
14-16 Power Electronics and Motor Drives
where θ
k
is the angle between the α axis and the current space vector k. Since all the space vectors have
the same amplitude |V
k
| = |V
k+1
| = 2V
dc
/3, they can be replaced in (14.14) and (14.15). en the only
unknown variables le in (14.14) and (14.15) are t
k
and t
k+1
. us, the following set of equations to solve
the duty cycles can be obtained:
t
T V
V
k
m s
dc
k
k
= − −
−
3
2
3
|
*
|
cos( ) sinθ θ
θ θ
(14.16)
t
T V
V
k
m s
dc
k
+
=
−
1
3
3
|
*
|
sin( )θ θ
(
14.17)
t T t t
m k k0 1
+
(14.18)
Note that (14.18) is simply obtained from (14.13) once the two nonzero vector duty cycle times have
been computed, in order to complete ...