Digital Simulation of Pwm Inverter-im Dirve System for Electric Vehicles

8/14/2019 Digital Simulation of Pwm Inverter-im Dirve System for Electric Vehicles

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DIGITALSIMULATIONOFPWMINVERTER-INDUCTION OTOR DIRVESYSTEMFORELECTRICVEHICLESC.C. HAN*,enior Member IEEE, . WU**,.L. HU** andT.W.HAN*

* Dept. f Electrical& Electronic Engineering,Universityof Hong Kong, ong KongInstituteof Radio& Automation,South China University of Technology, uangzhou, hina

**

Abstract - This paper presents a new digitalsimlation approach for closed loop PWM inverterdrive system. The main features of this approach liein : (i) its suitability for closed loop PWM inverterdrive system with any control law, and (ii) providingreal time control simulation, since both themodulation index and the frequency ratio of a PWMscheme are considered to be real time variables. Thissimulation approach was used to study the steady stateand dynamic performance of a PWM inverter-inductionmotor closed loo^ drive svstem for electric vehicles.

NOMENCLATURE

stator phase voltagepole voltage of inverterphase angle, radiansmodulation indexfrequency rat iofunction of carrier waveformfunction of modulating waveforma mod b is the remainder when a divided by bslope of line segment xy

INTRODUCTIONPulse-width Modulated (PWM) inverter systems have

been widely used in many industrial processes rangingfrom uninterruptable power supplies (UPS ) tovariable-voltage variable-frequency (VVVF) speedcontrol drives. The operational advantages of PWMinverters are well recognized, and there are manyliteratures [12341 oncerning the improvement ofdigital computer simulations and computer-aideddesign techniques for PWM inverter systems. Theoperational characteristics of PWM inverters dependintrinsically upon quite complex modulation processesand, for this reason, very few theoretical andexperimental results have been published concerningthe digital simulation for closed loop PWM inverterdrive systems. The available simulation approachesfor open loop system are constrained that bothmodulation index (M) and frequency ratio ( R I should beconstant values over a PWM period. This constraint,however, cannot be satisfied for closed loop systems.

Therefore, this paper introduces a new simulationapproach for closed loop PWM inverter-induction motordrive systems, in which M and R can be simultaneouslychanged. This simulation approach was used for thestudy of a PWM inverter-induction motor drive systemfor electric vehicles. The simulation results agreedclosely with the actual system test results.

KEY WORDS: Digital simulation technique, Variablespeed a.c.drives, PWM inverter drives, Electricvehi c es

H

0Fig. Inverter

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SURVEY OF PWM TECHNIQUEAND SIMULATION OF PWM INVERTER

Fig. shows an ideal pole-voltage modulatedbridge inverter. Since the output voltages ofinverter are the pole voltages, these voltages have tobe transformed to phase voltages UA, U and Uc :B

A0BO ] (1)jcoTo clarify the survey of PWM techniques, i t is

helpful to recognize three distinct approachescurrently in vogue to formulate the PWM switchingstrategy. These are (i) Natural sampled PWM; (ii)Regular sampled PWM and (iii) Optimised PWM.

Most analogue implemented PWM inverter controlschemes employ natural sampling technique. Inpractical implementation, a triangular carrier wave iscompared directly with a sinusoidal wave to determinethe switch instants and the resultant pulse widths.The intersection points between the carrier waveformand the modulating waveform are formulated by :e. =- . sine. + (i-O.5)E i=1,2,.,2R (2)M2R (-111 R

This means 2R intersection points will beproduced over one cycle of the modulating waveform.Equation (2)can be solved by Newton-Raphson iterationmethod provided that M and R are kept constant over aperiod of modulating wave.

In regular symmetric PWM, the switching anglescan be analytically specified. In a regularsymmetrically sampled wave with modulation depths lessthan unity, the switching angles lie strictly withinsuccessive intervals of length n/R in the phasevariable. For modulation depth exceeds unity, someswitching points may spill over into neighbouringdivisions. In general, the pulse may be limited toits nominal phase interval and the intersection pointscan be classified by the following equations :

=- 4i - 3 - M sin(2i-1): } and=- 4i - 1 + M sin(2i-1)- }ezi-1 lR RTI II2R R2

From equation (31, the output pole voltage of aPWM inverter is either positive constant magnitude ornegative, if both values of M and R are kept inconstant over a cycle of the modulating wave.

Unfortunately, the values of M and R areinstantaneously changed if a closed loop controlsystem is employed. The intersection points cannotdirectly be calculated from equation (2) orequation ( 3 ) . In accordance with the modulationprinciple of PWM waveforms, a new simulation approachis introduced and the intersection points can bedetermined only by the modulating waveform and themagnitude of the carrier waveform.

The concept is illustrated in Fig.2. Atriangular wave with altitude of 2 units and frequencyof R, is to represent the carrier signal. It isshifted vertically by one unit so as to suit thesituation in closed loop control systems. The shiftedwaveform is shown in Fig.3. The slope of sides OA andAD of the shifted waveform are :

9nOA =-2RsI 1

2% JrnAD = --n

(4)

The height of the shifted waveform can beexpressed by eitherf (tl) = 3lIOA(tl) mod 4f:2(tl) =depending on when the time t l is applied. Therefore,the original triangular waveform fc(t) can be deducedby :

orcl{ 311AD(tl) mod 4 1 + 4

f (t) = min t fc;(t). :PcH(t) } - 1 ( 5 )f , ( t )4

-1 FI g.2 Trianglar carrier waveform

I Fig.3 Shifted triangular carrier waveformIECON 88 I 805

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To generate a PWM waveform, it is simple andconvenient for a sinsoidal waveform to represent amodulating signal. Consider a sine wave :f (t) = M sin(wst-#)where both altitude and frequency can bevarying and 0 5 M 5 1,# = C l o r ? - .

(6)m

2 R3Since both R and M can be varying with time

without affecting the PWM waveform, this mathematicalmodel can be employed in closed loop PWM inverterdrive systems. It is illustrated in Fig.4.When fm(t) > fc(t) ; U = +vWhen fm(t) 5 fcft) U = -v

The main features of this new approach are :(i ) few calculations are involved,(ii)(111) real-time calculation can be implemented,(iv)

the equations are not necessary to be solved,

the effect of changing M and R on PWM waveformcan be reflected, hence, closed loop controlsystem analysis can be performed.

Fig.5 shows the flow-chart which is suitable forboth natural sampled PWM and regular PWM techniques.

Fig.4 PWM generation

Read parameter(7)f , , ( t ) z: L 2Ro , i~ I t nod 4

f , , ( t f 3 t[ 2Rw,/n I t Mod 4 ) t 4It o phase vol tage

Print results

UFig.5 Flow chart for PWM generation

SIMULATION OF PUM INVERTER DRIVE SYSTEMFOR ELECTRIC VEHICLES

A substantial research program on the developmentof high-performance PWM inverter drive systems forelectric vehicles was launched in the University ofHong Kong. 5 s 1 This new simulation approach was usedfor the study of the system.

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A. CONTROL STRATEGYThe controller of the electric vehicle consists

of execution unit, logic unit, pulse-widthcompensation unit and protection unit for overcurrent,overvoltage, and overtemperature. The execution unitof the system is designed to optimize the overalldrive system with the following main features :(i) Proper matching between various subsystems,

including battery, inverter, and motor so as tomaximize the utilization of the equipment and toextend the driving range of the vehicle.

(ii) Providing maximum-available torque at givenmotor and inverter rating, and betteracceleration performance and climbingcapability.

(iii) Providing constant high torque at the lowerspeed range and constant high power at higherspeed range in order to satisfy bothacceleration and high-speed cruising.Providing smooth acceleration and deceleration.Fig. shows the block diagram for the execution

unit subject to the above-mentioned control strategy.In accordance with the transfer functions in eachblock, the equations for the performance of thecontroller can be expressed. In order to ensure themotor operates within the allowable torque-speedregion, the signal w is passed through clampercircuits to limit the slip within the positive andnegative maximum-allowable values, which are frequencydependent (Fig.6). At any time, not more than oneclamper is working. At normal motoring mode thepositive clamper works, while at regenerative brakingor down-hill driving mode the negative clamper works.

(iv)

B. LOAD CHARACTERISTI[C AND CONTROL INPUTTo process the real-time digital simulation for

closed loop PWM inverter-induction motor drive system,other than the initial conditions of each variable andparamenters for element, the load characteristic forthe motor must be known, and the type of inputs to theelectric vehicle should be identified.

When climbing a sllope, the typical load torque ofthe vehicle is a step function and the frictionaltorque is proportional to the vehicle speed.

When the vehicle is cruising, the signal from theaccelerating padel via a ramp input clamper within 0.2seconds becomes the input of the controller. When theinitial conditions of each variable are set, theoutputs of the controller and the PWM inverter can becalculated, hence the performance of the drive systemcan be found. The real-time simulation for dynamicperformance of the c:losed-loop drive system werecarried out by repeating the iteration process.

The overall system consists of three parts: (i)the controller, (ii) PWM inverter and (iii) theinduction motor. To simulate the induction motor, thesynchronous rotating axis method'" is adopted in thissimulation system. Fig.7 shows the flow-chart forsimulation of closed loop system.

C. SIMULATION RESULTSThe simulation computer program for closed-loop

drive system was writtsen in BASIC language on IBM-PCso as to make i t simple and easy to implement. Thesimulation was performed for on-road test of anelectric vehicle.

R a m pI n ut IWR

( AccePe*at* ng)

wB braking speed commandwM motor speedw slipwR required synchronous speedw synchronous speedTM load torque Fig.6 Block diagram of the control system

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The PWM waveform for line voltage is shown inFig.8. Fig.9 shows the simulated motor currentwaveforms which agreed closely with the actual testresult shown in Fig.10.

Fig. 1 shows the simulated rotor angular speed,electromagnetic torque and load torque. In Fig. lla,the command speed was applied, it can be seen that thesystem was able to accelerate up to command speed. InFig.llc, a sudden disturbance is applied, hence thespeed reduced and the electromagnetic torque ischanged accordingly.

The actual on-road test results of the vehicle isshown in Fig.12. The vehicle is run at constant speedand then the foot brake is applied. It can be seenthat the simulation result agreed with the actual testresult (Fig. 2).

When the motor speed increased steadily andsmoothly at above constant rate, the motor torqueshould be about constant, this was verified by thesimulation of the electromagnetic torque shown inFig. llb.

N oc>re-set time 3tI Display the results(-2-)

Fig.7 Flow chart for simulation ofclosed loop control system

50Ji3

1-50 2 3 4 5* .CQ5 sec

(*81

Fig.10 Actual current waveform

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ICONCLUSION

c-50 ic

1 2 3 4 11 5 * 1 .2 sec; I , , , I I , ! I , . 8 )i

Fig llb Transient response of electromagnetic torque( * . it

This approach is proven able to simulate theperformance of a closed loop PWM inverter-inductionmotor drive system. [ts main feature is not only tomake calculations simple, but the effect of change offrequency ratio and modulation index also can bestudied. Moreover, i t is also suitable for closedloop PWM inverter drive systems with any control law.On the whole, this simulation approach is convenient,flexible and tally with actual results.

REFERENCE

Asisk K. De Sarkar and Gunnar J. Berg, "DigitalSimulation of Three-phase Inductance Motor," IEEETransactions on Power Apparatus and Systems,vol. AS-89, NO. , July/August 1970, pp. 1031-1037.Edward Y.Y. Ho and Paresh C. Sen, "Digital

Simulation of PWM Inductance Motor Drives forTransient and Steady-state Performance, IEEETransactions on Industrial Electronics,vol.IE-33,No. , February 1986, pp.66-77.S. R. Bowes and R. . Clements, "Digital computerSimulation of Varjable-speed PWM Inverter-MachineDrive,D IEE Proc., vol.130, Pt.B, No.3, May 1983,pp.149-160.S. R. Bowes and R. . Clements, "Computer-aidedDesign of PWM Inverter Systems," IEE Proc.,vol.129, Pt.B, No.1, January 1982, pp. 1-17.C.C. Chan and W.C. Lo, "PWM Power TransistorizedInverter Drive System for Electric Vehicle,"Proceedings, IECOH'84, October 1984, pp. 283-287.C.C. Chan and W.C. Lo, "Control Strategy of PWMInverter Drive System for Electric Vehicle," IEEETransactions on Industrial Electronics, vol.IE34,No.4, November 1987, pp.447-456.

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Digital Simulation of Pwm Inverter-im Dirve System for Electric Vehicles