
AC Electrical Machine Torque Harmonics 10-11
For h = k, L
kk
is denoted as self inductance coecient including the leakage inductance, for h ≠ k, L
kh
corresponds to a mutual inductance coecient between windings k and h.
In
t
he
fo
llowing,
a l
inear
m
agnetic
c
ircuit
i
s
c
onsidered
(
L
kh
does not depend on i
h
but only on θ).
S
o
∂
=
kh
0 and Equation 10.31 becomes
v r i
d
dt
i
L
L
di
dt
k k k h
kh
n
kh
h
n
= +
∂
∂
+
= =
∑ ∑
θ
θ
(
10.32)
Let us consider the total energy dW
t
= pdt applied to the system during the time interval dt:
v i dt r i d t i d
k k
k
n
k k
k
n
k
k
n
k
= = =
∑ ∑ ∑
= +
1
2
1 1
ψ (10.33)
Let dW denote the energy applied to the idealized system (initial system without ...