Gang He

September 19, 2022

- 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?

- Thermodynamic
**efficiency**

- Comparing different technologies

- Thermodynamics provides physic limits

Heat -> Mechanical energy (work)

Source: Wikipedia

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.”

Read more: Wikipedia

- 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;

\(\eta_2 =\frac{\eta_1}{\eta_c}\)

Read more: Sadi Carnot

Source: Wikipedia

Jet engine, gas turbine

Steam engine, steam turbine

Read more: Wikipedia Brayton cycle and Rankine cycle

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

Source: Google Map, read more: Nowhere to hide

Read more: Tennessee Valley Authority

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

Where,

\(\rho\) = Density (kg/m3)

\(A\) = Swept Area (m2) = \(\pi r^2\)

\(v\) = Wind Speed (m/s)

\(P\) = Power (W)

Photo by Gang He

Source: Masters (2013)

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

Read more: Masters (2013)

Read more: NREL, Validation of Power Output for the WIND Toolkit

- 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)

Read more: Masters (2013)

- 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

Read more: Masters (2013)

Hydropower

Pumped storage hydropower (PSH)

Source: TVA

Nuclear fission

Nuclear fussion

Read more: EIA, Nuclear explained; DOE, Nuclear fusion reactions

- Theory - learn and understand the physics of energy technologies:
- thermaldynamics (fossil)

- kinematics (wind)

- light and semiconductor (solar)

- gravity (hydro, tidal)

- atomic (nuclear)

- thermaldynamics (fossil)
- 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

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