Digital Simulation Of Pwm Inverter-im Dirve System For Electric Vehicles

DIGITAL SIMULATION OF PWM INVERTER-INDUCTIONMOTOR DIRVE SYSTEM FOR ELECTRIC VEHICLES C.C.CHAN*,Senior Member IEEE,J. WU**,G.L.ZHU** and T.W. CHAN*

* **

-

Abstract simlation

Institute of Radio & Automation, South China University of Technology,Guangzhou,China

for closed loop PWM inverter

in : (i) its suitability for closed loop PWM inverter time

Pulse-width Modulated (PWM) inverter systems have

The main features of this approach lie

drive system with any control law, and (ii) providing real

INTRODUCTION

This paper presents a new digital

approach

drive system.

Dept.of Electrical & Electronic Engineering, University of Hong Kong,Hong Kong

control

simulation,

since

both

the

modulation index and the frequency ratio of a PWM scheme are considered to be real time variables. This simulation approach was used to study the steady state and dynamic performance of a PWM inverter-induction motor closed loo^ drive svstem for electric vehicles.

been widely used in many industrial processes ranging from

uninterruptable

power

supplies

(UPS)

(VVVF)

to

variable-voltage

variable-frequency

speed

control drives.

The operational advantages of PWM

inverters are well recognized, and there are many literatures [1’2’3’41concerning digital

computer

the

improvement of

simulations and computer-aided

design techniques for

PWM

inverter systems.

The

operational characteristics of PWM inverters depend intrinsically upon quite complex modulation processes NOMENCLATURE

and, for

this

reason, very

few theoretical

and

experimental results have been published concerning stator phase voltage

the digital simulation for closed loop PWM inverter

pole voltage of inverter

drive systems.

phase angle, radians

for open

modulation index

The available simulation approaches

loop system

are

constrained

that

both

modulation index (M) and frequency ratio ( R I should be

frequency rat io

constant values over a PWM period.

function of carrier waveform

This constraint,

however, cannot be satisfied for closed loop systems.

function of modulating waveform a mod b is the remainder when a divided by b slope of line segment xy

Therefore, this paper introduces a new simulation approach for closed loop PWM inverter-induction motor drive systems, in which M and R can be simultaneously changed.

This simulation approach was used for the

study of a PWM inverter-induction motor drive system

for electric vehicles.

The simulation results agreed

closely with the actual system test results.

KEY WORDS: speed

Digital simulation technique, Variable

a.c.drives, PWM

inverter

drives,

Electric

vehic1es. H

0

Fig.1

Inverter

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Fig.1 bridge

shows

an

inverter.

ideal

Since

PWM inverter is either positive constant magnitude or negative, if both values of M and R are kept in

pole-voltage modulated

the

output

voltages

constant over a cycle of the modulating wave.

of

Unfortunately,

the

inverter are the pole voltages, these voltages have to

instantaneously changed

be transformed to phase voltages UA, U and Uc B

system is employed.

]

‘A0

‘BO

:

directly (1)

recognize

three

distinct

approaches

These are (i) Natural sampled PWM; (ii)

Regular sampled PWM and (iii) Optimised PWM. employ

natural

if a closed

and

R

are

loop control

The intersection points cannot

calculated

from

equation

(2)

or

In accordance with the modulation

magnitude of the carrier waveform.

sampling

The

technique.

concept

is

illustrated

in

Fig.2.

A

triangular wave with altitude of 2 units and frequency of

Most analogue implemented PWM inverter control schemes

M

determined only by the modulating waveform and the

currently in vogue to formulate the PWM switching strategy.

of

is introduced and the intersection points can be

To clarify the survey of PWM techniques, it is to

be

equation ( 3 ) .

values

principle of PWM waveforms, a new simulation approach

jco helpful

the output pole voltage of a

From equation (31,

SURVEY OF PWM TECHNIQUE AND SIMULATION OF PWM INVERTER

R”,

is to represent the carrier signal.

It is

shifted vertically by one unit so as to suit the

In

situation in closed loop control systems. The shifted

practical implementation, a triangular carrier wave is

waveform is shown in Fig.3. The slope of sides OA and

compared directly with a sinusoidal wave to determine

AD of the shifted waveform are

:

the switch instants and the resultant pulse widths. The intersection points between the carrier waveform 9nOA =

and the modulating waveform are formulated by

e.

:

n M = - -. sine. + (i-O.5)E ; i=1,2,.,2R 2R (-111 R This

means

2R

intersection points

2R”s II

(2)

rnAD

=

2%

-

1J

(4)

n

will

be

The

height

of

the

produced over one cycle of the modulating waveform.

expressed by either

Equation (2) can be solved by Newton-Raphson iteration

f’ (tl) = 3lIOA(tl) mod 4 cl

method provided that M and R are kept constant over a In regular symmetric PWM, the switching angles can

be

analytically

specified.

In

a

regular

symmetrically sampled wave with modulation depths less than unity, the switching angles lie strictly within successive intervals of variable.

length n/R

For modulation depth

in the phase

{

can be

or

311AD(tl) mod 4 1 + 4

depending on when the time tl is applied.

Therefore,

the original triangular waveform fc(t) can be deduced by

:

f (t) = min t fc;(t). :PcH(t)

}

- 1

(5)

f,(t)

exceeds unity, some

4

switching points may spill over into neighbouring divisions.

=

f:2(tl)

period of modulating wave.

shifted waveform

In general, the pulse may be limited to

its nominal phase interval and the intersection points can be classified by the following equations :

=

ezi-1 e2i

=

-{

lR TI

2R

{

4i

-

3

-

M sin(2i-1):

R II 4i - 1 + M sin(2i-1)R

}

-1

FI g.2 Trianglar carrier waveform

and

}

I

Fig.3 Shifted triangular carrier waveform

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(7)

To generate a PWM waveform, it is simple and convenient for a sinsoidal waveform to represent a

Read parameter

modulating signal. Consider a sine wave : f (t) = M sin(wst-#) m where both altitude varying and 0

5

M

5

(6)

and

frequency

can

be

1,

f’,,(t)

2R

#=Clor?-. 3

f’,,(tf

Since both R and M can be varying with time without affecting the PWM waveform, this mathematical

3

z:

L 2Ro,i~ I t

t[ 2Rw,/n I t

nod 4 Mod

4)

t

4

I

model can be employed in closed loop PWM inverter drive systems.

It is illustrated in Fig.4.

When fm(t) > fc(t) ;

U =

+v

When fm(t)

U =

-v

5

fcft) ;

The main features of this new approach are : (i)

few calculations are involved,

(ii) (111)

the equations are not necessary to be solved,

(iv)

real-time calculation can be implemented, the effect of changing M and R on PWM waveform can be reflected, hence, closed loop control system analysis can be performed.

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

t o phase voltage

Print results

U Fig.5 Flow chart for PWM generation

SIMULATION OF PUM INVERTER DRIVE SYSTEM FOR ELECTRIC VEHICLES

A substantial research program on the development

of high-performance PWM inverter drive systems for electric vehicles was launched in the University of Fig.4 PWM generation

Hong Kong.[ 5 ’ s 1 This new simulation approach was used for the study of the system.

IECON ’88 I806

A.

B.

CONTROL STRATEGY

LOAD CHARACTERISTI[C AND CONTROL INPUT To process the real-time digital simulation for

The controller of the electric vehicle consists pulse-width

closed loop PWM inverter-induction motor drive system,

compensation unit and protection unit for overcurrent,

other than the initial conditions of each variable and

overvoltage, and overtemperature. The execution unit

paramenters for element, the load characteristic for

of

execution

unit,

logic

unit,

of the system is designed to optimize the overall

the motor must be known, and the type of inputs to the

drive system with the following main features

electric vehicle should be identified.

Proper

(i)

matching

:

When climbing a sllope, the typical load torque of

between various subsystems,

including battery, inverter, and motor

so

as to

maximize the utilization of the equipment and to

the vehicle is a step function and the frictional torque is proportional to the vehicle speed. When the vehicle is cruising, the signal from the

extend the driving range of the vehicle. Providing maximum-available

(ii)

motor

and

inverter

acceleration

torque

rating,

performance

at

and

and

given

accelerating padel via a ramp input clamper within 0.2

better

seconds becomes the input of the controller. When the

climbing

(iii)

initial conditions of each variable are set, the outputs of the controller and the PWM inverter can be

capability. Providing constant high torque at the lower

calculated, hence the performance of the drive system

speed range and constant high power at higher

can be found.

speed

performance of

range

in

order

to

satisfy

both

the c:losed-loop drive system were

carried out by repeating the iteration process.

acceleration and high-speed cruising.

The overall system consists of three parts: (i)

Providing smooth acceleration and deceleration.

(iv)

The real-time simulation for dynamic

Fig.6 shows the block diagram for the execution

PWM inverter and (iii) the To simulate the induction motor, the

the controller, (ii)

unit subject to the above-mentioned control strategy.

induction motor.

In accordance with the transfer functions in each

synchronous rotating axis method'"

block, the equations for the performance of the

simulation system.

controller can be expressed.

In order to ensure the

simulation of closed loop system.

motor

allowable torque-speed

operates within

the

region, the signal w

is passed

through clamper

C.

is adopted in this

Fig.7 shows the flow-chart for

SIMULATION RESULTS

circuits to limit the slip within the positive and

The simulation computer program for closed-loop

negative maximum-allowable values, which are frequency

drive system was writtsen in BASIC language on IBM-PC

dependent (Fig.6).

At any time, not more than one

At normal motoring mode the

clamper is working.

positive clamper works, while at regenerative braking

so as to make

it simple and easy to implement.

simulation was performed for on-road test

The

of an

electric vehicle.

or down-hill driving mode the negative clamper works.

Ramp

I

I n ut

( AccePe*at*

ng)

WR

wB

braking speed command

wM motor speed w

slip

wR

required synchronous speed

w

synchronous speed

TM

load torque

Fig.6 Block diagram of the control system IECON '88I807

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The PWM waveform for line voltage is shown in Fig.8.

Fig.9

shows the simulated motor current

waveforms which agreed closely with the actual test

50

J

result shown in Fig.10. Fig.11 shows the simulated rotor angular speed, electromagnetic torque and load torque.

i3

In Fig.lla,

the command speed was applied, it can be seen that the system was able to accelerate up to command speed.

In

Fig.llc, a sudden disturbance is applied, hence the speed

reduced

and

the

electromagnetic torque

is

changed accordingly. The actual on-road test results of the vehicle is shown in Fig.12. The vehicle is run at constant speed and then the foot brake is applied.

-50

1

2

3

1

(58 *

It can be seen

that the simulation result agreed with the actual test result (Fig.12). When the motor speed

increased steadily and

smoothly at above constant rate, the motor torque should be about constant, this was verified by the simulation of the electromagnetic torque shown in Fig.llb.

No

I

c> pre-set time

3

t Display the results

(-2-) Fig.10 Actual current waveform Fig.7 Flow chart for simulation of closed loop control system IECON '88I808

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4

5* .CQ5 sec

ICONCLUSION

This approach is proven able to simulate the performance of a closed loop PWM inverter-induction motor drive system.

[ts main feature is not only to

make calculations simple, but the effect of change of frequency ratio and modulation index also can be studied.

Moreover, it is also suitable for closed

loop PWM inverter drive systems with any control law. On the whole, this simulation approach is convenient, flexible and tally with actual results.

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c

vol.PAS-89, NO.6, July/August 1970, pp. 1031-1037.

-50 i

c

i

;

2

1 I

, , , I

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3

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4 !

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5

* 1.2

I , .

Edward Y.Y. Ho and Paresh C. Sen, "Digital sec 8

Simulation of PWM Inductance Motor Drives for

)

Fig llb Transient response of electromagnetic torque (*

.i)

t

Transient and Steady-state Performance,"

IEEE

Transactions on Industrial Electronics,vol.IE-33, No. 1, February 1986, pp.66-77. S.

R. Bowes and R.R. Clements, "Digital computer

Simulation of Varjable-speed PWM Inverter-Machine Drive, IEE Proc., vol.130, Pt.B, No.3, May 1983, ID

pp. 149-160. S. R.

Bowes and R.R. Clements, "Computer-aided

Design 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 Transistorized Inverter Drive System for Electric Vehicle," Proceedings, IECOH'84, October 1984, pp.283-287. C.C. Chan and W.C. Lo, "Control Strategy of PWM Inverter Drive System for Electric Vehicle," IEEE Transactions on Industrial Electronics, vol.IE34, No. 4, November 1987, pp.447-456.

IECON '88I 8 0 9

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