Utilization of Electrical Engineering (EX-603 (A)) - Unit 4 Short Notes

UNIT 4: UTILIZATION OF ELECTRICAL ENGINEERING

Comprehensive Short Notes (Based on RGPV Past Papers)

I. ILLUMINATION ENGINEERING

A. Fundamental Laws

1. Inverse Square Law

   Illumination \( E \) on a surface from a point source is inversely proportional to the square of the distance \( d \) from the source:

$$ E = \frac{I}{d^2} $$

where \( I \) = luminous intensity (candela, cd).

[!TIP] Valid only for point sources and small surfaces perpendicular to the source.

2. Lambert’s Cosine Law

   Illumination on a surface is proportional to the cosine of the angle \( \theta \) between the normal to the surface and the direction of the incident light:

$$ E = \frac{I \cos \theta}{d^2} $$

[!TIP] Combines with inverse square law for tilted surfaces.

B. Lighting Schemes

C. Design Considerations

• Room dimensions → Cavity ratio \( R = \frac{5 \times \text{room length} \times \text{width}}{\text{total} \times \text{height}} \).

• Mounting height \( h \) → Affects spacing and uniformity.

• Surface reflectances → Ceiling, wall, floor reflectances (ρc, ρw, ρf) impact utilization factor (UF).

• Utilization Factor (UF) → Fraction of lamp lumens reaching work plane (from photometric data).

• Maintenance Factor (MF) → Accounts for dirt/depreciation (typically 0.7–0.8).

D. Illumination Calculations

1. Point Source on Horizontal Surface

$$ E = \frac{I \cos \theta}{d^2} \quad \text{(lux)} $$

where \( d = \sqrt{h^2 + x^2} \), \( \cos \theta = h/d \), \( h \) = mounting height, \( x \) = horizontal distance.

2. Multiple Point Sources (Two Lamps)

Total illumination = sum of contributions from each lamp.

[!EXAMPLE] Two 50 CP lamps at height 5 m, 20 m apart:

• Under each lamp: \( E = \frac{50}{5^2} = 2 \, \text{lux} \).

• Midway: \( d = \sqrt{10^2 + 5^2} = 11.18 \, \text{m} \), \( \cos \theta = 5/11.18 = 0.447 \),

\( E_{\text{single}} = \frac{50 \times 0.447}{11.18^2} = 0.179 \, \text{lux} \), total \( E = 0.358 \, \text{lux} \).

3. Number of Lamps Required

\boxed{N = \frac{E \times A}{\text{lamp lumens} \times UF \times MF}}

where:

• \( E \) = required illuminance (lux)

• \( A \) = area (m²)

• Lamp lumens = lamp wattage \( \times \) efficacy (lm/W)

• \( UF \) = utilization factor (from tables)

• \( MF \) = maintenance factor

[!TIP] Always check units: 1 lumen/m² = 1 lux.

E. Energy-Efficient Lighting

Comparison:

• Incandescent: Low efficacy (10–15 lm/W), high heat loss.

• Fluorescent: Moderate (50–100 lm/W), requires ballast.

• LED: Highest efficacy, no mercury, directional.

II. ELECTRICAL HEATING

A. Advantages & Disadvantages

B. Types of Electrical Heating

1. Resistance Heating

   • Principle: \( P = I^2 R = V^2/R \).

   • Types:

     • Space heating: Baseboard, radiant panels.

     • Immersion heating: Water heaters, industrial vats.

   • Applications: Domestic water heaters, ovens, furnaces.

2. Induction Heating

   • Principle: Electromagnetic induction → eddy currents in workpiece → \( I^2R \) heating.

   • Furnaces:

     • Coreless: For melting metals (high frequency).

     • Channel: For holding/molten metals (low frequency).

   • Applications: Melting, hardening, brazing.

   • Limitations: High cost, limited to conductive materials, skin effect.

3. Dielectric Heating

   • High-frequency AC (MHz) applied to non-conductors → molecular friction.

   • Applications: Wood drying, food processing (microwave is special case).

4. Arc Heating

   • Electric arc between electrodes → high temperature (~3000°C).

   • Applications: Steelmaking (arc furnace), welding.

C. Heating Calculations

Power in Resistive Circuits:

• Series: \( P = \frac{V^2}{R_1 + R_2 + ...} \)

• Parallel: \( P = V^2 \left( \frac{1}{R_1} + \frac{1}{R_2} + ... \right) \)

[!EXAMPLE] Toaster with two 100 Ω elements, 250 V:

• Parallel: \( R_{eq} = 50 \, \Omega \), \( P = \frac{250^2}{50} = 1250 \, \text{W} \).

• Series: \( R_{eq} = 200 \, \Omega \), \( P = \frac{250^2}{200} = 312.5 \, \text{W} \).

Efficiency: \( \eta = \frac{\text{useful heat output}}{\text{electrical input}} \times 100\% \).

Losses: conduction, convection, radiation from surfaces.

D. HVAC Load Estimation

1. Calculate heat gain from:

   • Transmission through walls/windows (U-value × area × ΔT).

   • Solar radiation through glazing.

   • Occupants, equipment, lighting (sensible + latent).

2. Total cooling load = sum of all gains (in Watts or BTU/h).

3. Select AC unit with capacity ≥ total load, considering safety factor (1.1–1.2).

III. WELDING TECHNOLOGIES

A. Classification of Welding Processes

B. Detailed Welding Methods

1. Arc Welding

   • SMAW (Shielded Metal Arc): Consumable electrode with flux coating. Manual, versatile.

   • GMAW (Gas Metal Arc): Continuous wire electrode + shielding gas (CO₂/Ar). Semi-automatic/automatic.

   • Principle: Arc between electrode and workpiece melts metal.

   • Equipment: Power source (transformer/rectifier), electrode holder, cables, shielding gas.

2. Resistance Welding

   • Principle: Heat from \( I^2R \) at joint interface under pressure.

   • Spot Welding: Two electrodes clamp sheets, pulse current.

   • Seam Welding: Rotating wheels for continuous weld (e.g., tanks).

   • Applications: Automotive bodies, sheet metal.

3. Electron Beam Welding

   • Principle: High-velocity electrons (accelerated in vacuum) strike workpiece → kinetic energy to heat.

   • Advantages: Deep penetration, no filler, precise.

   • Limitations: Vacuum chamber required, high cost, alignment critical.

   • Applications: Aerospace, nuclear, high-value components.

C. Welding Equipment

Welding Transformers:

• Types:

  • AC transformer: Simple, rugged, drooping V-I characteristic.

  • Rectifier: AC to DC, stable arc, suitable for SMAW/GMAW.

• Characteristics:

  • Drooping V-I curve: Maintains constant current despite voltage changes (essential for manual welding).

  • Open Circuit Voltage (OCV): 50–100 V (safe limit).

  • Short Circuit Current: Maximum current during electrode contact.

IV. ELECTROCHEMICAL PROCESSES

A. Faraday’s Laws of Electrolysis

1. First Law:

   Mass of substance deposited \( W \propto \) total charge \( Q \):

   \boxed{W = Z \cdot Q = Z \cdot I \cdot t}

   where \( Z \) = electrochemical equivalent (kg/C), \( I \) = current (A), \( t \) = time (s).

2. Second Law:

   For same charge, masses deposited are proportional to chemical equivalents \( E \):

   \boxed{\frac{W_1}{E_1} = \frac{W_2}{E_2}}

   where \( E = \frac{\text{atomic weight}}{\text{valency}} \).

Relation: \( Z = \frac{E}{F} \), \( F \) = Faraday constant = 96500 C/mol.

B. Electroplating and Electrodeposition

• Process: Workpiece as cathode, metal anode in electrolyte. Current deposits metal ions onto cathode.

• Applications:

  • Corrosion protection (zinc, nickel).

  • Decoration (gold, chrome).

  • Electronics (copper on PCBs).

• Parameters: Current density, temperature, agitation, electrolyte composition.

C. Deposition Calculations

\boxed{W = \frac{I \cdot t \cdot E}{F}}

where \( E \) = equivalent weight (g/eq).

[!EXAMPLE] Gold deposition: \( I = 3 \, \text{A} \), \( t = 30 \, \text{min} = 1800 \, \text{s} \), \( E_{\text{Au}} = 197 \, \text{g/mol} / 1 = 197 \, \text{g/eq} \), \( F = 96500 \, \text{C} \).

\( W = \frac{3 \times 1800 \times 197}{96500} = \frac{1,063,800}{96,500} \approx 11.02 \, \text{g} \).

Note: If given electrochemical equivalent \( Z = 0.065 \, \text{mg/C} \), then \( W = I \cdot t \cdot Z = 3 \times 1800 \times 0.065 = 351 \, \text{mg} = 0.351 \, \text{g} \).

V. ELECTRIC DRIVES

A. Advantages Over Other Drives

B. Types: Group vs Individual Drive

C. Motor Selection Criteria

1. Load Characteristics:

   • Constant torque (cranes, conveyors).

   • Variable torque (fans, pumps: \( T \propto N^2 \)).

2. Environmental Factors: Dust, moisture, explosion-proof (choose enclosure: TEFC, drip-proof).

3. Efficiency & Power Rating: Match with load duty (continuous, intermittent).

4. Speed Control Range: DC/AC drives with VFD for variable speed.

5. Cost & Maintenance: Consider life-cycle cost, spare parts availability.

VI. ELECTRIC TRACTION SYSTEMS

A. Traction System Requirements

• High starting torque.

• Smooth speed control over wide range.

• Regenerative braking capability.

• Robustness to withstand overloads, vibrations.

• Simple operation and maintenance.

B. Traction Motors

DC Series Motor:

• Characteristics:

  • Torque \( T \propto I_a^2 \) (high starting torque).

  • Speed \( N \propto \frac{V - I_a R}{I_a} \) → decreases with load (self-protecting).

  • Suitability: Ideal for traction (high starting torque, simple control).

• Limitations: Poor speed regulation at light load, requires series-parallel control.

AC Motors:

• Induction Motor: Robust, maintenance-free, but lower starting torque → requires VFD or rotor resistance.

• Synchronous Motor: Constant speed, used for high-power AC traction (with power electronics).

C. Train Motion Analysis

General Speed-Time Curve (Main Line)

Trapezoidal Speed-Time Curve

Assumptions:

• Acceleration \( \alpha \) constant, braking \( \beta \) constant.

• No coasting (or negligible).

• Distance \( S \), total time \( T \), average speed \( V_{avg} = S/T \).

Derivation:

1. Acceleration time: \( t_1 = \frac{V_m}{\alpha} \), distance \( s_1 = \frac{1}{2} \alpha t_1^2 = \frac{V_m^2}{2\alpha} \).

2. Constant speed time: \( t_2 \), distance \( s_2 = V_m t_2 \).

3. Braking time: \( t_3 = \frac{V_m}{\beta} \), distance \( s_3 = \frac{V_m^2}{2\beta} \).

4. Total distance:

   \boxed{S = \frac{V_m^2}{2} \left( \frac{1}{\alpha} + \frac{1}{\beta} \right) + V_m t_2}

5. Total time:

   \boxed{T = V_m \left( \frac{1}{\alpha} + \frac{1}{\beta} \right) + t_2}

6. Given \( S \) and \( T \), solve for \( V_m \) and \( t_2 \).

[!EXAMPLE] Train: \( S = 1400 \, \text{m} \), \( V_{avg} = 42 \, \text{km/h} = 11.67 \, \text{m/s} \), \( \alpha = 1.7 \, \text{km/h/s} = 0.472 \, \text{m/s}^2 \), \( \beta = 3.3 \, \text{km/h/s} = 0.917 \, \text{m/s}^2 \).

\( T = S / V_{avg} = 1400 / 11.67 \approx 120 \, \text{s} \).

Let \( k = \frac{1}{\alpha} + \frac{1}{\beta} = 2.118 + 1.091 = 3.209 \, \text{s}^2/\text{m} \).

From \( T = V_m k + t_2 \) → \( t_2 = 120 - 3.209 V_m \).

Substitute in \( S \):

\( 1400 = \frac{V_m^2}{2} \times 3.209 + V_m (120 - 3.209 V_m) = 1.6045 V_m^2 + 120 V_m - 3.209 V_m^2 \)

\( \Rightarrow 1.6045 V_m^2 - 120 V_m + 1400 = 0 \).

Solve: \( V_m = 14.47 \, \text{m/s} \) (52 km/h), \( t_2 = 73.6 \, \text{s} \), \( t_1 = 30.6 \, \text{s} \), \( t_3 = 15.8 \, \text{s} \).

D. Train Resistance and Effective Weights

• Dead Weight (W): Actual weight of train (tonnes).

• Acceleration Weight (W_e): \( W_e = W + \frac{W \cdot a}{g} \) (includes inertia effect).

• Train Resistance (R):

  \( R = r_1 + r_2 v + r_3 v^2 \) (N/tonne)

  where \( r_1 \) = mechanical (rolling) resistance, \( r_2 v \) = rail friction, \( r_3 v^2 \) = air resistance.

E. Specific Energy Consumption (SEC)

\boxed{SEC = \frac{\text{total energy consumed (kWh)}}{\text{tonne-km}}}
Factors affecting SEC:

• Gradient (uphill increases SEC).

• Acceleration/deceleration cycles.

• Train resistance (speed, aerodynamics).

• Braking (regenerative braking reduces SEC).

• Auxiliary loads (lighting, HVAC).

F. Electrical Braking

Regenerative Braking:

• Requires compatible power supply (DC bus or AC grid).

• Used in metros, EVs.

• Energy recovery efficiency ~60–80%.

G. Load Equalization

• Principle: Use inertial storage (flywheel) or capacitor bank to absorb peak power during acceleration and release during braking.

• Application in Traction:

  • Reduces peak demand from supply.

  • Smoothes power draw, avoids high tariffs.

  • Flywheel stores kinetic energy during braking, supplies during acceleration.

VII. ELECTRIC VEHICLES AND HYBRID SYSTEMS

A. Electric Vehicles (EVs)

Components:

1. Battery: Li-ion (high energy density), NiMH, lead-acid.

2. Electric Motor: AC induction or permanent magnet synchronous.

3. Controller/Power Electronics: Inverter (DC-AC), converter (DC-DC).

4. Charger: On-board (AC) or off-board (DC fast charging).

5. Transmission:

   • Single-speed reduction: Common (simplicity, EVs have wide torque range).

   • Multi-speed gearbox: For high-performance EVs (extend speed range).

Advantages: Zero tailpipe emissions, quiet, high efficiency (~60–70% vs. 20–30% ICE).

B. Hybrid Electric Vehicles (HEVs)

Advantages of HEVs:

• Improved fuel economy (20–40%).

• Reduced emissions.

• Regenerative braking.

• No range anxiety (ICE backup).

C. Energy Conservation in Transportation

• EVs: Shift energy source from oil to grid (can be renewable). Higher well-to-wheel efficiency.

• HEVs: Optimize engine operation, recover braking energy.

• Comparison with Conventional:

  • ICE efficiency: ~20–30% (thermal losses).

  • EV efficiency: ~60–70% (motor + battery).

  • HEV: ~35–40% (combined).

• Role in Energy Conservation: Reduce fossil fuel dependence, lower per-km energy consumption, enable renewable integration.

END OF UNIT 4 NOTES
These notes cover all high-frequency topics from past RGPV papers. Focus on derivations (trapezoidal curve), formulas (illumination, Faraday, SEC), and comparisons (lighting, welding, drives, EVs).