Electrical Machines and Transformers
What this domain tests
Expect questions on transformer equivalent circuits and tests, DC machine equations, induction motor slip and torque, synchronous machine excitation, losses, and efficiency.
Core rules
- Transformer EMF: E = 4.44 f N Phi_m. Turns ratio a = N1/N2 = V1/V2. Impedance referred to the primary is multiplied by a^2.
- Open-circuit test gives iron loss and magnetising branch data; short-circuit test gives copper loss and series impedance. Core loss is approximately constant with load; copper loss varies with current squared.
- Induction motor synchronous speed n_s = 120 f/p; slip s = (n_s - n_r)/n_s. Rotor frequency = s f.
- DC machine: E = k Phi omega and T = k Phi I_a. Shunt, series and compound connections change the flux-current relationship.
- Synchronous machine: excitation controls reactive power; prime-mover input controls real power. Parallel operation requires matching voltage, frequency, phase sequence and phase angle.
Worked example
A 50 Hz, 4-pole induction motor runs at 1440 rpm. Find slip. n_s = 120 x 50/4 = 1500 rpm. s = (1500 - 1440)/1500 = 60/1500 = 0.04, or 4%. Rotor frequency is 0.04 x 50 = 2 Hz.
Traps
- Using line voltage where phase voltage is needed, or omitting sqrt(3) in three-phase calculations.
- Treating core loss as load-dependent or copper loss as constant.
- Assuming a synchronous machine's excitation changes real power output.
- Forgetting that slip is negative in generator operation and greater than 1 during braking.