Unit 3: Fundamentals of electrical machines

Electrical machines convert energy between electrical and mechanical forms (or between two electrical levels) using the interaction of magnetic fields with current-carrying conductors. Every device in this unit rests on Faraday's law of electromagnetic induction and the force on a conductor in a magnetic field.

• Faraday's law: an EMF is induced in a circuit equal to the rate of change of flux linkage: e = -N·(dΦ/dt), where N = number of turns, Φ = flux in webers (Wb).
• Lenz's law: the negative sign shows the induced EMF opposes the change producing it.
• Motor action: force on a conductor, F = B·I·L, with B in tesla (T), I in amperes (A), L in metres (m).
• Generator action: motional EMF, e = B·L·v, with v the velocity in m/s.
• Core convention: magnetic flux prefers low-reluctance iron paths; windings are the electrical ports, the core is the magnetic link.

II. Mutual Inductance and Mutual Coupling

How current in one coil induces voltage in a magnetically linked neighbour — the basis of all transformer action.

A. Mutual inductance and mutual coupling phenomena in transformer

Two coils on a common core share flux, so a changing current in one links and drives the other.

• Mutual inductance (M): the ratio of EMF induced in coil 2 to the rate of change of current in coil 1:
  
  TEXT

    e2 = -M·(di1/dt)      M = k·√(L1·L2)

  
  M in henries (H), L1, L2 are self-inductances, k is the coupling coefficient.
• Coupling coefficient (k): fraction of flux from one coil that links the other, 0 ≤ k ≤ 1; iron-cored transformers approach k ≈ 0.98–0.99.
• Mutual flux in a transformer: the primary magnetising current sets up a common (mutual) flux Φm in the core that links both windings and transfers energy.
• Leakage flux: the small portion that links only one winding, reducing effective coupling and causing voltage drop.

III. The Transformer

A static device transferring AC power between circuits through a shared magnetic flux without electrical connection.

A. Transformer – working

A primary winding magnetises the core; the alternating mutual flux induces an EMF in the secondary.

• Principle: mutual induction only — no moving parts; works on AC only.
• EMF equation: E = 4.44·f·N·Φm, where f = supply frequency (Hz), N = turns, Φm = peak flux (Wb).
• No-load behaviour: a small magnetising current produces Φm; the induced primary EMF nearly balances the applied voltage.
• On load: secondary current creates a demagnetising MMF; primary draws extra current to restore Φm, so power flows across the core.
• Ideal relation: V1·I1 = V2·I2 (volt-amperes conserved), neglecting losses.
• Losses: copper loss I²R in windings and iron loss (hysteresis + eddy currents) in the core; laminated cores limit eddy currents.

B. Concept of turns ratio and applications

The ratio of winding turns fixes the voltage and current transformation.

• Turns ratio (a):
  
  TEXT

    a = N1/N2 = V1/V2 = I2/I1

• Step-up vs step-down:
  1. Step-up: N2 > N1, voltage rises, current falls — used at generating stations.
  2. Step-down: N2 < N1, voltage falls, current rises — used at distribution ends.
• Worked example: a 230 V primary, N1 = 500, N2 = 100 gives V2 = 230·(100/500) = 46 V.
• Applications: power transmission (minimise I²R loss by high-voltage transfer), domestic adapters, impedance matching in audio, isolation for safety.

C. Transformer on DC

A transformer cannot operate on direct current — a key diagnostic point.

• Reason: DC gives constant flux, so dΦ/dt = 0 and no EMF is induced.
• Consequence: only winding resistance limits current, so a large current flows and the primary overheats and burns out.
• Implication: confirms the transformer is inherently an AC machine relying on flux variation.

D. Auto-transformer

A single tapped winding serves as both primary and secondary.

• Construction: one continuous winding with a tapping point; part of the winding is common to both circuits.
• Operation: energy transfers partly by conduction (shared turns) and partly by induction.
• Advantages: less copper, smaller size, higher efficiency, lower cost for ratios near unity.
• Drawback: no electrical isolation — a break in the common winding puts full input on the output.
• Applications: motor starters (e.g. auto-transformer starter), voltage regulation (variac), interconnecting nearby voltage levels.

E. Instrument transformers

Transformers that scale down high voltages/currents for safe metering and protection.

• Current transformer (CT): primary in series with the line; steps current down to a standard 5 A or 1 A. Secondary must never be left open-circuited (dangerous high voltage).
• Potential transformer (PT): primary across the line; steps voltage down to a standard 110 V for meters and relays.
• Purpose: isolate instruments from high-voltage circuits and extend meter range safely.

IV. DC Machines

Machines that generate or use DC through a commutator that rectifies the internally alternating EMF.

A. DC machines – working principles

A conductor rotating in a magnetic field generates EMF; carrying current in that field it experiences torque.

• Generator: e = B·L·v; the commutator converts the AC armature EMF into unidirectional DC at the brushes.
• Motor: F = B·I·L produces torque; a back-EMF Eb = (PΦZN)/(60A) opposes the supply and regulates current.
• Symbols: P = poles, Z = armature conductors, N = speed (rpm), A = parallel paths, Φ = flux/pole.
• Torque: T ∝ Φ·Ia, where Ia = armature current.

B. Classification

DC machines are grouped by how the field winding connects to the armature.

• Separately excited: field fed from an independent source; precise flux control.
• Shunt: field in parallel with armature; nearly constant speed.
• Series: field in series with armature; high starting torque, speed varies strongly with load.
• Compound: both series and shunt fields — cumulative (adds torque) or differential.

C. Starting

A stationary motor has zero back-EMF, so starting current is dangerously high.

• Problem: at start Eb = 0, so Ia = V/Ra, a very large value because Ra is small.
• Three-point starter: adds external resistance in the armature circuit at start, cut out gradually as speed and Eb rise.
• Protection: includes no-volt and overload release coils.

D. Speed control

Speed follows N ∝ (V − Ia·Ra)/Φ, giving three control handles.

• Flux control: vary field current to change Φ — raises speed above base (field weakening).
• Armature/rheostatic control: insert resistance to drop armature voltage — lowers speed, wastes power.
• Voltage control: vary applied armature voltage (Ward-Leonard) — smooth wide-range control.

E. Applications of DC motors

Choice follows the torque-speed characteristic.

• Shunt: lathes, fans, pumps — constant speed.
• Series: cranes, hoists, electric traction — high starting torque.
• Compound: rolling mills, lifts, presses — need both torque and steady speed.

V. AC Induction Motors

Rotor currents are induced by a rotating stator field — no electrical connection to the rotor.

A. Working principle of single and three phase induction motors

A rotating magnetic field induces rotor currents that produce torque chasing the field.

• Synchronous speed: Ns = 120·f/P (rpm), f = frequency, P = poles.
• Slip: s = (Ns − N)/Ns; the rotor always runs below Ns, otherwise no induction.
  1. Three-phase motor: three windings 120° apart create a self-starting rotating field; rugged and widely used.
  2. Single-phase motor: one winding gives a pulsating, not rotating, field — not self-starting; needs an auxiliary (start) winding or capacitor to create a phase shift.

B. Applications of AC motors

Robustness and low maintenance make them the industrial workhorse.

• Three-phase: pumps, compressors, conveyors, machine tools, large fans.
• Single-phase: domestic fans, refrigerators, washing machines, small pumps.
• Reason for dominance: no commutator or brushes, so low cost and high reliability.

VI. Fleming's Rules

Mnemonics linking the directions of field, current, force and motion in machines.

A. Fleming's left hand and right hand rule

The two hands separate motor action from generator action.

• Thumb–forefinger–middle finger: mutually perpendicular, representing Force/motion (thumb), Field (forefinger), Current (middle finger).
  1. Left-hand rule (motors): gives the direction of force on a current-carrying conductor in a field — the motoring case.
  2. Right-hand rule (generators): gives the direction of induced current when a conductor moves in a field — the generating case.
• Use: fixes winding and brush polarity so predicted rotation or EMF direction is correct.