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A new forecasting framework for volatile behavior in net electricity

consumption: A case study in Turkey

*

Salih Tutun

a

,

b

,

*

,

1

,

2

, Chun-An Chou

b

, Erdal Canıyılmaz

c

a

Turkish Military Academy, Institute of Defense Science, Ankara, Turkey

b

State University of New York at Binghamton University, Department of Systems Science and Industrial Engineering, Binghamton, NY, USA

c

Erciyes University, Department of Industrial Engineering, Kayseri, Turkey

article info

Article history:

Received 29 April 2015

Received in revised form

10 August 2015

Accepted 17 October 2015

Available online xxx

Keywords:

Forecasting

Energy management

Regularization

Adaptive optimization

Time series analysis

abstract

Electricity is a signiﬁcant form of energy that cannot be stored physically and is usually generated as

needed. In most research studies, the main aim is to ensure that sufﬁcient electricity is generated to meet

future needs. In order to avoid waste or shortage, a good system needs to be designed to constantly

maintain the level of electricity needed. It is necessary to estimate independent factors because future

electricity volume is based not only on current net consumption but also on independent factors. In this

paper, a new framework is proposed to ﬁrst estimate future independent factors using SARIMA (seasonal

auto-regressive iterative moving average) method and NARANN (nonlinear autoregressive artiﬁcial

neural network) method, both of which are called a ”forecasted scenario approach”. Subsequently, based

on these scenarios, a LADES (LASSO-based adaptive evolutionary simulated annealing) model and a

RADES (ridge-based adaptive evolutionary simulated annealing) model are applied to forecast the future

NEC (net electricity consumption). The proposed approaches are then validated with a case study in

Turkey. The experimental results show that our approach outperforms others when compared to pre-

vious approaches. Finally, the results show that the NEC can be modeled, and it can be used to predict the

future NEC.

©2015 Elsevier Ltd. All rights reserved.

1. Introduction

Electricity is one of the main forms of energy affecting the

development of modern life, and it does so in technical, social, and

economic ways [1]. With regards to development, electricity de-

mand planning is a vital part of energy policies in developed and

developing countries, allowing them to make cost efﬁcient in-

vestments in capacity planning [2]. To obtain optimal planning,

policymakers have focused on the modeling and forecasting of

projections that are able to obtain quality and problem-free con-

ditions [3,4].

Due to limited primary energy sources, energy policies in many

countries depend on foreign countries to supply energy. With

optimal planning, governments need to purchase energy sources

from foreign countries. Moreover, electricity is a difﬁcult energy

source for investment, and it is hard to measure physical ﬂow

because electricity consumption has a volatile structure. The gov-

ernment needs a model that forecasts electricity demand for un-

stable situations [5]. Due to the fact that electricity cannot be

stored, and its production is costly, the net consumption of elec-

tricity energy has to be estimated by an optimal production model.

In the meantime, forecasting errors could cause either shortages or

excess capacity that are undesirable for energyplanning. In the case

of excess capacity, the remaining part is wasted. On the other hand,

an inadequate supply of electricity causes either increased cost or

cuts in electricity [6].

Governments use planning organizations to forecast energy

demands and consumption. In Turkey, energy forecasting studies

have been ofﬁcially conducted by the SPO (State Planning Organi-

zation) and the MENR (Ministry of Energy and Natural Resources)

by means of the MAED (Model of Analysis of Energy Demand) [7].

The MAED is a simulation-based approach that has been used to

assess medium-long term energy demand by using historical data

for the last two decades [6]. However, this approach is not adequate

*

Fully documented templates are available in the elsarticle package on CTAN.

*Corresponding author. State University of New York at Binghamton University,

Department of Systems Science and Industrial Engineering, Binghamton, NY, USA.

E-mail addresses: stutun1@binghamton.edu (S. Tutun), cachou@binghamton.edu

(C.-A. Chou), erdalc@erciyes.edu.tr (E. Canıyılmaz).

1

Supported for Ph.D. Education from Turkish Military Academy.

2

Ph.D. Candidate in State University of New York at Binghamton University.

Contents lists available at ScienceDirect

Energy

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

http://dx.doi.org/10.1016/j.energy.2015.10.064

0360-5442/©2015 Elsevier Ltd. All rights reserved.

Energy 93 (2015) 2406e2422

to represent future planning because of insufﬁcient data gathered

during two decades [8] and signiﬁcant errors in the data to be

analyzed [9]. For this reason, other improved forecasting tech-

niques could be used instead of the MAED model.

Many studies such as Toksarı[10,11], Erdo

gdu [12] and Ünler

[13] use future independent factors (scenarios), in which it is

assumed that independent factors increase at a constant growth

rate as days pass, although this is not practically feasible in dynamic

energy systems. At the same time, these studies have not consid-

ered the electricity consumption of Turkey in the medium term. In

order to compare energy models with the MAED, net electricity

consumption is estimated monthly. Therefore, we will give results

which are close to actual values. In this paper, the aim is to offer

new models for forecasting the NEC and new scenario approaches

that use reliable energy models. In order to obtain actual values of

future demand for scenarios, the SARIMA (seasonal auto-regressive

iterative moving average) method, and the NARANN (nonlinear

auto-regressive based on artiﬁcial neural network) method are

used in the forecasted scenario approach. Thereafter, the new

LASSO (Least Absolute Shrinkage and Selection Operator) base

adaptive evolutionary simulated annealing (LADES) and RADES

(ridge base adaptive evolutionary simulated annealing) energy

models with linear and quadratic behavior are constituted to

forecast the NEC to show the efﬁcacy of the proposed approach.

Meanwhile, researchers such as Toksarı[10,11], Ünler [13],

€

Oztürk et al. [14] and Ceylan and €

Oztürk [15] have used some meta-

heuristic approaches to optimize the parameters of energy models

in the literature. However, they have not considered over-training

in their algorithms. In the proposed framework, the LASSO and

ridge regression are used to prevent over-training by adding reg-

ularization. ES (evolutionary strategy) and SA (simulated anneal-

ing) as meta-heuristic approaches are ﬁrst studied to optimize

coefﬁcients of energy models. The hybrid meta-heuristic approach

is used to get optimal coefﬁcients for the proposed models because

they use the complex LASSO and ridge regression-based

formulation.

The rest of the paper is organized as follows. In the literature

review, applications are presented for the forecasting of energy

demand and consumption. In Section 2, the methods used in the

new proposed approaches are explained brieﬂy. Section 3de-

scribes in detail how the proposed methodology is used to fore-

cast the NEC. The net electricity consumption is estimated

monthly and annually for the years 2010e2020. The proposed

framework is discussed for the forecasting of the NEC based on

new scenario approaches with sensitivity analysis. Finally, Section

4shows the improvement in forecasting and the contribution of

the paper.

1.1. Literature reviews

Since the early 1970s, several studies on energy demand have

been performed using various estimation methods. Many studies

have aimed to evaluate the impact of economic activity and energy

planing on energy demand [12]. In recent years, because predictive

models are of vital importance for policymakers, they have used

these models to forecast and model energy consumption and de-

mand (see Table 1). In order to accurately forecast future energy

demand and consumption, several studies have presented models

that use artiﬁcial intelligence, econometric and hybrid approaches.

RA (regression analysis), ARIMA (auto-regressive iterative moving

avarage), SARIMA (seasonal auto-regressive iterative moving avar-

age), cyclic patterns and grey theory have been presented as the

econometric approaches. For example, Ediger and Tatlıdil [9] pro-

posed a technique involving the analysis of cyclic patterns of annual

additional amounts relevant to energy consumption. Tunç et al. [16]

estimated the electricity consumption demand with RA.

Kavaklıo

glu [17] combined multivariate regression with SVD (sin-

gular value decomposition) so as to downsize the problem to es-

timate the electricity consumption. Afterwards, Ediger and Akar

[18] made estimates on the electricity energy demand by using

the ARIMA and SARIMA methods. For electricity consumption,

Chujai et al. [4] found a model to forecast by using the ARIMA

method. Moreover, in recent years, researchers have focused on

grey theory. The grey forecasting model was used by Lee and Tong

[2] to make an electricity consumption estimate. GPRM (grey pre-

diction with the rolling mechanism) was utilized by Akay and Atak

[19] for an electricity demand estimate. Thereafter, optimized grey

modeling was proposed by Hamzaçebi and Es [20] to forecast

electricity consumption. Discrete grey forecasting and the Markov

approach based on the quadratic programming model were used by

Nai-ming et al. [5] to forecast energy production and consumption.

The results was showed that these methods were not adequate to

capture nonlinear behavior of energy demand and consumption.

Furthermore, artiﬁcial intelligence approaches have been pre-

sented to propose some models capturing nonlinear characteristics

for modeling of energy demand and consumption. An ANN

Nomenclature

w(k,i) weight between k and i nodes

Y

1

(k)¼a

1

(k) output of cell K

εerror for cell j

C(j,i) cost for weights

r

learning factor

New w

1

(j,i) new weight between j and i

Y(t) predicted output at time t

dnumber of delays

funknown smooth function

f

i

εði¼1;2;3;…pÞset of weight parameters for lags

q

j

εðj¼1;2;…qÞset of weight parameters for random errors

e

t

random error at time t

xindependent variable

M

L

penetration parameter for the LADES model

M

R

penetration parameter for the RADES model

net(S

i

(k) net input value

F

R

ﬁnal result for the RADES model

F

L

ﬁnal result for the LADES model

b

0

and

b

i

scalar and P-vector respectively, namely coefﬁcients of

models.

l

non-negative regularization parameter

Nthe number of observations

t

1

trend of gross production

t

2

trend of electricity energy imports

t

3

trend of transmitted electricity energy

t

4

trend of electricity energy exports

x

1

value of gross production

x

2

value of electricity energy imports

x

3

value of transmitted energy

x

4

value of electricity energy exports

OI output of import for forecasted scenarios

OE output of export for forecasted scenarios

OT output of transmitted energy for forecasted scenarios

OG output of gross production for forecasted scenarios

S. Tutun et al. / Energy 93 (2015) 2406e2422 2407

(artiﬁcial neural network) algorithm was used to estimate elec-

tricity demand and consumption by Kermanshahi and Iwamiya

[21],S

€

ozen et al. [22] and Kavaklıo

glu et al. [23]. In the meantime,

some researchers focused on comparing the ANN with other

methods in order to decide the best model for forecasting the

electricity consumption. They used linear and nonlinear methods to

show behavior of energy demand and consumption. The ANN

method and the RA method were compared as linear and nonlinear

models by Pao [24]. The ANN method and the ARIMA method were

compared by Hamzaçebi and Kutay [25]. The SVM (support vector

machine) method and the ANN method were used to estimate

demand and consumption. After the SVR (support vector regres-

sion) method was used by Kavaklıo

glu [3] to make an NEC estimate,

O

gcu et al. [26] compared the ANN with SVM methods in order to

estimate electricity consumption. The RA, ANN and LSSVM (least

squares support vector machines) were compared by Kaytez et al.

[27] to forecast electricity consumption. Azadeh et al. [28e30] used

methods such as ANN, GA (genetic algorithm), ANFIS (adaptive

neural fuzzy inference system), MCS (Monte Carlo simulation), PSO

(particle swarm optimization), and AIS (artiﬁcial immune system)

to compare forecasting results of electricity consumption. The re-

searchers used the artiﬁcial intelligence approach to show they

predicted better than econometric approach. However, they could

be improved for forecasting accuracy of energy models.

Finally, the researchers focused on hybrid approaches in an

attempt to improve energy models. The dimension reduction

approach (e.g. PCA (principal component analysis) and DEA (data

envelopment analysis)) and ANN were combined by Kheirkhah

et al. [31] to estimate electricity consumption. Furthermore, meta-

heuristic approaches were used to optimize the parameters of some

models using an artiﬁcial intelligence approach. Two different

nonlinear models that have quadratic and exponential behaviors

were developed using the GA method and the RA method by €

Oztürk

et al. [14] to estimate the energy demand. An ACOEDE (ant colony

optimization energy demand estimate) model is developed by

Toksarı[10]. Toksarı[11] established two different models to esti-

mate net electricity production and electricity demand by using

ACO (ant colony optimization). Ünler [13] developed an electricity

energy demand estimate model by using a PSO technique. Conse-

quently he made the energy estimate by using three different

scenarios and the results obtained were compared with the

ACOEDE model results of Toksarı[10]. Gürbüz et al. [32] used an

ABC (artiﬁcial bee colony) to optimize regression models for fore-

casting of electricity consumption. At the sametime, some re-

searchers focused on other artiﬁcial methods for hybrid methods.

Optimized regression and ANN using IPSO (improved particle

swarm optimization) were used by Ardakani and Ardehali [1] to

forecast electricity consumption. The ANN and PSO methods were

used to forecast electricity consumption by Jiang et al. [33]. Shi-wei

and Ke-jun [34] used a hybrid algorithm with GA and PSO methods

to forecast energy demand. As a result, when using hybrid methods,

energy models can be improved by the researchers. However, as the

researchers used these methods, they assumed that independent

factors are increased with a constant growth rate for scenarios. New

scenario approaches can be proposed for forecasting demand and

consumption. At the same time, because researchers used meta-

heuristic approaches, over-training needs to be prevented in en-

ergy models. The researchers need to propose better models in

order to obtain accurate results for energy demand and forecasting.

For example, they need to consider extensive data, over-training,

accurate scenarios for the future and hybrid optimization

algorithms.

2. Methodology

In this paper, the LADES and RADES energy models with

linear and quadratic function are developed for projections. The

adaptive evolutionary strategy is used to optimize the initial

coefﬁcients of these models, while the adaptive simulated

annealing algorithm makes a local search to ﬁnd the proper

Table 1

Summary of energy modeling and/or forecasting studies.

Method used Type of method Author(s) Forecasted variable

Econometric approach RA Tunç et al. [16] Electricity consumption

ARIMA and SARIMA Ediger and Akar [18] Electricity demand

ARIMA Chujai et al. [4] Electricity consumption

Cyclic patterns Ediger and Tatlıdil [9] Energy consumption

RA and SVD Kavaklıo

glu [17] Electricity consumption

Grey theory approach Grey theory Lee and Tong [2] Electricity consumption

GPRM Akay and Atak [19] Electricity demand

Optimized Grey model Hamzaçebi and Es [20] Energy demand

Grey Theory, Markov approach Nai-ming et al. [5] Energy demand

Artiﬁcial inteligence approach ANN Kermanshahi and Iwamiya [21] Electricity demand

ANN Kavaklıo

glu [23] Electricity consumption

GA, ANN and Fuzzy Azadeh et al. [28] Electricity demand

ANFIS, GA and ANN Azadeh et al. [28] Electricity consumption

AIS, GA and PSO Azadeh et al. [30] Electricity consumption

ANN and SVM O

gcu et al. [26] Electricity consumption

SVR Kavaklıo

glu [3] Electricity consumption

ANN and RA Pao [24] Electricity consumption

ANN S€

ozen et al. [22] Energy consumption with

economic indicators

Hybrid approach GA €

Oztürk et al. [14] Energy demand

ACO Toksarı[10] Energy demand

PSO Ünler [13] Electricity demand

ACO Toksarı[11] Electricity demand

ANN, PCA and DEA Kheirkhah et al. [31] Electricity consumption

ANN and ARIMA Hamzaçebi and Kutay [25] Electricity consumption

ANN and PSO Jiang et al. [33] Electricity consumption

RA, ANN and LSSVM Kaytez et al. [27] Electricity consumption

RA and ANN Ardakani and Ardehali [1] Electricity consumption

ABC Gürbüz et al. [32] Energy consumption

GA, PSO Shi-wei and Ke-jun [34] Energy consumption

S. Tutun et al. / Energy 93 (2015) 2406e24222408

coefﬁcients. Over-training is prevented by using the LASSO and

ridge regression methods in the models. In addition, we pro-

posed new approaches, namely forecasted scenarios, for fore-

casting the future values of independent factors such as imports,

exports, gross generation and transmitted energy. In the fore-

casted scenarios, the SARIMA and NARANN methods are imple-

mented respectively to obtain linear and nonlinear volatile

behavior for the future. Then, we deﬁne the best models for

forecasting by comparing the performance indicators. Finally, the

forecasting results are obtained by combining the proposed

approach and scenarios, as seen in Fig. 2.

2.1. A nonlinear auto-regressive model based on a neural network

ANNs (artiﬁcial neural networks) were originally developed to

mimic basic biological neural systems. The human brain has

interconnected simple processing elements (neurons or nodes) to

carry information. In ANNs, the information is carried by the

networks between input and output. In daily life, users draw

conclusions from the information obtained from samples, and

after that, they are able to make similar decisions in similar cases

and process incomplete information in uncertain cases. Each

neuron in ANNs takes an input signal from other neurons to

process an activation function for transforming output. ANNs can

make decisions by establishing relevant relationships between

events after gaining information with the help of data. After

training the network, it is possible to deal with incomplete in-

formation and give results even if there is incomplete informa-

tion on recently obtained examples. The information distributed

on the network has a distributed memory as numeric informa-

tion [35].

At the beginning in ANNs, weights are assigned randomly. For

the distribution of weights in the networks, each input value is

summed up by being multiplied by its own weight (summarization

function). In this way, the net input value that comes to the network

is calculated. Then the optimum weights can be reached as being

bound to the value.

Net ¼S

1

ðkÞ¼Xðw

1

ðk;iÞa

0

ðiÞ(1)

This shows that the net input value comes to the NET process

element. This value is acquired with the summarization function in

Eq. (1). Therefore, activation functions, which are the sigmoid

function in Eq. (2), detect the output that comes from net input

value.

Y

1

ðkÞ¼a

1

ðkÞ¼ 1

1þe

ð1s

1

ðkÞÞ

(2)

Therefore, the output of the node in Eq. (2) is the value that is

determined by the activation function.

ε

j

¼a

1

ðjÞy

r

ðjÞ(3)

The result is constituted on the output layer of the MLPANN

(multi-layer perceptron artiﬁcial neural network), which is

compared with the activation function. If there is a difference (error

signal in Eq. (3)) between the estimated value and actual value, the

weights in nodes are rearranged to reduce this difference. The

calculated outputs are compared with actual values and, if any, the

error is deﬁned at the outcome. The error signal is used in changing

the weights in the output unit among the hidden layer elements.

The effects of each output unit on error are obtained by calculating

C(j,i) values in Eq. (4) to ﬁnd optimal new weights [35].

C

1

ðj;iÞ¼X

p

r¼1

εðjÞa

1

ðjÞð1a

1

ðjÞÞ a

0

ðjÞ(4)

To achieve these procedures, the MLPANN can be used by ﬁrst

assigning the value of zero to the C(j,i). At the same time,

r

(the

learning factor) is determined beforehand and new weight units

can be reached, as is seen in Eq. (5).

w

0

1

ðj;iÞ¼w

1

ðj;iÞrC

1

ðj;iÞfor j ¼1;…;ni¼1;…;n(5)

The procedure is repeated by deducting the error signals of

every system that has many hidden layers from the corrected

procedures of the previous layer. Finally, the procedure is continued

until the system ﬁnds the desired point by trial and error, which is

called the back propagation algorithm of the error [36]. The delta

rule is used in this system for the training process in Eq. (5). The

training algorithm dispersing the error back is an iterative gradient

algorithm that was developed for minimizing the square of the

errors between the outputs obtained from a forward distributed

network and acquired target outputs.

The NARANN (nonlinear auto-regressive based on neural

network) is mentioned as it displays the motivation for clear

research [37]. Many auto-regressive-approach based papers (e.g.

Valipour et al. [37], Jeong et al. [38], Ruiz-Aquilar et al. [39] and

Zhang et al. [40]) exist in the literature for non-stationary time

series, and the neural network based nonlinear auto-regressive

model is offered to improve the auto-regressive approach [41].In

Fig. 1. Deﬁnes the best model regarding the LASSO. Notes: Combinations are made with parameters such as sigma, number of movements, initial temperature, random walk, and

lambda, respectively.

S. Tutun et al. / Energy 93 (2015) 2406e2422 2409

this section, this method can be analyzed to forecast the next lag

value in time-series data. The neural network is predicted using a

time lag model in Eq. (6) [42].

YðtÞ¼fðyðt1Þ;yðt2Þ;…;yðtdÞÞÞ þεðtÞ(6)

The model assumes that error is IID (independent and identi-

cally distributed), and in order to ﬁnd the optimal predictor with

minimum error of y(t), the model used is a conditional mean, as

seen in Eq. (7). We can ﬁnd the output when past time lags as inputs

are given.

YðtÞ¼EðyðtÞjyðt1Þ;yðt2Þ;…;yðtdÞÞÞ

¼fðyðt1Þ;yðt2Þ;…;yðtdÞÞÞ As t dþ1 (7)

In our model, there are hidden layers with neurons, weights and

bias which are calculated using training algorithms such as Lev-

enbergeMarquardt, Bayesian Regularization, and Scaled Conjugate

Gradient.

2.2. Seasonal auto-regressive iterative moving average method

In the literature, the ARIMA (auto-regressive iterative moving

average) method has been used in many ﬁelds during the last three

decades [38]. It is a well-known method in the time-series

approach, which was proposed by Box and Jenkins [40]. This

method has three linear components: the AR (auto-regressive

term), the integration term (I), and the MA (moving average term).

After selecting a suitable factor, the model can forecast future

values by looking at the linear function of past observations and

random error. The Seasonal ARIMA model is also an extension of

the ARIMA model. If the time-series data contains seasonality, the

model is called SARIMA (p,d,q)(P,D,Q)S, in which pis the auto-

regressive order, qis the moving average order, dis the number

of differing operations, and P,D, and Qare seasonal orders of

p,dand q[39]. In this paper, the model

x

t

¼fa

t1

þfa

t1

þ…þfa

tp

þe

t

þqe

t1

qe

t2

…qe

tq

for scenarios is constituted using the SARIMA method with sea-

sonality [40]. Models can be deﬁned by ﬁnding optimal orders for

this equation.

In order to use this model, there are four steps: stationary check,

identiﬁcation, diagnosis, and forecasting, as seen in Fig. 3. In the

ﬁrst step, the time-series data are checked as to whether or not the

mean, variance, and auto-correlation function are stationary. If the

data display non-stationary behavior, regularization is made by

using differentiation for time lags until stationary. Thereafter, the

model parameters are calculated by comparing the estimated and

actual values. The model is then statistically checked for signiﬁ-

cance. Finally, the forecasting is made using the SARIMA model

[38].

2.3. The proposed methodology for the forecasting of net electricity

consumption

The new energy models are offered using adaptive evolutionary

strategy and adaptive simulated annealing with LASSO and ridge

regression. At the same time, the new scenario approaches are

presented using the SARIMA and NARANN methods.

2.3.1. Hybrid approach

In the model, SA (simulated annealing) is a random search

technique and a trajectory found by using single-based optimi-

zation. The base of the idea was ﬁrst presented by Metropolis in

1953. Then Kirkpatric et al. [43] offered a simulation search model

by using the annealing approach to ﬁnd an optimal solution. This

Fig. 2. The ﬂow chart of the new framework for forecasting net electricity consumption.

S. Tutun et al. / Energy 93 (2015) 2406e24222410

algorithm mimics the annealing process in materials physics as

metals freeze and cool into a crystalline state with minimum en-

ergy level by using bigger crystal sizes to decrease defects. The

efﬁciency of the algorithm for optimization depends on the control

of temperature and cooling schedule. Moreover, in order to move

to new solutions, the algorithm uses random walk, which de-

scribes the movement of the algorithm by searching randomly

from the current solution to a neighborhood solution in order to

explore the optimal feasible solution [43]. In addition, the tem-

perature is reheated when the new solution is not suitable for

movement, and the method is made adaptive to prevent prema-

ture convergence.

In ES (evolutionary strategy), new solutions as children are

compared with old solutions as parents. The ES is used to ﬁnd a

good initial solution for the simulated annealing method because

the ES is a population-based algorithm, which can search out more

solutions for the global optimum in large search areas. At the same

time, these methods can cause over-ﬁtting because a meta-

heuristic approach is used. In order to eliminate this situation,

regularization is added to the objective function. LASSO and ridge

regression are used for regularization of coefﬁcients to ﬁnd the

optimal regression model by optimizing parameters with a hybrid

based on the ES and SA algorithms.

The proposed algorithm is described in the following steps:

Step 1: Initialization with the ES algorithm that sets the bounds

of parameters. The initial values of the parameters are then

generated for the models. If the ES has better offspring as par-

ents, the standard deviation for movement to a new solution is

decreased for the adaptive model.

Step 2: Temporal state for the SA algorithm that makes a

random move to change the current system state by using the

optimal initial parameters for the ES.

Step 3: Acceptance checking that looks at the following equa-

tions to understand whether there is acceptance or rejection of

the temporal state. If there is rejection, the temperature is

reheated as the adaptive model in the SA.

>The temporal state is accepted if the energy of the new

solution >the energy of the old solution and p, which is a

random number, <P, which is the accepted rate with the new

solution as 0 p1.

>The temporal state is accepted if the energy of the new

solution the energy of the old solution.

>The temporal state is rejected, otherwise.

Step 4: Finding a solution with regularization that ﬁnds the

optimal solution by comparing all solutions. The algorithm with

regularization (the LASSO and ridge regression) is also checked

for over-training by comparing testing and training errors.

Step 5: Feature selection with the LASSO: The algorithm uses the

LASSO method to improve the subset of features for analysis. If

the algorithm uses the same features, go to Step 6; otherwise, go

to Step 2 with new features.

Step 6: Deciding the best scenario for future independent fac-

tors by comparing forecasted scenarios.

Step 7: Use as expert system. The new energy models predict

future electricity consumption through the forecasted scenario

approach for decision-making.

The proposed model is explained with all steps in Fig. 2. The best

model is ﬁnally found, which guides future planning.

2.3.2. Coupling evolutionary strategy with simulated annealing

In the proposed models, there can be different behavioral

models (e.g. quadratic, cubic, exponential and so on) that increase

the decision variables exponentially. In order to solve this problem,

the ES is used to ﬁnd initial solutions for decision variables (coef-

ﬁcient of the models) by giving initial ranges. Thereafter, by using

the SA based on a single solution, the algorithm searches the

neighborhood of the initial solution because a random walk is used

for the next solution. It moves to new solutions for decision vari-

ables by using a normal random number. This means that the al-

gorithm can get stuck unless it has a good initial solution. For

instance, as is seen in Fig. 4, it begins to ﬁnd solutions from S

0

to S

3

.

Fig. 3. Flow chart of the SARIMA model.

S. Tutun et al. / Energy 93 (2015) 2406e2422 2411

After arriving at S

3

, the algorithm tends to accept this point as the

optimal solution for decision variables, but it is a local optimum.

The algorithm needs to search in a global way to ﬁnd the opti-

mum solution. Thus the ES algorithm can ﬁnd good (close to the

optimal solution) initial solutions that can be used in the SA algo-

rithm. When started with these solutions, the SA algorithm can ﬁnd

the optimal solution by looking in the neighborhood of initial

solutions.

2.3.3. Formulation for new energy models

In the literature, researchers (e.g. Toksarı[10], Ünler [13], Toksarı

[11] and Ceylan and €

Oztürk [15]) use linear and quadratic regres-

sion to obtain new models for electricity consumption. However,

when they use a meta-heuristic approach for training, they need to

consider overtraining. In the models, the LASSO and ridge regres-

sion are used in order to prevent over-training. They are regression

methods that involve penalizing the absolute and squaresize of the

regression coefﬁcients. In the formulation, forecasting models are

ﬁrst decided using linear and quadratic regression, as seen in Eq. (8)

and Eq. (11), respectively.

F

1

¼b

5

þb

1

x

1

þb

2

x

2

þb

3

x

3

þb

4

x

4

(8)

Fp

L

¼M

L

ðb

5

þb

1

x

1

þb

2

x

2

þb

3

x

3

þb

4

x

4

Þ(9)

Fp

R

¼M

R

ðb

5

þb

1

x

1

þb

2

x

2

þb

3

x

3

þb

4

x

4

Þ(10)

F

2

¼b

15

þb

1

x

1

þb

2

x

2

þb

3

x

3

þb

4

x

4

þb

5

x

1

x

2

þb

6

x

1

b

3

þb

7

x

1

x

4

þb

8

x

2

x

3

þb

9

x

2

b

4

þb

10

x

3

x

4

þb

11

x

2

1

þb

12

x

2

2

þb

13

x

2

3

þb

14

x

2

4

(11)

The LADES and RADES energy models with linear and quadratic

behaviors are used as objective functions in order to optimize the

coefﬁcients (decision variables) in Eqs. (12)e(15). LASSO as linear

and quadratic objective functions are used for the LADES energy

model, as is seen in Eqs. (12) and (13).

For a given value of

l

>0,

min

b

0

;b

1

;b

2

;b

3

;b

4

0

@

1

2NX

N

i¼1

ðY

i

ðF

1

ÞÞ

2

þlX

p

j¼1

b

j

1

A(12)

min

b

0

;b

1

;b

2

;b

3

;b

4

;…;b

15

0

@

1

2NX

N

i¼1

ðY

i

ðF

2

ÞÞ

2

þlX

p

j¼1

b

j

1

A(13)

As

l

increases, the number of nonzero components of

b

de-

creases [44].

Ridge regression as linear and quadratic objective functions is

used for the RADES energy model, as seen in Eqs. (14) and (15).

min

b

0

;b

1

;b

2

;b

3

;b

4

0

@

1

2NX

N

i¼1

ðY

i

ðF

1

ÞÞ

2

þlX

p

j¼1

b

j

2

1

A(14)

min

b

0

;b

1

;b

2

;b

3

;b

4

;…;b

15

0

@

1

2NX

N

i¼1

ðY

i

ðF

2

ÞÞ

2

þlX

p

j¼1

b

j

2

1

A(15)

2.3.4. Evaluation criteria of forecast performance

Measuring the accuracy of the method is achieved by ﬁnding the

difference between the actual value and the estimated value in

keeping with the rareness of error values. Mean absolute percent-

age error (MAPE) in Eq. (16) is a measure ofaccuracy for building up

ﬁtted time series values. It commonly asserts accuracy as a per-

centage. The results can be obtained more clearly with a

percentage.

MAPE ¼P

n

i¼1

Y

i

F

i

F

i

n100 (16)

RMSE (root mean square error) in Eq. (17) performs sample

standard deviation of differences between estimated (F) values and

actual values (Y). It is the square root of variance, which is called

standard deviation.

RMSE ¼ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

P

n

i¼1

ðY

i

F

i

Þ

2

n

s(17)

MSE (mean square error) in Eq. (18) is a variant of estimator. This

approach is used as objective function in the proposed models. We

evaluated MSE with LASSO and ridge regularization.

MSE ¼P

n

i¼1

ðY

i

F

i

Þ

2

n(18)

MAE (mean absolute error) in Eq. (19) is a batch that measures

how close estimations are to possible results.

Fig. 4. Coupling the ES and the SA to explain how to prevent getting stuck in a local optimum.

S. Tutun et al. / Energy 93 (2015) 2406e24222412

MAE ¼P

n

i¼1

Y

i

F

i

n(19)

SSE (sum square error) in Eq. (20) measures any contradiction

between estimated and actual values.

SSE ¼X

n

i¼1

ðY

i

F

i

Þ

2

(20)

The results can be compared to ﬁnd the best model structure by

using these performance indicators.

3. Forecasting of Turkey's net electricity consumption

Net electricity consumption in Turkey is forecasted by using pre-

processed data. The necessary data, including each variable and

covering a period of 35 years, are divided into two sets: 336 and 84

monthly observations data as training and testing, obtained from

the TEIAS (Turkish electricity transmission company). As inde-

pendent factors, the transmitted energy, gross generation, imports

and exports, which have high efﬁciency, are chosen according to

previous studies (e.g. Hamzaçebi [7], Toksarı[11],S

€

ozen [45] and

S€

ozen [46]) conducted on the NEC of Turkey. At the same time, our

analysis determined that the NEC is inﬂuenced by these indepen-

dent factors.

In order to make a better analysis of Turkey's situation, it is

necessary to review indicators such as imports, gross generation,

exports and transmitted energy. Imports and exports are ﬁnancial

transactions of international trade. For energy, exports mean

shipping goods and services for energy out of the port of a country;

imports mean receiving goods and services for energy from a

foreign country. The energy imports and exports of Turkey are

strong indicators of manufacturing activity. Electricity energy,

which can be easily transmitted to homes, is related to consump-

tion. Optimal transmitted energy improves living standards

because it can prevent electricity cuts and increase the delivery of

electricity for consumption. At the same time, gross generation is

important as it allows the country to provide electrical energy on

time. We tried to understand how the relationship between easy

energy and price affects net electricity consumption by using these

independent factors.

In this paper, the projections for independent factors are

determined by forecasted scenarios using the SARIMA and

NARANN methods. The data from January 1990 to December

2005 formed the training set, and those from January 2006 to

December 2010 formed the testing set of independent factors. At

the same time, forecasting errors are calculated from 2001 to

Fig. 5. Forecasted values of the NARANN of gross production for testing data. (Actual and estimated values are almost the same as is seen for R

2

value).

S. Tutun et al. / Energy 93 (2015) 2406e2422 2413

2010 one-by-one to show how the scenarios work better than

previous approaches. The best estimate value is reached by

calculating the MAPE, RMSE and R

2

values. The results are

compared by looking at performance indicators to achieve

optimal future planning. This approach is better than other ap-

proaches in the literature for preparing future independent fac-

tors and projections.

3.1. Forecasted scenarios

The constant growing values used in the literature for future

independent factors do not reﬂect actual future values of inde-

pendent factors because they always assume an augmentation of

estimated factors such as linear behavior. For this reason, forecast-

based scenarios are offered to forecast future independent factors.

The SARIMA and NARANN methods are used to forecast the value of

each future independent factor.

3.1.1. The results of nonlinear auto-regressive model based on

neural network scenario

The nonlinear approach (NARANN) in Figs. 5e8is used in

forecasting to decide the best scenario structure. This algorithm is

shown in Eqs. (21)e(24) with high Rvalues for the forecasted

scenario of independent factors. The method is constituted by

deciding the number of hidden neurons, the number of delays, the

percentage of training validation, and testing data as shown in

Table 3. The results are evaluated by MSE (mean squared error) and

R

2

.

OI ¼0:88target þ6:8 (21)

OE ¼0:78target þ11 (22)

OG ¼0:99target þ52 (23)

OT ¼0:98target þ110 (24)

In order to compare the results of the scenarios, as seen in

Figs. 5e8, the Rvalues are calculated for the testing data of inde-

pendent factors by using the NARANN method. After using Eqs.

(21)e(24), forecasting values for the independent factors are found

for the future years. Target is the lag value for the NARANN method.

When using past values as targets in equations, scenarios are

forecasted for independent factors. However, we realize that these

equations work well for the short term (e.g. two or threeyears). For

long-term forecasting, we need to improve on this approach. For

this reason, the SARIMA method is proposed to compare the results.

Fig. 6. Forecasted values of the NARANN of import for testing data. Note: actual and estimated values are in keeping with high R

2

value.

S. Tutun et al. / Energy 93 (2015) 2406e24222414

3.1.2. The results of an auto-regressive iterative moving average

scenario

Predictive models are found for independent factors by using

the SARIMA method in Fig. 9. The future values of independent

factors are forecasted by using these models. As seen in Table 2, the

best parameters are decided by using the SARIMA method for in-

dependent factors when comparing the testing data for the years

2006 through 2010. The future independent factors are then esti-

mated for forecasting with the proposed energy models.

Therefore, the best model in the SARIMA method can use these

forecasted values instead of growth rate because when looking at

Figs.11e12, we can see that the forecasted scenarios approach has a

low SSE for ten years. In order to show how forecasted scenarios

work, forecasted values are obtained by SARIMA as the best sce-

nario approach for the years 2006 through 2010, as seen in

Figs. 9e10. After showing the results for 2006 through 2010,

detailed results are demonstrated to prove scenarios will work for

the future years. Therefore, the best model found in the study is

used to forecast future net electricity consumption. The NEC of

Turkey from 2011 through 2020 is forecasted to constitute new

capacity plans, as seen in Fig. 16.

3.2. The results of the proposed energy models

In the proposed energy models, when increasing independent

factors, the decision variables are increased exponentially for the

quadratic model, and there are square and absolute values in

objective functions in Eqs. (12)e(15) of the proposed energy

models. This means that this is a non-polynomial hard problem in

which coefﬁcients must be optimized with meta-heuristic ap-

proaches. After using the proposed methods to optimize the co-

efﬁcients of the models in Eqs. (8)e(11), the models are found to

forecast future values in Eqs. (25)e(28).

The best structure for energy models is constituted through

training and testing sets for the proposed approach. As parameters

of the proposed algorithms for optimization, the Boltzmann con-

stant, initial temperature, number of movements, standard devia-

tion for random walk, and tuning parameter (

l

) are given

respectively in order to ﬁnd the best model structure for the LASSO

method.

The best parameters of the hybrid approach are deﬁned for the

LADES and RADES energy models in order to avoid over-training.

With an increased tuning parameter, the MAPE for training

increased while the MAPE for testing decreased. The best model

framework with the LASSO based formulation is decided for pa-

rameters as seen in Table 4. Because

l

is more than 150, the testing

error does not change sharply in Fig. 1.

Parameters in Table 5 are decided for the best model struc-

ture with ridge regression based formulation because as long as

l

is increased, the testing errors do not change sharply in Fig. 13.

This shows that overﬁtting is prevented for the best energy

model.

Fig. 7. Forecasted values of the NARANN of transmitted energy for testing data.

S. Tutun et al. / Energy 93 (2015) 2406e2422 2415

Fð1Þ

L

¼150:1763 þð0:5440Þx

1

þð0:0012Þx

2

þð0:2946Þx

3

þð0:0027Þx

4

þð0:1241Þð150:1763 þð0:5440Þx

1

þð0:0012Þx

2

þð0:2946Þx

3

þð0:0027Þx

4

Þ

(25)

Fð1Þ

R

¼150:119 þð0:4380Þx

1

þð0:0458Þx

2

þð0:4269Þx

3

þð0:1102Þx

4

þð0:0097Þð150:119 þð0:4380Þx

1

þð0:0458Þx

2

þð0:4269Þx

3

þð0:1102Þx

4

Þ

(26)

Fð2Þ

L

¼146:81 þð0:0756Þx

1

þð0:033Þx

2

þð0:0124Þx

3

þð0:1103Þx

4

þð0:0223Þx

1

x

2

þð0:0352Þx

1

x

3

þð0:0671Þx

1

x

4

þð0:0037Þx

2

x

3

þð0:0185Þx

2

x

4

þð0:0328Þx

3

x

4

þð0:0319Þx

2

1

þð0:024Þx

2

2

þð0:0236Þx

2

3

þð0:1272Þx

2

4

(27)

Fð2Þ

R

¼146:83 þð0:0962Þx

1

þð0:0682Þx

2

þð0:0050Þx

3

þð0:106Þx

4

þð0:0245Þx

1

x

2

þð0:0508Þx

1

w

3

þð0:1151Þx

1

x

4

þð0:01842Þx

2

x

3

þð0:0246Þx

2

w

4

þð0:0461Þx

3

x

4

þð0:0324Þx

2

1

þð0:04240Þx

2

2

þð0:0566Þx

2

3

þð0:1288Þx

2

4

(28)

Scenarios from the SARIMA method are used for future values of

independent factors from 2010 through 2020 to show accuracy of

the proposed framework. Forecasting, which is found according to

the best model, is done for future months and years by using the

estimated values of independent factors. Hence, future demand is

predicted monthly and annually by using these approaches.

The main aim of a modeling study is to produce a model which

can present the nature of the problem. Almost all relationships in

the real world are nonlinear, and the nature of the model should

capture non-linearity. We have added penetration, which is the

mean value of errors for past years, to the proposed models. This

penetration allows the linear models to catch nonlinear behavior

for the future. At the same time, a quadratic model is used to

capture the behavior of the net electricity consumption. For

Fig. 8. Forecasted values of the NARANN of export for testing data.

S. Tutun et al. / Energy 93 (2015) 2406e24222416

penetration, we calculated the mean value of difference, which is

the difference between the actual and the forecasted values for

each year. Thereafter, we calculatedthe percentage of difference for

the models. Finally, we added this percentage according to the

models for years 2011 through 2020.

As a result, better forecasting is possible for future years when

compared with the literature because in the new framework

monthly data are used to train the best model, and forecasted

scenarios are used to predict future independent factors instead of

the constant mean growth rate [11]. After ﬁnding the values of the

future independent factors, the proposed energy models are

constituted as mentioned in the methodology. Using the new en-

ergy models with scenarios, the projection is presented for future

planning, as seen in Fig. 16. By using the new models in Eqs.

(25)e(28), as seen in Figs. 14e15, the results show that the models

work well to forecast the net electricity consumption. The LADES

energy model (the best model) can be used in planning energy

needs for both the medium term and the long term.

3.3. Sensitivity analysis

The model in this study more accurately forecasts energy con-

sumption than do the models in other studies conducted to

determine the NEC. Better results are obtained than in the studies

carried out by Hamzaçebi et al. [25], MENR [6] and Erdo

gdu [12] for

estimated electricity consumption. When the conducted studies are

analyzed in Table 6, more realistic values are obtained for the years

2008e2009. A very small error value occurred between the

Table 2

Comparison of testing data for independent factors with the SARIMA with (p,d,q)(P,D,Q).

Imports Exports

Years (301) (101) Actual values Mape errors (101) (101) Actual values Mape errors

2006 805.89 573.20 0.29 1722.89 2235.70 0.23

2007 925.96 864.33 0.07 2312.32 2422.22 0.05

2008 998.05 789.40 0.21 1546.99 1122.20 0.38

2009 923.02 811.95 0.12 1376.76 1545.85 0.11

2010 1031.93 1143.83 0.11 1966.41 1917.59 0.03

Transmitted energy Gross generation

Years (101) (332) Actual values Mape errors (211) (131) Actual values Mape errors

2006 139242.90 143015.90 0.03 171777.90 176299.80 0.03

2007 2312.32 2422.22 0.05 194634.70 191558.10 0.02

2008 178289.30 172635.20 0.03 205248.50 198417.90 0.03

2009 177545.90 172187.70 0.03 188294.90 194812.90 0.03

2010 188852.70 184334.90 0.02 211304.50 211207.80 0.0005

Table 3

Parameters of NARANN models for independent factors. (Note: Dataset are divided into training, validation and testing subsets).

Parameters Gross production (x

1

) Imports (x

2

) Transmitted energy (x

3

) Export (x

4

)

Hidden Layers 10 5 10 10

Lags 7 3 4 4

Data-sets 75-15-15 75-15-15 75-15-15 75-15-15

Fig. 9. Forecasted values obtained by SARIMA for ﬁve years.

S. Tutun et al. / Energy 93 (2015) 2406e2422 2417

Fig. 10. MAPE errors between actual and forecasted values for ﬁve testing years.

Fig. 11. Forecasted values obtained by net electricity consumption for 10 years using the best model with SARIMA.

Fig. 12. The MAPE errors of net electricity consumption for 10 years.

Table 4

The best model structure for the LADES.

Training level Testing level LADES parameters

SSE 19,006 SSE 4,106,300 Sigma 0.95

MSE 56.57 MSE 48,885 Number of movements 1500

RMSE 0.41 MRSE 24.12 Initial Temperature 120

MAE 6.21 MAE 189.53 Random Walk 0.01

MAPE 0.18 MAPE 1.60 Lambda 150

Table 5

The best model structure for the RADES.

Training level Testing level RADES parameters

SSE 434,080 SSE 6,926,200 Sigma 0.95

MSE 1291.9 MSE 82,455 Number of movements 150

RMSE 1.96 MRSE 31.33 Initial Temperature 100

MAE 30.89 MAE 244.49 Random Walk 0.01

MAPE 1.03 MAPE 1.96 Lambda 1100

Fig. 13. Determine the best model regarding with ridge regression. Deﬁnes the best model regarding the ridge. Notes: Combinations are made with parameters such as sigma,

number of movements, initial temperature, random walk, and lambda, respectively.

Fig. 14. Scattering and distribution graphics of training level and testing level for the best LADES energy model.

S. Tutun et al. / Energy 93 (2015) 2406e2422 2419

estimated values and actual values because while the actual values

are 161.95 and 156.89 TWh for 2008e2009 in the data, the model

has predicted values of 159.5958 and 157.3347 TWh. Percentage

errors are estimated at 1.475% and 0.2826% MAPE error ratio, which

is lower than in previous studies, as shown in Table 6.

In order to demonstrate how the framework functions in energy

planning, we can check our forecasted results with actual values.

We know monthly data for independent and dependent variables

until December 2010. We also know annual values of net electricity

consumption for 2011 and 2012. The scenarios are forecasted by

Fig. 15. Scattering and distribution graphics of training and testing level, respectively, for the best RADES energy model.

Fig. 16. Monthly forecasting of the NEC with two scenarios between 2011 and 2020.

Table 6

Comparison with MAPE errors in the literature for forecasting of net electricity consumption. Note: the bold values show that NEC is forecasted better in the literature.

Years Actual value Forecasted values for the LADES (TWh) with mean absolute percent error (MAPE)

(TWh) This study MAPE MENR MAPE Hamzacebi MAPE Erdogdu MAPE Kavaklioglu MAPE

2008 161.95 159.643574 (1.475) 168.60 (4.1) 173.59 (7.2) 146.37 (9.6) 165.94 2.46

2009 156.89 157.168505 (0.283) 184.40 (13.86) 189.47 (16.99) 145.14 (10.4) 175.04 11.57

S. Tutun et al. / Energy 93 (2015) 2406e24222420

using the SARIMA based approach (the best scenario approach) for

these years. At the same time, the proposed models as LADES and

RADES are used to ﬁnd future values. As seen in Table 7, actual net

electricity consumption is 186.100 TWh for 2011. When using sce-

narios and proposed methods, forecasted net electricity con-

sumption is found as 186.323 TWh in 2011. The NEC in 2011 and

2012 is forecasted with 0.96% and 0.09%, respectively, which is less

than one percent MAPE error, by using the LADES model. The

RADES model also forecasted future NEC with 0.62% and 5.46%

MAPE errors, respectively. This proves that our framework can

forecast the future net electricity consumption efﬁciently, as seen in

Fig. 16.

4. Conclusion

In modern life, forecasting is extremely important in the effec-

tive application of energy policies. Governments need to know how

much electricity must be generated to meet the energy demand

and consumption. In Turkey, the NEC (net electricity consumption)

for projections is ofﬁcially obtained from the MAED simulation

technique in MENR with high forecasting errors. Forecasts need to

guide the MENR in developing the best energy policy.

The primary conclusion of this paper is that electricity con-

sumption of Turkey is modeled as the new LADES and RADES en-

ergy models with linear and quadratic behavior. New energy

models are used in such forms that future forecasting is possible.

We also present the signiﬁcance of alternative forecasting methods.

Scenarios in the literature, which assume that independent factors

increase at a constant growth rate over time, are improved so as to

forecast the future values of independent factors by using the

SARIMA method and the NARANN method in the forecasted sce-

nario approach.

In the light of the results and discussion presented so far in this

study, the NEC is estimated to show how the framework works for

the future by using proposed scenarios and the best energy model.

The proposed best model forecasts Turkeys electricity consumption

with 1.59% MAPE error ratio on average for 34 years, while the

MENR forecasts more than 10% error ratio for some years. This

means that this framework can be used by the Turkish government

and related organizations to forecast future values in order to

ensure good future planning. These models can be used in different

countries as well. A new planning strategy can be developed with

this study by looking at the future values. Policymakers can use this

framework both to plan new investments and to determine

appropriate export and import amounts. Moreover, the new energy

models can be deﬁned by using different evaluation criteria of er-

rors (e.g. SSE, MAE, MAPE and so on.) as objective function to

improve models. New energy models with hybrid techniques can

be developed to conduct better studies.

To conclude, in Turkey and other nations, inadequate forecasting

of energy demand has often led to power shortages and outages.

This hinders the development of the economy and leads to irrita-

tion and inconvenience for the average citizen. By forecasting

actual energy demand, the model proposed in this study would

help avoid these power outages, thus allowing Turkey to develop

more rapidly and to improves the quality of life for its citizen using

electrical power.

Acknowledgments

The authors wish to thank the Turkish Electricity Transmission

Company, and the Turkish Minister of Energy and Natural Re-

sources for their help in providing data.

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