Electric Motor Drives

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HW4PVstoPWMSVM2019.docx
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ECE4/595 Electric Drive Systems Prof Ka C Cheok

PWM and SVM of 3-Phase Inverter

Switching of 3-Phase Inverter

Figure 1 shows an electrical circuit representation of a 3-phase inverter connected to a 3-phase stator. Switching of are normally done at high rate (300 to 20 kHz) and coordinated using PWM (pulse-width-modulation) or SVM (space vector modulation).

3-phase motor stator

Figure 1. Electrical circuit for 3-phase inverter and stator connection

PWM (pulse-width-modulation) & SVM (space vector modulation)

Figure 2 shows a PWM & SVM switching scheme for controlling the magnetic field in a 3-phase motor stator.

Space vector

field current from

Clarke Transform

Inverse

Clarke Transform

PWM & SVM

3-phase

inverter

driver circuit

3-phase stator

Y- circuit

Hardware

Software

Figure 2. PWM scheme for controlling magnetic field in a 3-phase motor stator

PWM switching process is explained below.

1) Embedded controller software/firmware

a.

Specify, representing magnitude & orientation of the desired magnetic field.

b.

Apply Inverse Clarke Transform (ICT) to calculate desired .

c.

Use to turn on to generate PWM switching.

2) Inverter & stator hardware, and stator magnetic field

a.

Modulated (PWM or SVM) stator voltages is delivered by the 3-phase inverter.

b.

Stator currents flow according to the stator circuit equations which include back emf voltages .

c.

An equivalent field oriented stator current vector is produced by the stator currents.

d.

generates an effective magnetic field in the stator.

VD = Vdc = 300 va = 200 vb = 120 vc = 30

Duty cycle A = 200/300 = 66%

Duty cycle B = 120/300 = 40%

Duty cycle C = 30/300 = 10%

SVM (space vector modulation)

Figure 3 shows a SVM switching scheme for controlling the magnetic field in a 3-phase motor stator.

Space vector

field current from

Clarke Transform

Space Vector Modulation

3-phase

inverter

driver circuit

3-phase stator

Y- circuit

Hardware

Software

Figure 3. SVM scheme for controlling magnetic field in a 3-phase motor stator

Basic phase voltage vectors - 3 x 1

Basic space vector field voltages - 2 x 1 (Clarke Transform)

Switching

state

ON

switches

Phase

vector

notation

Space

Vector

notation

0

S4 S6 S2

1

S1 S6 S2

2

S1 S3 S2

3

S4 S3 S2

4

S4 S3 S5

5

S4 S6 S5

6

S1 S6 S5

7

S1 S3 S5

Note that 2d space can be divided in 6 sectors as indicated by the notations, , in the diagram. As an illustration, the desired space vector falls in Sector , and is sandwiched by .

In general, if falls in Sector , then is sandwiched by . The SVM switching process consists of translating in to a sequence of carefully timed voltages which can be represented by

where

and are two adjacent state vectors from the set that sandwich the desired field vector ,

,

are durations when are applied, and

is the duration when or (off state vector) is applied.

The variables satisfy

and

Example of SVM. Suppose that and the modulation duration is . What is a space vector modulation for?

Step 1. lies between , and hence lies in sector Sect = 1. How do we check this? which is between . Use a computer program to calculate the angle and find the sector. See previous lecture note.

Step 2.

Step 3.

Step 4. Implementation of SVM

A sketch of the SVM sequence and switching is illustrated below.

Homework 4: Electric Motor Drives

Issued: 6 Jun ’19 Due: 13 Jun ‘19

Problem

Points

Score

1

Inverse Clarke transform

20

2

PWM duty cycle and sketch

30

3

SVM timing sequence

50

TOTAL

100

You may use Matlab to help you calculate numerical values and solve the problems.

INVERSE CLARK TRANSFORM

Problem 1. (Inverse Clarke transform & sketch) 20%

Find the phase voltages where must all be nonnegative, for the field voltage vector . Sketch and .

PULSE WIDH MODULATION

Problem 2. (PWM duty cycles and sketch) 30%

Consider a PWM scheme that would take an input and switches in the 3-phase inverter to produce a PWM modulated which averages to . The PWM frequency is 1 kHz, and the DC power supply to the inverter is (see inverter diagram in Fig 2.) Sketch the waveforms of the variables and complete the missing info for the duty cycles in the following timing diagram.

SPACE VECTOR MODULATION

Problem 3. (SVM sequence) 50%

You are asked to convert a desired voltage field vector [V] into its SVM equivalence. The SVM frequency is 1 kHz, and the 3-phase inverter DC power supply is . Sketch the waveforms for the variables and complete the timing information in the following diagram.

HW5 PWM SVM 2015.docx 1 11 Jun ‘15

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ECE4/595 Electric Drive Systems

Prof Ka C Cheok

HW5 PWM SVM 2015.docx

1

11 Jun ‘15

PWM and SVM of

3

-

Phase Inverter

Switching of 3

-

Phase Inverter

Figure 1 shows an electrical circuit representation of a 3

-

phase inverter connected to a 3

-

phase stator.

Switching of

123456

,,,,,

SSSSSS

are

normally done at high rate (300 to 20

kHz) and coordinated using PWM (pulse

-

width

-

modulation) or SVM (space vector modulation).

Figure

1. Electrical circuit for 3

-

phase inverter and stator connection

ECE4/595 Electric Drive Systems Prof Ka C Cheok

HW5 PWM SVM 2015.docx 1 11 Jun ‘15

PWM and SVM of 3-Phase Inverter

Switching of 3-Phase Inverter

Figure 1 shows an electrical circuit representation of a 3-phase inverter connected to a 3-phase stator. Switching of

123456

,,,,,SSSSSS

are normally done at high rate (300 to 20 kHz) and coordinated using PWM (pulse-width-

modulation) or SVM (space vector modulation).

Figure 1. Electrical circuit for 3-phase inverter and stator connection