Energy 93 (2015) 2406e2422
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Energy journal homepage: www.elsevier.com/locate/energy
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 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 b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 April 2015 Received in revised form 10 August 2015 Accepted 17 October 2015 Available online xxx
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 previous 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.
Keywords: Forecasting Energy management Regularization Adaptive optimization Time series analysis
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 demand planning is a vital part of energy policies in developed and developing countries, allowing them to make cost efficient investments 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 conditions [3,4]. Due to limited primary energy sources, energy policies in many countries depend on foreign countries to supply energy. With
*
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:
[email protected] (S. Tutun),
[email protected] (C.-A. Chou),
[email protected] (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. http://dx.doi.org/10.1016/j.energy.2015.10.064 0360-5442/© 2015 Elsevier Ltd. All rights reserved.
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 government needs a model that forecasts electricity demand for unstable situations [5]. Due to the fact that electricity cannot be stored, and its production is costly, the net consumption of electricity 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 energy planning. 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 Organization) 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
S. Tutun et al. / Energy 93 (2015) 2406e2422
Nomenclature w(k,i) weight between k and i nodes Y1(k) ¼ a1(k) output of cell K ε error for cell j C(j,i) cost for weights r learning factor New w1(j,i) new weight between j and i Y(t) predicted output at time t d number of delays f unknown smooth function fi ε ði ¼ 1; 2; 3; …pÞ set of weight parameters for lags qj ε ðj ¼ 1; 2; …qÞ set of weight parameters for random errors et random error at time t x independent variable ML penetration parameter for the LADES model MR penetration parameter for the RADES model net(Si(k) net input value
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 techniques could be used instead of the MAED model. du [12] and Ünler Many studies such as Toksarı [10,11], Erdog [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 considered 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 metaheuristic 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 regularization. ES (evolutionary strategy) and SA (simulated annealing) 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 3 describes in detail how the proposed methodology is used to forecast the NEC. The net electricity consumption is estimated monthly and annually for the years 2010e2020. The proposed
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final result for the RADES model final result for the LADES model b0 and bi scalar and P-vector respectively, namely coefficients of models. l non-negative regularization parameter N the number of observations t1 trend of gross production t2 trend of electricity energy imports t3 trend of transmitted electricity energy t4 trend of electricity energy exports x1 value of gross production x2 value of electricity energy imports x3 value of transmitted energy x4 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
FR FL
framework is discussed for the forecasting of the NEC based on new scenario approaches with sensitivity analysis. Finally, Section 4 shows 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 demand (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 avarage), cyclic patterns and grey theory have been presented as the econometric approaches. For example, Ediger and Tatlıdil [9] proposed 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. lu [17] combined multivariate regression with SVD (sinKavaklıog gular value decomposition) so as to downsize the problem to estimate 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 prediction 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 presented to propose some models capturing nonlinear characteristics for modeling of energy demand and consumption. An ANN
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Table 1 Summary of energy modeling and/or forecasting studies. Method used
Type of method
Author(s)
Forecasted variable
Econometric approach
RA ARIMA and SARIMA ARIMA Cyclic patterns RA and SVD Grey theory GPRM Optimized Grey model Grey Theory, Markov approach ANN ANN GA, ANN and Fuzzy ANFIS, GA and ANN AIS, GA and PSO ANN and SVM SVR ANN and RA ANN
Tunç et al. [16] Ediger and Akar [18] Chujai et al. [4] Ediger and Tatlıdil [9] lu [17] Kavaklıog Lee and Tong [2] Akay and Atak [19] Hamzaçebi and Es [20] Nai-ming et al. [5] Kermanshahi and Iwamiya [21] lu [23] Kavaklıog Azadeh et al. [28] Azadeh et al. [28] Azadeh et al. [30] cu et al. [26] Og lu [3] Kavaklıog Pao [24] € zen et al. [22] So
GA ACO PSO ACO ANN, PCA and DEA ANN and ARIMA ANN and PSO RA, ANN and LSSVM RA and ANN ABC GA, PSO
€ Oztürk et al. [14] Toksarı [10] Ünler [13] Toksarı [11] Kheirkhah et al. [31] Hamzaçebi and Kutay [25] Jiang et al. [33] Kaytez et al. [27] Ardakani and Ardehali [1] Gürbüz et al. [32] Shi-wei and Ke-jun [34]
Electricity consumption Electricity demand Electricity consumption Energy consumption Electricity consumption Electricity consumption Electricity demand Energy demand Energy demand Electricity demand Electricity consumption Electricity demand Electricity consumption Electricity consumption Electricity consumption Electricity consumption Electricity consumption Energy consumption with economic indicators Energy demand Energy demand Electricity demand Electricity demand Electricity consumption Electricity consumption Electricity consumption Electricity consumption Electricity consumption Energy consumption Energy consumption
Grey theory approach
Artificial inteligence approach
Hybrid approach
(artificial neural network) algorithm was used to estimate electricity demand and consumption by Kermanshahi and Iwamiya €zen et al. [22] and Kavaklıog lu et al. [23]. In the meantime, [21], So 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 regreslu [3] to make an NEC estimate, sion) method was used by Kavaklıog cu et al. [26] compared the ANN with SVM methods in order to Og 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 researchers 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, metaheuristic 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 estimate 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. Consequently 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 forecasting of electricity consumption. At the sametime, some researchers 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 metaheuristic approaches, over-training needs to be prevented in energy 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
S. Tutun et al. / Energy 93 (2015) 2406e2422
coefficients. Over-training is prevented by using the LASSO and ridge regression methods in the models. In addition, we proposed new approaches, namely forecasted scenarios, for forecasting the future values of independent factors such as imports, exports, gross generation and transmitted energy. In the forecasted scenarios, the SARIMA and NARANN methods are implemented 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 information and give results even if there is incomplete information on recently obtained examples. The information distributed on the network has a distributed memory as numeric information [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 ¼ S1 ðkÞ ¼
X
ðw1 ðk; iÞ a0 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.
Y1 ðkÞ ¼ a1 ðkÞ ¼
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1 1 þ eð1 s1 ðkÞÞ
(2)
Therefore, the output of the node in Eq. (2) is the value that is determined by the activation function.
εj ¼ a1 ðjÞ yr 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].
C1 ðj; iÞ ¼
p X
εðjÞ a1 ðjÞð1 a1 ðjÞÞ a0 ðjÞ
(4)
r¼1
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).
w01 ðj; iÞ ¼ w1 ðj; iÞ rC1 ðj; iÞ for j ¼ 1; …; n i ¼ 1; …; 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.
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Fig. 2. The flow chart of the new framework for forecasting net electricity consumption.
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].
YðtÞ ¼ f ðyðt 1Þ; yðt 2Þ; …; yðt dÞÞÞ þ εðtÞ
(6)
The model assumes that error is IID (independent and identically 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.
YðtÞ ¼ EðyðtÞjyðt 1Þ; yðt 2Þ; …; yðt dÞÞÞ ¼ f ðyðt 1Þ; yðt 2Þ; …; yðt dÞÞÞ As t d þ 1
(7)
In our model, there are hidden layers with neurons, weights and bias which are calculated using training algorithms such as LevenbergeMarquardt, 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 p is the auto-
regressive order, q is the moving average order, d is the number of differing operations, and P,D, and Q are seasonal orders of p,d and q [39]. In this paper, the model xt ¼ fat1 þ fat1 þ … þ fatp þ et þ qet1 qet2 … qetq for scenarios is constituted using the SARIMA method with seasonality [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 significance. 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 optimization. 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
S. Tutun et al. / Energy 93 (2015) 2406e2422
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Fig. 3. Flow chart of the SARIMA model.
algorithm mimics the annealing process in materials physics as metals freeze and cool into a crystalline state with minimum energy 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 describes 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 temperature is reheated when the new solution is not suitable for movement, and the method is made adaptive to prevent premature 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 metaheuristic 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 parents, 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 equations 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, 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 factors 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 (coefficient 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 variables by using a normal random number. This means that the algorithm can get stuck unless it has a good initial solution. For instance, as is seen in Fig. 4, it begins to find solutions from S0 to S3.
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Fig. 4. Coupling the ES and the SA to explain how to prevent getting stuck in a local optimum.
After arriving at S3, 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 optimum solution. Thus the ES algorithm can find good (close to the optimal solution) initial solutions that can be used in the SA algorithm. When started with these solutions, the SA algorithm can find the optimal solution by looking in the neighborhood of initial solutions.
0 1 minb0 ;b1 ;b2 ;b3 ;b4 ;…;b15 @ 2N
N X
1 p X bj A ðYi ðF2 ÞÞ þ l 2
i¼1
(13)
j¼1
As l increases, the number of nonzero components of b decreases [44]. Ridge regression as linear and quadratic objective functions is used for the RADES energy model, as seen in Eqs. (14) and (15).
0
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 regression 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 regression are used in order to prevent over-training. They are regression methods that involve penalizing the absolute and square size 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.
F1 ¼ b5 þ b1 x1 þ b2 x2 þ b3 x3 þ b4 x4
(8)
FpL ¼ ML ðb5 þ b1 x1 þ b2 x2 þ b3 x3 þ b4 x4 Þ
(9)
FpR ¼ MR ðb5 þ b1 x1 þ b2 x2 þ b3 x3 þ b4 x4 Þ
(10)
0 1 minb0 ;b1 ;b2 ;b3 ;b4 ;…;b15 @ 2N
þ b7 x1 x4 þ b8 x2 x3 þ b9 x2 b4 þ b10 x3 x4 þ b11 x21 þ b12 x22 þ b13 x23 þ b14 x24 (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, p N X 1 X bj A minb0 ;b1 ;b2 ;b3 ;b4 @ ðYi ðF1 ÞÞ2 þ l 2N i¼1 j¼1
MAPE ¼
(12)
i¼1
1 p X 2 ðYi ðF2 ÞÞ þ l bj A 2
(15)
j¼1
Pn Yi Fi i¼1 Fi n
100
(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.
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 i¼1 ðYi Fi Þ RMSE ¼ n
(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.
Pn MSE ¼
1
N X
(14)
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 percentage error (MAPE) in Eq. (16) is a measure of accuracy for building up fitted time series values. It commonly asserts accuracy as a percentage. The results can be obtained more clearly with a percentage.
F2 ¼ b15 þ b1 x1 þ b2 x2 þ b3 x3 þ b4 x4 þ b5 x1 x2 þ b6 x1 b3
0
1 p N X 2 1 X 2 @ minb0 ;b1 ;b2 ;b3 ;b4 ðY ðF1 ÞÞ þ l bj A 2N i¼1 i j¼1
i¼1 ðYi
n
Fi Þ2
(18)
MAE (mean absolute error) in Eq. (19) is a batch that measures how close estimations are to possible results.
S. Tutun et al. / Energy 93 (2015) 2406e2422
MAE ¼
Pn Yi Fi i¼1
n
(19)
SSE (sum square error) in Eq. (20) measures any contradiction between estimated and actual values.
SSE ¼
n X
ðYi Fi Þ2
(20)
i¼1
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 preprocessed 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 independent factors, the transmitted energy, gross generation, imports and exports, which have high efficiency, are chosen according to €zen [45] and previous studies (e.g. Hamzaçebi [7], Toksarı [11], So €zen [46]) conducted on the NEC of Turkey. At the same time, our So
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analysis determined that the NEC is influenced by these independent 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 consumption. 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 R2 value).
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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 R2 values. The results are compared by looking at performance indicators to achieve optimal future planning. This approach is better than other approaches in the literature for preparing future independent factors 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 independent factors because they always assume an augmentation of estimated factors such as linear behavior. For this reason, forecastbased 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. 5e8 is used in forecasting to decide the best scenario structure. This algorithm is shown in Eqs. (21)e(24) with high R values 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 R2.
OI ¼ 0:88target þ 6:8
(21)
OE ¼ 0:78target þ 11
(22)
OG ¼ 0:99target þ 52
(23)
OT ¼ 0:98target þ 110
(24)
In order to compare the results of the scenarios, as seen in Figs. 5e8, the R values are calculated for the testing data of independent 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 three years). 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 R2 value.
S. Tutun et al. / Energy 93 (2015) 2406e2422
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Fig. 7. Forecasted values of the NARANN of transmitted energy for testing data.
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 independent factors when comparing the testing data for the years 2006 through 2010. The future independent factors are then estimated 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 scenario 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 approaches. After using the proposed methods to optimize the coefficients 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 constant, initial temperature, number of movements, standard deviation 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 parameters 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 structure 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.
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Fig. 8. Forecasted values of the NARANN of export for testing data.
Fð1ÞL ¼ 150:1763 þ ð0:5440Þx1 þ ð0:0012Þx2 þ ð0:2946Þx3 þ ð0:0027Þx4 þ ð0:1241Þð150:1763 þ ð0:5440Þx1 þ ð0:0012Þx2 þ ð0:2946Þx3 þ ð0:0027Þx4 Þ (25)
Fð2ÞR ¼ 146:83 þ ð0:0962Þx1 þ ð0:0682Þx2 þ ð0:0050Þx3 þ ð0:106Þx4 þ ð0:0245Þx1 x2 þ ð0:0508Þx1 w3 þ ð0:1151Þx1 x4 þ ð0:01842Þx2 x3 þ ð0:0246Þx2 w4 þ ð0:0461Þx3 x4 þ ð0:0324Þx21 þ ð0:04240Þx22 þ ð0:0566Þx23 þ ð0:1288Þx24 (28)
Fð1ÞR ¼ 150:119 þ ð0:4380Þx1 þ ð0:0458Þx2 þ ð0:4269Þx3 þ ð0:1102Þx4 þ ð0:0097Þð150:119 þ ð0:4380Þx1 þ ð0:0458Þx2 þ ð0:4269Þx3 þ ð0:1102Þx4 Þ (26)
Fð2ÞL ¼ 146:81 þ ð0:0756Þx1 þ ð0:033Þx2 þ ð0:0124Þx3 þ ð0:1103Þx4 þ ð0:0223Þx1 x2 þ ð0:0352Þx1 x3 þ ð0:0671Þx1 x4 þ ð0:0037Þx2 x3 þ ð0:0185Þx2 x4 þ ð0:0328Þx3 x4 þ ð0:0319Þx21 þ ð0:024Þx22 þ ð0:0236Þx23 þ ð0:1272Þx24 (27)
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
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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 2007 2008 2009 2010
805.89 925.96 998.05 923.02 1031.93
573.20 864.33 789.40 811.95 1143.83
0.29 0.07 0.21 0.12 0.11
1722.89 2312.32 1546.99 1376.76 1966.41
2235.70 2422.22 1122.20 1545.85 1917.59
0.23 0.05 0.38 0.11 0.03
Transmitted energy
Gross generation
Years
(101) (332)
Actual values
Mape errors
(211) (131)
Actual values
Mape errors
2006 2007 2008 2009 2010
139242.90 2312.32 178289.30 177545.90 188852.70
143015.90 2422.22 172635.20 172187.70 184334.90
0.03 0.05 0.03 0.03 0.02
171777.90 194634.70 205248.50 188294.90 211304.50
176299.80 191558.10 198417.90 194812.90 211207.80
0.03 0.02 0.03 0.03 0.0005
Table 3 Parameters of NARANN models for independent factors. (Note: Dataset are divided into training, validation and testing subsets). Parameters
Gross production (x1)
Imports (x2)
Transmitted energy (x3)
Export (x4)
Hidden Layers Lags Data-sets
10 7 75-15-15
5 3 75-15-15
10 4 75-15-15
10 4 75-15-15
penetration, we calculated the mean value of difference, which is the difference between the actual and the forecasted values for each year. Thereafter, we calculated the 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 energy 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 consumption than do the models in other studies conducted to determine the NEC. Better results are obtained than in the studies du [12] for carried out by Hamzaçebi et al. [25], MENR [6] and Erdog 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
Fig. 9. Forecasted values obtained by SARIMA for five years.
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.
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Table 4 The best model structure for the LADES. Training level SSE MSE RMSE MAE MAPE
Testing level 19,006 56.57 0.41 6.21 0.18
SSE MSE MRSE MAE MAPE
LADES parameters 4,106,300 48,885 24.12 189.53 1.60
Sigma Number of movements Initial Temperature Random Walk Lambda
6,926,200 82,455 31.33 244.49 1.96
Sigma Number of movements Initial Temperature Random Walk Lambda
0.95 1500 120 0.01 150
Table 5 The best model structure for the RADES. Training level SSE MSE RMSE MAE MAPE
Testing level 434,080 1291.9 1.96 30.89 1.03
SSE MSE MRSE MAE MAPE
RADES parameters 0.95 150 100 0.01 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.
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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.
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
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
2008 2009
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
161.95 156.89
159.643574 157.168505
(1.475) (0.283)
168.60 184.40
(4.1) (13.86)
173.59 189.47
(7.2) (16.99)
146.37 145.14
(9.6) (10.4)
165.94 175.04
2.46 11.57
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Table 7 Sensitive analysis for two models (the LADES and RADES results). Years
Actual values for the NEC
The LADES model for NEC
The RADES model for the NEC
MAPE for the LADES model
MAPE for the RADES model
2011 2012
186099.55 194923.35
184323.47 195094.78
184951.72 206180.79
0.96 0.09
0.62 5.46
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 scenarios and proposed methods, forecasted net electricity consumption 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 effective 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 consumption of Turkey is modeled as the new LADES and RADES energy 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 scenario 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 errors (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 irritation 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 Resources for their help in providing data.
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