Electrical Machine-II (EX-501) - Unit 3 Short Notes

UNIT 3: DC MACHINES

Construction & Parts

Core Parts:

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

• Poles: Includes pole core (carries field winding) and pole shoe (spreads flux, shapes field).

• Field Winding: Wound on pole core, produces main flux when excited (shunt, series, compound).

• Armature: Rotating part, consists of laminated core (reduces eddy current loss) with slots for armature winding.

• Commutator: Segmented copper cylinder, provides mechanical rectification (AC to DC).

• Brushes: Carbon/graphite, maintain contact with commutator segments, collect current.

• Bearings: Support rotating armature shaft.

Windings:

• Lap Winding: A = P (Number of parallel paths = Poles). Low voltage, high current. Used in high current machines.

• Wave Winding: A = 2 (always). High voltage, low current. Used in high voltage machines.

[!TIP] Exam Focus: Difference between lap & wave is a very frequent 7-mark question. Remember A = P vs A = 2.

EMF Equation & Calculations

Generated EMF (DC Generator):

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

Where:

• $\phi$ = Flux per pole (Wb)

• $Z$ = Total number of armature conductors

• $N$ = Speed (rpm)

• $P$ = Number of poles

• $A$ = Number of parallel paths

For DC Motor (Back EMF):

$$ E_b = \frac{\phi Z N P}{60 A} = V - I_a R_a $$

[!TIP] Common Pitfall: Use correct A based on winding type. In numericals, Z is total conductors, not coils.

Armature Reaction & Commutation

Armature Reaction: Effect of armature flux on main field flux.

• Demagnetizing AT: Component of armature AT that opposes main field flux. Reduces net flux.

• Cross-Magnetizing AT: Component at 90° to main field, distorts main field but does not reduce net flux.

• Effect on Terminal Voltage:

  • Generating (Lagging PF): Demagnetizing effect → Voltage drop.

  • Motoring (Leading PF): Can be magnetizing → Voltage rise.

Commutation: Process of current reversal in an armature coil as it passes under a brush.

• Ideal Commutation: Coil current changes linearly from +I to -I in commutation period.

• Actual Commutation: Induced e = L (di/dt) (reactance voltage) causes sparking. Current reversal is delayed.

• Improvement Methods:

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

  2. Compensating Winding: Embedded in pole faces, connected in series with armature. Neutralizes cross-magnetizing AT under pole faces.

[!TIP] Key Diagram: Always sketch distortion of main field under different loads (unity, lag, lead PF) for alternators/DC generators.

Starters

Purpose: Limit high starting current (I_start ≈ V/R_a, very large) and provide no-voltage release.

• 2-Point Starter: Simple, for shunt/series. No overload protection.

• 3-Point Starter: Has no-voltage release (NVR) via holding magnet and overload release (OLR). Drawback: If field weakens, NVR may release unexpectedly (hunting).

• 4-Point Starter: Solves 3-point drawback. NVR coil connected directly to line supply, independent of field circuit. More reliable.

[!TIP] Exam Focus: Compare 3-point vs 4-point starter drawback/advantage is a sure-shot question.

Speed Control Methods

1. Armature Resistance Control: Add R in series with armature. N ∝ (V - I_a R) / φ. Simple, inefficient (losses in R). Used for below base speed.

2. Field Flux Control: Vary shunt field current using R in field circuit. N ∝ 1/φ. Above base speed only (field weakening). Efficient.

3. Series-Parallel Control (Series Motor): For traction. Motors in series → low speed, high torque. In parallel → high speed, low torque.

4. Rheostatic (Shunt) Control: For shunt motors, similar to armature control.

[!TIP] Remember: For shunt motor, speed control above rated is only by field weakening.

Characteristics

[!TIP] Crucial: Series motor must never run at no-load (dangerous overspeed). Sketch all 3 characteristics.

Braking Methods

1. Plugging (Reverse Current): Reverse armature connections while maintaining field. Motor runs as brake, energy wasted in R_a. Stops quickly.

2. Dynamic Braking: Disconnect armature from supply, connect to external R. Motor acts as generator, energy dissipated in R. Smooth stop.

3. Regenerative Braking: Motor runs as generator, feeds energy back to supply. Requires E_b > V (possible in descending loads or over-excited synchronous). Most efficient.

Losses & Efficiency

Losses:

• Copper Losses: I_a²R_a (armature), I_sh²R_sh (field), I_se²R_se (series).

• Iron Losses: Stator core (hysteresis + eddy current) – constant.

• Mechanical Losses: Friction, windage – constant.

• Stray Losses: Unaccounted (brush friction, harmonics).

Efficiency:

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

Condition for Maximum Efficiency:

Variable losses = Constant losses.

For DC generator: I_a²R_a = Core + Friction + Stray.

For DC motor: I_a²R_a = Core + Friction + Stray + Mechanical Output? (More complex, but principle same).

[!TIP] Swinburne's Test: No-load test on shunt machine. Finds constant losses (W_0 = V I_0). Then efficiency at any load can be computed without loading the machine. Convenient & economical for large machines.

Testing Methods

• Swinburne's Test: Run machine as motor at no-load. Measure V, I_0, I_sh. Compute I_a = I_0 - I_sh, W_0 = V I_0, R_a from voltmeter-ammeter method. Then:

$$ \eta_{motor} = \frac{V I_a - I_a^2 R_a}{V I_a + W_0 - I_a^2 R_a} \quad \eta_{generator} = \frac{V I_a}{V I_a + W_0 + I_a^2 R_a} $$

**Adv:** No load needed. **Disadv:** Assumes constant losses same at load (iron loss changes slightly).

• Hopkinson's Test (Field Test): Two identical shunt machines coupled. One as generator, other as motor. Regenerative test. Both machines loaded simultaneously. Efficient, simulates loading.

UNIT 3: ALTERNATORS (SYNCHRONOUS GENERATORS)

Construction

• Salient Pole Rotor: Large diameter, short axial length. Used for low-medium speed (hydro, diesel). Poles project out. Damper winding (copper bars in pole faces) embedded to provide damping against hunting and aid starting.

• Cylindrical (Turbo) Rotor: Smooth, small diameter, long length. Used for high speed (steam turbines). Non-salient, forged steel. Damper winding in slots.

[!TIP] Why Damper Winding? Acts like squirrel-cage in induction motor → provides starting torque & damps oscillations (hunting).

EMF Equation & Winding Factors

EMF per Phase:

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

Where:

• f = frequency (Hz)

• φ = flux per pole (Wb)

• T_ph = Turns per phase

• K_w = Winding Factor = K_d * K_p

Pitch Factor (K_p): For full-pitch coil (α=180°), K_p = 1. For chorded coil (α < 180°), K_p = sin(α/2). Distribution Factor (K_d): For m slots/pole/phase, K_d = sin(mβ/2) / (m sin(β/2)), where β = 180°/(# slots per pole).

Numerical Example (Distribution Factor):

For 6 slots/pole, m = 6, β = 30°.

• All slots wound: K_d = sin(6*15°)/(6 sin15°) = sin90°/(6 sin15°) = 1/(6*0.2588) ≈ 0.644

• 4 slots/pole wound: m=4, β=30° (same slot pitch), K_d = sin(4*15°)/(4 sin15°) = sin60°/(4 sin15°) = 0.866/(4*0.2588) ≈ 0.836

Armature Reaction

• Effect on Terminal Voltage: Depends on Power Factor (PF) of load.

  • Unity PF: Armature reaction is cross-magnetizing only (distortion). E_t drop is small.

  • Lagging PF: Armature reaction is demagnetizing + cross-magnetizing. Large drop in V_t.

  • Leading PF: Armature reaction is magnetizing + cross-magnetizing. V_t may rise.

• Phasor Diagrams: Must draw for all 3 PFs showing E_t, I_a, E_o (internal generated EMF), I_a X_s drop, and resultant flux.

Voltage Regulation

Definition: % Reg = (E_o - V_t) / V_t * 100% at constant I_a, V_t, PF. E_o = no-load EMF at same excitation. Importance: Indicates voltage stability when load changes.

Methods:

1. EMF Method (Synchronous Impedance): Uses Z_s = sqrt(R_a² + X_s²). E_o = V_t + I_a Z_s (vector). Most pessimistic (gives highest regulation) because it assumes I_a X_s drop at angle φ + ψ where ψ = tan⁻¹(X_s/R_a) (max drop). Why optimistic? It overestimates voltage drop by assuming worst-case phase angle.

2. MMF (Amortisseur) Method: Assumes saturation ignored. F_R = F_φ + F_AT. More accurate but complex.

3. Potier Triangle Method: Most accurate. Separates armature reaction voltage drop (I_a X_{ar}) from impedance drop (I_a R_a + I_a X_{σ}). Uses Potier Reactance X_p (≈ leakage reactance X_σ). Draws Potier Triangle.

[!TIP] Key Point: EMF method is pessimistic (gives highest regulation) because it uses synchronous impedance Z_s which includes both leakage reactance and effect of armature reaction, and assumes maximum drop angle.

Phasor Diagrams & Equivalent Circuit

• Equivalent Circuit: E_o = V_t + I_a (R_a + jX_s)

• Salient Pole Generator Phasor Diagram (Lagging PF): Must show E_o, V_t, I_a, I_d (direct axis), I_q (quadrature axis), jI_d X_d, jI_q X_q, I_a R_a. X_d > X_q.

Parallel Operation & Load Sharing

• Condition: Same voltage, frequency, phase sequence, phase angle (synchronized).

• Load Sharing: Governed by speed regulation (droop characteristic). Machine with higher speed regulation (%) takes less load.

• Numerical: Given regulations R_A% and R_B% (from FL to NL), total load P_total.

  Load on A: P_A = P_total * [ (R_B/100) / (R_A/100 + R_B/100) ]? No! Correct: Machine with lower regulation (flatter curve) takes more load.

  Let ΔV/V = - (Reg/100) * (P/P_rated).

  For two machines: (P_A/P_A_rated) * Reg_A = (P_B/P_B_rated) * Reg_B (since ΔV same).

  For equal ratings P_rated: P_A / Reg_A = P_B / Reg_B and P_A + P_B = P_total.

[!TIP] Formula: P_A : P_B = 1/Reg_A : 1/Reg_B. Lower Reg → Higher share.

Excitation Systems

• Need for DC on Rotor: Rotating field (DC) is practical (slip rings for small current DC vs large AC on stator). Stator AC is directly connected to load. Why not AC on stator? Then rotor would need DC? No, excitation is to produce rotating magnetic field. DC on rotor + rotation → rotating field. AC on stator would produce stationary field (if single phase) or rotating but then slip rings needed for high current AC? Actually, standard: Stator = 3-phase AC output (connected to load). Rotor = DC excitation (to create rotating magnetic field that induces AC in stator). If rotor had AC, it would induce AC in rotor itself? No, but the principle is: Induced EMF in stator requires relative motion between stator winding and magnetic field. Having DC on rotor (rotating) and stationary stator winding achieves this. Having AC on stator would require rotor to have DC to induce? Actually, in an alternator, the output is taken from the stationary part (stator) for easy connection. So the field (exciting) winding must be on the rotating part (rotor). The field current must be DC to produce a constant (not rotating) magnetic field on the rotor. As rotor rotates, this constant field rotates relative to stator, inducing AC in stationary stator windings. If field was AC on rotor, it would produce a rotating magnetic field on rotor itself, which would not induce a steady AC in stator (complex, not standard).

• Types:

  1. DC Exciter: Small DC generator on same shaft.

  2. Static Excitation: Transformer + rectifier (thyristor) from stator output.

  3. Brushless Excitation: AC exciter on rotor, rotating rectifier on same shaft. No brushes/slip rings for main field.

UNIT 3: SYNCHRONOUS MACHINES (MOTORS & GENERATORS)

Two-Reaction Theory (Blondel)

For salient pole machines, reactance differs in direct (d) and quadrature (q) axes.

• X_d > X_q (due to larger pole face, more flux path in d-axis).

• Phasor Diagram (Lagging PF Load):

  • Resolve I_a into I_d (along E_o) and I_q (90° lagging E_o).

  • Voltage drops: jI_d X_d (large, in phase with E_o), jI_q X_q (smaller, quadrature).

  • E_o = V_t + I_a R_a + jI_d X_d + jI_q X_q.

Reactances

• Synchronous Reactance (X_s): X_s = X_{ar} + X_σ (armature reaction reactance + leakage reactance). For non-salient, X_d = X_q = X_s.

• Transient Reactance (X_d'): During sudden load change, damper winding & field winding effects. X_d' < X_d.

• Subtransient Reactance (X_d''): During initial cycle of fault (e.g., 3-phase short circuit). X_d'' < X_d'. Includes effect of damper winding.

• Negative Sequence Reactance (X_2): Reactance to negative sequence currents (reverse rotation). ≈ X_d'' (for solid rotor) or X_q (salient).

• Zero Sequence Reactance (X_0): Reactance to zero sequence currents (same phase). Small, depends on winding & grounding.

• Slip Test: To find X_d and X_q on salient pole.

  • Procedure: Rotor excited with low DC, stator not connected (open). Drive machine at ~5% slip (slightly below synchronous speed) using external motor. Stator voltage induced has positive & negative sequence components. Negative sequence current produces reversing rotating field relative to rotor. This field aligns with d & q axes as rotor oscillates.

  • Readings: Measure V (line) and I (line) on stator. V_max when rotor d-axis aligns with negative sequence MMF (high reluctance path? Actually: When negative sequence field is along q-axis, reluctance is low → high current? Let's derive: Negative sequence current produces reverse-rotating field. As rotor slips, this field appears to rotate slowly past rotor poles. When this field aligns with q-axis (low reluctance), X_q is effective → lower impedance → higher current I_max. When aligns with d-axis (high reluctance), X_d effective → higher impedance → lower current I_min). So:

    • I_max occurs when negative sequence field is along q-axis → X_q = V_max / (√3 I_max)

    • I_min occurs when along d-axis → X_d = V_min / (√3 I_min)

Characteristics

• V-Curves: Plot of I_a (armature current) vs I_f (field current) at constant load (P, PF). U-shaped curve. Minimum I_a at unity PF (normal excitation). Over-excited → I_a increases (lagging PF). Under-excited → I_a increases (leading PF). Used for power factor correction.

• Power-Angle (δ) Characteristics:

  • Non-Salient (Cylindrical): P = (V_t E_o / X_s) sin δ (sinusoidal).

  • Salient: P = (V_t E_o / X_d) sin δ + (V_t² / 2) (1/X_q - 1/X_d) sin 2δ.

  • Stability: δ < 90° for stable operation. At δ = 90°, dP/dδ = 0 → maximum power (pull-out). Beyond 90°, dP/dδ < 0 → unstable, loses synchronism.

• Hunting (Synchronizing): Oscillations of δ about steady-state value due to sudden load changes.

  • Cause: Prime mover governor action + electrical torque changes → δ swings.

  • Effects: Mechanical stress, voltage/current fluctuations, heating.

  • Reduction: Damper winding (provides damping torque), inertia of rotor, governor control (slow response).

Starting Methods

Why Non-Self-Starting? At standstill, δ varies rapidly, average torque is zero (sin δ average over cycle = 0). Methods:

1. Pony Motor: Small auxiliary motor brings up to near synchronous speed.

2. Damper Winding (Amortisseur): Acts as squirrel-cage → starts as induction motor. Pulls into synchronism.

3. Auxiliary Motor: Separate motor on same shaft.

4. Variable Frequency (Soft Starter): Gradually increase supply frequency to synchronous.

Synchronization

Need: To connect alternator to live bus-bars (infinite bus) without causing disturbances. Conditions:

1. Voltage magnitude: V_alt = V_bus.

2. Frequency: f_alt = f_bus.

3. Phase Sequence: Same (R-Y-B).

4. Phase Angle: δ = 0 at closing instant.

Methods:

1. Dark Lamp (One Lamp): Lamps between corresponding phases. Close when lamp dark (voltage difference zero). Not reliable for phase sequence check.

2. Bright Lamp (One Lamp): Close when lamp brightest (voltage difference max, but in-phase? Actually: Bright lamp method: lamp connected between phases. When voltages are in-phase and equal, lamp is dark? Wait: For two AC sources, lamp brightness ∝ |V1 - V2|. When in-phase and equal magnitude, V1 - V2 = 0 → dark. When 180° out, V1 - V2 = 2V → brightest. So "bright lamp" method closes when brightest? That would be 180° out! That's wrong. Correction: Standard:

   • Dark Lamp Method: Close when dark (in-phase, equal mag).

   • Bright Lamp Method: Close when brightest? Actually, "bright lamp" method uses lamp connected such that it's bright when in-phase? Let's recall: In three-lamp method, lamps connected between alt and bus phases. When all lamps dark → in-phase. When all bright → 180° out. So for two-lamp (bright lamp) method, it's designed so lamp is bright when in-phase? I think there's confusion. Standard textbooks:

     • Two Dark Lamp Method: Two lamps between alt and bus. Close when both dark (in-phase).

     • Two Bright Lamp Method: Two lamps. Close when both bright (in-phase)? Actually, in "two bright lamp" method, the lamps are connected in a way that they are bright when in-phase? Let's derive: Suppose lamp between alt R and bus R. If alt R leads bus R by small angle, lamp dim. If alt R lags, lamp dim. When in-phase, voltage difference zero? No, if both same magnitude and phase, difference zero → lamp dark. So bright means large difference. So "bright lamp" method would close when brightest would be when δ = 180° → DANGEROUS. Therefore, standard practice:

       • Dark Lamp: Close at dark (δ=0).

       • Bright Lamp: Close at brightest? Wait, I've seen "two bright lamp" method where lamps are connected in series across the two systems? Actually, common method: Three-Lamp Method. Three lamps between alt and bus (R-R, Y-Y, B-B). When all three lamps dark → in-phase, same mag, same seq. When all three brightest → 180° out. So for three-lamp, close at darkest.

       • Synchroscope: Shows relative speed & phase. Close when pointer stationary at 12 o'clock (in-phase).

   Correction based on standard RGPV teaching:

   • Three-Lamp Method: Lamps connected between corresponding phases (R-R, Y-Y, B-B). When all lamps are dark → V_alt = V_bus, f_alt = f_bus, δ=0. Close switch at this instant.

   • Why "brightest" is wrong? In some old texts, "bright lamp" method uses two lamps in a different connection? But RGPV consistently asks: "Why close at 'brightest' in three-lamp method?" This is a trick question. The correct answer is: You close at 'darkest', not 'brightest'. But the question phrasing "Why close at 'brightest'?" is incorrect. However, in past papers (May 2023), they asked: "Why, in the three bright lamp method... the switch has to be closed when the lamps are 'brightest'?" This is a common misconception. Actually, in three-lamp method, you close when darkest. The "bright lamp" method is a different (less common) method where you close when brightest? Let's check: In two-lamp bright method, lamps are connected in series between alt and bus? I think the standard safe method is "dark lamp" or "three dark lamp". The "bright lamp" method is not used because closing at 180° out-of-phase is catastrophic. So the exam question likely has a typo or expects explanation of why closing at brightest is wrong. But the exact quote from May 2023 paper: "Why, in the three bright lamp method for generator synchronization, the switch has to be closed when the lamps are 'brightest'? How does it ensure no phase difference?" This is incorrect. The correct method is three dark lamp. I will answer based on correct engineering practice: Close when darkest. But since the question says "brightest", I must address it as a common pitfall.

   Answer for Exam (if asked as in May 2023): The statement is misleading. In the standard three-lamp method, the switch is closed when the lamps are darkest, indicating zero voltage difference and zero phase difference. Closing when lamps are brightest would mean maximum voltage difference (180° phase difference), causing a severe shock and damage. The "bright lamp" method is not recommended for synchronization.

   Correct Conditions for Closing: Lamps dark → |V_alt - V_bus| = 0 → δ=0.

UNIT 3: SPECIAL MOTORS

Brushless DC Motors (BLDC)

• Construction: Rotor: Permanent magnets (PM). Stator: 3-phase concentrated windings (similar to PMSM). Electronic Commutator: Position sensors (Hall effect) + power electronics (transistors) replace brushes/commutator.

• Three-Phase Three-Pulse (Half-Wave) Operation: Each phase conducts for 120°. At any time, two phases are connected to DC supply (+ and -) via transistors, third phase open. Torque produced by interaction of stator MMF and rotor PM field.

• Torque-Angle Characteristic: Similar to synchronous motor: T ∝ sin δ. δ is angle between E (PM EMF) and V (supply). Stable for |δ| < 90°.

• Applications: Computer disk drives, fans, pumps, electric vehicles (high reliability, no brush maintenance).

Hysteresis Motors

• Construction: Rotor: Solid cylindrical core made of hard magnetic material (high coercivity, e.g., Alnico). Stator: 3-phase winding (like induction motor).

• Working Principle:

  1. Stator produces rotating magnetic field at synchronous speed n_s.

  2. Rotor material has hysteresis lag (φ_hyst). Rotor magnetization B_r lags behind stator field H.

  3. This lag creates a constant torque from zero to synchronous speed.

  4. At n = n_s, rotor locks in (synchronous) and rotates at exactly n_s with constant φ_hyst.

• Torque-Speed Characteristic: High starting torque (due to hysteresis), smooth, constant torque from start to n_s. No slip at synchronous speed.

• Applications: High-precision drives (clocks, turntables, timers), where constant speed is critical.

Repulsion Motors

• Construction: Like DC motor: Commutator, brushes (usually 2, shorted or open). Stator: 3-phase or single-phase winding. Rotor: Wound (like DC armature).

• Working: Stator AC produces rotating field. Induces EMF in rotor coils. Brushes shorted (or open) cause currents that repel the stator field (like Lenz's law). Torque direction such that rotor tries to escape the field → rotation.

• Characteristics: High starting torque (similar to series motor). Speed varies with load (not constant). Can be single-phase.

• Types: Compensated (with compensating winding), non-compensated.

Stepper Motors

• Principle: Convert digital pulses into mechanical steps. Rotor moves in discrete angular increments (θ_s = 360°/(N_r * N_s) where N_r= rotor teeth, N_s= steps/cycle).

• Types:

  1. Variable Reluctance (VR): Toothed rotor (soft iron). Stator has multiple phases. Rotor aligns with nearest stator tooth when phase excited. No PM.

  2. Permanent Magnet (PM): Rotor has PM. Stator has windings. Rotor aligns with stator field.

  3. Hybrid (HB): Combines VR & PM. Toothed rotor with PM. Highest resolution & torque.

• Applications: Printers, plotters, CNC machines, robotics (open-loop position control).

Switched Reluctance Motors (SRM)

• Construction: Both stator & rotor are salient-pole, laminated. No PM, no windings on rotor. Stator has concentrated windings (each phase on one pole pair).

• Torque Expression:

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

Where `L` = inductance, `θ` = rotor position. Torque produced when `dL/dθ > 0` (inductance increasing with `θ`).

• Operation: Phases excited sequentially. Rotor moves to position of maximum inductance (aligned with excited stator pole). Simple drive, robust.

• Characteristics: High starting torque, torque-speed curve can be controlled by current profiling. Acoustic noise & torque ripple are disadvantages.

• Advantages: Simple, rugged, low cost, wide speed range.

Permanent Magnet DC Motors (PMDC)

• Construction: Stator: Permanent magnets (instead of field windings). Rotor (Armature): Same as conventional DC motor (laminated core, windings, commutator).

• Characteristics: Linear torque-speed (N ∝ V - I_a R_a, T ∝ I_a). No field current → no field copper loss → higher efficiency. Cannot weaken field for speed control above base (unless with additional winding).

• Applications: Automobile accessories (wipers, windows), toys, small appliances, servo systems.

[!TIP] Special Motors Focus: Compare BLDC vs PMSM vs SRM. BLDC has trapezoidal back-EMF, sinusoidal PMSM has sinusoidal. SRM has no PM or rotor windings. Hysteresis motor runs at exact synchronous speed always.