Q3Advanced Electric Drives

Shunt Motor Speed Calculation Under Reduced Source Voltage

Given a 200V, 10.5A, 2000 rpm shunt motor with armature resistance Ra = 0.5 ohm and field resistance Rf = 400 ohm, the back-EMF at rated conditions is Eb1 = V1 - Ia1Ra = 200 - 10.50.5 = 194.75 V. The rated shunt field current is Ish1 = V1/Rf = 200/400 = 0.5 A.

Since the load torque is stated to remain constant at the rated motor torque, and torque T = KphiIa, with flux phi proportional to the shunt field current Ish (assuming an unsaturated magnetic circuit), the condition of constant torque requires Ia1Ish1 = Ia2Ish2 (since K is a constant). When the source voltage drops to V2 = 175V, the new shunt field current becomes Ish2 = V2/Rf = 175/400 = 0.4375 A.

Solving for the new armature current using the constant-torque condition (and noting Ish is directly proportional to source voltage V for a fixed Rf, so the ratio Ish1/Ish2 simplifies to V1/V2): Ia2 = Ia1(V1/V2) = 10.5(200/175) = 12 A.

The new back-EMF is Eb2 = V2 - Ia2Ra = 175 - 120.5 = 169 V. Since back-EMF is related to speed and flux by Eb = KphiN, and flux phi is proportional to the shunt field current Ish (and hence to source voltage V, for constant Rf), the ratio of speeds can be found from:

Substituting the known values: N2 = 2000(169/194.75)(200/175) = 1983.5 rpm. This result illustrates an important and somewhat counter-intuitive characteristic of shunt-connected DC motors under constant-torque loading and reduced supply voltage: because the field flux weakens proportionally with the reduced source voltage (since the shunt field is directly connected across the same supply as the armature), a larger armature current is required to maintain the same developed torque, and the two competing effects (reduced back-EMF requiring lower speed, but also reduced flux requiring higher speed for the same back-EMF) very nearly cancel, so the motor speed changes only modestly (dropping from 2000 rpm to about 1983.5 rpm, a decrease of less than 1%) despite the substantial 12.5% reduction in supply voltage - this near speed-regulation behavior under voltage sag is a distinctive characteristic of shunt (as opposed to series) DC motors operating under constant-torque load conditions.