + ea − L

d(ic + ib)

dt−R(ic + ib) = 0 (A.5)

49

when ib = 0

− Vd − 2Ri− 2Ldi

dt− ec + ea = 0 (A.6)

− Vab − eb + ea − Ldi

dt−Ri = 0 (A.7)

(A.6) and (A.18) gives

Vab =1

2(Vd + ec + ea − 2eb) (A.8)

so the three phase-to-phase voltages will be

Vab =1

2(Vd + ec + ea − 2eb) (A.9)

Vbc =1

2(Vd − ec − ea + 2eb) (A.10)

Vca = −Vd (A.11)

50

A.2 Case 120− 180◦

eb

ec

VnVd

ea

ic = 0

ic ≠ 0 +


ib ia

ec

eaebL LR R

( )Vd

Vca

D2

L

R

Vn


ia 6= 0

Vab = −Vd (A.12)

Vbc = Vd (A.13)

Vca = 0 (A.14)

When ia = 0 Kirchhoff’s voltage law are applied around each mesh in Figure A.4to obtain the three phase-to-phase voltages

Vd −Rib − Ldibdt− eb + ec − L

d(ib + ia)

dt−R(ib + ia) = 0 (A.15)

− Vca −Ria − Ldiadt− ea + ec − L

d(ib + ia)

dt−R(ib + ia) = 0 (A.16)

51

when ia = 0

Vd − 2Ri− 2Ldi

dt− eb + ec = 0 (A.17)

− Vca − ea + ec − Ldi

dt−Ri = 0 (A.18)


Vca =1

2(−Vd + eb + ec − 2ea) (A.19)


Vab =1

2(−Vd − eb − ec + 2ea) (A.20)

Vbc = Vd (A.21)

Vca =1

2(−Vd + eb + ec − 2ea) (A.22)

52

A.3 Case 180− 240◦

eb

ec

VnVd

ea

ic = 0

ic ≠ 0 +

Figure A.5: 1Current path through the three phase inverter for the interval180− 240◦ where the green path represents the current through the active phasesand the red path represents the commutating current from the previous switchingsequence

ia ic

eb

eceaL LR R

( )Vd

Vbc

D5

L

R

Vn


ic 6= 0

Vab = −Vd (A.23)

Vbc = 0 (A.24)

Vca = Vd (A.25)

When ic = 0 Kirchhoff’s voltage law are applied around each mesh in Figure A.6to obtain the three phase-to-phase voltages

− Vd −Ria − Ldiadt− ea + eb − L

d(ia + ic)

dt−R(ia + ic) = 0 (A.26)

− Vbc −Ric − Ldicdt− ec + eb − L

d(ia + ic)

dt−R(ia + ic) = 0 (A.27)

53

when ic = 0


dt− ea + eb = 0 (A.28)

− Vbc − ec + eb − Ldi

dt−Ri = 0 (A.29)


Vbc =1

2(Vd + ea + eb − 2ec) (A.30)


Vab = −Vd (A.31)

Vbc =1

2(Vd + ea + eb − 2ec) (A.32)

Vca =1

2(Vd − ea − eb + 2ec) (A.33)

54

A.4 Case 240− 300◦

eb

ec

VnVd

ea

ic = 0

ic ≠ 0 +


ic ib

ea

ebecL LR R

( )Vd

Vab

D4

L

R

Vn


ib 6= 0

Vab = 0 (A.34)

Vbc = −Vd (A.35)

Vca = Vd (A.36)

When ib = 0 Kirchhoff’s voltage law are applied around each mesh in Figure A.8to obtain the three phase-to-phase voltages

Vd −Ric − Ldicdt− ec + ea − L

d(ic + ib)

dt−R(ic + ib) = 0 (A.37)

− Vab −Rib − Ldibdt− eb + ea − L

d(ic + ib)

dt−R(ic + ib) = 0 (A.38)

55

when ib = 0

Vd − 2Ri− 2Ldi

dt− ec + ea = 0 (A.39)

− Vab − eb + ea − Ldi

dt−Ri = 0 (A.40)


Vab =1

2(−Vd + ec + ea − 2eb) (A.41)


Vab =1

2(−Vd + ec + ea − 2eb) (A.42)

Vbc =1

2(−Vd − ec − ea + 2eb) (A.43)

Vca = Vd (A.44)

56

A.5 Case 300− 360◦

eb

ec

VnVd

ea

ic = 0

ic ≠ 0 +


ib ia

ec

eaebL LR R

( )

Vd

Vca

D1

L

R

Vn


ia 6= 0

Vab = Vd (A.45)

Vbc = −Vd (A.46)

Vca = 0 (A.47)

When ia = 0 Kirchhoff’s voltage law are applied around each mesh in Figure A.10to obtain the three phase-to-phase voltages

− Vd −Rib − Ldibdt− eb + ec − L

d(ib + ia)

dt−R(ib + ia) = 0 (A.48)

− Vca −Ria − Ldiadt− ea + ec − L

d(ib + ia)

dt−R(ib + ia) = 0 (A.49)

57

when ia = 0


dt− eb + ec = 0 (A.50)

− Vca − ea + ec − Ldi

dt−Ri = 0 (A.51)


Vca =1

2(Vd + eb + ec − 2ea) (A.52)


Vab =1

2(Vd − eb − ec + 2ea) (A.53)

Vbc = −Vd (A.54)

Vca =1

2(Vd + eb + ec − 2ea) (A.55)

58

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GPI

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GPI

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GPI

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GPI

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94

GPI

O53

95

GPI

O54

96

GPI

O55

97

GPI

O56

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GPI

O57

99

GPI

O58

100

GPI

O59

110

GPI

O60

111

GPI

O61

112

GPI

O62

113

GPI

O63

114

GPI

O64

115

GPI

O65

116

GPI

O66

119

GPI

O67

122

GPI

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123

GPI

O69

124

GPI

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GPI

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GPI

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GPI

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GPI

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GPI

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VSS 92

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VDD101

VSS 103

VSS 106

VDDIO107

VSS 108

VDD109

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VSS 118

VSS 120

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VSS 125

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X1

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IC7


























PIC7101 PIC7102COC

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PIC920

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PIC9

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PIC9

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PIC9

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PIC9

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PIC10901 PIC10902COC109

PIC11001 PIC11002COC110

PIIC701

PIIC702

PIIC703

PIIC704

PIIC705

PIIC706

PIIC707

PIIC708

PIIC709

PIIC

7010

PIIC

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PIIC

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PIIC

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PIIC7014

PIIC7015

PIIC

7016

PIIC

7017

PIIC

7018

PIIC

7019

PIIC

7020

PIIC

7021

PIIC7022

PIIC7023

PIIC

7024

PIIC

7025

PIIC

7026

PIIC

7027

PIIC

7028

PIIC7029

PIIC7030

PIIC7031 PIIC7032PIIC7033

PIIC7034

PIIC

7035

PIIC

7036

PIIC

7037

PIIC

7038

PIIC

7039

PIIC

7040

PIIC

7041

PIIC

7042

PIIC

7043

PIIC7044

PIIC7045

PIIC

7046

PIIC

7047

PIIC

7048

PIIC

7049

PIIC

7050

PIIC

7051

PIIC

7052

PIIC

7053

PIIC

7054

PIIC

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PIIC

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PIIC

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PIIC7058PIIC7059

PIIC7060

PIIC7061

PIIC

7062

PIIC

7063

PIIC

7064

PIIC

7065

PIIC

7066

PIIC

7067

PIIC

7068

PIIC

7069

PIIC7070

PIIC7071

PIIC

7072

PIIC

7073

PIIC

7074

PIIC

7075

PIIC

7076

PIIC

7077

PIIC

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PIIC

7079

PIIC

7080

PIIC

7081

PIIC

7082

PIIC7083

PIIC7084

PIIC

7085

PIIC

7086

PIIC

7087

PIIC

7088

PIIC

7089

PIIC

7090

PIIC

7091

PIIC7092

PIIC7093

PIIC

7094

PIIC

7095

PIIC

7096

PIIC

7097

PIIC

7098

PIIC

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PIIC70100

PIIC70101

PIIC70102

PIIC70103

PIIC70104

PIIC70105

PIIC70106

PIIC70107

PIIC70108

PIIC70109

PIIC70110

PIIC70111

PIIC70112

PIIC70113

PIIC70114

PIIC70115

PIIC70116

PIIC70117

PIIC70118

PIIC70119

PIIC70120

PIIC70121

PIIC70122

PIIC70123

PIIC70124

PIIC70125

PIIC70126

PIIC70127

PIIC70128

PIIC70129

PIIC70130

PIIC70131

PIIC70132

PIIC70133

PIIC70134

PIIC70135

PIIC70136

PIIC70137

PIIC70138

PIIC70139

PIIC70140

PIIC70141

PIIC70142

PIIC70143 PIIC70144

PIIC70145

PIIC70146

PIIC70147

PIIC70148

PIIC70149

PIIC70150

PIIC70151

PIIC70152

PIIC70153

PIIC70154

PIIC70155

PIIC70156

PIIC70157

PIIC70158

PIIC70159 PIIC70160

PIIC70161

PIIC70162

PIIC70163

PIIC70164

PIIC70165

PIIC70166

PIIC70167

PIIC70168

PIIC70169

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PIIC70171

PIIC70172

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PIIC70174

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PIC2402PIC2502

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PIC3402PIC3602

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PIIC

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PIIC

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PIIC

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PIIC

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PIIC

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PIIC

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PIIC

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PIIC

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PIIC

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PIIC

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PIIC

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PIIC

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PIIC70110

PIIC70111

PIIC70112

PIIC70113

PIIC70114

PIIC70115

PIIC70116

PIIC70119

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PIIC70124

PIIC70127

PIIC70128

PIIC70129

PIIC70130

PIIC70131

PIIC70132

PIIC70135

PIIC70136

PIIC70137

PIIC70138

PIIC70141

PIIC70142

PIIC70145

PIIC70148

PIIC70149

PIIC70150

PIIC70151

PIIC70152

PIIC70153

PIIC70156

PIIC70157

PIIC70158

PIIC70161

PIIC70162

PIIC70163

PIIC70164

PIIC70165

PIIC70168

PIIC70169

PIIC70172

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PIIC70174

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PIIC

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74

75

Documents

Design, Control and Evaluation of a Prototype Three Phase Inverter …publications.lib.chalmers.se/records/fulltext/183933/183933.pdf · Drive System for an Ultra-Light Electric Vehicle