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Module 4 · Solar Energy: Photovoltaic Cells
A solar (photovoltaic) cell converts light energy directly into electricity via the photovoltaic effect. Photons absorbed by a semiconductor create electron-hole pairs, separated by the p-n junction to produce current. Cells connect in series for voltage, parallel for current.
Solar Energy Overview
$$\boxed{E_{solar} = 1.6 \times 10^{18}\;\text{kWh/year (Earth receives)}}$$
$$G \approx 1000\;\text{W/m}^2\;\text{(peak, clear sky)} \quad G_{avg} \approx 200\text{–}250\;\text{W/m}^2\;\text{(India avg)}$$
Solar Cell Output
$$\boxed{P_{cell} = V_{OC} \times I_{SC} \times FF}$$
$$V_{OC} \approx 0.5\text{–}0.7\;\text{V} \quad I_{SC}\;\text{(A)} \quad FF \approx 0.7\text{–}0.85\;\text{(fill factor)}$$
Cell Efficiency
$$\eta_{cell} = \frac{P_{max}}{G \times A_{cell}} \quad \eta_{Si} \approx 15\text{–}22\% \quad \eta_{multi\text{-}junction} \approx 40\%+$$
PV Operation Steps
$$\text{1. Light absorption} \rightarrow \text{2. e-h pair generation} \rightarrow \text{3. Charge separation}$$
$$\rightarrow \text{4. External circuit extraction} \rightarrow \text{5. Battery storage} \rightarrow \text{6. Load (utility)}$$
Panel Scaling
$$\text{Cell} \xrightarrow{\text{series}} \text{Module} \xrightarrow{\text{series/parallel}} \text{Panel} \xrightarrow{\text{series/parallel}} \text{Array}$$
$$V_{total} = n_s \times V_{cell} \quad I_{total} = n_p \times I_{cell}$$
$$\boxed{P_{array} = n_s \times n_p \times V_{cell} \times I_{cell} \times FF}$$
Temperature Effect
$$P_{actual} = P_{rated}[1 - 0.004(T - 25)] \quad \text{STC: } G=1000\;\text{W/m}^2,\;T=25°C$$
☀️ Solar Cell & Panel Scaling
SOLAR CELL CROSS-SECTION
☀️ Sunlight (photons) ↓
Anti-reflection coating
N-type silicon (e⁻ rich)
═══ P-N Junction (depletion zone) ═══
P-type silicon (h⁺ rich)
Back contact (metal)
e⁻ → N-layer → external circuit → P-layer → current flows!
SOLAR ARRAY CALCULATOR
TEMPERATURE DERATING
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Module 4 · Solar Energy: Thermal & Systems
Concentrated Solar Power (CSP) uses mirrors or lenses to focus sunlight, generating high temperatures for power generation. Types include parabolic trough, solar tower, dish Stirling, and linear Fresnel — complementing PV with thermal storage capability.
Solar Thermal Formulas
$$Q_{absorbed} = \alpha G A_{collector} \quad Q_{useful} = \dot{m}c_p(T_{out} - T_{in})$$
$$\eta_{collector} = \frac{Q_{useful}}{G \cdot A} = \alpha - \frac{U_L(T_c - T_a)}{G}$$
Collector Types
$$\eta_{FPC} \approx 50\text{–}70\%\;\text{(flat plate, low temp, hot water)}$$
$$\eta_{CSP} \approx 15\text{–}25\%\;\text{(concentrating, high temp)} \quad T_{focus} = 200\text{–}1000°C$$
CSP Types
$$\text{1. Parabolic Trough (linear focus)} \quad \text{2. Solar Tower (central receiver)}$$
$$\text{3. Parabolic Dish (point focus, highest T)} \quad \text{4. Linear Fresnel Reflector}$$
Solar Power & Capacity Factor
$$P_{solar} = G \times A \times \eta_{panel} \quad CF_{solar} \approx 15\text{–}25\%\;\text{(daylight only)}$$
India Solar Status
$$\text{Potential: 748 GW} \quad \text{Installed: } \approx 73\;\text{GW (2024)} \quad \text{Target: 280 GW by 2030}$$
$$\text{Irradiance (India avg): } 4\text{–}7\;\text{kWh/m}^2\text{/day — JNNSM}$$
☀️ CSP Types & India Solar
CSP TECHNOLOGIES
Parabolic Trough
Linear focus · 400°C · Most deployed CSP
Solar Tower
Central receiver · 600°C · Heliostat field
Parabolic Dish
Point focus · 1000°C · Highest T · Stirling
Linear Fresnel
Flat mirrors · 300°C · Lower cost
FLAT PLATE vs CONCENTRATING
FPC: T_max=80°C (hot water only)
CSP: T_max=500°C+ (power gen!)
🇮🇳 INDIA SOLAR TARGET
JNNSM — Jawaharlal Nehru National Solar Mission
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Module 4 · Non-Conventional Energy: Wind, Tidal, Geothermal & Biogas
Non-conventional (renewable) energy sources — wind, tidal, geothermal, and biogas — provide sustainable alternatives to fossil fuels. Wind power follows the cube law (doubling wind speed = 8× power), constrained by the Betz limit of 59.3% maximum efficiency.
Wind Energy
$$\boxed{P_{wind} = \frac{1}{2}\rho_{air} A v^3 C_p} \quad A = \pi R^2 \quad C_{p,max} = \frac{16}{27} \approx 0.593\;\text{(Betz limit)}$$
$$v_{cut\text{-}in} \approx 3\text{–}4\;\text{m/s} \quad v_{rated} \approx 12\text{–}15\;\text{m/s} \quad v_{cut\text{-}out} \approx 25\;\text{m/s}$$
$$\text{India: Installed } \approx 44\;\text{GW} \quad \text{Potential: 695 GW} \quad \text{Best: TN, Gujarat, Rajasthan}$$
Tidal Energy
$$\boxed{E_{tidal} = \frac{1}{2}\rho g A h^2} \quad \text{per tidal cycle} \quad h = \text{tidal range} \quad h > 5\;\text{m (minimum viable)}$$
$$\text{India potential: Gulf of Kutch, Gulf of Khambhat}$$
Geothermal Energy
$$Q_{geo} = \dot{m}c_p(T_{geo} - T_{surface}) \quad T_{geo} = 150\text{–}350°C \quad \text{Gradient: } 25\text{–}30°C/\text{km}$$
$$\eta_{geo} \approx 10\text{–}23\% \quad \text{Types: Dry steam} \cdot \text{Flash steam} \cdot \text{Binary cycle}$$
$$\text{India: Puga Valley (Ladakh), Tattapani (MP), Manikaran (HP)}$$
Biogas / Biomass
$$\text{Biogas: } CH_4 + CO_2 \;\text{(from organic waste)} \quad CV \approx 20\text{–}25\;\text{MJ/m}^3 \quad \eta \approx 20\text{–}25\%$$
$$C_6H_{12}O_6 \xrightarrow{\text{anaerobic}} 3CH_4 + 3CO_2$$
🌿 Wind, Tidal & Geothermal
💨 WIND POWER CALCULATOR
🌊 TIDAL ENERGY CALCULATOR
RENEWABLE SOURCES AT A GLANCE
Wind
44 GW | CF: 25-35%
Solar
73 GW | CF: 15-25%
Hydro
47 GW | CF: 40-60%
Geothermal
η: 10-23% | CF: 80-90%
Tidal
h > 5m | Kutch, Khambhat
Biogas
20-25 MJ/m³ | η: 20-25%
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Module 4 · Module 4 Complete Reference
Master reference for Module 4: Diesel cycle, Brayton cycle, solar PV & thermal, wind power, tidal energy, geothermal, and biogas — with complete comparison of all power plant types, India's renewable targets, and interactive quiz.
Diesel & Gas Turbine
$$\eta_{Diesel} = 1 - \frac{1}{r^{\gamma-1}} \cdot \frac{r_c^{\gamma}-1}{\gamma(r_c-1)} \quad \eta_{Brayton} = 1 - r_p^{-(\gamma-1)/\gamma}$$
$$\eta_{GT,simple} = 32\text{–}38\% \quad BWR = \frac{W_C}{W_T} \approx 40\text{–}80\%$$
Solar PV & Thermal
$$P_{cell} = V_{OC} \cdot I_{SC} \cdot FF \quad P_{array} = n_s \cdot n_p \cdot P_{cell} \quad \eta_{cell} = \frac{P_{max}}{G \cdot A}$$
$$E_{sun} = 1.6 \times 10^{18}\;\text{kWh/yr} \quad \eta_{coll} = \alpha - \frac{U_L(T_c-T_a)}{G}$$
Wind & Tidal
$$P_{wind} = \frac{1}{2}\rho Av^3 C_p \quad C_{p,max} = \frac{16}{27} \quad E_{tidal} = \frac{1}{2}\rho gAh^2$$
Non-Conventional Summary Table
| Source | Efficiency | CF | Best For |
|---|---|---|---|
| Solar PV | 15–22% | 15–25% | Distributed |
| Solar CSP | 15–25% | 25–40% | Large utility |
| Wind | 35–45% | 25–35% | Open terrain |
| Hydro | 85–92% | 40–60% | Base+Peak |
| Geothermal | 10–23% | 80–90% | Baseload |
| Biogas | 20–25% | 60–80% | Rural waste |
📊 India Targets & Quiz
🇮🇳 INDIA 2030 RENEWABLE TARGETS
MODULE 4 QUICK QUIZ
Q1: Betz limit for wind turbine Cp_max is?
POWER PLANT MASTER COMPARISON
Module 4 Part 2 — Solar Energy Deep Dive
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Module 4.2 · Solar Constant & Solar Spectrum
The solar constant is the amount of energy normally falling on a unit area (1 m²) of Earth's atmospheric surface per second when Earth is at its mean distance from the Sun. Most infrared photons (E < 1.12 eV) cannot generate electricity in silicon cells.
Solar Constant
$$\boxed{G_{sc} = 1367\;\text{W/m}^2 = 1.36\;\text{kW/m}^2}$$
$$\text{Sun radiates: } 3.5 \times 10^{26}\;\text{kW} \quad \text{Earth receives: } 2 \times 10^{17}\;\text{kW}$$
Solar Spectrum Composition
$$\text{Ultraviolet: } 7\% \quad \text{Visible: } 46\% \quad \text{Infrared: } 47\%$$
$$G_{surface} = G_{sc} \times \tau_{atm} \approx 800\text{–}1000\;\text{W/m}^2\;\text{(clear sky)}$$
$$G_{diffuse} \approx 100\text{–}200\;\text{W/m}^2$$
Band Gap & Photon Energy
$$\boxed{E_{g,Si} = 1.12\;\text{eV}} \quad E_{photon} = h\nu = \frac{hc}{\lambda} \quad h = 6.626 \times 10^{-34}\;\text{J}{\cdot}\text{s}$$
$$E_{photon} < E_g: \text{ NOT absorbed} \quad E_{photon} > E_g: \text{ excess → heat} \quad E_{photon} = E_g: \text{ max η}$$
Shockley–Queisser Limit
$$\boxed{\eta_{SQ} \approx 33.7\%} \quad \text{at } E_g \approx 1.34\;\text{eV (optimal)}$$
$$\text{Si: } E_g = 1.12\;\text{eV (near optimal)} \quad \text{Best range: } E_g = 1\text{–}1.5\;\text{eV}$$
$$\text{Multi-junction: } \eta > 33.7\% \quad \text{Record: } \eta > 47\%\;\text{(4+ junction, concentrated)}$$
☀️ Solar Spectrum & Band Gap
SOLAR SPECTRUM
300 nmUV← Visible →Infrared2500 nm
⚠️ IR below 1.12 eV (λ > 1107 nm) → cannot generate power in Si cells
PHOTON ABSORPTION
🔴
IR Photon
E < 1.12 eV
✗ Passes through
🟢
Visible Photon
E ≈ E_g
✓ Creates e-h pair!
🟣
UV Photon
E >> E_g
⚡ Excess → heat
PHOTON ENERGY CALCULATOR
SHOCKLEY–QUEISSER LIMIT
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Module 4.2 · Solar Cell I-V & P-V Characteristics
The solar cell I-V curve defines output — from short circuit current (I_sc) at V=0 to open circuit voltage (V_oc) at I=0. The Maximum Power Point (MPP) is where P = V×I is maximized. Fill Factor measures how close to ideal the cell operates. Shadow effects dominate in series configuration.
I-V Characteristic
$$\boxed{I = I_L - I_0\left[\exp\!\left(\frac{qV}{nkT}\right) - 1\right]}$$
$$\text{At } V=0:\; I_{sc} = I_L \quad \text{At } I=0:\; V_{oc} = \frac{nkT}{q}\ln\!\left(\frac{I_L}{I_0}+1\right)$$
$$V_{oc} \approx 0.5\text{–}0.7\;\text{V (per Si cell)} \quad I_{sc} \propto G \quad V_{oc} \propto \ln(G)$$
P-V & Maximum Power Point
$$P = V \times I = V\left[I_L - I_0\!\left(e^{qV/nkT}-1\right)\right]$$
$$\frac{dP}{dV} = 0 \Rightarrow \text{Maximum Power Point (MPP)} \quad \boxed{P_{mp} = I_{mp} \times V_{mp}}$$
Fill Factor & Efficiency
$$\boxed{FF = \frac{V_{mp} \times I_{mp}}{V_{oc} \times I_{sc}}} \quad \text{Ideal: } FF=1 \quad \text{Practical: } FF \approx 0.7\text{–}0.85$$
$$\boxed{P_{max} = I_{sc} \times V_{oc} \times FF} \quad \boxed{\eta\% = \frac{I_{sc} \cdot V_{oc} \cdot FF}{G \cdot A} \times 100}$$
Shadow Effects
$$\text{Shadow more dominant in SERIES than parallel}$$
$$\text{One shaded cell} \rightarrow \text{entire series string limited!}$$
$$\text{Without bypass: } P_{lost} = P_{string} \quad \text{With bypass: } P_{lost} = P_{module\;only}$$
📈 I-V Curve, Fill Factor & Shadow
I-V CHARACTERISTIC
FILL FACTOR & EFFICIENCY
SHADOW EFFECT (Click cells to shade)
Cell 1
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→
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Cell 2
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→
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Cell 3
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→⚡
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Series: All lit → Full current ✓
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Module 4.2 · Solar Cell Materials
Thin-film technologies reduce the active material to under 5 μm (vs 180 μm for crystalline Si), cutting costs by up to 90%. Key types include monocrystalline, polycrystalline, thin-film (CdTe, CIGS, a-Si), and bifacial cells — each balancing efficiency, cost, and lifespan.
Efficiency Comparison
$$\eta_{mono} \approx 18\text{–}22\% \quad \eta_{poly} \approx 15\text{–}18\% \quad \eta_{thin\,film} \approx 10\text{–}13\%$$
$$\eta_{bifacial} \approx 20\text{–}24\% \quad \eta_{CdTe} \approx 10\text{–}12\% \quad \eta_{CIGS} \approx 12\text{–}15\%$$
Rankings
$$\text{Efficiency: Bifacial} > \text{Mono} > \text{Poly} > \text{Thin film}$$
$$\text{Cost (cheapest first): Thin film} < \text{Poly} < \text{Mono} < \text{Bifacial}$$
$$\text{Lifespan: Bifacial} \approx \text{Mono (30 yr)} \geq \text{Poly (25 yr)} > \text{Thin (15 yr)}$$
Thin Film Materials
$$\text{1. CdTe (Cadmium Telluride)} \quad \text{2. CIGS (Cu-In-Ga-Se)} \quad \text{3. a-Si (Amorphous Si)}$$
$$\text{Thin film thickness: } < 5\;\mu\text{m} \quad \text{vs Si wafer: } \approx 180\;\mu\text{m}$$
$$\text{→ 90\% less material than crystalline Silicon}$$
Applications
$$\text{1. Rural electrification} \quad \text{2. Solar lamps} \quad \text{3. Agriculture} \quad \text{4. Water heaters}$$
🔬 Solar Cell Materials & Comparison
CELL TYPE COMPARISON
MONO-Si
η: 18–22%
Life: 25–30 yr
Cost: ₹₹₹
POLY-Si
η: 15–18%
Life: 20–25 yr
Cost: ₹₹
THIN FILM
η: 10–13%
Life: 10–20 yr
Cost: ₹
BIFACIAL
η: 20–24%
Life: 25–30 yr
Cost: ₹₹₹₹
CdTe
η: 10–12%
Life: 15–20 yr
Cost: ₹
CIGS
η: 12–15%
Life: 15–20 yr
Cost: ₹₹
LIFESPAN COMPARISON
STRUCTURE CROSS-SECTION
CELL TYPE RECOMMENDER
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Module 4.2 · Solar Cell Power Plant
Solar power plants convert sunlight to electricity at scale. Three system types exist: ON Grid (exports excess to grid, no battery), OFF Grid (fully independent with battery), and Hybrid (battery + grid — best reliability). Panel sizing depends on daily load, peak sun hours, and system efficiency.
Solar Energy Scale
$$\text{Sun radiates: } 3.5 \times 10^{26}\;\text{kW} \quad \text{Earth: } 2 \times 10^{17}\;\text{kW}$$
$$\boxed{P_{harness} \approx 2 \times 10^{13}\;\text{kW}} \quad \text{≡ burning 17 million tonnes of coal}$$
System Types
$$\text{i. ON Grid:} \quad \text{Solar} \rightarrow \text{Inverter} \rightarrow \text{Transformer} \rightarrow \text{Meter} \rightarrow \text{Grid}$$
$$P_{export} = P_{generated} - P_{consumed} \quad \text{(net metering, no battery)}$$
$$\text{ii. OFF Grid:} \quad \text{Solar} \rightarrow \text{Charge controller} \rightarrow \text{Battery} \rightarrow \text{Inverter} \rightarrow \text{Load}$$
$$\text{iii. Hybrid:} \quad \text{ON grid + OFF grid} \quad \text{Priority: Solar} \rightarrow \text{Battery} \rightarrow \text{Grid}$$
System Sizing
$$\boxed{P_{panel} \geq \frac{E_{daily}}{H_{peak} \times \eta_{system}}} \quad H_{peak} \approx 4\text{–}6\;\text{hrs/day} \quad \eta_{sys} \approx 0.75$$
$$\boxed{C_{bat} = \frac{E_{daily} \times \text{Autonomy days}}{DOD \times \eta_{bat} \times V_{bat}}} \quad DOD = 0.5\text{–}0.8$$
Components
$$\text{1. Solar panel array} \quad \text{2. Charge controller} \quad \text{3. Battery bank}$$
$$\text{4. DC/AC Inverter} \quad \text{5. Monitoring system} \quad \text{6. Switchgear/Meter}$$
🏭 Solar Power Plant Systems
☀️ ON GRID
🔋 OFF GRID
⚡ HYBRID
No battery needed · Net metering · Grid-tied
Battery essential · Remote areas, islands
Best reliability · Battery + Grid backup
SYSTEM SIZING CALCULATOR
🔋 BATTERY BANK SIZING
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Module 4.2 · Solar Complete Reference
Master reference for Module 4 Part 2: solar constant, photon physics, I-V characteristics, cell materials, and solar power plant systems. All formulas, rankings, and system types consolidated with an interactive quiz.
All Solar Formulas
$$G_{sc} = 1367\;\text{W/m}^2 \quad E_{photon} = hc/\lambda \quad E_{g,Si} = 1.12\;\text{eV}$$
$$\eta_{SQ} = 33.7\%\;(E_g = 1.34\;\text{eV}) \quad I = I_L - I_0[e^{qV/nkT}-1]$$
$$V_{oc} = \frac{nkT}{q}\ln(I_L/I_0+1) \quad FF = \frac{V_{mp}I_{mp}}{V_{oc}I_{sc}}$$
$$P_{max} = V_{oc} \cdot I_{sc} \cdot FF \quad \eta = \frac{I_{sc} \cdot V_{oc} \cdot FF}{G \cdot A}$$
$$P_{panel} \geq \frac{E_{daily}}{H_{peak} \cdot \eta_{sys}} \quad C_{bat} = \frac{E \cdot \text{days}}{DOD \cdot \eta_{bat} \cdot V_{bat}}$$
Material Rankings
$$\eta:\;\text{Bifacial} > \text{Mono} > \text{Poly} > \text{CIGS} > \text{CdTe} > \text{a-Si}$$
$$\text{Cost:}\;\text{Thin film} < \text{Poly} < \text{Mono} < \text{Bifacial}$$
System Types
$$\text{ON grid: export/import | No battery} \quad \text{OFF grid: battery essential | Remote}$$
$$\text{Hybrid: best reliability | Battery + Grid}$$
📊 Solar Deep-Dive Quiz & Summary
QUICK I-V ANALYSIS
SYSTEM COMPARISON
| Feature | ON Grid | OFF Grid | Hybrid |
|---|---|---|---|
| Battery | No | Yes (essential) | Yes |
| Grid | Required | Not needed | Optional |
| Cost | Lowest | High | Highest |
| Reliability | Grid-dependent | Battery-dependent | Best |
| Best For | Urban rooftop | Remote areas | Critical loads |
SOLAR DEEP-DIVE QUIZ
Q1: What is the solar constant?
CELL EFFICIENCY RANKING
☀️ MODULE 4 PART 3 — Solar Collectors, Solar Thermal & Heliostats