Thermo-Fluid Ch 8

Authors and Acknowledgements

• John Andrews and Nick Jelley (2017).
• Lecture 13: Photovoltaics by Ramesh K. Agarwal, Washington University in St. Louis. Contact: rka@wustl.edu

Textbook Reference

• Andrews & Jelley: Energy Science, 3rd Edition
• Photovoltaic Effect: An Introduction to Solar Cells

References

• The Physics of Solar Cells by Jenny Nelson, Imperial College Press, 2003.
• Solar Cells by Marin A. Green, The University of New South Wales, 1998.
• Silicon Solar Cells by Martin A. Green, The University of New South Wales, 1995.

Solar Energy Potential

• Theoretical energy available:
  • 1.76 × 10^5 TW striking the Earth
• Practical energy harnessing potential:
  • 600 TW (considering 2% of Earth’s surface area)
• Conversion Efficiency:
  • Approximately 10%
• Electricity Generation Potential:
  • Approximately 60 TW
• Estimated Global Demand in 2050:
  • Between 30-35 TW

Land Area Required for Solar Energy

• Distribution of Energy Generation in Various Regions:

  • Europe
  • North America
  • Asia and Russia
  • South America
  • Africa
  • Australia and Oceania

• Example Calculation:

  • 6 Boxes at 4.2 TW each = 25 TW (Source: EB, Inc. 1998)

Solar Land Area Requirement in the U.S.

• Geographical Spread:
  • Various states detailed with approximate land area requirements for solar energy setup based on land-use efficiency.

Photovoltaic Energy Conversion Technologies

• First Generation (I):
  • Crystalline PV
• Second Generation (II):
  • Thin Film PV
• Third Generation (III):
  • Based on nanotechnology, utilizing collections of atoms from semiconducting materials.
  • Films with nano-crystalline structures and nanostructured conducting polymers designed to absorb a vast portion of the solar spectrum.
  • Expected high efficiency and low cost from PV cells made from thinly stacked plastic sheets.

Role of Photo-Electrochemistry in Solar Cells

• Converging area between solar cell technology and battery or fuel cell technology.
• Plays a significant role in the development of organic solar cells.

Photovoltaic Efficiency Over Time

• Power Conversion Efficiency (%):
  • Crystalline Si, Amorphous Si, Nano TiO₂, CIS/CIGS, CdTe from 1950-2000 shown over several decades graphically.

Cost Trends in Photovoltaics

• Cost of Electricity Generated by Photovoltaics:
  • Levelized cost of electricity (COE) trends in cents/kWh from 1980 to 2020.

The Solar Spectrum

• Definition:
  • Corresponds to the spectrum of a black body at 5800 K.
• Impact of Atmosphere:
  • Sunlight intensity reduced from 1.36 kW/m² (AM0) to 1.0 kW/m² (AM1.5).
  • AM1.5 considers that sunlight's effective path through the atmosphere is approximately 1.5 times the height of the standard atmosphere.
  • Corresponds to sunlight at an angle of 48 degrees to the vertical.
• Absorption of Wavelengths:
  • Water vapor, CO2, and CH4 mostly absorb in the infrared region, corresponding to photon energies below 1.7 eV.
  • Visible light energy ranges from ~ 3 eV (400 nm) to ~ 1.7 eV (700 nm).

Incident Solar Radiation Data

• Total Incident Power from the Sun:
  • Approximately 150,000 TW.
• Comparison with Global Power Consumption (2022):
  • Approximately 23 TWth.
• Average Solar Flux on Earth:
  • ~ 1 kW/m² with attenuation from 1.37 kW/m² to 1.0 kW/m² due to the atmosphere.
• Silicon Photovoltaic (PV) Cells:
  • ~20% conversion efficiency observed.
  • Installed capacity and growth statistics from 2015 to 2021:
  • 2015: 242 GWh, 2021: 950 GWh.
• Cost Competitiveness:
  • PV systems becoming competitive or cheaper than fossil fuel generation in various sunny regions.

Solar Radiation Characteristics

• Radiation Types:
  • Direct and Diffuse radiation percentages affected by clarity of sky (Average yearly: 30%).
• Variability with Geography:
  • Total radiation ranges from 2300 kWh/m² in tropics to ~800 kWh/m² in arctic regions.
  • Intensity on cloudy versus sunny days noted (10% near arctic vs. 50% in tropics).
• Insolation Definition:
  • Average energy hitting earth daily (kWh/m²/day); varies by latitude and seasonal changes.

Overview of Solar Cells

• Definition of Solar Cell:
  • Fundamental unit in photovoltaic systems, converting solar radiation to electric current. Typically made from semiconductors.
• Semiconductor Classification:
  • Materials can conduct electricity.
  • Metals: Good conductors.
  • Insulators: Poor conductors.
  • Semiconductors: Intermediate class with moderate conductivity, affected by temperature and impurities.

Example Calculations in Solar Energy

• Example 8.1:
  • Calculation for energy incident on a solar cell given intensity 200 W/m² and an area of 0.1 m².
  • Calculation of Incident Power (P):
  • $P = I imes A = 200 imes 0.1 = 20 ext{ W} = 0.02 ext{ kW}$
  • Calculation of Incident Energy (E):
  • $E = P imes t = 0.02 ext{ kW} imes 24 ext{ h} = 0.48 ext{ kWh}$
  • Also calculated as $E = P imes t = 20 ext{ W} imes 24 imes 60 imes 60s = 1.73 ext{ MJ}$
• Variation with Sunlight Angle:
  • If sunlight arrives at an angle of 30°:
  • The incident power is reduced by factor $ext{cos}(30°)$.
  • New incident energy is $E = 0.42 ext{ kWh} ext{ or } 1.50 ext{ MJ}$

Understanding Photons in Photovoltaics

• Definition of Photon:
  • Smallest energy unit transferred in atomic processes, specifically a quantum of light.
• Einstein’s Relation for Photons' Energy (ε):
  • Given by the formula: ext{Energy}
    ightarrow ext{ } ext{ε} = h imes v
  • Where $h$ = Planck's constant = 6.62 × 10^-34 joule-sec and $v$ = frequency in cycles/s.
• Wavelength Calculation:
  • Relationship given by: $c = ext{λ} imes v$
  • Where $c$ = speed of light = 3 × 10^8 m/s and $ext{λ}$ = wavelength in meters.
• Energy Quantization:
  • Radiation is in whole multiples of hv (as photons).

Power Relations in Photovoltaic Applications

• Incident Power Formula:
  $P = I imes A$
• Incident Energy Calculation:
  $E = P imes t$
• Photon Flux Definition:
  • Number of photons crossing a unit area per second. Quantified in PV calculations.
• Energy of a Photon Record:
  • For a red light wavelength of $λ = 6000A$ (or 6000 × 10^-10 m).

Example 8.2 Reflection and Photon Flux Calculation

• Photon Flux Calculation:
  • Light with a wavelength of 510 nm (green) and intensity of 500 W/m² incident on a solar cell.
• Calculating Photon Energy:
  • The energy of a photon:
    $E_ ext{λ} = h \frac{c}{λ} = \frac{1240}{510} = 2.43 eV$
  • After conversion to Joules:
    $E_ ext{λ} = 2.43 imes 1.6 imes 10^{-19} = 3.89 imes 10^{-19} J$
• Photon Flux (F) Derivation:
  • $F = \frac{I}{E_ ext{λ}} = \frac{500}{3.89 imes 10^{-19}} ext{ photons/m²/s}$
  • Result: $F hickapprox 1.29 imes 10^{21} ext{ photons m}^{-2} ext{s}^{-1}$

Semiconductor Properties and Band Structure

• Overview of Semiconductors:
  • Common materials include silicon, gallium arsenide, germanium, and more.
• band Gap Concept:
  • Energy difference between valence band and conduction band measured in electron volts (eV).
  • Photovoltaic materials only capture photons with energy >= band gap.
  • Example: Silicon is transparent to photons < 1.1 eV due to its band gap.

Doping of Semiconductors

• Doping Process:
  • Impurities introduce charge carriers, creating n-type (excess electrons) and p-type (excess holes) semiconductors.
• p-n Junction Formation:
  • The junction between p-type and n-type forms the basis of photovoltaic solar cells.

p-n Junction Diode Characteristics

• Diode Operation Principle:
  • When illuminated, a net current flows connecting p-type and n-type regions.
  • Solar cell functionality demonstrated by circuit behavior under light impact.

Electrical Behavior of p-n Junctions

• Current-Voltage (I-V) Dynamics in Diodes:
  • A diode's asymmetric response contrasts with resistors, showing exponential I-V behavior rather than linear.
  • Forward and Reverse bias explained:
  • Forward bias: Allows current flow when the applied voltage exceeds the barrier (0.7 V for silicon).
  • Reverse bias: Increases depletion zone width, thus impeding current.

Performance Calculations in Solar Cells

• Open Circuit Voltage (Voc) Explanation:
  • Voltage developed when no current is drawn, analogous to battery e.m.f.
• Short Circuit Current (Isc):
  • Current when terminals shorted together reflects maximum current output.

Characteristics of a Photocell

• Photocell Current Calculation Example:
  • Relations for reverse light-induced (IL) and photocell current (IC) derived using equations involving the saturation current (IS) and current density (Jsc).
• Power Generation from Photocell:
  • Power generated expressed as:
    $P_c = IC imes V$

Efficiency of Photovoltaic Cells

• Example Efficiency Calculation:
  • For a photocell with given saturation and short circuit current.
• Evaluation of maximum power output and fill factor obtained through operational formulas.
  • Typical figures illustrated for efficiency outcomes in varied operational conditions.

Summary on Solar Cell Modules

• Series Connection for Voltage Generation:
  • PV cells connected in series form modules, typically 28-36 in a series to yield 12 V DC.
• Blocking Diodes:
  • Employed to prevent power loss from failing cells.

Production Overview of Solar Cells

• Commercial Solar Cell Types:
  • Silicon cells vs. thin film cells.
  • Market shares and trends, including cost reductions through scaling.

Global Trends in Solar Energy

• Expansion of Capacity:
  • Growth from 41 GWp in 2010 to 950 GWp in 2022, with average capacity factors across regions noted.
• Projected Potential by 2050:
  • Estimated 2000 - 5000 GWe potential for solar energy generation, especially in developing and hot countries.
• Environmental Impact:
  • Low CO2 emissions associated with solar energy generation noted.

Key Points in Solar Energy Utilization

• Resource Availability and Use:
  • Solar energy resource ability is vastly underutilized.
• Conversion Efficiencies:
  • Increasing possible efficiencies with technology advancements (perovskites).
• Cost Trends and Production Capacities:
  • Significant drops in electricity generation costs achieving grid parity in sunny regions.
• Future Prospects for Solar Energy:
  • Potential to exceed 40% contribution of global electricity needs by 2050 and necessitating optimized deployment strategies for variability concerns.