Bidirectional Converterto supply a Permanent Magnet Synchronous Machine

Bernardo Torrejanobernardo.torrejano@ist.utl.pt

Instituto Superior Tecnico, Lisboa, Portugal

September 2017

Abstract

Exhaust gases from combustion engines contribute to the greenhouse effect, hencecar manufacturers are developing new electrical drives. An innovative inverter topology,the Z-source inverter (ZSI), was presented recently aiming to improve performanceand safety compared to conventional ones and its analysis is the main subject of thisthesis. The advantages of this converter type are buck-boost capability in a singleconversion stage and actively using the shoot-through event without damaging thedevices. The chosen motor to integrate the drive is the permanent-magnets synchronousmachine because of its relevant characteristics for automotive applications. The designedclosed-loop controller is based on a modified field-oriented control technique. A systemwas assembled in Simulink with all the devices models. Four distinct tests were drawnto evaluate the complete system performance: acceleration, braking, load torque andcomplete cycle tests. The designed electric drive was able to produce the necessarytorque to follow the desired reference speed in each test, both operating in motor andgenerator modes. Regenerative braking is achieved employing the bidirectional ZSI andpart of the kinetic energy is fed back to the source. These simulations demonstratethat the ZSI is a viable option to integrate future drive designs and its attributes areattractive to electric vehicles.Keywords: Electric Vehicle, Bidirectional Z-Source Inverter, Permanent-Magnet SynchronousMachine, Field-Oriented Control, Electric Drive

1. Introduction

Most vehicles today are equipped with internalcombustion engines. However, this type of pro-pelling system is responsible for releasing harm-ful exhaust gases into the atmosphere, contribut-ing to the greenhouse effect. Governments havebeen putting into place restrictions to traditionalengines and incentives for electric driven vehicles.Consequently, the automotive industry is currentlyadapting to this new reality and developing newelectrical drives. [1]

Two different types of solution have come to light,purely electric and hybrid electric vehicles. The for-mer in its simplest architecture is composed by abattery pack, an inverter and an electrical motor.Tesla Motors models are examples of such type ofcar. Hybrid electric vehicles operate dynamicallythe electric drive together with the combustion en-gine, providing considerable mileage range as wellas energy savings. Toyota Prius and Honda CivicHybrid are examples of early developments of thislast category. [2]

Depending on the automobiles hybridization adistinctive designation is used before the name Hy-brid: Micro, Mild or Full. The degree of hybridiza-tion is intimately related to electric machine powerand subsequently its role, with energy savings thatcan range from 5% in micro to 50% in full hybridvehicles. In Micro Hybrids the electric motor is onlyaiding the engine during start and stop, providinga short boost and recovering energy respectively.Mild Hybrids operate more often their electricalmachine, increasing the overall system efficiency.Full Hybrids, and Plug-In Hybrids, can sometimesuniquely rely on electrical propulsion, including fullelectric mode with autonomous range up to 50 km.

Hybrid vehicles present four main internal topolo-gies. Series architecture is conceptually the sim-plest. The combustion engine is coupled with a gen-erator and is only employed to produce electricity,which can be directly used to supply the inverterand electric motor or stored in a battery pack. Themost common is the Parallel topology. Its first ad-vantage is the lower number of components, lack-

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ing a dedicated generator compared to the previous.Both engine and motor are connected to the driveshaft via clutches, granting combined, engine aloneor motor alone drive. In Series-Parallel a secondmotor/generator is added. This enables the com-bustion engine to directly feed this electric machineor work together with the first one to drive the ve-hicle. Complex architecture is an evolution of theearlier, yet it does not add any major features. Itincorporates a second power converter in order toallow simultaneous propulsion by the two motorsand the engine. It aims maximum efficiency andalso widens the control system capability. [3]

1.1. Electric Machines

Electric machines are power converters that convertelectrical energy into mechanical, or the other wayaround, in a process called electromechanical con-version. The former is labelled a motor and thelatter a generator, some machines can even per-form both. Every machine is composed by a sta-tionary part, the stator, and a moving one, therotor. Current can be conducted through coilsor cages bar, while the magnetic flux is directedalong the ferromagnetic materials. Depending ontheir arrangement several topologies with differentcharacteristics exist. For the automotive indus-try, the most relevant ones are brushed DC ma-chine, switched reluctance machine, induction ma-chine and permanent-magnet machine. [4]

In a brushed DC machine, the stator creates astable magnetic field excitation windings. A squarealternating current flows in rotors coil, also creat-ing an alternating magnetic flux. The interactionof both fluxes creates a magnetomotive force mak-ing the shaft spin. Its most straightforward advan-tage is simple control. However, the main prob-lem of these machines occurs in the commutatorand brushes, making it unreliable and requiring pe-riodic maintenance. A switched reluctance motordoes not have wires or magnets in moving parts.Instead, the rotor poles without active elements aresalient. Excitation is performed through the sta-tor windings, which can have multiple phases. Therotor tries to align the magnetic fluxes, thereforetorque occurs due to reluctance minimization in astepwise fashion. Control complexity, torque rippleand acoustic noise are some of the identified dis-advantages. Nonetheless it has a simple and cheapconstruction, as well as good torque-speed relationregarding automotive requirements. [5]

In spite of previous machines perks, the dominantdrive units are powered by induction or permanentmagnet synchronous machines. Rotor has a differ-ent construction for each machine. Cage windingsin induction machines, often called squirrel cage dueto resemblance, short-circuit the induced currents.

In the synchronous machines rotor several magnetsare incorporated, which reduce Joule losses. On theother hand, the stator of both machines is similaras in Figure 1. In the internal surface, there areaxial slots facing the air gap, space between sta-tor and rotor. Inside these slots are three-phasewindings. A revolving magnetic field is createdwhen through them flow three sinusoidal currentswith the same amplitude, same frequency and ini-tial phases shifted 2/3.

Figure 1: Stator architecture of a three-phase elec-tric machine.

The principle of operation of an induction motoris based on the change of magnetic flux in the short-circuited rotor windings. If the rotor revolved at thesame speed as the stator magnetic field, there wouldbe no relative variation of the flux and no counter-electromotive force would be induced. Ergo, rotorfrequency must be a little bit slower than the statorcurrent one, developing a slip between them. Thisway a certain current will be continually inducedin the cages bar as intended. The interaction be-tween stator field and rotor current will result inelectromagnetic torque.

The stator of permanent magnet synchronousmachine may be supplied with two different voltagewaveforms. Depending on the magnets dispositioninside the rotor, a sinusoidal or trapezoidal counter-electromotive force can be measured in phase wind-ings. While the former needs to be supplied with asinusoidal voltage, the latter can be operated withsquare waves, conceiving the commonly known per-manent magnet DC machine. The principle of oper-ation for this machine is based on the rotors angularfrequency being equal to the synchronous one, thusrevolving without changing displacement. The ori-entation of magnetic field created by the magnetsis only dependent on the rotors relative position.Electromagnetic torque is proportional to the vectorproduct of stators and rotors fluxes, thus it is max-imum when the angle between them is 90. Thismachine type has a higher efficiency, higher specificpower, higher specific torque and lower losses com-pared to the induction one, thus was chosen to thisstudy.

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1.2. Power Electronic Units

Semiconductor devices are the backbone of elec-tronic circuits. Ideal power switches desirably havethe following characteristics: large forward and re-verse blocking voltages; high conducting current ca-pability; fast and easy switching; cause low elec-tromagnetic interference; good reliability; have lowcost and long lifetime. Diodes are used in rectifiers,DC-DC converters and as anti-parallel freewheel-ing path for the inductive load current. In elec-tric vehicles, the active switches of choice are MOS-FETs and IGBTs. For applications below 300 V theformer are adopted, whereas higher voltages andcurrents demand for IGBTs. Although, the lattercannot be operated at high frequencies, 50 kH isa state-of-the-art limit. Currently, silicon carbidepower devices are substituting purely silicon ones.Properties such as higher dielectric breakdown field,quicker switching frequency, higher operating tem-peratures and good thermal conductivity are someof the proved advantages. [6]

Power electronics units are static power convert-ers that transform electrical energy from one formto an- other more suitable to the load requirements.They integrate semiconductors, transformers, ca-pacitors and inductors in their circuits. There arefour different groups, regarding their function: rec-tifiers; DC-DC converters; inverters; and AC-ACconverters. For electric and hybrid vehicles only thefirst three of the previous categories of devices arecommonly used. High reliability, high power den-sity, high efficiency and low cost are requirementsespecially relevant in automotive.

Connecting the vehicles to the grid requires a rec-tifier circuit to feed direct current in. These can beeither mounted on board or at the charging stations.In order to ensure high energy quality and low dis-tortion impact to the grid, contemporary chargersincorporate boost converters for active power factorcorrection. [7]

Numerous DC-DC converters incorporate the ve-hicle, moreover in EVs. They are responsible forconnecting different voltages links with efficienciesover 90%. Modern converters are operated at highfrequencies, normally above 50 kH, in order to re-duce the size of transformers, inductors and capac-itors. To counter the increase of switching losses,soft-switching techniques have been implemented:zero-voltage and zero-current switching. [8]

The keys to connect electric machines with theDC links are three-phase inverters. As the machinesare intended to work with bidirectional energy flow,inverters may also operate as rectifiers. [9]

Voltage source inverts, with hard switching, arethe most popular architecture among automotiveindustry. Three legs with a pair of IGBTs and alarge capacitor bank make them a simple inverter,

with high efficiency and relatively easy control. Yet,it is a buck-type inverter and the output peak volt-age is limited to the DC link level. Additionally,switches from the same leg cannot be turned onsimultaneously due to short-circuit of the link. Adead time is implemented as a safeguard causingsome distortion in the output.

Substituting the parallel capacitor by a series in-ductance turns the previous topology into a currentsource inverter. It becomes a boost-type converter,meaning greater peak AC voltage can be suppliedto the motor. Capacitors are smaller as the DClink voltage is also lower, leading to higher densityunits. Efficiencies achieved are however not so highin practical applications.

As a derivation from the voltage source inverter,a soft switching converter may be designed. Higherefficiencies can be achieved as switching losses aregreatly reduced. However, more active elementsmake these units less reliable, heavier and more ex-pensive. They are more suited to static applica-tions, where efficiency is paramount and volume isnot a constraint.

Z-source inverters are a recent technology gainingparticular interest. They do not need any other con-verter connected because they belong to the buck-boost family, achieving a wide voltage range at theoutput. This property is also very interesting for ve-hicles in order to control the electric motor. Shoot-through time is allowed making them more reliablethan voltage source ones. The technology needs yetto be maturated in practical applications. Weight-ing the arguments previously discussed, a bidirec-tional Z-source inverter will be studied and imple-mented in this work.

2. Z-Source InverterAiming to surpass existing limitations, Mr. FangZheng Peng proposed a new inverter topology in2003 [10]. It couples the DC source with the tra-ditional inverter arms through a LC filter, thus thelink cannot be described neither as a voltage nor asa current source. It is a two-port impedance linkconsisting of two similar inductors and two similarcapacitors connected in X shape, Figure 2. This Znetwork is coupled between the power source andthe inverter bridges, enabling the boost of DC-linkand empowering the converter with buck-boost fea-ture. Adding an anti-parallel source IGBT to theoriginal proposed circuit, makes bidirectional powerflow conceivable.

Three-phase Z-source inverters permit nine possi-ble states, six active vectors which impress the linkvoltage on the load, two zero vectors that isolate theZ-network the legs and apply zero voltage to themotors phases and one shoot-through vector thatactively short-circuits the link. Seven combinationscan realize this last state, shoot-through via any one

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Figure 2: Bidirectional Z-source inverter, coupled with a DC power source and an inductive load.

leg, any two legs or all legs at the same time. Thebridges behaviour can be described by three possi-ble circuits, depending on the state vector appliedto the three-phase inverter.

When one of the six active modes is triggered, apositive or negative voltage is applied to the load.Due to its inductive properties, almost constantcurrent will flow through the link impedance. Toimplement null voltage in the motor phases, bothzero and shoot-through vectors achieve such result.While the former disrupts legs current, equivalentto an open circuit, the latter is used to control theboost characteristic, zero voltage drops in inverterlink is equivalent to a no impedance path. [11, 12]

2.1. Continuous Conduction OperationWhen in a shoot-through state, the Z impedancenetwork becomes isolated and energy is exchangedfrom capacitors to inductors, where TS and T0 arerespectively the switching and shoot-through peri-ods.

vO(t) = 0 (1)

vL(t) = VC (2)

Across the diode there is a negative voltage, re-verse biasing the device, that blocks any current.

vD(t) = VDC − 2VC (3)

iIN (t) = 0 (4)

iL(t) = −iC(t) (5)

Considering now one of the nonshoot-throughmodes, during T1 = TS − T0. Diode is conductingand the inverter behaves as a current source.

vD(t) = 0 (6)

vL(t) = VDC − VC (7)

vO(t) = 2VC − VDC (8)

iL(t) = iC(t) + IO (9)

iIN (t) = IO + 2iC(t) (10)

In steady-state the average voltage at the termi-nals of an inductor and capacitor’s current has tobe null, (2), (5), (7), (9) and assuming iL(t) ≈ IL.

vL =T0 · VC + T1 · (VDC − VC)

TS= 0 (11)

VCVDC

=T1

T1 − T0(12)

iC =T0 · (−IL) + T1 · (IL − IO)

TS= 0 (13)

ILIO

=T1

T1 − T0(14)

VC =T1

T1 − T0VDC (15)

Successive application of shoot-through state in-creases the average capacitor voltage. Therefore,available to the inverter bridges there is a boostedsource voltage vO.

vO = 2VC − VDC =TS

T1 − T0VDC (16)

The impedance network boost factor B is definedby (18), where D0 is the shoot-through duty cycle.B is always greater or equal to 1. From the conven-tional PWM techniques, the relation between max-imum output alternated voltage and input constantone is known as modulation index M .

D0 =T0TS

(17)

B =TS

T1 − T0=

1

1 − 2D0(18)

vac = M · vO2

= M ·B · VDC2

(19)

The overall Z-source inverter buck-boost factorBB is defined and its values range from zero to in-finity.

BB = M ·B =M

1 − 2D0(20)

vac = BB · VDC2

(21)

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2.2. Dynamic Model

A transient analysis of the z-source network is nec-essary to develop the controller, knowing the vari-ables response to stimulus. A state space averagedsmall-signal modelling is performed, and conse-quently the system transfer functions are deducted.In this analysis the inverter circuit can be simplified.The AC side is equivalent to an inductive load inparallel with a switch, which has the opposite statethan the source one, hence controlling the shoot-through feature. For a symmetric impedance mesh,the converter has only three state variables.

x(t) = [iL(t) vC(t) iO(t)]T

(22)

For the shoot-through mode, the system differen-tial equations are (23-25). They can be rewrittenin the matrix form Kx = A1x.

Ld iL(t)

dt= vC(t) (23)

Cd vC(t)

dt= −iL(t) (24)

LOd iO(t)

dt= −R · iO(t) (25)

Similarly for the active state, the equations are(26-28). The matrix form has the configurationKx = A2x+B2vDC .

Ld iL(t)

dt= vDC(t) − vC(t) (26)

Cd vC(t)

dt= iL(t) − iO(t) (27)

LOd iO(t)

dt= 2vC(t) − vDC(t) −R · iO(t) (28)

The average space state takes into account thetwo states (34), d0 represents the instantaneousshoot-through duty-cycle value. [13]

Kd

dt

∆iL(t)∆vC(t)∆iO(t)

=

0 2D0 − 1 01 − 2D0 0 D0 − 1

0 2 − 2D0 −R

∆iL(t)∆vC(t)∆iO(t)

+

1 −D0 2VC − VDC0 IO − 2IL

D0 − 1 VDC − 2VC

[vDC(t)

d0(t)

](29)

G1 =(1 −D0)

[LOCs

2 +RCs+ (1 −D0)]

LLOCs3 + LRCs2 + [2(1 −D0)2L+ (1 − 2D0)2LO] s+ (1 − 2D0)2R(30)

G2 =LOCγ1s

2 + [RCγ1 + (1 − 2D0)LOγ2] s+ (1 − 2D0) [Rγ2 − (1 −D0)γ2]

LLOCs3 + LRCs2 + [2(1 −D0)2L+ (1 − 2D0)2LO] s+ (1 − 2D0)2R(31)

G3 =(1 −D0) [[(1 −D0)L+ (1 − 2D0)LO] s+ (1 − 2D0)R]

LLOCs3 + LRCs2 + [2(1 −D0)2L+ (1 − 2D0)2LO] s+ (1 − 2D0)2R(32)

G4 = −LLOγ2s2 − [[(1 −D0)γ1 −Rγ2]L+ (1 − 2D0)LOγ1] s− (1 − 2D0)Rγ1

LLOCs3 + LRCs2 + [2(1 −D0)2L+ (1 − 2D0)2LO] s+ (1 − 2D0)2R(33)

Kx = [d0A1 + (1 − d0)A2]x+ (1 − d0)B2vDC(34)

Following a perturbation in the source volt-age and shoot-through duty-cycle is considered,vDC(t) = VDC + vDC(t) and d0(t) = D0 + d0(t)),disturbances will be caused to the state variables,x = X + ∆x. Small relative perturbations are con-sidered and therefore the second order terms arenegligible and equation system simplifies to (29).

Laplace transformation of the equation systemwill allow to obtain the transfer functions regardingthe different variables. G1,3 are the variables gain

when d0(s) = 0. G2,4 are the variables gain whenvDC(s) = 0. To simplify the transfer functions (30-33), γ1 = (2VC − VDC) and γ2 = (2IL − IO).

∆iL(s) = G1 · vDC(s) +G2 · d0(s) (35)

∆vC(s) = G3 · vDC(s) +G4 · d0(s) (36)

3. Permanent Magnet Synchronous MachineCurrent running in the stator windings originatesa magnetomotive force and establishes a magneticflux flowing through the iron tooth and the air gap.The contribution of all individual phases shapes therevolving stator magnetomotive force.

Magnetic field rotational speed is called syn-chronous speed ΩS and its value is determined bythe power supply characteristics and machine con-struction, more specifically by the three-phase sys-tem angular frequency ωs and the number of phase’spole pairs ps.

ΩS =ωsps

(37)

Rotor magnetic field is established by perma-nent magnets and a constant magnetic flux Φr isachieved, being its orientation uniquely defined by

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the rotors position. When operating, rotor and sta-tor magnetic fields will lock and rotate togetherat synchronous speed, having stator and rotor thesame number of pole pairs, pr = ps. Shaft angularfrequency is therefore equal to synchronous speed.

Ωm = ΩS (38)

The interaction between both fluxes producesan electromagnetic torque, which depends on theirmagnitude and relative angle. Electromagneticforces tend to bring the opposite stator and rotormagnetic poles in close proximity. As the speed ofstator and rotor fluxes is equal, their relative po-sition does not change and a stable angle betweenthe two is maintained.

3.1. Machine Mathematical ModelA mathematical model is considered to simplify theanalysis and control of phase currents. To formulatethis model a three-phase synchronous machine withone pair of poles is considered, ps = 1.

Clarke transformation, also called alpha-betatransformation, is a mathematical instrument tosimplify the analysis of three-phase systems. It re-sults in the representation of variables in a station-ary two-phase coordinate frame, with orthogonalaxis forcing null mutual inductance.

Projecting the stator current vector on the alpha-beta axis result in the equivalent phase currents ofthe transformed system.[

iα(t)iβ(t)

]= KClarke

[1 − 1

2 − 12

0√32 −

√32

]ia(t)ib(t)ic(t)

(39)

There are several combinations of transform co-efficients and windings turns relation that can beemployed. For further analysis, the following con-vention will be adopted, granting impedance invari-ance and equal peak values of variables waveforms.However, it is not power-invariant.

NsNαβ

= KClarke =2

3(40)

Pαβ =2

3Pabc (41)

After Park transformation, the new dq coordinateframe has two orthogonal axis revolving at the rotorspeed, where θm is the rotor position angle. The d-axis is made collinear with the rotors magnetic fluxvector and the q-axis is 90 in advance.

θdq(t) = θm(t) = ωs · t+ θm(0) (42)[id(t)iq(t)

]=

[cos(θm) sin(θm)− sin(θm) cos(θm)

] [iα(t)iβ(t)

](43)

The transform matrix determinant is equal to 1,hence a complex vector with the same amplitude is

obtained by this transformation. Additionally, thisproperty grants impedance and power invariance.

Variable vectors can be represented in a complexnotation.

iSαβ = iα + j · iβ (44)

iSdq = id + j · iq = e−jθm(iα + j · iβ) (45)

The voltage balance for the αβ system is de-ducted from Ohm’s law and the inductance matrix.

uSαβ = uα + j · uβ = Rs · iSαβ +d

dtΨSαβ (46)

The voltage vector in the dq frame is obtained byapplying the Park transform to the αβ voltage andflux. An additional factor, j · ωs · Ψdq, appears dueto the rotational transform.

ΨSdq = e−jθm · ΨSαβ (47)

uSdq = Rs · iSdq +d

dtΨSdq + j · ωs · ΨSdq (48)

ud(t) = Rs · id(t) +d

dtΨd(t) − ωs · Ψq(t) (49)

uq(t) = Rs · iq(t) +d

dtΨq(t) + ωs · Ψd(t) (50)

Electromagnetic torque is derived from the bal-ance of power, which is composed by independentfactors. The windings’ copper losses PCu are de-fined by the Joule’s law. The second factor is therate of magnetic energy change dWmag/dt due tofield coupling. The last part refers to the desiredelectromechanical conversion power Pem. It rep-resents the transformation of electrical energy intomechanical work.

Pele(t) = PCu(t) + dWmag(t)/dt+ Pem(t) (51)

PCu(t) = Rs3

2

[id(t)

2+ iq(t)

2]

(52)

dWmag(t)

dt=

3

2

[id(t) ·

d

dtΨd(t) + iq(t) ·

d

dtΨq(t)

](53)

Pem(t) =3

2· ωs · Ψr · iq(t) (54)

The torque expression can be derived and it isonly dependent on the stator quadrature current.

Tem(t) =Pem(t)

Ωm=

3

2· ps · Ψr · iq(t) (55)

3.2. Steady-StateDuring steady-state operation, Ωm = ΩS , vectorsprojection do not change and subsequently vari-ables’ derivatives are equal to zero.

Ud = Rs · Id − ωs · Ls · Iq (56)

Uq = Rs · Iq + ωs (Ls · Id + Ψr) (57)

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The steady-state voltage balance and equivalentcircuit is constructed, Figure 4, Rs and Xs are thestator windings resistance and reactance, and E0 isthe electromotive force.

US = Rs · IS + j · ωs · Ls · IS + j · ωs · Ψr (58)

Xs = ωs · Ls (59)

E0 = j · ωs · Ψr (60)

Figure 4: Steady-state equivalent circuit.

4. Field-Oriented ControlAutomotive applications experience unpredictabledisturbances during operation, such as fluctuatingmechanical torque. Therefore, several variables areconstantly measured and compared to their respec-tive reference values, process known as feedbackmonitoring. In this manner, the controller not onlyprovides a means to correct for any error in theoutput variable, but also enables a stable responsecharacteristic.

For controlling permanent magnet synchronousmachines, two main closed-loop techniques are com-monly used, Field Oriented Control and DirectTorque Control. The former was chosen to be im-plemented and it is here presented.

Field oriented control principal is based on thedecomposition of flux and torque regulation. Thestator current can be split into a magnetic fluxgenerating component and a torque producing one,

originating two control loops. As previously seen,produced torque is only dependent on quadraturecurrent. While the direct component is responsi-ble to regulate the flux. For a desired torque thecorresponding current can be calculated.

Iq(Tem) =2

3 · ps · ΨrTem (61)

During normal operation, the goal is to createa stator flux which is perpendicular to the rotorflux. In order to maintain this characteristic, thereference value of direct current is kept null, Id

∗ =0. Highest torque per current value and efficiencyare achieved due to decreased stator current.

Both direct and quadrature current references arecompared to the machines actual values and theseerrors are once again fed to a PI block, so to min-imize their errors and provide a good dynamic re-sponse to disturbances.

Following the reference direct and quadraturevoltages determination, including the steady-statecoupling terms, these are converted back to theoriginal three-phase system. Simultaneously tothe transformation, the modulation index, shoot-through duty cycle and the amplitude of the refer-ence three-phase voltages are computed.

Then a modified pulse-width modulation algo-rithm is implemented to generate the IGBTs gatesignals. Complementing the traditional PWM logicthere is an algorithm to create the shoot-throughactivation signal, which is inspired in the open-loopsimple boost control. Additionally, the activationsignal for bidirectional power flow is generated as acomplement of the previous signal. [10]

5. SimulationsIn Figures 5, 6 and 7 the main Simulink modelscreated to test the complete electric drive.

Figure 3: Field-oriented control diagram for the machine drive

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Figure 5: Simulink model of the inverter bridges circuit.

Figure 6: Simulink model with the different blocks in the modified FOC controller.

Figure 7: Simulink model for the drive system of the vehicle.

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5.1. Simulation ParametersFor the vehicle dimensions a small compact caris considered, and the simulation parameters pre-sented in Table 1.

Table 1: Vehicle parameters for simulation.

Gross Mass 1000 kgFrontal Area 1.7m2

Aerodynamic Drag Coefficient 0.3Tyre Radius 0.336m

Z-network Capacitance 500µFZ-network Inductance 5mHSwitching Frequency 1 kHzIGBT’s Internal Resistance 20mΩDiode’s Forward Voltage 1.5V

Number of Pole Pairs 2Armature Resistance 0.2 ΩArmature Inductance 4mHFlux Linkage 0.8WbRotor Inertia 0.1 kg.m2

Rotor Viscous Friction 0.01N.m.s

For the conversion between wheel angular speedand vehicle linear speed, tyre perimeter has to befound.

TyrePerimeter = 2 · π · rT ≈ 2.111m (62)

Air density, ρair = 1.2 kg/m3, is responsible forthe resistive drag force applied against the car ata certain speed. The resulting drag torque for thesystem simulation can be found by multiplying theforce by the lever arm.

Fd =1

2· cd · ρair ·AF · (ωm · rT )2 (63)

Td = Fd · rT ≈ 0.0116 kg.m2 · ωm2 (64)

The maximum voltage to be applied to the mo-tor phases is limited to vOmax = 800V , thereforethe maximum capacitor’s voltage, buck-boost fac-tor and shoot-through duty cycle are determined.

VCmax =vOmax + VDC

2= 550V (65)

BBmax =VCmaxVDC

≈ 1.833 (66)

D0max =BBmax − 1

2 ·BBmax − 1= 0.3125 (67)

The nominal voltage of the machine is equal tothe maximum DC link voltage. The rated speed isset to be 150 km/h, which is a reasonable value fora vehicle. The rated torque is also defined.

VN = 800V (68)

ωmN ≈ 124 rad/s (69)

TemN = 300N.m (70)

The nominal power PN of the virtual machine isthen estimated.

PN = TemN · ωmN = 37.2 kW (71)

5.2. Vehicle TestsThe first test consists on an acceleration simulation.The reference speed increases from 0 to 120 km/hat 3 s, then it is to be maintained constant until theend of the simulation.

The braking test is intended to assess the systemcapability of providing negative torque as well as ofrecovering some of the vehicle’s kinetic energy backinto the battery pack. The machine starts at aninitial high speed of 120 km/h. Then it deceleratesto 60 km/h between 1.5 s < t < 3 s.

The third test consists of a performance evalua-tion of the vehicle when submitted to an externalmechanical torque. The imaginary road to be cre-ated has a grade of slope of 8 %. The referencespeed is maintained at 90 km/h for the entirety ofthe test. At t = 1 s the vehicle starts to climb thehill road and by t = 2 s the slope corresponds to8 % slope grade.

The last test consists of several accelerations andbraking events as well as some periods where thespeed is constant. The vehicle starts in a staticcondition and accelerates to 80 km/h in 2 s. Then,it maintains its speed for half a second before in-creasing it again until 140 km/h at t = 4.5 s. Highspeed is conserved for 1.5 s and followed by a severebraking event that drives the vehicle to 50 km/h att = 7.5 s. Steady speed is kept for 1 s and a new de-celeration follows. The vehicle decreases its speedto 0 km/h at t = 9.5 s, which is maintained untilthe end of the test.

5.3. Simulation ResultsFor the test simulations, several signals demonstrat-ing the vehicle performance are depicted in Figures8, 9, 10 and 11.

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(a) Speed

(b) Torque

(c) Capacitor’s Voltage

(d) Inductor’s Current

(e) Control Signals

Figure 8: Simulation results for acceleration test.

(a) Speed

(b) Torque

(c) Capacitor’s Voltage

(d) Inductor’s Current

(e) Average Input Power

Figure 9: Simulation results for braking test.

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(a) Speed

(b) Torque

(c) Capacitor’s Voltage

(d) Inductor’s Current

(e) Power

Figure 10: Simulation results for load torque test.

(a) Speed

(b) Torque

(c) Capacitor’s Voltage

(d) Inductor’s Current

(e) Power

Figure 11: Simulation results for complete cycletest.

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6. Conclusions

The automotive industry is evolving with the elec-trification process of vehicles. Though, this changeneeds to be closely followed by some technology de-velopment to fulfil the product expectations. Powerelectronics and electrical machines are core elementsin vehicle electrification and have received more andmore attention recently.

A new architecture known as z-source inverterwas proposed to overcome some limitations and try-ing at the same time to increase the performancecompared to traditional inverter designs. Thistopology has the interesting buck-boost capability,which allows for stepping up and down the voltagein a single conversion stage. Additionally, by ac-tively using the shoot-through state it increases theinverter safety.

A theoretical analysis of a bidirectional z-sourceinverter, permanent magnet synchronous machineand field-oriented controller is presented. Once un-derstood the operation of each element, a simula-tion model was assembled. In all tests, the vehiclewas able to closely follow the reference speed re-quired, including during acceleration, braking andconstant speed events. The controller generatedthe buck-boost factor, modulation index and shoot-through duty-cycle according to the drive require-ments. During motor mode, the machine was ablenot only to follow the requested speed but also toovercome high opposing torque. Regenerative brak-ing is observed in both braking and complete cycletests, when the inductors current is negative andthe source IGBT provides an alternative path toconduct back the energy to the battery.

The goal of gaining insight in electrical drives forautomotive industry was fulfilled. A new topologyposed a challenge in terms of making a meticulousanalysis of its operation and contributed to an in-dependent capability of studying innovative archi-tectures.

Acknowledgements

The author thanks Professors Beatriz Borges andDuarte Sousa for the guidance and knowledge trans-mitted. He is also grateful for the personal supportprovided by family and friends.

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