# 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;
$\eta_2 =\frac{\eta_1}{\eta_c}$

## 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

## 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)

## 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

## 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)

## 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 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.