65
V
Ri L
di
dt
L i
d
d
d
q
q q
s
Z
(4.11)
V
Ri L
di
dt
L i
q
q
q
q
d d
m
s
Z
ZO
(4.12)
Here, the torque is represented by [5]
T
i
L L i i
q
d
q d q
e
ª
¬
º
¼
1 5
. U O
(4.13)
where L q represents the q axis induction, L d represents the d axis induction, i q represents
the q axis charge, i d represents the d axis charge, V q represents the q axis volts, V d represents the d axis volts, ω r represents the angular speed of the rotor, λ represents flux
induction, and p represents the number of pairs of poles for electricity energy generation and thus the below equation is calculated in order to integrate it with a stationed
d–q frame of dynamic modeling to confirm the production of net electricity energy:
V
V
V
V
R pL
p L
R pL
p L
pL
L
R
q
d
q
d
s
s
r
r
s
s
m
s
s
m
m
rm
ª
¬
«
«
«
«
«
º
¼
»
»
»
»
»
0
0
0
0
Z
r r
r
r r
r m
m
r r
r
r
s
s
r
r
ª
¬
«
«
«
«
º
¼
»
»
»
»
ª
¬
«
«
«
«
pL
L
L
p L
L
R pL
i
i
i
i
q
d
q
d
Z
Z
Z
« «
º
¼
»
»
»
»
»
(4.14)
From the rotor force, the equation is calculated as
O
O
d
d
d
q
q
d
d
d
L i
L i
L i
L i
L L L
L L L
V
Ri
s
s s
m r
s
s s
m r
s
l s
m
r
l r
m
s
s s
d d
dt
V
Ri
d
dt
d
q
q
q
O
O
s
s
s s
s
(4.15)
and from the rotor side, the equation is calculated as
O
O
O Z O
d
d
d
q
q
q
d
d
d
q
q
L i
L i
L i
L i
V
Ri
d
dt
V
R
r
r r
m s
r
r r
m s
r
r r
r
r
r
r
r
i i
d
dt
q
q
d
r
r
r
r
O Z O
(4.16)
Materials and Methods