UNIT 3: RENEWABLE ENERGY CONVERSION TECHNOLOGIES

I. SOLAR ENERGY

A. Solar Radiation Fundamentals

• Measurement Instruments:

  • Pyranometer: Measures global solar radiation (diffuse + direct) on a horizontal surface.

  • Pyrheliometer: Measures direct normal irradiance (DNI).

  • Pyrometer: Measures total radiation (includes long-wave).

• Units: W/m² or kWh/m²/day.

• Wavelength-Energy Relationship:

  • Energy of a photon: $$\displaystyle E = \frac{hc}{\lambda} $$

  • Where $h$ = Planck's constant, $c$ = speed of light, $\lambda$ = wavelength.

  • Example: $$\displaystyle \lambda = 1\ \mu m = 10^{-6}\ m \rightarrow E \approx 1.24\ eV $$.

• Sun-Earth Relationship:

  • Solar Constant ($$\displaystyle G_{sc} $$): ~1361 W/m² (extraterrestrial radiation on a plane perpendicular to sun's rays at 1 AU).

  • Extraterrestrial Radiation ($$\displaystyle H_0 $$): On a horizontal surface at Earth's outer atmosphere, varies with day of year.

[!TIP] Common Exam Question: "Show that λ = 1 μm corresponds to 1.24 eV." Use $$\displaystyle E(eV) = \frac{1240}{\lambda(nm)} $$.

B. Solar Geometry

• Key Angles:

  • Solar Altitude Angle ($\alpha$): Angle between sun's rays and horizontal plane.

  • Solar Azimuth Angle ($$\displaystyle \gamma_s $$): Angle of sun's projection on horizontal plane from south (N. Hemisphere).

  • Angle of Incidence ($\theta$): Angle between sun's rays and normal to surface.

• Solar Time: $$\displaystyle ST = LT + \frac{4(L_{st} - L_{loc})}{60} + EOT $$ (in minutes).

• Radiation on Tilted Surface:

$$H_T = H_b \cos\theta + H_d \left(\frac{1+\cos\beta}{2}\right) + H \rho_g \left(\frac{1-\cos\beta}{2}\right)$$

Where $\beta$ = tilt angle, $$\displaystyle \rho_g $$ = ground reflectance.

[!TIP] For south-facing tilted surface in N. Hemisphere, $$\displaystyle \cos\theta = \sin\delta\sin\phi\cos\beta - \sin\delta\sin\beta\cos\phi\cos\gamma + \cos\delta\cos\phi\cos\beta\cos\omega + \cos\delta\sin\beta\sin\phi\cos\gamma\cos\omega + \cos\delta\sin\beta\sin\gamma\sin\omega $$.

C. Solar Thermal Systems

• Classification:

  • Flat Plate Collectors: Low temperature (<100°C), no tracking.

  • Concentrating Collectors: High temperature (>100°C), use optics (parabolic trough, dish, tower).

• Flat Plate Collector Construction:

  • Components: Absorber plate (black coated), riser tubes, glazing (glass), insulation, casing.

  • Working: Solar radiation passes through glazing, absorbed by plate, heats fluid in tubes.

• Solar Water Heating Systems:

  • Thermosyphon (Natural Circulation): Density-driven flow, no pump. Tank above collector.

  • Forced Circulation: Pump circulates fluid, allows flexible tank placement.

• Applications: Domestic hot water, swimming pool heating, industrial process heat, drying.

D. Photovoltaic (PV) Systems

• Principle of Photovoltaic Conversion:

  1. Photon Absorption: Photon with $$\displaystyle E > E_g $$ (bandgap) excites electron from valence to conduction band.

  2. p-n Junction: Built-in electric field separates electron-hole pairs.

  3. Current Flow: Electrons move to n-side, holes to p-side → DC current.

• Solar Cell Types:

  | Type | Material | Efficiency | Features | |----------|--------------|----------------|--------------| | Crystalline Si | Mono-Si, Multi-Si | 15-22% | Mature, durable, high cost | | Thin-Film | a-Si, CdTe, CIGS | 7-13% | Low cost, flexible, less material |

• PV System Components:

  • PV modules/arrays

  • Inverter (DC-AC conversion)

  • Charge Controller (prevents overcharge)

  • Battery Bank (for storage, e.g., lead-acid, Li-ion)

  • Mounting structures, wiring.

• Applications:

  • Standalone (remote homes, street lights)

  • Grid-connected (rooftop, solar farms)

  • Specific: PV-powered water pumps, telecom towers.

• Limitations:

  • Low efficiency (~20% max)

  • Intermittent (day/night, weather)

  • High initial cost, need for storage/inverters.

• Maximum Power Point Tracking (P&O Algorithm):

  1. Measure initial $$\displaystyle V_{mp}, I_{mp} $$, calculate $$\displaystyle P_{mp} $$.

  2. Perturb voltage (ΔV) slightly.

  3. Measure new $P$.

  4. If $$\displaystyle P_{new} > P_{old} $$ → continue perturbation in same direction.

  5. If $$\displaystyle P_{new} < P_{old} $$ → reverse perturbation direction.

  6. Repeat periodically.

[!TIP] P&O causes power oscillation around MPP under rapidly changing irradiance. Use "dP/dV" or "dP/dI" for improved versions.

E. Solar Energy Calculations

• Solar Geometry Problem Steps:

  1. Calculate day angle $\delta$ (use approximations or NREL charts).

  2. Find solar time, hour angle $\omega$.

  3. Compute $\cos\theta$ for given $\phi, \beta, \gamma$.

  4. Calculate $$\displaystyle H_T $$ using available $$\displaystyle H_b, H_d $$.

• Wavelength-Energy Conversion:

$$E(eV) = \frac{1240}{\lambda(nm)}$$

Example: $$\displaystyle \lambda = 1\ \mu m = 1000\ nm \rightarrow E = 1.24\ eV $$.

II. WIND ENERGY

A. Wind Fundamentals

• Aerofoil:

  • Definition: Shape designed to generate lift when air flows over it.

  • Lift: Force perpendicular to flow direction (primary for HAWT).

  • Drag: Force parallel to flow (parasitic).

  • Types:

    • Symmetrical: Zero lift at 0° AoA.

    • Cambered: Curved, generates lift at 0° AoA.

• Power in Wind Derivation:

  • Mass flow rate: $$\displaystyle \dot{m} = \rho A v $$

  • Kinetic energy/sec: $$\displaystyle P_{wind} = \frac{1}{2} \dot{m} v^2 = \frac{1}{2} \rho A v^3 $$

  • Betz Limit: Max $$\displaystyle C_p = \frac{16}{27} \approx 0.593 $$ (theoretical max).

  • Actual turbine power:

$$P = \frac{1}{2} \rho A v^3 C_p$$

• Power Curve:

  • Cut-in speed ($$\displaystyle v_{ci} $$): ~3-4 m/s, turbine starts.

  • Rated speed ($$\displaystyle v_r $$): Design speed, max power.

  • Cut-out speed ($$\displaystyle v_{co} $$): ~25 m/s, turbine stops for safety.

B. Wind Energy Conversion Systems (WECS)

• Types:

  | Type | Axis | Examples | Pros/Cons | |----------|----------|--------------|---------------| | HAWT | Horizontal | 3-bladed, upwind/downwind | High efficiency, need yaw control, tall tower | | VAWT | Vertical | Darrieus (lift), Savonius (drag) | Omni-directional, low tower, low efficiency (Savonius) |

• Components:

  • Rotor (blades, hub)

  • Gearbox (increases generator speed)

  • Generator (AC/DC)

  • Tower (height ↑ wind speed)

  • Control systems (yaw, pitch, brake).

• Diagrams:

  DiagramSEARCH: "HAWT 3-blade upwind diagram"
  ,
  DiagramSEARCH: "Darrieus VAWT diagram"
  .

C. Wind Resource Assessment

• Weibull Distribution:

  • Probability density: $$\displaystyle f(v) = \frac{k}{c} \left(\frac{v}{c}\right)^{k-1} e^{-(v/c)^k} $$

  • $k$ = shape parameter (2-3 typical), $c$ = scale parameter (mean wind speed).

• Wind Rose: Graphical representation of wind speed/frequency by direction.

• Energy Density: $$\displaystyle E_d = \frac{1}{2} \rho \int_0^\infty v^3 f(v) dv $$ (kWh/m²/year).

D. Challenges and Limitations

• Intermittency: Variable wind → grid stability issues.

• Grid Integration: Need for backup/flexible generation.

• Environmental: Noise, bird/bat mortality, visual impact.

• Cost: High capital, O&M, transmission to remote sites.

• Site Specific: Requires high wind resource (>6 m/s avg).

E. Hybrid and Integrated Systems

• Wind-Diesel Hybrid:

  • Configuration: Wind turbines + diesel gensets + battery/flywheel storage.

  • Operation: Wind supplies base load, diesel fills gaps; reduces fuel consumption by 30-60%.

  • Advantages: Reliable power in remote areas, lower emissions, fuel savings.

III. BIOMASS ENERGY

A. Biomass Resources

• Definition: Organic material from plants/animals (carbon-based).

• Usefulness: Renewable, carbon-neutral (closed CO₂ cycle), waste-to-energy.

• Types:

  • Energy crops (switchgrass, miscanthus)

  • Agricultural residues (straw, bagasse)

  • Forest waste (wood chips, sawdust)

  • Municipal solid waste (organic fraction)

  • Animal manure.

• Photosynthesis:

  | Pathway | CO₂ Fixation | Efficiency | Examples | |-------------|-----------------|----------------|--------------| | C3 | Rubisco, 3-carbon compound | Lower (photorespiration) | Wheat, rice, trees | | C4 | PEPCase, 4-carbon compound | Higher (no photorespiration) | Maize, sugarcane, sorghum |

B. Biomass Conversion Processes

• Thermochemical:

  • Combustion: Direct burning → heat/steam (e.g., biomass boiler).

  • Gasification: Partial oxidation → producer gas (CO, H₂, CH₄).

    • Types: Updraft, downdraft, crossdraft, fluidized bed.

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

• Biochemical:

  • Anaerobic Digestion: Microbial breakdown → biogas (CH₄ + CO₂).

  • Fermentation: Sugars → ethanol (via yeast).

• Detailed Biochemical Process (Anaerobic Digestion):

  1. Hydrolysis: Complex organics → simple sugars, amino acids.

  2. Acidogenesis: Sugars → volatile fatty acids, alcohols, CO₂, H₂.

  3. Acetogenesis: Acids/alcohols → acetic acid, H₂, CO₂.

  4. Methanogenesis: Acetic acid/H₂/CO₂ → CH₄ + CO₂ (methanogens).

C. Biogas Production

• Digester Types:

  | Type | Design | Operation | Use | |----------|------------|---------------|---------| | Batch | Fixed volume, loaded once | Simple, low cost | Small scale | | Continuous | Continuous feed/output | Steady production | Common | | Fixed Dome | Concrete/ masonry dome | No moving parts | Rural India (KVIC) | | Floating Drum | Movable gas holder | Easy pressure control | Bangladesh |

• Biogas Plant Components:

  • Inlet (feed slurry), digester tank (anaerobic zone), gas holder, outlet (effluent), heating system (maintain 35-40°C), agitation.

D. Biomass Gasification for Power Generation

• Power Generation Types:

  1. Direct (Open Cycle): Producer gas → engine/gas turbine → electricity.

  2. Indirect (Closed Cycle): Gas cleaned → gas turbine (higher efficiency, cleaner).

  3. Combined Cycle: Gas turbine + steam turbine (from heat recovery) → highest efficiency (~40%).

IV. HYDRO ENERGY

A. Hydropower System Classification

B. Turbines

• Impulse Turbines (Pelton):

  • High head (100-2000 m), low flow.

  • No pressure change in runner; water jets hit buckets.

• Reaction Turbines:

  • Francis: Medium head (10-300 m), medium flow. Spiral casing, wicket gates, runner.

  • Kaplan: Low head (2-20 m), high flow. Adjustable blades.

  • Bulb: Very low head (<10 m), bulb generator inside flow.

• Selection Criteria:

$$n \approx \frac{H^{0.5}}{Q^{0.25}}$$

(specific speed $$\displaystyle n_s $$)

• High $$\displaystyle n_s $$ → Kaplan, low $$\displaystyle n_s $$ → Pelton.

• Francis Turbine Diagram:

  DiagramCANVAS: "Spiral casing → stay vanes → wicket gates → runner (flow over blades) → draft tube (pressure recovery)"
  .

C. Hydropower Plant Operation

• Speed Regulation: Governor senses speed deviation → adjusts wicket gates → maintains constant speed (freq).

• Voltage Regulation: Excitation system controls generator field current → maintains terminal voltage.

• Load-Frequency Control: Primary (governor droop), secondary (AGC), tertiary (dispatch).

• Main Components of Small Hydro:

  • Dam/weir → Penstock (pressure pipe) → Turbine → Generator → Transformer → Grid/Load.

V. GEOTHERMAL ENERGY

A. Geothermal Resources

• Types of Deposits:

  | Type | Description | Temp | Example | |----------|-----------------|----------|-------------| | Hydrothermal | Hot water/steam in porous rock | 150-350°C | The Geysers (dry steam), Larderello | | Geopressured | Hot brine under high pressure | 90-180°C | Gulf Coast, USA | | Hot Dry Rock (HDR) | Impermeable hot rock, need fracturing | >150°C | Soultz, France | | Magma | Molten rock | >600°C | Iceland (experimental) |

• Site Selection:

  1. Resource Assessment: Geological, geochemical, geophysical surveys.

  2. Drilling: Exploratory wells to confirm T, flow rate.

  3. Environmental: Emissions (H₂S, CO₂), land use, seismic risk.

  4. Proximity to Load: Transmission cost.

B. Geothermal Power Generation

• Processes:

  • Dry Steam: Direct use of geothermal steam → turbine.

  • Flash Steam: High-pressure hot water → flash tank (partial vaporization) → steam to turbine.

  • Binary Cycle: Geothermal fluid heats secondary fluid (low bp, e.g., isobutane) → vapor → turbine (closed loop, no emissions).

• Thermodynamics: Based on Rankine cycle.

  • Heat source: geothermal reservoir.

  • Working fluid: water (dry/flash) or organic fluid (binary).

  • Condenser cooling (air/water).

C. Environmental Aspects

• Benefits:

  • Low GHG emissions (5% of coal plant).

  • Small land footprint (per MW).

  • Base-load capability (high capacity factor >90%).

  • Minimal fuel cost (resource is free).

• Concerns: Subsidence, induced seismicity (HDR), brine disposal, H₂S emissions (mitigated).

VI. OCEAN ENERGY

A. Tidal Energy

• Principle: Convert potential energy of tidal rise/fall into kinetic energy via turbines.

• Single Basin System:

  • Basin separated from sea by barrage with sluices and turbines.

  • Filling: Tide rises → open sluices → water enters basin → close sluices at high tide → open turbines → empty basin through turbines (generation).

  • Energy per cycle:

$$E = \frac{1}{2} \rho g A H^2 \eta_t \ \text{(Joules)}$$

Where $H$ = tidal range (m), $A$ = basin area (m²), $$\displaystyle \eta_t $$ = turbine-gen efficiency.

• Double Basin: Two basins at different phases → continuous generation.

B. Ocean Thermal Energy Conversion (OTEC)

• Principle: Exploit temperature gradient ($\Delta T \approx 20°C$) between warm surface water and cold deep water.

• Cycles:

  • Closed Cycle: Working fluid (e.g., ammonia) evaporates in warm water → turbine → condenses with cold water.

  • Open Cycle: Warm seawater flash-evaporated → steam → turbine → condensed (produces desalinated water).

  • Hybrid: Combination.

• Efficiency: Low (~3-4%) due to small $\Delta T$.

C. Wave Energy

• Significant Wave Height ($$\displaystyle H_{1/3} $$): Average height of highest one-third of waves in a record. Statistical measure of wave energy potential.

VII. FUEL CELLS

A. Working Principle

• Electrochemical Reactions:

  • Anode: Fuel (H₂) → $$\displaystyle H_2 \rightarrow 2H^+ + 2e^- $$

  • Cathode: Oxidant (O₂) + $$\displaystyle 4H^+ + 4e^- \rightarrow 2H_2O $$

  • Overall: $$\displaystyle 2H_2 + O_2 \rightarrow 2H_2O + \text{heat} + \text{electricity} $$

• Key: Electrolyte allows ion (H⁺, O²⁻, CO₃²⁻) flow but blocks electrons → external circuit.

B. Classification (by electrolyte & temperature)

C. Fuel Cell Systems for Electricity Generation

• Components:

  1. Fuel Processor: Reforms hydrocarbon fuel → H₂ (e.g., steam methane reformer).

  2. Fuel Cell Stack: Series of cells → DC output.

  3. Power Conditioner: Inverter (DC-AC), power electronics.

  4. Heat Recovery System: For CHP (combined heat and power).

D. Advantages and Applications

• Advantages:

  • High efficiency (40-60%, up to 85% with CHP).

  • Low emissions (only H₂O if H₂ fuel).

  • Modular, scalable.

  • Quiet, no moving parts in stack.

• Applications: Transportation (FCEVs), stationary power (homes, data centers), portable devices.

VIII. ECONOMIC AND POLICY ASPECTS

A. Electricity Tariffs

• Types:

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

  • Block Rate: Increasing slabs (higher consumption → higher rate).

  • Time-of-Use (TOU): Different rates for peak/off-peak hours.

  • Renewable Energy Tariffs: Feed-in tariffs (FiT) for renewable generators, preferential rates.

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

IX. CROSS-CUTTING CALCULATIONS AND NUMERICAL PROBLEMS

A. Solar Geometry and Radiation

• Example (Solar Angle):

  Given: $$\displaystyle \phi = 28°35'N $$, $$\displaystyle \beta = \phi + 10° $$, south-facing, Dec 1, 9:00 AM solar time.

  Steps:

  1. $\delta$ (Dec 1) ≈ -21.5° (approx).

  2. $$\displaystyle \omega = 15° \times (9 - 12) = -45° $$.

  3. $$\displaystyle \cos\theta = \sin\delta\sin\phi\cos\beta - \sin\delta\sin\beta\cos\phi\cos\gamma + ... $$ (use formula with $$\displaystyle \gamma=0° $$ for south).

  4. Compute $\theta$.

B. Wind Power and Energy Estimation

• Weibull Mean Power:

$$P_{avg} = \frac{1}{2} \rho A C_p \int_0^\infty v^3 f(v) dv = \frac{1}{2} \rho A C_p c^3 \Gamma\left(1+\frac{3}{k}\right)$$

Where $\Gamma$ = gamma function.

• Annual Energy: $$\displaystyle E = P_{avg} \times 8760\ h \times $$ availability factor.

C. Tidal Energy Calculation (Single Basin)

• Formula:

$$E = \frac{1}{2} \rho g A H^2 \eta_t$$

Given: $$\displaystyle A = 30 \times 10^6\ m^2 $$, $$\displaystyle H = 12\ m $$, $$\displaystyle \eta_t = 0.73 $$, $$\displaystyle \rho = 1025\ kg/m^3 $$, $$\displaystyle g = 9.81\ m/s^2 $$.

$$E = \frac{1}{2} \times 1025 \times 9.81 \times 30 \times 10^6 \times 12^2 \times 0.73\ J$$

Convert to kWh: divide by $$\displaystyle 3.6 \times 10^6 $$.

\boxed{E \approx 5.07 \times 10^9\ kWh} (verify with precise calc).

D. Solar Radiation Wavelength-Energy Conversion

• Formula:

$$E(eV) = \frac{1240}{\lambda(nm)}$$

For $$\displaystyle \lambda = 1\ \mu m = 1000\ nm $$:

$$E = \frac{1240}{1000} = 1.24\ eV$$

Assumptions: Photon energy in vacuum, $$\displaystyle hc = 1240\ eV·nm $$.

[!TIP] Tidal energy: Only effective head $$\displaystyle H_{eff} = H - h_{min} $$ if turbine stops below $$\displaystyle h_{min} $$. Here $$\displaystyle H_{eff} = 12 - 3 = 9\ m $$? Actually formula uses full range $H$ but turbine operates only when head >3m. In single basin filling/emptying, effective head varies. Simplified calculation often uses average head ≈ $2H/3$ or integrate. Exact: $$\displaystyle E = \frac{1}{2} \rho g A \eta_t \int_0^H h^2 dh $$? No, energy = $$\displaystyle \rho g A \eta_t \int_0^H h\ dh $$ (potential energy) = $$\displaystyle \frac{1}{2} \rho g A H^2 \eta_t $$ if turbine operates full range. But if stops below 3m, effective $$\displaystyle H_{eff} = 9\ m $$? Actually the energy extracted is from head 12m down to 3m, so average head = (12+3)/2 = 7.5m? Better: $$\displaystyle E = \rho g A \eta_t \int_{h_{min}}^{H} h\ dh = \frac{1}{2} \rho g A \eta_t (H^2 - h_{min}^2) $$. So $$\displaystyle H^2 - h_{min}^2 = 144 - 9 = 135 $$. Then $$\displaystyle E = \frac{1}{2} \times 1025 \times 9.81 \times 30 \times 10^6 \times 135 \times 0.73\ J $$. This is more accurate.