UNIT 4: Wind and Solar Energy and Renewable Power Systems
1. Introduction to Energy and Power Generation
Energy sources are classified as conventional (fossil fuels, nuclear, large hydro) and renewable (solar, wind, biomass, small hydro, geothermal, ocean).
Relative Merits and Demerits
| Source | Merits | Demerits |
|---|---|---|
| Conventional | High capacity, reliable, base-load capability | Pollution (air, water, thermal), finite reserves, greenhouse gases |
| Renewable | Inexhaustible, low operational emissions, decentralized potential | Intermittency, lower capacity factor, higher initial cost, land use |
[!TIP] Exam Focus: Compare solar vs wind in terms of capacity factor, land requirement, and predictability. Renewable sources are location-specific.
Renewable Energy Scenario in India
-
Installed capacity (as of 2024): ~190 GW renewable (including large hydro ~52 GW).
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Top states: Tamil Nadu (wind), Rajasthan/Gujarat (solar), Karnataka (mixed).
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Targets: 500 GW non-fossil capacity by 2030.
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Prominent sources: Solar PV (due to high insolation) and Wind (coastal & peninsular regions).
Future Energy Strategies
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Hybrid systems (solar-wind-storage) for reliability.
-
Green hydrogen for storage and industrial decarbonization.
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Floating solar and offshore wind to save land.
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Smart grids and demand response for integration.
2. Conventional Power Plants (Contextual Overview)
2.1 Hydroelectric Power Plants
Layout and Components
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Dam/Reservoir: Stores water, creates head.
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Penstock: Large pipe conveying water to turbine.
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Surge Tank: Controls pressure surges in penstock.
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Turbine: Converts hydraulic energy to mechanical (Pelton for high head, Kaplan for low head).
-
Generator: Converts mechanical to electrical.
-
Tailrace: Discharges water back to river.
Types of Turbines
| Turbine | Head Range | Flow | Application | Key Feature |
|---|---|---|---|---|
| Pelton | High (>300 m) | Low | Mountainous regions | Bucket-shaped nozzles, impulse |
| Kaplan | Low (<30 m) | High | Plains, large rivers | Adjustable blades, reaction type |
Site Selection Considerations
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Hydrology: High rainfall, reliable flow.
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Topography: Narrow gorge for dam, steep gradient.
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Geology: Stable rock foundation.
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Proximity to load centers to reduce transmission loss.
Hydrograph, Flow Duration Curve (FDC), Power Duration Curve (PDC)
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Hydrograph: Plot of discharge (m³/s) vs time (daily/monthly). Shows seasonal variation.
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FDC: Discharge sorted descending vs time percentage. Used to estimate firm capacity.
-
PDC: Power derived from FDC (P = ρgHQη) sorted descending. Gives firm power (minimum power >90% time).
Pumped Storage Power Plants
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Working: Uses two reservoirs (upper/lower). Off-peak: pump water up. Peak: release to generate.
-
Merits: Quick response, load balancing, energy storage.
-
Demerits: High capital cost, geographical constraints, evaporation losses.
Small Scale Hydro (Micro <100 kW, Mini 100 kW–1 MW, Small 1–25 MW)
- Run-of-river type, minimal reservoir, low environmental impact.
2.2 Thermal Power Plants (Steam-based)
Layout of Modern Steam Plant
Boiler → Turbine → Generator → Condenser → Cooling Tower
↑
Economiser, Air-preheater, Feedwater heaters
Key Components Functions
| Component | Function |
|---|---|
| Steam Turbine | Expands steam to produce shaft work. |
| Economiser | Preheats feedwater using flue gas, improves efficiency. |
| Feed Water Heater | Uses extracted steam to heat feedwater, reduces boiler load. |
| Cooling Tower | Cools condenser cooling water via evaporation. |
| Air-preheater | Preheats combustion air using flue gas, improves combustion. |
Water Treatment Plant
-
Necessity: Prevent scaling, corrosion, fouling in boilers.
-
Processes: Sedimentation, filtration, softening (ion exchange), deaeration (remove O₂, CO₂).
Thermo-electric Conversion System
- Components: Boiler (heat to steam), Turbine (steam to mech), Generator (mech to elec), Condenser (steam to water), Cooling system.
Site Selection for Thermal Stations
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Fuel availability (coal near mines).
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Water source (river, sea) for cooling.
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Land availability (flat, cheap).
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Proximity to load centers.
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Ash disposal area.
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Transport facilities (rail, road).
2.3 Nuclear Power Plants
Components of Nuclear Reactor
-
Fuel: Enriched U-235 or Pu-239.
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Moderator: Slows neutrons (graphite, heavy water).
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Control Rods: Absorb neutrons (Cd, B₄C) to control reaction.
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Coolant: Removes heat (water, gas, liquid metal).
-
Pressure Vessel: Houses core.
-
Shielding: Concrete/lead to absorb radiation.
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Steam Generator: Transfers heat to water.
CANDU Reactor (Canada Deuterium Uranium)
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Working: Heavy water moderator and coolant. Natural uranium fuel. Pressure tubes instead of pressure vessel.
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Advantages: Uses natural U, online refueling, high neutron economy.
-
Disadvantages: Heavy water expensive, large size, tritium production.
Nuclear Fission vs Fusion
| Fission | Fusion |
|---|---|
| Heavy nucleus splits | Light nuclei combine |
| Neutron-induced | High T & P required |
| Radioactive waste | Less waste (He product) |
| Commercial today | Experimental (ITER) |
Nuclear Fuel in India
-
Uranium: Jaduguda (Jharkhand), Tummalapalle (AP), Singhbhum (Jharkhand).
-
Thorium: Abundant in Kerala, Odisha, Andhra Pradesh (3-stage program: PHWR → FBR → AHWR).
Nuclear Waste Disposal
-
Low-level: Near-surface disposal.
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Intermediate-level: Shielded containers, shallow burial.
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High-level: Vitrification, deep geological repositories (e.g., KBS-3 method).
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Importance: Prevent radioactive contamination of biosphere.
Radioactive Pollution & Shielding
-
Pollution: Leakage of radionuclides (I-131, Cs-137) into air/water/soil.
-
Shielding: Materials with high atomic number/density (lead, concrete) to absorb γ-rays; borated polyethylene for neutrons.
2.4 Gas Turbine Power Plants
Layout and Classification
-
Simple cycle: Compressor → Combustor → Turbine → Exhaust.
-
Combined cycle: Add HRSG (Heat Recovery Steam Generator) → Steam turbine.
-
Classification: By cycle (simple, combined), by application (peak load, base load).
Working Principle
-
Air compressed in compressor.
-
Fuel injected and combusted.
-
Hot gases expand in turbine (drive compressor + generator).
-
Exhaust heat wasted in simple cycle; recovered in combined cycle.
Methods to Improve Thermal Efficiency
-
Regeneration: Use exhaust heat to preheat compressed air.
-
Intercooling: Cool air between compressor stages.
-
Reheating: Reheat gases between turbine stages.
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Combined cycle: Utilize exhaust heat in steam cycle (efficiency ~60%).
2.5 Diesel Power Stations
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Fuel System: Storage tank → filters → injection pump → injectors.
-
Exhaust System: Silencer (reduce noise), turbocharger (improve efficiency), catalytic converter (reduce emissions).
2.6 Magneto-Hydro Dynamic (MHD) Systems
Principle
-
Direct energy conversion: Ionized hot gas (plasma) passed through magnetic field → induces EMF (Faraday’s law).
-
No moving parts in generator.
Working
-
Air preheater → Combustor (with seed material like K₂CO₃ to ionize flue gas).
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Plasma enters MHD generator (channel with electrodes, magnetic field).
-
DC power extracted.
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Seed recovery from exhaust.
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Bottoming cycle (steam turbine) for remaining heat.
[!TIP] MHD Efficiency: Theoretical ~70%, practical ~40%. Requires high temperature (~2500 K). Not commercial yet.
3. Solar Energy Systems
3.1 Solar Radiation and Geometry
Terms to Locate Point on Earth
-
Latitude (φ): Angular distance from equator.
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Longitude (λ): Angular distance from Prime Meridian.
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Declination (δ): Angle between sun-Earth line and equatorial plane. Varies ±23.45°.
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Hour Angle (ω): Angular displacement of sun from local meridian. ω = 15° × (hours from solar noon).
-
Solar Altitude (α): Angle between sun’s rays and horizontal plane.
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Solar Azimuth (γ): Angle between sun’s projection on horizontal plane and south (N hemisphere).
Calculation of Sun’s Altitude and Azimuth
$$ \sin \alpha = \sin \phi \sin \delta + \cos \phi \cos \delta \cos \omega $$
$$ \sin \gamma = \frac{\cos \delta \sin \omega}{\cos \alpha} $$
[!TIP] Numerical Example: On Sep 1 (δ ≈ 8.3°), at 9 AM solar time (ω = -45°), φ = 23°N. Compute α and γ.
3.2 Solar Thermal Systems
Flat Plate Solar Collectors: Main Components
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Absorber Plate: Black-coated surface to absorb solar radiation.
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Tubes/Pipes: Carry heat transfer fluid (water/air/glycol).
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Glazing: Transparent cover (glass/plastic) to reduce convection loss.
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Insulation: Back/side insulation to minimize conduction loss.
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Housing: Structural support.
Classification of Solar Collectors
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Non-concentrating: Flat plate, evacuated tube (temperature <100°C).
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Concentrating: Parabolic trough, dish, tower (requires tracking, >100°C).
Factors Affecting Performance
| Optical | Thermal | Environmental |
|---|---|---|
| Transmittance (τ) | Absorptance (α) | Ambient temperature (Ta) |
| Reflectance (ρ) | Emittance (ε) | Wind speed |
| Tracking accuracy | Heat transfer coefficient | Dust/snow on glazing |
Solar Thermal Power Generation
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Layout: Solar field (collectors) → HTF pump → Steam generator → Turbine → Generator → Condenser → Cooling tower.
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Working: Collectors heat HTF → produce steam → drive turbine.
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Types: parabolic trough (most common), solar tower, dish-Stirling.
Principle of Conversion
Solar radiation → thermal energy (absorber plate heats fluid) → mechanical (steam turbine) → electrical.
3.3 Solar Photovoltaic Systems
Principle: Photoelectric Effect
- Photons with energy > bandgap excite electrons from valence to conduction band → electron-hole pairs → electric field at p-n junction separates charges → DC current.
Key Elements of PV Cell
I-V Characteristics
-
Open Circuit (Voc): No load, max voltage.
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Short Circuit (Isc): Zero voltage, max current.
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Maximum Power Point (MPP): (Vm, Im) where Pmax = Vm × Im.
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Fill Factor (FF): FF = (Vm Im) / (Voc Isc) → indicates “squareness” of curve.
Performance Parameters
- Efficiency (η):
$$ \eta = \frac{P_{out}}{P_{in}} = \frac{V_m I_m}{G \cdot A} $$
where G = irradiance (W/m²), A = cell area (m²).
- Fill Factor:
$$ FF = \frac{V_m I_m}{V_{oc} I_{sc}} $$
- Maximum Power:
$$ P_{max} = V_m \times I_m $$
[!TIP] Numerical Example (from Dec 2024 paper):
Given: Voc=0.24 V, Isc=10 mA, Vm=0.14 V, Im=6.5 mA, Intensity=24 W/m², Area=4 cm² = 4×10⁻⁴ m².
Calculate:
- Pmax = 0.14 × 6.5×10⁻³ = 0.91 mW
- FF = (0.14×6.5)/(0.24×10) = 0.91/2.4 = 0.379
- η = (0.91×10⁻³)/(24×4×10⁻⁴) = 0.91/(9.6) = 0.0948 → 9.48%
Applications
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Standalone (rural homes, street lights).
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Grid-connected (rooftop, solar farms).
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Water pumping.
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Space applications (satellites).
4. Wind Energy Systems
4.1 Principle of Wind Power Generation
Betz Limit: Maximum possible power coefficient Cp_max = 16/27 ≈ 0.593 (59.3%). No turbine can extract all kinetic energy.
Wind Power:
$$ P = \frac{1}{2} \rho A v^3 C_p $$
where ρ = air density (kg/m³), A = swept area (πR²), v = wind speed (m/s), Cp = power coefficient (<0.593).
[!TIP] Power ∝ v³: Small increase in wind speed → large increase in power. Cut-in (3–4 m/s), rated (12–15 m/s), cut-out (25 m/s).
4.2 Types of Wind Energy Systems
| Type | Axis | Subtypes | Pros | Cons |
|---|---|---|---|---|
| Horizontal Axis | Horizontal | Upwind, Downwind | High efficiency, variable pitch | Needs yaw mechanism, gearbox |
| Vertical Axis | Vertical | Darrieus (lift), Savonius (drag) | Omni-directional, no yaw needed | Lower efficiency, cyclic torque |
4.3 Components of Wind Turbine Generators
Horizontal Shaft Windmill Diagram & Functions
| Component | Function |
|---|---|
| Blades/Rotor | Capture wind kinetic energy, convert to rotational. |
| Nacelle | Houses gearbox (increases speed), generator (produces electricity). |
| Gearbox | Steps up rotor speed (20–50 rpm) to generator speed (1500 rpm). |
| Generator | Types: DFIG (Doubly Fed Induction Generator), PMSG (Permanent Magnet Synchronous Generator). |
| Tower | Supports rotor/nacelle at height (higher wind speed). |
| Yaw System | Rotates nacelle to face wind (via motor/gears). |
| Controller | Monitors wind speed, starts/stops turbine, controls pitch/brakes. |
Wind Turbine Generators
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DFIG: Partial-scale converter, variable speed, reactive power control.
-
PMSG: Full-scale converter, no gearbox (direct drive), high efficiency at low wind.
4.4 Wind Characteristics and Performance
Wind Speed Distribution: Weibull Distribution
$$ f(v) = \frac{k}{c} \left( \frac{v}{c} \right)^{k-1} e^{-(v/c)^k} $$
where k = shape parameter (2–3 typical), c = scale parameter (m/s).
Factors Affecting Performance
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Air density ρ (decreases with altitude/temperature).
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Wind speed v (cubic relation).
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Swept area A.
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Cp (depends on tip speed ratio λ = ωR/v).
Control Schemes
| Scheme | Method | Used For |
|---|---|---|
| Pitch Control | Rotate blades to change angle of attack. | Above rated wind, limit power. |
| Stall Control | Fixed blades; aerodynamic stall limits power. | Below rated wind. |
| Voltage/Reactive Power | Power electronics ( converters ) regulate voltage, VAR support. | Grid code compliance. |
Calculation of Energy Output
$$ E = \frac{1}{2} \rho A C_p \cdot \sum (v_i^3 \cdot t_i) \cdot \eta_{gear} \cdot \eta_{gen} $$
where t_i = time at wind speed v_i (from wind rose/Weibull).
[!TIP] Numerical Example (from May 2024):
Blade length R=10 m, efficiency η_total=40%, v=15 kph = 4.167 m/s, P=1013.25 hPa, T=15°C=288.15 K.
ρ = P/(R_specific T) = 101325/(287×288.15) ≈ 1.225 kg/m³ (standard).
A = πR² = 314.16 m².
P_available = 0.5 × 1.225 × 314.16 × (4.167)³ ≈ 0.5×1.225×314.16×72.34 ≈ 13,900 W.
P_output = 13,900 × 0.4 = 5,560 W.
Energy in 3 h = 5.56 × 3 = 16.68 kWh.
Limitations in Energy Conversion
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Intermittency: Wind not always available.
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Low Cp: Betz limit, mechanical losses.
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Turbulence: Fatigue loads.
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Grid integration: Variability requires backup/storage.
4.5 Site Selection for Wind Farms
Criteria
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Wind Resource: Mean speed >6 m/s at hub height, low turbulence.
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Topography: Smooth, hilltops, coastal areas.
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Accessibility: Road access for transport/installation.
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Environmental Constraints: Avoid bird migration paths, noise limits for nearby residents.
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Grid Proximity: Near substation to reduce transmission cost.
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Land Use: Non-agricultural, minimal obstacles.
[!TIP] Wind Mapping: Use wind atlases, on-site measurements (anemometers at multiple heights), Weibull fitting.
4.6 Safety and Environmental Aspects
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Noise: Aerodynamic (blade swish) and mechanical (gearbox). Mitigation: siting, blade design.
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Visual Impact: Large structures; community acceptance.
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Impact on Birds/Bats: Collision risk; avoid migratory routes.
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Safety: Lightning protection, fire suppression, emergency shutdown, safe working heights during installation.
5. Biomass Energy Systems
5.1 Biomass Resources and Applications
Sources
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Agricultural residue (straw, husk).
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Forestry waste (branches, sawdust).
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Animal dung (cow dung).
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Municipal solid waste (organic fraction).
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Energy crops (sugarcane bagasse, jatropha).
Applications in Detail
| Technology | Process | Output |
|---|---|---|
| Direct Combustion | Burn biomass in boiler. | Steam → electricity/heat |
| Gasification | Partial oxidation → producer gas (CO+H₂). | Syngas for engine/boiler |
| Anaerobic Digestion | Microbial breakdown → biogas (CH₄+CO₂). | Biogas for cooking/electricity |
| Pyrolysis | Thermal decomposition without O₂ → bio-oil, char, gas. | Liquid fuel |
| Landfill Gas | Capture methane from decomposing waste. | Electricity generation |
| Cogeneration | Combined heat & power from biomass. | High overall efficiency |
Environmental Problems from Agriculture/Organic Waste
-
Open burning → air pollution (PM, CO, VOCs).
-
Uncontrolled decomposition → methane (GHG) release.
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Water contamination from leachate.
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Odor and vector breeding.
5.2 Biogas Generation
Anaerobic Digestion Stages
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Hydrolysis: Complex organics → sugars, amino acids.
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Acidogenesis: Sugars → volatile fatty acids, alcohols, CO₂, H₂.
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Acetogenesis: Acids → acetic acid, H₂, CO₂.
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Methanogenesis: Acetic acid/H₂+CO₂ → CH₄ + CO₂.
Types of Biogas Plants
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Deen Bandhu (KVIC Model):
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Working: Floating drum (steel) on digester slurry; drum rises/falls with gas pressure.
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Diagram: Fixed dome (brick) with moving gas holder.
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Features: Low cost, common in India, but steel drum corrodes.
-
-
Pragati Design (Floating Drum Improvement):
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Working: Cylindrical digester, separate gas holder on guides.
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Features: Better mixing, less scum, higher efficiency.
-
-
Community Biogas Plants:
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Serve multiple households/farm.
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Problems: Feedstock collection coordination, sludge disposal, maintenance, social conflicts.
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Materials for Biogas Generation
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Feedstock: Dung, crop residue, food waste (C/N ratio 20–30:1).
-
Inoculum: Seed slurry from existing digester.
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Nutrients: Trace elements (Ni, Co) for microbes.
Advantages & Environmental Benefits
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Renewable fuel for cooking/electricity.
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Reduces deforestation.
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Nutrient-rich slurry as fertilizer.
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Mitigates methane emissions from waste.
5.3 Other Biomass Conversion Technologies
Pyrolysis: Principle & Small Scale Unit
-
Principle: Thermal decomposition 300–900°C in absence of O₂.
-
Small Scale Unit: Feedstock → reactor (heated externally) → vapors → condenser → bio-oil; char collected from bottom.
-
Products: Bio-oil (liquid fuel), biochar (soil amendment), syngas.
Landfill Gas Power Generation
Basic Advantages: Captures methane (powerful GHG), generates electricity, reduces odor/explosion risk.
5.4 Environmental Impact of Biomass
-
Air Pollution: Combustion emits PM, NOx (but lower than coal if managed).
-
GHG Reduction: Carbon-neutral cycle (CO₂ absorbed during growth).
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Ash Disposal: Can be used as fertilizer (if low heavy metals).
-
Sustainability: Must avoid deforestation, compete with food crops.
6. Other Renewable Energy Sources
6.1 Ocean Thermal Energy Conversion (OTEC)
Principle
-
Ocean Temperature Gradient: Warm surface water (25–30°C) vs cold deep water (5–10°C). ΔT ≥ 20°C required.
-
Working Fluid (e.g., ammonia) evaporates at warm temperature, expands in turbine, condenses at cold temperature.
Closed OTEC System Schematic
Working:
-
Warm seawater heats ammonia in evaporator → vapor.
-
Vapor drives turbine-generator.
-
Cold seawater condenses vapor in condenser → liquid ammonia.
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Pump returns liquid to evaporator.
6.2 Tidal Energy
Site Selection for Tidal Power Plants
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Tidal Range: >4 m for barrage type.
-
Basin Configuration: Large estuary, narrow inlet.
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Geology: Solid foundation for barrage.
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Environmental Impact: Effects on sediment, mangroves, fish migration.
-
Proximity to Grid.
Schematic Layout of Tidal Power House (Barrage Type)
Components: Barrage, gates, turbines (bulb type), sluices, lock for ships.
Mode of Electricity Generation
-
Potential Energy: Water stored in basin at high tide → released through turbines at low tide (ebb generation).
-
Kinetic Energy: Tidal currents drive turbines (in-stream turbines, no barrage).
6.3 Geothermal Energy
Geothermal Resources in India
-
Low-to-medium enthalpy: Himalayas (Parvati valley), Gujarat (Cambay basin), Rajasthan (Son-Narmada-Tapti line).
-
High enthalpy: None commercially; Himalayas have potential.
Binary Fluid Power Plant
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Working: Geothermal hot water (150–200°C) heats secondary fluid (isobutane, pentane) with low boiling point in heat exchanger → vapor drives turbine → condensed and recycled.
-
Why no flashing? Flashing requires fluid above boiling point at given pressure. Low-temperature fluids (<150°C) won’t flash spontaneously; binary cycle avoids scaling/corrosion.
Hybrid Geothermal-Fossil Systems
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Bottoming Hybrid: Geothermal preheats feedwater for fossil plant.
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Topping Hybrid: Fossil superheats geothermal vapor.
-
Mixed Steam: Combine geothermal steam with fossil steam.
Advantages of Geothermal Energy
-
Base-load: Constant output.
-
Low emissions: Minimal CO₂, NOx.
-
Small footprint.
-
High efficiency (binary cycle ~10–15%, flash ~20–30%).
6.4 Hydrogen Energy
Advantages and Disadvantages
| Advantages | Disadvantages |
|---|---|
| High energy per mass (120–142 MJ/kg) | Low density → storage/transport difficult |
| Zero emissions at point of use | Production costly (electrolysis) |
| Can be stored long-term | Safety: flammable, explosive |
| Versatile (fuel, feedstock) | Infrastructure lacking |
Methods of Hydrogen Production
-
Electrolysis: Water → H₂ + O₂ (using renewable electricity → green H₂).
-
Steam Reforming: CH₄ + H₂O → CO + 3H₂ (gray H₂, with CCS → blue).
-
Biomass Gasification: Biomass → syngas → shift reaction → H₂.
Hydrogen Storage Methods
| Method | Principle | Pros | Cons |
|---|---|---|---|
| Compressed Gas | High-pressure tanks (350–700 bar) | Simple, mature | Low volumetric density, heavy |
| Liquefied Hydrogen | Cool to -253°C | Higher density | High boil-off, energy-intensive |
| Metal Hydrides | Absorb into metal alloys (e.g., LaNi₅) | Safe, moderate pressure | Heavy, slow kinetics |
| Chemical Storage | Compounds like NH₃, methanol | High density, easy transport | Requires cracking, energy loss |
6.5 Fuel Cells
Classification by Electrolyte
| Type | Electrolyte | Operating Temp | Applications |
|---|---|---|---|
| PEMFC | Polymer membrane | 60–80°C | Vehicles, backup power |
| SOFC | Solid oxide (Y₂O₃-ZrO₂) | 800–1000°C | Stationary power, CHP |
| MCFC | Molten carbonate | 600–700°C | Utility-scale |
| AFC | Alkaline (KOH) | 60–90°C | Spacecraft (Apollo) |
Working Principle
-
Electrochemical reaction: H₂ at anode → 2H⁺ + 2e⁻; O₂ at cathode + 4H⁺ + 4e⁻ → 2H₂O.
-
Components: Anode (catalyst), cathode, electrolyte, bipolar plates.
-
Output: DC electricity, water, heat.
7. Hybrid Renewable Energy Systems
Concept
Integration of two or more renewable sources (e.g., solar-wind, wind-hydro) with/without energy storage (batteries, hydrogen) to improve reliability and reduce storage size.
Types
-
Solar-Wind-Battery: Common for off-grid.
-
Wind-Hydro: Hydro as storage/backup.
-
Solar-Biomass: Biomass for night operation.
-
Geothermal-Solar: Solar preheats for geothermal.
Advantages
-
Reliability: Complementary generation (solar day, wind night/non-monsoon).
-
Reduced Storage: Smoothing effect lowers battery size.
-
Optimal Utilization: Better capacity factor.
-
Grid Stability: Inertia from hydro/turbines.
Challenges
-
Complex Control: Multiple sources, storage management.
-
Higher Initial Cost: Multiple technologies.
-
Site-Specific: Requires co-location or strong grid.
-
Maintenance: Diverse expertise needed.
8. Economic and Operational Aspects of Power Plants
8.1 Cost Considerations
Fixed vs Operating Costs
| Fixed Costs | Operating Costs |
|---|---|
| Capital cost (land, plant, equipment) | Fuel cost (coal, gas, uranium) |
| Interest on loans | Maintenance (routine, overhaul) |
| Taxes, insurance | Labor (operators, staff) |
| Depreciation | Water, chemicals, consumables |
| Return on investment | Waste disposal, emissions control |
8.2 Load Management
Key Curves
-
Load Curve: Power (MW) vs time (hourly/daily). Shows variation.
-
Load Duration Curve (LDC): Load sorted descending vs time percentage. Used for capacity planning.
-
Flow Duration Curve (FDC): Discharge sorted descending (for hydro).
Performance Factors
- Load Factor (LF):
$$ LF = \frac{\text{Average Load}}{\text{Maximum Demand}} = \frac{\text{Energy produced in period}}{\text{Max demand} \times \text{Time}} $$
Always <1 because average < peak.
- Capacity Factor (CF):
$$ CF = \frac{\text{Actual energy output}}{\text{Rated capacity} \times \text{Time}} $$
<1 due to maintenance, outages, low demand.
- Utilisation Factor (UF):
$$ UF = \frac{\text{Maximum Demand}}{\text{Rated capacity}} $$
<1 because capacity > peak demand for reliability.
- Demand Factor (DF):
$$ DF = \frac{\text{Maximum Demand}}{\text{Connected load}} $$
<1 because not all connected load operates simultaneously.
[!TIP] Relations:
- Energy = Max demand × Time × LF.
- Reserve capacity = Rated capacity – Max demand.
- CF = LF × UF.
Numerical Example (from Dec 2024):
Max demand = 15000 kW, LF=60%, CF=40%, UF=45%.
-
Annual energy = Max demand × 8760 × LF = 15000 × 8760 × 0.6 = 79.44 GWh.
-
Reserve capacity = Rated capacity – Max demand.
CF = Energy / (Rated × 8760) → Rated = Energy/(CF×8760) = 79.44×10⁶/(0.4×8760) ≈ 22670 kW.
Reserve = 22670 – 15000 = 7670 kW.
-
Hours not in service = (Reserve / Rated) × 8760 = (7670/22670)×8760 ≈ 2965 hours.
Load Forecasting
-
Qualitative: Expert opinion, market research.
-
Quantitative: Time series (ARIMA), regression, neural networks.
-
Importance: Unit commitment, economic dispatch, maintenance scheduling.
8.3 Economic Dispatch and Scheduling
Economic Load Scheduling (ELS)
-
Objective: Minimize total fuel cost while meeting load and constraints.
-
Equal Incremental Cost Criterion (neglecting losses):
$$ \frac{dC_1}{dP_1} = \frac{dC_2}{dP_2} = \lambda $$
where λ = Lagrange multiplier (system incremental cost).
Incremental Fuel Cost & Numerical Problem
Given cost functions C₁(P₁), C₂(P₂), total load P_D, find P₁, P₂ such that dC₁/dP₁ = dC₂/dP₂ and P₁+P₂=P_D.
Example (from Jun 2025):
C₁ = 50 + 2P₁ + 0.005P₁², C₂ = 100 + 2P₂ + 0.01P₂², P_D=350 MW, neglect losses.
dC₁/dP₁ = 2 + 0.01P₁, dC₂/dP₂ = 2 + 0.02P₂.
Set equal: 2+0.01P₁ = 2+0.02P₂ → P₁ = 2P₂.
P₁+P₂=350 → 2P₂+P₂=350 → P₂=116.67 MW, P₁=233.33 MW.
λ = 2+0.01×233.33 = 4.333 Rs/MWh.
Penalty Factor and Transmission Losses
With losses, condition: dCᵢ/dPᵢ = λ (1 - ∂P_L/∂Pᵢ).
Penalty factor for plant i:
$$ \alpha_i = \frac{1}{1 - \frac{\partial P_L}{\partial P_i}} $$
Example (from Jun 2025):
Given: dC₁/dP₁ = 0.15P₁+150, dC₂/dP₂ = 0.25P₂+175, P₁=P₂=400 MW, ∂P_L/∂P₂=0.2.
Compute: dC₂/dP₂ = 0.25×400+175 = 275.
275 = λ (1 - 0.2) → λ = 275/0.8 = 343.75.
dC₁/dP₁ = 0.15×400+150 = 210.
210 = 343.75 (1 - ∂P_L/∂P₁) → 1 - ∂P_L/∂P₁ = 210/343.75 = 0.611 → ∂P_L/∂P₁ = 0.389.
Penalty factor α₁ = 1/(1-0.389) = 1/0.611 = 1.637.
8.4 Tariffs and Pricing
Types of Tariffs
| Tariff | Description | Suitable For |
|---|---|---|
| Flat Rate | Fixed charge per kWh. | Residential (simple) |
| Block Rate | Decreasing/increasing block prices. | Domestic, commercial |
| Two-Part | Fixed charge + variable energy charge. | Industrial, commercial |
| Time-of-Day (TOD) | Different prices for peak/off-peak hours. | Demand management |
| Seasonal | Higher in summer/winter. | Seasonal industries |
Peak Load Pricing
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Concept: Higher tariff during peak demand hours to reflect true cost (capacity, fuel).
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Application: Incentivize load shifting, reduce peak demand.
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Benefits: Better capacity utilization, lower overall cost, deferred investment.
8.5 Cogeneration
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Concept: Combined Heat and Power (CHP) – produce electricity and useful thermal energy (steam, heat) from same fuel.
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Advantages: Overall efficiency 70–90% (vs 30–40% for condensing plants), reduced fuel cost, lower emissions.
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Applications: Process industries (sugar, paper, chemicals), district heating.
9. Environmental Impact and Sustainability
Environmental Benefits of Renewables
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Reduced GHG: No CO₂ during operation.
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Lower Air Pollution: No SOx, NOx, PM (except biomass combustion).
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Water Conservation: Solar PV/Wind use negligible water vs thermal/nuclear.
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Land Use: Can be dual-use (agrivoltaics, grazing under wind).
Tech-Specific Environmental Aspects
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Wind: Noise, visual, bird/bat mortality.
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Solar Farms: Land use, habitat fragmentation, end-of-life panel recycling.
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Biomass: Air emissions if combustion inefficient, ash disposal.
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Geothermal: Induced seismicity, brine disposal, H₂S emissions.
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Hydro: Ecosystem disruption, fish migration, methane from reservoirs.
Waste Management
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Biomass residue: Ash used in cement/fertilizer.
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Nuclear waste: Deep geological disposal.
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Solar panels: Recycling of glass, aluminum, silicon; toxic CdTe panels handled carefully.
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Wind blades: Composite material recycling challenge (currently landfill or cement co-processing).
Sustainable Energy Strategies
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Energy Resources Reserve: Proven reserves vs resources. Importance for long-term planning.
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Life Cycle Assessment (LCA): Cradle-to-grave environmental impact (manufacturing, operation, decommissioning). Shows renewables have low lifecycle emissions.
[!TIP] Exam Focus: Compare lifecycle emissions (gCO₂eq/kWh): Coal ~1000, Gas ~500, Solar PV ~40, Wind ~10, Nuclear ~12.