UNIT 1: RENEWABLE ENERGY TECHNOLOGY - SHORT NOTES

I. INTRODUCTION & FUNDAMENTALS

Definition & Need for Renewable Energy

• Renewable Energy (RE): Energy derived from natural sources that replenish themselves on a human timescale (e.g., solar, wind, biomass, hydro, geothermal, ocean). It is inexhaustible under proper management.

• Need/Importance:

  • Energy Security: Reduces dependence on finite fossil fuels.

  • Environmental Protection: Mitigates air/water pollution and greenhouse gas (GHG) emissions.

  • Sustainability: Meets present needs without compromising future generations.

  • Rural Development & Employment: Especially in biomass, small hydro, and decentralized systems.

  • Climate Change Mitigation: Primary tool to reduce carbon footprint.

• Classification of RE Sources:

  • Solar: Direct (PV) and indirect (thermal, biomass).

  • Wind: Onshore, offshore.

  • Hydropower: Large, small, micro, mini.

  • Biomass: Solid, liquid (biofuels), gaseous (biogas).

  • Geothermal: Hydrothermal, enhanced, etc.

  • Ocean: Tidal, wave, OTEC, salinity gradient.

Energy, Environment & Climate

• Effect of Fossil Fuels: Burning releases CO₂, SOₓ, NOₓ, particulates → Global Warming (rise in avg. Earth temperature) & Climate Change (altered weather patterns, sea-level rise).

• Greenhouse Effect: Natural process where greenhouse gases (CO₂, CH₄, H₂O, etc.) trap outgoing infrared (IR) radiation, warming the Earth's surface. Enhanced Greenhouse Effect is the human-accelerated version due to increased GHG concentrations.

• Sensible vs. Latent Heat:

  • Sensible Heat: Heat exchanged that causes a temperature change (e.g., heating water from 20°C to 80°C).

  • Latent Heat: Heat exchanged during a phase change without temperature change (e.g., evaporation of water, melting of ice). Crucial in atmospheric processes and solar thermal applications.

Energy Systems & Management

• Energy Storage Management: Critical for intermittent RE sources (solar, wind). Balances supply-demand mismatch. Technologies: Batteries (Li-ion), Pumped Hydro, Flywheels, Thermal Storage, Hydrogen.

• Various Types of Tariffs in Electricity:

  • Flat Rate Tariff: Fixed charge per unit, independent of time/load.

  • Block Rate Tariff: Different rates for different consumption blocks (slab system).

  • Time-of-Day (TOD) Tariff: Varying rates based on peak/off-peak hours to incentivize load shifting.

  • Two-Part Tariff: Fixed charge + variable energy charge.

  • Power Factor Tariff: Incentive/penalty based on power factor (cos φ).

• Environmental Benefits (e.g., Geothermal): Minimal GHG emissions (mostly steam & minor CO₂/H₂S), small land footprint, low visual impact, baseload capability reduces need for fossil peaker plants.

[!TIP] Exam Focus: Distinguish between Global Warming & Climate Change. Know the 4 main types of tariffs and their purpose. Link energy storage to grid stability.

II. SOLAR ENERGY

Solar Radiation & Geometry

• Sun-Earth Relationship: Earth's revolution (365.25 days) around Sun causes seasons. Rotation (24 hrs) causes day/night.

• Key Angles & Formulas:

  • Declination (δ): Angle between Sun's rays & equatorial plane. Varies ±23.45° annually.

$$ \delta = 23.45^\circ \sin\left(\frac{360}{365}(284 + n)\right) $$

where n = day number.

*   **Hour Angle (ω):** Angular displacement of Sun from local solar noon. ω = 15° × (hours from solar noon).

*   **Solar Altitude Angle (α):** Angle between Sun's rays & horizontal plane.

$$ \sin\alpha = \sin\phi\sin\delta + \cos\phi\cos\delta\cos\omega $$

where φ = latitude.

*   **Zenith Angle (θ_z):** Angle between Sun's rays & vertical. θ_z = 90° - α.

*   **Incidence Angle (θ):** Angle between Sun's rays & normal to the surface.

    For a surface tilted at angle β from horizontal and azimuth γ (from south):

$$ \cos\theta = \sin\phi\sin\delta\cos\beta - \sin\phi\sin\delta\sin\beta\cos\gamma + \cos\phi\sin\delta\sin\beta\sin\gamma + \cos\phi\cos\delta\cos\beta\cos\omega + \sin\phi\cos\delta\sin\beta\cos\gamma\cos\omega + \cos\delta\sin\beta\sin\gamma\sin\omega $$

    **For south-facing surface (γ=0):**

$$ \cos\theta = \sin\phi\sin\delta\cos\beta + \cos\phi\cos\delta\cos\beta\cos\omega + \cos\phi\sin\delta\sin\beta\sin\omega $$

• Solar Radiation on Tilted Surface (I_T):

$$ I_T = I_b \cos\theta + I_d \left(\frac{1+\cos\beta}{2}\right) + I_r \left(\frac{1-\cos\beta}{2}\right) $$

Where `I_b` = beam radiation, `I_d` = diffuse radiation, `I_r` = ground-reflected radiation (≈ 0.2 * (I_b cosθ_z + I_d) for grass/soil).

• Measurement: Pyranometer (global), Pyrheliometer (direct), Pyrgeometer (IR), Sunshine recorder (duration).

Solar Thermal Systems

• Solar Collectors Classification:

  • By Concentration: Non-concentrating (flat plate), Concentrating (parabolic trough, dish, tower).

  • By Heat Transfer Fluid: Liquid (water, oil, glycol), Air (air heaters).

  • By Temperature: Low (<100°C), Medium (100-250°C), High (>250°C).

• Flat Plate Collector (FPC):

  • Construction: Absorber plate (selective coating) with fluid tubes, insulated back, transparent glazing (low iron glass), casing.

    DiagramCANVAS: Show cross-section: glass, air gap, black absorber plate with serpentine tubes, insulation at back

  • Working: Sunlight passes through glazing, absorbed by plate → heats fluid in tubes → useful heat extracted. Glazing reduces convective/radiative losses.

  • Applications: Water heating (domestic, industrial), space heating, industrial process heat.

• Solar Water Heating Systems:

  • Thermosyphon (Natural Circulation): Tank above collector. Density difference drives flow (hot fluid rises). Simple, no pump, reliable. Requires careful mounting.

  • Forced Circulation: Pump circulates fluid. Allows flexible mounting (tank can be below), better control, larger systems. Requires power for pump & controller.

• Example: A typical domestic system: 2-3 m² FPC, 200L insulated tank, thermosyphon configuration for 4-5 persons.

Solar Photovoltaic (PV) Systems

• Principle of Photovoltaic Conversion (Photoelectric Effect):

  1. Photon (energy E = hν = hc/λ) strikes semiconductor (e.g., Si).

  2. If photon energy > bandgap (E_g), electron excites from valence to conduction band, creating electron-hole pair.

  3. PN Junction: Built-in electric field at depletion region separates e-h pairs → electrons to N-side, holes to P-side.

  4. External circuit connected → DC current flows. No moving parts, silent operation.

• Solar Cell Technology:

  • Crystalline Silicon (c-Si): Dominant (>90% market).

    • Monocrystalline (mono-Si): Single crystal, high efficiency (18-24%), uniform dark blue, expensive.

    • Polycrystalline (poly-Si): Multiple crystals, lower efficiency (15-20%), blue speckled, cheaper.

  • Thin-Film: Semiconductor layer (few µm) on substrate (glass, plastic).

    • Amorphous Silicon (a-Si): Lower efficiency (6-10%), less temperature sensitive, flexible.

    • CdTe, CIGS: Higher efficiency thin-film (15-22%), cheaper material usage.

• PV System Components:

  • Standalone: PV array → Charge Controller → Battery → Inverter (AC) → Load.

  • Grid-Connected: PV array → Inverter (synchronized with grid) → Grid + Load (net metering).

• Limitations of SPV Systems:

  • Intermittency & Variability: Depends on weather, day/night, season.

  • Low Conversion Efficiency: Typically 15-22% for commercial modules.

  • High Initial Cost: Though LCOE decreasing.

  • Storage Requirement: For off-grid/night supply (adds cost).

  • Land Area: Large utility-scale farms require significant space.

  • Temperature Sensitivity: Efficiency decreases with rising temperature (~0.4%/°C for Si).

• Maximum Power Point Tracking (MPPT) - Perturb & Observe (P&O):

  1. Measure initial PV array voltage (V) & current (I), calculate power (P).

  2. Perturb: Slightly increase/decrease duty cycle (D) of DC-DC converter → changes V.

  3. Observe: Measure new P. If P increases, continue perturbing in same direction. If P decreases, reverse perturbation direction.

  4. Repeat → converges to Maximum Power Point (MPP).

  • Simple, but oscillates around MPP under rapidly changing irradiance.

• Energy-Wavelength Relation: Photon energy $$\displaystyle E = h\nu = \frac{hc}{\lambda} $$.

  • Given: $$\displaystyle \lambda = 1\ \mu m = 10^{-6}\ m $$, $$\displaystyle h = 6.626 \times 10^{-34}\ J\cdot s $$, $$\displaystyle c = 3 \times 10^8\ m/s $$, $$\displaystyle 1\ eV = 1.602 \times 10^{-19}\ J $$.

$$ E = \frac{(6.626 \times 10^{-34}) \times (3 \times 10^8)}{10^{-6}} = 1.988 \times 10^{-19}\ J $$

$$ E = \frac{1.988 \times 10^{-19}}{1.602 \times 10^{-19}} \approx 1.24\ eV \ \boxed{} $$

[!TIP] Exam Focus: Derive/state PV principle. Know 3 types of Si cells & 2 thin-film types. Explain P&O algorithm steps. Calculate incidence angle & tilted radiation. Common Pitfall: Forgetting to convert units in E=hc/λ calculation.

III. WIND ENERGY

Wind Resource & Aerodynamics

• Energy Estimation of Wind Regimes: Characterized by Weibull distribution (k = shape, c = scale). Mean power density depends on wind speed frequency. Requires long-term (1+ yr) wind data at hub height.

• Derivation of Power Developed from Wind:

  1. Mass flow rate through rotor: $$\displaystyle \dot{m} = \rho A v $$ (ρ = air density, A = swept area, v = wind speed).

  2. Kinetic energy/sec (power) in wind: $$\displaystyle P_{wind} = \frac{1}{2} \dot{m} v^2 = \frac{1}{2} \rho A v^3 $$.

  3. Betz Limit: Not all wind power can be extracted. Maximum theoretical power coefficient $$\displaystyle C_{p,max} = \frac{16}{27} \approx 0.593 $$ (59.3%).

$$ \boxed{P_{developed} = \frac{1}{2} \rho A v^3 C_p} $$

where $$\displaystyle C_p \leq 0.593 $$.

• Power Coefficient (Cp): Ratio of power extracted by rotor to available wind power. Depends on Tip Speed Ratio (λ = ωR/v) and blade pitch.

• Aerofoil (Airfoil): Cross-sectional shape of a wind turbine blade. Generates lift (perpendicular to flow) and drag (parallel). Goal: Maximize lift/drag ratio (L/D).

  • Types: Symmetric (zero lift at 0° AoA), Cambered (positive lift at 0° AoA). Blades use varying aerofoil along span.

Wind Energy Conversion Systems (WECS)

• Explanation & Types of WECS:

  • Horizontal Axis Wind Turbine (HAWT): Rotating axis parallel to ground/wind. Most common. Requires yaw mechanism. Higher efficiency.

  • Vertical Axis Wind Turbine (VAWT): Rotating axis perpendicular to ground. Omni-directional (no yaw), gearbox can be at ground. Lower efficiency (Darrieus: high speed, Savonius: low speed, high torque).

  • By Power Rating: Micro (<1 kW), Mini (1-100 kW), Small (100 kW - 1 MW), Large (>1 MW).

• Components of Wind Turbine:

  • Rotor (Blades + Hub): Captures wind energy.

  • Nacelle: Housing on top of tower containing:

    • Gearbox: Increases rotor speed to generator speed (often 1:50 to 1:100).

    • Generator: Converts mechanical to electrical (asynchronous/synchronous).

    • Controller: Monitors wind speed, yaws, brakes, etc.

  • Tower: Supports rotor & nacelle. Height increases wind speed (wind shear).

  • Yaw System: Turns nacelle to face wind (HAWT).

  • Braking System: Mechanical, aerodynamic (pitch), electrical.

• Wind Turbine Power Curve: Graph of power output (kW) vs. wind speed (m/s).

  • Cut-in Speed (v_ci): ~3-4 m/s. Turbine starts generating.

  • Rated Speed (v_r): Speed at which rated power is reached.

  • Cut-out Speed (v_co): ~25 m/s. Turbine shuts down for safety.

  • Region II (v_ci < v < v_r): Power increases with $$\displaystyle v^3 $$ (increasing Cp).

• Limitations/Barriers to Large-Scale Utilization:

  • Intermittency & Variability: Unpredictable, requires backup/storage.

  • Grid Integration Challenges: Voltage/frequency fluctuations, need for advanced inverters & grid codes.

  • Land Use & Siting: Requires large areas with consistent high winds; conflicts with agriculture, aviation, wildlife (birds/bats).

  • Noise Pollution: Aerodynamic & mechanical noise.

  • Visual Impact: "Not in my backyard" (NIMBY) opposition.

  • High Capital Cost & Long Payback: Especially offshore.

  • Transmission Needs: Often remote windy sites require new transmission lines.

Hybrid Systems

• Wind-Diesel Hybrid System: Combines wind turbines with diesel generators. Wind reduces diesel consumption & emissions. Diesel provides backup & grid stability. Requires sophisticated control (dump load, battery buffer).

[!TIP] Exam Focus: DERIVE wind power formula & state Betz limit. Draw & label HAWT/VAWT. Explain power curve regions. List at least 5 barriers. Define aerofoil & its purpose.

IV. BIOMASS ENERGY

Biomass Resources & Properties

• Biomass: Organic material from plants/animals (wood, crops, residues, manure, MSW). Stores solar energy via photosynthesis.

• Usefulness: Renewable, carbon-neutral (in sustainable cycle), can be converted to solid, liquid, gaseous fuels. Reduces waste.

• Types: Wood & forest residues, Agricultural residues (straw, husk), Energy crops (sugarcane, jatropha), Animal waste, Municipal Solid Waste (MSW), Industrial waste (sawdust, bagasse).

Biomass Conversion Processes

• Biochemical Conversion:

  • Anaerobic Digestion (Biogas): Microbes break down biomass in absence of O₂. Produces biogas (CH₄ ~55-65%, CO₂ ~35-45%, traces) & digested slurry (fertilizer).

  • Types of Digesters:

    • Batch vs. Continuous: Batch: feed & discharge at intervals; Continuous: constant feed/output, more efficient.

    • Fixed Dome (Chinese): Concrete dome, gas stored above slurry. Simple, low cost, but gas leakage issues.

    • Floating Drum (KVIC): Steel drum floats on slurry as gas holder. Good gas pressure, but steel corrosion/cost.

    • Deenbandhu (India): Modified fixed dome with partition wall, cheaper, reduced gas leakage.

  • Design of Biogas Plant: Key parameters: Retention time (15-50 days), Carbon:Nitrogen ratio (20-30:1 optimal), Moisture content (80-90%), pH (6.6-7.6), Temperature (mesophilic 30-38°C or thermophilic 50-55°C). Sizing based on daily feedstock & retention time.

• Thermochemical Conversion:

  • Biomass Gasification: Partial combustion at 700-900°C with limited air/oxygen → producer gas (CO, H₂, CH₄, CO₂, N₂). Used in engines/gas turbines.

    • Types:

      • Updraft (Countercurrent): Air from bottom, gas from top. High tar, high efficiency.

      • Downdraft (Co-current): Air & gas from same zone. Low tar, suitable for engines.

      • Crossdraft: Air/gas perpendicular. High temp, low tar.

      • Fluidized Bed: Particles suspended by air. Good mixing, uniform temp, scalable.

  • Combustion: Complete oxidation → heat/steam for power.

  • Pyrolysis: Thermal decomposition in absence of air → bio-oil, char, gas.

Biofuels & Photosynthesis

• Photosynthesis: $$\displaystyle 6CO_2 + 6H_2O + light \rightarrow C_6H_{12}O_6 + 6O_2 $$. Converts solar to chemical energy.

  • C3 Plants: First stable product is 3-carbon compound (e.g., rice, wheat, soybean). More efficient under cool/moist conditions, but photorespiration loss at high temp.

  • C4 Plants: First stable product is 4-carbon compound (e.g., maize, sugarcane, sorghum). Minimize photorespiration, more efficient under high light/temp/drought. Higher biomass yield per area.

• Bioethanol: Fermentation of sugar/starch crops (sugarcane, corn) → distillation → fuel. Used in blends (E10, E85).

• Biodiesel: Transesterification of vegetable oils (jatropha, palm) or animal fats with alcohol (methanol) → methyl esters + glycerol. Used in diesel engines (B20, B100).

[!TIP] Exam Focus: Differentiate batch/continuous, fixed dome/floating drum/Deenbandhu. Draw & label any one digester. Compare updraft/downdraft gasifier. Explain C3 vs C4 photosynthesis. List biofuel feedstocks.

V. HYDRO ENERGY

Hydropower Systems Classification

• Based on Installed Capacity:

  • Large Hydro: > 100 MW (often > 25 MW). Major dams, significant environmental impact.

  • Small Hydro (SHP): < 25 MW (or 10-15 MW per Indian definition). Run-of-river or small storage.

  • Mini Hydro: 100 kW - 1 MW.

  • Micro Hydro: < 100 kW (often 5-100 kW). For village/community.

• Key Differentiators (Micro vs. Mini vs. Small):

  • Capacity: Micro (<100 kW), Mini (100 kW - 1 MW), Small (1-25 MW).

  • Head: Micro/Mini often low-medium head (2-30 m), Small can be high head.

  • Civil Works: Micro/Mini minimal, often no large dam (run-of-river). Small may have small weir/dam.

  • Grid Connection: Micro/Mini often isolated/mini-grid. Small usually grid-connected.

  • Environmental Impact: Increases with size; Micro/Mini have minimal footprint.

Hydropower Plant Components & Operation

• Main Components of Small Hydropower System:

  1. Intake/Headrace: Diverts water from river, screens debris.

  2. Penstock: Pressurized pipe delivering water to turbine.

  3. Turbine: Converts hydraulic energy to mechanical.

  4. Generator: Converts mechanical to electrical.

  5. Tailrace: Returns water to river.

  6. Control System: Gates, valves, governor.

• Speed and Voltage Regulation:

  • Speed Regulation: Maintained by governor which adjusts turbine guide vanes/nozzles to keep speed constant as load changes. Critical for grid-connected plants (frequency stability).

  • Voltage Regulation: Achieved by excitation system of generator (adjusting field current) and sometimes tap-changing transformers. Maintains terminal voltage within limits.

Hydraulic Turbines

• Definition & Types (based on Head & Flow):

  • Impulse Turbines (High Head, Low Flow): Pelton Wheel. Nozzles direct high-velocity jets onto buckets (cups) on runner. Pressure constant (atmospheric) in runner. Efficiency high at part-load. Used for H > 300 m.

  • Reaction Turbines (Low-Medium Head, High Flow): Pressure changes as water flows through runner.

    • Francis Turbine (Medium Head): Spiral casing → guide vanes → radial-flow runner → draft tube. Most common, wide range (H=10-300 m).

    • Kaplan Turbine (Low Head): Axial-flow, adjustable blades. Used for H=2-20 m, high flow (e.g., river dams).

  • ** propeller Turbine:** Fixed blades, axial flow, lower efficiency than Kaplan.

• Selection of Turbine for Hydro Plant:

  • Primary Factor: Net Head (H) and Design Flow (Q).

  • Rule of Thumb:

    • H > 300 m: Pelton (Impulse)

    • H = 30-300 m: Francis (Reaction)

    • H < 30 m: Kaplan/Propeller (Reaction, Axial)

  • Also consider: Flow variability, part-load efficiency, cavitation risk, cost, site constraints.

[!TIP] Exam Focus: DRAW & LABEL Pelton, Francis, or Kaplan turbine. State selection criteria clearly with head ranges. Differentiate micro/mini/small hydro on capacity, head, civil works.

VI. GEOTHERMAL ENERGY

Geothermal Resources & Deposits

• Various Types of Geothermal Deposits:

  • Hydrothermal (Most Common): Hot water/steam in permeable rock.

    • Vapor-dominated (Dry Steam): Steam with minor gases (e.g., The Geysers, USA). Direct use for turbines.

    • Liquid-dominated (Wet Steam): Hot water (150-300°C) under pressure → flashes to steam when brought to surface (e.g., Wairakei, NZ). Requires separation.

  • Geo-pressured: Hot water/brine under high pressure (from deep sedimentary basins). Contains dissolved methane.

  • Hot Dry Rock (HDR/EGS): Hot impermeable rock (150-300°C). Requires Enhanced Geothermal Systems (EGS): Inject water to create fractures → circulate → produce steam. Technology developing.

  • Magma: Molten rock (>600°C). Extremely high temp, but technically challenging & risky (drilling into magma).

Geothermal Power Generation

• Generation Process:

  1. Exploration & Drilling: Identify reservoir, drill production & injection wells.

  2. Production: Hot fluid (steam/water) brought to surface.

  3. Separation (if wet steam): Steam separated from water/brine.

  4. Power Generation: Steam drives turbine → generator. Rankine Cycle is standard.

     • Conventional (Single-Flash): Steam directly to turbine.

     • Double-Flash: Steam flashed at two pressures → higher efficiency.

     • Binary Cycle: Hot geothermal fluid heats secondary working fluid (e.g., isobutane, pentane) with lower boiling point in heat exchanger. Vapor drives turbine. Allows lower temp resources (100-150°C). No direct contact with geothermal fluid → less scaling/corrosion.

  5. Condensation & Reinjection: Steam condensed, fluid reinjected to sustain reservoir.

• Principle of Thermodynamics (Rankine Cycle):

  • Basic cycle: Pump (1→2, isentropic compression of liquid) → Boiler/Heat Exchanger (2→3, constant pressure heat addition) → Turbine (3→4, isentropic expansion) → Condenser (4→1, constant pressure heat rejection).

  • Net Work Output: $$\displaystyle W_{net} = (h_3 - h_4) - (h_2 - h_1) $$

  • Thermal Efficiency: $$\displaystyle \eta = \frac{W_{net}}{Q_{in}} = \frac{(h_3 - h_4) - (h_2 - h_1)}{(h_3 - h_2)} $$

  • Binary cycle uses Organic Rankine Cycle (ORC).

• Site Selection of Geothermal Power Plant:

  • High Subsurface Temperature: >150°C for power.

  • Permeable Reservoir: Good natural permeability or amenable to EGS.

  • Adequate Recharge: Sustainable resource.

  • Proximity to Load Centers: To reduce transmission cost.

  • Water Availability: For cooling & reinjection.

  • Minimal Seismic/Volcanic Risk.

  • Accessibility & Infrastructure.

• Environmental Benefits: Very low GHG emissions (mostly steam), small land footprint per MW, baseload power reduces fossil fuel use, minimal visual impact.

[!TIP] Exam Focus: Classify 4 types of geothermal deposits with examples. Draw & explain Binary Cycle ORC. List site selection criteria. Compare vapor vs liquid dominated.

VII. OCEAN ENERGY

Tidal Energy

• Principle of Tidal Energy Conversion:

  • Tides caused by gravitational pull of Moon/Sun → periodic rise/fall in sea level.

  • Potential Energy stored in height difference (tidal range) between high & low tide.

  • Conversion: Trap water at high tide in basin → release through turbines during low tide (or vice versa) → hydraulic head drives turbine → generator.

  • DiagramCANVAS: Single basin tidal plant: dam with gates & turbines separating ocean and basin. Show high tide filling, low tide emptying through turbines.

• Tidal Power Plant Configurations:

  • Single Basin (One-way/Two-way): Simplest. Basin fills on flood tide (may generate or not), empties on ebb tide (generates). Two-way generation possible with reversible turbines.

  • Double Basin: Two basins at different levels. Pumping or generation between them. Smoother output.

  • Barrage: Dam across estuary (like Rance, France). High cost, environmental impact on estuary.

  • Tidal Stream/Turbine: Underwater turbines in fast tidal currents (like wind turbines underwater). No dam, lower environmental impact.

• Numerical Problem (Single Basin, Ebb Generation):

  • Basin Area = A (m²), Tidal Range = R (m), Minimum Operating Head = h_min (m), Turbine-Generator Efficiency = η.

  • Available Potential Energy (per cycle): $$\displaystyle E_{avail} = \frac{1}{2} \rho g A R^2 $$ (assuming linear fall).

  • Useful Energy Generated: $$\displaystyle E_{gen} = \eta \times \frac{1}{2} \rho g A (R - h_{min})^2 $$? Wait, standard formula:

    The energy is extracted only when head > h_min. The effective head for generation is from (R - h_min) down to h_min? Actually, the turbine operates from max head R down to h_min. The average head over the generating period is approximately $$\displaystyle (R + h_{min})/2 $$. But the standard exam formula is:

$$ E_{gen} = \eta \cdot \frac{1}{2} \rho g A (R - h_{min})^2 \quad \text{?} $$

    **Correction:** The potential energy available for generation (when head > h_min) is:

    Volume generated = A × (R - h_min)

    Average head during generation = (R + h_min)/2

    So, $$\displaystyle E_{gen} = \eta \cdot \rho g A (R - h_{min}) \times \frac{(R + h_{min})}{2} = \eta \cdot \frac{1}{2} \rho g A (R^2 - h_{min}^2) $$.

    Often simplified if h_min << R: $$\displaystyle E_{gen} \approx \eta \cdot \frac{1}{2} \rho g A R^2 $$.

    **In past papers (May 2023, May 2024), the formula used is:**

$$ \boxed{E = \eta \cdot \frac{1}{2} \rho g A (R - h_{min})^2} $$

    **But this is incorrect for the stated condition.** The correct derivation gives $$\displaystyle (R^2 - h_{min}^2) $$. However, **for exam purposes, follow the formula pattern from past solutions if provided, or derive logically.** The typical problem states: "turbine stops when head falls below 3m" → generating head range = (12m - 3m) = 9m? No, head varies from 12m to 0m, but operates only when head > 3m. So the **effective head** for energy calculation is the **average head during operation** = (12 + 3)/2 = 7.5m. The **volume** used = A × (12 - 3) = 9A.

    Thus, $$\displaystyle E = \eta \cdot \rho g \cdot (A \cdot 9) \cdot 7.5 = \eta \cdot \rho g A \cdot 67.5 $$.

    The formula $$\displaystyle \frac{1}{2}\rho g A (R^2 - h_{min}^2) = \frac{1}{2}\rho g A (144 - 9) = 67.5 \rho g A $$. **This matches.**

    So the **correct boxed formula** is:

$$ \boxed{E = \eta \cdot \frac{1}{2} \rho g A (R^2 - h_{min}^2)} $$

    where E in Joules, convert to kWh (1 kWh = 3.6e6 J).

Ocean Thermal Energy Conversion (OTEC)

• Principle: Exploits temperature difference between warm surface water (25-30°C) and cold deep water (5-10°C). Small ΔT (~20°C) → low Carnot efficiency (~3-4%).

  • Working Fluid: Low boiling point (e.g., ammonia, freon).

• Types:

  • Closed-Cycle: Warm surface water vaporizes working fluid in evaporator → vapor drives turbine → cold deep water condenses vapor in condenser → liquid pumped back. Most common.

  • Open-Cycle: Warm surface water flash-evaporated in vacuum chamber → low-pressure steam drives turbine → condensed by cold deep water → produces fresh water as by-product.

  • Hybrid-Cycle: Combines aspects (e.g., closed-cycle with flash evaporation).

  • DiagramCANVAS: Closed-cycle OTEC: surface water → evaporator (working fluid vapor) → turbine → condenser (deep water) → pump → back to evaporator.

• Challenges: Low efficiency, high capital cost (large heat exchangers, deep water pipe), biofouling, remote locations.

Wave Energy

• Sea Waves: Generated by wind transferring energy to water surface. Irregular in amplitude & period.

• Significant Wave Height (H_s or H_1/3): Average height of the highest one-third of waves in a given record. Statistically represents wave energy (energy ∝ H_s²). Standard measure for wave climate.

[!TIP] Exam Focus: DRAW single basin tidal plant. DERIVE/STATE tidal energy formula correctly: $$\displaystyle E = \frac{1}{2}\eta\rho g A (R^2 - h_{min}^2) $$. Explain OTEC closed-cycle. Define Significant Wave Height.

VIII. FUEL CELLS

Fundamentals & Working

• Working (Electrochemical): Converts chemical energy of fuel (H₂, CH₄, etc.) & oxidant (O₂/air) directly into electricity via electrochemical reactions. Not combustion.

• Basic Components & Reactions:

  • Anode: Fuel (H₂) is oxidized: $$\displaystyle H_2 \rightarrow 2H^+ + 2e^- $$ (in acidic) or $$\displaystyle H_2 + 2OH^- \rightarrow 2H_2O + 2e^- $$ (alkaline).

  • Cathode: Oxidant (O₂) reduced: $$\displaystyle \frac{1}{2}O_2 + 2H^+ + 2e^- \rightarrow H_2O $$ (acidic) or $$\displaystyle \frac{1}{2}O_2 + H_2O + 2e^- \rightarrow 2OH^- $$ (alkaline).

  • Electrolyte: Conducts ions (H⁺, OH⁻, O²⁻, CO₃²⁻) but blocks electrons. Determines FC type.

  • External Circuit: Electrons flow from anode to cathode → DC electricity.

• Overall Reaction: $$\displaystyle H_2 + \frac{1}{2}O_2 \rightarrow H_2O + \text{Heat} + \text{Electricity} $$. High efficiency (40-60% electrical, >80% with CHP).

Classification & Types (based on Electrolyte)

Applications & Aspects

• Applications: Transportation (fuel cell vehicles), Stationary power (homes, buildings, utilities), Portable power (laptops, phones), Backup power.

• Fuel Cell System Components: Fuel processor (reformer, shift converter, CO cleanup), Fuel cell stack, Power conditioner (DC-AC inverter), Heat recovery system, Controls.

• Advantages:

  • High efficiency (electrical & overall).

  • Zero emissions at point of use (only H₂O for H₂ fuel).

  • Quiet, vibration-free, modular.

  • Fuel flexibility (in high-T types).

  • Rapid refueling (vs. batteries).

[!TIP] Exam Focus: DRAW & LABEL a fuel cell (show anode, cathode, electrolyte, external circuit). Write anode/cathode reactions for acidic medium. Classify 5 types with electrolyte & temp. List 4 advantages.

IX. CROSS-CUTTING & MISCELLANEOUS TOPICS

• Biochemical Conversion Process: Involves microorganisms/enzymes. Anaerobic Digestion (4 stages: Hydrolysis, Acidogenesis, Acetogenesis, Methanogenesis) → Biogas. Fermentation (e.g., ethanol from sugar). Composting (aerobic). Key factors: temperature, pH, C/N ratio, retention time, moisture.

• Power Electronics/Control Context:

  • Solar (MPPT): DC-DC converters (buck/boost) controlled by MPPT algo (P&O, Incremental Conductance) to keep PV at MPP.

  • Wind: Power electronics for variable speed operation (AC-DC-AC converters), grid synchronization, pitch/yaw control.

  • Hydro: Governor controls wicket gates/nozzles for speed regulation; excitation system for voltage.

  • General: Inverters (DC-AC), converters, controllers for grid interfacing, maximum energy capture, and power quality.

• Specific Definitions (from short questions):

  • Solar Collector: Device that absorbs solar radiation and converts it to useful thermal energy (heat).

    DiagramSEARCH: flat plate collector diagram

  • Tidal Energy Conversion: Process of harnessing potential energy of tidal rise/fall by trapping water in a basin and releasing it through turbines.

  • Power Curve of Wind Turbine: Graph showing relationship between wind speed at hub height and electrical power output of the turbine. Defines cut-in, rated, cut-out speeds.

  • Selection of Turbine for Hydro Plant: Based primarily on Net Head (H) and Design Flow (Q). High Head → Impulse (Pelton); Medium Head → Reaction (Francis); Low Head → Reaction Axial (Kaplan). Also consider flow variability, cavitation, cost.

[!TIP] Exam Focus: Link power electronics to each technology's control need. Be ready to define any term from the list concisely. For diagrams, practice neat labeled sketches of PV cell, FPC, HAWT, Pelton/Francis, tidal basin, fuel cell, OTEC.