UNIT 4: Power Generation Technologies & Economics

1. Fundamentals of Energy Sources and Conversion

Primary vs Secondary Energy Sources

• Primary Energy Sources: Naturally occurring sources in raw form, directly usable or convertible.

  Examples: Coal, crude oil, natural gas, uranium (nuclear), solar radiation, wind, hydro (potential energy of water).*

• Secondary Energy Sources: Derived from primary sources after conversion/processing.

  Examples: Electricity, gasoline, diesel, hydrogen, processed biomass (pellets).*

• Interconvertibility: Energy can be converted from one form to another, governed by the First Law of Thermodynamics (conservation) and limited by the Second Law (efficiency losses).

  Example: Chemical energy (coal) → Thermal energy → Mechanical energy (turbine) → Electrical energy.

[!TIP] Exam often asks to list examples and explain why direct use of primary sources (like solar thermal) is sometimes preferable to conversion to secondary (like PV electricity).

Direct Energy Conversion Methods

Classification:

1. Electromagnetic: Solar PV (photovoltaic).

2. Electrochemical: Fuel cells, batteries.

3. MagnetoHydroDynamic (MHD): Direct conversion of thermal/kinetic energy to electricity without rotating machinery.

MagnetoHydroDynamic (MHD) Converter

• Working Principle: Based on Faraday's Law of Electromagnetic Induction. Ionized hot gas (combustion products seeded with alkali metal vapour like potassium) is passed through a magnetic field. The motion of charged particles (ions/electrons) across the magnetic field induces an electromotive force (EMF) across electrodes placed perpendicular to both flow and field.

• Sketch Description: A duct with inlet, outlet, electrodes on side walls, magnet poles above/below. Seeded combustion gases enter hot, exit cooler.

• Factors Limiting Commercial Use:

  • Material Limitations: Electrodes and ducts exposed to ~2000°C corrosive plasma.

  • Low Electrical Conductivity: Requires high-temperature seeding, adding complexity.

  • Seed Recovery & Corrosion: Potassium seed must be recovered, handling corrosive by-products.

  • High Initial Cost & Complexity.

  • Competition from more mature combined cycle plants.

Fuel Cells

• Definition: An electrochemical device that converts chemical energy of a fuel (anode) and oxidant (cathode) directly into electricity and heat, bypassing Carnot cycle limitations.

• Working Principle:

  1. Fuel (e.g., H₂) oxidized at anode: $$\displaystyle \text{H}_2 \rightarrow 2\text{H}^+ + 2\text{e}^- $$

  2. Oxidant (O₂ from air) reduced at cathode: $$\displaystyle \frac{1}{2}\text{O}_2 + 2\text{H}^+ + 2\text{e}^- \rightarrow \text{H}_2\text{O} $$

  3. Ions migrate through electrolyte; electrons flow through external circuit.

• Thermodynamic Equations:

  • Reversible cell voltage: $$\displaystyle E = \frac{-\Delta G}{nF} $$ (ΔG = Gibbs free energy change)

  • Open circuit voltage ≈ 1.23 V for H₂/O₂ at 25°C.

  • Efficiency: $$\displaystyle \eta = \frac{\Delta G}{\Delta H} $$ (theoretical max ~83% at 25°C), can exceed 60% in practice.

• Types:

  • PEMFC (Polymer Electrolyte Membrane): Low temp (~80°C), solid polymer electrolyte, quick start, for vehicles/backup.

  • SOFC (Solid Oxide Fuel Cell): High temp (600-1000°C), ceramic electrolyte, high efficiency, fuel flexible, for stationary power.

  • Others: AFC (Alkaline), PAFC (Phosphoric Acid), MCFC (Molten Carbonate).

Hybrid Energy Systems

• Definition: Integration of two or more energy conversion/ storage technologies (e.g., solar PV + diesel generator + battery) to improve overall system reliability, efficiency, and cost-effectiveness.

• Feasible Options in India:

  • Solar-Wind-Diesel-Battery: For remote villages/islands (e.g., Lakshadweep).

  • Solar-Biomass: Biomass gasifier provides base load, solar peaks during day.

  • Hydro-Solar (Floating PV): On reservoir surfaces, reduces evaporation, uses existing grid infrastructure.

  • Wind-Solar-Pumped Hydro: Excess renewable energy pumps water to upper reservoir; stored hydro generates when renewables low.

2. Renewable Energy Sources: Solar and Wind

Solar Energy

• Factors Affecting Solar Intensity:

  • Astronomical: Earth-Sun distance, solar declination.

  • Atmospheric: Cloud cover, aerosols, water vapour, air mass.

  • Geographical: Latitude, altitude, sunshine hours.

  • Local: Orientation & tilt of collector, shading.

• Indian Scenario (Key Data):

  • High Potential Regions: Rajasthan (Jaisalmer, Bikaner ~5.5-6.5 kWh/m²/day), Gujarat, Andhra Pradesh, Karnataka, Tamil Nadu.

  • National Avg: ~4-6 kWh/m²/day.

  • States with Significant Installations: Rajasthan, Gujarat, Karnataka, Tamil Nadu, Maharashtra.

• Advantages: Abundant, inexhaustible, no fuel cost, low O&M, modular, suitable for distributed generation.

• Limitations: Intermittent (day/night, weather), low capacity factor (15-25%), requires large area, storage needed for 24x7 supply, initial cost high.

Wind Energy

• Factors Affecting Wind Velocity:

  • Geographical: Terrain roughness, topography (passes, hills), elevation (wind speed ↑ with height).

  • Meteorological: Pressure gradients, Coriolis force, local temperature differentials.

  • Seasonal/Monsoonal: Stronger during specific seasons (SW monsoon in India).

• Indian Scenario (Key Data):

  • High Potential States: Tamil Nadu (largest installed, sites like Muppandal), Gujarat, Maharashtra, Rajasthan, Karnataka, Andhra Pradesh.

  • Offshore Potential: Gulf of Khambhat, Gulf of Kutch, Tamil Nadu coast.

  • Wind Power Density: 200-400 W/m² at hub height in good sites.

• Advantages: Clean, renewable, land under turbines can be used for agriculture, low operating cost.

• Limitations: Intermittent & variable, noise, visual impact, threat to birds/bats, needs suitable wind regime (avg speed >6 m/s), grid integration challenges.

Comparative Analysis for Indian Conditions

[!TIP] For comparison, highlight complementarity: Solar peaks in hot sunny days, wind often peaks in monsoon evenings/nights. Hybrid systems can smooth output.

3. Thermal Power Plants (Fossil Fuel Based)

Coal Handling System

• Elements & Process Flow:

  1. Receipt & Unloading: Coal from rail/road/ship → wagon tippler/unloader.

  2. Crushing: Reduces size for pulverizers (if required).

  3. Screening & Separation: Removes foreign material.

  4. Storage: Stockyard (outdoor) or silos (indoor).

  5. Conveying: Belt conveyors from storage to boiler house.

  6. Weighing & Sampling: For accounting and quality control.

  7. Pulverizing (if needed): For pulverized coal firing → coal mills.

  8. Feeding: To boiler furnace via burners.

• Sketch: Show flow from wagon tippler → crusher → conveyor → stacker/reclaimer in yard → boiler house conveyors → coal hoppers → mills → burners.

Combustion Systems

Fluidized Bed Combustion (FBC)

• Working Principle: Solid fuel (coal, biomass) is fed into a bed of inert material (sand, limestone) through which air is blown at velocity sufficient to suspend the particles (fluidization). Combustion occurs at relatively low temperatures (800-900°C) throughout the bed.

  • Bubbling Fluidized Bed (BFB): Air velocity creates bubbles; good for smaller units.

  • Circulating Fluidized Bed (CFB): Higher velocity, solids carried out → cyclone separator → return to bed. Excellent for large units, fuel flexibility.

• Sketch: Show boiler enclosure with air distributor at bottom, fuel/limestone feed ports, bed material, freeboard, cyclone (for CFB), heat exchange tubes in bed.

• Advantages over Conventional (Pulverized Fuel):

  • Fuel Flexibility: Can burn low-grade coals, biomass, waste.

  • In-Situ SO₂ Control: Limestone added captures SO₂ as CaSO₄ at low temp.

  • Lower NOₓ Formation: Low combustion temperature (<900°C) suppresses thermal NOₓ.

  • Higher Combustion Efficiency for low-grade fuels.

  • Flexibility in Load Variation.

Fuel Burning Systems (Coal)

• Overfeed Principle: Coal fed above the burning fuel bed. Coal moves downward by gravity, drying, devolatilizing, and burning as it descends. Common on chain grate stokers.

• Underfeed Principle: Coal fed from below the grate. Coal moves upward, burning as it ascends. Used in underfeed stokers (retort type). Better for low-volatile coals, more controlled combustion.

Steam Cycle Enhancements

Reheat in Gas Turbine Plants

• How it Improves Efficiency: In a simple open cycle gas turbine, turbine inlet temperature (TIT) is limited by material limits. Reheat involves expanding the gas in a high-pressure turbine, then reheating it in a combustion chamber (reheat burner) before expanding in a low-pressure turbine.

  • Thermodynamic Benefit: Increases the average temperature of heat addition (T_avg) to the cycle (closer to TIT), thereby increasing thermal efficiency according to Carnot principle. Also reduces moisture content at final turbine stage.

  • Result: Higher power output for same compressor work and TIT, or same power with lower TIT → better component life.

Boiler Technology Trends

• Size: Trend towards supercritical (SC) and ultra-supercritical (USC) units (parameters: >22.1 MPa, >580°C for SC; >25 MPa, >600°C for USC) for higher efficiency (45-48% vs 35-38% subcritical).

• Selection: Based on fuel type (coal rank), load requirement, emission norms (NOₓ, SOₓ, particulates), redundancy, and site constraints.

• Operations: Focus on flexibility (ramp rates, low-load operation), digitalization (AI/ML for optimization), low-NOₓ burners, fabric filters/ESP for particulate control, FGD for SO₂ control.

Feed Water Treatment

• Elements of Treatment Plant:

  1. Pre-treatment: Aeration, filtration, softening (lime-soda process) to remove suspended solids, hardness (Ca²⁺, Mg²⁺).

  2. Demineralization: Ion exchange (cation → anion → mixed bed) to remove all dissolved salts → high-purity water.

  3. Degasification: Deaerator removes dissolved oxygen (corrosion) and CO₂ using steam stripping.

  4. Chemical Dosing: Oxygen scavengers (e.g., hydrazine, now less used; alternatives: carbohydrazide, hydroxylamine) and pH control (ammonia, morpholine) to prevent corrosion in boiler and condensate lines.

  5. Filtration: Final polishing filters (e.g., 5µ) before boiler feed pump.

Plant Heat Balance

• Concept: Quantitative accounting of all energy inputs (fuel LHV) and outputs (steam/heat, electrical energy, losses) in a power plant over a given period (usually annually). Basis for calculating heat rate and thermal efficiency.

• Example (Fossil Fuel Plant):

  Input: Fuel energy = $$\displaystyle \dot{m}_f \times \text{LHV} $$

  Outputs:

  • Net electrical energy = $$\displaystyle P_{net} $$

  • Heat loss in flue gases (stack loss)

  • Heat loss in ash/slag

  • Radiation & convection losses from boiler

  • Pump work (auxiliary consumption)

  Efficiency: $$\displaystyle \eta_{thermal} = \frac{P_{net}}{\dot{m}_f \times \text{LHV}} $$

  Heat Rate: $$\displaystyle HR = \frac{3600}{\eta} $$ (kJ/kWh)

Auxiliary Systems: Cooling Towers

• Purpose: Reject waste heat from condenser cooling water to atmosphere via evaporation and sensible heat transfer, enabling closed-loop cooling (water conservation).

• Types & Working:

  • Natural Draft: Hyperbolic shape creates chimney effect. Warm, moist air rises naturally. Low power consumption, large capacity.

  • Mechanical Draft: Use fans to force/induce air flow.

    • Forced Draft: Fan at air inlet (positive pressure).

    • Induced Draft: Fan at air outlet (negative pressure, common).

    • Induced/Forced Combination: Better control.

  • Fill (Packing): Increases contact area/time between water and air (film or splash type).

4. Nuclear Power Plants

Nuclear Fission Phenomenon

• Basic Principle: A heavy nucleus (e.g., ²³⁵U) absorbs a thermal neutron, becomes unstable, and splits into two lighter nuclei (fission fragments), releasing ~200 MeV energy, 2-3 fast neutrons, and gamma radiation. The released neutrons can cause further fissions → chain reaction.

• In Reactor Context: Sustained, controlled chain reaction. Requires criticality (k_eff = 1). Neutrons are moderated (slowed) to thermal energies to increase probability of fission in ²³⁵U (or ²³⁹Pu).

Reactor Components and Moderators

• Moderator Function: Slow down fast fission neutrons to thermal energies (via elastic collisions) to maximize fission probability in fissile isotopes (²³⁵U, ²³⁹Pu).

• Types & Characteristics:

  | Moderator | Material | Neutron Absorption Cross-Section | Slowing Power (ξ) | Pros | Cons | | :--- | :--- | :--- | :--- | :--- | :--- | | Light Water (H₂O) | Ordinary water | High (absorbs neutrons) | Moderate | Cheap, good coolant | Requires enriched fuel | | Heavy Water (D₂O) | Deuterium oxide | Very Low | Moderate | Allows natural uranium fuel | Expensive, scarce | | Graphite | Carbon | Very Low | High | Allows natural/ slightly enriched fuel | Low density, fire risk (Windscale) | | Beryllium | Beryllium/BeO | Low | High | Good reflector & moderator | Toxic, expensive, activation |

Reactor Types

Pressurized Heavy Water Reactor (PHWR)

• Working (Sketch Description):

  1. Fuel: Natural uranium (0.7% ²³⁵U) oxide pellets in zircaloy pressure tubes.

  2. Moderator/Coolant: Heavy water (D₂O). Moderator is at lower pressure in a calandria surrounding pressure tubes; coolant (D₂O) is pressurized (~100 bar) and circulates through pressure tubes.

  3. Heat Transfer: Coolant heated in core → steam generators (where it transfers heat to secondary light water loop, producing steam) → coolant recirculated.

  4. Control: Adjuster rods (liquid cadmium) for power regulation, shut-off rods (fall by gravity) for scram.

• Key Feature: On-power refueling (fuel channels can be opened individually).

Advanced Gas Cooled Reactor (AGR)

• Description: Second generation of UK's Magnox design. Uses graphite moderator and carbon dioxide (CO₂) gas coolant at ~40 bar. Fuel is enriched uranium (2.5-3.5% ²³⁵U) in stainless steel cladding. Heat transferred to secondary water/steam circuit via steam generators.

• Fission Context: Graphite moderator slows neutrons; CO₂ coolant removes heat. Enriched fuel compensates for higher neutron absorption in stainless steel cladding compared to Magnox.

Thermal vs Fast Breeder Reactors

Reactor Control and Safety

• Principles of Control:

  • Reactivity Control: Adjust neutron population via control rods (B₄C, Ag-In-Cd, Hf) inserted/withdrawn.

  • Chemical Shim: Dissolving boric acid in coolant (PWR) for fine control.

  • Temperature Feedback: Negative temperature coefficient of reactivity (most designs) provides inherent stability.

• Reliability Features:

  • Multiple, Diverse Safety Systems: Redundant shutdown systems (SCRAM), emergency core cooling systems (ECCS), containment structures (reinforced concrete/steel).

  • Defense-in-Depth: Physical barriers (fuel cladding, reactor pressure vessel, containment) + operational procedures.

  • Passive Safety Systems: Gravity-driven water injection, natural circulation cooling (e.g., AP1000).

  • Severe Accident Management: Hydrogen recombiners, core catchers.

5. Hydro Power Plants

Hydraulic Turbines

• Types & Specific Characteristics:

• Selection Factors:

  • Net Head (available head after losses)

  • Design Discharge / Flow

  • Specific Speed (Ns): Primary parameter linking head & flow to turbine type.

  • Part-load Efficiency & Regulation (Kaplan better for varying flow).

  • Cavitation Susceptibility (Francis/Kaplan more prone).

  • Site Constraints (size, orientation).

Site Selection Criteria

• Parameters:

  1. Hydrology: Reliable, high annual rainfall → consistent river flow. Catchment area, runoff data.

  2. Topography: Steep valleys for high head with small dam; broad valley for storage dam.

  3. Geology & Foundation: Sound rock for dam, powerhouse; seismic stability.

  4. Accessibility: Proximity to load centers, road/rail access.

  5. Environmental & Social Impact: Submergence area, displacement, forest/ecosystem loss.

  6. Economic: Cost of dam, tunnel, powerhouse; distance to grid.

• Comparison with Other Plants:

  • vs Fossil: Hydro sites fixed by geography; fossil fuel sites near mines/transport. Hydro has high capital, low O&M; fossil has fuel cost volatility. Hydro is renewable, fossil depleting.

  • vs Renewable (Solar/Wind): Hydro sites are location-specific but can provide dispatchable power (with storage); solar/wind are intermittent, site-specific but more distributed. Hydro often has larger environmental footprint per MW than solar/wind.

Small Hydro Power

• Micro vs Pico Hydro:

  | Feature | Micro Hydro | Pico Hydro | | :--- | :--- | :--- | | Capacity | 100 kW to 10 MW | < 100 kW (often < 10 kW) |

  Head | Low to Medium | Very Low to Low |

  Application | Mini-grids, village power, feed to grid | Standalone systems for homes/small communities |

  Civil Works | Small dam/weir, penstock | Minimal (run-of-river, no dam) |

  Turbine | Francis, Kaplan, Turgo | Propeller, Crossflow, Pelton (very low head) |

  Cost & Complexity | Moderate, requires some grid integration | Very low, simple, often community-managed |

Spillways

• Purpose: Safely pass flood flows exceeding the capacity of the power outlet works, protecting the dam from overtopping and failure.

• Types:

  1. Overflow (Ogee) Spillway: Crest shaped like inverted S (ogee). Most common for gravity dams. Controlled by gates or ungated.

  2. Side Channel Spillway: Flow passes through a channel parallel to dam axis. For wide valleys.

  3. Shaft (Morning Glory) Spillway: Circular, vertical shaft leading to tunnel. Good for narrow canyons.

  4. Chute Spillway: Steeply sloping open channel from crest to river. Often with flip bucket for energy dissipation.

  5. Siphon Spillway: Operates on siphon principle; self-priming.

6. Power Plant Economics and Operation

Key Performance Indicators

• Maximum Demand (MD): The highest load (power) occurring during a specified period (usually monthly or annually). Units: kW or MW.

• Load Factor (LF): Ratio of average load to maximum demand over a given period.

$$ \text{Load Factor} = \frac{\text{Average Load}}{\text{Maximum Demand}} = \frac{\text{Total Energy (kWh)}}{\text{Max Demand (kW)} \times \text{Period Hours}} $$

*Indicates how uniformly load is drawn.*

• Diversity Factor (DF): Ratio of sum of individual maximum demands to the coincident maximum demand of the whole system.

$$ \text{Diversity Factor} = \frac{\sum \text{Individual Peak Loads}}{\text{System Peak Load}} $$

*DF > 1 indicates non-coincident peaks.*

• Plant Factor (PF): Ratio of actual energy produced to the maximum possible energy if operated at full capacity 24/7 over a period.

$$ \text{Plant Factor} = \frac{\text{Actual Annual Energy (kWh)}}{\text{Rated Capacity (kW)} \times 8760 \text{ h}} $$

*Reflects overall utilization of installed capacity.*

Load Analysis Curves

• Load Duration Curve (LDC): Load values arranged in descending order vs. cumulative time (percentage). Shows how often a certain load level is exceeded. Area under curve = total energy.

• Power Duration Curve: Similar to LDC but power (MW) on Y-axis. Used for capacity planning.

• Significance: Determines base load (flat part, >80% time), intermediate load, peak load (steep part). Guides unit commitment and tariff design.

Tariff Structures

• Types:

  1. Flat Rate: Fixed charge per kWh, independent of load factor/MD.

  2. Two-Part Tariff: Fixed Charge (based on MD or connected load) + Energy Charge (per kWh). Most common for industrial/commercial.

  3. Three-Part Tariff: Fixed Charge + Energy Charge + Maximum Demand Charge (based on actual MD). For large consumers.

  4. Time-of-Day (TOD) Tariff: Different rates for peak, off-peak, and normal hours. Encourages load shifting.

  5. Seasonal Tariff: Different rates in high/low demand seasons.

Depreciation and Cost Analysis

• Purpose: Allocate initial capital cost (fixed capital) over useful life.

• Sinking Fund Method: Annual depreciation payment ($A$) is such that future value of all payments at interest rate $i$ equals initial cost minus salvage value.

$$ A = \frac{P - S}{\frac{(1+i)^n - 1}{i}} $$

Where $P$ = initial cost, $S$ = salvage value, $n$ = life.

• Straight Line Method: Equal annual depreciation charge.

$$ \text{Annual Depreciation} = \frac{P - S}{n} $$

• Example Calculation (from past paper):

  Given: $$\displaystyle P = \text{Rs. }90,000 $$, $$\displaystyle S = \text{Rs. }5,000 $$, $$\displaystyle n = 15 $$ years, $$\displaystyle i = 6\% = 0.06 $$.

  Sinking Fund:

  $$\displaystyle A = \frac{90000 - 5000}{\frac{(1.06)^{15} - 1}{0.06}} = \frac{85000}{\frac{2.3966 - 1}{0.06}} = \frac{85000}{23.275} \approx \text{Rs. }3,651 $$

  Straight Line:

  $$\displaystyle A = \frac{90000 - 5000}{15} = \frac{85000}{15} \approx \text{Rs. }5,667 $$

Plant Economics Problem (Standard Approach)

• Given: Individual peak loads, Diversity Factor (DF), Annual Load Factor (LF).

• To Find: (i) Maximum Demand on Station, (ii) Annual Energy Supplied.

• Formulas:

  1. System Max Demand (MD_sys) = $$\displaystyle \frac{\sum \text{Individual Peaks}}{\text{Diversity Factor}} $$

  2. Average Load = MD_sys × Load Factor

  3. Annual Energy (GWh) = Average Load (MW) × 8760 h / 1000

• Example (Dec 2025 Paper):

  Peaks: 10, 5, 8, 7 MW → Σ = 30 MW. DF = 1.5. LF = 0.6.

  (i) MD_sys = 30 / 1.5 = 20 MW

  (ii) Avg Load = 20 × 0.6 = 12 MW

  Annual Energy = 12 MW × 8760 h = 105,120 MWh = 105.12 GWh

  \boxed{\text{Max Demand} = 20,\text{MW}}

  \boxed{\text{Annual Energy} = 105.12,\text{GWh}}