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AN4043 Datasheet(PDF) 44 Page - STMicroelectronics

Part # AN4043
Description  In recent years the variable speed motor control market has required high performance
PDF  60 Pages
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Manufacturer  STMICROELECTRONICS [STMicroelectronics]
Direct Link  http://www.st.com
Logo STMICROELECTRONICS - STMicroelectronics

AN4043 Datasheet(HTML) 44 Page - STMicroelectronics

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Power losses and dissipation
AN4043
44/60
Doc ID 022726 Rev 2
Assuming that:
1.
The application is a variable voltage variable frequency (VVVF) inverter based on
sinusoidal PWM technique.
2.
The switching frequency is high and therefore the output currents are sinusoidal.
3.
The load is ideal inductive.
Under these conditions, the output inverter current is given by:
Equation 19
where Î is the current peak,
θ stands for ωt and φ is the phase angle between output voltage
and current.
The conduction power losses can be obtained as:
Equation 20
Equation 21
where
ξ is the duty cycle for this PWM technique and is given by:
Equation 22
and ma is the PWM amplitude modulation index.
Finally, solving
Equation 20Equation 20 and Equation 21Equation 21, we have:
Equation 23
Equation 24
()φ
=
-
θ
cos
Iˆ
i
()
() θ
φ
θ
ξ
π
⋅
+
θ
φ
θ
ξ
π
⋅
=
∫
∫
φ
+
π
φ
+
π
−
φ
+
π
φ
+
π
−
d
-
cos
2
Iˆ
R
d
-
cos
2
Iˆ
V
P
2
2
2
2
2
2
CE
TO
cond_IG BT
() ()
()
( )
∫
∫
φ
+
π
φ
+
π
−
φ
+
π
φ
+
π
−
θ
φ
θ
ξ
−
π
+
θ
φ
θ
ξ
−
π
=
2
2
2
2
d
-
cos
1
2
Iˆ
R
d
-
cos
1
2
Iˆ
V
P
2
2
AK
FO
cond_Diode
2
cos
m
1
a
θ
⋅
+
=
ξ
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
π
φ
⋅
+
π
⋅
+
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
φ
⋅
+
π
⋅
=
3
cos
m
8
1
2
Iˆ
R
8
cos
m
2
1
Iˆ
V
P
a
2
CE
a
TO
cond_IGBT
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
π
φ
⋅
−
π
⋅
+
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
φ
⋅
−
π
⋅
=
3
cos
m
8
1
2
Iˆ
R
8
cos
m
2
1
Iˆ
V
P
a
2
AK
a
FO
cond_Diode



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