Lecture 7 Energy Conversion Technologies

Gang He

October 21, 2024

Solar

Solar spectrum

Solar constant: 1.361 kW/m2

Harvesting the sun

Heqing Solar Cooker Project in Zhangye

Young NaDEET students in Namibia learning to use a parabolic solar cooker

Silicon

P and N type

P-N Junction

How solar works

Solar irradiance

• Direct normal irradiance (DNI)
  
• Diffuse horizontal irradiance (DHI)
• Ground reflected irradiance (GRI)
  
• Global horizontal irradiance (GHI)
  
• Plane-of-array irradiance (POA)

GHI=DNI+DHI+GRI

POA = GHI \(\times \cos \theta\)

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

The quest for efficiency

Global and U.S. distribution

Air pollution and dust

Prioritize solar installation

Solar thermal: CSP

Wind

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

Where,
\(\rho\) = Air Density (\(kg/m^3\))
\(A\) = Swept Area (\(m^2\)) = \(\pi r^2\)
\(v\) = 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: \(\frac{v}{v_0}=(\frac{H}{H_0})^\alpha\) (\(\alpha\) is the friction coefficient)

Class of wind resources

Class	10 m (33 ft)		50 m (164 ft)
	Wind power density (W/m2)	Speed m/s (mph)	Wind power density (W/m2)	Speed m/s (mph)
1	0 - 100	0 - 4.4 (0 - 9.8)	0 - 200	0 - 5.6 (0 - 12.5)
2	100 - 150	4.4 - 5.1 (9.8 - 11.5)	200 - 300	5.6 - 6.4 (12.5 - 14.3)
3	150 - 200	5.1 - 5.6 (11.5 - 12.5)	300 - 400	6.4 - 7.0 (14.3 - 15.7)
4	200 - 250	5.6 - 6.0 (12.5 - 13.4)	400 - 500	7.0 - 7.5 (15.7 - 16.8)
5	250 - 300	6.0 - 6.4 (13.4 - 14.3)	500 - 600	7.5 - 8.0 (16.8 - 17.9)
6	300 - 400	6.4 - 7.0 (14.3 - 15.7)	600 - 800	8.0 - 8.8 (17.9 - 19.7)
7	400 - 1000	7.0 - 9.4 (15.7 - 21.1)	800 - 2000	8.8 - 11.9 (19.7 - 26.6)

Global wind power density map

Higher and bigger

Offshore wind

Challenges

Low speed wind

Smaller generator. \(\rightarrow\) Decreased generator weight and cost.

Operating at higher capacity in lower wind speeds. \(\rightarrow\) Greater generator efficiency.

Decreased tower head mass. \(\rightarrow\) Decreased foundation and tower costs.

Decreased PE system rating. \(\rightarrow\) Decreased PE system costs

Unexpected benefits

Climate change impact

Pros and Cons

Pros	Cons
Renewables	Variable & integration
Low emissions	Land use & NIMBY
Low costs	Distribution

Hybrid power systems

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

A gas turbine engine

A steam coal plant

Brayton cycle vs. Rankine cycle

Jet engine, gas turbine

Steam engine, steam turbine

Brayton cycle vs. Rankine cycle

Brayton Cycle	Rankine Cycle
Jet, Gas turbine	Steam turbine
Open	Open/closed circuits
Working fluid in gaseous phase	Working fluid phase change

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

CCGT diagram

Updating an Rosenfeld Plant?

	2010	2021
Size (MW)	500	940
Capacity Factor	70%	43%
Generation (TWh/yr)	~ 3	~ 3.6
Emissions (Mt/yr)	~ 3	~ 3.5

• NYC electricity use in 2020: ~4 TWh/year

Nuclear

Nuclear fission

Nuclear fussion

Nuclear power plants

Nuclear plant design

Diagram of a boiling-water nuclear reactor

Diagram of a pressurized-water nuclear reactor

Nuclear fuel cycle

Social > technology challenges

• Public engagement
  
• Lower capital costs
  
• Social and decision sciences
  
• Science and technology study
  
• Nuclear waste siting
  
• Best practices

Next generation of nuclear technology

• Modality
  
• Lower capital costs
  
• Siting flexibility
  
• Higher efficiency
  
• Safe and security
  
• Industry and manufacture
  
• Economic

Livermore Fusion breakthrough

Hydro

Hydropower

Pumped storage hydropower (PSH)

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

How a lithium-ion battery works

Battery management system

• Rated power capacity
  
• Energy capacity
  
• Storage duration
  
• Cycle life/lifetime
  
• Self-discharge
  
• State of charge
  
• Round-trip efficiency

Long duration storage

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

Bergin, Mike H, Chinmay Ghoroi, Deepa Dixit, James J Schauer, and Drew T Shindell. 2017. “Large Reductions in Solar Energy Production Due to Dust and Particulate Air Pollution.” Environmental Science & Technology Letters 4 (8): 339–44.

Chen, Shi, Xi Lu, Chris P. Nielsen, Michael B. McElroy, Gang He, Shaohui Zhang, Kebin He, Xiu Yang, Fang Zhang, and Jimin Hao. 2023. “Deploying Solar Photovoltaic Energy First in Carbon-Intensive Regions Brings Gigatons More Carbon Mitigations to 2060.” Communications Earth & Environment 4 (October): 369. https://doi.org/10.1038/s43247-023-01006-x.

Dowling, Jacqueline A., Katherine Z. Rinaldi, Tyler H. Ruggles, Steven J. Davis, Mengyao Yuan, Fan Tong, Nathan S. Lewis, and Ken Caldeira. 2020. “Role of Long-Duration Energy Storage in Variable Renewable Electricity Systems.” Joule 4 (9): 1907–28. https://doi.org/10.1016/j.joule.2020.07.007.

Koomey, Jonathan, Hashem Akbari, Carl Blumstein, Marilyn Brown, Richard Brown, Chris Calwell, Sheryl Carter, et al. 2010. “Defining a Standard Metric for Electricity Savings.” Environmental Research Letters 5 (1): 014017. https://iopscience.iop.org/article/10.1088/1748-9326/5/1/014017.

Liu, Laibao, Gang He, Mengxi Wu, Gang Liu, Haoran Zhang, Ying Chen, Jiashu Shen, and Shuangcheng Li. 2023. “Climate Change Impacts on Planned Supply–Demand Match in Global Wind and Solar Energy Systems.” Nature Energy 8 (8): 870–80. https://doi.org/10.1038/s41560-023-01304-w.

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