Lecture 7 Energy Conversion Technologies: Solar and Wind

Gang He

October 23, 2023

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

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.

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.