Future of renewable energy consumption in France, Germany, Italy, Spain, Turkey and UK by 2030 using optimized fractional nonlinear grey Bernoulli model

Sustainable Production and Consumption 25 (2021) 1–14

Contents lists available at ScienceDirect

Sustainable

Production

and

Consumption

journal homepage: www.elsevier.com/locate/spc

Research

article

Future

of

renewable

energy

consumption

in

France,

Germany,

Italy,

Spain,

Turkey

and

UK

by

2030

using

optimized

fractional

nonlinear

grey

Bernoulli

model

Utkucan

¸S

ahin

Department of Energy Systems Engineering, Faculty of Technology, Mu ˘gla Sıtkı Koçman University, 480 0 0, Mu ˘gla, Turkey

a

r

t

i

c

l

e

i

n

f

o

Article history: Received 8 May 2020 Revised 15 July 2020 Accepted 15 July 2020 Available online 17 July 2020 Editor: Prof. Adisa Azapagic Keywords:

Forecasting Optimization

Fractional nonlinear grey Bernoulli model Renewable energy consumption Gross final energy consumption Countries

a

b

s

t

r

a

c

t

In this study, gross final energy consumption (GFEC), energy consumption of renewable energy sources (RES) and its share in France, Germany, Italy, Spain, Turkey and the United Kingdom (UK) are forecasted by 2030. A novel model is proposed in this study which is called optimized fractional nonlinear grey Bernoulli model, briefly as OFANGBM(1,1). In this model, three parameters, which are background value

λ, power index value γ and fractional order value r, are optimized by genetic algorithm (GA) method. Re-

sults of OFANGBM(1,1) show that GFEC in France, Germany, Italy, Spain, Turkey and UK will reach to 151.7

Mtoe, 227.6 Mtoe, 110.8 Mtoe, 84.5 Mtoe, 173.4 Mtoe and 132.2 Mtoe, respectively, in 2030. Additionally,

energy consumption from RES in France, Germany, Italy, Spain, Turkey and UK is forecasted as 28.5 Mtoe,

53.8 Mtoe, 22.2 Mtoe, 23.2 Mtoe, 26.1 Mtoe and 39.3 Mtoe, respectively, for the year 2030. Results of this

study are compared with the national target of these countries on the share of RES in GFEC. Moreover, it

is estimated that RES can satisfy 18.8%, 23.6%, 20.0%, 27.5%, 15.1% and 29.7% of GFEC in France, Germany, Italy, Spain, Turkey and UK in 2030, respectively.

© 2020 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

1. Introduction

While the need of energy increases, conventional sources are rapidly running out. To overcome this handicap, renewable energy sources with their advantages are an alternative way for govern- ments’ energy strategy ( Pacesila et al., 2016 ). In 2017, World fi- nal energy consumption was reported as 9717 Mtoe with a growth rate of 1.9% and the European countries had the share of 14.5% in World final energy consumption ( IEA, 2020 ). In 2018, gross final energy consumption among the European countries was the high- est in Germany (223.3 Mtoe), followed by the France (154.5 Mtoe), the United Kingdom (UK) (133.7 Mtoe), Italy (121.5 Mtoe), Turkey (105.0 Mtoe) and Spain (89.2 Mtoe), respectively ( Eurostat, 2020a ). Additionally, the share of renewable sources in gross final energy consumption in the European Union (EU) reached from 8.5% in 2004 to 18.0% in 2018. The EU targets to raise this share up to 20% by 2020 and 32% by 2030 ( Eurostat, 2020b ). Forecasting of this target has been subject to many researchers ( Knopf et al., 2015 ; Nikolaev and Konidari, 2017 ; Liobikiene and Butkus, 2017 ; Cucchiella et al., 2018 ; Mehedintu et al., 2018 ; Simionescu et al., 2020 ). Forecasting of energy consumption plays a key role of en- ergy management ( Wei et al., 2019 ). Even since the last two years,

E-mail address: [email protected]

grey prediction models have been widely used as a forecasting tool by many researchers in this field ( Li and Zhang, 2019 ; Zhang et al., 2019 ; Ye et al., 2019 ; Wang and Song, 2019 ; Wang et al., 2019 ; Lu, 2019 ; Wang et al., 2020 ; Ma and Wang, 2020 ).

The simplest form of grey prediction models is GM(1,1), firstly proposed by Deng ( Deng, 1982 ). The main advantage of this model is that it can be used to predict a small number of sequence data ( Liu et al., 2016 ). The methodology of GM(1,1) is based on the first- order single variable prediction ( Ma et al., 2013 ) and this method was used in forecasting of energy by researchers ( Yuan et al., 2016 ; Tsai, 2016 ; Li and Li, 2017 ; ¸S ahin, 2018 ). The GM(1,1) assumes that the background value (

λ

) is equal to 0.5, but researchers have tried to optimize the parameter

λ

which is in the range of 0-1 and is called optimized grey prediction model, briefly as OGM(1,1). Many studies ( Wen et al., 20 0 0 ; Shang and Pei, 2009 ; Zhou et al., 2009 ; Zhao et al.,2012; Ma et al., 2013 ; Ene and Öztürk, 2017 ) showed that the OGM(1,1) presents higher prediction performance than GM(1,1). Multivariable grey models are the other improved forms of the GM(1,1) and the basic multivariable grey model is GM(1,N), where N denotes the number of variables of the modeling equation ( Hsu and Wang, 2009 ). Hsu and Wang (2009) showed the GM(1,N) gives higher prediction performance than GM(1,1). Hsu (2009) and Zhong et al. (2017) investigated the prediction performance due to the optimization of the parameter

λ

in GM(1,N). The optimized https://doi.org/10.1016/j.spc.2020.07.009

2 U. ¸S ahin / Sustainable Production and Consumption 25 (2021) 1–14

Nomenclatures

AAGR average annual growth rate (%)s

AGO accumulated generating operation

APE absolute percentage error (%)

GM(1,1) basic grey model

FANGBM(1,1) fractional nonlinear grey Bernoulli model

MAPE mean absolute percentage error (%)

NGBM(1,1) nonlinear grey Bernoulli model

OGM(1,1) optimized grey model

ONGBM(1,1) optimized nonlinear grey Bernoulli model OFANGBM(1,1) optimized fractional nonlinear grey Bernoulli

model

λ

background value

γ

power index value

r fractional order value

GM(1,N) is called as OGM(1,N) ( Hu, 2020 ). Tien (2005) proposed grey prediction model with convolution integral (GMC(1,N)) to im- prove the traditional GM(1,N). Wang (2015) showed that the MAPE value of the GMC(1,N) is lower than that of the GM(1,N). Then, the background value

λ

of GMC(1,N) is optimized by Wang and Hao (2016) for the prediction of industrial energy consumption in China and the model is named as OGMC(1,1). Additionally, ef- fect of optimization of the parameter

λ

on prediction performance has been investigated in the another grey model which is based on “rolling” or “metabolism” technique. The main advantage of this technique is that this method gives better prediction results using the latest data sequence ( Chang et al., 2005 ). When the rolling mechanism technique is used in GM(1,1), the model is called metabolic grey model, briefly as MGM(1,1). Many studies showed that the MGM(1,1) presents more accurate results than the GM(1,1) (Zhao et al.,2012; Ma et al., 2013 ; Boran, 2015 ; Zhao et al., 2016 ; Zhao and Guo, 2016 ; Wang et al., 2017 ). Also, researchers have improved the MGM(1,1) by optimizing the parameter

λ

and the improved model is called optimized metabolic grey model, briefly as OMGM(1,1). There are many studies that the OMGM(1,1) gives higher prediction performance than the MGM(1,1) (Zhao et al.,2012; Ma et al., 2013 ; Liu et al., 2014 ; Wang et al., 2017 ; Li et al., 2018 ; ¸S ahin, 2019 ). In the further studies, re- searchers investigated the nonlinearity of MGM(1,1) and the model is called nonlinear metabolic grey model, briefly as NMGM(1,1). The biggest difference between the NMGM(1,1) and MGM(1,1) is that the NMGM(1,1) has characterized with the power coeffi- cient value (

α

) which denotes the nonlinearity ( An et al., 2019 ). Wang et al. (2018) and ¸S ahin (2019) showed that NMGM(1,1) gives higher prediction performance than MGM(1,1). ¸S ahin (2019) has improved the NMGM(1,1) by optimizing the parameter

λ

and the model is called optimized nonlinear metabolic grey model (ON- MGM(1,1)) and compared these models for the for the forecast- ing of Turkey’s greenhouse gas emissions. The results show that mean absolute percentage error (MAPE) of the NMGM(1,1) is lower than that of the MGM(1,1) which means NMGM(1,1) gives higher prediction results than MGM(1,1) for this study. The another im- proved grey model is nonlinear grey Bernoulli model (NGBM(1,1)) which is proposed by Chen ( Chen, 2008 ). In this model, power index value (

γ

) is used to fit the curve of actual data. When

γ

is equal to 0, the NGBM(1,1) reduces to the GM(1,1) ( Wu et al., 2019a ). Researchers show that the NGBM(1,1) gives higher predic- tion performance than the GM(1,1) ( Chen, 2008 ; Chen et al., 2008 ; Chen et al., 2010 ; Hsu, 2010 ; Tsai, 2016 ; Pei and Li, 2019 ; Wu and Zhang, 2020 ). Chen et al. (2008) improved the NGBM(1,1) by opti- mizing the background value (

λ

) and the improved model is called optimized nonlinear grey Bernoulli model (ONGBM(1,1) or Nash

nonlinear grey Bernoulli model (NNGBM(1,1)) ( Chen et al., 2010 ). Many studies present that the optimized NGBM(1,1) gives a higher accuracy than that of the traditional NGBM(1,1) ( Chen et al., 2008 ; Zhou et al., 2009 ; Chen et al., 2010 ; Wang et al., 2011 ; Wang, 2013 ; Lu et al., 2016 ). Also recently, NGBMC(1,n) and NGBM(1,1,k,c) have been proposed as improved versions of the NGBM(1,1) by Ma et al. (2019a) and Wu et al. (2020) , respectively. Table 1 sum- marizes effect of optimizing the background value

λ

in the grey prediction models, mentioned in the literature review above, on the MAPE values. It is obvious that the background value

λ

value varying from 0 to 1 instead of 0.5 in grey prediction models im- proves the prediction accuracy.

In addition to the above grey prediction models, a new tech- nique “fractional order accumulation” is firstly applied into the GM(1,1) by Wu et al (2013) . The novel model, is called frac- tional grey prediction model, inspired many researchers due to its superior predictive performance, especially used as a forecasting tool in energy researches. Fractional grey prediction models have been applied to predict China’s electricity consumption ( Yang and Xue, 2016 ), China’s nuclear energy consumption ( Wu et al., 2018 ), China’s crude oil consumption ( Duan et al., 2018 ), China’s wind en- ergy consumption ( Zhang et al., 2019 ), China’s natural gas and coal consumption ( Ma et al., 2019b ), renewable energy consumption in China ( Wu et al., 2019a ), China’s energy consumption ( Wu et al., 2019b ), natural gas consumption of countries ( Ma et al., 2020 ), Turkey’s electricity generation and installed capacity ( ¸S ahin, 2020 ) and China’s annual electricity consumption ( Xie et al., 2020 ). Re- cently, Wu et al. (2019) firstly applied fractional order accumula- tion into the nonlinear grey Bernoulli model and the new model is called as fractional nonlinear grey Bernoulli model, briefly as FANGBM(1,1). The prediction performance of the FANGBM(1,1) de- pends on optimizing the two parameters which are power in- dex value (

γ

) and fractional order value ( r). These two parame- ters characterize the model’s ability to adapt to actual data. Then, ¸S ahin, 2020 used the FANGBM(1,1) to forecast Turkey’s electric- ity generation and installed capacity from total renewable and hy- dro energy. In another study ( ¸S ahin and ¸S ahin, 2020 ), this model was used to forecast the cumulative number of confirmed cases of COVID-19 in many countries. In these studies, the background value

λ

of FANGBM(1,1) is equal to 0.5.

When the above-mentioned literature is carefully reviewed, the idea that FANGBM(1,1) can be improved by optimizing the back- ground value

λ

has emerged. This study proposed a novel model which is called as optimized fractional nonlinear grey Bernoulli model, abbreviated as OFANGBM(1,1). In the novel model, effect of optimizing

λ

on the prediction performance is investigated.

Moreover, fractional grey prediction models can be used to fore- cast the renewable energy consumption and total energy consump- tion for European countries due to their high prediction perfor- mance. In this way, projections on the share of renewable sources in energy consumption for these countries can be made and pro- vide information on how far to approach future targets. As far as the author’s knowledge, EU’s target on the share of renewable sources in gross final energy consumption has not forecasted yet by using fractional grey prediction models. As a result, it is be- lieved that this study fills the gap in the literature. Therefore, this study aims to forecast renewable energy consumption and gross fi- nal energy consumption of selected European countries, which are Germany, France, Italy, Spain, Turkey and the United Kingdom us- ing FANGBM(1,1) and OFANGBM(1,1) by 2030. The reason for these countries being selected is the highest gross final energy consump- tion in European countries for the year 2018, according to the data of Eurostat.

The novelty of this study is an improved fractional nonlinear grey Bernoulli model is proposed. The difference of the new pro- posed model from the FANGBM(1,1) is that the background value

U. ¸S ahin / Sustainable Production and Consumption 25 (2021) 1–14 3

Table 1

The overview of comparison of MAPE values between grey prediction models and optimized grey prediction models in the literature.

Reference Study Grey prediction models MAPE (%)

Wen et al., 2000 Cage-net amounts of fish GM(1,1) 10.32

OGM(1,1) 7.86

Shang and Pei, 2009 Chinese rural gross domestic product GM(1,1) 4.45

OGM(1,1) 4.06

Ene and Öztürk, 2017 End-of-life vehicles of West Anatolia region GM(1,1) 4.83

OGM(1,1) 4.62

Hsu, 2009 Taiwan’s integrated circuit industry output GM(1,N) 0.29

OGM(1,N) 0.24

Zhong et al., 2017 Photovoltaic power generation (for April) GM(1,N) 3.53

OGM(1,N) 7.14

Wang and Hao, 2016 Industrial energy consumption in China GMC(1,N) 11.24

OGMC(1,N) 8.34

Zhou et al., 2009 Power load of Hubei electric power network GM(1,1) 3.63

OGM(1,1) 3.61

NGBM(1,1) 1.79

ONGBM(1,1) 1.78

Zhao et al., 2012 Per capita annual net income of rural households in China

GM(1,1) 8.29

OGM(1,1) 7.88

MGM(1,1) 4.69

OMGM(1,1) 2.79

Ma et al., 2013 Iron ore import of China GM(1,1) 16.88

OGM(1,1) 14.45

MGM(1,1) 6.70

OMGM(1,1) 2.31

Liu et al., 2014 Financial intermediation in Beijing MGM(1,1) 8.36

OMGM(1,1) 0.05

Real estate in Beijing MGM(1,1) 61.77

OMGM(1,1) 0.99

Semiconductor industry production in Beijing MGM(1,1) 10.52

OMGM(1,1) 8.38

Wang et al., 2017 Beijing’s tertiary industry GM(1,1) 4.54

OGM(1,1) 4.05

MGM(1,1) 4.54

OMGM(1,1) 0.07

Beijing’s other services industry GM(1,1) 12.11

OGM(1,1) 11.22

MGM(1,1) 8.04

OMGM(1,1) 0.12

Li et al., 2018 Spontaneous combustion of the stockpiled coal MGM(1,1) 1.83

OMGM(1,1) 0.50

¸S ahin, 2019 Turkey’s GHG emissions from the energy sector MGM(1,1) 5.55

OMGM(1,1) 5.26

NMGM(1,1) 5.25

ONMGM(1,1) 5.19

Wang et al., 2011 Opto-electronics components in Taiwan NGBM(1,1) 4.82

ONGBM(1,1) 4.04

Opto-electronics application in Taiwan NGBM(1,1) 4.10

ONGBM(1,1) 3.10

Lu et al., 2016 Foreign exchange rates in Taiwan NGBM(1,1) 0.25

ONGBM(1,1) 0.10

(

λ

) is also optimized in the range of 0-1. Therefore, it is aimed that having more accurate results than that of the FANGBM(1,1) by optimizing three parameters are

λ

,

γ

and r.

The main contributions of this study can be given as:

(1) The background value

λ

of the FANGBM(1,1) is equal to 0.5. However, in many improved grey prediction models, which are OGM(1,1), OMGM(1,1), ONMGM(1,1) and NNGBM(1,1), this parameter is in the range of 0-1. This phenomena can be used in the FANGBM(1,1). In other words, the FANGBM(1,1) can be improved by optimizing the parameter

λ

and as far as the author’s knowledge, this issue is probably the first in the literature. In this study, a new model is proposed which is called optimized fractional nonlinear grey Bernoulli model, briefly as OFANGBM(1,1).

(2) In the OFANGBM(1,1), the background value (

λ

), power in- dex value (

γ

) and fractional order value ( r) are optimized by using genetic algorithm (GA) technique for this study. In this way, the proposed model with higher prediction perfor- mance can be used for the further studies.

(3) The OFANGBM(1,1) is used to forecast the renewable en- ergy consumption, gross final energy consumption and its share in Germany, France, UK, Italy and Turkey by the year 2030. Except for the previous studies ( Cucchiella et al., 2018 ; Mehedintu et al., 2018 ; Simionescu et al., 2020 ), forecasting on this issue is very scarce in the literature whereas these studies present projections by the year 2020. This study not only tests the national targets of the selected countries in 2020, but also provides projections on this issue by 2030. (4) The results of this study are expected to provide important

information to researchers and energy decision makers.

The rest of this study is: In Section 2 , the methodology of the OFANGBM(1,1) is given. Additionally, the optimization technique and how the prediction performance is measured is mentioned. In Section 3 , the results of this study are presented and also com- pared with the literature. Finally, Section 4 presents the conclu- sions, suggestions and limitations.

4 U. ¸S ahin / Sustainable Production and Consumption 25 (2021) 1–14

2. Methodology

This section presents the methodology of the proposed novel model, optimized fractional nonlinear grey Bernoulli model (OFANGBM(1,1)). Additionally, the cycle scheme on how the OFANGBM(1,1) reduces to GM(1,1) is mentioned. At the end of this section, how the optimal parameter is obtained and which metric is used for evaluating performance are given.

2.1.ThestructureofoptimizedfractionalnonlineargreyBernoulli model

The principle of fractional order accumulated is based on the r-th accumulated generation operation (r-AGO) and Wu et al. (2013) presented this methodology with the following definitions.

The original non-negative sequence X(0)_{is indicated as:} X(0)₌



_X(0)

₍

₁

₎

_,X(0)

₍

₂

₎

_,X(0)

₍

₃

₎

_{, ........,X}(0)

₍

_n

₎

_{, n≥ 4}



₍₁₎

X(0)_{transforms to the X}(r)_as:

X(r)₌



_X(r)

₍

₁

₎

_,X(r)

₍

₂

₎

_,X(r)

₍

₃

₎

_{, ........,X}(r)

₍

_n

₎



₍₂₎

Where X(r) _{is the r-th accumulated generating operation (r-}

AGO) sequence of X(0) _{and r denotes the fractional order value} r_> 0. Additionally, X(r) _{can be formulated as:}

X(r)

₍

_k

₎

= k  i=1 X(r−1)

₍

_i

₎

₌k i=1



k− j+r− 1 k− j



X(0)

₍

_i

₎

_{, k=1,2,.....,n} (3) where



k− j+r− 1 k− j



=

(

r+k− i− 1

)

(

r+k− i

₍

− 2_k

)

(

r+k− i− 3

)

...

(

r+1

)

r − i

)

! (4) When r=1 , X(r)_{( k) reduces to X}(1)

₍

_k

₎

₌k i=1 X(0)

₍

_i

₎

_{which de-}

notes the first-order accumulated generating operation (1-AGO) se- quence of X(0)_.

Wu et al. (2019a) presented the whitening equation of frac- tional nonlinear grey Bernoulli model (FANGBM(1,1)) as:

dX(r)

₍

_k

₎

dt +aX(

r)

₍

_k

₎

_=b



_X(r)

₍

_k

₎

γ ₍₅₎

and the discrete form can be given as,

X(r)

₍

_k

₎

_{− X}(r)

₍

_{k− 1}

₎

_+az(r)

₍

_k

₎

_{= b}



_z(r)

₍

_k

₎

γ ₍₆₎

where

γ

indicates the power index value.

When r= 1 , the whitening equation and the discrete form can be written respectively, as ( Lu et al., 2016 ):

dX(1)

₍

_k

₎

dt +aX(

1)

₍

_k

₎

_=b



_X(1)

₍

_k

₎

γ ₍₇₎

X(1)

₍

_k

₎

_{− X}(1)

₍

_{k− 1}

₎

_+az(1)

₍

_k

₎

_{= b}



_z(1)

₍

_k

₎

γ ₍₈₎

and this model is called the nonlinear grey Bernoulli model, briefly as NGBM(1,1)), firstly proposed by Chen (2008) .

When

γ

₌ 0 and r₌ 1 , the whitening equation and the dis- crete form can be presented by the following equations (Wu e al., 2019a),

dX(1)

₍

_k

₎

dt +aX

(1)

₍

_k

₎

_{=b (9)}

Fig. 1. Cyclic scheme of the grey prediction models for this study.

X(1)

₍

_k

₎

_{− X}(1)

₍

_{k− 1}

₎

_+az(1)

₍

_k

₎

_{=b (10)}

and this model is called the grey model, briefly as GM(1,1), firstly proposed by Deng (1982) .

In Eq. (6) , the form of z(r)_{( k) is given by (Mao et al., 2016) as:} z(r)

₍

_k

₎

₌

_λ

_∗X(r)

₍

_k

₎

₊

₍

₁₋

_λ

₎

_{∗ X}(r)

₍

_{k− 1}

₎

_{, k=2,3,4,.....,n}

(11)

where

λ

denotes the background value which is which is in the range of 0-1 ( Ma et al., 2013 ). In FANGBM(1,1), the background value

λ

is equal to 0.5 ( Wu et al., 2019a ). When

λ

is in the range of 0-1, the model is called the optimized nonlinear fractional grey Bernoulli model, abbreviated as OFANGBM(1,1) in this study. There- fore, constraints of the parameters of the OFANGBM(1,1) can be given as 0 <

λ

< 1,

γ

 = 0, and r> 0.

Additionally, when

λ

ranges from 0 to 1 in the Eq. (8) and (10) , the model is called as optimized nonlinear grey Bernoulli model (ONGBM(1,1)) and optimized grey model (OGM(1,1)), respectively. This cycle can be summarized in Fig. 1 . By this way, it is explained that how the OFANGBM(1,1) reduces to GM(1,1) with the changing of parameters

λ

,

γ

and r.

Once given the background value (

λ

), power index value (

γ

) and fractional order value ( r), parameters a and b of the whitening equation of grey prediction models can be calculated by the least squares method as:

a b



=



BT_B

−1

_BT_{Y (12)} where B=

⎡

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎣

−z(r)

₍

₂

₎



_z(r)

₍

₂

₎

γ −z(r)

₍

₃

₎



_z(r)

₍

₃

₎

γ −z(r)

₍

₄

₎



_z(r)

₍

₄

₎

γ . . . ... . . . ... −z(r)

₍

_n

₎



_z(r)

₍

_n

₎

γ

⎤

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎦

Y=

⎡

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎣

X(r)

₍

₂

₎

_{− X}(r)

₍

₁

₎

X(r)

₍

₃

₎

_{− X}(r)

₍

₂

₎

X(r)

₍

₄

₎

_{− X}(r)

₍

₃

₎

. . . . . . X(r)

₍

_n

₎

_{− X}(r)

₍

_{n− 1}

₎

⎤

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎦

(13)

[

OGM( I, I)

]

,\ =0,5

[

GM(l,1)

)

..,,

~

1

1-1

1

,;:i,' 9 <-:,;'\ II <::i· II ;,... ),1- ;,... 0 ( OF BM(l,I) ) ,I= 0.5 0 II FA.'iGBM(l.l) II

,._

_;,...

~

1

_~

₁

0 l:l)M(l,I) NGBM(l,1)

]

U. ¸S ahin / Sustainable Production and Consumption 25 (2021) 1–14 5

Fig. 2. The flowchart scheme of the OFANGBM(1,1) in this study.

Finally, the predicted values can be calculated by the following equations:

⎧

⎪

⎪

⎨

⎪

⎪

⎩

ˆ X(r)

₍

₁

₎

_=X(0)

₍

₁

₎

ˆ X(r)

₍

_k

₎

=





Xˆ(r)

₍

₁

₎

1

−γ ₋b a



e−a∗(1−γ )(k−1)₊b a



1 1−γ , k=2,3,....,n (14) 2.2. Optimizationoftheparametersandmetricsforevaluating performance

In this study, finding the optimal value of the parameters is based on reaching the smallest mean absolute percentage error (MAPE) value of the prediction model. To achieve this, genetic

algorithm (GA) method is used which has been widely used as an optimization technique in literature ( Wang and Hsu, 2008 ; Hsu, 2009 ; Hsu, 2010 ). The GA is solved by installing a software package on the Microsoft Excel for this study and runtime is con- tinued until the change of the MAPE value reaches to 0.01% in the simulation process.

In this study, the error between the original data and predicted data is obtained by calculating of the absolute percentage error (APE). Additionally, prediction performance between FANGBM(1,1) and OFANGBM(1,1) is compared by using MAPE. The formulation of the APE and MAPE is given by the following equation ( Ding et al., 2020 ):

APE

(

%

)

=





X

(

i

)

− ˆX

(

i

)

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6 U. ¸S ahin / Sustainable Production and Consumption 25 (2021) 1–14

Fig. 3. Actual values of GFEC (a) and energy consumption from RES (b) for the selected countries from 2004 to 2018.

Fig 4. Goodness of fit values of FANGBM(1,1) and OFANGBM(1,1) for the prediction of gross final energy consumption (a) and energy consumption from RES (b) in the selected countries. MAPE

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U. ¸S ahin / Sust ainable Pr oduction and Consum p tion 25 (202 1) 1–1 4 7 Fi g 5. Fo re ca st in g result s of OF AN GBM(1 ,1) fo r (a) GFEC, (b) ener gy consump tion fr om RES and (c) it s shar e in F rance by 2030. The flo w chart sc heme of the OF AN GBM(1 ,1) for this st u d y is pr esent e d in Fi g . 2 . 3. Re su lt s and discussions This section pr esent s the pr e diction re sults of fr actional nonlin-ear gr e y Bernoulli model (F AN GBM(1 ,1)) and op timize d fr actional nonlinear gr e y Bernoulli model (OF A N G BM(1 ,1)). A dditionall y, com-parison of the mean absolut e per cent ag e err o r (MAPE) v alues and g oodness of fit b e tw een FA N G B M (1 ,1 ) and OF AN GBM(1 ,1) for the select e d countries ar e gi v en. Fu rt h e rm o re , for e cas ting re sults of FA N G B M (1 ,1 ) and OF AN GBM(1 ,1) for gr oss final ener gy consum p -tion, rene w able ener gy consum p tion and it s shar es in the select e d countries ar e pr esent e d and com par e d with the lit er atur e. 3. 1. Dat a descrip tion In this st u d y, tw o indicat ors, whic h ar e ener gy consum p tion of rene w able sour ces and gr oss final ener gy consum p tion (GFEC), ar e ev a lu a te d for the pr e diction and for e cas ting. R ene w able ener gy sour ces (RES) consis t of hy d ro , wind, ge ot h e rm a l ener gy and all forms of biomass ( Eur os tat, 2020b ). GFEC deno tes the ener gy sup-plie d in households, indus tr y, services including public services, tr ansport, agricultur e, for e str y and fisheries, including the con-sum p tion of electricity and heat by the ener gy br anc h for electric-ity and heat pr oduction and including losses of electricity and heat in dis tribution and tr ansmission ( Eur opean Commission, 2020 ). The sta tis tic a l data of GFEC and ener gy consum p tion of RES is ta k e n fr om the dat abase of Eur os tat ( Eur os tat, 2020a ). In this st u d y, Fr a n ce , German y, It al y, Spain, Tu rk e y and the U nit e d Kingdom (UK) ar e select e d be ca u se of ha ving the highes t GFEC in Eur opean coun-tries for the ye a r 20 18. The data of GFEC and ener gy consum p tion of RES is av ailable fr om the ye a r 20 0 4 to 20 18 for these countries and is pr esent e d in Fi g . 3 . 3.2. Com parison of pr ediction perf ormance By using ge n e tic alg orithm me thod, op timal par ame ters of FA N G B M (1 ,1 ) and OF AN GBM(1 ,1) in pr e diction of gr oss final ener gy oc: 0

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8 U. ¸S ahin / Sust ainable Pr oduction and Consum p tion 25 (202 1) 1–1 4 Fi g 6. Fo re ca st in g result s of OF AN GBM(1 ,1) fo r (a) GFEC, (b) ener gy consump tion fr om RES and (c) it s shar e in German y by 2030. consum p tion (GFEC) and ener gy consum p tion fr om RES in Fr a n ce , German y, It al y, Spain, Tu rk e y and UK ar e obt aine d and lis te d in Table 2 . Not ic e that the bac kgr ound va lu e

λ

of OF AN GBM(1 ,1) is in the ra n g e of 0-1 wher eas this va lu e is eq ual to 0.5 in FA N G B M (1 ,1 ). The op timal par ame ters of FA N G B M (1 ,1 ) and OF AN GBM(1 ,1) ar e obt aine d accor ding to mean absolut e per cent ag e err o r (MAPE) of these gr e y pr e diction models re a ch e s the smalles t va lu e in the simulation pr ocess. By using Eq. (1 6) , MAPE re sults of FA N G B M (1 ,1 ) and OF AN GBM(1 ,1) for the pr e diction of GFEC and ener gy consum p tion form RES in the select e d countries ar e sho wn in Table 3 . It is ob vious that OF AN GBM(1 ,1) has smaller MAPE v alues than that of FA N G B M (1 ,1 ) in all cases whic h contribut es to OF AN GBM(1 ,1) pr esent s higher pr e diction performance than FA N G B M (1 ,1 ) for this st u d y. Conseq uentl y, op timizing of the bac kgr ound va lu e

λ

has im pr o v e d the pr e diction performance of fr actional gr e y pr e diction model as with ot h e r gr e y pr e diction model st u d ie s whic h is gi v en in Table 1 . A dditionall y, g oodness of fit v alues of FA N G B M (1 ,1 ) and OF AN GBM(1 ,1) for the pr e diction of GFEC and ener gy consum p tion fr om RES in the select e d countries ar e pr esent e d in Fi g . 4 . 3.3. Fo re ca st in g re su lts In this section, for e cas ting re sults of OF AN GBM(1 ,1) for GFEC, ener gy consum p tion fr om RES and it s shar e in Fr a n ce , German y, It al y, Spain, Tu rk e y and UK ar e pr esent e d. A dditionall y, for e casting re sults of this st u d y ar e discusse d with the lit er atur e. Fi g . 5 pr esent s the pr e diction and for e cas ting re sults of OF AN GBM(1 ,1) for gr oss final ener gy consum p tion (GFEC), ener gy consum p tion fr om RES and it s shar e in Fr a n ce . GFEC has de-cr ease d fr om 16 4 .8 Mt oe in 20 0 4 to 15 4 .5 Mt oe in 20 18. It is for e cast e d that GFEC will decr ease to 151 .7 Mt oe in 2030 with the av e ra g e annual gr o wth ra te (AA GR) is -0.2% for the period 20 18-2030 ( Fi g . 5 a). Ener gy consum p tion fr om RES has incr ease d fr om 15 .7 Mt oe in 20 0 4 to 25.6 Mt oe in 20 18 and it is for e cast e d that this va lu e will re a ch to 28.5 Mt oe in 2030 with the AA GR is 0.9% for the period 20 18-2030 ( Fi g . 5 b). A dditionall y, the shar e of RES in GFEC is es timat e d as 17. 2 % in 2020 and 18 .8 % in 2030 ( Fi g . 5 c). The national ta rg et of Fr a n ce on this issue is eq ual to 23% in 2020 ( Eur os tat, 2020b ). Mor eo v er , this shar e in 2020 is es timat e d as 17 .0-20.2% by Cucc hiella et al. (20 18) and 17. 3 % by Share of RES in GFEC (%) - - - t.J 0 ~ A ~ ~ ~ N A O ~ 0

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"--U. ¸S ahin / Sust ainable Pr oduction and Consum p tion 25 (202 1) 1–1 4 9 Fi g 7. Fo re ca st in g result s of OF AN GBM(1 ,1) fo r (a) GFEC, (b) ener gy consump tion fr om RES and (c) it s shar e in It al y by 2030. Ta b le 2 Op timal par ame te rs of FA N G B M (1 ,1 ) and OF AN GBM(1 ,1) fo r this st u d y. Indicat ors Countries FA N G B M (1 ,1 ) OF AN GBM(1 ,1) λγ r λγ r GFEC Fr ance 0.5 -0.4500 0.7134 0.5123 -0.4507 0.7095 German y 0.5 -28.3165 0.0587 0.4509 -26.8081 0.0567 It al y 0.5 1.7061 0.1141 0.6960 -0.2663 0.1158 Spain 0.5 0.5826 2.5499 0.5101 0.5527 2.3742 Tu rk e y 0.5 -1.4600 0.4168 0.4688 -1.5390 0.3890 UK 0.5 -17.9968 1.00E-300 0.5718 -29.9451 3.06E-09 Ener gy consump tion fr om RES Fr ance 0.5 -0.1889 0.3129 0.3249 2.8733 0.0618 German y 0.5 0.5070 1.8237 0.4930 0.5083 1.8246 It al y 0.5 1.4034 5.68E-300 0.4152 1.6750 1.00E-300 Spain 0.5 -2.1037 0.1859 0.6442 0.2661 1.2838 Tu rk e y 0.5 -2.1429 0.4549 0.3671 -0.3025 0.9167 UK 0.5 0.8124 0.1293 0.5727 0.6827 0.1371 Simionescu et al. (2020) . Ther efor e, re su lt of this st u d y is consis-te n t with the lit er atur e. The pr e diction and for e cas ting re sults of OF AN GBM(1 ,1) for gr oss final ener gy consum p tion (GFEC), ener gy consum p tion fr om RES and it s shar e in German y ar e pr esent e d in Fi g . 6 . German y has the highes t GFEC and ener gy consum p tion fr om RES v alues among the Eur opean countries in 20 18. Especiall y, ener gy con-sum p tion fr om RES has incr ease d fr om 14 .3 Mt oe in 20 0 4 to 36.8 Mt oe in 20 18 with the AA GR is %7 . OF AN GBM(1 ,1) pr esent s that this va lu e will re a ch to 53.8 Mt oe in 2030 with the AA GR is 3.2% fr om 20 18 to 2030 ( Fi g . 6 b). The shar e of RES in GFEC is es ti-mat e d as 17. 6 % in 2020 and 23.6% in 2030 is pr esent e d in Fi g . 6 c. The national ta rg et of German y on this issue is eq ual to 18 % in 2020 ( Eur os tat, 2020b ). A dditionall y, the shar e of RES in GFEC in 2020 is es timat e d as 18 .3 -2 1.1 % by Cucc hiella et al. (20 18) and 16 .1 % by Simionescu et al. (2020) . Ther efor e, it can be said that OF AN GBM(1 ,1) gi v es closer re sults to the ta rg et of German y in 2020. 0 w ()'I

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10 U. ¸S ahin / Sust ainable Pr oduction and Consum p tion 25 (202 1) 1–1 4 Fi g 8. Fo re ca st in g result s of OF AN GBM(1 ,1) fo r (a) GFEC, (b) ener gy consump tion fr om RES and (c) it s shar e in Spain by 2030. Ta b le 3 MAPE va lu e s of FA N G B M (1 ,1 ) and OF AN GBM(1 ,1) fo r this st u d y. Countries Gr oss final ener gy consump tion Ener gy consump tion fr om RES FA N G B M (1 ,1 ) OF AN GBM(1 ,1) FA N G B M (1 ,1 ) OF AN GBM(1 ,1) Fr ance 1.3019 1.2943 3.6105 3.5362 German y 1.7638 1.7588 1.8769 1.8707 It al y 1.1933 1.1476 2.7416 2.7139 Spain 2.7167 2.6893 2.4503 2.3551 Tu rk e y 2.5699 2.5580 1.3287 1.3042 UK 1.6771 1.5780 6.5525 6.5416 Fi g . 7 sho w s the pr e diction and for ecas ting re sults of OF AN GBM(1 ,1) for GFEC, ener gy consum p tion fr om RES and it s shar e in It al y. GFEC has decr ease d fr om 13 7.4 Mt oe in 20 0 4 to 12 1.5 Mt oe in 20 18. It is for e cast e d that GFEC will decr ease to 11 0.8 Mt oe in 2030 with the AA GR is -0.8% for the period 20 18-2030 ( Fi g . 7 a). Ener gy consum p tion fr om RES has incr ease d fr om 8.7 Mt oe in 20 0 4 to 21 .6 Mt oe in 20 18 and it is es timat e d that this va lu e will incr ease at a diminishing ra te by 2030. The re sults of OF AN GBM(1 ,1) pr esent that the ener gy consum p tion fr om RES in It al y will re a ch to 22.2 Mt oe in 2030 with the AA GR is 0.2% for the period 20 18-2030 ( Fi g . 7 b). Fi g . 7 c pr esent s the shar e of RES in GFEC in It al y and it is es timat e d that this va lu e will be 18 .7 % in 2020 and 20.0% in 2030. The national ta rg et of It al y on this issue is eq ual to 17 % in 2020 ( Eur os tat, 2020b ). A dditionall y, this shar e in 2020 is es timat e d as 1 9.2-23.3% by Cucc hiella et al. (20 18) and 18 .9 % by Simionescu et al. (2020) . Ther efor e, re su lt of this st u d y is closer to Simionescu et al. (2020) . In Spain, GFEC has decr ease d fr om 97 .9 Mt oe in 20 0 4 to 89.2 Mt oe in 20 18 and is for e cast e d as 84.5 Mt oe in 2030 ( Fi g . 8 a). On the ot h e r hand, ener gy consum p tion fr om RES has incr ease d ,-.,

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U. ¸S ahin / Sust ainable Pr oduction and Consum p tion 25 (202 1) 1–1 4 11 Fi g 9. Fo re ca st in g result s of OF AN GBM(1 ,1) fo r (a) GFEC, (b) ener gy consump tion fr om RES and (c) it s shar e in Tu rk e y by 2030. fr om 8. 1 Mt oe in 20 0 4 to 15 .5 Mt oe in 20 18 with the AA GR is %4.7 and it is es timat e d that this va lu e will re a ch to 23.2 Mt oe in 2030 with the AA GR is 3.4% fr om 20 18 to 2030 ( Fi g . 8 b). Fi g . 8 c pr esent s that the shar e of RES in GFEC will be 19 .0 % in 2020 and 27 .5 % in 2030 accor ding to the re sults of OF AN GBM(1 ,1). Spain has se t the national ta rg et on this issue as 20% for the ye a r 2020 ( Eur os tat, 2020b ). A dditionall y, the shar e of RES in GFEC in 2020 is es timat e d as 1 6.8-20.0% by Cucc hiella et al. (20 18) and 18 .8 % by Simionescu et al. (2020) . Ther efor e, it can be said that re su lt of this st u d y is consis tent with the lit er atur e. The pr e diction and for e cas ting re sults of OF AN GBM(1 ,1) for gr oss final ener gy consum p tion (GFEC), ener gy consum p tion fr om RES and it s shar e in Tu rk e y ar e pr esent e d in Fi g . 9 . Tu rk e y ra n k s the fif th place in GFEC among the Eur opean countries in 20 18. GFEC of Tu rk e y has incr ease d fr om 63.9 Mt oe in 20 0 4 to 10 5 .0 Mt oe in 20 18 and it is for e cast e d that this va lu e will incr ease to 17 3 .4 Mt oe in 2030 with the AA GR is 4.3% for the period 20 18-2030. A dditionall y, ener gy consum p tion fr om RES has incr ease d fr om 10 .3 Mt oe in 20 0 4 to 14 .3 Mt oe in 20 18 with the AA GR is %2.4. OF AN GBM(1 ,1) pr esent s that this va lu e will re a ch to 26. 1 Mt oe in 2030 with the AA GR is 5. 1% fr om 20 18 to 2030 ( Fi g . 9 b). The shar e of RES in GFEC is es timat e d as 13 .9 % in 2020 and 15 .0 7 % in 2030 is pr esent e d in Fi g . 9 c. The national ta rg et of Tu rk e y on the shar e of RES in GFEC is 20.5% for the ye a r 2023 ( ETKB, 20 14 ). In this st u d y, this va lu e is es timat e d as 14 .6 % in 2023. Fi g . 10 pr esent s the pr e diction and for e cas ting re sults of OF AN GBM(1 ,1) for gr oss final ener gy consum p tion (GFEC), ener gy consum p tion fr om RES and it s shar e in UK. GFEC has decr ease d fr om 1 53.8 Mt oe in 20 0 4 to 13 3 .7 Mt oe in 20 18. It is for e cast e d that GFEC will decr ease to 1 32.2 Mt oe in 2030 with the AA GR is -0. 1% for the period 20 18-2030 ( Fi g . 10 a). Ener gy consum p -tion fr om RES has incr ease d fr om 1. 4 Mt oe in 20 0 4 to 14 .7 Mt oe in 20 18 with the AA GR is 18 .3 % and it is for e cast e d that this va lu e will re a ch to 39.3 Mt oe in 2030 with the AA GR is 8.5% for the period 20 18-2030 ( Fi g . 10 b). A dditionall y, the shar e of RES in GFEC is es timat e d as 13 .4 % in 2020 and 29.7% in 2030 ( Fi g . 10 c). The national ta rg et of UK on this issue is eq ual to 15 % in 2020 ( Eur os tat, 2020b ). Mor eo v er , this shar e in 2020 is es timat e d as 11 .8-1 3.7% by Cucc hiella et al. (20 18) and 9.6% by

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12 U. ¸S ahin / Sust ainable Pr oduction and Consum p tion 25 (202 1) 1–1 4 Fi g 10 . Fo re ca st in g result s of OF AN GBM(1 ,1) fo r (a) GFEC, (b) ener gy consump tion fr om RES and (c) it s shar e in UK by 2030. Simionescu et al. (2020) . Ther efor e, it can be said that re su lt of this st u d y is closer to the national ta rg et of UK for the ye a r 2020. Conclusions This st u d y pr esent s an im pr o v e d form of fr actional nonlin-ear gr e y Bernoulli model (F AN GBM(1 ,1)) whic h is calle d op timize d fr actional nonlinear gr e y Bernoulli model, briefl y as OF AN GBM(1 ,1). The main dif fer ence of OF AN GBM(1 ,1) fr om FA N G B M (1 ,1 ) is that the bac kgr ound va lu e

λ

of OF AN GBM(1 ,1) is in the ra n g e of 0-1 , no t eq ual to 0.5. To obtain op timal par ame ters of gr e y pr e diction models, ge n e tic alg orithm (G A) me thod is use d. The pr e diction per -formance of tw o models ar e com par e d for the pr e diction of gr oss final ener gy consum p tion (GFEC) and ener gy consum p tion fr om rene w able ener gy sour ces (RES) in Fr a n ce , German y, It al y, Spain, Tu rk e y and UK for the data of 20 0 4-20 18. By using OF AN GBM(1 ,1), GFEC, ener gy consum p tion fr om RES and it s shar e in these coun-tries ar e for e cast e d by 2030. The follo wing conclusions ar e ob-taine d as: • It is obt aine d that OF AN GBM(1 ,1) gi v es higher pr e diction re sults than that of FA N G B M (1 ,1 ) in all cases. • GFEC in Fr a n ce , German y, It al y, Spain, Tu rk e y and UK for the ye a r 2030 is es timat e d as 151 .7 Mt oe, 22 7.6 Mt oe, 11 0.8 Mt oe, 84.5 Mt oe, 17 3 .4 Mt oe and 1 32.2 Mt oe, respecti v el y. • Ener gy consum p tion fr om RES in Fr a n ce , German y, It al y, Spain, Tu rk e y and UK for the ye a r 2030 is es timat e d as 28.5 Mt oe, 53.8 Mt oe, 22.2 Mt oe, 23.2 Mt oe, 26. 1 Mt oe and 39.3 Mt oe, re -specti v el y. • The shar e of RES in GFEC in Fr a n ce , German y, It al y, Spain, Tu rk e y and UK for the ye a r 2030 is for e cast e d as 18.8%, 23.6%, 20.0%, 2 7.5%, 15 .1 % and 29.7%, respecti v el y. • A dditionall y, the national ta rg et of these countries on the shar e of RES in GFEC ar e com par e d with the re su lt of this st u d y. Some sugg es tions can be outline d for further st u d ie s: • In this st u d y, rene w able ener gy sour ces ar e consider e d in to -ta l. Fo r the further st u d ie s, hy d ro , solar , wind, ge ot h e rm a l and biomass ener gy can be for e cast e d separ at el y with using this model. By this wa y, the shar e of these rene w able ener gy sour ces in tot a l RES can be es timat e d. • OF AN GBM(1 ,1) can be combine d with the ro lling mec hanism tec hniq ue or mac hine learning models or ke rn e l base d me thod and re sults of this st u d y can be com par e d with it. C I,)

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