Electrical Engineering - Electrical Machines
Electrical Machines covers transformers, DC machines, three-phase induction motors and synchronous machines. The exam tests equivalent circuits, losses and efficiency, torque-speed behaviour, starting methods and excitation.
Transformer
The open-circuit test gives core loss and the magnetizing branch; the short-circuit test gives copper loss and leakage reactance. Efficiency is maximum when copper loss equals core loss. Voltage regulation = (V_no-load − V_full-load)/V_full-load.
Induction motor
N_s = 120f/P; slip s = (N_s − N_r)/N_s; rotor frequency = sf. Torque is proportional to sE₂²R₂/[R₂² + (sX₂)²]. Deep-bar rotors exploit skin effect to raise starting torque.
Synchronous machine
For a cylindrical rotor, E_f = V + jI_aX_s. V-curves relate armature current and field current. Synchronous motors run at N_s and can supply leading VARs when overexcited.
Worked example
A 50 Hz, 4-pole induction motor runs at 1440 rpm. N_s = 120 × 50/4 = 1500 rpm. Slip = (1500 − 1440)/1500 = 0.04 = 4%. Rotor frequency = sf = 0.04 × 50 = 2 Hz. If load torque rises, slip increases until motor torque balances it; the motor cannot run above 1500 rpm in motoring mode.
Traps
Using rotor speed instead of synchronous speed for N_s; forgetting that slip is negative in generation; treating the open-circuit test as copper loss; ignoring base change in transformer pu values; and assuming a synchronous motor can start on direct AC without damper windings.