Figure B.1 shows a reluctance motor because there is no winding in the rotor which is main difference between the doubly excited system and the reluctance motor.
The stator inductance is expressed by
Lss = L0 + 2L cos2θ (B.1)
This is a function of rotor position θ.
The stator current is
is = Ism sinωt (B.2)
The position of the rotor at any time t is expressed by
θ = ωmt + δ (B.3)
where δ is the initial angle of the rotor wrt stator axis and ωm is the angular velocity of the rotor.
Figure B.2 shows the variation of stator self-inductance with the position of the rotor. For θ = 0° and θ = 90°, Ld and Lq are the maximum and minimum values of Lss, respectively. Ld represents the direct axis inductance and Lq represents the quadrature axis inductance. The expression for Lis given by
Here ir = 0 because there is no rotor winding and the torque expression becomes
In Equation (B.5), there are three sinusoidal terms. The average value of each of these three sinusoidal terms is zero over a cycle except in certain conditions.
If ωm = 0, we have
The average torque is
If ωm = ±ω, we have
Equation (B.7) shows that the reluctance motor develops average torque when it rotates at a synchronous speed (at the supply frequency) in either direction. The average torque is proportional to sin2δ.
18.188.198.94