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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 klarson@winona.edu.

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