Hardware Reference
In-Depth Information
In the CV-BLDC mode, the average EM torque is
R
T
em
(α)=
2π
0
T
em
(θ)dθ
R
£
¡
¢¤ £
¡
¢¤
α+π/3
α
6E
m
2πΩR
a
2π
3
θ−
2
3
=
sin(θ) −sin
V
dc
−E
m
sin(θ)+E
m
sin
dθ
√
√
3E
m
3cos(2α)+9sin(2α)]
(4.104)
In CV-BLDC mode, any variation in the commutation angle α changes
both the average torque and the armature current. Therefore, equation 4.104
cannot be used for determining analytically the optimal commutation angle.
It is different from the case of CC-BLDC mode introduced in section 4.4.2. We
must use a different method to
fi
nd the optimal angle.
=
8πΩR
a
4V
dc
[3 cos(α)+
3sin(α)] −E
m
[4π+3
In the CV-BLDC mode, the drive voltage is constant during the energized
state. Therefore, the average copper loss of the winding is related to the
commutation angle, and it can be calculated as
Z
2π
R
a
2π
[i
2
A
(θ)+i
2
B
(θ)+i
C
(θ)]dθ
P
cu
=
(4.105)
0
Z
∙
µ
¶¸
2
α+π/3
3R
a
π
θ−
2π
3
=
V
dc
−E
m
sin(θ)+E
m
sin
dθ
0
−3E
m
V
dc
cos(α)−
√
πV
dc
3
3R
a
π
=
3E
m
V
dc
sin(α)+
√
E
2
m
8
[4π+3
3cos(2α)+9sin(2α)].
Now we can de
fi
ne the ratio between the average EM torque and the copper
loss as the objective function, i.e.,
O(α)=
T
em
(α)
P
cu
(α)
.
(4.106)
The value of α that maximizes this objective function is the optimal commu-
tation angle. It can be found by equating the derivative of O(α) to zero and
then solving for α.
(α)=
dO(α)
O
dα
=0.
(4.107)
By solving this equation, we get,
³
´
π
6
O
=0.
(4.108)
