**What is energy consumption?**

We use regression analysis to shape the historical energy profile of four states. And we set the goals and criteria for the four-state interstate energy compact. Furthermore, we use a gray model based forecasting system to predict the usage of cleaner ,renewable energy profiles of four states in 2025 and 2050 . Based on the analysis of historical, current and forecast data, we provide a reliable target for the compact.

**Firstly, we use k-means analysis to categorize the energy data of the four states. **

Secondly, we establish a regression analysis model to shape the historical profile. Based on the results of profile, we select the standard deviation of renewable energy usage in each state as a quantitative indicator of the similarities and differences in the development of cleaner ,renewable energy sources in four states .And we extend the regression analysis model to analyze the influence of five factors: geography, industry , population, climate, economy .

Thirdly, we choose the proportion of renewable energy in the total energy and the growth rate of renewable energy as the influencing factors. We take the coefficient of the two factor weighting as a quantitative index, and establish the criteria of four states in 2009.

Fourthly, based on the historical evolution and similarities and differences between the four states, we establish a predictor system to predict the energy profile of every state in 2025 and 2050 ,which is based on a gray forecasting model, assisted by regression forecasting and an auto regressive integrated moving average model.

Finally, through the comparison of the four states, the best standards and the forecast results, we present the goals of renewable energy usage in the four states in 2025 and 2050, and make analysis on the targets of the four states’ renewable energy usage. The overall goal of the renewable energy usage of the compact, at the same time, we proposed three actions to promote the realization of these goals.

Based on the provided data, we have drawn conclusions about the consumption of energy. As a whole, the usage of traditional energy was far larger than the clear, renewable energy in all states. Besides, transportation and industry were the main aspects of the consumption of energy in each state. Additionally, the growths of traditional energy consumption were all faster than that of clean energy. However, the major energy consumed was different from each other, and you can see it in our article.

Additionally, we predict the consumption and growth rate of fossil energy and renewable energy in each state. Overall, the total amount and growth rate of fossil energy is higher than renewable energy. For fossil energy, Taxes will be the most energy-consuming state among these four states both in 2025 and 2050. For renewable energy, in 2025, California will be the most energy-consuming state. Taxes will overpass California and become the first.

In the end,through comprehensive consideration,we set the targets, which is the ratio of renewable energy in total energy, as follows:

State 2025 2050

Arizona 14% 19%

California 13% 15%

New Mexico 9% 12%

Texas 6% 10%

**We sincerely hope this article is helpful for you.**

Energy is a significant driving force of economic development and the key factor that determines the quality of life. However, with the sustained and rapid development of the world economy and the improvement of people’s living standards, the problems of energy shortage, environmental pollution and ecological deterioration have gradually deepened, and the contradiction between energy supply and demand has become increasingly serious. Thus, allocating energy resources rationally and exploiting renewable energy play more and more important roles in today’s life.

In fact, National energy policies are usually too fragmented to solve such problems conductively to some extent. So, some organizations aim to foster cooperation between their partners for the development and management of energy. The interstate compact, a contractual arrangement made between two or more states in which these states agree on a specific policy issue and either adopt a set of standards or cooperate with one another on a particular regional or national matter, is a typical example in the USA like the Western Interstate Energy Compact (WIEC).

In America, California (CA), Arizona (AZ), New Mexico (NM), and Texas (TX) are four states bordering Mexico and they want to form a practical new-energy compact for increasing usage of cleaner, renewable energy sources.

**Restatement of The Problem **

To achieve this goal, we need to analyze and perform data of the above for states and to build models to inform their development of a set of goals.

To be more specific, the problem is able to be divided into these parts:

1) Form an energy profile for each of the four states according to the data provided.

2) Build a model to characterize how the energy profile of each of the four states has evolved from 1960 to 2009.

3) Analyze and interpret the usage of cleaner, renewable energy sources of the four states, and focus on similarities and differences between the four states in the meantime.

4) Choose a state that has the “best” profile for usage of cleaner, renewable energy in 2009 from such four states.

5) Predict the energy profile of each state for 2025 and 2050 in the absence of any policy changes by each governor.

6) Determine renewable energy usage targets for 2025 and 2050 and state them as goals for this new four-state energy contract.

7) Identify and discuss at least three actions the four states might take to meet their energy compact goals.

Firstly, we analyze the existing data and take data visualization including Average energy consumption, industry consumption percentage, traditional energy and renewable energy in each state.

Secondly, we employ the regression analysis to obtain the evolutionary features of the energy profile of every state, then choose standard deviation for comparative analysis on similarities and differences.

Thirdly, based on the data of each states’ geographic, industry, population, climate and economy, considering energy profile, we regard the growth rate of renewable energy and the proportion of new energy consumption in total energy as our criteria and through the regression analysis, we evaluate the “best state”.

Fourthly, according to the history evolution of energy usage in these states, through the gray forecast model, we predict the energy performance of each state for 2025 and 2050 in the absence of any policy.

Finally, based on the above solutions, we determine the usage targets and regard them as goals for the four -state energy compact, then we set 3 actions for the four states respectively to achieve this goal.

2 Notations

Symbols Definition

∂ reliability coefficient

β* _{i}*linear regression analysis coefficient

*a** _{im }*linear regression analysis independent variable observed value

*b** _{n }*linear regression analysis dependent variable observed value

ε error sum of square

*Q *error sum of square

*s *root mean squared error

*U *sum of squares for regression

*S S T *sum of squares for total

ξ criteria coefficient

ω* _{n }*weight

α_{1 }renewable energy percentage

α_{2 }renewable energy growth ratio

*x*^{(}^{n}^{) }gray model independent variable observed value

*z*^{(}^{n}^{) }gray model dependent variable observed value

*g** _{t }*ARIMA independent variable

3 Assumptions and Explanations

Because energy statistics, consumption and forecasting are affected by many factors in real life, it is impossible to discuss all of these factors in the discussion of the issues. Therefore, we simplify the analysis of issues by making assumptions and explanations:

Firstly, in order to make our analysis of the goals of establishing the new energy compact realistic and reliable, the data provided is supposed to reflect the actual energy situation to the permitted-error extent.

Secondly, since there are no clear quantitative criteria for geography and climate, it is assumed that the value of geographic and climatic for the four states in the discussion can reflect the reality,of course,the value is reasonable.

Thirdly, based on our understanding of the 1970 Interstate Compact on Nuclear, we propose the corresponding targets for 2025 and 2050. Here,we assume there is a linear relationship between this goal and actions, such as the policy of promoting renewable energy development. This will lead to the usage of renewable energy growing faster in 2025 and 2050.

##### Reliability Analysis

DeVellis (1991) considered that when the reliability coefficient for a variable belongs to 0.60ï¡d0.65, ¯ we had better not to accept this variable; when it belongs to 0.65ï¡d0.70, the variable is the minimum ¯ acceptable value; when it belongs to 0.70ï¡d0.80, the variable is quite good. Furthermore, when it belongs to ¯ 0.80ï¡d0.90, the variable is very good. This measure called Alpha reliability coefficient method is the most commonly used reliability coefficient. The formula is as follow

_{n }_{− 1) ∗ (1 −(}^{P}*S*^{2}*i** *

_{∂= (}*n *

*S*^{2}* _{t}*)

Where,*n *is the number of years in the scale,*S*^{2}* _{i}*is the variance for year

*i*, and

*S*

^{2}

*is the variance for the total value for all years. It can be seen from the formula,∂ coefficient evaluation is the consistency of the data in the scale of the year, belonging to the intrinsic consistency coefficient. Based on the theory, we tested the provided data and the result is 0.74756372. So, we consider the provided data to be good and we can put it to our questions directly.*

_{t}##### Overview

First, we conducted a reliability analysis and K-means analysis on the data provided and obtained 12 major energy data after analysis.

Secondly, visualize the data and add up the analysis of the charts, we form the energy profile of problem A. The regression analysis of the data will provide the energy profiles of problem B, then quantify the similarities and differences and we can get the value of it, using regression analysis.

The impact of factors will be exposed; based on the analyzed data ,calculating the criteria and we will see the “best” state; analyze the conclusion of A and the similarities and differences between four states,we’ll get the targets.

**Thirdly, through the analysis and understanding of problem BCD, we get the goals of using new energy and three actions based on the goals. **

We confirm that the problem is a big data analysis problem and choose k-means clustering algorithm for data mining, because the proprietary intelligence of this algorithm is usually faster and more efficient than the other algorithms, especially in big data processing problems.

Then, through the k-means clustering algorithm we define a “state” dataset (California, Arizona, New Mexico and Texas). In cluster analysis, these four states can be called observers. According to the data provided, we know all kinds of energy information for each state, such as aviation gasoline, coal, distillate fuel, geothermal energy, which are vectors expressing the characteristics of each state.

##### After pre-clustering analysis and characterizing the four states.

We found that the provided data has been intelligently clustered into 12 energy categories, which has provided help for our subsequent data analysis and data visualization.

In Arizona, coal was the most consumed energy, followed by motor gasoline and natural gas. Besides, nuclear fuel played an important role among the clearer energy and its consumption was larger than the consumption of jet fuel and oil in traditional energy. Last but not least, hydroelectricity was also a prominent energy source. We can see that transportation accounted for the largest part in energy consumption with 55.43%, and the consumption percentage of industrial, commercial and residential was similar with each other.

California was a state with poor consumption of coal while with lots of consumption of gas and motor gasoline between 1960 and 2009. Although the hydroelectricity consumption was a bit higher among the clearer energy, traditional energy consumption was the main choice. About the use of energy, transportation took up a large number (59.17%) followed by the industrial (22.41%).

In New Mexico, natural gas, coal and motor gasoline were the three main energy sources, and among them, natural gas was the biggest consumption factor followed by coal and motor gasoline from 1960 to 2009. Such energy is traditional energy whose total consumption was far higher than the clean and renewable energy in New Mexico during that period.

It is obvious that the transportation consumption took up the largest proportion (44.17%) followed by the industrial consumption (37.81%), while the percentage of the consumption of commercial and residential was less than 10% respectively.

Texas is an industrial center, many industrial units are located here. We can also see the main energy source was traditional sources including natural gas, coal, motor gasoline, LPG, etc. In the meantime, the consumption of clearer energy was low. Besides, energy consumption took up the main proportion about 60.15%, followed by transportation with 29.44%.

We built a Regression Analysis Model to propose a linear regression of the historical data for the 12 categories of energy that we have categorized, then we calculate the straight-line slope of energy consumption of fifty years. Besides, combined with the data’s direct fit curve, we make a more detailed analysis of the energy profile of the four states.Then, we set standard deviation as the value of similarities and differences. For the analysis of the factors that influence the similarities and differences, we use the combination of subjective analysis and objective regression analysis to acquire the impact of key factors including geography, industry, population, climate and economy.

**The Regression Analysis Model **

The Model

The multivariate linear regression analysis model is:

y = β_{0 }+ β_{1 }*x*_{1 }+ · · · +mxm* _{ }*+ ε, ε(0, σ

^{2}) (1)

Where: β_{0}, β_{1}, · · · , β* _{m}*, σ

^{2}are unknown parameters that are irrelevant with

*x*

_{1},

*x*

_{2}, · · · ,

*x*

*respectively. Besides, β*

_{m }_{0}, β

_{1}, · · · , β

*are called the regression coefficients. The independent observation data of n years are [*

_{m }*b*

*,*

_{i}*a*

_{i}_{1},

*a*

_{i}_{2}, · · · ,

*a*

*], where*

_{im}*is*the observation of y,

*a*

_{i}_{1},

*a*

_{i}_{2}, · · · ,

*a*

*are the observations of*

_{im }*x*

_{1},

*x*

_{2}, · · · ,

*x*

*respectively. From the formula (1) we can get the following formula:*

_{m }*b _{i }*= β

_{0 }+ β

_{1}

*a*

_{i}_{1 }+ · · · + β

*+ ε*

_{m}a_{im }*, ε(0, σ*

_{i}^{2}),

*i*= 1, · · · ,

*n*

That is

*X *=

^{}_{}1 . . . *a*_{1}_{m}* *

^{..}_{.}^{..}_{.}^{..}.

1 · · · *a*_{nm}* *

^{}

*Y *=

^{}_{}*b*_{1}

^{..}.

*b*_{n}* *

^{}

ε = (ε_{1}, · · · , ε* _{n}*)

^{T}

β = (β_{0}, β_{1}, · · · , β* _{m}*)

^{T}

7.1.2 Parameter Estimation

The parameters β_{0}, β_{1}, · · · , β* _{m }*of formula (1) in the least squares estimation is

^{∧}

β* _{j}*, and when β

*=*

_{j }∧

β* _{j}*,

*j*= 0, 1, · · · ,

*m*, we can get

(*b** _{i }*− β

_{0 }− β

_{1}

*a*

_{i}_{1 }− · · · − β

_{m}*a*

*)*

_{im}^{2}

Order ^{∂}^{Q}* *

min *Q *=

X^{n}* i*=1

ε_{i}^{2 }_{=}X^{n}* i*=1

(*b*_{i }_{− }* _{b}*ˆ

*)*

_{i}^{2 }

_{=}X

^{n}*i*=1

∂β* _{j}*= 0,

*j*= 0, 1, · · · ,

*n*We can get

^{}^{∂}^{Q}* *

∂β_{0}_{= −2}P^{n}_{i}_{=1}(*b** _{i }*− β

_{0 }− β

_{1}

*a*

_{i}_{1 }− β

_{m}*a*

*) = 0*

_{im}∂β_{1}_{= −2}P^{n}_{i}_{=1}(*b** _{i }*− β

_{0 }− β

_{1}

*a*

_{i}_{1 }− β

_{m}*a*

*)*

_{im}*a*

*= 0*

_{i }∂*Q** *

Calculate the formal equations:

^{}_{}P^{n}_{i}_{=1}*b** _{i }*=

*n*β

_{0 }+ β

_{1}P

^{n}

_{i}_{=1}

*a*

_{i}_{1 }+ · · · + β

*P*

_{m}

^{n}

_{i}_{=1}

*a*

_{im}

P^{n}* i*=1

*a*_{i}_{1}*b** _{i }*=

*n*β

_{0 }+ β

_{1}P

^{n}

_{i}_{=1}

*a*

_{i}_{1 }+ · · · + β

*P*

_{m}

^{n}

_{i}_{=1}

*a*

*2*

_{im}The formal form of the matrix is:

*X*^{T}*X*β = *X*^{T }*Y *

When the matrix *X *is column full rank, *X*^{T}*X *is a reversible matrix, the solution of the above formula is :^{∧}β = (*X*^{T}*X*)^{−1}*X*^{T }*Y *

Plug^{∧}β into the original model, the estimated value of y is as follows:

^{∧}* ^{y }*=

^{∧}

β_{0 }+^{∧}

β_{1 }*x*_{1 }+^{∧}

So, the fitted value of this set of data is

^{∧}*b _{i }*=

^{∧}

β_{1 }*a*_{i}_{1 }+ · · · +^{∧}

β_{m }*a** _{im}*, (

*i*= 1, · · · ,

*n*)

The above formula is also Recorded as^{∧}*Y *= *X*^{∧}β _{=} ^{∧}*b*_{1}, · · · ,^{∧}*b** _{n}*!

*, and the fitting error*

^{T}*e*=

*Y*−

^{∧}

*Y*

is called residual that is able to be used as an explanatory variable for random errors. And the Q is residual sum of squares, the formula is as followed:

(*b*_{i }_{−}^{b}*b** _{i}*)

^{2}

##### Statistical Analysis

*Q *=

X^{n}* i*=1

*e*_{i}^{2 }_{=}X^{n}* i*=1

(1)^{∧}β is the Linear Unbiased Minimum Variance Estimation of β, the expectation of^{∧}β is equal to β, and^{∧}β is the minimum in linear unbiased estimation of β.

(2) Based on the *Q*, *E*(*Q*) = (*n *− *m *− 1)σ^{2}and

*Q *

σ^{2}∼ χ^{2}(*n *− *m *− 1)

##### We can get the unbiased estimation of σ^{2}, the equation is as follows:

*S*^{2 }_{=}*Q *

_{n }_{− }_{m }_{− 1}= σ∧^{2}

Where *S*^{2}is the residual variance, *S *is the residual standard deviation

_{(3) decomposing the sum of the total squares }_{S S T }_{=}P^{n}* i*=1

(*b** _{i }*−

*b*)

^{2}, we can get equations:

*S S T *= *Q *+ *U*, *U *=

X^{n}* i*=1

_{(}^{b}*b** _{i }*−

*b*)

^{2}

Where *b *=^{1}* _{n}*P

^{n}

_{i}_{=1}

*b*

*, and*

_{i}*U*is a regression square sum, reflecting the effect of independent variables on y.

##### Hypothesis Test of Regression Model

Complex decision coefficient is the index to measure the degree of correlation between y and

*x*_{1}, *x*_{2}, · · · , *x** _{m}*, the equation is 7.1.5 The Interval Estimation

*R*^{2 }_{=}*U S S T *

_{Under the condition of a given confidence degree like α, if}^{ } *t*_{j}^{ } < *t *^{α}(_{2}*n *− *m *− 1), we accept the original hypothesis *H*_{0 }, otherwise, we reject it. Under the confidence level of 1 − α, the confidence

interval of β* _{j}*is

β* _{j }*−

*t*

^{α}

_{2}

_{(}

_{n }_{− }

_{m }_{− 1)}

_{s}^{√}

~~c~~

_{j j}^{∧}

[^{∧}

_{Where }_{s }_{=}^{√}~~Q~~~~/(~~~~n ~~~~− ~~~~m ~~~~− 1)~~

β* _{j }*+

*t*

^{α}

_{2}

_{(}

_{n }_{− }

_{m }_{− 1)}

_{s}^{√}

~~c~~

_{j j}##### The Value of similarities and differences

We calculate the standard deviation of growth rate of energy consumption in four states to quantify such similarities and differences.The standard deviation formula is as follows:

(*X** _{i }*−

*u*)

^{2}

*n *

##### The Impacts of key factors

σ=

^{vuut}P^{ }^{n}* i*=1

We extend the regression analysis model to analyze the influence of five factors: geography, industry , population,climate, economy.

Specifically, the trend of usage of petrochemical headstock. Moreover, the trend of consumption of petrochemical headstock, renewable energy and clear energy of Arizona from 1960 to 2009 was fluctuating upward all the time, while the tendency of renewable energy was fluctuating from 1934 to 2009. For the trend of cleaner energy, which had slightly risen before 1982 while had fluctuated upward since 1983, and reached the peak in 2008. Besides, the total consumption of petrochemical headstock was larger than other kinds of energy.

We can see the same situation in California. The trend of petrochemical headstock, renewable energy and clear energy were all fluctuant, especially the petrochemical headstock. And the amount of usage of petrochemical headstock was also larger than others.

In New Mexico, we cannot see the role of renewable energy and the value of cleaner energy is low. For the tendency, petrochemical headstock was fluctuating upward while the cleaner energy maintained the level similar as before. The peak appeared at 2006 about 7000000

**In Texas, the consumption of petrochemicals between 1996 and 2008 was obviously higher than before. The consumption of renewable and cleaner energy was almost zero to some extent.**

After the analysis of the slope of the energy consumption curve and the data’s direct fit curve, We have a more detailed description of the energy profile in the four states.

We can see in Arizona, coal had the highest rate of rise followed by the nuclear fuel that was a bit below. Besides, the growth rate of motor gasoline and natural gas were higher than other energy growth rates. We conclude that traditional energy was the major source of fuel.

Moreover, in California, the fastest growth energy is gasoline consumption whose number exceeded 20000. Thus, while the growth rate of coal and residual oil decreased. Combined with other changes in energy consumption, we can judge that California transfers more consumption of new energy from the consumption of traditional energy.

**However, in New Mexico, except coal consumption had a bit increase, others had little alteration. **

The energy consumption of Texas had changed a lot, especially the consumption of coal and liquefied petroleum gas. Besides, the total energy consumption has increased over the past 50 years.

Next, through further analysis of the provided data and checked reference. We discuss the geography, industry, population, climate and economic development as major factors influencing the similarities and differences. Furthermore, after extending the regression model, we draw a regression line that reflects the influence of the difference among such five factors on energy consumption differences of four states. In addition, the coefficient of each variable of the line is used as the contribution value of each factor. (the higher the value of contribution is, the greater the impact on the difference)

**Conclusions: **

As a whole, industry and population are two important factors about the seven clearer energy. However, while the coefficients between factors including geography, climate and economic development. In addition, these kinds of energy are below one, which means such points had little influence on the consumption of clear energy.

Specially, the coefficient of population is the biggest number among influential factors of fuel ethanol, so, population exerted the most critical impact on this energy. Besides, industry also had a non-negligible influence on it. Similarly, population was the most vital factor of Liquefied petroleum gas, Nuclear fuel and Other Renewables. Additionally, industry was the most significant point of Hydroelectricity, Natural gas and Biomass.

We set up a new special standard to measure the energy situation in four states. In order to achieve an agreement of the contractual objectives of clean and renewable energy, we select the standard coefficient ξ as the criterion of the energy situation of the four states. (The greater the value of ξ, the higher the use of new energy in all energy sources and the better the usage of new energy.)

ξ = ω_{1}α_{1 }+ ω_{2}α_{2}

Where α_{1 }=^{S }*N *

*S ** _{T}*is the proportion of new energy in total energy, α

_{2 }=

*K*

^{(1)}

New energy, ω_{1}, ω_{2 }is the weight of α_{1}, α_{2 }that are both 0.5 here.

* _{cl}*is the forecast growth of

State α_{1 }α_{2 }ξ

Arizona 0.23795472 0.230120723 0.234037722

California 0.139797589 0.433762558 0.286780074

New Mexico 0.040490185 0.007784213 0.024137199

Texas 0.066205553 0.328332506 0.197269029

Conclusion:

According to the number of ξ, California had the maximum value. Thus, California had the “best” profile for use of cleaner, renewable energy in 2009.

Comparison Between Models

Reference sequence *x*^{(0) }= (*x*^{(0)}(1), *x*^{(0)}(2), · · · , *x*^{(0)}(*n*)) cumulates once.

And generates sequence *x*^{(1) }= (*x*^{(1)}(1), *x*^{(1)}(2), · · · , *x*^{(1)}(*n*)) = (*x*^{(0)}(1), *x*^{(0)}(1) + *x*^{(0)}(2), · · · , *x*^{(0)}(1) + · · · + *x*^{(0)}(*n*))

Where *x*^{(1)}_{(}_{k}_{) =}P^{k}* i*=1

The corresponding whitening differential equation is

*dx *

* _{dt}*+

*ax*

^{(1)}(

*t*) =

*b*(2)

We can obtain the minimum

^{..}.

^{..}.

−*z*^{(1)}(*n*)

1

estimated value of *J*(*u*) = (*Y *− *Bu*)* ^{T}*(

*Y*−

*Bu*) is

_{u}_{ˆ =}^{ }_{a}_{ˆ, }_{b}_{ˆ} ^{T}_{=}^{ }*B*^{T }_{B}_{−1}

We extend the usage of the regression model to predict the value. As a result, we don’t exhibit the core model again here.

##### The Core ARIMA Model

First of all, we should calculate the autocorrelation function. And partial correlation function of sample *g*_{1}, *g*_{2}, · · · , *g _{n}*, if at least one of such functions is not truncation or trailing,

*g*is not smooth. We can solve the autocorrelation function and partial correlation function through feasible region ∇

_{t}*g*,

_{t}*t*=

2, 3, · · · , *n*. Furthermore, we can abstain from the functions of the sample. Repeat the above steps until ∇^{d}*g** _{t}*is a stationary sequence. If we know the initial value

*g*

_{1},

*g*

_{2}, · · · ,

*g*

*, we can get*

_{t}*P*

*= ∇*

_{t }

^{d}*g*

*,*

_{t}*t*=

*d*+1, · · · ,

*n*and calculate the

*g*

*, the formula is*

_{t}*g** _{t }*=

*g*

_{1 }+

X^{t}^{−1} *j*=1

*P*_{j}_{+1 }=*g** _{k }*+

X^{t}^{−}^{k}* j*=1

*P*_{j}_{+}* _{k}*,

*t*>

*k*≥ 1

Assume {*g** _{t}*,

*t*= 0, ±1, ±, · · · } is the sequence of

*ARIMA*(

*p*,

*d*,

*q*) When d = 1, ∇

*g*

*=*

_{t }*P*

*, we can get*

_{t}*ˆ*

_{g }*(*

_{k}*m*) −

*g*

_{k}

_{m}_{ˆ − 1 = }

*ˆ*

_{P }*(*

_{k}*m*)

So,

* _{g }*ˆ

*(*

_{k}*m*) −

*g*

_{k}_{( ˆ}

_{m }_{− 1) = }

*ˆ*

_{P }*(*

_{k}*m*) =

*g*

_{k }_{+}X

^{m}*i*=1

*P** _{k}*(

*j*)

##### The Result of Choosing Models

It is obvious that the Gray Model is the best way to predict energy consumption.

Calculation Process

Test and Processing of data

In order to ensure the feasibility of the modeling method, it is necessary to do the inspection of data. Suppose the reference data is *x*^{(0) }= (*x*^{(0)}(1), *x*^{(0)}(2), …, *x*^{(0)}(*n*)) , the formula of stepwise ratios of alignment is as followed :

_{λ(}_{k}_{) =}*x*^{(0)}(*k *− 1)

*x*^{(0)}_{(}_{k}_{)}, *k *= 2, 3, …, *n *

_{If all stepwise ratios are within the capacitive cover, alignment Θ = }^{ }*e*^{−}^{2}

^{n}^{+2 }_{,}^{ }can be used

^{n}, ^{+1 }*e*^{2}

as the data of the GM(1,1) model to make gray predictions. Otherwise, we need to take transformation processing for sequence *x*^{(0)}, to make sure that the sequence is within the capacitive cover. That is, taking the proper constant c to do parallel transformation

*y*^{(0)}(*k*) = *x*^{(0)}(*k*) + *c*, *k *= 1, 2, …, *n*

To make the stepwise radios of sequence^{(0) }= (*y*^{(0)}(1), *y*^{(0)}(2), …, *y*^{(0)}(*n*)) is

λ_{y}_{(}_{k}_{) =}*y*^{(0)}(*k *− 1)

*y*^{(0)}_{(}_{k}_{)}∈ Θ, *k *= 2, 3, …, *n *

8.2.2 Build The Model

According to the corresponding whitening differential equation, we establish GM(1,1) model, and the getting the forecast value is

And

*x*ˆ^{(1)}(*k *+ 1) = *x*ˆ^{(1)}(*k *+ 1) =

*x*^{(0)}_{(1) −}_{b}^{ˆ}_{a}_{ˆ}^{!}*e*^{−}^{ak}^{ˆ }_{+}_{b}^{ˆ}_{a}_{ˆ}, *k *= 0, 1, · · · , *n *− 1 *x*^{(0)}_{(1) −}_{b}^{ˆ}_{a}_{ˆ}^{!}*e*^{−}^{ak}^{ˆ }_{+}_{b}^{ˆ}_{a}_{ˆ}, *k *= 0, 1, · · · , *n *− 1

8.2.3 Test The Forecast value

(1) Residual Test

Order residual as ε(*k*), calculate:

_{ε(}_{k}_{) =}*x*^{(0)}(*k*)

*x*^{(0)}_{(}_{k}_{)}, *k *= 1, 2, …, *n *

Where ˆ*x*^{(}0) = *x*^{(0)}(1), if ε(*k*) < 0.2 ,it may be considered to meet the general requirements; if ε(*k*) < 0.1 , it may be considered to meet the higher requirements

(2) stepwise ratio deviation test

First, we use the reference data to calculate the stepwise radio, and use the development coefficient to calculate the corresponding level deviation.

ρ(*k*) = 1 −

^{ }1 − 0.5*a *1 + 0.5*a *

!

λ(*k*)

If ρ(*k*) < 0.2 ,it may be considered to meet the general requirements; if ρ(*k*) < 0.1, it may be considered to meet the higher requirements.

8.2.4 Prediction

We can abstain the Predictive values within a specified interval from GM(1,1) Now, we take Arizona as the example to compare such three models.

We compare the predictive value of the gray model with the practical value of the other two states, and the gray model is the most realistic one.Then, we employ the gray model to predict the renewable energy consumption of four states. According to this result, In Arizona, the consumption of renewable energy is 3.6×10^{5 }billion Btu and 11.2×10^{5 }billion Btu in 2015 and 2050 respectively. For fossil energy, the consumption is 2.5 × 10^{6}Btu and 5.7 × 10^{6}respectively. We draw the conclusion that although the usage of traditional is also far higher than the clear energy, the growth speed of clear energy is faster than traditional, which means the gap is narrowing.

The consumption of energy in California calculated by the gray model. In 2025, the consumption of fossil will increase to 7.1 × 10^{6 }billion Btu while the number of clear energy is just about 1 × 10^{6}billion Btu. In 2050, the amount of traditional energy will jump to 8.9 × 10^{6 }while the amount of renewable energy will not change a lot. So, in the next 22 years, fossil energy will be the major used source. In New Mexico, the consumption of fossil energy is about 9 × 10^{6 }billion Btu and surpasses 11 × 10^{6}billion Btu in 2025 and 2050 respectively.

For renewable energy, the quantity is about 1 × 10^{6 }billion Btu and 1.5 × 10^{6 }billion Btu in 2025 and 2050 respectively. Besides, we can see the growth rate of traditional energy will be consumed a lot in 2025(11 × 10^{6 }billion Btu) and 2050(overpass 13 × 10^{6 }billion Btu), while the consumption of new energy will still be below 2 × 10^{6 }billion Btu.

#### Part II

Firstly, through the investigation and understanding of the interstate energy goals, we use the proportion of new energy consumption in total energy consumption as the targets of renewable energy usage.

Secondly, based on Part I problem D of renewable energy usage in 2025 and 2050, we show the targets for usage in 2025 and 2050.

Thirdly ,I mentioned the comparison between the four states , such as the difference of geography of the four states and the criteria of energy profile in each state.

State 2025 2050 Arizona 12.46% 16.42% California 12.53% 10.81% New Mexico 8.93% 11.86% Texas 7.31% 11.20%

State 2025 2050 Arizona 14% 19% California 13% 15% New Mexico 9% 12% Texas 6% 10%

And we state them as goals for the new four-state energy compact.

##### Actions:

(a) Encourage and promote cooperation among the party states in the promotion of energy efficiency ,the development of new energy and related technologies as well as their application to industry, electric power and other fields.

(b) Promote the Promulgation of the relevant laws and rules and the consummation of other standards, regulations and administrative practices. Recommend such changes in, or amendments or additions to the laws, codes, rules, regulations and administrative procedures or local laws or ordinances of the party states of their subdivisions in energy and related fields.

(c) Conduct, or cooperation in conducting, programs of training for state and local personnel engaged in any aspects of Energy industry, education, theory or medicine. The formulation or administration of measures designed to promote safety in any matter related to the development, use or the productivity and usage of energy, materials, wastes or to safety in the related applications. Applying relevant scientific advances or discoveries, and any industrial commercial, transportation or other processes results.

12 Strengths and weaknesses

**Strengths **

• The strength of part I problem B:

The regression analysis model can restore the history profile of four states effectively. In addition, provide data support for the growth of renewable energy.

We have analyzed the effects of geography, industry, population, climate and economy on the differences.

Which is more comprehensive and specific.

• The strength of part I problem C:

Furthermore, the development speed of renewable energy. And the ratio of renewable energy to total energy in the year are double factor standards. So that the standard can be better adapted to the evaluation under different circumstances.

##### • The strength:

The gray model has a better long-term prediction effect than the ARIMA model. And has a better realistic prediction effect than the regression prediction model.

##### Weaknesses

We only used the linear relationship to reflect the energy profile, but did not discuss more forms of energy profile.

The prediction results of the neural network model(LSTM) have not been achieved. If they are achieved, the prediction of the future can be more optimized.

#### Back To News

#### What is energy consumption?

**References **

[1] U.S. Energy Information Administration. https://www.eia.gov/state/seds/seds-data complete.php?sid=US

[2] Research and analysis of distributed energy system. http://xueshu.baidu.com/s?wd=paperurieba

[3] The relationship between the difference of Energy consumption and the level of Economic Development. http://data-planet.libguides.com/SEDS

[4] The 19th World Energy Congress, 15th September 2004, Sydney

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[7] The home of the U.S. Government’s open data. https://www.data.gov/

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[11] Herzlich Willkommen bei Compact Energy. http://www.compact-energy.de/