Electrical Machine-II (EX-501) Unit 1 Notes

UNIT 1: DC MACHINES & SYNCHRONOUS MACHINES (ALTERNATORS & MOTORS)

1.0 DC MACHINES - FUNDAMENTALS & CONSTRUCTION

1.1 Basic Parts of a DC Machine

A DC machine consists of two main parts:

Stator (Field System): Provides main magnetic flux. Includes yoke, pole cores, pole shoes, and field windings.
Rotor (Armature): The rotating part where EMF is induced. Includes armature core, armature winding, commutator, and shaft. Other Parts: Brushes, brush gear, bearings, end covers.

1.2 Detailed Construction

Yoke: Outer frame, provides mechanical support and carries magnetic flux.
Pole Core & Pole Shoe: Pole core carries field winding; pole shoe spreads flux uniformly over armature periphery and is laminated to reduce eddy currents.
Field Winding:
- Shunt Winding: Many turns of fine wire, connected in parallel with armature.
- Series Winding: Few turns of heavy wire, connected in series with armature.
- Compound Winding: Both shunt and series windings.
Armature Core & Winding:
- Core: Laminated to reduce eddy current loss, has slots for windings.
- Winding: Conductors placed in slots, connected to commutator segments.
- Lap Winding: Number of parallel paths (A) = Number of poles (P). Used for high current, low voltage.
- Wave Winding: A = 2 (always). Used for high voltage, low current.
Commutator & Brushes:
- Commutator: Segmented copper cylinder, provides mechanical rectification (AC to DC).
- Brushes: Usually carbon, maintain contact with commutator, collect current.

1.3 Principle of Operation (DC Generator)

Based on Faraday's Law of Electromagnetic Induction.

When armature conductors rotate in the magnetic field produced by the field winding, an alternating EMF is induced in each conductor.
The commutator converts this alternating EMF into a unidirectional (DC) output across the brushes.

1.4 Principle of Operation (DC Motor)

Based on Lorentz Force Law.

When current-carrying armature conductors are placed in the magnetic field, a force is produced, causing rotation (torque).
As the armature rotates, it cuts flux and induces a back EMF (E_b) opposing the applied voltage. At steady state: V = E_b + I_a R_a.

2.0 DC MACHINES - PERFORMANCE & CHARACTERISTICS

2.1 Armature Reaction

Definition: The effect of armature flux on the main field flux under the pole.
Effects:
1. Flux Distortion: Main flux is distorted, becoming non-uniform.
2. Shift of Neutral Plane (MNP): The plane where induced EMF is zero shifts in the direction of rotation for a generator. This causes poor commutation.
Types:
- Demagnetizing Effect: Armature flux opposes main field flux (under poles where conductors carry current in opposite direction to field winding). Reduces net flux.
- Cross-magnetizing Effect: Armature flux distorts main field flux (under poles where conductors carry current in same direction as field winding). Shifts MNP.
Methods to Reduce Armature Reaction:
1. Interpoles (Commutating Poles): Small poles placed in MNP, with winding in series with armature. Provide local flux to neutralize armature reaction at commutator zone.
2. Compensating Windings: Embedded in pole faces, connected in series with armature. Produce flux opposite to armature cross-magnetizing flux, neutralizing it under the poles.

2.2 Commutation

Definition: The process of reversing the current in an armature coil as it passes through the neutral plane, from one brush to the next. It is the change from one direction to the opposite.
Ideal Commutation: Current reversal is linear and completes exactly when the coil is shorted by the brush.
Practical Commutation: Due to self-inductance (L) of the coil, current reversal is delayed, causing sparking.
Causes of Poor Commutation:
1. Armature reaction (shifts MNP).
2. Inductance of armature coil.
Methods to Improve Commutation:
1. Resistance Commutation: Use high-resistance carbon brushes to limit current during reversal.
2. EMF Commutation: Use Interpoles to induce an EMF in the commutating coil that opposes the self-induced EMF, aiding current reversal.
Commutation Time Calculation:

$$ t_c = \frac{\text{Brush Width (mm)}}{\text{Peripheral Speed (m/s)}} = \frac{w_b}{\pi D N / 60} $$

where `w_b` = brush width, `D` = commutator diameter, `N` = speed (rpm).

2.3 Losses & Efficiency

Types of Losses:
- Copper Losses: I_a^2 R_a (Armature), I_f^2 R_f (Field).
- Iron Losses (Core Losses): Hysteresis + Eddy currents in armature core.
- Mechanical Losses: Friction (bearings) + Windage (air friction).
- Stray Losses: Miscellaneous (e.g., brush contact loss, harmonic effects).
Efficiency:

$$ \eta = \frac{\text{Output Power}}{\text{Input Power}} = \frac{\text{Input Power} - \text{Total Losses}}{\text{Input Power}} $$

Condition for Maximum Efficiency (for DC Generator):

Occurs when Variable losses = Constant losses.

$$ \text{Iron losses} + \text{Mechanical losses} + \text{Stray losses} = I_a^2 R_a $$

2.4 Testing & Characteristics

Swinburne's Test (No-load Test):
- Method: Run machine as motor at rated speed without load. Measure I_0 (no-load current) and V. Calculate no-load losses (iron, mechanical, stray). Armature copper loss at no-load is I_0^2 R_a (negligible). Field copper loss is I_f^2 R_f.
- Efficiency at any load (I_a):

$$ \eta = \frac{V I_a}{V I_a + (I_a^2 R_a + I_f^2 R_f + \text{No-load losses})} $$

*   **Advantages:** Economical, convenient (machine runs as motor, no load needed).

Hopkinson's Test (Back-to-Back Test): Two identical machines coupled, one as generator, other as motor. More accurate for full-load efficiency.
Characteristics of DC Motors:
- Shunt Motor:
  - Speed-Current: Slightly decreases with load (N ∝ (V - I_a R_a)/φ). φ ≈ constant.
  - Torque-Current: Linear (T ∝ I_a).
  - Speed-Torque: Slightly drooping.
- Series Motor:
  - Speed-Current: Very high at light load (N ∝ (V - I_a(R_a+R_se))/I_a). Dangerous to run at no-load.
  - Torque-Current: T ∝ I_a^2 (parabolic).
  - Speed-Torque: Hyperbolic.
- Compound Motor:
  - Cumulative Compound: Series flux aids shunt flux. Characteristics between shunt and series. Used for heavy starting torque with limited top speed (e.g., cranes).
  - Differential Compound: Series flux opposes shunt flux. Speed increases with load (dangerous). Rarely used.

3.0 DC MACHINES - STARTING & SPEED CONTROL

3.1 Starting of DC Motors

Problem: At start, E_b = 0, so I_a(start) = V / R_a is very large (can be 10-20 times rated current), damaging commutator and windings.
Starters: Introduce external resistance in armature circuit during start, gradually cut out as motor picks up speed.
- Two-Point Starter: Simple, only protects against over-current. No protection against field failure.
- Three-Point Starter: Has Start, Run, and Overload release points. Uses a no-volt release (NVR) coil in series with shunt field. Drawback: If field weakens, NVR releases, cutting off supply—can cause unstable operation at weak fields (field current adjusts to a new unstable point).
- Four-Point Starter: Solves three-point drawback. NVR coil is connected directly across supply via a separate resistor. Field current is independent of starter arm position, ensuring stable operation even if field weakens.

3.2 Speed Control of DC Motors

For Shunt Motors:
1. Armature Resistance Control (Rheostat in armature circuit): N ∝ (V - I_a R_a)/φ. Simple, but wasteful (losses in resistor). Used for below-rated speed.
2. Field Flux Control (Field Rheostat): N ∝ V/φ. By weakening field flux (φ), speed increases. Efficient (small power loss in field rheostat). Used for above-rated speed (limited by poor commutation at high speed).
For Series Motors:
1. Armature Resistance Control: Same as shunt, but speed reduction is more pronounced.
2. Series-Parallel Control (Tapped Field): For traction. Motors connected in series for high torque/low speed at start, then switched to parallel for higher speed.
Ward-Leonard System: Vary applied voltage using a motor-generator set. Provides smooth, wide-range speed control in both directions. Used for heavy-duty applications (e.g., elevators, rolling mills).

3.3 Braking of DC Motors

Plugging (Reverse Current Braking): Supply polarity reversed while motor running. E_b and V aid, causing high current and deceleration. Energy wasted in resistors. Used for quick stop.
Dynamic (Rheostatic) Braking: Armature disconnected from supply, connected to a braking resistor. Motor acts as generator, dissipating kinetic energy in resistor. Smooth stop.
Regenerative Braking: Motor runs above synchronous speed (shunt) or back EMF > supply voltage (series). E_b drives current back into supply. Energy fed to grid. Used in traction and where supply can accept power.

4.0 SYNCHRONOUS MACHINES (ALTERNATORS) - FUNDAMENTALS

4.1 Construction & Principle

Salient-Pole Rotor: Poles project out. Used for slow-speed machines (hydro-generators, > 6 poles). Large diameter, short axial length.
Cylindrical (Non-Salient) Rotor: Smooth cylinder. Used for high-speed machines (turbo-alternators, 2 or 4 poles). Small diameter, long axial length.
Principle: Rotor (field) is excited with DC and rotated at synchronous speed (N_s = 120f/P). Stator (armature) has 3-phase windings. Rotating magnetic field cuts stationary stator coils, inducing 3-phase AC EMF.
Why DC Excitation on Rotor?
1. Slip Rings: Only two slip rings needed for low-power DC excitation vs. three heavy slip rings for high-power 3-phase AC.
2. Stationary Armature: Stator can handle high-voltage, high-current 3-phase output easily (better insulation, cooling, mechanical strength).
3. Ease of Control: Field current easily adjustable to control voltage/reactive power.

4.2 EMF Equation

Average EMF per conductor: E_avg = (P * φ * N) / 60 (P=poles, φ=flux/pole, N=speed rpm).
RMS Value of Phase EMF:

$$ E_{ph} = 4.44 \cdot f \cdot \phi \cdot T_{ph} $$

where `f` = frequency, `T_ph` = turns/phase.

Including Winding Factors:

$$ E_{ph} = 4.44 \cdot f \cdot \phi \cdot T_{ph} \cdot K_d \cdot K_c $$

Distribution Factor (K_d): Accounts for fact that coil sides of a phase are distributed in several slots under a pole, not all in one slot. EMFs are not in phase.

$$ K_d = \frac{\sin(m \beta / 2)}{m \sin(\beta / 2)} $$

where `m` = slots/pole/phase, `β` = slot angle (electrical degrees).

Pitch Factor (K_c) or Coil Span Factor: Accounts for coils not being full-pitch (chorded). Reduces harmonics.

$$ K_c = \cos(\alpha / 2) $$

where `α` = short-pitch angle (electrical).

4.3 Armature Reaction in Alternators

Definition: Effect of armature (stator) MMF on the main field flux.
Effect on Terminal Voltage (V_t) depends on load Power Factor (pf):
1. Unity pf (I_a in phase with V_t): Armature MMF is cross-magnetizing only. Distorts main field, shifts MNP. Terminal voltage drops due to increased leakage reactance drop (I_a X_{al}), but flux magnitude unchanged.
2. Lagging pf: Armature MMF has demagnetizing (opposes main field) + cross-magnetizing components. Net flux decreases, causing greater voltage drop than at unity pf.
3. Leading pf: Armature MMF has magnetizing (aids main field) + cross-magnetizing components. Net flux increases, causing voltage rise (V_t > E_f at no-load).

5.0 SYNCHRONOUS MACHINES - VOLTAGE REGULATION & SYNCHRONIZATION

5.1 Voltage Regulation (VR)

Definition: Change in terminal voltage from no-load to full-load, at constant speed and excitation, expressed as % of rated voltage.

$$ VR\% = \frac{E_{0} - V_{rated}}{V_{rated}} \times 100\% $$

(`E_0` = no-load induced EMF at same excitation).

Methods:
1. EMF (Synchronous Impedance) Method:
  - Obtain Open-Circuit Characteristic (OCC) and Short-Circuit Characteristic (SCC).
  - Calculate Synchronous Impedance (Z_s) from air-gap line of OCC and SCC: Z_s = (V_oc at If) / (I_sc at same If).
  - Draw phasor diagram: E_0 = V + I_a Z_s (for lagging pf, I_a Z_s leads I_a by φ_s, angle of Z_s).
  - Why Optimistic? Assumes constant main field flux (from OCC air-gap line). In reality, armature reaction demagnetizes at lagging pf, so actual E_0 needed is higher than calculated → VR is underestimated (optimistic).
2. MMF (Ampere-turn) Method:
  - Uses OCC and SCC but assumes constant MMF (field excitation).
  - More complex phasor addition of MMFs.
  - Why Pessimistic? Assumes constant field MMF. In reality, at lagging pf, demagnetizing armature reaction reduces net flux, so less excitation is needed than assumed → Calculated E_0 is higher than actual → VR is overestimated (pessimistic).
3. Potier Triangle Method (Most Accurate):
  - Uses OCC, Zero Power Factor (ZPF) Characteristic (terminal voltage vs. field current at full-load, lagging pf 0), and SCC.
  - Construction of Potier Triangle:
    - Draw OCC.
    - Plot point A: V_rated at I_a lagging 0, find corresponding I_f on OCC → point A.
    - From A, draw vector I_a X_{al} (lagging I_a by 90°) to meet OCC at B. I_f at B = I_f'.
    - Triangle OAB is Potier triangle. OA = I_a X_{al} (armature reaction MMF drop), AB = I_a R_a (voltage drop), OB = I_a Z_s (synchronous impedance drop).
  - Steps: For given load, find I_f from OCC for V_t. Draw I_a phasor. Complete Potier triangle to find E_0. Calculate VR.
  - Advantage: Separates voltage drop due to armature leakage reactance (I_a X_{al}) and armature reaction effect (separate MMF drop), more realistic.

5.2 Synchronization (Parallel Operation)

Necessity: Increase capacity, reliability, and efficiency.
Conditions for Synchronization:
1. Voltage magnitude must be equal.
2. Frequency must be equal.
3. Phase sequence must be identical.
4. Phase angle must be zero (i.e., voltages in phase).
Methods of Synchronizing:
1. Three-Lamp Method:
  - Connect three lamps (or two bright, one dark) between alternator terminals and busbars.
  - Dark Lamp Method: Close switch when all lamps are darkest (voltage difference zero, phase difference zero). Risk: if phase sequence wrong, lamps may not all dark simultaneously.
  - Bright Lamp Method: Close when all lamps are brightest (voltage difference max, but phase difference 180°? Actually, for correct sequence, lamps brighten and dim together; close at maximum brightness indicates zero phase difference? Correction: In standard "One Dark, Two Bright" method, close when one lamp is dark and other two are equally bright. This ensures correct phase sequence and zero phase difference. The "brightest" condition in some texts refers to the point where the two bright lamps are at maximum intensity, which coincides with the dark lamp being off, indicating synchronism.
2. Synchroscope: Instrument showing relative speed and phase difference. Needle rotates clockwise if generator fast (high freq), anticlockwise if slow. Close when needle points vertically (12 o'clock, zero phase difference).
Load Sharing between Parallel Alternators:
- Governed by speed regulation (droop) characteristic.
- Droop % = (No-load speed - Full-load speed) / Full-load speed × 100% (for governors).
- Load Sharing Rule: The alternator with higher droop (%) (softer characteristic) will take less load.
- Example: Alternator A (100-104%) has droop 4%, Alternator B (100-105%) has droop 5%. B is softer → takes less load. For total load P_total, load on A: P_A = P_total × (Droop_B / (Droop_A + Droop_B)).

6.0 SYNCHRONOUS MACHINES - THEORY & PHENOMENA

6.1 Phasor Diagrams & Equivalent Circuits

Phasor Diagram (General): Reference: V_t (terminal voltage).
- I_a drawn at angle φ (load pf angle).
- I_a R_a drop in phase with I_a.
- I_a X_s drop perpendicular to I_a (leading for lagging load).
- E_f (excitation EMF) = V_t + I_a R_a + I_a jX_s.
Equivalent Circuit (Synchronous Impedance Model):

$$ E_f = V_t + I_a (R_a + jX_s) $$

6.2 Two-Reaction Theory (Blondel's Theory)

Applicable for Salient-Pole Machines (since X_d ≠ X_q).
Concept: Resolve armature MMF (and hence reactance) into two orthogonal components:
1. Direct Axis (d-axis): Axis along the main field pole (axis of symmetry). Reactance X_d (direct axis synchronous reactance).
2. Quadrature Axis (q-axis): Axis perpendicular to d-axis (inter-polar region). Reactance X_q (quadrature axis synchronous reactance). X_q < X_d.
Phasor Diagram for Salient-Pole Generator (Lagging pf):
- Draw V_t reference.
- Draw I_a at lagging angle φ.
- Resolve I_a into I_d (along d-axis, magnetizing direction) and I_q (along q-axis, cross-magnetizing direction).
- Voltage drops:
  - I_d R_a (in phase with I_d)
  - I_d jX_d (leads I_d by 90°)
  - I_q R_a (in phase with I_q)
  - I_q jX_q (leads I_q by 90°)
- E_f = V_t + I_d R_a + jI_d X_d + I_q R_a + jI_q X_q.

6.3 Reactances & Stability

Synchronous Reactances (Transient & Subtransient):
- Steady-state X_d: Reactance during slow changes (load changes).
- Transient X_d': Lower than X_d. Effective during sudden load changes (e.g., fault, switching). Accounts for damper winding and rotor induced currents.
- Subtransient X_d'': Even lower. Effective during the first few cycles of a severe fault (e.g., 3-phase short circuit). Accounts for stator transients and damper winding.
- X_q: Quadrature-axis reactance (salient pole only).
Negative Sequence Reactance (X_2): Reactance seen by negative sequence currents (reverse rotating field). X_2 ≈ X_d' (for salient pole). Causes double-frequency currents in rotor, leading to heating.
Zero Sequence Reactance (X_0): Reactance seen by zero sequence currents (co-phasal). Depends on winding connection and grounding. Usually small.
Hunting (Synchronous Oscillations):
- Cause: Sudden change in load or system disturbance causes rotor to oscillate about its steady-state position (power angle δ).
- Effects: Fluctuating speed, alternating currents, mechanical stress.
- Reduction Methods:
  1. Damper Winding (Amortisseur): Copper bars in rotor slots, short-circuited at ends. Provides damping torque (like squirrel cage in induction motor).
  2. Inertia: Heavy rotor (flywheel effect) reduces oscillation amplitude.
  3. Electrical Damping: From stator circuit (e.g., connecting resistors).
V-Curves (Synchronous Motor):
- Plot of armature current (I_a) vs. field current (I_f) at constant load (constant power input).
- Shape: U-shaped (inverted V if plot I_a vs. power factor).
- Significance:
  - Minimum I_a occurs at unity power factor.
  - Left of minimum (I_f low): Under-excited, lagging pf.
  - Right of minimum (I_f high): Over-excited, leading pf.
  - Shows power factor control capability.
Power-Angle Characteristic (Salient Pole):

$$ P = \frac{V_t E_f}{X_d} \sin \delta + \frac{V_t^2}{2} \left( \frac{1}{X_q} - \frac{1}{X_d} \right) \sin 2\delta $$

*   First term: Synchronous power (like cylindrical rotor).

*   Second term: **Reluctance power** (due to saliency, `X_d > X_q`). Provides additional stability.

Stability:
- Why operate at δ << 90°? Maximum power transfer occurs at δ = 90° for cylindrical rotor (P_max = V_t E_f / X_d). Operating close to 90° leaves little margin for disturbances; a small increase in δ can cause loss of synchronism (pole slipping).
- When δ > 90°: Power starts decreasing (sin δ decreases), electrical torque cannot balance mechanical torque → rotor accelerates uncontrollably → loss of synchronism.
- Salient-Pole Advantage: The sin 2δ term provides additional positive power for δ > 90° up to a point, giving greater stability margin than cylindrical rotor.

7.0 SYNCHRONOUS MOTORS

7.1 Principle & Starting

Why Non-Self-Starting? At rest, stator rotating field moves at N_s. Rotor has no initial torque (no locked rotor torque like induction motor). Average torque over a cycle is zero.
Starting Methods:
1. Auxiliary Motor (Pony Motor): Small induction motor on same shaft brings rotor to near N_s before connecting to supply.
2. Damper Winding: Rotor has amortisseur winding (like squirrel cage). Initially, motor starts as induction motor. Once near N_s, DC excitation applied, pulls into synchronism.
3. As Synchronous Induction Motor: Use variable frequency supply (from inverter) starting at low frequency, gradually increase to rated frequency while applying DC excitation.

7.2 Operation & Characteristics

Phasor Diagram & Excitation:
- E_f (internal induced EMF) = V_t + I_a Z_s.
- Normal Excitation: E_f ≈ V_t. Motor operates at unity or slightly lagging pf.
- Over-excited: E_f > V_t. I_a leads V_t (leading pf). Motor absorbs leading reactive power (behaves like capacitor).
- Under-excited: E_f < V_t. I_a lags V_t (lagging pf). Motor absorbs lagging reactive power (behaves like inductor). Limited by stability (minimum I_f to avoid pulling out).
Why E_f > V_t in Over-excited? From phasor: E_f = V_t + I_a jX_s. For leading I_a, I_a jX_s is in phase with V_t (since I_a leads V_t by φ, jX_s rotates by +90°, so I_a jX_s leads I_a by 90°, which can be in same direction as V_t). Thus E_f magnitude > V_t.
Torque Equation:

$$ T \propto \frac{V_t E_f}{X_d} \sin \delta + \frac{V_t^2}{2} \left( \frac{1}{X_q} - \frac{1}{X_d} \right) \sin 2\delta $$

V-Curves & Inverted V-Curves: As described in 6.3.
Power Factor Control: By varying field excitation:
- Over-excite → leading pf (supply reactive power).
- Under-excite → lagging pf (absorb reactive power).
- Normal excite → unity pf.
- Used for power factor correction in industries.

8.0 SPECIAL ELECTRICAL MACHES

8.1 Brushless DC Motors (BLDC)

Construction: Rotor: Permanent magnets (PM). Stator: 3-phase concentrated windings. No commutator/brushes. Electronic commutator (position sensors + power electronics) replaces mechanical commutator.
Three-Phase, Three-Pulse (Half-Wave) BLDC:
- Each phase conducts for 120° electrical.
- Rotor position sensors (Hall effect) determine which two phases to energize.
- Torque produced by interaction of PM rotor field with stator MMF.
Torque-Angle Characteristic: Similar to synchronous motor: T ∝ sin θ (θ = torque angle between E_f (PM) and V_t). Trapezoidal back-EMF shape gives constant torque over 120° conduction.
Applications: Computer disk drives, fans, pumps, electric vehicles (high reliability, no brush maintenance).

8.2 Hysteresis Motor

Construction: Stator: 3-phase (or single-phase) winding. Rotor: Cylindrical core made of hard magnetic material (high coercivity, e.g., Alnico). No windings, no slots.
Working Principle:
1. Stator produces rotating magnetic field.
2. Rotor material gets magnetized (induced) but lags behind the stator field due to hysteresis (magnetic memory).
3. This lag creates a constant hysteresis torque (T_h ∝ sin δ, δ = lag angle) from zero to synchronous speed.
Torque-Speed Characteristics:
- Synchronous: Runs exactly at N_s.
- Constant Torque from Pull-in to N_s: Unique feature. Smooth, quiet operation.
- Pull-in Torque: High, ensures easy synchronization.
Applications: High-precision drives (clocks, turntables, timers), small pumps, fans.

8.3 Reluctance Motors

Switched Reluctance Motor (SRM):
- Construction: Both stator and rotor have salient poles. Stator has concentrated windings, rotor has no windings or PMs (simple, robust).
- Working Principle: Torque produced by tendency of rotor to align with stator pole (minimum reluctance). Windings energized sequentially as rotor approaches alignment.
- Torque Expression (from co-energy):

$$ T = \frac{1}{2} i^2 \frac{dL(\theta)}{d\theta} $$

    where `L(θ)` = inductance varying with rotor position θ. Torque exists only when `dL/dθ > 0` (inductance increasing with θ).

*   **Torque-Speed Characteristics:** High starting torque, torque ripples, suitable for variable-speed applications.

Reluctance Motor (Single-phase/Three-phase):
- Construction: Similar to induction motor but with salient-pole squirrel-cage rotor (laminated with poles).
- Working: Starts as induction motor, but salient poles create reluctance torque that pulls it to synchronous speed.
- Characteristics: Lower power factor, lower efficiency than induction motor. Used in small constant-speed applications (clocks, recorders).

8.4 Repulsion Motor

Construction: Similar to DC motor: laminated stator with 1-phase/3-phase winding, rotor with commutator and brushes (usually 2, short-circuited or connected to each other).
Working Principle:
1. Stator winding connected to AC supply produces alternating flux.
2. Flux induces EMFs in rotor bars (like transformer secondary).
3. Since brushes are shorted, currents flow in rotor bars.
4. Interaction of stator flux and rotor currents produces repulsion torque (like series motor).
Types:
- Compensated Repulsion Motor: Has compensating winding in stator to improve commutation and power factor.
- Differential Repulsion Motor: Brushes shifted opposite to rotation direction → poor commutation, rarely used.
Characteristics: High starting torque, high speed (no-load speed > synchronous), poor power factor. Used in high-speed applications (e.g., grinders).

8.5 Permanent Magnet DC Motors (PMDC)

Construction: Stator field replaced by permanent magnets (instead of field winding). Armature and commutator-brush arrangement same as DC motor.
Working Principle: Same as DC motor. Torque T ∝ I_a (since φ constant from PMs).
Characteristics: Linear torque-speed, good speed control, no field power loss → higher efficiency. No risk of field failure.
Applications: Automobile accessories (windows, wipers), toys, small appliances, servo systems.

[!TIP] Exam Focus from Past Papers:

DC Machines: Swinburne's test (procedure, efficiency calc), armature reaction (demag/cross-mag), commutation process & improvement, starters (3-point vs 4-point drawbacks), speed control methods (esp. field flux for shunt, series-parallel for series), characteristics (sketch shunt/series/compound), braking types.

Alternators: EMF equation (with K_d, K_c), armature reaction effect at different pfs (phasor diagrams), voltage regulation methods (EMF optimistic, MMF pessimistic, Potier triangle steps), synchronization (lamp methods, load sharing with droop), two-reaction theory (d-q axis), V-curves, power-angle characteristic (salient pole stability).

Special Machines: BLDC (3-phase 3-pulse working), hysteresis motor (construction, constant torque), SRM (torque expression, characteristics), repulsion motor (working), PMDC.

Numericals: Generated EMF (DC & AC), distribution factor, commutation time, speed regulation sharing, voltage regulation (EMF/MMF/Potier), slip test for X_d, X_q, power angle calculation for salient pole.