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4

Table 4-2.

Expressions of the duty cycles in each sector

I n t h

e

C

o n c o r d i a f r a m e , a n y s t a t o r v o l t a g e

s V

=

β α V j V = +

s m V

cos

) ( θ s m V j +

) s i n ( θ

l

o c a t e d i

n s i d e

this hexagon belongs to one of the six sectors, and can be expressed as a linear combination of t h e t w o n o n - z e r o p h a s e v o l t a g e s w h i c h d e l i m i t t h i s s e c t o r : . E q u a t i n g 1 1 + + + = k k k k s V d V d V

t o i n e a c h s e c t o r l e a d s t o t h e e x p r e s s i o n s o f t h e d u t y c y c l e s s h o w n i n T a b l e 4 - 2 . S i n c e t h e i n v e r t e r c a n n o t i n s t a n t a n e o u s l y g e n e r a t e , t h e s p a c e - 1 1 + + + k k k k V d V d ) s i n ( ) c o s ( θ θ s m s m V j V + s V

v e c t o r P W M p r i n c i p l e c o n s i s t s i n p r o d u c i n g a , b y g e n e r a t i n g d u r i n g a n d s T s V k V s k k T d T = 1 + k V

  • -

    periodic voltage whose average value equals

during

Tk +1

=d

s k T 1 +

. Since

dk + dk +1

1

, these

voltages must be completed over the switching period Ts by V0 and/or V7 . Several solutions are possible [3,4], and the one which minimizes the total harmonic distorsion of the stator current

consists in applying

a n d 0 V

d u r i n g t h e s a m e d u r a t i o n 7 V

T T 7 0 = =

1dk dk +1

2

s T

.

i s e q u a l l y 0 V

applied at the beginning and at the end of the switching period, whereas V7 is applied at the middle. As an illustration, the upper side of Figure 4-4. shows the waveforms obtained in sector 1.

Application Note

7546A–AVR–12/05

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