Lecture 5 Energy Sources and Technologies

Gang He

September 19, 2022

Sample analytic questions

• How many solar/wind capacities are needed to meet global energy need?
  
• How much coal can be saved/emissions can be mitigated if China’s average coal power efficiency increased by 1 percentage point?
  
• Why combined heat and power saves energy?
  
• How to design the layout of solar/wind farms to improve production?

Thermodynamics

• Thermodynamic efficiency
  
• Comparing different technologies
  
• Thermodynamics provides physic limits

Heat engine

Heat -> Mechanical energy (work)

Laws of thermodynamics

• Zeroth law
  “If two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other.”

• First law
  “In a process without transfer of matter, the change in internal energy, \(\Delta U\), of a thermodynamic system is equal to the energy gained as heat, \(Q\), less the thermodynamic work, \(W\), done by the system on its surroundings.”

• Second law
  “Heat does not spontaneously flow from a colder body to a hotter body.”

• Third law
  “As the temperature of a system approaches absolute zero, all processes cease and the entropy of the system approaches a minimum value.”

Three efficiencies

• 1st law: actual, thermal efficiency;
  \(\eta_1 =\frac{W_{net}}{Q_{in}}=\frac{Q_{high}-Q_{low}}{Q_{high}}=1-\frac{Q_{low}}{Q_{high}}\)
• Carnot: maximum possible efficiency;
  \(\eta_c =\frac{W_{net}}{Q_{high}}=\frac{T_{high}-T_{low}}{T_{high}}=1-\frac{T_{low}}{T_{high}}\) (Kelvin)
  
• 2nd law: comparing 1st and Carnot;
  \(\eta_2 =\frac{\eta_1}{\eta_c}\)

How steam coal plants work

Brayton cycle vs. Rankine cycle

Jet engine, gas turbine

Steam engine, steam turbine

Largest coal plant in the U.S.

Georgia Power plant Scherer (3,720 MW)

Can you identify the components

• Coal storage
  
• Generating unit
  
• Cooling stack
  
• Bottom ash landfill
  
• Sub-station
  
• Transimission lines
  
• Waste/pollution management
  

Combined cycle

Wind

\(P=\frac{1}{2}\rho \pi r^2 v^3\)

Where,
\(\rho\) = Density (kg/m3)
\(A\) = Swept Area (m2) = \(\pi r^2\)
\(v\) = Wind Speed (m/s)
\(P\) = Power (W)

Betz’s law: 59.3%

Average power

Rayleigh (a special type of Weibull) distribution

\(f(v)=\frac{2v}{c^2}\exp [-(\frac{v}{c})^2]\)

\(\bar{P}=\frac{6}{\pi}\cdot \frac{1}{2}\rho \pi r^2 \bar{v}^3=1.91P\)

Use average power when dealing with average wind speed

Power curve

Important corrections

• Temperature: \(\rho = \frac{P\times M.W. \times 10^{-3}}{RT}=\frac{1 atm\times 28.97 g/mol \times 10^{-3}kg/g}{8.2056\times 10^{-5}m^3\cdot atm/(K\cdot mol)\times(273.15+T)K}\)
  
• Altitude: \(P=P_0 e^{-1.185\times 10^{-4}H}\) (H is elevation in meters)
  
• Tower height: \(\frac{v}{v_0}=(\frac{H}{H_0})^\alpha\) (is the friction coefficient)

Solar

How solar works

Key corrections

• Solar position at any time of day: altitude angle, latitude, zaimuth angle, hour angle
  
• Radiation: direct beam, diffusion, reflected
  
• Tracking: fixed, 1-axis, 2-axis

Hydro

Hydropower

Pumped storage hydropower (PSH)

\(E=\rho mg(h_2-h_1)\)

Nuclear

Nuclear fission

Nuclear fussion

Summary

• Theory - learn and understand the physics of energy technologies:
  • thermaldynamics (fossil)
    
  • kinematics (wind)
    
  • light and semiconductor (solar)
    
  • gravity (hydro, tidal)
    
  • atomic (nuclear)
    
• Practice - learn all kinds of corrections based on real-world situation
  
• The physics doesn’t change, corrections help us to do better jobs in simulation and projections

References

Masters, Gilbert M. 2013. Renewable and Efficient Electric Power Systems. John Wiley & Sons.