Electrical Machine-II (EX-501) - Unit 4 Short Notes

UNIT 4: DC MACHINES & SYNCHRONOUS MACHINES

Based on RGPV Past Papers (Jun 2025 – Nov 2023)

I. DC MACHINES

A. Construction and Parts

Key Components:

• Yoke: Outer frame, provides mechanical support and carries magnetic flux.

• Pole core & pole shoe: laminated to reduce eddy currents; pole shoe shapes flux distribution.

• Field winding: Copper coils on pole cores, produces main flux when excited.

• Armature core: Laminated cylindrical core, holds armature windings, provides low-reluctance path.

• Armature winding: Conductors in slots, connected to commutator; EMF generated here.

• Commutator: Segmented copper cylinder, converts AC armature EMF to DC.

• Brushes & brush gear: Carbon brushes maintain contact with commutator; spring pressure ensures good contact.

• Bearings: Support rotating armature.

[!TIP]

Exam Focus: Draw and label a neat diagram of DC machine construction. Remember: laminated core to reduce eddy currents, pole shoe for flux spreading.

B. EMF Equation and Numerical Problems

Generated EMF (Generator):

$$ E_g = \frac{\phi Z N P}{60 A} $$

Where:

• $\phi$ = flux per pole (Wb)

• $Z$ = total conductors

• $N$ = speed (rpm)

• $P$ = number of poles

• $A$ = number of parallel paths ($$\displaystyle A = P $$ for lap, $$\displaystyle A = 2 $$ for wave)

For Motors (Back EMF):

$$ E_b = V - I_a R_a $$

Numerical Tips:

• Identify winding type (lap/wave) to find $A$.

• Convert all units to SI (Wb, rpm, ohms).

• For wave winding, $$\displaystyle A = 2 $$ regardless of $P$.

[!TIP]

Common Pitfall: Forgetting to convert speed to rps or flux to Wb. Always use consistent units.

C. Armature Reaction

Definition: Distortion of main field flux by armature flux.

Effects:

• Demagnetizing: Armature flux opposes main flux (under poles). Reduces net flux → voltage drop in generators, speed rise in motors.

• Cross-magnetizing: Armature flux distorts main flux axis → shifting of neutral plane.

Brush Shift from GNA:

• If brushes shifted by angle $\theta$, demagnetizing AT = $$\displaystyle 2 I_a Z \frac{\theta}{360^\circ} $$ (for simplex wave).

• Cross-magnetizing AT = $$\displaystyle 2 I_a Z \left( \frac{1}{2} - \frac{\theta}{360^\circ} \right) $$.

Remedies:

1. Interpoles (Commutating Poles): Small poles in pole shoes, winding in series with armature → provides voltage to cancel reactance voltage.

2. Compensating Windings: Embedded in pole faces, connected in series with armature → produces opposite MMF to armature reaction.

3. Brush Shifting: Shift brushes in direction of rotation for generators, opposite for motors.

[!TIP]

Exam Question: Derive demagnetizing and cross-magnetizing AT for brush shift. Use diagram showing pole faces and brush position.

D. Commutation

Process: Reversal of current in an armature coil as it passes through neutral plane.

Reactance Voltage:

$$ E_{rx} = 2\pi f L I_a $$

Where $f$ = frequency of current reversal, $L$ = inductance of coil, $$\displaystyle I_a $$ = armature current.

Commutation Period:

$$ t_c = \frac{\text{Brush width}}{\text{Commutator peripheral speed}} $$

Methods to Improve Commutation:

1. Resistance Switching: Use high-resistance carbon brushes → voltage drop limits sparking.

2. Capacitor Switching: Capacitor across commutator segments → absorbs energy.

3. Interpoles: Provide auxiliary voltage to neutralize reactance voltage.

Sparking Causes:

• Poor brush position, high armature reaction, high inductance, high speed.

Minimization: Proper brush setting, interpoles, compensating windings.

[!TIP]

Numerical: Calculate commutation time given brush width and commutator diameter/speed.

E. Starters

Need: Limit high starting current ($$\displaystyle I_{start} \approx \frac{V}{R_a} $$) to safe value.

Two-Point Starter:

• Simple: No-voltage protection only (holds switch closed when voltage present).

• Drawback: No overload protection.

Three-Point Starter:

• Construction: Three points – line (L), armature (A), field (F). No-volt release coil in series with shunt field.

• Working: Overload release opens circuit if current high; no-volt release opens if supply fails.

• Drawbacks:

  1. No proper overload protection (no-volt coil in series with shunt field – if field weak, coil may not release).

  2. Field weakening at high speeds may cause runaway.

Four-Point Starter:

• Construction: Four points – L, A, F, and separate no-volt coil across supply.

• Advantage: No-volt coil independent of field current → reliable protection even if field weak.

[!TIP]

Diagram: Sketch three-point and four-point starters. Highlight connection of no-volt release coil.

F. Speed Control Methods

Armature Control (Voltage Control):

• Vary $V$ via rheostat in armature circuit.

• Speed $$\displaystyle N \propto \frac{V - I_a R_a}{\phi} $$.

• Used for below base speed.

Field Control (Flux Control):

• Vary field current via rheostat in field circuit.

• $$\displaystyle N \propto \frac{1}{\phi} $$ (above base speed).

• Limited to no-load speed increase (flux cannot reduce beyond saturation).

Series-Parallel Control (Series Motors):

• Motors mechanically coupled, connected in series or parallel.

• Series: high torque, low speed; Parallel: low torque, high speed.

• Used in traction.

Numerical Relationship:

$$ \frac{N_2}{N_1} = \frac{V_2}{V_1} \cdot \frac{\phi_1}{\phi_2} \quad \text{(assuming constant torque)} $$

G. Characteristics

[!TIP]

Exam: Sketch all three characteristics on same graph for comparison.

H. Braking Methods

1. Rheostatic Braking:

   • Disconnect supply, connect armature to external resistor.

   • Kinetic energy dissipated in resistor.

2. Plugging (Reverse Current):

   • Reverse supply polarity while motor running.

   • High braking torque, but energy wasted in resistance.

3. Regenerative Braking:

   • Motor runs as generator, feeds back to supply.

   • Requires supply to accept power (e.g., in traction).

I. Losses and Efficiency

Losses:

• Copper losses: $$\displaystyle I_a^2 R_a $$ (armature), $$\displaystyle I_f^2 R_f $$ (field).

• Iron losses: Hysteresis ($$\displaystyle \propto f \phi^{1.6} $$) and eddy current ($$\displaystyle \propto f^2 \phi^2 $$). Reduced by laminations.

• Mechanical losses: Friction, windage.

• Stray losses: Unaccounted (e.g., harmonics).

Efficiency:

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

Maximum Efficiency Condition:

$$ \text{Variable losses} = \text{Constant losses} $$

For DC generator: $$\displaystyle I_a^2 R_a = \text{Core + Mechanical + Stray losses} $$.

Power Flow Diagram:

Input → Stray + Iron + Mechanical + Copper → Output.

[!TIP]

Numerical: Given loss data, compute efficiency at various loads.

J. Swinburne’s Test

Applicable for: DC shunt/series machines (as motor or generator).

Procedure:

1. Run machine at rated speed no-load.

2. Measure $$\displaystyle I_0 $$, $V$, $$\displaystyle I_f $$.

3. Compute:

   • Armature copper loss no-load = $$\displaystyle (I_0 - I_f)^2 R_a $$

   • Stray losses = Input no-load – (Armature Cu loss + Field Cu loss)

   • Constant losses $$\displaystyle P_c = \text{Stray} + \text{Iron} + \text{Mechanical} $$.

Efficiency at Any Load:

$$ \eta = \frac{V I_a - (I_a^2 R_a + P_c)}{V I_a} \quad \text{(as motor)} $$

$$ \eta = \frac{V I_a}{V I_a + (I_a^2 R_a + P_c)} \quad \text{(as generator)} $$

Advantages:

• Convenient, economical (no-load test only).

• Can predetermine efficiency at any load.

Condition for Maximum Efficiency:

$$ I_a^2 R_a = P_c $$

[!TIP]

Exam: Derive efficiency expressions. State why it’s suitable only for shunt machines (field current constant).

K. Special DC Motors – Permanent Magnet DC (PMDC)

Construction: Permanent magnets (ferrite/rare-earth) instead of field winding.

Features:

• No field Cu loss → higher efficiency.

• Compact, lightweight.

• Flux constant → speed inversely proportional to torque.

• No risk of field collapse.

Applications:

• Automotive (wipers, windows), small appliances, robotics.

II. SYNCHRONOUS MACHINES

A. Construction and Excitation

Salient Pole:

• Large diameter, short axial length.

• Used for low-speed (hydro, diesel).

• Poles projected, with damper winding.

Cylindrical (Non-Salient):

• Small diameter, long axial length.

• Used for high-speed (turbo-alternators).

• Smooth rotor, no damper winding usually.

Why DC Excitation on Rotor?

• Slip rings easier for rotating low-voltage DC supply.

• Stator carries high-voltage AC → easier insulation and stationary arrangement.

• Field current controllable for voltage regulation.

B. Alternator Fundamentals

EMF Equation:

$$ E = 4.44 f \phi T K_w $$

Where:

• $$\displaystyle f = \frac{P N}{120} $$ (frequency)

• $\phi$ = flux per pole (Wb)

• $T$ = total turns per phase ($$\displaystyle T = \frac{Z}{2P \cdot m} $$, $m$ = phases)

• $$\displaystyle K_w = K_p K_d $$ (winding factor)

Winding Factors:

• Pitch Factor ($$\displaystyle K_p $$): $$\displaystyle K_p = \sin\left(\frac{\gamma}{2}\right) $$, $\gamma$ = short-pitch angle.

• Distribution Factor ($$\displaystyle K_d $$):

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

$\beta$ = slot angle, $m$ = slots/pole/phase.

Numerical: Given $Z$, $P$, slots, conductors/slot, speed, flux → compute $E$.

C. Voltage Regulation

Definition:

$$ \text{Regulation} = \frac{E_0 - V}{V} \times 100\% $$

$$\displaystyle E_0 $$ = no-load EMF at same excitation, $V$ = rated terminal voltage.

Methods:

1. EMF Method (Synchronous Impedance Method):

   • Use $$\displaystyle E = \sqrt{(V \cos \phi + I_a R_a)^2 + (V \sin \phi + I_a X_s)^2} $$.

   • Optimistic? For leading PF, it gives lower regulation than actual because it neglects demagnetizing effect of armature reaction? Actually, EMF method is pessimistic for lagging PF (overestimates regulation) and optimistic for leading PF (underestimates) because it assumes constant $$\displaystyle X_s $$ and ignores saturation? Standard: EMF method gives higher regulation than actual for lagging PF due to use of saturated $$\displaystyle X_s $$? Clarify: EMF method uses $$\displaystyle X_s $$ from short-circuit test (unsaturated), but under load, saturation reduces effective $$\displaystyle X_s $$, so actual regulation less → EMF method pessimistic for lagging PF. For leading PF, armature reaction magnetizing, actual $$\displaystyle E_0 $$ higher, but EMF method may underestimate → optimistic.

2. MMF Method (Amortisseur Method):

   • Solve phasor diagram using MMFs.

   • Optimistic? Yes, assumes linear magnetic circuit (no saturation) → underestimates required field current → lower regulation.

3. Potier Triangle Method:

   • Procedure:

     a. Plot OCC (open-circuit characteristic).

     b. Plot ZPF (zero power factor) lagging characteristic.

     c. Draw Potier triangle: $$\displaystyle I_a R_a $$ drop, $$\displaystyle I_a X_{al} $$ (leakage reactance), and $$\displaystyle I_a X_{ar} $$ (armature reaction MMF).

     d. From load point, drop $$\displaystyle I_a R_a $$, then $$\displaystyle I_a X_{al} $$ horizontally, then move parallel to ZPF curve to OCC → read $$\displaystyle E_0 $$.

   • More accurate as separates leakage and armature reaction.

4. ZPF Method: Similar to Potier but uses ZPF curve directly.

Numerical: Given $V$, $$\displaystyle I_a $$, $\cos \phi$, $$\displaystyle R_a $$, $$\displaystyle X_s $$, find regulation at various PF.

D. Armature Reaction in Alternators

Effect on Terminal Voltage:

• Unity PF: Armature flux cross-magnetizing → distorts main flux, slight voltage drop due to distortion.

• Lagging PF: Armature flux demagnetizing → reduces main flux → significant voltage drop.

• Leading PF: Armature flux magnetizing → increases main flux → voltage rise (negative regulation).

Phasor Diagrams (Salient Pole):

• Show $$\displaystyle E_f $$, $V$, $$\displaystyle I_a $$, $$\displaystyle I_d $$, $$\displaystyle I_q $$, $$\displaystyle X_d $$, $$\displaystyle X_q $$.

• For lagging PF: $$\displaystyle I_a $$ lags $V$, $$\displaystyle I_d $$ demagnetizing, $$\displaystyle I_q $$ cross.

• For leading PF: $$\displaystyle I_a $$ leads, $$\displaystyle I_d $$ magnetizing.

Cross & Demagnetizing Components:

• $$\displaystyle I_d = I_a \sin(\delta + \psi) $$ (demag/mag)

• $$\displaystyle I_q = I_a \cos(\delta + \psi) $$ (cross)

E. Parallel Operation and Load Sharing

Conditions:

1. Same rated voltage.

2. Same frequency.

3. Same phase sequence.

Load Sharing:

• Governed by speed regulation (droop).

• For two alternators with regulations $$\displaystyle SR_1 $$ and $$\displaystyle SR_2 $$:

$$ \frac{\text{Load on A}}{\text{Load on B}} = \frac{SR_2}{SR_1} $$

(Assuming same rating).

Numerical: Given speed regulations from full-load to no-load (e.g., 100% to 104% means regulation = 4%), compute load sharing.

[!TIP]

Common Error: Speed regulation = (no-load speed – full-load speed)/full-load speed × 100%. For alternators, it’s voltage regulation analog.

F. Synchronization

Three-Lamp Method (Bright Lamp):

• Connect three lamps between corresponding phases of alternator and busbar.

• Close switch when lamps brightest because:

  • Lamps connected with opposite polarity? Actually, in bright lamp method, lamps are connected such that when voltages are in phase and equal, the voltage across each lamp is $$\displaystyle |V_{gen} + V_{bus}| $$ (if opposite polarity) → maximum → brightest.

  • Brightest indicates zero phase difference and equal voltage magnitudes.

Synchroscope:

• Rotating pointer shows relative speed and phase.

• Pointer stationary at 12 o’clock → in phase, same frequency.

Dark Lamp Method:

• Close when lamps dark (zero voltage difference).

Synchronizing Torque:

• When in phase, torque zero; out of phase, torque pulls into synchronism.

G. Two-Reaction Theory (Blondel’s Theory)

Direct Axis ($$\displaystyle X_d $$): Axis along rotor pole (high permeance → lower reluctance? Actually, $$\displaystyle X_d > X_q $$ due to field winding effect).
Quadrature Axis ($$\displaystyle X_q $$): Axis midway between poles (lower permeance).

Equivalent Circuit Model:

• Armature current split into $$\displaystyle I_d $$ (along $$\displaystyle X_d $$) and $$\displaystyle I_q $$ (along $$\displaystyle X_q $$).

• Voltage equation: $$\displaystyle E_f = V + I_a R_a + j(I_d X_d + I_q X_q) $$.

Phasor Diagram (Lagging PF):

• $$\displaystyle I_a $$ lags $V$.

• $$\displaystyle I_d = I_a \sin(\delta + \psi) $$ (demagnetizing)

• $$\displaystyle I_q = I_a \cos(\delta + \psi) $$

• $$\displaystyle E_f = V + I_a R_a + j I_d X_d + j I_q X_q $$.

H. Reactances

• Synchronous Reactance ($$\displaystyle X_s $$): $$\displaystyle X_s = X_l + X_{ar} $$ (leakage + armature reaction).

• Transient Reactance ($$\displaystyle X_d' $$): During sudden load change, damper winding active → $$\displaystyle X_d' < X_d $$.

• Subtransient Reactance ($$\displaystyle X_d'' $$): During fault, damper and field winding effects → $$\displaystyle X_d'' < X_d' $$.

• Negative Sequence Reactance ($$\displaystyle X_2 $$): Reactance to negative sequence currents (≈ $$\displaystyle X_d'' $$).

• Zero Sequence Reactance ($$\displaystyle X_0 $$): Reactance to zero sequence currents (small, depends on grounding).

Measurement:

• $$\displaystyle X_s $$: Short-circuit test (find $$\displaystyle I_{sc} $$ at rated $V$ → $$\displaystyle X_s = V / I_{sc} $$).

• $$\displaystyle X_d' $$, $$\displaystyle X_d'' $$: Sudden short-circuit test (from oscillograms).

I. Slip Test

Purpose: Determine $$\displaystyle X_d $$ and $$\displaystyle X_q $$ for salient-pole alternator.

Procedure:

1. Drive alternator at near synchronous speed (slip < 1%).

2. Keep field winding open.

3. Apply reduced 3-phase voltage to stator.

4. Measure stator current and voltage across field winding as rotor revolves.

Interpretation:

• Minimum stator current → d-axis aligned → $$\displaystyle X_d = \frac{V_{ph}}{I_{min}} $$ (where $$\displaystyle V_{ph} $$ = applied phase voltage).

• Maximum stator current → q-axis aligned → $$\displaystyle X_q = \frac{V_{ph}}{I_{max}} $$.

• Field voltage maximum at d-axis, minimum at q-axis.

Numerical Example (May 2024):

Given phase values: $$\displaystyle V_{max}=108V $$, $$\displaystyle V_{min}=96V $$, $$\displaystyle I_{max}=12A $$, $$\displaystyle I_{min}=10A $$.

Assuming applied voltage constant? Actually, from data, if we assume the measured voltage is the terminal voltage and it varies due to source impedance, then:
$$\displaystyle X_d = \frac{V_{max}}{I_{min}} = \frac{108}{10} = 10.8\ \Omega $$,
$$\displaystyle X_q = \frac{V_{min}}{I_{max}} = \frac{96}{12} = 8\ \Omega $$.

(If applied voltage given, use that directly.)

J. Hunting and Damper Winding

Hunting (Synchronizing Oscillations):

• Cause: Sudden load changes cause rotor to oscillate about equilibrium position.

• Effects: Mechanical stress, instability, voltage fluctuations.

Damper Winding (Amortisseur):

• Copper bars in rotor slots, short-circuited at ends.

• Acts like squirrel-cage → provides damping torque.

• Also aids in starting (as induction motor).

K. V-Curve and Power Angle

V-Curve:

• Plot of armature current $$\displaystyle I_a $$ vs field current $$\displaystyle I_f $$ at constant load.

• Shape: U-shaped. Minimum $$\displaystyle I_a $$ at unity PF.

• Significance: Shows how $$\displaystyle I_a $$ changes with excitation. Over-excited → leading PF, $$\displaystyle I_a $$ increases; under-excited → lagging PF, $$\displaystyle I_a $$ increases.

Power Angle ($\delta$):

• Angle between $$\displaystyle E_f $$ and $V$.

• Power Equation (Salient Pole):

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

• Stability: Operate at $$\displaystyle \delta < 90^\circ $$ for stable operation. If $$\displaystyle \delta > 90^\circ $$, power decreases → unstable, loss of synchronism.

L. Synchronous Motor

No Self-Starting Torque:

• Average torque zero because torque $\propto \sin \theta$, and $\theta$ changes sign every half cycle.

Starting Methods:

1. Pony Wheel: Mechanical starting by external motor.

2. Damper Winding: Rotor acts as squirrel-cage → starts as induction motor, then pull into synchronism.

3. Auxiliary Motor (Pony Motor): Separate motor brings rotor to near synchronous speed.

Over-Excited Condition:

• $$\displaystyle E_f > V $$ → motor draws leading current (supplies reactive power).

• Used for power factor correction.

Calculation of $$\displaystyle E_f $$ and $\delta$:

• Use phasor diagram: $$\displaystyle E_f = \sqrt{(V + I_a R_a \cos \phi \pm I_a X_s \sin \phi)^2 + (I_a R_a \sin \phi \mp I_a X_s \cos \phi)^2} $$.

• $$\displaystyle \delta = \tan^{-1}\left( \frac{I_a R_a \sin \phi \mp I_a X_s \cos \phi}{V + I_a R_a \cos \phi \pm I_a X_s \sin \phi} \right) $$.

M. Excitation Systems

1. DC Excitation: Brushes and slip rings with DC generator/exciter.

2. AC Excitation with Rectifiers: AC exciter + rotating diodes → DC on rotor.

3. Static Excitation: Thyristor-controlled DC from stator side via slip rings or without (brushless).

III. SPECIAL MOTORS

A. Brushless DC Motor (BLDC)

Construction:

• Stator: Three-phase winding (similar to induction motor).

• Rotor: Permanent magnets (surface-mounted or embedded).

• Electronic Commutation: Position sensors (Hall effect) + inverter.

Three-Phase Three-Pulse (Half-Wave) Operation:

• Each phase conducts for 120° electrical.

• Rotor position sensors trigger switching of transistors.

• Torque produced by interaction of stator MMF and rotor flux.

Torque-Angle Characteristic:

$$ T \propto \sin \theta $$

(similar to synchronous motor).

Applications:

• Robotics, aerospace, computer drives, appliances (fans, pumps).

[!TIP]

Diagram: Show stator windings, rotor magnets, Hall sensors, and inverter switching.

B. Hysteresis Motor

Construction:

• Stator: Three-phase winding (like induction motor).

• Rotor: Cylindrical core of hard magnetic material (e.g., Alnico) – no windings or slots.

Working Principle:

• Stator rotating field magnetizes rotor surface.

• Due to hysteresis, rotor flux lags stator flux → torque.

• Runs at synchronous speed (no slip).

Characteristics:

• High starting torque (due to hysteresis).

• Constant speed under varying load.

• Quiet operation.

Applications:

• Timers, recorders, precision drives, clocks.

C. Repulsion Motor

Construction:

• Stator: Single-phase or three-phase winding.

• Rotor: Wound like DC armature with commutator, brushes short-circuited.

Working Principle:

• Stator field induces EMF in rotor coils.

• Brushes shorted → currents produce flux that repels stator flux → torque.

• Compensated Type: Additional compensating winding in stator to improve PF.

Characteristics:

• High starting torque (up to 2.5× full-load).

• Speed varies with load (similar to series motor).

D. Reluctance Motor

Construction:

• Stator: Salient pole with single-phase or three-phase winding.

• Rotor: Salient pole (no windings), made of soft iron.

Working Principle:

• Rotor aligns with minimum reluctance position relative to stator field.

• Torque produced due to tendency to move from high to low reluctance.

Torque-Speed:

• Low starting torque, pulls into synchronism.

• Constant speed at synchronism.

Applications:

• Control systems, signaling devices, clocks.

E. Switched Reluctance Motor (SRM)

Construction:

• Stator: Salient pole with concentrated windings.

• Rotor: Salient pole, no windings or magnets.

• Simple, robust, low cost.

Torque Expression:

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

Where $L$ = inductance, $\theta$ = rotor position, $i$ = phase current.

• Torque produced when inductance increasing with $\theta$.

Characteristics:

• High starting torque.

• Torque independent of direction of current.

• Acoustic noise, torque ripple.

Applications:

• Traction, industrial drives, appliances.

F. Stepper Motor

Basic Principle: Digital pulses → angular displacement.

Types:

1. Variable Reluctance (VR): Toothed rotor, stator phases energized sequentially.

2. Permanent Magnet (PM): Rotor with permanent magnets, stator phases switched.

3. Hybrid: Combination of VR and PM → higher resolution.

Characteristics:

• Step angle: $$\displaystyle \theta_s = \frac{360^\circ}{N_r \cdot N_s} $$ (for hybrid).

• Holding torque: Torque when energized at standstill.

• Detent torque: Torque with no excitation (due to PM).

Applications:

• Printers, CNC machines, robotics, plotters.

[!TIP]

Exam: Compare VR, PM, and hybrid stepper motors.

END OF UNIT 4
Always refer to diagrams for clarity. Practice numericals from past papers.