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Space-Vector PWM With TMS320C24xF24x Using Hardware and Software Determined Switching Patterns.pdf 341KB

Application Report

SPRA524

Digital Signal Processing Solutions March 1999

Space-Vector PWM With

TMS320C24x/F24x Using Hardware and

Software Determined Switching Patterns

Zhenyu Yu Digital Signal Processing Solutions

Abstract

Space-vector (SV) pulse width modulation (PWM) technique has become a popular PWM

technique for three-phase voltage-source inverters (VSI) in applications such as control of AC

induction and permanent-magnet synchronous motors. This document gives an in-depth

discussion of the theory and implementation of the SV PWM technique.

Two different SV PWM waveform patterns, one using the regular compare function on the Texas

Instruments (TI

) TMS320C24x/F24x digital signal processors (DSPs) and another implemented

with the SV PWM hardware module on the TI TMS320C24x/F24x DSPs are presented, with

complete code examples for the TMS320F243/1. At the end, a complete AC induction motor

control application is discussed to show the effectiveness of both approaches.

PWM waveforms of the presented implementations and experimental data in the form of motor

currents are shown and discussed. A full TMS320F243/1 program example is attached. The

observation of dead band imbalance for the hardware-implemented SVPWM pattern in this report

has not been seen in other publications.

Contents

Introduction ......................................................................................................................................................2

Background......................................................................................................................................................3

Theory of SV PWM Technique..................................................................................................................3

SV PWM Waveform Patterns....................................................................................................................9

Application in Three-Phase AC Induction Motor Control................................................................................20

Experimental Results .....................................................................................................................................22

Conclusions ...................................................................................................................................................22

References.....................................................................................................................................................24

Appendix A. Program for Open-Loop Three-Phase AC Induction Motor Control With SV PWM Technique

and Constant V/Hz Principle ..........................................................................................................................25

Application Report

SPRA524

Space-Vector PWM With TMS320C24x/F24x Using Hardware and Software Determined

Switching Patterns 2

Figures

Figure 1. Symmetric and Asymmetric PWM Signals.....................................................................................2

Figure 2. Three-Phase VSI Diagram.............................................................................................................3

Figure 3. The Basic Space Vectors (Normalized w.r.t. V

) and Switching States ........................................5

Figure 4. Software Determined SV PWM Waveform Pattern......................................................................10

Figure 5. Switching Direction for Software Determined SV PWM Pattern...................................................11

Figure 6. SV PWM Outputs With Carrier Filtered Out.................................................................................13

Figure 7. SV PWM Outputs With Carrier Filtered Out and Dead Band Enabled .........................................14

Figure 8. Hardware-Implemented SV PWM Waveform Pattern ..................................................................15

Figure 9. SV PWM Outputs With Carrier Filtered Out.................................................................................19

Figure 10. SV PWM Outputs With Carrier Filtered Out and Dead Band Enabled .........................................19

Figure 11. Program Flow Chart.....................................................................................................................20

Figure 12. Block Diagram of an Open-Loop AC Induction Motor Control System.........................................22

Figure 13. Motor Current and Spectrum Obtained With the Software Approach...........................................23

Figure 14. Motor Current and Spectrum Obtained With the Hardware Approach .........................................23

Tables

Table 1. Device On/Off States and Corresponding Outputs of a Three-Phase VSI ........................................4

Table 2. Determination of the Sector of U

out

Based on

................................................................................8

Table 3. Hardware and Software Determined SV PWM Switching Pattern Comparison.................................9

Introduction

Because of advances in solid state power devices and microprocessors, PWM inverters

are becoming more and more popular in today’s motor drives. PWM inverters make it

possible to control both the frequency and magnitude of the voltage and current applied

to a motor. As a result, PWM inverter-powered motor drives offer better efficiency and

higher performance compared to fixed frequency motor drives. The energy that a PWM

inverter delivers to a motor is controlled by PWM signals applied to the gates of the

power transistors, as shown in Figure 1.

Figure 1. Symmetric and Asymmetric PWM Signals

PWM

period

PWM

period

PWM

period

PWM

period

Asymmetric PWM

Symmetric PWM

Different PWM techniques (ways of determining the modulating signal and the switch-

on/switch-off instants from the modulating signal) exist. Popular examples are sinusoidal

PWM, hysteric PWM and the relatively new space-vector (SV) PWM. These techniques

are commonly used for the control of AC induction, BLDC and Switched Reluctance (SR)

motors. The SV PWM technique for three-phase voltage-source inverter (VSI) is

addressed in this application.

Application Report

SPRA524

Space-Vector PWM With TMS320C24x/F24x Using Hardware and Software Determined

Switching Patterns 3

Background

Theory of SV PWM Technique

The structure of a typical three-phase VSI is shown in Figure 2. As shown below,

and

are the output voltages of the inverter.

through

are the six power transistors

that shape the output, which are controlled by

’,

and

’. When an upper

transistor is switched on (i.e., when

is 1), the corresponding lower transistor is

switched off (i.e., the corresponding

’,

’ or

’ is 0). The on and off states of the upper

transistors,

and

, or equivalently, the state of

and

, are sufficient to

evaluate the output voltage for the purpose of this discussion.

Figure 2. Three-Phase VSI Diagram

motor phases

c'b'

Q6Q4Q2

Q5Q3Q1

The relationship between the switching variable vector [

]

and the line-to-line output

voltage vector [

]

and the phase (line-to-neutral) output voltage vector [

]

is given by equation 1 and equation 2 below.

110

01 1

10 1

(equation 1)

211

12 1

112

(equation 2)

where

is the DC supply voltage, or bus voltage.

As shown in Figure 2, there are eight possible combinations of on and off states for the

three upper power transistors. The eight combinations and the derived output line-to-line

and phase voltages in terms of DC supply voltage

, according to equations 1 and 2,

are shown in Table 1.

SV PWM refers to a special way of determining the switching sequence of the upper

three power transistors of a three-phase VSI. It has been shown to generate less

harmonic distortion in the output voltages and or currents in the windings of the motor

load and provides more efficient use of DC supply voltage, in comparison to direct

sinusoidal modulation technique.

Application Report

SPRA524

Space-Vector PWM With TMS320C24x/F24x Using Hardware and Software Determined

Switching Patterns 4

Table 1. Device On/Off States and Corresponding Outputs of a Three-Phase VSI

abcv

000000000

1 0 0 2/3 –1/3 –1/3 1 0 –1

1 1 0 1/3 1/3 –2/3 0 1 –1

0 1 0 –1/3 2/3 –1/3 –1 1 0

0 1 1 –2/3 1/3 1/3 –1 0 1

0 0 1 –1/3 –1/3 2/3 0 –1 1

1 0 1 1/3 –2/3 1/3 1 –1 0

111000000

Assume

and

are the fixed horizontal and vertical axes in the plane of the three motor

phases. The vector representations of the phase voltages corresponding to the eight

combinations can be obtained by applying the following so-called

transformation to

the phase voltages:

dq-abc

T (equation 3)

This transformation is equivalent to an orthogonal projection of [

]

onto the two

dimensional plane perpendicular to the vector [1, 1, 1]

in a three-dimensional coordinate

system, the results of which are six non-zero vectors and two zero vectors as shown in

Figure 3. The nonzero vectors form the axes of a hexagonal. The angle between any

adjacent two non-zero vectors is 60 degrees. The zero vectors are at the origin and apply

zero voltage to a three-phase load. The eight vectors are called the Basic Space Vectors

and are denoted here by

120

180

240

300

000

and

111

The same

transformation can be applied to a desired three-phase voltage output to

obtain a desired reference voltage vector

out

in the

plane as shown in Figure 3. Note

that the magnitude of

out

is the rms value of the corresponding line-to-line voltage with

the defined d-q transform.

The objective of SV PWM technique is to approximate the reference voltage

out

instantaneously by combination of the switching states corresponding the basic space

vectors. One way to achieve this is to require, for any small period of time

, the average

inverter output be the same as the average reference voltage

out

as shown in equation

4. Note,

and

in equation 4 are the respective durations for which switching states

corresponding to

x and

x+60

(or

x-60

) are applied.

x and

x+60

(or

x-60

) are the basic

space vectors that form the sector containing

out

. However, if we assume that the

change in reference voltage

out

is tiny within

, then equation 4 becomes equation 5,

where

TTT

£+

. Therefore, it is critical that

be small with respect to the speed of

change of

out.

In practice the approximation is done for every PWM period,

pwm

Therefore it is critical that the PWM period be small with respect to the speed of change

out

Application Report

SPRA524

Space-Vector PWM With TMS320C24x/F24x Using Hardware and Software Determined

Switching Patterns 5

Figure 3. The Basic Space Vectors (Normalized w.r.t.

) and Switching States

axis

300

(101)

240

(001)

(100)

180

(011)

120

(010)

(110)

111

(111)

000

(000)

out

()

1612,

()

230,

()

1612,

()

230,

()

16 12,

()

16 12,

)(

6021

)1(

out

UTUT

(equation 4)

)(

6021

xxout

UTUT

nTU (equation 5)

Equation 5 means that for every PWM period,

out

can be approximated by having the

inverter in switching states

and

x+60

(or

x-60

) for

and

duration of time

respectively. Since the sum of

and

should be less than or equal to

pwm

, the inverter

needs to be in

000

111

state for the rest of the period. Therefore, equation 5 becomes

equation 6 in the following, where

TTT T

opwm

++= =

TU TU TU T or

pwm out x x

=+ +

1 2 60 0 000 111

00() (equation 6)

From equation 6, we get equation 7 for

and

[] [ ]

outxxpwm

UUUTTT

6021

(equation 7)

where

[]

is the normalized decomposition matrix for the sector.

Assume the angle between

out

and

is a . From Figure 3, we can also obtain equation

8 in the following for

and

)sin(2

)30cos(2

outpwm

UTT

°+=

(equation 8)

Depending on specific application, calculation of

and

can be done either with

equation 7 or equation 8. Equation 7 is sector dependent. However, the matrix inverse

can be calculated off-line for each sector and obtained via a look-up table during on-line

calculation. This approach is useful when

out

is given in the form of vector [

]

Equation 8 is independent of sector and is useful when

out

is given in the form of

magnitude and phase angle.

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