AN2154

Space vector modulation theory

5/16

Figure 2.

Space vector diagram

Each one of the reference voltages V100, V110,… corresponds to one of the switching

states reported in Table 1. In order to obtain sine wave voltages on the motor phases, a

continuously rotating vector V must be produced so that one complete turn of the vector V

on the complex plan represents one electrical turn of the motor (coincident with one

mechanical turn in case of one pole pair motor). As it will be subsequently demonstrated,

when linear modulation is applied, the circumference described by the rotating vector must

stay inside the hexagon shown in Figure 2. The goal of space vector modulation is exactly to

generate the appropriate PWM signals so that any vector V inside the hexagon can be

produced by "time weighting" the two reference vectors that bound the sector in which V

lies. Considering Figure 2, vector V can be expressed as:

Equation 1

, with respect to

and

.

As mentioned earlier, vectors

and

will be generated by applying respectively the

reference vectors

and

,

and

(or

)

inside the PWM period, it is possible to write:

Equation 2

with

Equation 3

VV

a

V

b

+

=

V

V

001

V

011

V

a

V

b

V

001

V

011

V

V

111

V

000

VV

a

V

b

t

a

T

0

------

V

001

t

b

T

0

------V

011

t

0

T

0

------ V

()

++

⋅

=

+

=

t

a

V

a

V

001

------------

T

0

⋅

=