Electrical Machine-II (EX-501) Unit 2 Notes

UNIT 2: DC & SYNCHRONOUS MACHINES – EXAM-FOCUSED SHORT NOTES

I. DC MACHINES (GENERATORS & MOTORS)

A. Fundamentals & Construction

Constructional Parts:
- Yoke: Mechanical support & flux return path (cast iron/steel).
- Poles & Pole Shoes: House field winding; pole shoes shape flux.
- Field Winding: Creates main flux (shunt, series, compound).
- Armature Core: Laminated to reduce eddy currents; holds armature winding.
- Armature Winding: Conductors where EMF is induced; Lap (more parallel paths, low V/high I) & Wave (2 parallel paths, high V/low I).
- Commutator: Segments for AC to DC conversion.
- Brushes & Brush Gear: Carbon brushes maintain contact with commutator.
EMF Equation of DC Generator:

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

Where, $P$=poles, $\phi$=flux/pole (Wb), $Z$=total conductors, $N$=speed (rpm), $A$=parallel paths.

For **Lap**: $$\displaystyle A = P $$; **Wave**: $$\displaystyle A = 2 $$.

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

B. Armature Reaction & Commutation

Armature Reaction: Effect of armature flux on main field flux.
- Demagnetizing AT: AT component opposes main field flux (under poles).
- Cross-Magnetizing AT: AT component distorts main field flux (at right angles).
- Effect on Terminal Voltage: At unity PF, net flux reduces → terminal voltage drops. At leading PF, cross-magnetizing effect may increase voltage.
Commutation: Process of current reversal in an armature coil.
- Ideal: Current changes linearly at zero coil voltage.
- Practical: Reactance Voltage $$\displaystyle e_R = 2 \pi f L_{av} I_a $$ causes delay → sparking.
Methods to Improve Commutation:
1. Interpoles/Compensating Windings: Provide local flux to induce opposite reactance voltage.
2. Brushes Shifted to MNA (for specific load PF).
3. Capacitors (for high-speed machines).
Commutation Time:

$$t_c = \frac{W_b}{v_b}$$

Where $$\displaystyle W_b $$ = brush width (m), $$\displaystyle v_b $$ = commutator peripheral speed (m/s).

C. Performance & Losses

Losses:
- Copper Losses: $$\displaystyle I_a^2 R_a $$ (armature), $$\displaystyle I_s^2 R_s $$ (series field), $$\displaystyle I_f^2 R_f $$ (shunt field).
- Iron Losses: Hysteresis + Eddy currents in core.
- Mechanical Losses: Friction, windage.
- Stray Losses: Miscellaneous (e.g., sparking).
Efficiency:

$$\eta = \frac{Output}{Input} = \frac{Output}{Output + Total Losses}$$

**Condition for Maximum Efficiency** (for generator):

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

i.e., $$\displaystyle I_a^2 R_a = W_c $$ (core + mechanical + shunt field copper).

Swinburne's Test (No-load test for shunt machines):
- Procedure: Run machine at rated speed as motor with no load. Measure $$\displaystyle I_0 $$, $V$, $$\displaystyle I_f $$.
- Determination:
  1. No-load armature copper loss = $$\displaystyle (I_0 - I_f)^2 R_a $$.
  2. Constant losses $$\displaystyle W_c = V I_0 - (I_0 - I_f)^2 R_a $$.
  3. Efficiency at any load $$\displaystyle I_a $$:

$$\eta = \frac{V I_a}{V I_a + I_a^2 R_a + W_c}$$

*   **Advantages**: Economical, convenient, separate loss determination.

*   **Limitation**: Assumes constant losses at all loads; iron losses at no-load ≠ at full-load.

D. Starting & Speed Control

Necessity of Starter: To limit high starting current ($$\displaystyle I_{start} \approx V/R_a $$).
Starters:

| Type | Working | Drawback | | :--- | :--- | :--- | | 2-Point | Series resistance in armature circuit. | No protection against field failure (speed rise). | | 3-Point | Adds hold-on coil in series with field to bypass starter resistance when field weakens. | Over-voltage issue: If field weakens, hold-on coil de-energizes → starter opens → field collapses → high voltage. | | 4-Point | Separate voltage supply for hold-on coil (from line). | Eliminates over-voltage issue; field failure doesn't open starter. |
Speed Control Methods:
1. Armature Control (Rheostatic): Vary $$\displaystyle R_a $$. Speed ∝ $$\displaystyle V - I_a R_a $$. Used for below-rated speed.
2. Field Control: Vary $$\displaystyle R_f $$. Speed ∝ $1/\phi$. Used for above-rated speed (shunt/series).
3. Series-Parallel Control (Series Motors): Motors in series (low speed, high torque) → parallel (high speed, low torque). Used in traction.
Characteristics:
- Shunt Motor: $$\displaystyle N \propto V - I_a R_a $$ (nearly constant speed).
- Series Motor: $$\displaystyle N \propto (V - I_a R_a)/I_a $$ (inverse relationship; never run without load).
- Compound Motor: Cumulative (constant speed), Differential (dangerous, used in welding).
Braking:
- Plugging: Reverse armature connections → rapid stop.
- Dynamic Braking: Disconnect supply, connect armature to external resistor → kinetic energy dissipated.
- Regenerative Braking: Motor acts as generator, feeds back to supply (requires speed > synchronous in special cases).

E. Special DC Machines

Brushless DC Motor (BLDC):
- Construction: 3-phase stator winding, permanent magnet rotor, electronic commutator (position sensors + power electronics).
- Working: Rotor magnets create field. Stator phases energized sequentially by controller based on rotor position → rotating magnetic field.
- Torque-Angle Characteristic: Trapezoidal (for 3-phase, 3-pulse).
- Applications: Aerospace, pumps, fans, EVs (high reliability, no brush maintenance).
Permanent Magnet DC (PMDC) Motor:
- Construction: Permanent magnets provide field (stator or rotor).
- Characteristics: Linear torque-speed, high starting torque, small size.
- Applications: Automotive (wipers, windows), toys, portable tools.

II. SYNCHRONOUS MACHINES (ALTERNATORS & MOTORS)

A. Alternator Fundamentals & EMF

Construction:
- Salient Pole: Large diameter, few poles (hydro-generators). Poles projected.
- Cylindrical (Non-Salient): Small diameter, many poles (turbo-alternators). Smooth rotor.
EMF Equation:

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

Where $f$=frequency, $\phi$=flux/pole, $$\displaystyle T_{ph} $$=turns/phase, $$\displaystyle K_p $$=pitch factor, $$\displaystyle K_d $$=distribution factor.

\boxed{E_{ph} = 4.44 f \phi T_{ph} K_p K_d}

Pitch Factor ($$\displaystyle K_p $$):

$$K_p = \cos \frac{\alpha}{2}$$

$\alpha$ = short-pitch angle (chording angle). Reduces harmonics.

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

$$K_d = \frac{\sin \frac{m \beta}{2}}{m \sin \frac{\beta}{2}}$$

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

\boxed{K_d = \frac{\sin \frac{m \beta}{2}}{m \sin \frac{\beta}{2}}}

*Reduces harmonics due to distributed winding.*

B. Voltage Regulation & Methods

Voltage Regulation (%):

$$\% Reg = \frac{E_0 - V}{V} \times 100\% \text{ (at constant I, cos\phi, speed)}$$

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

Methods:

| Method | Procedure | Nature | Phasor Diagram Basis | | :--- | :--- | :--- | :--- | | Synchronous Impedance (EMF) | $$\displaystyle I_a Z_s $$ drop subtracted from $V$. $$\displaystyle Z_s = \sqrt{R_a^2 + X_s^2} $$. | Optimistic (overestimates regulation) | Assumes entire $$\displaystyle I_a Z_s $$ drop is reactive. | | MMF/Ampere-turn | $$\displaystyle I_a $$ converted to AT; subtract net AT from $$\displaystyle F_f $$. | Pessimistic (underestimates regulation) | Assumes iron saturation neglected; all AT oppose $$\displaystyle F_f $$. | | Potier Triangle | Separate Potier Reactance $$\displaystyle X_p $$ (≈ leakage reactance) & Armature Reaction MMF. Uses ZPF characteristics. | Most Accurate | $$\displaystyle I_a X_p $$ drop (vertical) & $$\displaystyle I_a R_a $$ (horizontal) form triangle with $$\displaystyle I_a $$ & $$\displaystyle E_0 $$. | | ZPF/SCR | From open-circuit & zero-PF lagging characteristics. $$\displaystyle Reg = \frac{I_a R_a \cos\phi + I_a X_s \sin\phi}{V} \times 100\% $$ (approx). | Moderate | Uses $$\displaystyle X_s $$ from short-circuit test. |

C. Armature Reaction & Phasor Diagrams (Salient Pole)

Armature Reaction: Effect of stator MMF on rotor field.
- Lagging PF: Net flux weakened (demagnetizing effect dominant).
- Leading PF: Net flux increased (magnetizing effect dominant).
- Unity PF: Flux distorted (cross-magnetizing).
Phasor Diagrams (using Blondel's Two-Reaction Theory):
- Resolve $$\displaystyle I_a $$ into Direct Axis (d-axis) component $$\displaystyle I_d = I_a \sin\delta $$ (magnetizing/demagnetizing) and Quadrature Axis (q-axis) component $$\displaystyle I_q = I_a \cos\delta $$ (cross-magnetizing).
- Voltage drops: $$\displaystyle I_d X_d $$, $$\displaystyle I_q X_q $$, $$\displaystyle I_a R_a $$.
- General Phasor Equation:

$$E_0 = V + I_a R_a + j(I_d X_d + I_q X_q)$$

D. Synchronous Reactances & Sequences

Synchronous Reactances (during steady-state & disturbances):
- $$\displaystyle X_d $$ (Synchronous): Steady-state d-axis reactance (includes leakage + mutual).
- $$\displaystyle X_d' $$ (Transient): During sudden load change (field flux linkage constant). < $$\displaystyle X_d $$.
- $$\displaystyle X_d'' $$ (Subtransient): During sudden short-circuit (damper winding active). < $$\displaystyle X_d' $$.
Sequence Reactances:
- Negative Sequence ($$\displaystyle X_2 $$): Opposes reverse rotation field. Measured by slip test or single-phase to 3-phase conversion.
- Zero Sequence ($$\displaystyle X_0 $$): Paths for zero-sequence currents. Very high (≈ $$\displaystyle X_d $$ or $$\displaystyle X_q $$) due to 3rd harmonic paths.
Slip Test (to find $$\displaystyle X_d $$ & $$\displaystyle X_q $$):
- Procedure: Rotor unexcited, stator fed with reduced 3-phase voltage. Measure $V$ (across two terminals) & $I$ (line current) while slowly driving rotor at near-synchronous speed.
- Results: $$\displaystyle V_{max} $$ & $$\displaystyle I_{min} $$ occur when salient pole axis (d-axis) aligns with rotating field → gives $$\displaystyle X_d = V_{max}/I_{min} $$. $$\displaystyle V_{min} $$ & $$\displaystyle I_{max} $$ when quadrature axis (q-axis) aligns → gives $$\displaystyle X_q = V_{min}/I_{max} $$.

E. Synchronous Motor Operation & Characteristics

Non-Self-Starting: Average torque zero at standstill (rotor inertia prevents instant alignment with rotating field).
Starting Methods:
1. Damper Winding (Amortisseur): Short-circuited bars in rotor poles → acts as squirrel cage → starts as induction motor. Excited at near-sync speed.
2. Auxiliary Motor (Pony Motor): Brings rotor to near-sync speed.
3. Asynchronous Starting: Most common (using damper winding).
V-Curves:
- Plot of Armature Current ($$\displaystyle I_a $$) vs. Field Current ($$\displaystyle I_f $$) at constant input (or constant load angle).
- Shape: U-shaped curve. Minimum $$\displaystyle I_a $$ at unity PF.
- Significance: Shows effect of excitation on PF & $$\displaystyle I_a $$. Over-excited → leading PF; Under-excited → lagging PF.
Power-Angle (P-δ) Characteristic:
- Non-Salient (Cylindrical):

$$P = \frac{V E_0}{X_s} \sin\delta$$

*   **Salient Pole**:

$$P = \frac{V E_0}{X_d} \sin\delta + \frac{V^2}{2} \left( \frac{1}{X_q} - \frac{1}{X_d} \right) \sin 2\delta$$

*   **Stability Limit**: $$\displaystyle \delta < 90^\circ $$ for stable operation. Beyond $$\displaystyle 90^\circ $$, power decreases → unstable.

Over-Excitation: $$\displaystyle E_0 > V $$ → motor draws leading PF current (supplies vars to grid).

F. Synchronization & Parallel Operation

Conditions for Synchronization:
1. Voltage magnitude equal.
2. Frequency equal.
3. Phase sequence same.
4. Phase of voltage identical (no phase difference).
Three-Lamp (Bright-Dark) Method:
- Connect three lamps (or two bright, one dark) between alternator & busbar phases.
- Switch closed when lamps are DARKEST (or BRIGHTEST for synchroscope) → ensures zero phase difference.
- Why Darkest?: Lamps dim when voltages are in phase & equal magnitude (phasor difference zero).
Load Sharing:
- Governed by Speed Regulation (Droop) characteristic.
- kW Sharing Formula:

$$\frac{P_1}{P_2} = \frac{\text{Reg}_2}{\text{Reg}_1}$$

    Where $$\displaystyle \text{Reg} = \frac{\text{No-load speed} - \text{Full-load speed}}{\text{Full-load speed}} \times 100\% $$.

*   **Example**: Alternator A (Reg 100-104%), B (100-105%). Load 1000 kW.

$$P_A : P_B = 5 : 4 \Rightarrow P_A = \frac{5}{9} \times 1000 = 555.6 \text{ kW}, P_B = 444.4 \text{ kW}$$

G. Hunting & Damper Winding

Hunting: Oscillation of rotor about equilibrium position due to sudden load/frequency changes.
Causes: Inertia of rotor, elastic coupling, load fluctuations.
Effects: Increased losses, heating, mechanical stress.
Reduction Methods:
1. Damper Winding: Provides damping torque (like squirrel cage) to suppress oscillations.
2. Electrical Damping: Use of power system stabilizers.
3. Increase Rotor Inertia.

H. Special Synchronous & Reluctance Motors

Hysteresis Motor:
- Construction: Smooth cylindrical rotor (hard magnetic material like Alnico), no winding.
- Working: Rotating stator field magnetizes rotor; hysteresis lag creates torque. Runs at synchronous speed.
- Characteristics: Perfectly smooth, quiet, high starting torque, constant speed.
- Applications: Clocks, recorders, timers.
Reluctance Motor (Switched Reluctance Motor - SRM):
- Construction: Salient poles on both stator & rotor; no windings/PM on rotor.
- Working: Torque produced by ** tendency to align minimum reluctance path**. Stator phases energized sequentially.
- Torque Expression (conceptual):

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

    Where $L(\theta)$ = phase inductance variation with rotor position $\theta$.

*   **Characteristics**: High starting torque, robust, simple rotor.

*   **Applications**: Traction, industrial drives.

Repulsion Motor:
- Construction: Like DC motor; commutator & brushes shorted (or open).
- Working: Stator field induces EMF in rotor; repulsion between like poles creates torque.
- Characteristics: High starting torque, poor speed regulation.
- Applications: High-torque starts (e.g., printing presses).

I. Excitation Systems

Why Rotor Excitation (DC) instead of Stator (AC)?
1. Rotating Field: Easier to supply DC to rotating part via slip-rings than AC to stationary part for high-speed machines.
2. High Voltage Insulation: Stator deals with high terminal voltage; rotor only with low DC voltage.
3. Simpler Construction: Stationary armature (stator) can be directly connected to load.
Types:
- Separate DC Exciter (old).
- Static Excitation: Transformer + rectifier on stator terminals.
- Brushless Excitation: Small AC exciter on same shaft → rotating rectifier → DC to main rotor (no brushes).

III. HIGH-PRIORITY TOPICS – QUICK RECAP

Swinburne's Test: No-load test → find constant losses → predict efficiency at any load.
Armature Reaction: Demagnetizing (weakening flux) vs. Cross-magnetizing (distorting flux). Effects on terminal voltage vary with PF.
Commutation: Reactance voltage $$\displaystyle e_R = 2\pi f L_{av} I_a $$. Improved by interpoles (best method).
Starters: 4-point > 3-point (solves over-voltage) > 2-point (no field failure protection).
Speed Control: Armature control (below base), Field control (above base), Series-parallel (series motors).
Voltage Regulation:
- EMF Method: Optimistic → $$\displaystyle E_0 = V + I_a Z_s $$.
- MMF Method: Pessimistic → subtract ATs.
- Potier Method: Most accurate → uses Potier reactance $$\displaystyle X_p $$ & ZPF characteristics.
Blondel's Two-Reaction Theory: Resolve $$\displaystyle I_a $$ into $$\displaystyle I_d $$ (d-axis, affects $$\displaystyle X_d $$) & $$\displaystyle I_q $$ (q-axis, affects $$\displaystyle X_q $$).
V-Curves: $$\displaystyle I_a $$ vs $$\displaystyle I_f $$ at constant load. Minimum $$\displaystyle I_a $$ at unity PF.
Synchronization: Three-lamp method → close switch at darkest (zero phase difference).
Load Sharing: Inversely proportional to speed regulation (droop).
Slip Test: $$\displaystyle X_d = V_{max}/I_{min} $$ (d-axis aligned), $$\displaystyle X_q = V_{min}/I_{max} $$ (q-axis aligned).
Hunting: Suppressed by damper winding.
Special Motors:
- BLDC: Electronic commutation, PM rotor, trapezoidal torque.
- Hysteresis: Smooth rotor, hysteresis torque, synchronous speed.
- SRM: Salient poles, no rotor winding, $$\displaystyle T \propto i^2 dL/d\theta $$.
- Repulsion: Brushes shorted, repulsion torque.

Exam Tips:

Always draw phasor diagrams for alternator regulation & armature reaction questions.

In regulation problems, clearly state method used & its assumptions (e.g., EMF method assumes $$\displaystyle I_a Z_s $$ drop entirely reactive).

For starters, sketch is mandatory; explain hold-on coil function.

For speed control, specify which method for above/below base speed.

In load sharing, convert % regulation to decimal (e.g., 104% = 1.04) before using formula.

Distinguish between $$\displaystyle X_d $$, $$\displaystyle X_d' $$, $$\displaystyle X_d'' $$ and their significance during steady-state, transient, subtransient conditions.

Account

Electrical Machine-II (EX-501) - Unit 2 Short Notes