Electrical Machines: Transformers, Motors and Generators
Scope
Expect rating, losses, speed and starting calculations for transformers, three-phase induction motors, single-phase motors and DC machines.
Core rules
- Transformer EMF: E = 4.44 f N Φ_m. Turns ratio a = N₁/N₂ = V₁/V₂ = I₂/I₁. Rating is in kVA because losses and heating depend on voltage and current, not on load power factor.
- Open-circuit test gives iron loss; short-circuit test gives full-load copper loss. Maximum efficiency occurs when copper loss equals iron loss.
- Synchronous speed N_s = 120f/P; slip s = (N_s − N)/N_s; rotor frequency = sf.
- Star–delta starting reduces the starting current and torque to one-third of direct-on-line values.
- DC generator EMF: E = ΦNZP/60A, where Z is total armature conductors, P poles, A parallel paths, N rpm.
Worked example
A 4-pole, 50 Hz three-phase induction motor runs at 1,440 rpm. N_s = 120 × 50/4 = 1,500 rpm. Slip s = (1,500 − 1,440)/1,500 = 0.04, i.e. 4%. Rotor frequency = s × f = 0.04 × 50 = 2 Hz. If the same motor were started star–delta, its line starting current would fall to one-third of the DOL value while the starting torque would also fall to one-third - acceptable only for loads that can start unloaded.
Traps that cost marks
Calling a transformer 100 kW instead of 100 kVA; adding iron and copper loss at all loads (copper loss varies with current squared); taking slip as a percentage of rotor speed instead of synchronous speed; and starting a star–delta motor on load. A DC series motor must never be started unloaded.