Appendix B

Reluctance Motor

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.

Figure B.1 Reluctance Motor

The stator inductance is expressed by

L_ss = L₀ + 2L cos2θ            (B.1)

This is a function of rotor position θ.

The stator current is

i_s = I_sm sinωt             (B.2)

The position of the rotor at any time t is expressed by

θ = ω_mt + 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 Variation of L_ss with Rotor Position

Figure B.2 shows the variation of stator self-inductance with the position of the rotor. For θ = 0° and θ = 90°, L_d and L_q are the maximum and minimum values of L_ss, respectively. L_d represents the direct axis inductance and L_q represents the quadrature axis inductance. The expression for Lis given by

Here i_r = 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.

Case 1:

If ω_m = 0, we have

The average torque is

Case 2:

If ω_m = ±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.