1. IEEE ICIT 2017
IEEE International Conference of Industrial Technology (2017) Regression Analysis on Solar PV and Wind Generation and Various Predictors within the United States Narjes Nouri, Mohammad Hasan Balali, Otieno Wilkistar, Mohammad Rashidi, Adel Nasiri University of Wisconsin-Milwaukee

2. Overview Introduction Litreture Methodology Discussion Conclusion
IEEE ICIT 2017
Introduction
Litreture
Methodology
Discussion
Conclusion

3. Introduction
IEEE ICIT 2017
With increasing concerns about the environmental problems caused by fossil fuels and the global uncertainty about the fuel cost and its continuity in the future, a lot of attentions have been paid from the side of governments, investors and researchers all around the world to find and expand the new solutions for the world’s growing need for energy resources.
Renewable energy resources have been utilized as an alternative for the conventional fossil fuels for electricity generation.
There are several benefits for renewable energy resources (RER) applications:
Environment friendly
Least fuel consumption
Can be installed as a small or large scale power generation
Wind and solar energy are the two biggest potential and actively utilized alternative power generation.
Besides all of the advantages of renewable based power sources, there are some important demerits for the application of RERs and especially wind and solar systems:
Their need to be combined with the proper converter for utilization with standard grid.
The dependency of wind and solar systems to the weather condition which causes a significant amount of uncertainty.
Uncertainty would impact on the reliability of the systems due to the intermittent nature of sources.

4. Introduction
IEEE ICIT 2017
Table 1:Total Estimated Technical Potential Generation and Capacity by Technology
Technology
Generation Potential (TWh)
Capacity Potential (GW)
Urban utility-scale PV
2200
1200
Rural utility-scale PV
280600
153000
Rooftop PV
800
664
Concentrating solar power
116100
38000
Onshore wind power
32700
11000
Offshore wind power
17000
4200
Bio-power
500 62
Hydrothermal power systems
300 38
Enhanced geothermal systems
31300
4000
Hydropower 60
Table 2:US Electricity generation shares by different fuel types
Fuel Type
2015-Billion kWh
2015-Percentage
2030-Billion kWh
2030-Percentage
Nuclear
798 20 17
Coal
1355 33
972 21
Natural Gas
1348
1702 37
Wind/Solar
227 6
683 15
Other
362 9
443 10

5. Introduction
IEEE ICIT 2017
Estimating the optimal number of PV panels and wind turbines to install in a region needs considering some social variables which are unique for each specified region. For instance, the number of installed facilities are directly affected by government incentives and restrictions.
To get more insight on how social variables can change the number of installed facilities consider population as a single variable. Obviously, cities with higher population need more energy to meet their demand. A regression model will provide the ratio with which the generation increases per person.
Another case could be the effect of available land on the renewable energy generation. Constructing a wind farm which is too close to residential areas is not allowed in most of the regions. It looks that there is a possible relationship between available land and total installed capacity of wind turbines and solar PV panels which could be estimated by a regression model.
The main goal of this study is presenting the best regression model to estimate the solar PV panels and wind turbine generation in each US state based on social parameters.

6. Literature
IEEE ICIT 2017
The effect of various variables on the total PV panel and wind turbine generation has been studied.
The least square method is being used to minimize the error. The basic concept of least square method is minimizing the summation of squared differences between the actual and expected amount of the unknown variable by a regression model.
Ordinary least square (OLS) regression is a common algorithm of least square method . OLS gives a way of taking complicated outcomes and explaining behavior (trends) using linearity concepts. The simplest example of OLS is fitting a line for a series of data.
Variable selection is one of the important steps in regression analysis which helps to find the most important variables which have major effect on the results.
Efficient use of variable selection methods leads to extracting more information from the variables and reaching more accurate results.
Regression analysis shows how the value of the dependent variable (respond) changes when any of the independent variables change, while the other independent variables are held fixed

7. Methodology
IEEE ICIT 2017
This study focuses on finding the possible relationship between the PV and wind generation by considering some specific variables which have the potential of effecting it.
Response variables
Solar PV generation
Wind generation
Predictor variables
Population
Area
Average salary of the middle class families
Electricity price profile
tax rate
Available water sources
Homeownership rate
Total Energy Generation

8. Methodology
IEEE ICIT 2017
The relationship between response and predictor variables will be analyzed within 50 US states.
All data used in this study have been found based on the latest available and reliable reports.
R software has been used for computational analysis.
In this Figure each point is representing the data for one state.
It can be seen that other than one or two abnormal points in each variable
the rest of states are within an average and standard deviation.

9. Analysis Raw data Transformed data
IEEE ICIT 2017
Raw data
Transformed data
The results of an OLS regression model on the raw data.
The data in our model is violating linear regression assumptions due to a trend in the residuals vs fit graph.
One remedy for refining a model exhibiting excessive non-constant variance includes applying a variance-stabilizing transformation.
This paper used log transformation package provided by R to transform the response variable.
All the responses were transformed to their log and the least square method was done using the transformed data.
Most of the regression assumptions are met.
However, since R-squared is a measure of goodness of fit of the predictive model on the data, R2 = is very low to trust.

10. Analysis
IEEE ICIT 2017
There can be seen a slight heteroscedasticity in the results after transformation which means transformation was not able to stabilize the variance. However, it can be solved using weighted least square (WLS) method instead of OLS.
OLS assumes that there is constant variance in the errors. WLS on the other hand, can be used when there is heteroscedasticity between the variances.
The results for the WLS shows no heteroscedasticity and improves the R-squared to 94.3%.
Ln (Solar PV Generation) = (Energy Generation) (Electricity Price) (Area) e-08 (Population) e-05 (Water) (Tax rate) (Average salary)

11. Analysis
IEEE ICIT 2017
The result for regressing the predictors on the WTG shows that the distribution of the residuals seems to come from two normal distributions with different parameters hence, the amount of Wind Turbine Generation cannot be predicted using one regression line. This paper classifies US states in two different categories with positive (P) and negative (N) residuals.
Class P regression line:
Ln(Wind Turbine Generation) = Energy Generation e-09 Population e-06 Water Tax rate e-06 Average salary e-03 Homeownership
Class N regression line:
Ln(Wind Turbine Generation) = Energy Generation e-09 Population e-06 Water Tax rate e-06 Average salary e-03 Homeownership

12. Conclusion
IEEE ICIT 2017
This study found a predictive model with high R-squared which is a measure of the suitability of the model to estimate the response.
Using each of those predictive models we are able to estimate the amount of solar PV and wind generation in each state using the amount of the predictors for that specific state.
It is crucial for the states to know how much of a change in these factors such as tax rate can change the amount of energy generation by a level. To serve this purpose sensitivity analysis can also be done using this model.
For instance, one unit change in the tax rate can increase ln(Wind Turbine Generation) by 0.12 which is a huge change
Since, predictors under study can all be controlled by state laws and regulations, this study can help policy makers to decide on the best amount of each variable to balance between predictors and the amount of renewable energy that they are trying to reach.
Numerical example based on the presented models:
state
actual
predicted
Solar
California
Wind
Arizona

13. Thanks for your Attention
IEEE ICIT 2017
Thanks for your Attention