UNIT 1: COMPREHENSIVE POWER GENERATION & RENEWABLE ENERGY

1.0 INTRODUCTION TO POWER GENERATION & ENERGY SOURCES

1.1 Overview of Electrical Power Generation

• Conventional (Non-Renewable) Sources: Thermal (coal, gas, diesel), Hydro, Nuclear. Depend on finite fossil fuels or specific geography.

• Non-Conventional (Renewable) Sources: Solar, Wind, Biomass, Geothermal, Ocean, Hydrogen. Inexhaustible, environmentally benign.

1.2 Classification of Energy Sources

1.3 Global and Indian Energy Scenario

• Global: Shift towards renewables; solar & wind dominating new capacity. Fossil fuels still ~80% of primary energy.

• India:

  • Current Mix (as of 2024): Thermal ~60%, Renewable ~40% (Wind ~10%, Solar ~15%, Bio ~2%, Hydro ~10%).

  • Targets: 500 GW non-fossil capacity by 2030 (NDC), net-zero by 2070.

  • Policy: National Solar Mission, Wind Policy, Biomass Power/Cogen Programme, International Solar Alliance (ISA).

1.4 Relative Merits and Demerits of Power Generation Sources

[!TIP] Exam Focus: Be prepared to compare at least 3 sources in detail. Highlight capacity factor, environmental impact, and cost as key comparison parameters.

2.0 CONVENTIONAL (NON-RENEWABLE) POWER GENERATION SYSTEMS

2.1 Hydroelectric Power Plants

2.1.1 Site Selection Criteria

• Water Availability: Consistent high flow, good catchment area.

• Head: Height difference (higher head → smaller turbine size). Gross head = reservoir level - tailrace level.

• Geology: Strong rock foundation for dam.

• Accessibility: Proximity to load centers, transport for equipment.

• Environmental & Social: Minimal displacement, ecological impact.

2.2.2 Layout of Hydroelectric Power Plant

1. Dam: Creates reservoir, stores water.

2. Intake: Controls water entry, screens debris.

3. Penstock: Large pipe carries water under pressure to turbine.

4. Surge Tank: Mitigates water hammer pressure rise.

5. Turbine: Converts hydraulic energy to mechanical rotation.

6. Generator: Converts mechanical to electrical energy.

7. Tailrace: Discharges used water back to river.

2.1.3 Types of Turbines

2.1.4 Hydrograph, Flow Duration Curve (FDC), Power Duration Curve (PDC)

• Hydrograph: Graph of discharge (m³/s) vs time (daily, monthly, annual). Shows seasonal variation.

• Flow Duration Curve: Discharge sorted descending vs % time exceeded. Used to estimate firm capacity.

• Power Duration Curve: Power output sorted descending vs % time exceeded. Derived from FDC using $$\displaystyle P = \rho g Q H \eta $$.

2.1.5 Pumped Storage Power Plants

• Principle: Use surplus grid power to pump water from lower to upper reservoir; generate during peak demand by releasing water.

• Layout: Two reservoirs (upper/lower), reversible pump-turbine, penstocks.

• Merits: Rapid response, peak load management, energy storage.

• Demerits: High capital cost, geographical constraints, evaporation losses.

2.1.6 Small-Scale Hydro-Electric Plants

• Capacity: Typically < 10 MW (India: < 5 MW for "small").

• Features: Run-of-river (no large dam), minimal storage, lower environmental impact.

• Applications: Remote area power, mini-grids.

2.2 Thermal (Steam) Power Plants

2.2.1 Site Selection Factors

• Fuel Availability: Proximity to coal mines/ports.

• Water Source: Abundant water for cooling and steam cycle.

• Land: Cheap, levelled, load center proximity.

• Transport: Railway/road for coal handling.

• Environmental: Away from populated areas, pollution dispersion.

2.2.2 Layout of a Modern Steam Power Plant & Heat Line Diagram

1. Coal Handling: Unloading, storage, crushing, pulverizing.

2. Boiler: Burns coal to produce high-pressure steam.

3. Steam Turbine: HP, IP, LP stages expand steam.

4. Generator: Coupled to turbine.

5. Condenser: Condenses exhaust steam to water (creates vacuum).

6. Cooling Tower: Cools condenser cooling water (natural/induced draft).

7. Feedwater Cycle: Economiser, feedwater heaters, pump to boiler.

8. Ash Handling: Collects fly ash & bottom ash.

2.2.3 Key Components and Functions

2.2.4 Water Treatment Plant

• Necessity: Prevent scale (Ca/Mg salts), corrosion (dissolved O₂, CO₂), fouling in boiler tubes.

• Process Overview:

  1. Clarification: Sedimentation, coagulation.

  2. Filtration: Sand filters remove suspended solids.

  3. Softening: Ion exchange (zeolite) removes hardness.

  4. Demineralization: For high-pressure boilers (ion exchange resins).

  5. Deaeration: Removes dissolved gases (O₂, CO₂).

2.2.5 Diesel Power Plant

• Fuel System: Storage tank → filters → fuel pump → injector → combustion chamber.

• Exhaust System: Exhaust manifold → muffler/silencer → chimney. Often includes turbocharger.

2.3 Nuclear Power Plants

2.3.1 Basic Principle

• Nuclear Fission: Heavy nucleus (U-235, Pu-239) splits into lighter nuclei + neutrons + energy (∼200 MeV/fission). Chain reaction sustained.

• Nuclear Fusion: Light nuclei (H, He) combine → heavier + energy (sun). Not yet commercial for power.

2.3.2 Components of a Nuclear Reactor

2.3.3 Types of Reactors

[!TIP] Common Pitfall: LWR uses light water as both coolant and moderator → requires enriched uranium because light water absorbs some neutrons. CANDU uses heavy water (D₂O) as moderator → less neutron absorption → can use natural uranium.

2.3.4 Radioactive Pollution & Environmental Aspects

• Sources: Routine releases (tritium, noble gases), accidents (Chernobyl, Fukushima), waste disposal.

• Impacts: Ionizing radiation → cancer, genetic mutations. Long-lived isotopes (Cs-137, Sr-90) contaminate soil/water.

• Mitigation: Multi-barrier containment, monitoring, exclusion zones.

2.3.5 Nuclear Waste Management

1. Classification: Low-level (clothing, tools), Intermediate-level (reactor components), High-level (spent fuel).

2. Disposal Methods:

   • Near-surface disposal: For low/intermediate waste in engineered vaults.

   • Deep geological repository: For high-level waste (e.g., Yucca Mountain, Finland's Onkalo).

   • Reprocessing: Recover U/Pu from spent fuel (India: Tarapur, Kalpakkam).

3. Storage: Interim storage in pools (wet) or dry casks.

2.3.6 Availability of Nuclear Fuel in India

• Uranium: Limited reserves (Jaduguda, Singhbhum, Tummalapalle). Import-dependent.

• Thorium: Abundant (world's largest reserves in Kerala sands). India's three-stage program: PHWR (U-238 → Pu-239) → Fast Breeder (Pu-239 + Th-232 → U-233) → Thorium-based reactors.

• Current: Mostly PHWRs (CANDU-type), some LWRs (Kudankulam).

2.4 Gas Turbine Power Plants

2.4.1 Principle – Brayton Cycle

Ideal cycle: Isentropic compression → Constant-pressure heat addition → Isentropic expansion → Constant-pressure heat rejection.

• Efficiency: $$\displaystyle \eta = 1 - \frac{1}{r^{(\gamma-1)/\gamma}} $$, where $r$ = pressure ratio, $\gamma$ = specific heat ratio.

2.4.2 Layout of Simple Gas Turbine Plant

1. Compressor: Draws air, compresses (axial/centrifugal).

2. Combustor: Fuel (natural gas, diesel) injected, ignited → high-temperature gases.

3. Turbine: Expands gases to drive compressor & generator.

4. Generator: Output electricity.

5. Exhaust: High-temperature gases released (can use for HRSG in combined cycle).

2.4.3 Classification

• Open Cycle: Air from atmosphere, exhaust to atmosphere (most common).

• Closed Cycle: Working fluid (He, CO₂) recirculated, heat added via external source (nuclear, solar).

2.4.4 Methods to Improve Thermal Efficiency

2.5 Other Conventional Systems – MHD Generation

• Principle: Direct energy conversion. Hot ionized gas (plasma) from combustion passed through magnetic field → induces EMF (Faraday's law) → electricity without moving parts.

• Working: Seeded plasma (e.g., potassium vapor) → high conductivity → electrodes collect current.

• Advantages: High efficiency (theoretical 60-70%), no rotating parts, fast start-up.

• Disadvantages: Very high temperatures (∼2500 K), material challenges, seed recovery needed.

• Status: Experimental (e.g., Soviet U-25, US AVCO).

3.0 RENEWABLE ENERGY SOURCE (RES) TECHNOLOGIES

3.1 Solar Energy

3.1.1 Solar Radiation and Geometry

• Extraterrestrial Radiation: $$\displaystyle I_{sc} = 1367 \ \text{W/m}^2 $$ (solar constant).

• Terrestrial Radiation: Reduced by atmosphere (absorption, scattering).

• Terms for Locating a Point:

  • Latitude (φ): Angular distance from equator.

  • Longitude (λ): Angular distance from Prime Meridian.

  • Declination (δ): Angle between sun-Earth line & equatorial plane. $$\displaystyle \delta = 23.45 \sin\left(\frac{360}{365}(284 + n)\right) $$ degrees, $n$ = day number.

  • Hour Angle (ω): Angular displacement from solar noon. $$\displaystyle \omega = 15^\circ \times \text{hours from noon} $$.

  • Altitude Angle (α): Angle of sun above horizon.

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

• Azimuth Angle (γ): Sun's projection on horizontal plane from south (N Hemisphere).

$$\cos\gamma = \frac{\sin\alpha\sin\phi - \sin\delta}{\cos\alpha\cos\phi}$$

[!TIP] Exam Alert: Solar geometry calculations are frequent. Remember: solar noon when ω=0, α maximum. Sunrise/sunset when α=0.

Example: Calculate α and γ at 9 AM solar time on Sept 1 at φ=23°N.

• $n$ for Sept 1 = 244 → $$\displaystyle \delta \approx 8^\circ $$ (using formula).

• 9 AM solar time → 3 hours from noon → $$\displaystyle \omega = 15 \times 3 = 45^\circ $$.

• $$\displaystyle \sin\alpha = \sin23\sin8 + \cos23\cos8\cos45 = (0.3907)(0.1392) + (0.9205)(0.9903)(0.7071) = 0.0544 + 0.645 = 0.6994 $$ → $$\displaystyle \alpha \approx 44.3^\circ $$.

• $$\displaystyle \cos\gamma = \frac{\sin\alpha\sin\phi - \sin\delta}{\cos\alpha\cos\phi} = \frac{(0.699)(0.3907) - 0.1392}{(0.714)(0.9205)} = \frac{0.273 - 0.1392}{0.657} = \frac{0.1338}{0.657} = 0.2036 $$ → $$\displaystyle \gamma \approx 78.3^\circ $$ (east of south).

3.1.2 Solar Thermal Systems

• Principle: Solar radiation → heat → working fluid (water, oil, air) → thermal energy.

• Classification of Collectors:

  • Flat Plate Collectors:

    • Components: Transparent cover (glass), absorber plate (black-coated), insulation (back/sides), housing.

    • Working: Sunlight passes cover, absorbed by plate → heats fluid in tubes → insulation reduces losses.

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

  • Concentrating Collectors:

    • Parabolic Trough: Linear focus, tracks sun in one axis, heats fluid in tube at focus (e.g., SEGS, India).

    • Parabolic Dish: Point focus, high temperature, Stirling engine or PV at focus.

    • Solar Tower: Heliostats reflect to central receiver on tower → steam generation.

• Performance Factors:

  • Orientation & Tilt: Equator-facing, tilt = latitude for annual max.

  • Insulation: Minimize thermal losses (conduction, convection, radiation).

  • Efficiency: $$\displaystyle \eta = \frac{\text{useful output}}{\text{incident radiation}} $$.

3.1.3 Solar Photovoltaic (PV) Systems

• Principle: Photoelectric effect. Photons with energy > bandgap excite electrons in semiconductor (p-n junction) → electron-hole pairs → electric field separates charges → DC current.

• Key Elements:

  • Solar Cell: Basic unit (silicon, thin-film).

  • Module/Panel: Series/parallel cells encapsulated.

  • Array: Multiple modules.

  • Inverter: DC → AC conversion.

  • Balance of System (BOS): Mounting, wiring, charge controller, batteries (if off-grid).

• Solar Cell I-V Characteristics:

  • Open Circuit Voltage ($$\displaystyle V_{oc} $$): No load, max voltage.

  • Short Circuit Current ($$\displaystyle I_{sc} $$): No voltage, max current.

  • Maximum Power Point (MPP): $$\displaystyle (V_m, I_m) $$ where $$\displaystyle P_m = V_m I_m $$ max.

  • Fill Factor (FF):

$$\text{FF} = \frac{V_m I_m}{V_{oc} I_{sc}}$$

(ideal ≈ 0.7-0.8).

• Efficiency ($\eta$):

$$\eta = \frac{P_m}{\text{incident solar power}} = \frac{V_m I_m}{G \cdot A}$$

, $G$ = irradiance (W/m²), $A$ = cell area (m²).

[!TIP] Numerical Alert: Given $$\displaystyle V_{oc}, I_{sc}, V_m, I_m, G, A $$ → compute FF, $$\displaystyle P_m $$, $\eta$. Ensure units: $A$ in m², $G$ in W/m² → $$\displaystyle P_m $$ in W.

Example (from Dec 2024 paper): $$\displaystyle V_{oc}=0.24 \ \text{V}, I_{sc}=10 \ \text{mA}, V_m=0.14 \ \text{V}, I_m=6.5 \ \text{mA}, G=24 \ \text{W/m}^2, A=4 \ \text{cm}^2 = 4 \times 10^{-4} \ \text{m}^2 $$.

• $$\displaystyle P_m = V_m I_m = 0.14 \times 6.5 \times 10^{-3} = 0.00091 \ \text{W} = 0.91 \ \text{mW} $$.

• Incident power = $$\displaystyle G \cdot A = 24 \times 4 \times 10^{-4} = 0.0096 \ \text{W} = 9.6 \ \text{mW} $$.

• $$\displaystyle \eta = \frac{0.91}{9.6} \times 100\% = 9.48\% $$.

• $$\displaystyle \text{FF} = \frac{0.14 \times 6.5 \times 10^{-3}}{0.24 \times 10 \times 10^{-3}} = \frac{0.00091}{0.0024} = 0.379 $$.

• Types of Solar Cells:

  • Crystalline Silicon: Mono-Si (high efficiency, costly), Poly-Si (lower cost, lower efficiency).

  • Thin Film: CdTe, a-Si, CIGS (flexible, low material, lower efficiency).

3.1.4 Solar Thermal Power Generation

• Schemes:

  1. Steam Rankine: Solar field (troughs/tower) → heat transfer fluid (HTF) → steam generator → steam turbine.

  2. Brayton (Gas): Solar → compressed air → gas turbine.

  3. Combined Cycle: Gas turbine exhaust → HRSG → steam turbine.

• Schematic: Solar field → HTF pump → steam generator → turbine → condenser → cooling tower.

3.2 Wind Energy

3.2.1 Principle

Wind kinetic energy → rotor blades → mechanical rotation → generator → electricity.

3.2.2 Wind Characteristics

• Power in Wind:

$$P_w = \frac{1}{2} \rho A V^3$$

$\rho$ = air density (∼1.225 kg/m³ at sea level), $$\displaystyle A = \pi R^2 $$ (swept area), $V$ = wind speed.

• Wind Speed Distribution: Often follows Weibull distribution: $$\displaystyle f(V) = \frac{k}{c} \left(\frac{V}{c}\right)^{k-1} e^{-(V/c)^k} $$, where $k$ = shape parameter, $c$ = scale parameter.

• Betz Limit: Maximum power extractable = $$\displaystyle \frac{16}{27} \approx 59.3\% $$ of $$\displaystyle P_w $$ due to momentum conservation.

3.2.3 Classification of Wind Turbines

• By Axis:

  • HAWT: Horizontal rotor shaft, yaw mechanism to face wind. Most common (3-blade).

  • VAWT: Vertical rotor shaft (Darrieus – lift type, Savonius – drag type). Omni-directional, no yaw needed.

• By Power Rating: Small (<100 kW), Medium (100 kW–1 MW), Large (>1 MW).

3.2.4 Components of HAWT

1. Blades: Aerodynamic profiles (airfoils) capture wind energy.

2. Rotor: Hub + blades.

3. Nacelle: Housing on top of tower containing:

   • Gearbox: Increases rotor speed (∼20 rpm) to generator speed (∼1500 rpm).

   • Generator: Usually induction or synchronous.

   • Yaw System: Motor-driven to orient nacelle into wind.

   • Brakes: Mechanical (disk) or aerodynamic (blade pitch).

4. Tower: Supports nacelle & rotor, height ↑ wind speed.

5. Foundation: Concrete base.

3.2.5 Site Selection for Wind Power Plants

• Wind Resource Assessment: Wind maps, anemometer mast data (≥1 year), Weibull parameters.

• Topography: Hills, ridges, coastal areas for high wind.

• Grid Proximity: Near transmission lines to reduce evacuation cost.

• Environmental & Social: Avoid bird migration paths, noise limits, visual impact, land use.

3.2.6 Performance and Limitations

• Betz Limit: Theoretical max efficiency 59.3%.

• Capacity Factor: $$\displaystyle \text{CF} = \frac{\text{actual annual energy output}}{\text{rated power} \times 8760 \ \text{h}} $$ (typically 20-40%).

• Intermittency: Wind speed varies → not dispatchable.

• Noise: Aerodynamic (blade swish) & mechanical (gearbox).

• Visual Impact: Large structures, often in scenic areas.

• Avian/Bat Mortality: Collision risk.

3.2.7 Control Schemes

• Pitch Control: Adjust blade angle to regulate power at high wind (above rated).

• Stall Control: Fixed blades; aerodynamic stall limits power naturally (passive).

• Yaw Control: Align nacelle with wind direction (active).

• Power Regulation: Also via generator torque control.

3.2.8 Safety and Environmental Aspects

• Safety: Lightning protection, braking systems, emergency shutdown.

• Environmental: Noise limits, shadow flicker, bird/bat mortality studies, decommissioning plan.

3.3 Biomass Energy

3.3.1 Biomass Resources

• Agricultural residue (straw, husk), forest residue (twigs, bark), energy crops (jatropha, sugarcane), municipal solid waste (MSW), animal waste (dung).

3.3.2 Biomass Conversion Technologies

3.3.3 Biogas Plants

• Principle: Anaerobic digestion (4 stages):

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

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

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

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

• Types:

  • Floating Drum (KVIC): Movable steel drum on slurry, gas collects under drum → constant pressure.

    DiagramSEARCH: KVIC biogas plant floating drum

  • Fixed Dome (Deen Bandhu): Brick/cement dome, gas collects above slurry. Inlet/outlet chambers.

    DiagramSEARCH: Deen Bandhu biogas plant fixed dome

  • Pragati Design: Improved fixed dome with separate inlet/outlet, better mixing.

• Community Biogas Plants: Larger scale (50-100 m³/day) for villages. Operational Problems: Scum formation, temperature control, feed consistency, pathogen survival.

• Materials Used: Cattle dung, poultry litter, food waste, sewage sludge, agricultural residue.

3.3.4 Landfill Gas (LFG) Power Generation

• Principle: Organic waste in landfill decomposes anaerobically → methane (50%) + CO₂ (50%).

• Schematic: Wells drilled in landfill → gas collection system → compressor → cleanup (H₂S, moisture removal) → engine/generator → electricity.

• Advantages: Reduces GHG emissions, energy from waste, odor control.

3.3.5 Biomass Applications

• Power Generation: Direct combustion in boilers → steam turbine.

• Cogeneration (CHP): Simultaneous heat & power (e.g., sugar mills).

• Biofuels:

  • Bioethanol: Fermentation of sugars (sugarcane, corn) → distillation.

  • Biodiesel: Transesterification of vegetable oils/animal fats.

3.3.6 Environmental Problems from Unmanaged Waste

• Open burning → air pollution (PM, CO, VOCs).

• Decomposition → methane (GHG 25× CO₂), leachate → groundwater contamination.

• Vector breeding (mosquitoes, rodents).

3.4 Other Renewable Sources

3.4.1 Geothermal Energy

• Principle: Earth's internal heat (radioactive decay) → hot water/steam reservoirs.

• Types of Resources:

  • Dry Steam: Direct use of steam (e.g., Larderello, Italy).

  • Flash Steam: High-pressure hot water → flashes to steam when brought to surface.

  • Binary Cycle: Moderate temp (100-150°C) geothermal fluid heats secondary fluid (isobutane, pentane) with low boiling point → vapor drives turbine.

    DiagramSEARCH: binary cycle geothermal power plant

• Why Geothermal Fluid Cannot Always Be Flashed? If temperature < 150°C, pressure not high enough to flash → need binary cycle.

• Potential in India: Himalayas (Manikaran), Aravallis, Andaman-Nicobar, Cambay basin. Estimated 10,000 MW.

• Hybrid Geothermal-Fossil Systems:

  • Series: Geothermal preheats feedwater for fossil plant.

  • Parallel: Both supply steam separately to same turbine.

  • Fossil-fired: Geothermal supplements fossil heat.

• Advantages: Baseload, low emissions, small footprint.

3.4.2 Ocean Energy

• Tidal Energy:

  • Principle: Gravitational potential energy of tides (Moon, Sun).

  • Site Selection: High tidal range (>4 m), narrow inlet (barrage feasible), e.g., Gulf of Kutch, Cambay.

  • Schematic Layout (Barrage):

    DiagramSEARCH: tidal barrage power plant layout
    Dam across estuary → sluice gates → turbines in caissons. Low tide generation (ebb), flood generation, or two-way.

• Ocean Thermal Energy Conversion (OTEC):

  • Principle: Temperature gradient between warm surface (∼25°C) and cold deep water (∼5°C) → heat engine.

  • Closed OTEC System: Working fluid (ammonia) evaporates in evaporator (warm seawater) → expands in turbine → condenses in condenser (cold seawater) → pumped back.

    DiagramSEARCH: closed cycle OTEC system diagram

• Wave Energy: Oscillating water column, point absorber, overtopping devices. Brief principle: wave motion → air displacement → turbine.

3.4.3 Hydrogen & Fuel Cells

• Hydrogen as Energy Carrier:

  • Advantages: Clean combustion (H₂O), high energy density (mass), versatile.

  • Disadvantages: Low density (volumetric), storage/transport challenges, production cost (electrolysis energy-intensive).

• Hydrogen Production Methods:

  • Electrolysis (water splitting), Steam reforming (natural gas), Coal gasification, Biomass gasification.

• Hydrogen Storage Methods:

  | Method | Principle | Advantages | Disadvantages | |---------------------|----------------------------------------|---------------------------------|---------------------------------| | Compressed Gas | High-pressure tanks (350-700 bar) | Simple, mature | Low density, heavy tanks | | Liquid Hydrogen | Cryogenic storage (-253°C) | High density | Boil-off losses, costly | | Metal Hydrides | H₂ absorbed in metal lattice (e.g., LaNi₅) | Safe, moderate pressure | Heavy, slow kinetics | | Chemical Hydrides| Chemical compounds (e.g., NaBH₄) | Stable, high H₂ density | Requires chemical reaction |

• Fuel Cells:

  • Principle: Electrochemical conversion: H₂ + ½O₂ → H₂O + electricity + heat. No combustion.

  • Classification by Electrolyte:

    • PEMFC (Polymer Electrolyte): Low temp (80°C), quick start, transport/portable.

    • AFC (Alkaline): High efficiency, space applications.

    • MCFC (Molten Carbonate): High temp (650°C), fuel flexible, stationary.

    • SOFC (Solid Oxide): Very high temp (1000°C), high efficiency, stationary.

3.5 Hybrid and Integrated Systems

• Concept: Combine two or more RES (e.g., solar-wind, solar-biomass, wind-diesel) to overcome intermittency.

• Need: Improve reliability, reduce storage size, optimal resource use.

• Configuration: Parallel (independent sources feed common bus), Integrated (shared converter/storage).

• Advantages: Smooth power output, reduced downtime, better capacity factor.

• Cogeneration (CHP): Simultaneous generation of electricity and useful heat (steam, hot water) from same fuel source. Efficiency 70-90%. Applications: industries, district heating, biomass plants.

4.0 ECONOMICS, OPERATION & PLANNING OF POWER SYSTEMS

4.1 Power Plant Economics

4.1.1 Cost of Electricity Generation

[!TIP] Key Point: Fixed costs incurred regardless of generation; operating costs vary with output.

4.1.2 Tariffs for Electrical Energy

• Peak Load Pricing: Higher tariffs during peak demand hours (e.g., 6-10 PM) to shift load → flatter load curve, reduce need for peaking plants.

4.2 Load Analysis & Forecasting

4.2.1 Key Definitions

• Maximum Demand (Peak Load): Highest load during a period (kW/MW).

• Load Factor (LF): $$\displaystyle \text{LF} = \frac{\text{Average Load}}{\text{Maximum Demand}} < 1 $$ because load varies.

• Capacity Factor (CF): $$\displaystyle \text{CF} = \frac{\text{Actual Energy Output}}{\text{Rated Capacity} \times \text{Time}} < 1 $$ due to maintenance, outages.

• Utilization Factor (UF): $$\displaystyle \text{UF} = \frac{\text{Maximum Demand}}{\text{Installed Capacity}} < 1 $$ because capacity > max demand for reliability.

• Diversity Factor (DF): $$\displaystyle \text{DF} = \frac{\sum \text{Individual Max Demands}}{\text{System Max Demand}} > 1 $$ because peaks don't coincide.

• Plant Load Factor (PLF): Same as CF for a plant.

[!TIP] Why LF, CF, UF < 1? Because systems are not operated at full capacity all the time due to demand variation, maintenance, and reserve requirements.

4.2.2 Load Curves

• Daily Load Curve: Load (kW) vs time (24 h). Shows peak/off-peak.

• Weekly/Monthly/Annual: Aggregated curves for longer periods.

• Load Duration Curve (LDC): Load values sorted descending vs % time. Used for economic dispatch, capacity planning.

• Flow Duration Curve (FDC): Similar for water discharge in hydro plants.

4.2.3 Load Forecasting

• Importance: Unit commitment, maintenance scheduling, fuel procurement, economic dispatch.

• Types:

  • Short-term (hourly/daily): Load following, security.

  • Medium-term (weekly/monthly): Maintenance, fuel planning.

  • Long-term (annual/5-year): Capacity expansion, infrastructure.

4.3 Economic Load Dispatch & Scheduling

4.3.1 Concept

Allocate load among generating units to minimize total fuel cost while meeting demand and constraints.

4.3.2 Incremental Fuel Cost (λ)

• $$\displaystyle \lambda = \frac{dC}{dP} $$ = marginal cost (Rs/MWh).

• Equal Incremental Cost Criterion: For optimum, $$\displaystyle \lambda_1 = \lambda_2 = \cdots = \lambda_n $$ (without losses).

4.3.3 Economic Load Scheduling (Two Units, No Losses)

Given fuel cost functions $$\displaystyle C_1 = a_1 + b_1 P_1 + c_1 P_1^2 $$, $$\displaystyle C_2 = a_2 + b_2 P_2 + c_2 P_2^2 $$, and total load $$\displaystyle P_D = P_1 + P_2 $$.

• Condition: $$\displaystyle \frac{dC_1}{dP_1} = \frac{dC_2}{dP_2} = \lambda $$.

• Solve: $$\displaystyle b_1 + 2c_1 P_1 = b_2 + 2c_2 P_2 $$ and $$\displaystyle P_1 + P_2 = P_D $$.

Example (Jun 2025): $$\displaystyle C_1=50+2P_1+0.005P_1^2 $$, $$\displaystyle C_2=100+2P_2+0.01P_2^2 $$, $$\displaystyle P_D=350 $$ MW.

• $$\displaystyle \frac{dC_1}{dP_1}=2+0.01P_1 $$, $$\displaystyle \frac{dC_2}{dP_2}=2+0.02P_2 $$.

• Set equal: $$\displaystyle 2+0.01P_1 = 2+0.02P_2 $$ → $$\displaystyle P_1 = 2P_2 $$.

• $$\displaystyle 2P_2 + P_2 = 350 $$ → $$\displaystyle P_2 = 116.67 $$ MW, $$\displaystyle P_1 = 233.33 $$ MW.

• $$\displaystyle \lambda = 2 + 0.01 \times 233.33 = 4.333 $$ Rs/MWh.

4.3.4 Effect of Transmission Losses – Penalty Factor

• Loss Formula: $$\displaystyle P_L = \sum_{i=1}^{n} \sum_{j=1}^{n} P_i B_{ij} P_j $$ (B-coefficients).

• Incremental Loss: $$\displaystyle \frac{\partial P_L}{\partial P_i} $$.

• Penalty Factor (PF): $$\displaystyle \text{PF}_i = \frac{1}{1 - \frac{\partial P_L}{\partial P_i}} $$.

• Economic Dispatch with Losses: $$\displaystyle \lambda_i \cdot \text{PF}_i = \lambda $$ (common incremental cost).

Example (Jun 2025): $$\displaystyle \frac{dC_1}{dP_1}=0.15P_1+150 $$, $$\displaystyle \frac{dC_2}{dP_2}=0.25P_2+175 $$, $$\displaystyle P_1=P_2=400 $$ MW, $$\displaystyle \frac{\partial P_L}{\partial P_2}=0.2 $$. Find PF₁.

• At $$\displaystyle P_1=P_2=400 $$: $$\displaystyle \lambda_1 = 0.15 \times 400 + 150 = 210 $$ Rs/MWh, $$\displaystyle \lambda_2 = 0.25 \times 400 + 175 = 275 $$ Rs/MWh.

• PF₂ = $$\displaystyle 1/(1 - 0.2) = 1.25 $$.

• Economic dispatch: $$\displaystyle \lambda_1 \cdot \text{PF}_1 = \lambda_2 \cdot \text{PF}_2 $$.

• $$\displaystyle 210 \cdot \text{PF}_1 = 275 \times 1.25 = 343.75 $$ → $$\displaystyle \text{PF}_1 = 343.75 / 210 = 1.637 $$.

4.3.5 Economic Load Scheduling Problem (Numerical)

Always follow steps:

1. Write incremental cost equations.

2. Set equal (without losses) or with penalty factors (with losses).

3. Use power balance equation.

4. Solve simultaneous equations.

5.0 ENERGY RESOURCE ASSESSMENT & FUTURE PROSPECTS

5.1 Energy Resource Reserve

• Proven Reserves: Quantified, economically recoverable with current technology.

• Probable Reserves: Likely recoverable, less certain.

• Possible Reserves: Potentially recoverable, speculative.

5.2 Renewable Energy Achievements and Applications in India

• Installed Capacity (as of 2024): Total RE ∼190 GW (Wind ∼45 GW, Solar ∼75 GW, Bio ∼11 GW, Hydro ∼52 GW).

• Major Programs:

  • National Solar Mission (100 GW solar by 2022, now 280 GW by 2030).

  • Wind Power Program (repowering, offshore wind).

  • Biomass Power/Cogen (agro-residue based).

  • Small Hydro (subsidies).

  • International Solar Alliance (ISA) – treaty-based org for solar promotion.

5.3 State-wise Renewable Scenario: Tamil Nadu

• Wind: Largest in India (∼9 GW). Favorable sites: Coimbatore, Tirunelveli, Kanyakumari (southern tip).

• Solar: Rapid growth (∼5 GW). High insolation (5-6 kWh/m²/day).

• Policy: Tamil Nadu Solar Energy Policy 2019, wind evacuation infrastructure.

5.4 Future of Renewable Energy in India

• Most Prominent Sources: Solar PV (cost decline, scalability), Onshore Wind (mature, cost-competitive).

• Challenges:

  • Grid integration (variability, need for storage/backup).

  • Land acquisition.

  • Financing.

  • Manufacturing base (solar modules, wind turbines).

• Government Initiatives:

  • Green Energy Corridors: Strengthen transmission for RE.

  • PLI Scheme: Solar module manufacturing.

  • Rooftop Solar: Subsidies for residential/commercial.

  • Offshore Wind: Draft policy, potential in Gujarat/Tamil Nadu.

5.5 Environmental and Safety Aspects of Major RES

• Wind: Noise, shadow flicker, bird/bat mortality, decommissioning.

• Solar: Land use, water consumption (cleaning), toxic materials in thin-film (Cd, Te) – recycling needed.

• Biomass: Air pollution (if combustion inefficient), feedstock sustainability.

• Nuclear: Radioactive waste, accident risk, proliferation concerns.

• Hydro: Displacement, aquatic ecosystem disruption, methane from reservoirs.

[!TIP] Exam Focus: Compare environmental impacts of RES vs conventional. Highlight life-cycle assessment (manufacturing, operation, decommissioning).