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India is the 7th country by area, the 2nd populous country in the world [2]and its demand of energy is increasing rapidly and limited conventional resources and climate-changing problems associated with them underline the need for new and sustainable energy supply options that use different sources of RE. For now, green and clean energy is considered to be an important criterion for sustainable development of any country.

Sims [11] compares the costs of renewable energy systems with fossil fuel-derived energy services and considers how placing a value on carbon emissions will help provide convergence. Jorge [12] reviews the prospects for RE as a source of electricity in Mexico. In this study, it is concluded that Mexico is at crossroads with respect to renewable energy. Frede [13] analyze two RE governance systems in relation to a set of main characteristics of RE systems, which should be taken into consideration when establishing a RE institutional framework. In the description above he also emphasized an institutional context which will be able to ‘‘catch’’ some useable analytical results within these RE characteristics. Kumar et al. [10] examines some aspects of Renewable energy for sustainable development in India as current status, future prospects, challenges, employment, and investment opportunities. Paliwal et al. [9] reviews the availability and current status of RE in Rajasthan and also an attempt is made to summarize the availability and utilization of RE sources in Rajasthan using various charts (pie, bar, histogram etc.) for representation and comparison of districts of Rajasthan. Bhukya [8] has done a study on the potential and opportunities of electric power generation through renewable energy in the state of Rajasthan. Swarnkar et al. [7] investigated the Indian renewable energy Scenario based on survey data and also find the energy potential of India in terms of sources, per-capita energy consumption. In this paper two statistical analysis are proposed. One is the statistical analysis of installed capacity, generation and consumption of fossil fuels and renewable energy in India and other one is the statistical analysis of two solar power plants located at different geographical locations in India.

Potential of Wind Energy in India:

The Ministry, through NationalInstitute of Wind Energy (NIWE), has installed 967 wind-monitoring stations all over the country andissued wind potential maps at 50 m, 80 m, 100 m and 120 m above ground level.

The latest assessmentindicates gross wind power

potential of 302.25 GW and 695.50 GW in the country at 100-meter and120 meters respectively, above ground level. Most of this potential exists in seven windy ates en in table1 and fig.1[5].

Installed capacity of Wind Power in the country:

The installed capacity of grid-interactive wind power in the country as on 31.12.2021 is 40.0827 GW and state-wise installed capacity (in MW) is shown in table 2 and fig.2[1].

Table 1:  Potential of Wind Energy in India
S. No.	State	Wind Power Potential at 120 mtragl (GW)
1 2 3 4 5 6 7 8	Andhra Pradesh Gujarat Karnataka Madhya Pradesh Maharashtra Rajasthan Tamil Nadu Other States	74.9 142.56 124.15 15.4 98.21 127.75 68.75 43.78
All India Total		695.5
Source: MNRE https://mnre.gov.in

Table 2: Installed capacity of Wind Power in the country
S. No.	State	Installed Capacity (MW)
1 2 3 4 5 6 7 8 9 10	Andhra Pradesh Gujarat Karnataka Madhya Pradesh Maharashtra Rajasthan Tamil Nadu Telangana Kerala Others	4096.65 9007.72 5077.2 2519.89 5012.83 4326.82 9846.69 128.10 62.5 4.30
Total		40082.7
Source: MNRE https://mnre.gov.in

Fig.2:State-wise Wind Power Installed Capacity (in MW)

Share of Wind Energy in total energy:

As on 30-dec-22, share of wind power in total energy is 10.2% including both offshore and onshore wind generation across India which is shown in table 3 and fig.3.

Methodology and Statistical tools:

Data collection: Secondary data is taken from MNRE generation report.

Scatter plot: On the basis of scatter plot (between Year’s on x-axis and Electricity Generation in GW on y-axis) it is observed that a straight line is best suited to forecast the wind power generation.

Fig.4: Scatter plot

Least square method: From above plot consider a straight-line equation as

ŷ = a + bX

Where variable ŷ represents Generation (in GW), variable X represents Time (in Years) and a and b are constants to be obtained using the method of least squares.

To calculate these constants (a and b) for ‘n’ observations (x_i, y_i and i=1,2,3,…,n) the normal equations are:

Goodness of fit test (chi-square test):

To test the line obtained from the method of least squares the chi-square(χ2) test is performed and test statistic is given by:

Where are the observed values and  are the expected values (obtained from the trend line fitted from method of least squares) of the wind energy generation in GW.

Null hypothesis (H₀): There is no significant difference between Observed (O_i) andexpected (E_i) generation of wind energy over the time.

Alternative hypothesis(H₁): There is significant difference between observed (O_i) and expected (E_i) generation of wind energy over the time.

Decision criteria:

If , at (n-1) d.f. with level of significance (α), Accept H₀ i.e. There is no significant difference between Observed (O_i) and expected (E_i) generation of wind energy over the time.

And if at (n-1) d.f. with level of significance (α), Reject H₀ i.e. There is significant difference between observed (O_i) and expected (E_i) generation of wind energy over the time.

Graphical representation:

Bar plot: It is plotted between Year’s (on x-axis) and Electricity Generation in GW (on y-axis). From the plot, we can conclude that there exists an increasing trend in the wind power generation (in GW) as time (year’s) increases.

Fig.5: Bar plot of Wind energy generation year-wise 

Statistical analysis:

regression line using least square method:

S. No.	X	Y	X -Mx	Y -My	(X - Mx)2	(X -Mx)(Y - My)
1 2 3 4 5 6 7	2015 2016 2017 2018 2019 2020 2021	32.74 43.46 52.62 60.31 63.31 60.40 68.09	-3 -2 -1 0 1 2 3	-21.68 -10.96 -1.79 5.89 8.89 5.98 13.67	9 4 1 0 1 4 9	65039.598 21922.11 1796.29 0 8892.96 11962.47 41018.99
Total					SSx:28	SPxy: 150.62
Where Year =X, Generation In GW =Y

Calculation Summary:

Sum of X = 14126

Sum of Y = 380.93

Mean X (M_x)= 2018

Mean Y(M_y)= 54.4186

Sum of squares (SS_x) = 28

Sum of products (SP_xy) = 150.62

Regression Equation = ŷ = bX + a

b = SP_xy/SS_X = (150.62/28) = 5.37929

a = M_y - bM_x = 54.42 - (5.38*2018) = -10800.98

ŷ= 5.37929X - 10800.98                 …(3)

R2 =	SSRegression	=	Σ(ŷi - My)2	=	810.3617	= 0.8715
	SStotal		Σ(yi - My)2		929.891

Confidence Interval:

The confidence interval is the prediction interval for the mean value of the dependent variable.

Calculating the standard error:

S.E²ci = S²residual	(	1	+	(x₀-x̄)²	)
		n		SSx

 

S.E.²ci = (4.8894)²	(	1	+	(2030 – 2018)²	)	=(11.241)²
		7		28

S.E._ci =11.241
Calculating the confidence interval:

Ŷ ± T_1-α/2(n-2)*S.E_ci

118.978 ± T_1-0.05/2(7-2)*S.E_ci

118.978 ± 2.5706*11.241Σ

C.I.=[90.0822, 147.8738]

Chi-square test (Goodness of fit test)

From the table above chi square calculated = 2.35 with 6 degrees of freedom and critical value (or tabulated value) of chi-square = 12.596 at 95% confidence interval with 6 degrees of freedom.

Since, at 6 d.f. and α=0.05

Therefore, do not reject H₀ i.e.There is no significant difference between Observed (O_i) andexpected (E_i) generation of wind energy over the time.

4.5 Estimated wind power generation for the year 2030:          

The linear trendline is

ŷ= 5.37929X - 10800.98

and the Estimated wind power generation for the year 2030 is as:

Fig. 6:Fitted Straight line and predicted value for year 2030

Year(X)	Generation in GW (Y) prediction
2030	118.978

1. Central Electricity Authority, ministry of power. (https://cea.nic.in) 2. Frede Hvelplund (2006). Renewable energy and the need for local energy markets., 31(13), 2293–2302. doi:10.1016/j.energy.200 3. Hemani Paliwal and Vikramaditya Dave 2021 IOP Conf. Ser.: Earth Environ. Sci. 785 012007 4. Jorge M. Huacuz (2005). The road to green power in Mexico—reflections on the prospects for the large-scale and sustainable implementation of renewable energy., 33(16), 2087–2099. https://doi10.1016/j.enpol.2004.04.004 5. Kumar. J, C.R., Majid, M.A. Renewable energy for sustainable development in India: current status, future prospects, challenges, employment, and investment opportunities. Energ Sustain Soc 10, 2 (2020). https://doi.org/10.1186/s13705-019-0232-1 6. Ministry of External Affairs https://eoi.gov.in/eoisearch/MyPrint.php?8804?001/0029 7. Ministry of New and Renewable Energy (https://mnre.gov.in) 8. MNRE,Concessional Custom Duty Exemption Certificate (CCDC) (https://ccdcwind.gov.in//) 9. Muralidhar Nayak Bhukya et al 2021 J. Phys.: Conf. Ser. 1854 012004 10. National institute of wind energy Ministry of New and Renewable Energy, Government of India. (https://niwe.res.in) 11. Press Information Bureau Government of India(https://www.pib.gov.in/PressReleseDetailm.aspx?PRID=1685046 ) 12. Sims REH. Renewable energy: a response to climate change. Solar Energy 2004;76(1–3):9–17. 13. Swarnkar, Radhika & Ramachandran, Harikrishnan. (2021). Statistical Analysis Based Survey of Indian Renewable Energy Scenario. International Journal of Sustainable Development and Planning. 16. 379-384. 10.18280/IJSDP.160218.