Electrical Power Generation & Economy (EX-503 (A)) - Unit 3 Short Notes

UNIT 3: ELECTRICAL POWER GENERATION & ECONOMY

I. INTRODUCTION TO POWER GENERATION SOURCES

Classification of Energy Sources

[!TIP] Exam Focus: Be prepared to compare merits/demerits of at least 4 major sources (e.g., Hydro vs. Thermal vs. Solar vs. Wind). Key points: Capital cost, fuel availability, environmental impact, reliability, land requirement.

Global & Indian Energy Scenario

• Global: Shift towards renewables due to climate change; solar & wind leading.

• India:

  • Renewable Prospects: 5th largest renewable capacity. Solar (Thar Desert), Wind (Tamil Nadu, Gujarat, Maharashtra), Small Hydro (Himalayan states), Biomass (Punjab, Haryana).

  • Challenges: Intermittency, grid integration, storage, land acquisition, financing.

  • State-Specific (Tamil Nadu): Leader in wind power (~20 GW), significant solar potential, coastal for wind, has wind-solar hybrid policies.

II. CONVENTIONAL POWER PLANTS

A. HYDROELECTRIC POWER PLANTS

1. Site Selection Criteria

• Topography: Narrow valley with steep slopes for dam.

• Water Availability: High rainfall/snowmelt, large catchment area, perennial river.

• Geology: Sound rock foundation for dam & powerhouse.

• Accessibility: Proximity to load center, transport facilities.

• Environmental & Social: Minimal displacement, ecological impact.

2. Layout & Components (Neat Diagram Essential)

DiagramSEARCH: hydroelectric power plant layout penstock surge tank draft tube

• Dam/Reservoir: Stores water, creates head.

• Intake: Admits water to penstock, screens debris.

• Penstock: Large pipe carrying water under pressure to turbine.

• Surge Tank: Protects against water hammer; absorbs pressure surges.

• Turbine: Converts hydraulic to mechanical energy.

  • Pelton: High head (300m+), impulse type, uses nozzles.

  • Francis: Medium head (30m-300m), reaction type.

  • Kaplan: Low head (<30m), reaction type, adjustable blades.

• Generator: Converts mechanical to electrical energy.

• Draft Tube: Converts kinetic energy to pressure, increases net head.

• Tailrace: Returns water to river.

3. Hydrograph & Duration Curves

• Hydrograph: Graph of discharge (flow) vs. time for a river at a point. Shows seasonal variations.

  Significance: Determines firm power, reservoir sizing, and plant capacity.

• Flow Duration Curve (FDC): Discharge ranked descending vs. % of time exceeded.

  Use: Determines ** dependable flow** (e.g., flow available 90% of time).

• Power Duration Curve (PDC): Power derived from FDC (using $$\displaystyle P = \rho g Q H \eta $$) ranked vs. % time.

  Use: Represents energy production pattern; area under curve = total energy/year.

4. Pumped Storage Plants

• Working: Uses two reservoirs (upper & lower). During off-peak, excess grid power pumps water to upper reservoir. During peak, water released from upper to lower through turbine-generator.

• Merits: Peak load support, frequency control, quick start/stop.

• Demerits: High capital cost, geographical constraints, energy loss in pumping cycle (~25-30%).

B. THERMAL POWER PLANTS (Steam)

1. Site Selection Factors

• Fuel Transport: Proximity to coal mine/port/rail.

• Water Availability: Large, reliable water source for cooling & boiler feed.

• Land: Sufficient, cheap, stable land.

• Pollution: Away from populated areas; wind direction considered.

• Load Center: Near major demand to reduce transmission loss.

• Ash Disposal: Space for ash ponds.

2. Layout & Main Features (Neat Diagram Essential)

DiagramSEARCH: thermal power plant layout boiler turbine condenser cooling tower

• Boiler (Steam Generator): Burns fuel to produce high-pressure, high-temperature steam.

• Steam Turbine: Expands steam to produce shaft work (HP, IP, LP stages; reheat optional).

• Condenser: Condenses exhaust steam from turbine to water (creates vacuum, improves efficiency).

• Cooling Tower: Cools condenser cooling water (Natural draft: hyperbolic; Mechanical draft: induced/forced draft fans).

• Chimney (Stack): Disperses flue gases.

• Economiser: Preheats boiler feedwater using flue gas heat → improves boiler efficiency.

• Air Preheater: Preheats combustion air using flue gas → improves combustion efficiency.

• Feedwater Heater (Open/Closed): Uses steam extraction to heat feedwater → improves cycle efficiency.

• Ash Handling System: Collects & disposes of bottom/fly ash (mechanical, hydraulic, pneumatic).

3. Water Treatment Plant

• Necessity: Prevent scaling, corrosion, fouling in boiler/turbine. Impurities cause deposits, reduce heat transfer, damage blades.

• Processes:

  1. Pre-treatment: Screening, sedimentation, filtration.

  2. ** softening:** Lime-soda process to remove hardness.

  3. Demineralization: Ion exchange (cation/anion exchangers) to remove all salts → DM water.

  4. Degasification: Removes dissolved gases (O₂, CO₂) using deaerator.

C. NUCLEAR POWER PLANTS

1. Nuclear Fission vs. Fusion

2. Reactor Components (PWR Type - Common)

DiagramSEARCH: pressurized water reactor PWR schematic diagram

• Moderator: Slows down neutrons (Graphite, Heavy Water D₂O, Light Water H₂O).

• Control Rods: Absorb neutrons (Boron, Cadmium, Hafnium) to control reactivity.

• Coolant: Removes heat from core (Water, Heavy Water, Gas, Liquid Metal).

• Pressure Vessel: Contains core, coolant under high pressure.

• Heat Exchanger (Steam Generator): Transfers heat from primary coolant to secondary water/steam.

• Shielding: Concrete, lead, steel to absorb radiation (gamma, neutron).

3. CANDU Reactor (Canada Deuterium Uranium)

• Schematic: Uses natural uranium (0.7% U-235) as fuel, heavy water (D₂O) as moderator & coolant. Separate systems. Pressure tubes instead of pressure vessel.

• Working: Natural uranium fuel bundles in pressure tubes. Heavy water moderator in calandria surrounds tubes. Coolant (D₂O) flows through pressure tubes.

• Advantages:

  • Uses natural uranium → no enrichment needed.

  • On-line refueling → high capacity factor.

  • Excellent neutron economy → can breed plutonium (use in future).

• Disadvantages:

  • Expensive heavy water production & loss management.

  • Large size due to pressure tube design.

  • Higher capital cost than PWR.

4. Fuel Availability & Cycle in India

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

• Thorium: World's largest reserves (Kerala Monazite sands, Odisha, Andhra Pradesh). India's long-term strategy → Three-stage program: (1) PHWRs (U-233 from Th-232), (2) Fast Breeder Reactors (Pu-239 + Th-232 → U-233), (3) Thorium-based reactors.

• Fuel Cycle: Mining → Milling → Conversion → Enrichment (for some) → Fuel Fabrication → Reactor → Spent Fuel → Reprocessing (recover U, Pu) → Waste Disposal.

5. Nuclear Waste Management

• Types:

  • Low & Intermediate Level: Clothing, tools, filters. Shielded storage → near-surface disposal.

  • High Level: Spent fuel, reprocessing waste. Highly radioactive, generates heat.

• Disposal Methods:

  • Geological Repository: Deep underground in stable rock formations (e.g., granite, salt beds). Most accepted method.

  • Reprocessing: Recover usable U & Pu; reduces volume & radioactivity of waste.

  • Transmutation: Convert long-lived isotopes to short-lived (research stage).

• Importance: Protect environment & public health for millennia. Prevent proliferation.

6. Radioactive Pollution & Shielding

• Sources: Routine releases (regulated), accidental releases (Chernobyl, Fukushima), waste disposal leaks.

• Impact: Ionizing radiation damages cells, causes cancer, genetic mutations. Contaminates soil, water, food chain.

• Radiation Shielding:

  • Materials: Concrete (cheap, structural), Lead (dense, for gamma), Water/Graphite (for neutrons), Borated materials (neutron absorption).

  • Design: Thickness calculated based on radiation type & energy. Multi-layer (e.g., steel + concrete) common.

D. GAS TURBINE POWER PLANTS

1. Layout of Simple Gas Turbine Plant

DiagramSEARCH: simple gas turbine plant layout compressor combustor turbine

• Compressor: Axial/centrifugal; compresses ambient air.

• Combustor (Combustion Chamber): Fuel (natural gas, diesel) injected & burned with compressed air → high-temperature gases.

• Turbine: Expands hot gases to produce work (drives compressor & generator).

• Generator: Produces electricity.

• Exhaust: High-temperature gases released (~500°C) → waste heat.

2. Classification & Brayton Cycle

• Open Cycle: Air from atmosphere → exhaust to atmosphere. Most common.

• Closed Cycle: Working fluid (He, CO₂) circulates in closed loop with heat exchanger.

• With/without Regeneration: Regenerator (heat exchanger) recovers exhaust heat to preheat compressed air → improves efficiency.

• With Intercooling: Cools air between compressor stages → reduces compressor work → improves efficiency.

• With Reheating: Reheats gas between turbine stages → increases work output → improves efficiency.

• Combined Cycle: Gas turbine exhaust heat used in Heat Recovery Steam Generator (HRSG) to produce steam for steam turbine → very high efficiency (55-62%).

3. Thermal Efficiency Improvement Methods

1. Regeneration (Most common for simple cycle).

2. Intercooling (in multi-stage compression).

3. Reheating (in multi-stage expansion).

4. Combined Cycle (Gas + Steam turbine).

III. RENEWABLE & NON-CONVENTIONAL ENERGY SYSTEMS

A. SOLAR ENERGY

1. Solar Radiation Fundamentals

• Solar Constant ($$\displaystyle G_{sc} $$): ~1367 W/m² (radiation outside atmosphere on plane normal to sun).

• Insolation: Solar radiation reaching Earth's surface (W/m² or kWh/m²/day).

• Earth-Sun Angles:

  • 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 meridian. $$\displaystyle ω = 15^\circ \times (t - 12) $$, $t$ in solar time.

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

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

    where $\phi$ = latitude.

*   **Solar Azimuth (γ):** Angle of sun's projection on horizontal plane from south (N. Hemisphere).

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

> [!TIP] **Calculation:** Always compute **α first**, then **γ**. Check quadrant for γ using sign of $$\displaystyle \sin \gamma = \cos \delta \sin \omega / \cos \alpha $$.

2. Solar Thermal Systems

• Collectors Classification:

  | Flat Plate | Concentrating | | :--- | :--- | | Absorber plate (black), glazing (glass), insulation, casing. | Parabolic Trough, Dish, Tower. Use tracking. | | Temp: 30-100°C. | Temp: 100-1000°C+. | | Applications: Water heating, space heating. | Applications: Power generation (steam cycle). |

• Solar Thermal Power Generation: Concentrated sunlight → heats HTF → steam generator → steam turbine → generator → grid.

3. Solar Photovoltaic (PV) Systems

• Principle: Photoelectric effect in p-n junction. Photons excite electrons → DC current.

• Key Elements:

  • Cell: Basic unit (Si, thin-film). ~1W, 0.5-0.6V.

  • Module: Series/parallel connected cells encapsulated.

  • Array: Multiple modules.

  • Inverter: DC to AC conversion.

  • Balance of System (BoS): Mounting, wiring, charge controller (for standalone), batteries.

• I-V Characteristics:

  
  DiagramCANVAS: Draw I-V curve. Label axes: Current (I) vs Voltage (V). Mark point at Isc (V=0), Voc (I=0), and MPP (Vm, Im). Show power curve (parabola) peaking at MPP.
  
  

  • Open Circuit Voltage ($$\displaystyle V_{oc} $$): Voltage at I=0.

  • Short Circuit Current ($$\displaystyle I_{sc} $$): Current at V=0.

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

  • Fill Factor (FF): Measure of "squareness" of curve.

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

*   **Efficiency (η):**

$$\boxed{\eta = \frac{P_{max}}{\text{Input Solar Power}} = \frac{V_m I_m}{A \cdot G}}$$

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

• Factors Affecting Performance:

  • Temperature: ↑Temperature → ↓$$\displaystyle V_{oc} $$ → ↓η (for Si).

  • Irradiance: ↑Irradiance → ↑$$\displaystyle I_{sc} $$ (linear), slight ↑$$\displaystyle V_{oc} $$ → ↑P.

  • Spectrum: Cell response varies with wavelength.

  • Soiling, Shading: Drastically reduce output.

• Applications: Standalone (with battery), Grid-connected (without battery).

B. WIND ENERGY

1. Principle & Betz's Law

• Principle: Kinetic energy of wind → rotor blades → mechanical rotation → generator.

• Wind Power (Available): $$\displaystyle P_{wind} = \frac{1}{2} \rho A v^3 $$

  • $\rho$ = air density (kg/m³), $$\displaystyle A = \pi R^2 $$ = swept area, $v$ = wind speed.

  • Power ∝ $$\displaystyle v^3 $$ → critical factor.

• Betz's Law: Maximum theoretical power extracted by rotor = 59.3% of $$\displaystyle P_{wind} $$.

$$P_{max} = \frac{16}{27} \cdot \frac{1}{2} \rho A v^3 = 0.593 \cdot P_{wind}$$

*   **Power Coefficient ($$\displaystyle C_p $$):** Actual $$\displaystyle C_p < 0.593 $$ (typical 0.4-0.5).

2. Wind Turbine Classifications

• Horizontal Axis Wind Turbine (HAWT): Most common.

  
  DiagramSEARCH: horizontal axis wind turbine components nacelle gearbox generator tower yaw
  
  

  • Components: Blades (aerofoil), Nacelle (housing), Gearbox (increases speed), Generator, Tower, Yaw mechanism (faces wind).

• Vertical Axis Wind Turbine (VAWT):

  • Darrieus: "Egg-beater" shape; high efficiency, self-starting issue.

  • Savonius: Drag-type; low efficiency, self-starting, robust.

3. Wind Characteristics & Performance

• Wind Speed Distribution: Often follows Weibull distribution ($k$ = shape, $c$ = scale).

• Key Speeds:

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

  • Rated: ~12-15 m/s (rated power).

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

• Capacity Factor (CF):

$$\boxed{CF = \frac{\text{Actual Energy Output (kWh/yr)}}{\text{Rated Power (kW)} \times 8760 \text{ h/yr}}}$$

Typical: 20-40% (onshore), 40-50% (offshore).

• Energy Output Calculation:

$$E = P_{rated} \times CF \times \text{operating hours}$$

Or integrate power curve over wind speed distribution.

4. Site Selection for Wind Farms

• Wind Resource Assessment: Avg wind speed >6 m/s at hub height, low turbulence, favorable Weibull $k$.

• Terrain: Flat/open, hilltops, coastal areas. Avoid obstacles, forests.

• Accessibility: Road access for transport/erection.

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

• Environmental: Bird migration paths, noise restrictions, visual impact.

5. Control Schemes

• Pitch Control: Blade pitch angle adjusted to regulate power at high wind.

• Stall Control: Fixed pitch; aerodynamic stall limits power at high wind.

• Yaw Control: Rotates nacelle to align with wind direction.

C. BIOMASS ENERGY

1. Biogas Generation (Anaerobic Digestion)

4 Stages:

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

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

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

4. Methanogenesis: Acetic acid/H₂+CO₂ → CH₄ (60-70%) + CO₂.

• Optimum Conditions: C/N ratio (20-30:1), moisture (60-80%), pH (6.7-7.4), temperature (mesophilic 35°C or thermophilic 55°C).

2. Biogas Plant Types (Neat Diagrams Essential)

DiagramSEARCH: Deen Bandhu KVIC fixed dome biogas plant

DiagramSEARCH: Pragati design floating drum biogas plant

• Deen Bandhu (KVIC) - Fixed Dome:

  • Working: Inlet, digester (underground brick dome), outlet. Gas collects in fixed dome top. Pressure pushes slurry to outlet.

  • Merits: Low cost, no moving parts, long life.

  • Demerits: Gas leakage from dome, scraping difficulty.

• Pragati Design - Floating Drum:

  • Working: Inlet, digester, floating gas holder (steel drum) moves up/down with gas production. Weight provides constant pressure.

  • Merits: Constant gas pressure, easy to see gas volume.

  • Demerits: High cost (steel), corrosion, maintenance.

• Community Biogas Plants:

  • Schematic: Larger fixed/floating drum, common feeding.

  • Operational Problems: Feedstock irregularity, management issues, social conflicts.

3. Materials for Biogas Generation

• Agricultural Residue: Straw, husk (needs co-digestion with wet waste).

• Animal Dung: Cow dung (most common), poultry litter.

• Municipal Solid Waste (Organic fraction).

• Energy Crops: Napier grass, sugarcane trash.

• Key Parameters: C/N ratio (25 optimal), Moisture content (60-80%), pH (neutral), absence of inhibitors (antibiotics, heavy metals).

4. Pyrolysis

• Definition: Thermal decomposition of biomass in absence of air.

• Process: Biomass → (300-800°C) → Bio-oil (liquid), Bio-char (solid), Syngas (gas).

• Small-Scale Unit: Feedstock → reactor (heater) → vapors → condenser → bio-oil; char collected from bottom. Used for liquid fuel production.

5. Biomass Applications

• Direct Combustion: For heat/steam (industrial, cooking).

• Gasification: Partial combustion → producer gas (CO+H₂) → engine/gas turbine.

• Biogas: For cooking, electricity (dual-fuel engine), vehicle fuel (after purification).

• Biofuels: Ethanol (from sugarcane, corn), Biodiesel (from jatropha, vegetable oils).

D. OTHER RENEWABLE SOURCES

1. Geothermal Energy

• Types:

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

  • Flash Steam: Hot water (>180°C) → flashed to steam in separator → turbine.

  • Binary Cycle: Moderate temp (85-175°C) water heats secondary fluid (low boiling point: isobutane, pentane) → vapor → turbine. Most common for new plants.

    
    DiagramSEARCH: binary cycle geothermal power plant working fluid
    
    

• Potential in India: Low to moderate. Hot springs in Himalayas, Gujarat, Rajasthan, Tamil Nadu. Geothermal gradient ~30-40°C/km. Experimental projects in Puga Valley (Ladakh), Manikaran (HP).

• Hybrid Geothermal-Fossil: Geothermal preheats feedwater for fossil plant, or geothermal bottoming cycle for fossil waste heat.

2. Tidal Energy

• Site Selection: Large tidal range (>4m), suitable basin configuration (estuary, bay), minimal siltation.

• Working Principle: Potential energy of water at high tide → stored in basin → released through turbines at low tide.

• Types:

  • Tidal Barrage: Dam across estuary. Single basin (one-way generation) or dual basin (pumping for continuous generation).

  • Tidal Stream Generators (TSG): Underwater "wind turbines" in strong tidal currents.

• Schematic Layout of Tidal Power House:

  
  DiagramSEARCH: tidal barrage power plant schematic sluice gates turbine
  
  

  Shows: Basin, dam, sluice gates (fill/empty), turbines, ship lock.

3. Ocean Thermal Energy Conversion (OTEC)

• Principle: Exploits ocean temperature gradient: Warm surface water (25-30°C) vs. cold deep water (5-10°C). ΔT > 20°C required.

• Closed OTEC System:

  
  DiagramSEARCH: closed cycle OTEC system working fluid ammonia
  
  

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

  • Cycle: Warm surface water → evaporator → vapor → turbine → cold deep water → condenser → liquid → pump → repeat.

  • Challenges: Very low efficiency (~3-4%), huge pipe sizes for cold water, biofouling.

• Open Cycle (Flash Evaporation): Warm seawater itself flashed in vacuum chamber → steam → turbine → condensed to fresh water. Produces desalinated water.

4. Hydrogen Energy

• Advantages: High energy density (by mass), clean combustion (water), versatile (fuel, storage, industry).

• Disadvantages: Low density (by volume), storage/transport challenges, production cost (if from electrolysis), safety (flammable, embrittlement).

• Storage Methods:

  | Method | Principle | Pros | Cons | | :--- | :--- | :--- | :--- | | Compression | High pressure (350-700 bar) | Simple, mature | Energy-intensive, heavy tanks | | Liquefaction | Cool to -253°C | High density | Very energy-intensive, boil-off | | Metal Hydrides | Absorb in metal alloys | Safe, moderate pressure | Heavy, slow kinetics | | Chemical Carriers | LOHCs, ammonia | Existing infrastructure | Complex processing |

• Production Methods:

  • Electrolysis: $$\displaystyle 2H_2O \xrightarrow{electricity} 2H_2 + O_2 $$ (clean if renewable electricity).

  • Steam Methane Reforming (SMR): $$\displaystyle CH_4 + H_2O \rightarrow CO + 3H_2 $$ (fossil-based, with CCS cleaner).

5. Fuel Cells

• Classification (by Electrolyte):

  • AFC (Alkaline): Spacecraft, high efficiency.

  • PEMFC (Polymer Electrolyte Membrane): Transport, backup power; low temp (~80°C).

  • PAFC (Phosphoric Acid): Commercial CHP.

  • MCFC (Molten Carbonate): Power plants, high temp (~650°C).

  • SOFC (Solid Oxide): High temp (~1000°C), flexible fuel.

• Working Principle: Electrochemical conversion. Fuel (H₂) at anode → Oxidation (H⁺/e⁻); Oxidant (O₂) at cathode → Reduction (H₂O); electrons flow through external circuit → DC electricity.

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

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

6. Magneto-Hydro Dynamic (MHD) Generation

• Principle: Faraday's Law of Electromagnetic Induction. Ionized hot gas (plasma) from combustion passed through magnetic field → induces EMF across electrodes → direct electricity.

  
  DiagramSEARCH: MHD generator schematic channel electrodes magnet
  
  

• Advantages: No moving parts → high efficiency potential (50-60%), high power density, fast start.

• Challenges: Material science (electrode erosion at ~2000°C), ionization energy, seed material (potassium) recovery, high capital cost. Still experimental.

E. HYBRID SYSTEMS

• Concept: Integration of two or more renewable sources (e.g., solar-wind, PV-diesel, wind-biomass) with/without storage (batteries, fuel cells) to improve reliability and utilization.

• Advantages:

  • Improved reliability & power quality (complementary generation profiles).

  • Better resource utilization (e.g., solar day + wind night).

  • Reduced storage requirement (one source can charge batteries for other).

  • Optimized system sizing & cost.

• Examples:

  • Solar-Wind-Battery: Most common for off-grid/remote areas.

  • PV-Diesel: Diesel backup for no-renewable periods.

  • Hydrogen-based: Excess renewable → electrolysis → H₂ storage → fuel cell during deficit.

IV. ECONOMIC ASPECTS OF POWER GENERATION

A. COST ANALYSIS

• Incremental Fuel Cost: $$\displaystyle \lambda = \frac{dC_f}{dP} $$ (Rs/MWh). Slope of fuel cost vs. power curve. Used for economic dispatch.

• Total Cost & Cost per Unit:

$$C_{total} = C_{fixed} + C_{operating}(P)$$

$$\text{Cost/kWh} = \frac{C_{total}}{\text{Annual Energy Output (kWh)}}$$

*   **Inversely proportional to Load Factor.** Higher load factor → more units produced → lower average cost.

B. SYSTEM PARAMETERS & LOAD CHARACTERISTICS

1. Load Curve & Duration Curve

• Load Curve: Plot of power demand (kW/MW) vs. time (hourly/daily/monthly/annual).

  Significance: Shows variation, peak demand, energy consumption pattern.

• Load Duration Curve (LDC): Loads ranked in descending order vs. percentage of time exceeded.

  Significance: Directly gives number of hours a certain load level is exceeded. Area under LDC = total energy. Base for capacity planning & economic dispatch.

2. Key Factors (Always < 1)

• Interrelation: $$\displaystyle E = P_{max} \times T \times LF = P_{installed} \times 8760 \times CF $$

  Impact on Cost: Higher LF & CF → more units → lower cost/kWh. Lower UF indicates over-investment in capacity.

3. Load Forecasting

• Importance: For generation scheduling, fuel procurement, maintenance planning, transmission expansion, tariff setting.

• Methods:

  • Extrapolation/Trend: Extend past trend (linear, exponential).

  • Economic Indicators: Correlate with GDP, industrial production, population.

  • End-Use Modeling: Bottom-up: forecast by consumer sector (residential, commercial, industrial) based on appliance saturation, usage patterns.

C. ECONOMIC OPERATION & DISPATCH

1. Economic Load Scheduling (ELS) / Dispatch

• Objective: Minimize total fuel cost $$\displaystyle C_{total} = \sum C_i(P_i) $$ while meeting total load $$\displaystyle P_D $$ and generator limits.

• Principle (Neglecting Losses): Incremental fuel costs equalized across all online units.

$$\lambda = \frac{dC_1}{dP_1} = \frac{dC_2}{dP_2} = ... = \frac{dC_n}{dP_n}$$

where $\lambda$ = **system incremental cost** (Rs/MWh).

• Procedure for 2 units:

  1. Given $$\displaystyle C_1(P_1), C_2(P_2) $$ and $$\displaystyle P_D = P_1 + P_2 $$.

  2. Set $$\displaystyle \frac{dC_1}{dP_1} = \frac{dC_2}{dP_2} = \lambda $$.

  3. Solve with $$\displaystyle P_1 + P_2 = P_D $$ and $$\displaystyle P_{i min} \le P_i \le P_{i max} $$.

2. Including Transmission Losses

• Loss Formula (Simplified): $$\displaystyle P_L = \sum_{i=1}^{n} \sum_{j=1}^{n} B_{ij} P_i P_j $$ (B coefficients symmetric, $$\displaystyle B_{ii} > 0 $$, $$\displaystyle B_{ij} < 0 $$).

• Penalty Factor ($$\displaystyle \lambda_i $$): Accounts for loss allocation. Plant i's incremental cost adjusted for its contribution to system loss.

$$\boxed{\lambda_i = \frac{\lambda}{1 + \frac{\partial P_L}{\partial P_i}}}$$

where $$\displaystyle \frac{\partial P_L}{\partial P_i} = 2 \sum_{j=1}^{n} B_{ij} P_j $$.

• Optimal Dispatch Condition: $$\displaystyle \lambda_i $$ must be equal for all plants.

$$\frac{\lambda}{1 + \frac{\partial P_L}{\partial P_1}} = \frac{\lambda}{1 + \frac{\partial P_L}{\partial P_2}} = ...$$

• Calculation Example (from past paper):

  Given: $$\displaystyle \frac{dC_1}{dP_1}=0.15P_1+150 $$, $$\displaystyle \frac{dC_2}{dP_2}=0.25P_2+175 $$, $$\displaystyle P_1=P_2=400 $$ MW, $$\displaystyle \frac{\partial P_L}{\partial P_2}=0.2 $$.

  Find penalty factor of plant 1.

  Solution:

  At optimum, $$\displaystyle \lambda_1 = \lambda_2 $$.

  $$\displaystyle \lambda_1 = \frac{dC_1}{dP_1} = 0.15(400)+150 = 60+150 = 210 $$ Rs/MWh.

  $$\displaystyle \lambda_2 = \frac{dC_2}{dP_2} = 0.25(400)+175 = 100+175 = 275 $$ Rs/MWh.

  But $$\displaystyle \lambda_2 = \frac{\lambda}{1 + \frac{\partial P_L}{\partial P_2}} \Rightarrow 275 = \frac{\lambda}{1+0.2} \Rightarrow \lambda = 275 \times 1.2 = 330 $$ Rs/MWh.

  Now, $$\displaystyle \lambda_1 = \frac{\lambda}{1 + \frac{\partial P_L}{\partial P_1}} \Rightarrow 210 = \frac{330}{1 + \frac{\partial P_L}{\partial P_1}} $$.

  $$\displaystyle \Rightarrow 1 + \frac{\partial P_L}{\partial P_1} = \frac{330}{210} = 1.5714 $$.

  $$\displaystyle \Rightarrow \frac{\partial P_L}{\partial P_1} = 0.5714 $$.

  Penalty Factor of Plant 1: $$\displaystyle \lambda_1 / \lambda = 210 / 330 = \boxed{0.6364} $$.

  Alternatively, directly: $$\displaystyle PF_1 = 1 / (1 + \partial P_L/\partial P_1) = 1 / 1.5714 = 0.6364 $$.

3. Cogeneration

• Definition: Simultaneous generation of electricity and useful thermal energy (heat/steam) from a single fuel source.

• Types:

  • Topping Cycle: Fuel → prime mover (turbine/engine) → electricity → exhaust heat → process heat.

  • Bottoming Cycle: Fuel → furnace/boiler → process heat → waste heat → power generation (e.g., steam from industrial process → turbine).

• Advantages: Very high overall efficiency (70-90%), reduced fuel cost, lower emissions.

D. TARIFFS AND PRICING

• Tariff: Schedule of rates for electrical energy supplied to consumers.

• Objectives: Cost recovery, fairness (cross-subsidy), promote efficiency, encourage conservation.

• Types of Tariffs:

  | Tariff | Structure | Suitable For | Merits/Demerits | | :--- | :--- | :--- | :--- | | Flat Rate | Fixed charge per kWh | Street lighting, agriculture | Simple, but no load factor incentive. | | Block Rate | Different rates for different consumption blocks (increasing or decreasing). | Domestic, commercial. | Simple, progressive (increasing block). | | Two-Part Tariff | Fixed charge (per kW of max demand) + Energy charge (per kWh). | Industrial, commercial. | Recovers fixed & variable costs; encourages high load factor. | | Time-of-Day (TOD) | Different rates for peak, normal, off-peak hours. | All consumers with shiftable load. | Reflects cost of generation; shifts load. | | Peak Load Pricing | Higher charges during system peak hours (few hours/day). | Large industrial/commercial. | Directly reflects scarcity of peak capacity; strong load management incentive. |

• Comparison:

  • Domestic: Often subsidized, increasing block or flat rate.

  • Commercial: Two-part or TOD.

  • Industrial: Two-part, often with demand charge based on max demand (kVA).

V. ENVIRONMENTAL, SAFETY & EMERGING TRENDS

Environmental Impact Assessment

• Thermal: Air pollution (SOx, NOx, PM, CO₂), thermal pollution (cooling water), fly ash disposal.

• Nuclear: Radioactive waste (long-term), accident risk, thermal pollution.

• Hydro: Land submersion, displacement, ecosystem disruption (fish migration), sedimentation.

• Renewables:

  • Solar/Land use (large area).

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

  • Biomass: Air pollution (combustion), land use for energy crops.

  • Geothermal: H₂S emissions, water use, induced seismicity.

Safety Aspects in Wind Turbine Operation

• Structural Safety: Blades, tower, foundation against extreme wind, fatigue.

• Operational Safety: Lockout/tagout during maintenance, fire protection (nacelle), lightning protection.

• Environmental Safety: Noise limits, shadow flicker mitigation, avian monitoring.

Waste Disposal Methods

• Nuclear: Geological repository (high-level), near-surface (low-level), reprocessing.

• Biomass (Ash): Use in cement/construction, landfill, agricultural soil amendment (if non-toxic).

Renewable Energy in India: Achievements & Applications

• Achievements: 5th global renewable capacity; >150 GW installed (solar ~70 GW, wind ~45 GW). World's largest solar park (Bhadla, Rajasthan). World's largest renewable energy corporation (NTPC).

• Applications: Rural electrification (solar home systems), solar pumps, wind farms, solar-wind hybrids, green hydrogen mission, offshore wind (first project in Gujarat/TN).

• Government Policies & Targets: 175 GW by 2022 (achieved), 500 GW non-fossil by 2030, Net Zero by 2070. PLI schemes for solar manufacturing, ALMM (Approved List of Models and Manufacturers), Green Energy Corridors.

Future Energy Strategies

• Grid Integration: Smart grids, grid-scale batteries, pumped storage, demand response.

• Green Hydrogen: Production (electrolysis), storage, transport, use in industry, mobility, power.

• Offshore Wind: Massive potential in Gulf of Khambhat, Bay of Bengal.

• Floating Solar: On reservoirs, dams.

• Energy Storage: Li-ion, flow batteries, compressed air, thermal storage.

• Carbon Capture, Utilization & Storage (CCUS): For existing thermal plants.

Energy Resources Reserve (Indian Context)

• Assessment Categories:

  • Proven (1P): >90% certainty of commercial extraction.

  • Probable (2P): >50% certainty.

  • Possible (3P): >10% certainty.

• India's Reserves (Approx.):

  • Coal: 5th largest globally (~319 BT), but low quality (ash content).

  • Uranium: Limited (~1.5% world), but Thorium: World's largest (~3-5% world reserves in monazite sands).

  • Oil & Gas: Limited domestic; high import dependency (~85% oil).

  • Renewables: Vast potential (solar 5000 GW, wind 300 GW at 120m hub height).