Energy Demand Forecast of Residential and Commercial Sectors: Iran Case Study. Hamed. Shakouri.G 1, Aliyeh. Kazemi 2.

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1 Energy Demand Forecast of Residential and Commercial Sectors: Iran Case Study Hamed. Shakouri.G 1, Aliyeh. Kazemi 2 1 Department of Industrial Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran, hshakouri@ut.ac.ir 2 Department of Industrial Management, Faculty of Management, University of Tehran, Tehran, Iran, aliyehkazemi@ut.ac.ir Abstract: The main purpose of the present study is to provide a proper model for forecasting residential as well as commercial sectors in Iran that can be used as a tool of scenario analysis to predict the emerging energy demand in future. In this way, this paper proposes a systematically developed model based on a previously performed exogeneity investigation of various quantified variables. A certain model among a collection of models with different inputs is chosen as the most appropriate model. Structure of all competing models is established according to logical conjunctive and disjunctive relationships between variables. Different combinations of the exogenous variables generate these models. An automated fuzzy decision-making (FDM) process determines the winner model, which is a log-linear model, among the other remaining models. Furthermore, the energy demand of residential and commercial sector in Iran for the period of 2011 to 2020 is estimated. Keywords: Dynamics, Residential and commercial sectors, Energy demand forecasting, Fuzzy systems 1. Introduction There is no doubt how important energy is in lives of people today and how significant a role it has even in the international level relations among nations. The industrial revolution and much of its fast growth, the development of technologies and the ever increasing facilities which provide welfare for residents are all in some way dependent on energy. The importance of energy has been more touched especially after the energy crisis, and consequently its impact on the world economy was investigated by many researchers. Residential and commercial sectors takes the biggest shares in energy consumption in Iran; achieving to about 37% of the total energy consumption in Thus, residential and commercial demand forecasting becomes an essential function in planning for the future to design more efficient systems and control the demand by a proper price mechanism as well. During the past decades, a variety of residential and commercial energy forecasting methods have been developed. Some of these methods are genetic algorithms, autoregressive models, regression models, time series analysis, panel cointegration and neural networks. In this paper residential and commercial energy demand is forecasted using a system approach, by which all effective causes are included in a logically designed log-linear model. The special top-down method that the paper follows can be considered as a new approach in exogeneity investigations based on the possibility theory. An intelligent process will be followed to select the best model [1,2]. The remaining parts of the paper are organized as follows: In section 2, the model selection approach is introduced. Details of the proposed forecast strategy and numerical results are described in section 3. A brief review of the paper is given in section Model selection approach In general, the process of model selection may be schematically represented in Figure 1. According to this figure, several models, known as parallel models, may describe a common phenomenon. We should note that one criterion is properly determined in advance as a basis to select the best model called the winner. Corresponding author 337

2 Observations, experiments, descriptions & theories about the phenomenon Model no. 1 Model no Model no. N m A criterion to select the best model Selected model Figure 1. Evaluation process to select the best model among N m parallel models Integrating a set of different criteria simultaneously in order to determine the best model, the following question arises: Does a unified method that includes all required characteristics exist? To explain this, 2 suppose that several models are suggested for a given system and R, the covariance matrix, P, t- statistics, etc., are calculated. Now, it is requested to attain the best model. It means that the selected model is supposed to be the most suitable model that mimics the real phenomenon. For example, one model may be a good candidate based on residual characteristics but possesses weak properties as far as the parameters validity is concerned. On the contrary, another one may show the opposite. How can we choose one of them as a fair, acceptable, or good model, and what is the proper measure to clarify this concept? This paper discusses an alternative process to replace the selection stage in Fig. 1, which is represented by the FDM block shown in Figure 2. At this point, a systematically designed procedure is introduced to establish the aforementioned decision-making problem. The procedure is explained within four steps: Step 1: Collection and Classification of Criteria: First, a collection of criteria, which is important from the certain viewpoint of the model designer, should be specified. If the model is concerned with a physical phenomenon, there may be some particular criteria of interest, whereas for a humanistic problem, some other important criteria are collected. Moreover, the set of criteria should be organized according to the different classes that they belong. For example, all criteria may be classified into four classes due to the following: 1) Size of an error term, like the error in the objective function of parameter estimation, related to the of the model to explain historical experiments via pure simulation or full information prediction; 2) Time domain and/or frequency domain characteristics of the residuals based on presumptions that are vital for the solution of the parameter estimation problem; 3) Properties of the parameters satisfying logical relations and mathematical significance criteria; 4) Ability of the model to forecast, predict, and/or simulate the future truly. Figure 3 shows such a classification of desired criteria to enable logical construction of the rule base needed at this step, where a properly designed combination of AND/OR relations between the rules would build up the rule base. Set of criteria Utility function Model no. 1 Model no Model no. N m Restriction Fuzzy decisionmaking process Winner model Figure 2. FDM scheme to the model selection problem Model Prediction Simulation Time domain Frequency domain Logical Mathematical Prediction Simulation AND /OR Figure 3. Classification of criteria to construct a rule base for the model selection procedure. Step 2: Designing a Rule Base: In this step, a proper combination of the criteria should be designed. Logical relations, conjunctions, and disjunctions (AND/OR) will be used to combine the chosen and 338

3 categorized criteria within a rule base. Note that we, as the system designers, have of course a limited set of desired properties in our minds, and clearly, we will face difficulty to combine criteria for deciding on the best model; however, the proposed FDM allows consideration of any possible set of rules. For example, the most acceptable decisions to select the best model may employ the following rule base that is mainly based on the linguistic variables (LVs) highlighted hereafter. A given model is the best if it has the following: 1) Small error or high explanatory criterion; 2) Good characteristics for the residuals to admit presumptions of the model, e.g., acceptable normality or high independence; 3) Significant parameters by means of their sign or small variance of parameters; 4) High to forecast the future. Step 3: Possibility Measures: According to the proposed method, the utility function U(x) is a possibility measure, and therefore, it is formed by PDFs associated with each criterion, and g(x) contains restrictions on those PDFs. Thus, in the second step, these PDFs have to be defined properly [1]. Step 4: Construction of the Utility Function: A user-defined utility function should be formulated at this step. Usually, it is composed of conjunctions and disjunction between the PDFs. The more spacious is the rule base, the more accurate the model selection will be. In addition, there may be desired limitations on the minimum of the PDFs for the selected model [1]. 3. Application of the model to residential and commercial energy demand of Iran Data gathered which are supposed to be useful for estimation of the model are listed in this section. Data are taken from statistics given in annual reports of the Ministry of Energy, Petroleum Ministry and Central Bank of Iran (CBI). These signals are categorized in two sets (input and output), described below. Each data set (time series) is named by an abbreviation shown in front of each definition, and the corresponding units are read in brackets. The numbers in the parentheses indicate the years for which data was available (is probably useful for estimation of the model) Model output Energy consumed by the residential and commercial sectors: ER [10 MBOE] ( ) This is expected to stand on the left side of the model as a dependent variable. Figure 4 shows residential and commercial energy consumption of Iran from 1967 to Figure 4. Residential and commercial energy consumption of Iran from 1967 to Exogenous variables and input data As mentioned before, our approach is to test different combinations of various data sets, all considered as possibly explanatory variables, to find the best composition. All values given for the economic variables are normalized based on the fixed prices of 1997 (1997=100) Value added The whole value added of the four economic sectors, i.e. oil, industry + mining, commercial and agriculture, can be considered as a proper index for the income gained by the individuals/households to 339

4 expend for their energy needs and comfort. Moreover, it is shown by previous studies that the oil sector income has not direct effect on the consumption of the households. Therefore, the total sum of the value added can be divided to Oil and Non-Oil sectors. Finally the National Income given by the Central Bank of Iran can be another index. Thus, the following variables are considered as possibly effective signals: Value added of all economic sectors (total value added): VAT [10 3 BIRR] ( ) The total value Added minus that of the oil sector: VAN [10 3 BIRR] ( ) National Income: YNI [BIRR] ( ) Figure 5 shows Income indexes from 1967 to Buildings The investment for construction or the value of made constructions shows how much buildings are added annually which is a sign to measure how much energy is needed for heating, ventilation, and air conditioning (HVAC) systems. Always, new investments, compared to the old capita in use, have more impact on the activity level of a business. For the lack of data needed to measure the entire living space of households (plus the working space of the commercial sector), we have checked the investment for the buildings to find its role in energy consumption of the sector. These two categories are listed below: Gross fixed capital formation for the constructions: INVC [104 BIRR] ( ) Investment for the value of made constructions: BLD [104 BIRR] ( ) Figure 6 shows indexes for living/working from 1967 to It is seen that data for these two variables are very close to each other and the small difference is due to some costs not considered in evaluation of how much the buildings worth. Clearly, the integration of these values are more likely to determine the energy needed for heating/cooling the active space in houses, trade buildings, etc. Figure 5. Income indexes from 1967 to 2008 Figure 6. indexes for living/working from 1967 to 2008 Total capital invested for buildings (construction): KCT [BIRR] ( ) Cumulative sum of BLD: KBLD [BIRR] ( ) The same variable calculated considering a 5% annual depreciation rate: KBD It should be mentioned that old buildings, for their lack of good isolating mechanism, usually consume more energy. Therefore, although a building may last more than 20 years, it seems that the depreciation percentage should not set less than 1/ Population and labor Besides the population that obviously may have a certain impact on the energy consumption, labor is indeed that part of the people who leave the house for work during the day. This can decrease the energy consumption of the households. On the other side, dimension of each household affects their need to energy. Therefore the following variables can also be considered as explanatory variables: Population: PO [Million] Total Number of Households: HNT [Million] Total Labor: LT [Million] Population minus the Labor: PNL [Million] Figure 7 on the next page shows households and labor from 1967 to

5 Prices The Consumer Price Index has about 10 components among which the index introduced by the CBI for the fuel and power is used to measure energy price index, named Consumer Energy (Fuel) Price (PFC). Since the energy is an essential non-substitutable good for a household, we may also try this index normalized by the General Price Index. This means that the consumer adjusts the amount of his consumption with respect to the fuel prices in comparison to the other goods, not just by comparing it with its past prices. Figures 8, 9 and 10 show the variation of these two indexes. Figure 7. households and labor from 1967 to 2008 Figure 8. Consumer price index for energy (1997=100) Figure 9. Ration of energy price index to the general price index Figure 10. Price index of energy appliances (normalized by CPI) It is observed that the energy prices, not only has not increased, but also have been lowered compared to the general prices. This means encouraging people to consume more energy. Finally, the other price index is for the electrical and fuel burning appliances. These indexes are listed below: Consumer Energy (Fuel) Price Index: PFC Energy price index adjusted by the General Price Index: PFPG Electrical and Fuel Appliance price index: PAPL 3.3. Model structure Bases on Auto Regressive Moving Average (AR(p) MA(1)) structure, residential and commercial energy demand forecasting model structure is as equation (1): LEI(t) = α i LEI(t i) + β j u j (t) + e(t) + γ e(t 1) (1) where, the letter L stands for the Logarithm the unknown parameters, α i s, β j s and γ have to be estimated using the historical data. Also, u j (t) s are the input variables listed in the following table, with different cases considered for each one. Table 1. Input variables and cases Inputs Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 U1 LVAT LVAN LYNI - U2 LPO LHNT LPNL - U3 LBLD LINVC LKCD LKBD LKCT - U4 -LPFC -LPFPG - U5 -LPAPL - U6 -LLT - Moreover, a constant signal and a dummy variable, which indicates the especial conditions of the country in the revolution years and the ending years of the war, can be added to the model. Also, we may 341

6 consider different number of the lagged output terms, say p=1,2,3. These cases together lead to =13824 parallel models, each one may be selected as a suitable model Selected model Applying various criteria such as R 2, Jarque-Bera tests of Normality, The Global T-student statistics, The minimum of t-student statistics, Dynamicity Criterion, Prediction Power, Simulation Power, with respect to the properties of the models, the models are sorted. We have put away five sample points of the historical data at the estimation step, in order to predict/simulate the future by each model. Then the precise of prediction/simulation is considered as a criterion to measure of the models for forecast. Econometric analysis facilitated with appropriate software including Eviews and MATLAB programming will be taken in to use to do the estimations. After sorting the estimated models we found that p=2 led to better results. It should be mentioned that amoung the 20 best models no one needs differencing, all need the dummy variable and no one uses the LT variable. Moreover, it is interesting that none of the energy price indexes show effect on the energy consumption in this sector. The selected model (taking the first place) for the energy consumption in the sector is given below: Inputs: LVAT, LPO, -LPAPL, DUM Model Structure: AR(2)-MA(1) 3.5. Estimation results for the residential and commercial energy demand In this section residential and commercial energy demand of Iran from 2011 to 2020 is forecasted. It is done for a scenario of medium growth rate in the input variables regarding the historical data, by simulation of the model. The estimated residential and commercial energy demand from 2011 to 2020 can be seen in table 2. The energy demand will reach the level of 923 MBOE in Table 2. The forecasted residential and commercial energy demand Years Energy demand (MBOE) Years Energy demand (MBOE) Conclusions This paper proposed and demonstrated a new approach in modeling residential and commercial energy demand of Iran. This approach may be briefly stated as follows. Based on a previously performed exogeneity investigation of various quantified variables, First, a set of the most important criteria is listed. Second, both conjunctive and disjunctive relations among the listed criteria are determined. Afterward, a proper possibility distribution function is assigned to each criterion, and a utility function is defined as well. Maximizing the utility function leads to the solution of the model selection problem. In this way, the best model for forecasting resedetial and commercial energy deamnd of Iran was selected. Moreover, the energy demand from 2011 to 2020 was forecasted. 5. Acknowledgements This research was supported by the Institute for International Energy Studies (IIES). References [1] Hamed Shakouri G., Mohammad B. Menhaj, A Systematic Fuzzy Decision-Making Process to Choose the Best Model Among a Set of Competing Models, IEEE Transactions on Systems, Man and Cybernetics-Part A: Systems and Humans, 38(5), (2008). [2] H. Shakouri G., M. Rastad, J. Nazarzadeh, A Hybrid Nonlinear Model for the Annual Maximum Simultaneous Electric Power Demand, IEEE Transactions on Power Systems, 21(3), (2006). 342