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OpenRiver OpenRiver
Student Research and Creative Projects 2015-2016 Grants & Sponsored Projects
9-1-2015
Statistical Analysis and Forecasting Solar Radiation in Arizona Statistical Analysis and Forecasting Solar Radiation in Arizona
Yao Li Winona State University
Paige Ng Winona State University
Follow this and additional works at: https://openriver.winona.edu/studentgrants2016
Recommended Citation Recommended Citation Li, Yao and Ng, Paige, "Statistical Analysis and Forecasting Solar Radiation in Arizona" (2015). Student Research and Creative Projects 2015-2016. 9. https://openriver.winona.edu/studentgrants2016/9
This Grant is brought to you for free and open access by the Grants & Sponsored Projects at OpenRiver. It has been accepted for inclusion in Student Research and Creative Projects 2015-2016 by an authorized administrator of OpenRiver. For more information, please contact [email protected].
Yao Li & Paige Ng
Winona State University
Statistical Analysis and Forecasting Solar Radiation in Arizona
• Introduction• What is The Arizona Meteorological Network (AZMET)?• Map of Sensor Stations• Data Variables • Problems of Data Mining• OLS regression with lagged variables• Seasonal Decomposition• Exceedance Probabilities• Further Research Possibilities
Yao Li and Paige Ng Statistical Analysis and Forecasting Solar Radiation in Arizona WINONA STATE UNIVERSITY
Outline
• Goal: Determine profitable solar panel sites in Arizona
• Most essential variable Solar Insulation: a measure of solar radiation energy received on a given surface area and recorded during a given time
• High • Stable
Introduction
Yao Li and Paige Ng Statistical Analysis and Forecasting Solar Radiation in Arizona WINONA STATE UNIVERSITY
38 weather stations
• 28 stations are active
• 10 stations are deactivated
Arizona Meteorological Network
Yao Li and Paige Ng Statistical Analysis and Forecasting Solar Radiation in Arizona WINONA STATE UNIVERSITY
http://cals.arizona.edu/azmet/az-data.htm
Weather-based Information
Data Variable Unit
Year
Day of Year (DOY)
Air Temperature DegC
Relative Humidity %
Solar Radiation MJ/Sq M
Precipitation MM
Soil Temperature DegC
Wind Speed M/S
Wind Vector Magnitude M/S
Wind Vector Direction Deg
Wind Direction Standard Deviation Deg
Heat Units 30/12.8 C
Yao Li and Paige Ng Statistical Analysis and Forecasting Solar Radiation in Arizona WINONA STATE UNIVERSITY
• Missing data
• Mislabeled data
• Variables change
Problems of Data Mining
Yao Li and Paige Ng Statistical Analysis and Forecasting Solar Radiation in Arizona WINONA STATE UNIVERSITY
Station Selection
Station Name
1 Tucson
2 Yuma Valley
4 Safford
5 Coolidge
6 Maricopa
7 Aguila
9 Bonita
12 Phoenix Greenway
14 Yuma North Gila
15 Phoenix Encanto
19 Paloma
22 Queen Creek
23 Harquahala
24 Roll
26 Buckeye
Yao Li and Paige Ng Statistical Analysis and Forecasting Solar Radiation in Arizona WINONA STATE UNIVERSITY
15 active weather stations have complete data for 17 years from 1999 to the present
No obvious year-to-year trend for solar radiation
OLS Regression with Lagged Variables Reasoning
Solar Radiation by Year
Yao Li and Paige Ng Statistical Analysis and Forecasting Solar Radiation in Arizona WINONA STATE UNIVERSITY
• Obvious month-to-month trend
• Lagged variables: 12 month
• Backward elimination with p-value
OLS Regression with Lagged Variables Reasoning
Solar Radiation by Month
Yao Li and Paige Ng Statistical Analysis and Forecasting Solar Radiation in Arizona WINONA STATE UNIVERSITY
Mea
n(So
lar R
ad. -
Tot
al)
8
10
12
14
16
18
20
22
24
26
28
30
32
34
1 2 3 4 5 6 7 8 9 10 11 12
Month
yij = 9.2687 + αi + βj + γ𝑖𝑖𝑖𝑖
− 0.19460 ∗ LagMean Air Temp − Min
+ 0.05135 ∗ LagMean RH − Min
+ 0.10130 ∗ LagMean Solar Rad.−Total
+ 0.10333 ∗ LagMean Precipitation − Total
+ 0.15402 ∗ LagMean(4" Soil Temp − Max)
+ 0.37162 ∗ LagMean (4" Soil Temp − Min)
− 0.47267∗ LagMean(4" Soil Temp − Mean)
+ 0.52893∗ LagMean(Wind Speed − Mean)
− 0.47727∗ LagMean(Wind Vector Magnitude for Day)
+ 0.18475∗ LagMean (Heat Units)
OLS Regression with Lagged Variables Model Output
Yao Li and Paige Ng Statistical Analysis and Forecasting Solar Radiation in Arizona WINONA STATE UNIVERSITY
Note:i: Month Index j: Station Index
OLS Regression with Lagged Variables Accuracy of Predictions
RSquare: Closer to 1 indicates a better model fit
Yao Li and Paige Ng Statistical Analysis and Forecasting Solar Radiation in Arizona WINONA STATE UNIVERSITY
Percent Error =Actual Solar Radiation − Predicted Solar Radiation
Actual Solar Radiation∗ 100%
OLS Regression with Lagged Variables Accuracy of Predictions
Yao Li and Paige Ng Statistical Analysis and Forecasting Solar Radiation in Arizona WINONA STATE UNIVERSITY
OLS Regression with Lagged Variables Interpreting Overestimations
Yao Li and Paige Ng Statistical Analysis and Forecasting Solar Radiation in Arizona WINONA STATE UNIVERSITY
OLS Regression with Lagged Variables Interpreting Overestimations
Yao Li and Paige Ng Statistical Analysis and Forecasting Solar Radiation in Arizona WINONA STATE UNIVERSITY
OLS Regression with Lagged Variables Month and Station Interaction
Yao Li and Paige Ng Statistical Analysis and Forecasting Solar Radiation in Arizona WINONA STATE UNIVERSITY
OLS Regression with Lagged Variables Month and Station Interaction
Yao Li and Paige Ng Statistical Analysis and Forecasting Solar Radiation in Arizona WINONA STATE UNIVERSITY
Seasonal Decomposition Station 2
Yao Li and Paige Ng Statistical Analysis and Forecasting Solar Radiation in Arizona WINONA STATE UNIVERSITY
Standard Deviation (remainder)=Standard Deviation (data) – Standard Deviation (seasonal) – Standard Deviation (trend)
Seasonal Decomposition Internal Standard Deviations
Yao Li and Paige Ng Statistical Analysis and Forecasting Solar Radiation in Arizona WINONA STATE UNIVERSITY
Station SD(remainder)14 2.614499
2 2.66378624 2.73899326 2.86886523 2.974914
6 2.9771465 3.037263
15 3.08106222 3.216051
7 3.24770112 3.770044
Mean (Solar Rad – Total) vs. StationStandard Deviation (Remainder) vs. Station
Seasonal Decomposition Narrowing Down Sites
Yao Li and Paige Ng Statistical Analysis and Forecasting Solar Radiation in Arizona WINONA STATE UNIVERSITY
Other Considerations
• Earthquake risks
• Transportation convenience
• Metropolitan Phoenix is home to two-thirds of the state’s population alone
Exceedance Probabilities
Yao Li and Paige Ng Statistical Analysis and Forecasting Solar Radiation in Arizona WINONA STATE UNIVERSITY
P90 Exceedance Probability: 90% probability that a certain value will be exceeded
Bootstrap: approximation the distribution of values by resampling the data with replacement
Exceedance Probabilities Bootstrapping 1999-2014 Predictions
Yao Li and Paige Ng Statistical Analysis and Forecasting Solar Radiation in Arizona WINONA STATE UNIVERSITY
Future Research Possibilities
Yao Li and Paige Ng Statistical Analysis and Forecasting Solar Radiation in Arizona WINONA STATE UNIVERSITY
•Facility requirements
•Amount of investment
•Energy needs
Yao Li and Paige Ng Statistical Analysis and Forecasting Solar Radiation in Arizona WINONA STATE UNIVERSITY
Questions?
Thank you!
𝜶𝜶𝒊𝒊: Coefficient for the 𝐢𝐢𝐭𝐭𝐭𝐭 month 𝜷𝜷𝒋𝒋:Coefficient for the 𝐣𝐣𝐭𝐭𝐭𝐭 station 𝜸𝜸𝒊𝒊𝒋𝒋: Coefficient for the 𝐢𝐢𝒕𝒕𝒕𝒕 month 𝐣𝐣𝐭𝐭𝐭𝐭 station
OLS Regression with Lagged Variables Coefficient Indexing
Yao Li and Paige Ng Statistical Analysis and Forecasting Solar Radiation in Arizona WINONA STATE UNIVERSITY