Slip ring motor: starting, no-load, full-load currents

Given: 4-pole, 50 Hz, star stator and rotor, $R_2 = 0.8\ \Omega$, $X_2 = 4\ \Omega$ per phase at standstill, slip-ring emf $= 400$ V at standstill, turns ratio (stator : rotor) $= 4$, no-load speed 1490 rpm, full-load speed 1300 rpm. The list is cut off after (iii), so the rotor and the equivalent stator-side currents are given for the three conditions, with magnetising current neglected.

$$N_s = 1500\ \text{rpm}, \qquad E_2 = \frac{400}{\sqrt3} = 230.94\ \text{V per phase}$$

The rotor current at slip $s$ is $I_2 = \dfrac{sE_2}{\sqrt{R_2^2 + (sX_2)^2}}$, and the corresponding stator-side current is $I_2' = I_2/4$.

Slips: $s_{NL} = \frac{1500-1490}{1500} = 0.00667$ and $s_{FL} = \frac{1500-1300}{1500} = 0.1333$.

Results

• (i) Starting current: rotor $= 56.61$ A (stator side $= 14.15$ A)
• (ii) No-load current: rotor $= 1.92$ A (stator side $= 0.48$ A)
• (iii) Full-load current: rotor $= 32.03$ A (stator side $= 8.01$ A)

Rotor frequency at full load: $f_r = sf = 0.1333\times 50 = 6.67$ Hz.

Answer: rotor currents are 56.61 A, 1.92 A and 32.03 A at start, no load and full load (equivalent stator currents 14.15 A, 0.48 A and 8.01 A).