1
ASSIGNMENT 3
Trigonometric Identities
cos(A+B)=cosAcosB-sinAsinB
cos(A-B)=cosAcosB+sinAsinB
sin(A+B)=sinAcosB+cosAsinB
sin(A-B)=sinAcosB-cosAsinB
Question 1
The inductance of a single-phase reluctance machine is:
]
2
cos
[
d
B
A
a
L
L
L
θ
+
=
The single-phase winding is excited by a current
t
I
i
a
ω
cos
=
Let the rotor turn at synchronous speed so that
δ
ω
θ
+
=
t
d
(i)
What is the electromechanical torque
e
T
?
(ii)
What is the time invariant component
)
(
δ
f
T
ave
e
=
−
? Sketch
)
(
δ
f
T
ave
e
=
−
for
o
180
.
.
.
180
+
⟨
⟨
°
−
δ
.
(iii)
What are the even harmonic pulsating components of torque,
even
e
T
−
?
(iv)
The reluctance motor has a moment of inertia J and drives a load
L
T
. The
mechanical equation of motion is:
L
e
m
T
T
dt
d
J
−
=
ω
(1)
Let the rotor speed be the sum of a term at synchronous speed
ω
and
perturbation terms
m
ω
Δ
due to the even harmonic pulsating torque components.
Substituting in (1)
L
even
e
ave
e
m
T
T
T
dt

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*