Electrical Machine-I (EX-402) - Unit 3 Short Notes

UNIT 3: TRANSFORMERS & THREE-PHASE INDUCTION MOTORS

A. TRANSFORMERS

1. Constructional Features & Basic Principles

• Core Types:

  • Core-type: Windings surround the core limbs. Easier insulation, better cooling. Used for high voltage.

  • Shell-type: Core surrounds the windings. Shorter magnetic path, stronger mechanically. Used for low voltage/high current.

• Winding Arrangements: Cylindrical (most common), Helical (for high current), Cross-auto (for high voltage), Disc (for high current).

• Cooling Methods: Designated by codes: ONAN (Oil Natural Air Natural), ONAF (Oil Natural Air Forced), OFAF (Oil Forced Air Forced), OFWF (Oil Forced Water Forced).

• Principle: Mutual induction. Alternating flux in core links both windings.

• EMF Equation (Single-phase):

$$E_1 = 4.44 f N_1 \Phi_m \quad \text{and} \quad E_2 = 4.44 f N_2 \Phi_m$$

$$\frac{E_1}{N_1} = \frac{E_2}{N_2} = 4.44 f \Phi_m$$

Where $f$ = frequency, $N$ = turns, $$\displaystyle \Phi_m $$ = max flux.

• Ideal vs. Practical:

  • Ideal: No losses, $$\displaystyle \mu = \infty $$, $$\displaystyle R = 0 $$, $100\%$ efficiency, $$\displaystyle V_1/I_1 = V_2/I_2 $$.

  • Practical: Has core loss (hysteresis + eddy), copper loss ($$\displaystyle I^2R $$), leakage flux, winding resistance & leakage reactance, magnetizing current.

2. Transformer Tests & Equivalent Circuit

• Open Circuit (OC) / No-load Test:

  • Purpose: Determine core loss ($$\displaystyle W_0 $$), magnetizing current ($$\displaystyle I_m $$), and active component ($$\displaystyle I_c $$). Done on LV side with HV open.

  • Circuit:

    DiagramSEARCH: transformer open circuit test diagram

  • Calculations: $$\displaystyle I_0 = \sqrt{I_c^2 + I_m^2} $$, $$\displaystyle I_c = \frac{W_0}{V_1} $$, $$\displaystyle I_m = \sqrt{I_0^2 - I_c^2} $$.

• Short Circuit (SC) / Blocked-rotor Test:

  • Purpose: Determine equivalent resistance ($$\displaystyle R_{eq} $$) and leakage reactance ($$\displaystyle X_{eq} $$). Done at rated current, usually on HV side with LV shorted.

  • Circuit:

    DiagramSEARCH: transformer short circuit test diagram

  • Calculations: $$\displaystyle V_{sc} = I_{sc}(R_{eq} \cos\phi_{sc} + j X_{eq} \sin\phi_{sc}) $$. $$\displaystyle R_{eq} = \frac{W_{sc}}{I_{sc}^2} $$, $$\displaystyle Z_{eq} = \frac{V_{sc}}{I_{sc}} $$, $$\displaystyle X_{eq} = \sqrt{Z_{eq}^2 - R_{eq}^2} $$.

• Equivalent Circuit Parameters (Referred to LV side):

  • $$\displaystyle R_1' = R_1 + \frac{R_2}{k^2} $$, $$\displaystyle X_1' = X_1 + \frac{X_2}{k^2} $$ (where $$\displaystyle k = \frac{N_2}{N_1} $$).

  • $$\displaystyle R_c = \frac{V_1^2}{W_0} $$ (Core loss resistance).

  • $$\displaystyle X_m = \frac{V_1}{I_m} $$ (Magnetizing reactance).

• Sumpner's Test (Back-to-Back):

  • Purpose: Determine efficiency and temperature rise under actual loading conditions.

  • Procedure: Two identical transformers connected back-to-back. One supplies losses of both. Input power = total losses (core + copper of both).

    DiagramSEARCH: sumpner test transformer diagram

3. Losses, Efficiency & Voltage Regulation

• Core Losses ($$\displaystyle P_{core} $$):

  • Hysteresis loss ($$\displaystyle W_h \propto f B_m^{1.6} $$): Due to reversal of magnetization.

  • Eddy current loss ($$\displaystyle W_e \propto f^2 B_m^2 $$): Circulating currents in core.

  • Dependence: $$\displaystyle P_{core} \propto V^{1.6} f^{0.4} $$ (approx) if $V/f$ constant. If $V/f$ changes, $$\displaystyle \Phi_m $$ changes, affecting both losses non-linearly.

• Copper Losses ($$\displaystyle P_{cu} $$): $$\displaystyle I^2R $$ loss, varies with load squared ($$\displaystyle P_{cu} = P_{cu,fl} \times \text{load fraction}^2 $$).

• Efficiency ($\eta$):

$$\eta = \frac{\text{Output Power}}{\text{Input Power}} = \frac{V_2 I_2 \cos\phi_2}{V_2 I_2 \cos\phi_2 + P_{core} + P_{cu}}$$

*   **Condition for Max Efficiency:** $$\displaystyle P_{core} = P_{cu} $$ (i.e., variable loss = constant loss).

*   **Load for Max Efficiency:** $$\displaystyle \text{Load fraction} = \sqrt{\frac{P_{core}}{P_{cu,fl}}} $$.

*   **All-day Efficiency:** $$\displaystyle \eta_{ad} = \frac{\text{Energy output in 24h}}{\text{Energy input in 24h}} $$ (important for distribution transformers with varying load).

• Voltage Regulation (VR):

  • Definition: $$\displaystyle \text{VR} = \frac{V_{nl} - V_{fl}}{V_{fl}} \times 100\% $$ (at constant $$\displaystyle V_1 $$, same PF).

  • Phasor Diagram Derivation (Approx.):

$$VR \approx \frac{I(R \cos\phi \pm X \sin\phi)}{V_{fl}} \times 100\%$$

    (+ for lagging PF, - for leading PF).

*   **Condition for Zero Regulation:** $$\displaystyle R \cos\phi = -X \sin\phi $$ or $$\displaystyle \tan\phi = -\frac{R}{X} $$ (leading PF).

*   **Condition for Max Regulation:** $$\displaystyle \tan\phi = \frac{X}{R} $$ (lagging PF).

4. Auto-Transformer

• Construction: Single continuous winding with a tap. Common winding + series winding.

• Comparison with Two-winding:

  • Advantages: Smaller size/weight for same rating, higher efficiency, better voltage regulation, lower cost for $k \approx 1$.

  • Disadvantages: No electrical isolation, higher short-circuit current, more complex protection.

• Copper Saving: For same output, weight of auto-transformer $$\displaystyle \propto (1 - \frac{1}{k}) $$ times two-winding transformer.

• Applications: DOL starters for motors, voltage regulators, booster transformers, laboratory supplies.

5. Parallel Operation of Transformers

• Necessary Conditions:

  1. Same voltage ratio & polarity.

  2. Same phase sequence (3-φ).

  3. Percentage impedances ($$\displaystyle Z_{pu} $$) should be equal for equal load sharing. If unequal, load shared inversely proportional to ratings if $$\displaystyle Z_{pu} $$ are equal.

• Circulating Currents: Caused by unequal voltage ratios or impedances at no-load. No circulating current at no-load only if $$\displaystyle V_1/V_2 $$ ratios are identical.

• Load Sharing Calculation (Unequal Transformers): Load shared $$\displaystyle \propto \frac{\text{Rating}}{Z_{pu}} $$.

  DiagramCANVAS: Phasor diagram showing load sharing with different impedances

• 3-φ with Unequal Voltage Ratios: Causes circulating currents even at no-load, leading to unbalanced loading and overheating.

6. Special Connections & Applications

• Scott Connection (T-T): Converts 3-φ to 2-φ.

  • Main Transformer: Center-tapped on primary (connects to line AB). Secondary gives 90° shifted voltage.

  • Teaser Transformer: Primary connected between main's center-tap and line C. Primary turns = 86.6% of main's.

  • Proof: $$\displaystyle V_{AN} = V_{MT} \angle 0^\circ $$, $$\displaystyle V_{CN} = V_{TT} \angle 90^\circ $$. For balanced 3-φ, $$\displaystyle V_{CN} = \frac{1}{2} V_{AB} \angle 90^\circ $$ → $$\displaystyle V_{TT} = \frac{\sqrt{3}}{2} V_{AB} $$. Hence, $$\displaystyle N_{TT} = \frac{\sqrt{3}}{2} N_{MT} $$.

  • Neutral Point Division: $$\displaystyle N_{AN} : N_{NB} = 1:1 $$, so $$\displaystyle N_{AN} = N_{NB} = \frac{1}{2} N_{MT} $$.

• 3-φ Transformer Connections: Y-Y, Y-Δ, Δ-Y, Δ-Δ. Key for phase shift & harmonic suppression.

• Δ-Δ Bank with One Out: Remaining two form open-δ (V-V) connection. Each carries $$\displaystyle \frac{1}{\sqrt{3}} $$ (≈57.7%) of original 3-φ load. Total bank rating reduces to 57.7% of original.

7. Components & Auxiliaries

• Conservator & Breather:

  • Conservator: Sealed drum above main tank. Accommodates oil expansion/contraction. Reduces oil-air contact.

  • Breather: Contains silica gel (blue when dry, pink when wet). Allows air exchange during oil volume change, filters moisture & dust. Placed on conservator because air here is dry after passing through oil in conservator, protecting main tank oil.

• Tap Changer:

  • Off-load (OLTC): For no-load tap changing. Simple, used for distribution.

  • On-load (OLTC): For on-load voltage regulation. Uses resistive or reactive transition circuits to prevent arcing.

    DiagramSEARCH: on load tap changer diagram

• Buchholz Relay: Gas-actuated relay in pipe between tank & conservator. Detects minor faults (gas accumulation) and major faults (oil surge). Protects against internal faults.

• Radiators & Cooling Fans: Increase surface area for heat dissipation. Fans provide forced air (ONAF/OFAF).

8. Special Types of Transformers

• Power Transformer: >200 MVA, 400+ kV, high efficiency, used in transmission. Large size, oil-filled.

• Distribution Transformer: <200 kVA, <33 kV, lower efficiency, used in distribution. Smaller, often dry-type/cast resin.

• Pulse Transformer: For digital/pulse circuits. Fast response, low leakage, high isolation.

• High-Frequency Transformer: For SMPS. Ferrite core, high operating frequency (kHz), small size.

• Potential Transformer (PT/VT): Steps down high voltage for metering/protection. High accuracy, low VA rating.

• Current Transformer (CT): Steps down high current. Secondary must never be open (dangerous high voltage). Low VA, high accuracy.

• Welding Transformer: High current, low voltage, steeply drooping V-I characteristic.

• Furnace Transformer: For arc furnaces, high current, low voltage, robust construction.

B. THREE-PHASE INDUCTION MOTOR

1. Construction & Principle of Operation

• Stator: Laminated core, 3-phase distributed winding. Produces Rotating Magnetic Field (RMF).

• Rotor Types:

  • Squirrel Cage: Simple, rugged, cheap. Aluminium/copper bars short-circuited by end rings.

  • Slip Ring (Wound): 3-phase star-connected winding, slip rings, external resistance can be added.

• RMF Production: 3 balanced sinusoidal currents in 120° spatially displaced windings produce a constant magnitude RMF rotating at synchronous speed:

$$N_s = \frac{120f}{P} \text{ rpm}$$

Where $f$ = supply frequency, $P$ = number of poles.

• Slip ($s$):

$$s = \frac{N_s - N_r}{N_s}$$

Where $$\displaystyle N_r $$ = rotor speed. **$$\displaystyle s=1 $$ at standstill, $$\displaystyle s=0 $$ at synchronous speed.**

• Rotor EMF & Frequency:

  $$\displaystyle E_r = s E_{r0} $$ (standstill rotor EMF), $$\displaystyle f_r = s f $$.

2. Equivalent Circuit & Power Flow

• Exact Equivalent Circuit (Referred to Stator):

  DiagramSEARCH: induction motor exact equivalent circuit

  • $$\displaystyle R_1 $$, $$\displaystyle X_1 $$: Stator resistance & leakage reactance.

  • $$\displaystyle R_c $$, $$\displaystyle X_m $$: Core loss & magnetizing branch (referred to stator).

  • $$\displaystyle R_2' $$, $$\displaystyle X_2' $$: Rotator resistance & leakage reactance referred to stator.

  • $$\displaystyle R_2'(1-s)/s $$: Load component representing mechanical power developed.

• Thevenin's Equivalent: $$\displaystyle V_{th} = \frac{jX_m}{R_1 + j(X_1+X_m)} V_1 $$, $$\displaystyle Z_{th} = R_{th} + jX_{th} $$.

• Power Flow:

  • Rotor Input ($$\displaystyle P_2 $$): Power transferred across air-gap.

  • Rotor Cu Loss ($$\displaystyle P_{cu2} $$): $$\displaystyle s P_2 $$.

  • Mechanical Power Developed ($$\displaystyle P_m $$): $$\displaystyle (1-s)P_2 $$.

  • Rotor Output ($$\displaystyle P_{out} $$): $$\displaystyle P_m - \text{Friction \& Windage losses} $$.

  • Key Relation:

$$P_2 = \frac{P_{cu2}}{s} = \frac{P_m}{1-s}$$

3. Torque-Slip Characteristics

• Torque Equation:

$$T = \frac{k s E_r^2 R_r / s}{R_r^2 + (s X_r)^2} = \frac{k E_r^2 R_r / s}{R_r^2 + (s X_r)^2}$$

Where $k$ = constant, $$\displaystyle E_r $$ = rotor EMF per phase at standstill.

• Condition for Max Torque:

$$\frac{dT}{ds} = 0 \Rightarrow s_m = \frac{R_r}{X_r}$$

**Max Torque ($$\displaystyle T_m $$):**

$$T_m = \frac{k E_r^2}{2 X_r}$$

*   $$\displaystyle T_m $$ **independent of $$\displaystyle R_r $$** (but $$\displaystyle s_m $$ depends on $$\displaystyle R_r $$).

• Torque-Slip Curve:

  • Stable Region: $$\displaystyle 0 < s < s_m $$ (slip increases with torque).

  • Unstable Region: $$\displaystyle s_m < s < 1 $$ (slip decreases with torque increase).

  • Starting Torque ($$\displaystyle T_{st} $$): At $$\displaystyle s=1 $$, $$\displaystyle T_{st} = \frac{k E_r^2 R_r}{R_r^2 + X_r^2} $$.

  • Full-load Torque ($$\displaystyle T_{fl} $$): At normal operating slip ($$\displaystyle s_{fl} \approx 2-5\% $$).

• Effect of Rotor Resistance: Increases $$\displaystyle T_{st} $$ and $$\displaystyle s_m $$, but $$\displaystyle T_m $$ unchanged. Used in slip-ring motors for starting.

• Effect of Leakage Reactance: Higher $$\displaystyle X_r $$ reduces $$\displaystyle T_{st} $$ and $$\displaystyle T_m $$.

4. Starting Methods

• Direct-on-Line (DOL): Full voltage applied. High $$\displaystyle I_{st} $$ (5-8×$$\displaystyle I_{fl} $$), high $$\displaystyle T_{st} $$. Used for small motors (<5 kW).

• Star-Delta (Y-Δ): Reduced voltage ($1/\sqrt{3}$) during start. $$\displaystyle I_{st} = 1/3 $$ DOL, $$\displaystyle T_{st} = 1/3 $$ DOL. Used for delta-connected motors >5 kW.

• Auto-transformer Starter: Reduced voltage (e.g., 50%, 65%, 80%). $$\displaystyle I_{st} \propto V^2 $$, $$\displaystyle T_{st} \propto V^2 $$.

• Rotor Resistance Starting (Slip Ring): External resistors in rotor circuit. Increases $$\displaystyle T_{st} $$, reduces $$\displaystyle I_{st} $$, smooth acceleration. Resistors cut out as motor speeds up.

• Stator Resistance/Reactance Starting: Series impedance in stator. Simple but high losses, rarely used.

5. Speed Control Methods

• From Stator Side:

  • Voltage Control: $$\displaystyle T \propto V^2 $$. Poor regulation, limited use.

  • Frequency Control (V/f Control): Maintain $V/f$ constant for constant flux. Wide speed range, used in drives.

  • Pole Changing: Multiple stator windings or consequent-pole winding. Speed steps ($$\displaystyle N_s \propto 1/P $$).

  • Stator Winding Change (Δ-YY): For double-delta or double-star wound motors.

• From Rotor Side (Slip Ring Only):

  • Rotor Resistance Control: Increase rotor resistance → speed decreases (for constant load). Slip power loss in resistor → inefficient.

  • Cascading (Concatenation): Motor 1's rotor connected to motor 2's stator. Speeds: $$\displaystyle N_{c1} = N_{s1}(1-s_1 s_2) $$, $$\displaystyle N_{c2} = N_{s2}(1-s_1 s_2) $$. For identical motors, $$\displaystyle N_c = N_s(1-s^2) $$.

  • Injecting EMF into Rotor (Kramer, Scherbius): For slip power recovery. Used in large pumps/fans.

6. Performance Analysis & Tests

• No-load Test: $$\displaystyle I_0 $$, $$\displaystyle W_0 $$, $$\displaystyle V_1 $$. Determines $$\displaystyle R_c $$, $$\displaystyle X_m $$, core loss, friction & windage loss.

• Blocked-rotor Test: $$\displaystyle V_{sc} $$, $$\displaystyle I_{sc} $$, $$\displaystyle W_{sc} $$. Determines $$\displaystyle R_{eq} $$, $$\displaystyle X_{eq} $$ (referred to test side). $$\displaystyle R_1 $$, $$\displaystyle R_2' $$ separation from ratio of stator/rotor copper losses (often assumed equal).

• Circle Diagram:

  • Drawn from OC & SC test data on no-load line & short-circuit line.

  • Construction:

    DiagramSEARCH: induction motor circle diagram construction

  • Determination from Diagram: Full-load current & PF, max torque, starting torque, efficiency, slip at any load.

• Losses: Stator Cu loss, Rotor Cu loss, Core loss, Friction & windage loss.

• Efficiency: $$\displaystyle \eta = \frac{\text{Output}}{\text{Input}} = \frac{P_{out}}{P_{in}} = \frac{P_{in} - \text{Total losses}}{P_{in}} $$.

7. Phenomena & Abnormal Operation

• Crawling: Motor runs at ~1/7 $$\displaystyle N_s $$ due to 7th harmonic RMF. $$\displaystyle N_{s7} = N_s / 7 $$. Avoid by proper stator winding design.

• Cogging (Magnetic Locking): Rotor fails to start due to equal number of stator & rotor slots (lowest common multiple). Reluctance torque locks rotor. Avoid by using fractional slot winding.

• Double Cage & Deep Bar Rotor:

  • Double Cage: Outer cage (high $R$, low $L$) for high $$\displaystyle T_{st} $$; inner cage (low $R$, high $L$) for normal running. Higher $$\displaystyle T_{st} $$, lower $$\displaystyle s_m $$ than squirrel cage.

  • Deep Bar: Skin effect increases effective $R$ at start ($$\displaystyle f_r $$ high), decreases at run ($$\displaystyle f_r $$ low). Similar effect to double cage.

• Harmonics Impact: Additional core & copper losses, torque pulsations, cogging/crawling.

• Braking Methods:

  • Plugging: Reverse any two supply phases. $T$ opposes motion. High $$\displaystyle I_{st} $$, used for quick stop.

  • Dynamic Braking: Disconnect supply, connect stator to resistor. Rotor RMF induces current, producing braking $T$.

  • Regenerative Braking: $$\displaystyle N_r > N_s $$ (e.g., downhill). $$\displaystyle s < 0 $$, power fed back to supply.

8. Single-Phase Induction Motors

• Not Self-starting: Double revolving field theory. At start, two equal & opposite RMFs → net torque zero. Needs auxiliary means.

• Construction: Main winding + Auxiliary winding (with capacitor/resistor) spatially displaced (~90° electrical).

• Types & Applications:

  • Split-phase (Resistance Start): Auxiliary winding high $R/X$. Moderate $$\displaystyle T_{st} $$. Fans, small pumps.

  • Capacitor Start: Capacitor in series with auxiliary. High $$\displaystyle T_{st} $$, high PF. Compressors, pumps.

  • Capacitor Start-Capacitor Run: Two capacitors (start & run). Best PF & efficiency. HVAC, compressors.

  • Shaded-pole: Shaded pole creates delayed flux → small RMF. Very low $$\displaystyle T_{st} $$, low efficiency. Small fans, clocks.

  • AC Series (Universal): Series field & armature. High speed, high $$\displaystyle T_{st} $$. Portable tools, vacuum cleaners.

• Equivalent Circuit (Double Revolving Field): Forward & reverse field components. Net torque = difference.

• Starting Torque: $$\displaystyle T_{st} \propto \sin\delta $$, where $\delta$ = phase angle between main & auxiliary winding currents.

9. Special Motors & Applications

• Linear Induction Motor (LIM):

  • Construction: Flat primary (stator equivalent), reaction plate (aluminium/copper sheet on iron) as secondary.

    DiagramSEARCH: linear induction motor construction

  • Working: Travelling magnetic field from primary induces currents in reaction plate → Lorentz force → linear motion. Slip defined as $$\displaystyle s = \frac{v_s - v}{v_s} $$.

  • Applications: Maglev trains, conveyors, actuators, pumps, sliding doors.

• Stepper Motor: Digital-to-motion. Rotates in discrete steps. Open-loop control. Used in printers, CNC.

• Servo Motor: AC/DC motor with feedback (resolver/encoder). High precision speed/position control. Used in robotics, CNC, radar.

C. COMPARATIVE & MISCELLANEOUS TOPICS

1. Transformer vs. Induction Motor Topics

2. Problem-Solving Focus Areas

• Loss Calculation with Changed V & f:

  $$\displaystyle P_h \propto f B_m^{1.6} $$, $$\displaystyle P_e \propto f^2 B_m^2 $$. If $V/f$ constant, $$\displaystyle B_m $$ constant → $$\displaystyle P_h \propto f $$, $$\displaystyle P_e \propto f^2 $$.

• Efficiency at Various Loads/PFs:

  $$\displaystyle \eta = \frac{x \cdot S \cdot \cos\phi}{x \cdot S \cdot \cos\phi + P_{core} + x^2 P_{cu,fl}} $$, where $x$ = per unit load.

• Voltage Regulation: Use approximate formula $$\displaystyle VR \approx \frac{I(R \cos\phi \pm X \sin\phi)}{V_{fl}} \times 100\% $$. Sign (+ lag, - lead).

• Load Sharing in Parallel Transformers:

  $$\displaystyle I_A = \frac{S_{total} \cdot (Z_{pu,B})}{Z_{pu,A} + Z_{pu,B}} \cdot \frac{\text{Rating}_A}{\text{Total Rating}} $$ (if impedances in % on own ratings).

• Scott Connection Line Currents:

  $$\displaystyle I_A = I_{main} $$, $$\displaystyle I_B = I_{teaser} $$, $$\displaystyle I_C = \sqrt{I_A^2 + I_B^2} $$ (for balanced 2-φ loads).

• Torque, Slip, Speed in IM:

  $$\displaystyle s = \frac{N_s - N_r}{N_s} $$, $$\displaystyle T \propto \frac{s R_r}{R_r^2 + (s X_r)^2} $$.

• Circle Diagram: Plot from $$\displaystyle I_0 $$ (no-load) and $$\displaystyle I_{sc} $$ (blocked rotor) points. Diameter = $$\displaystyle V_1 / |Z_{eq}| $$.

3. Short Notes & Descriptive Topics (High Frequency)

• Tap Changer: Device to change transformer turns ratio. Off-load (manual, no load). On-load (OLTC, tap changing under load using diverter switches & resistors/ reactors for smooth transition). Essential for voltage regulation in power systems.

• Applications of AC Servo Motors: Robotics (joint actuation), CNC machines (tool positioning), radar/satellite dish positioning, flight control surfaces, automation (pick-and-place). Require fast response, high accuracy, smooth speed control.

• Linear Induction Motor (LIM):

  DiagramSEARCH: linear induction motor maglev train
  Converts electrical energy directly into linear motion. Primary on vehicle, secondary (reaction rail) fixed (or vice versa). Thrust $$\displaystyle F \propto \frac{s}{s^2 + (X/R)^2} $$. Used in maglev trains, roller coasters, conveyors, industrial actuators. Advantages: no mechanical contact, smooth, high speed. Disadvantages: low efficiency, high cost.

• Impact of Harmonics on IM Performance:

  • Additional Losses: Harmonic currents cause extra $$\displaystyle I^2R $$ loss in stator & rotor.

  • Torque Pulsations: Harmonic RMFs produce cogging (slot harmonics) & crawling (e.g., 7th harmonic → 1/7 $$\displaystyle N_s $$).

  • Increased Heating: Due to additional losses.

  • Neutral Current: In wye-connected stator, triplen harmonics (3rd, 9th...) add in neutral.

  • Reduced Efficiency & Torque: Especially at light loads.

• Cooling of Transformers: Methods: ONAN (natural), ONAF (forced air), OFAF (forced oil & air), OFWF (forced oil & water). Radiators, fans, pumps used. Oil serves as insulation & coolant.

• Excitation Phenomenon in Transformer: When transformer is switched on, inrush current ($$\displaystyle I_{inrush} $$) flows due to remanent flux & symmetrical flux requirement. $$\displaystyle I_{inrush} $$ can be 6-30× $$\displaystyle I_{fl} $$, lasts for a few cycles. Can cause protective relay maloperation (differential relay).

  DiagramSEARCH: transformer inrush current waveform

• Inrush Current in Transformer: Caused by DC offset in magnetizing current during energization to establish flux. Depends on point-on-wave of switching & remanence.

  DiagramSEARCH: transformer inrush current cause

• Compensating Winding in AC Series Motor: Embedded in pole faces, connected in series with armature. Purpose: To counteract armature reaction (cross-magnetizing effect) which distorts main field & causes poor commutation. Improves commutation, allows higher power output.

\boxed{\text{End of Unit 3 Notes - Focus on derivations, diagrams, and numerical problem-solving from past papers.}}