Electrical Machines

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This section covers transformer construction and types, the EMF equation, losses and efficiency, equivalent- circuit parameters from standard tests, voltage regulation, and three-phase, autotransformer and pulse transformer variants.

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Construction & Types A transformer is a static device (no moving parts) that transfers electrical energy between two circuits via electromagnetic induction, changing voltage/current level while frequency stays the same.

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Classified by turns ratio: step-up (raises voltage) or step-down (lowers voltage).

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By construction: core- type or shell-type.

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By application: power, distribution, or instrument transformers.

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The core is built from thin, laminated silicon-steel sheets to reduce eddy-current loss.

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EMF Equation & Operation EMF equation:

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E = 4.44·f·N·Φₘ (applies to both primary and secondary, using their respective turns N).

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Turns ratio: a = N₁/N₂ = V₁/V₂ = I₂/I₁ for an ideal transformer.

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On no-load, the primary draws only a small magnetizing current to set up the core flux; under load, the secondary current's demagnetizing MMF is balanced by additional primary current.

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Losses, Efficiency & Equivalent Circuit Tests Test Determines Open-circuit (OC) test Iron (core) loss, no-load current, and the shunt-branch parameters of the equivalent circuit Short-circuit (SC) test Copper loss and the equivalent series resistance/reactance of the equivalent circuit Copper loss (I²R) varies with load; iron loss (hysteresis + eddy current) is essentially constant, depending on flux/frequency.

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Maximum efficiency occurs at the load where copper loss = iron loss.

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Voltage regulation: the percentage change in secondary terminal voltage from no-load to full-load, expressed as a percentage of rated voltage.

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Three-Phase Transformers & Special Types A three-phase transformer is built either from three single-phase units or one integrated three-phase core; standard winding connections include star-star, delta-delta, star-delta, and delta-star.

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Autotransformer: uses a SINGLE winding shared between primary and secondary (electrically connected, not fully isolated) — smaller, cheaper, but offers no electrical isolation.

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Pulse transformer: designed to transfer fast rise-time pulses with minimal distortion — used in digital/switching applications.

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This section covers DC generator principles and construction, the EMF equation, magnetization/load characteristics, armature reaction and commutation, losses, and parallel operation.

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Principle & Construction A DC generator works on Faraday’s law: a dynamically induced EMF arises in a conductor moving through a magnetic field; a commutator converts this internally-generated AC into DC at the terminals.

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Main parts: field system (poles/yoke), armature (core + winding), commutator, brushes.

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Classified by excitation: separately excited, or self-excited (shunt, series, compound).

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EMF Equation & Characteristics EMF equation:

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E = PΦZN/60A (P = poles, Φ = flux/pole, Z = armature conductors, N = speed in rpm, A = parallel paths).

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Magnetization (no-load) characteristic: generated EMF E₀ vs. field current, at constant speed — shows the core’s saturation behaviour.

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Load characteristic: terminal voltage vs. load current — voltage drops with load due to armature resistance and armature reaction.

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Armature Reaction & Commutation Armature reaction: distortion/weakening of the main field flux caused by the armature’s own MMF when current flows.

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Commutation: the reversal of current in an armature coil as it passes under the brushes; poor commutation causes sparking.

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Interpoles (commutating poles) are added to improve commutation.

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Losses, Efficiency & Parallel Operation Losses: copper losses (armature, field), iron losses (hysteresis, eddy current), mechanical losses (friction, windage).

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Before paralleling two DC generators, they must have equal voltage and matched polarity, with similar external characteristics for proper load sharing.

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This section covers DC motor principles, back EMF, motor types and their characteristics, speed control and starting, brushless DC motors, testing, reversing and braking.

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Principle & Back EMF A DC motor works on the principle that a current-carrying conductor in a magnetic field experiences a force (F = BIL), converting electrical energy into mechanical energy.

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Back EMF (Eb): an induced EMF that OPPOSES the applied voltage, given by Eb = V − Ia·Ra; it increases with speed and self-regulates the armature current.

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Motor Types & Characteristics Motor Type Characteristic Shunt motor Nearly constant speed regardless of load; moderate starting torque Series motor High starting torque; speed varies greatly with load — unsafe (“runs away”) at no load Compound motor Combines shunt + series behaviour (cumulative): good starting torque with fairly constant speed Speed Control & Starting Speed ∝ Eb/Φ = (V − Ia·Ra)/Φ.

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Control methods: armature (voltage) control, field (flux) control, and armature resistance control.

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A starter (external resistance) is essential at start-up because Eb = 0 initially, so without it the armature current (Ia = V/Ra) would be dangerously high.

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BLDC Motors, Testing, Reversing & Braking A Brushless DC (BLDC) motor uses electronic commutation (power electronics + rotor position sensors) instead of a mechanical commutator/brushes — less maintenance, higher efficiency and speed capability.

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Swinburne’s test: a no-load test that determines losses and efficiency of a DC machine.

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Brake test: a direct-loading test that measures output torque directly.

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Reversing direction: reverse EITHER the armature or the field current connections (never both together).

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Plugging (reverse voltage applied), Dynamic/rheostatic braking (motor runs as a generator, energy dissipated in a resistor), Regenerative braking (kinetic energy fed back to the supply).

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This section covers induction motor principle and construction, synchronous speed and slip, torque-speed characteristics, starting and speed control, induction generators, and single-phase induction motor types.

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Principle & Construction A rotating magnetic field (from the 3-phase stator winding) induces currents in the rotor purely by electromagnetic induction — producing torque with no direct electrical connection to the rotor (in the squirrel-cage type).

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Squirrel cage rotor: conductor bars short-circuited by end rings — simple and rugged.

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Wound rotor: winding brought out via slip rings, allowing external resistance to be added for speed/torque control.

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Synchronous Speed & Slip Synchronous speed:

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Nₛ = 120f/P (P = number of poles).

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Slip: s = (Nₛ − N_r)/Nₛ, where N_r = actual rotor speed.

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At standstill, s = 1; at (theoretical) synchronous speed, s = 0.

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Rotor frequency: f_r = s×f (the rotor-induced EMF frequency equals slip times supply frequency).

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Torque-Speed Characteristics, Starting & Speed Control The torque-speed curve rises from zero at s=0, reaches a maximum (breakdown/pull-out torque), then falls to zero at s=1 (standstill).

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Direct-On-Line (DOL — simple, but high starting current), Star-Delta starter (reduces starting voltage/current), Auto-transformer starter, rotor-resistance starter (wound rotor only).

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Speed control: pole-changing, frequency (V/f) control via a Variable Frequency Drive (VFD), rotor- resistance control (wound rotor), slip-power recovery.

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Induction Generator When driven ABOVE synchronous speed by an external prime mover, an induction machine can act as an induction generator, feeding power back to the grid (it needs an external reactive-power source/grid connection for magnetizing).

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Single-Phase Induction Motors Type Feature Split-phase Starting winding with a different R/L ratio creates a phase difference for starting torque; moderate starting torque Capacitor-start Starting winding in series with a capacitor for higher starting torque; capacitor disconnected after starting Permanent split- capacitor (PSC) Capacitor stays in circuit continuously — smooth running, but lower starting torque Two-value capacitor Uses two capacitors — a high value for starting, a lower value for running — best overall start & run performance Shaded-pole Simplest/cheapest; a shading coil creates a slight rotating-field effect — very low starting torque and efficiency; used in small fans/appliances

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This section covers synchronous generator (alternator) construction, the speed-frequency relationship and EMF equation, voltage regulation, the equivalent circuit, synchronization, and Permanent Magnet Synchronous Generators (PMSG).

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Construction & Principle A synchronous generator (alternator) converts mechanical energy to AC electrical energy, running at a speed exactly synchronized with the output frequency.

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Construction: stationary armature (stator) carrying the 3-phase winding; rotating field (rotor) with DC excitation (via slip rings or a brushless exciter).

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Rotor types: salient-pole (low-speed, e.g., hydro plants) or cylindrical/non-salient (high-speed, e.g., steam/gas turbines).

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Speed, Frequency & EMF Equation Relationship: f = P·Nₛ/120 — the rotor must run at exactly synchronous speed to produce the required frequency.

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E = 4.44·K_c·K_d·f·Φ·T (K_c = coil/pitch factor, K_d = distribution factor, T = turns per phase).

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Equivalent Circuit, Voltage Regulation & Power Equivalent circuit: internal EMF (E) in series with synchronous impedance Zₛ = Rₐ + jXₛ (Xₛ usually dominates).

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Voltage regulation: the percentage RISE in terminal voltage when full load is removed, with field current and speed held constant.

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Power developed depends on the load (torque) angle δ between E and V:

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Synchronization & PMSG Synchronizing conditions for paralleling an alternator with the grid/another generator:

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(1) equal voltage magnitude, (2) equal frequency, (3) same phase sequence with matching phase angle.

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Common synchronizing methods: dark-lamp method, bright-lamp method, and the synchroscope.

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A Permanent Magnet Synchronous Generator (PMSG) uses permanent magnets on the rotor instead of a DC field winding — no separate excitation/slip rings needed, higher efficiency; widely used in wind turbines.

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This section covers synchronous motor principle and torque-angle characteristics, starting methods, counter EMF and armature reaction voltage, excitation-based power factor control, and speed control.

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Principle of Operation A synchronous motor runs at exactly synchronous speed (Nₛ = 120f/P), locked to the rotating stator field — unlike an induction motor, it has NO slip at steady state.

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It is NOT self-starting: at standstill, the rotor’s inertia prevents it from instantly following the rapidly rotating stator field.

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Torque-Angle Characteristics Developed torque T ∝ sinδ, where δ is the load (torque) angle between the rotor field and the stator field.

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Maximum (pull-out) torque occurs at δ = 90°; beyond this, the motor loses synchronism (“pulls out of step”).

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Starting Methods (1) Using a small auxiliary/pony motor to bring the rotor near synchronous speed, then applying DC excitation.

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(2) Using damper (amortisseur) windings — acting like a squirrel cage for asynchronous (induction- motor-like) starting; the most common modern method.

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(3) Using a Variable Frequency Drive (VFD) to ramp up the supply frequency gradually.

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Excitation, CEMF & Power Factor Control Counter EMF (CEMF): the motor’s internally generated EMF (due to rotor DC excitation) that opposes the applied stator voltage — analogous to a DC motor’s back EMF.

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Armature reaction voltage combines with the CEMF to determine terminal behaviour.

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Excitation Level Power Factor Behaviour Under-excited Motor draws LAGGING current (behaves inductively) Normally excited Unity power factor Over-excited Motor draws LEADING current (behaves capacitively) — used as a synchronous condenser for power-factor correction Speed control: since the motor runs strictly at synchronous speed (fixed by supply frequency and pole count), speed can ONLY be changed by varying the supply frequency (via a VFD) — not by voltage or resistance methods.