Short-Term Electricity Demand Forecasting: Impact Analysis of Temperature for Thailand

Abstract

Accurate electricity demand forecasting for a short horizon is very important for day-to-day control, scheduling, operation, planning, and stability of the power system. The main factors that affect the forecasting accuracy are deterministic variables and weather variables such as types of days and temperature. Due to the tropical climate of Thailand, the marginal impact of weather variables on electricity demand is worth analyzing. Therefore, this paper primarily focuses on the impact of temperature and other deterministic variables on Thai electricity demand. Accuracy improvement is also considered during model design. Based on the characteristics of demand, the overall dataset is divided into four different subgroups and models are developed for each subgroup. The regression models are estimated using Ordinary Least Square (OLS) methods for uncorrelated errors, and General Least Square (GLS) methods for correlated errors, respectively. While Feed Forward Artificial Neural Network (FF-ANN) as a simple Deep Neural Network (DNN) is estimated to compare the accuracy with regression methods, several experiments conducted for determination of training length, selection of variables, and the number of neurons show some major findings. The first finding is that regression methods can have better forecasting accuracy than FF-ANN for Thailand’s dataset. Unlike much existing literature, the temperature effect on Thai electricity demand is very interesting because of their linear relationship. The marginal impacts of temperature on electricity demand are also maximal at night hours. The maximum impact of temperature during night hours happens at 11 p.m., is 300 MW/${}^{°}$C, about $4\%$ rise in demand while during day hours, the temperature impact is only 10 MW/${}^{°}$C to 200 MW/${}^{°}$C about $1.4\%$ to $2.6\%$ rise.

1. Introduction

1.1. Motivation and Background

Thailand has 100% access to electricity [1] for both urban and rural areas with the second-largest economy and the fourth-largest country by population in Southeast Asia. Such population and the economic growth lead to an increment of electricity demand by an annual average of 684 MW since 1987 [2]. Among Asian countries, the People’s Republic of China (PRC) accounts for most of the energy demand in Asia whereas Thailand stands in the fifth followed after India, Korea, and Indonesia [3]. The Electric Supply Industry of Thailand consists of Electricity Generating Authority of Thailand (EGAT), Metropolitan Electricity Authority (MEA), and Provincial Electricity Authority (PEA); where EGAT is responsible for generation, MEA for distribution in the metropolitan area around Bangkok, and PEA distribution in the rest of the country. The scope of our paper is centered on the metropolitan areas.

Short-term electricity demand load forecasting has become an extremely important issue for energy suppliers, system operators, and other market participants. In many electricity deregulated markets, around the world electricity demand is fixed a day before the delivery by concurrent (semi-)hourly auctions. The improved accuracy of demand load forecasting can save the operating cost and the reliability of power supply. The volatile and complex behavior of electricity demand is always a challenging task when developing robust models for the researcher. Smart technologies like the internet of things, need sufficient power to connects “anything from anywhere” [4]. Industry automation and large penetration of plug-in electric vehicles are expected for reliable, economically competitive, environmentally sustainable electric system [4,5]. The fifth assessment report of the Intergovernmental Panel on Climate Change [6] suggested that global warming already made the world 0.74 ${}^{°}$C warmer and forecasted to 1.8–4 ${}^{°}$C by the end of century [7,8,9]. This increment in temperature has already shifted the highest peak demand load occurrence from evening hours to daytime hours due to the intensive use of the air conditioning (AC) systems in Jordan [7]. The outside temperature is demonstrated as the most influencing factor among all the variables that can be used to explain potential variations in demand [10,11]. Furthermore, this influence is typically linked to the penetration of electric cooling and heating appliances, mainly used by households and firms in residential and commercial sectors [11]. Heating, ventilation, and the AC system consume more than half of energy in the buildings of residential area [12]. In addition to temperature, deterministic variables such as day types and seasons also show their impacts on demand. The behavior of demand is highly dependent on the sectors where the electricity is used. The influence of residential sector behavior on energy consumption is getting increasingly significant [13]. Since the electricity cannot be stored efficiently, end-user demand must be tightly controlled for an effective power system management [14]. Therefore, the main objective of this article is to construct an accurate forecasting model, and quantitative analysis of demand load influencing factors that help to ensure the stability of the energy system in operation, maintain the secure, adequate, and efficient electricity supply by reducing blackout risk. To avoid an ambiguous presentation, we note that the rest of this paper uses two terms, “demand forecasting” and “demand” to refer to “electricity demand forecasting” and “electricity demand”.

In fact, electricity consumption fluctuates due to the random behavior of consumers while some of the predictable patterns such as seasonal, weekly, and daily patterns are found. The variation on the demand during morning hours, day hours, and night hours causes intraday patterns. To handle these intraday periodicities, the researcher has two alternatives: the first is to allocate the individual variables for each hour/half-hour [15,16], while the second is to construct separate models for each hour/half-hour so that intraday seasonality vanishes [17,18,19]. Similarly, weekdays seasonality is due to working and non-working days. To remove such seasonality, a similar methodology of individual variables for each day using dummy variables is implemented [17,18,19,20]. Annual seasonality occurs due to the hot and cold seasons, and dummy variables are used to remove such seasonality. Monthly seasonality is also taken care of by dummy variables. To improve the forecasting accuracy, the interaction of these seasonal variables is implemented in [15] for the Thai dataset.

Demand load forecasting with a linear model is challenging due to several levels of seasonality, non-linear factors such as temperature, holiday, and special events. Auto-regressive moving average (ARMA) structures can handle such seasonal and cyclic behavior. So the lag structure-based ARMA with exogenous variables (ARMAX) models are constructed similar to [16,17,20,21] because such models have been extensively applied in the demand forecasting literature for better accuracy [16]. The main limitation of ARMAX is over-forecasting for Saturdays and under-forecasting for Mondays [21]. The reason behind the over-forecasting on Saturday is due to higher demand on Fridays compared to Saturdays. Since one-day lag demand is used to forecast for Saturday, this causes the over-forecasting on Saturdays. Similarly, the possibility of under-forecasting on Mondays is due to the Saturday or Sunday demand based on one-day or two-day lagged demand. A simple way to deal with such an issue is the interaction variables between lagged demand with day-of-the-week dummy variables which is implied in our modeling.

1.2. Review of Related Works

Some existing literature on short-term demand forecasting (STDF) utilized the same 2009–2013 dataset [20,22,23,24,25]. This work still gives the norm for improvement in forecasting accuracy for Thailand. The behavior of Thai demand profiles such as many public holidays, religious long holidays, and special events which are described in Appendix A still require a careful study to improve the performance. The unexpected flooding period in Bangkok was approximately three months, also challenged on forecasting accuracy. For simplicity, related works are divided into the following subsections.

1.2.1. Temperature Effect

Overall peak demand in Thailand was observed on Tuesday, 24 April 2018 at $20.30$ h which was $0.84\%$ less than the previous year. However, the energy demand was increased to 1.29% [26]. EGAT has implemented demand-side management to reduce an unnecessary use of electricity, fuel import, and carbon dioxide emissions to maintain the overall stability during the peak period. The micro-study of temperature for short term load forecasting and impact analysis of climate change was conducted by Parkpoom et al. [8] using a simple regression model for Thai data. They discussed climate and socio-economic scenarios and predicted that peak electric demand could rise by 1.74–3.43% by 2020 with a mean annual temperature of 1.74 ${}^{°}$C rise. Another paper [27] based on Bangkok metropolitan data studied the impacts of climate and economic factors only on residential electricity consumption. The paper found that residential demand increased by $6.79\%$ for 1 ${}^{°}$C rise in temperature. Cian et al. [28] focus such increment in demand depends on the penetration of air-conditioning equipment, indoor comfort and thermal quality of buildings. The larger air-condition load increased consumption by 0.12%. The high degree of correlation between temperature and demand is discussed by Mirasgedies et al. [29] for Greece. Their study found that future climate change is expected to influence the annual demand by 3.6–5.5%. For the Bangladesh dataset, [30,31] explores the temperature sensitivity forecasting using linear regression. The findings of both articles reveal a similar conclusion that demand is highly dependent on temperature during the summer season rather than winter. In summer, the increment rate of demand was maximum to 53.14 MW/${}^{°}$C while only 2.14 MW/${}^{°}$C increment in winter. The effect of temperature in the rural area of China was studied by Zhang et al. [32,33]. They analyzed the impact of temperature using a simple linear model. Similar to [30,31] for Bangladesh, the effect of temperature in summer was higher than in winter by $0.015\%$ in the rural areas of China. The reason behind a higher rate of demand during summer is ‘temperature accumulation effect’ which is discussed in article [34].

The effect of temperature on demand is highly dependent on the sectors where the electricity is used. Research works conducted for European data [35], and Chinese data [36] suggested that demand for industrial, and commercial sectors are not significantly affected by temperature. The study on Korean demand by [37] found conclusive evidence that non-climatic, such as deterministic variables, influenced the demand response in the commercial sector rather than the residential sector. However, the influence of residential sector behavior on energy consumption is getting increasingly significant [13]. Ang et al. [38] studied two tropical and subtropical cities, Singapore and Hong Kong. With the comparable population and economy sizes: results show that a 1 ${}^{°}$C rise in temperature on sectoral demand corresponds to 4–5% rise in Hong Kong, while 3–4% rise in Singapore. In Hong Kong, the impact of urban temperature on energy consumption was found to differ according to the sectors. Fung et al. [39] examined the temperature and demand relationships conducted in domestic, commercial and industrial sectors which show an increment of 9.2%, 3%, and 2.4%, respectively. This indicates the highest impact of temperature is in residential sectors rather than other sectors. The higher demand from the residential sector comes due to cooling purposes rather than heating purposes in Jiangsu, China. The peak demand and the impacts of global warming in the industrial and residential areas of Pune, India based on an extreme value approach [40]. The findings showed that industrial activities are not much influenced by the temperature whereas residential activities show a 1.5–2% change in average demand for 1 ${}^{°}$C rise in temperature. Such extreme temperature results in more cooling demand in residential areas during summer [41].

Weather conditions are widely included in most of the models because of its crucial role in STDF [42]. The seasonality of commercial demand is higher in winter rather than in summer. The impact of atmospheric variables including humidity, solar radiation, wind chill, cloud cover, and the temperature was conducted for Hokkaido [19] which shows that the rise in temperature from 25 to 26 ${}^{°}$C causes 7% increase in demand during day hours while only 2% increase in night hour at 1 a.m. The AC system saturation data for 39 cities in the United States was studied in [43] to show the strong correlation between AC saturation and Cooling Degree Day (CDD). A $20\%$ increase in CDD can rise up the residential electricity consumption by $1\%$ to $9\%$. Such increment in temperature causes a rise in demand by $3.7\%$ during the summer season, and $5.4\%$ in peak hours. The econometric model to analyze the effect of climate change for residential electricity consumption was discussed [41] in Yangtze river delta, China. The result showed that annual electricity consumption was increased by 9.2%/${}^{°}$C while 36.1%/${}^{°}$C during peak demand. The influence of temperature in the urban area of Shanghai showed two peaks due to heating on winter and cooling effect in summer. The paper [41] explored the temperature and demand relationships for cold, warm and mild countries and found the increment in demand by $0.54\%$, $1.75\%$, and $0.15\%$, respectively.

1.2.2. Weekend, Holiday/Special Day Effects

It is obvious that electricity demand variation from Monday to Friday (working days) is quite stable, while the demand on weekends and holidays is volatile in nature [16,19]. Just one holiday within a week may result in lower accuracy for the whole week. The weekend and special day characteristics show a lower level of demand sensitive than working days to the weather condition that influences the forecasting accuracy. Therefore, [15,34] implemented the interaction of variable concepts to improve forecasting accuracy. The article [34] proposed the semi-parametric regression with the interaction of demand and weather variables after the separation of weekend data from working day demand. Such separation of weekend demand and working days, as well as interactive coupling with external temperature, reduced the prediction error down to less than 2% which was better than different Artificial Neural Network (ANN) models. However, ANN is the most implemented method in the literature of machine learning models that are listed in the SCOPUS database [44]. Therefore, the special days’ issue is needed much attention because of poor performance on accuracy. Each special day suffers from higher prediction losses compared to other days of a week. These higher prediction losses occur at peak hours. Therefore, such cases are special and important for utilities because of large peak errors. This research focuses on how to provide the proper information about this non-linearity of special days so that the forecasting model able to forecast accurately. Non-linearity of special days load profiles are overcome by using separate models for each hour and categorical variables for each type of day.

1.2.3. Grouping of Dataset

The grouping of a dataset based on working and non-working days helps to train and test two different groups of a dataset, separately. Initially, Darbellay and Slam [45] suggested splitting a dataset into working days and holidays which is followed by several studies [15,16,17,18,19,46,47]. The deep classification of day types and special days is essential for good accuracy. In most of the research work, all the days are classified into two or three large groups such as working days, weekends and holidays [17,19,21,44,48]. However, the weekends and holidays create some level of challenge while grouping the dataset due to the limited number of observational data. The issue of public holidays referenced from bank holidays similar to [49] is applied in this study and which are just about 10–15 days of a dataset for a Year is very low for training and testing. Such a small number of holidays data or special days issues are important and need much attention because of poor performance on accuracy and large errors on peaks.

Since the Sunday and holiday pattern behaves some similarities, paper [23,24,48] classified the dataset into three categories: Monday to Friday (working days) group, Saturday group, Sunday and holiday group. While forecasting for day-ahead leading hours, [48] shows a very attractive MAPE of value 0.62%, 0.83%, and 1.17% for working days group, weekends, and Sunday with public holiday groups, respectively. Hippert et al. [46] simply replaced the holiday by Sunday or weighted average of some past values followed in the Thai dataset by [23,50]. The non-linearity of special days load profile are overcome by using separate models for each hour and categorical variables for each type of days. Taylor et al. [16] tried to smooth out the special days by averaging the corresponding periods from two adjacent weeks before fitting and evaluation. Special-day effects have been explicitly included in forecasting models using dummy variables deterministic components, such as the trend, seasonality, and special-day effects. For example, [17] suggested employing dummy variables to reflect the effect of the day after a holiday. Later, Cottet et al. [51] added five day-type dummy variables, [52] implemented 15 different dummy codes for the days of the week, common holidays, special holidays, working days before and after a holiday. The study of the cold region conducted by Chapagain and Kittipiyakul [19] constructed Multiple Linear Regression (MLR) with the ARMAX model that contains 22 dummy variables including long holidays, and months types to get the impressive 2.51% MAPE for holidays where more than 51% prediction were less than 2%. Therefore, we have separated the aggregated dataset into four different groups.

1.3. Model Selection

Several modeling concepts for robust parameter estimation used prior to 1990 were discussed in [53], and concluded that MLR was superior [19,21,54]. Literature showed that the multiple equations approach has the potential to achieve a very competitive forecast accuracy. The main advantage of this approach is the interpretative capability of explanatory factors. Since the primary goal of this paper is to analyze the marginal impact of temperature on electricity demand, the construction of regression models is a good option [21]. However, the characteristics of electricity demand are highly non-linear. Due to the handling capability of artificial intelligence especially: ANN, fuzzy and Support Vector Machine (SVM) are popular among the researchers. For example, ANN-based methods [46,55,56], Fuzzy interaction regression methods [57], ANN with Particle Swarm Optimization (PSO) and GA [24] to optimized the weights to fall into local minima, SVM methods [23], Baysian methods [19], DNN methods [58] are implemented.

ANN-based STDF models are systematically summarized including the important critics on ANN by Hippert et al. [56]. They exposed that the existing ANN papers were claimed better performance without any solid support. An FNN: a simple deep neural network consists of more than the typical three layers of multiple layer perceptron. The deep structure increases the feature abstraction capability of neural networks. The number of layers and neurons are the key to modeling neural network structures. The network, having a single hidden layer can vary the number of neurons in a single hidden layer while the depth of the network can be varied in DNN. The number of hidden layers is selected based on forecasting accuracy. Darshana and Chawalit [50] designed a combined PSO algorithm and forecasted using the ANN technique. The overall MAPE for 2013 was found higher than $3.14\%$. The same authors [24] implemented hybrid PSO with the Genetic Algorithm (GA) to improve the yearly MAPE for 2013 forecasting accuracy to $2.86\%$ which is quite impressive for Thai data. The minimum and the maximum monthly average MAPE were found 2.164% (April) and 6.761% (December), respectively. The procedure of cleaning the dataset of this paper consists the main limitation; where the dataset of holidays, bridging days (working days between holidays), and the abnormal dataset is replaced with a weighted moving average of by randomly selected numbers and forecasting is performed on cleaning dataset, not the actual demand. Phyo et al. [22] also suggested the data be cleaned and grouped into similar days. The authors implemented a DNN methodology to forecast the year 2013. To improve the prediction accuracy, paper [22] is also tested with cleaned data similar to [24,50]. Su et al. [23] presented a similar methodology but a different algorithm. In both papers [22,23] length of training dataset and the temperature variables were equal and focused on cleansing to obtain better forecasting accuracy. However, their accuracy performance was still at a lower level compared to [24]. In this study, we used the same dataset provided by EGAT which was already implemented by papers [20,22,23,24,50] is implemented.

Due to limited literature for Thai data, similar studies of different regions and similar weather condition as Thailand are worthy of discussion. For example, Malaysia has approximately similar weather conditions to Thailand. Ismail et al. [54] implemented an MLR model to investigate the impact of temperature, holiday types with MAPE $1.71\%$ for a day-ahead forecast. Apart from artificial intelligence, other traditional and adaptive techniques such as Seasonal ARIMA (SARIMA) and Regregression ARIMA (RegARIMA) were compared to linear regression for cognate energy prediction with weather variable selection. The result showed that linear regression was highly effective and better than other sophisticated techniques for the majority of simulations in [59] in China. A RegSARIMA model for predicting short-term daily peak demand with a comparative analysis between SARIMA and Holt–Winters Triple (HWT) exponential smoothing models were discussed by Chikobvu and Sigauke [60] for South Africa. The empirical results showed that the RegSARIMA model is capable of capturing important driving factors of demand. In another study of authors [60,61], an additive regression model used to forecast the daily peak demand. They concluded that the demand in South Africa was highly sensitive to cold temperatures compared to hot temperatures because of sub-tropical mild climate. The small number of customers is another reason for the high sensitivity of temperature to the electricity demand discussed by Haben et al. [62] where they have studied for a low voltage grid up to 150 customers in the United Kingdom.

As usual, the result shows the correlation between demand and seasonality (temperature) where the best performing method was AR and HWT exponential smoothing. More robust modeling techniques comprise our concern to handle the stochastic behavior of variables. The use of categorical variables is needed to formulate such classification in a linear regression model is very common [17,21,30,44]. These categorical variables define the types of days translated into dummy variables that allow the regression model to eliminate each type of individual day. In the short lead time up to six hours ahead, univariate models are sufficient [16] for good accuracy. Taylor et al. [16] conducted a comparative study of univariate models against two benchmark models to obtained the MAPE less than $2\%$. The hidden reasons behind the selection of univariate models are just a few leading hours for prediction and the difficulties in accessing the costlier weather data [19,63]. Unlike [16], EGAT makes forecast at 2 p.m. for the next day which is 10 to 34 leading hours. On Friday, Thailand practice for the forecast is up to 106 h ahead, if Monday is a holiday and even longer during long holidays such as Songkran and New Year. Such long leading hour prediction is made by EGAT because the EGAT office is closed on weekends and holidays. However, this study is limited to the prediction up to 10 to 34 leading hours considering the data up to 2 p.m. is available to forecast for the next day only.

The MLR model with a dynamic error structure and adaptive adjustment of forecasted error proposed by Ramanathan et al. [17] was the winner of a demand forecasting competition. The reason behind the dynamic error structure is to overcome the limitation of simple OLS. The alternative model of [17] is the quantile regression model which is discussed and implemented by Sigauke et al. [64], and Botoc and Anton [65], for hourly electricity demand model, and to explain the profitability of firms, respectively. The Hong et al. [57] reviewed the modeling techniques of winning teams in the Global Energy Forecasting Competition 2012, where all four winning teams applied regression analysis, while only two teams implemented ANN. Therefore, we select the AR-based MLR model with uncorrelated error and adaptive adjustment for correlated error. For a comprehensive study, FF-ANN and hereafter named FF-ANN model are constructed using the TensorFlow deep learning platform.

1.4. Contributions

This paper follows the similar forecasting procedure of EGAT where the data until 2 p.m. is collected and predicted for the next day. The selection and implementation of the GLSAR model by taking care of error lags, a comprehensive study on OLS, GLSAR and FF-ANN, provides the novelty and pioneer contribution for an upcoming researcher. The major findings based on Thai electricity data for STDF as explained as,

• The marginal impact of temperature that leads to raising the demand for day hours and night hours is explored for Thailand which is quite useful for tropical countries.
• The quantitative analysis among the variables such as the impact of holidays, working days, working days after a holiday/long holiday, AR effect, special days/events such as Bangkok flood for the demand is discussed in detail.
• The unexpected Bangkok flood and lockdown situation were quite similar to the current Covid-19 in terms of electricity demand. Therefore, the researcher can extend this methodology to analyze the impact on electricity due to Covid-19.
• Construction of four different scenarios based on similar characteristics of demand which leads to achieving the best prediction capability among the existing literature of the Thai dataset.
• The strategy for the selection of variables, determination of the training length of a dataset, hidden layers and nodes are also major contributions for the improvement of the accuracy are also major contributions of this study.

The remainder of this paper is organized as follows. Section 2 describes the overall methods including data pre-processing, modeling strategy, and estimation process of models. Section 3 demonstrates an extensive empirical analysis of forecasting accuracy, the marginal impact of temperature and the quality of the model fit. Section 4 summaries the comprehensive discussion and concludes this paper.

2. Methods

In this section, proposed methods as depicted in Figure 1 are described. The proposed methods can be seen as four frameworks, namely: data pre-processing, model design, MLR/ANN estimation, and comparative discussions. The details of data pre-processing are presented in Appendix A to avoid an ambiguous presentation.

After the detailed discussion of data characteristics and variable identification in Appendix A, and grouping methods of dataset in Section 1.2.3, the Thai dataset is carefully divided into four different subsets or hereafter named scenarios. Each model is trained and tested for each scenario and divided as,

• Scenario 1: only demand for working days.
• Scenario 2: only demand for weekends.
• Scenario 3: only holiday demand and highly fluctuated demand from December 24 to New Years eve.
• Scenario 4: all the demand dataset.

For each scenario, the parametric MLR model and non-parametric FF-ANN model were included in a comprehensive study.

2.1. Model Design

The variables are identified and presented in Appendix A.4 to construct the MLR and ANN models. The experiments show that an MLR forecasting model shows strong capability to build the relationship between model output and affecting variables. Similarly, ANN models have the strong capability of mapping the complex input/output relationship where we can construct a robust model for better results. These models are described as,

2.1.1. MLR Model Description

The electricity demand data is observed every half-hour, therefore there are $N=48$ observations in a day. Since we have total 84,618 observations, these datasets are made the half-hourly sectional grouping into 48 subsets. Each group contains the demand load for a specific hour of the day. Now, the individual subset is treated as a single series of data and all 48 series are modeled and estimated independently. Therefore, we have 48 individual forecasting models to forecast for one-day. The main advantage of implementing such a sectional form of data is that intra-day patterns are automatically avoided [17]. The demand at day d and half-hour for $h=1,2,\cdots ,48$ modeled as,

$$\begin{array}{cc}\hfill D_{h,d}& =De{t}_{h,d}+Tm{p}_{h,d}+DHis{t}_{h,d}+ITerm{s}_{h,d}+{\mu }_{h,d},\hfill \end{array}$$

(1)

where $De{t}_{h,d}$, $Tm{p}_{h,d}$, $DHis{t}_{h,d}$ and $ITerm{s}_{h,d}$ are groups of deterministic, temperature, historical electrical demand, and interaction terms, respectively. The residual ${\mu }_{h,d}$ modeling is very sensitive and important in MLR because of the incorporation of an auto-regressive structure in the error term. Such correlated errors assumed to follow an autoregressive with previous days. Therefore, Equation (2) describes that the current value of the error term at hour h of the day d is denoted by ${\mu }_{h,d}$, which is the autoregressive sum of q previous days. We have run several models for different values of q. Mathematically,

$${\mu }_{h,d}=\sum _{i=1}^q{\rho }_{h,i}{\mu }_{h,d-i}+{ϵ}_{h,d}.$$

(2)

The terms ${\mu }_{h,d-i}$ is the serially-correlated error term and ${ϵ}_{h,d}=N(0,{\sigma }^2)$. The Durbin–Watson (DW) test is used to test the hypothesis that the residuals are serially correlated or not. The hypothesis being tested as, $H_0:\sigma =0$ for no serial correlation and $H_1:\sigma \ne 0$ for serially correlated error. The demand model can be written conveniently as a linear regression model,

$$Y_{d,h}=X_{d,h}{\beta }_d+{\mu }_{d,h}.$$

(3)

Equation (3) consists of p predictor variables and the classification of these p variables are as in Equation (1), where $\mu =N(0,\sum )$. Depending on the properties of ∑, model is classified as,

• OLS: where errors $\sum =\mathit{I}$
• GLS: for orbitrary covariance ∑
• GLSAR: where AR(p) $\sum =\sum \rho$

In our analysis, error terms are assumed to follow an AR(p) in days upto $p=7$, therefore GLS turned as GLSAR methods, and implemented as,

$${\mu }_{d,h}={\rho }_{h1}{\mu }_{d-1,h}+{\rho }_{h2}{\mu }_{d-2,h}+\cdots +{\rho }_{h7}{\mu }_{d-7,h}+{ϵ}_{d,h}$$

(4)

Combining all 48 equations together in Equation (3), the half-hourly demand model can be written as,

$$Y=X\beta +\mu .$$

(5)

Unlike simple regression context, $E(\mu$${\mu }^{\prime })=\mathsf{\Omega }$, which is Seemingly Unrelated Regression (SUR) system describes that each row of $\mu$ corresponds to one day of half-hourly residuals is contemporaneously correlated but not correlated over a half-hour. This methodology is thoroughly explained in [17]. The auto-correlation AR(p), p=7 to the previous days was taken into account by taking lags, but not among the hours. The order of AR is determined by the significance test of ACF and PACF.

2.1.2. OLS and GLSAR Estimation

The MLR model designed in Equation (5) can be setup as, ${\mathit{Y}}_h={\mathit{X}}_h{\beta }_h+{\mu }_h$, for $h=1,\cdots ,m$ is the regression model for each half-hour h. Here, ${\mathit{Y}}_h={(D_{h,1},D_{h,2},\cdots ,D_{h,T})}^{\prime }$, ${\mathit{v}}_h={({\mu }_{h,1},{\mu }_{h,2},\cdots ,{\mu }_{h,T})}^{\prime }$, and ${\beta }_h={({\beta }_{h,1},{\beta }_{h,2},\cdots ,{\beta }_{h,P_h})}^{\prime }$. These $P_h$ regressors in the regression model are for half-hour h, and ${\mathit{X}}_h$ is the corresponding $T\times P_h$ size matrix. This matrix contains the regressors from Equations (5). For instant, if $h=1,\cdots ,48$, there exists 48 regressions, then $\mathit{y}=\mathit{X}\beta +\mu$ where ${\mathit{y}}^{\prime }=({\mathit{y}}_1^{\prime },\cdots ,{\mathit{y}}_{48}^{\prime })$, ${\beta }^{\prime }={\beta }_1^{\prime },\cdots ,{\beta }_{48}^{\prime })$, and $\mathit{X}=bdiag({\mathit{X}}_1,\cdots ,{\mathit{X}}_{48})$ is a $(48d\times {\sum }_{h=1}^m{P}_i)$. The serially correlated error ${\mu }_h$ (Equation (4)) term should be transformed to the serially uncorrelated error ${ϵ}_h$ where ${ϵ}_h={\mu }_h^{*}={\mu }_h-{\rho }_{\mathit{i}}{\mu }_{h-i}$, and i represents the number or order of the lag. Similarly, ${\mathit{Y}}_h^{*}={\mathit{Y}}_h-{\rho }_{\mathit{i}}{\mathit{Y}}_{h-i}$, and ${\mathit{X}}_h^{*}={\mathit{X}}_h-{\rho }_{\mathit{i}}{\mathit{X}}_{h-i}$ removes the serial correlation [19].

2.1.3. Performance Measurements

The most common criterion that is used for evaluation of forecasting performance is $MAPE$. It measures the deviation of forecasted value from a real value in terms of percentage.

$$MAPE=\frac{1}{N\left|D\right|}\sum _{\alpha \in D}\sum _{k=1}^N\left|\frac{D_{h,d}-{\widehat{D}}_{h,d}}{D_{h,d}}\right|,$$

(6)

where D represents the set of test days in the test dataset, $D_{h,d}$ and ${\widehat{D}}_{h,d}$ represents the real demand and predicted demand, respectively at day d and half-hour h.

2.2. Artificial Neural Network Approach

A neural network is a popular multi-stage powerful modeling tool that can capture the non-linear behavior and complex input to the output relationship compared to conventional techniques. The motivation for ANN construction is because of intelligent characteristics of neurons similar to the human brain because: a neural network acquired knowledge through learning, and this knowledge is stored as the weights within the inter-neuron connections. The mathematical expression for learning is,

$$l_i=\sum _{j=0}^m{X}_j{W}_{ij}+b_i.$$

(7)

The output function will be $y_i=f\left(l_i\right)$, where $W_{ij}$ are the weights of each neurons; $f$ is a non-linear activation function.

2.2.1. Structure of ANNs

The structure of ANNs is composed of the numbers of layers and the neurons. The number of neurons is automatically fixed by the training data and the forecasting period. Moreover, the highlighted limitations associated with the ANN structure are that the training process oscillates and possible to converse at local minima. Some authors such as [24] discussed meta-heuristic methods to find the global minimum and selection of hidden neurons. Normally, the researcher gradually increases the number of neurons and compared them to the errors. Unlike shallow learning procedures, DNN refers to the combination of a large number of layers and neurons. Therefore, optimizing the depth and width of hidden layers is quite time consuming and not feasible to test all possible combinations. Therefore, we have determined the structure of DNN by the trial and error procedure and finally selected two hidden layers as discussed in Section 3.3 Table 5.

2.2.2. Activation Function

The activation function maps the resulting values by capturing the trends or feature patterns from the trained dataset. In ANN, the Rectified Linear Unit (ReLU) is considered as the excellent activation function to regularize the hidden layers. Since ReLU picks the $max(0,x)$, it avoids the vanishing gradient problem. Moreover, the advantage of ReLU is very quick to use and train the model so that computational cost is reduced compared to other activation functions. However, the learning process gets slow because of bias.

2.2.3. Resolving Overfitting

Over-fitting can be observed from the learning curve which describes the error rate according to the epochs. An epoch is just one cycle of iteration where the entire dataset is passed forward and backward in the network. Initially, a testing error is reduced by increasing the number of epochs in a trained model, but there exists a threshold point from where the testing error starts to increase even the training error seems improving. Therefore, over-fitting is a serious problem in ANN techniques which can be minimized by adding more observational data or using the concept of dropout. Dropout function randomly ignores or drops out some subset of nodes from a given layer during the training procedure so that it can prevent an over-fitting problem.

3. Results and Discussion

3.1. Selection of Training Length

To determine the best length of the training period, Scenario 1 was chosen due to less variation in the dataset. This dataset is implemented for OLS estimation considering the absence of serially correlated-error coefficients. The number of coefficients and size of the training dataset should not be over-parameterized. Scenario 1 consists of 54 coefficients and 236 to 911 set of observations obviously avoids the over-fitting problem [17]. Insufficient feature abstraction could happen in a short length of the training dataset. A longer length of training dataset provides more information to the forecasting model and obviously results in good accuracy. However, considering a longer training dataset, the forecasting accuracy can be affected if the historical pattern of data significantly differs from the most recent data [66]. Lusis et al. [66] suggested that just one-year length is sufficient for training to develop the residential electricity model. However, Clements et al. [21] implemented a three-year length of aggregate data for the Queensland region, Australia, where the model obtained quite impressive results with MAPE 1.36%. Since the length of the training dataset shows localized characteristics, four different sizes of training datasets, 911 days, 717 days, 475 days, and 236 days are tested. These four different sizes or cases are designed as,

• Case I: Training period: 911 days, test period: 239 days in the year 2013.
• Case II: Training period: 717 days, test period: 239 days in the year 2013.
• Case III: Training period: 475 days, test period: 239 days in the year 2013.
• Case IV: Training period: 236 days, test period: 239 days in the year 2013.

Forecasting accuracy and execution time were calculated for all four cases and tabulated in

Table 1. Mean Absolute Percentage Error (MAPE) measures for different training lengths using the Scenario 1 dataset.

			Simple OLS		FF-ANN
	Training Length (Days)	Testing Days	MAPE (%)	Exe. Time (Sec)	MAPE (%)	Exe. Time (Sec)
Case I	911	239	1.97	109.2	2.96	565.97
Case II	717	239	2.33	87.38	3.41	516.46
Case III	475	239	2.04	114.26	6.00	435.32
Case IV	236	239	2.44	78.82	18.00	309.81

. When the training length is more than three years, both the methods: simple OLS, and FF-ANN forecast with the lowest MAPE. The Table 1 depicted the execution time (both training and testing) for MLR approach: simple OLS method is about 110 Sec for 239 days which is fairly good and acceptable. Therefore, more than three years of training length is picked up for further experiments in this paper.

3.2. MLR Approach: Simple OLS Method

3.2.1. Model Selection

Normally, a perfect fit model can always be obtained by using a model with enough parameters and results in good training accuracy. However, better training accuracy does not guarantee better accuracy while forecasting with a testing dataset. Moreover, complexity is increased to analyze the interpretation of the model due to a large number of variables. Therefore,

Table 2. Effect of variables on MAPE: simple Ordinary Least Square (OLS).

Model	Deterministics and Interaction	Temp	Temp Square	Holiday	Holiday 2	MAPE (%)
OLS-(Scenario 1)	Yes	Yes	Yes	Yes	Yes	1.97
	Yes	Yes	No	No	No	2.00
	Yes	No	No	No	No	3.04
OLS-(Scenario 2)	Yes	Yes	Yes	Yes	Yes	1.78
OLS-(Scenario 3)	Yes	Yes	Yes	Yes	Yes	16.00
OLS-(Scenario 4)	Yes	Yes	Yes	Yes	Yes	2.94

presents the importance of some variables based on forecasting accuracy. The result reveals that the forecasting accuracy is improved by incorporating more independent variables. In this experiment, Senario 2 performs the best with MAPE of $1.78\%$. This means the weekend demand forecasting model by the grouping of weekend data separately can forecast with the best accuracy for Saturday and Sunday. The Scenario 1 stands with competitive MAPE which is less than 2% because of holiday free working days, while Scenario 3, which consists of holidays forecast with the worst MAPE of $16\%$. The model selection procedure for holiday is always challenging due to the significant variation of demand. The performance of Scenario 3 is the worst among others because of the most fluctuated dataset. Since Scenario 4 using all the dataset including holidays, can forecast with MAPE $2.94\%$, we choose this Scenario 4 for holiday forecasting purpose.

The continuous forecasting curves for Scenario 1 is presented Figure A8. The comparison of actual demand and prediction demand curves shows that most of the predictions are very closed to real demand. Since the forecasting is only for working days and non-holidays, only 239 days are predicted. Some predictions on the second week of December, the first weeks of January and April were found to have under-forecasted values because of the so-called holiday_effect affecting the bridge days of the holidays. Such occurrence of holidays adjacent to the working days forces to reduce the accuracy.

The columns of the

Table 3. Model description paramters: GLSAR-7 (Scenario 1).

HH	Rsq		Adj-Rsq		DW		HH	Rsq		Adj-Rsq		DW
	OLS	GLSAR-7	OLS	GLSAR-7	OLS	GLSAR-7		OLS	GLSAR-7	OLS	GLSAR-7	OLS	GLSAR-7
0	0.97	0.96	0.97	0.95	1.80	2.00	24	0.86	0.62	0.86	0.59	1.73	1.99
1	0.97	0.96	0.97	0.95	1.86	2.01	25	0.88	0.68	0.88	0.66	1.79	1.99
2	0.97	0.96	0.97	0.95	1.85	2.00	26	0.87	0.67	0.87	0.65	1.77	1.98
3	0.97	0.95	0.97	0.95	1.85	2.00	27	0.86	0.63	0.86	0.61	1.74	1.98
4	0.97	0.95	0.97	0.94	1.85	2.00	28	0.85	0.62	0.85	0.60	1.78	1.97
5	0.97	0.95	0.97	0.94	1.87	2.00	29	0.86	0.63	0.86	0.61	1.67	1.98
6	0.97	0.94	0.96	0.94	1.85	2.00	30	0.87	0.64	0.87	0.61	1.64	1.98
7	0.96	0.94	0.96	0.94	1.86	2.01	31	0.87	0.64	0.87	0.61	1.59	1.98
8	0.96	0.94	0.96	0.93	1.87	2.01	32	0.86	0.64	0.86	0.60	1.57	1.98
9	0.96	0.36	0.96	0.93	1.88	2.00	33	0.86	0.61	0.86	0.58	1.51	1.98
10	0.96	0.93	0.96	0.93	1.88	2.01	34	0.85	0.59	0.85	0.57	1.44	1.99
11	0.95	0.92	0.95	0.92	1.84	1.99	35	0.84	0.56	0.84	0.53	1.40	1.99
12	0.94	0.92	0.94	0.91	1.78	2.00	36	0.80	0.52	0.80	0.49	1.38	2.00
13	0.93	0.90	0.93	0.89	1.80	2.00	37	0.80	0.52	0.80	0.49	1.35	2.00
14	0.93	0.88	0.92	0.97	1.78	1.99	38	0.84	0.60	0.84	0.58	1.33	2.00
15	0.92	0.85	0.92	0.84	1.65	1.99	39	0.86	0.65	0.86	0.63	1.33	2.00
16	0.90	0.78	0.89	0.76	1.67	1.98	40	0.87	0.68	0.87	0.66	1.33	2.00
17	0.88	0.73	0.88	0.71	1.69	1.99	41	0.88	0.72	0.88	0.70	1.17	1.99
18	0.87	0.69	0.86	0.67	1.73	1.99	42	0.90	0.74	0.90	0.73	1.43	1.99
19	0.86	0.65	0.85	0.63	1.74	2.00	43	0.91	0.77	0.91	0.75	1.45	1.99
20	0.86	0.64	0.85	0.61	1.71	2.00	44	0.91	0.77	0.91	0.76	1.45	2.00
21	0.85	0.61	0.84	0.59	1.69	2.00	45	0.91	0.78	0.91	0.77	1.48	2.00
22	0.84	0.59	0.83	0.56	1.70	2.00	46	0.92	0.79	0.92	0.78	1.46	1.99
23	0.84	0.60	0.83	0.57	1.74	1.99	47	0.92	0.80	0.92	0.79	1.46	2.00

report R-squared, Adjusted R-squared, and DW values, respectively, for individual half-hours. R-squared and Adjusted R-squared are the goodness of fit measures.

Since these data are the results from the testing dataset, $79.7\%$ to $97.4\%$ of the variability in the testing dataset was accounted for by the predictor variable included in the model. Adjusted R-squared values are found normally lower than R-square indicating predictor variables improve the model. Adjusted R-squared increases only if the new term improves the model more than would be expected by chance. Similarly, the DW test is a statistical technique to determine whether the series follow auto-correlation or not. The residual for the individual half-hour was analyzed separately. DW statistic value is always between 0 and 4. Values less than 2 indicate positive auto-correlation and a value greater than 2 indicates negative autocorrelation. DW value equals 2 means there is no auto-correlation. Since most of the DW statistics for all 48 half-hours are found between $1.3$ to $1.9$ for simple OLS, there is some evidence to reject the null hypothesis. These statistics for simple OLS and GLSAR-7 are tabulated in Table 3 and compared DW values. The positively-correlated DW statistics (1.17–2.48) after 5 p.m. (HH$\ge 34$) which was the evidence of serially correlated error, is now significantly improved nearly $2.0$. This indicates that forecasting errors are now uncorrelated. The selection of a better statistical model from a set of candidate models is a crucial factor. Since the OLS results for Scenario 1 show MAPE $1.97\%$ which could still possibly to reduced by implementing AR lags on the model. To determine the number of AR lags, we have selected peak hour (2 p.m.) and tested for different lags such as 1 to 7 where p-values are found very small (less than 0.09), so we have strong evidence that the errors follow at least AR(7).

Table 4. MAPE measures for different model structures for Scenario 1.

Methods with AR(p)	MAPE(%)	Time Elapse (Sec)
OLS	1.97	47.00
GLSAR-1	1.92	223.00
GLSAR-2	1.94	247.00
GLSAR-3	1.92	223.00
GLSAR-4	1.90	223.00
GLSAR-5	1.90	230.00
GLSAR-6	1.90	232.00
GLSAR-7	1.88	241.00

presents the MAPE for GLSAR(1) to GLSAR(7) indicating that GLSAR(7) got the lowest MAPE value.

3.2.2. Temperature Effect

The temperature-related variable and their effects on demand are expressed in Figure 2. This figure describes the rate of demand variation per degree temperature change from Monday to Saturday for individual months of a year 2013. While interpreting the demand variation for a particular day, Sunday is considered as the reference day. Similarly, Figure 2 presents such a variation for February to December where January is the reference month.

The rate of demand variation per degree temperature is minimum 50 MW/${}^{°}$C approximately at morning hours 6 a.m.–7 a.m. and evening hours (5–6 p.m.) because most of the people during these hours are on the way to work or traveling back from work. The increment of 50 MW per 1 ${}^{°}$C is about $0.6\%$ of the average demand. Flat and consistent demand variation from 100 MW/${}^{°}$C–200 MW/${}^{°}$C which is 1.4–2.6% rise in demand throughout the day hours except on Saturday and Sunday. The graph line for Saturday and Sunday is significantly lower and different than other working days in the morning and office hours which is as our expectation. Since electricity demand reaches a peak during the day hours of summer in Thailand, our results surprisingly explain quite different scenarios. The highest demand variation per degree rise in temperature exists up to 300 MW/${}^{°}$C which is $4\%$ rise per 1 ${}^{°}$C at 11 p.m. because most of the people are at home during this time. Such increment is lower than Greece [29], similar to the impact on aggregate demand of Singapore [38]. Since the temperature impact on residential demand is quite high [28,38], our result matches only to the impact of aggregate demand. The most interestingly, climate impact studied by Parkpoom et al. [8] also mentioned the similar result to our findings for the peak electricity demand of Thai data, however, the information about hours and days are lacking.

3.2.3. Special Day and AR Effect

The STDF models for special days such as Songkran, New Year and other special days are always challenging. The MAPE performance of these days is also poor in our study. However, the interpretation of coefficients is found realistic and expressed in Figure 3. The results present the different and distinct pattern groups. The demand variation after the holiday and after the long holiday significantly increased; while the demand reduced sharply for the special days. However, the working day after the special days increased as our expectations. If there is a regular holiday, demand on the next working day is increased because the people do not have time to travel far and come back to work quickly. However, on the next working day of other special events such as Songkran, and New Year, electricity demand significantly decreases because of the festive vibes on people. Many people during such festive holidays travel out of Bangkok to their hometown or travel plans and return to work a bit slow. Except for the day after the holiday and the flooding period, the electricity demand had a similar effect in the morning hours up to 5 a.m. and night hours after 8 p.m., while the demand was consistently at a high level on the day after a holiday. Similarly, demand was consistently at a lower level during the flooding period. The sudden and unexpected flooding period happened in Bangkok because of the shutdown of industries, commercial sectors, and universities. This situation is similar to the current Covid-19 and lockdown condition of Thailand.

The contribution of AR error terms is plotted in Figure 4. AR1 represents the error terms of the same hour but one previous day, and AR2 represents the error terms of the same hour but two previous days. In this sequence, AR7 represents the error terms of the same hour but seven previous days which is ultimately the same weekday before a week. In our result, AR2–AR4 and AR6–AR7 show the normal correlation impact up to $20\%$ in the morning hours till 8 a.m. (HH$=20$). The maximum demand contribution is obtained from the one previous day which is up to $63\%$ while AR5 contributes to the lowest impact. The contribution pattern of AR1 is minimum early in the morning hours, while it increases gradually and reached a peak at 8 p.m. Since the demand profile of electricity is quite similar in the same hour of two consecutive days, it is obvious to have the maximum correlated error. As our expectation, AR7 contributes to the competitive impact on demand because of the same day and same hour of previous week i.e., similar day effect. A similar study for the lagged load correlations discussed in [17,21] also mentioned that the impact of AR1 has the highest contribution to the demand up to $52\%$

3.3. ANN Approach: FF-ANN: A Simple DNN

A simple FF-ANN is implemented to predict all the scenarios as defined before: Scenarios 1–4. Input variables were designed from patsy, a Python package already used for MLR methods. Since the non-linear relations between the variables are automatically captured by the DNN structure, initially we ignored the non-linear variables such as squared-temperature, and interactions of variables. However, later these terms were included in models due to improvement in accuracy.

Therefore, historical demand data with lag load1d_cut2pm, load7d, and Load2pmYesterday and their dependency terms on the temperature such as MaxTemp, MaxTempYesterday, MA2pmTemp are included in model. To avoid the over-fitting problem in DNN, selection of the best number of epochs, a number of hidden layers and nodes are very sensitive. An experiment was performed for various structures: 1, 2, 3, and 4 hidden layers with different nodes and few are tabulated in

Table 5. Selection of hidden layers, nodes and epochs for Scenario 1.

Nos of Hidden Layers	Nos of Neurons	MAPE (%)	Epochs
1	$128\times 1$	2.85	8000
	$64\times 1$	2.82	15,000
	$32\times 1$	2.92	22,000
2	$16\times 1$	2.78	45,000
	$8\times 1$	3.18	55,000
	$4\times 1$	3.06	75,000
	$2\times 1$	38.79	100,000
	$128\times 128$	2.78	3000
	$128\times 64$	2.72	4000
	$\mathbf{64}\times \mathbf{64}$	2.72	2500
3	$64\times 64\times 64$	2.75	3000
4	$64\times 64\times 64\times 64$	2.92	2500

, explains that two hidden layer structures with $64\times 64$ nodes shows the best MAPE approx. 2.72% for testing data.

Unlike ARMAX methods, a trained FF-ANN model was used to forecast all the days of 2013. While in simple OLS, rolling windows of the training dataset are used to train for one step forward prediction. The reason behind this unfair methodology implied that FF-ANN took much longer to train a model compared to simple OLS or GLSAR. Therefore, the test period 2013 is divided into a small number of prediction intervals, named as pred_intervals. For example, if pred_intervals = 2, both training and testing dataset is divided into two halves. For the first half, we use the dataset from 8 March 2009 to 2012 as training to make predictions for January–June, 2013. For the second half, we used 08 March 2009 to June 2013 as training to make predictions from July–December, 2013 and so on. Moreover, the prediction was still one-day ahead where today’s demand data was used to predict tomorrow’s demand. The prediction error and computational time in

Table 6. Prediction error and computational time.

Pre_Intervals	MAPE%		Exe Time (Sec.)
	Simple OLS	FF-ANN	Simple OLS	FF-ANN
1	2.03	2.89	2.96	273
2	2.03	2.69	3.22	539
3	2.03	2.70	3.04	800
4	2.05	2.65	3.20	1062
5	2.05	2.56	3.40	1585
239	1.97	NA	33.4	NA

compared the performance of simple OLS and FF-ANN in terms of MAPE and execution time. The result shows that the forecasting accuracy of simple OLS is better for the same pred_intervals. When pred_intervals were increased, forecasting accuracy was improved for FF-ANN, but both execution time and MAPE performance are higher than simple OLS. This tradeoff concludes that simple OLS shows better performance than FF-ANN for our dataset. Since the FF-ANN method unable to compete with simple OLS and GLSAR, FF-ANN was therefore excluded for further comparison in

Table 7. Forecasting accuracy (MAPE%) comparison: all scenarios.

Simple OLS (MAPE%)					GLSAR (MAPE%)
Parameters	Scenario 1	Scenario 2	Scenario 3	Scenario 4	Scenario 1	Scenario 2	Scenario 3	Scenario 4
Mon	1.99	NaN	19.21	4.37	2.10	NaN	18.47	4.70
Tue	1.72	NaN	15.49	2.54	1.84	NaN	22.96	2.89
Wed	1.96	NaN	12.49	2.44	1.99	NaN	25.85	2.96
Thu	1.78	NaN	26.01	2.32	1.9	NaN	30.44	2.86
Fri	1.59	NaN	11.28	2.18	1.55	NaN	23.97	2.87
Sat	NaN	1.76	NaN	3.17	NaN	1.77	NaN	2.69
Sun	NaN	1.77	NaN	3.62	NaN	1.69	NaN	2.54
Holiday	NaN	NaN	14.73	9.62	NaN	NaN	21.00	10.22
Holiday 2	NaN	NaN	16.62	10.92	NaN	NaN	22.58	9.68
Songkran	NaN	NaN	13.54	11.42	NaN	NaN	18.48	14.76
Newyear	NaN	NaN	26.35	17.85	NaN	NaN	30.48	17.96
DayAfterHoliday	5.13	NaN	NaN	5.22	4.97	NaN	NaN	7.06
DayAfterLongHoliday	7.38	NaN	NaN	2.73	6.41	NaN	NaN	6.59
DayAfterSongkran	3.10	NaN	NaN	2.03	1.82	NaN	NaN	6.09
DayAfterNewyear	15.77	NaN	NaN	12.18	13.82	NaN	NaN	6.46
DayAfterLabor	3.39	NaN	NaN	5.14	4.85	NaN	NaN	9.26
DayAfterReligion	5.54	NaN	NaN	5.54	5.18	NaN	NaN	6.04
Overall MAPE	1.81	1.77	16.63	2.95	1.88	1.74	22.59	3.08

. However, the MAPE of 2.56–2.89% obtained from FF-ANN was quite lower than some Thai-based published papers such as [22,23,50], where they implemented ANN-based methods for a half-hourly dataset.

A detailed comparison on performance in terms of forecasting accuracy shows that Scenario 1 from simple OLS predicted with lower MAPE compared to GLSAR for most of the working days except on Friday. The simple OLS can predict for Scenario 1 by MAPE value 1.81% which is quite impressive. However, forecasting accuracy for Friday, and working days after holidays are found better in GLSAR compared to simple OLS. The Scenario 3 did not perform well for holidays in either method, which concludes that grouping of holidays dataset can not forecast well. To predict holidays, Scenario 4 was better than Scenario 3 indicating that aggregate data grouping all datasets together provides a good result for holidays. However, the grouping of weekend datasets separately as Scenario 2 outperformed than simple OLS methods with MAPE value 1.74%. Darshana and Chawalit [24] implemented the hybrid PSO with GA for the same dataset again and improved the MAPE to $2.86\%$ which is still higher MAPE compared to this study.

3.4. Computation Time

A computational time in the forecast system was the length of execution time for a model. The main parameters of execution time are the length of training data, number of variables, processor speed of a computer, and forecasting methods. When the online forecast system is implemented for utility, real-time electricity demand observation data of each day automatically updated in the training dataset so that the execution time can increase. In our experimental setup three different forecasting methods were chosen by keeping other parameters constant. Although the computational time is not in the objective, the computation time of a model could be the crucial factor while choosing the best forecasting methods on similar performance. In this study, computational time to forecast for 24 h was approximately $0.79$ min for an OLS technique, whereas there was four times more computational time for GLSAR. If we follow a similar methodology, FF-ANN needs to forecast with Pre_intervals = 365 (Table 6) which may take several days, and we skipped it. These experiments were conducted on the system having the configuration, Intel Core i5 2.5 GHz processor with 8 GB of RAM.

3.5. Pro and Cons of the Methods

Under the consideration of linearity, homoscedasticity, and independent identically distributed data, the maximum likelihood solution to OLS is considered the best linear unbiased estimator. The implementation of OLS and its extension to GLSAR were the most efficient methods even for heteroscedasticity or auto-correlation to the interpretation of variables. The presence of non-linearity in the samples of a dataset can not be denied, therefore ANN is also implemented. However, these methods (OLS, GLSAR, and ANN) are sensitive to the outliers present in the dataset. Increasing the number of variables possibly causes over-fitting and increases the complexity of the interpretation of variables. For an unbiased estimate, we need the mean of the infinite beta parameter for an instance. In a real scenario, we have only one set of data for one instance. So, the possibility of ‘biased estimates’ cannot be denied. If we consider the quartile regression or Bayesian estimation, the possibility of unbiased estimation could be minimized.

4. Conclusions

This paper presents a novel approach for STDF by constructing four different scenarios so that the model can be trained with an appropriate training dataset. Selection of the proper variables for a model, length of the training dataset is conducted based on experiments. The performance on forecasting accuracy measured in terms of MAPE for Scenario 1 was obtained as 2.72%, $1.88\%$, and $1.97\%$ for FF-ANN, GLSAR(7), and OLS, respectively. This means the proposed simple OLS and its extension to GLSAR methods outperformed the deep learning methodology on forecasting accuracy among four scenarios. Nevertheless, GLSAR had longer execution time than OLS, but significantly shorter than FF-ANN. Therefore, a further comparison of forecasting accuracy is conducted between simple OLS and its extension GLSAR methods. Normally, the atmosphere of Thailand is very hot during day hours and the general belief is that this hot temperature results in high demand for electricity during day hours. The minimum increment rate of demand approximately 50 MW per 1 ${}^{°}$C rise occurs at the morning hours (6 a.m.–7 a.m.) and evening hours (4 p.m.–6 p.m.). The low impact in the morning and evening is because of people at the no work condition as well as the industrial shift changing time. Throughout the day, the impact of temperature responsible for increases by 100 MW–200 MW per 1 ${}^{°}$C rise in temperature. However, the result reveals that the maximum impact of temperature is during night hours rather than day hours at 11 p.m. In this time most people are at home and there is excessive use of electric appliances such as television and other cooling appliances. The comparative study concluded that the forecasting error after the grouping of training dataset according to working days ($1.81\%$), and weekends ($1.74\%$) provided better accuracy compared to the single group of training dataset Scenario 4 ($2.95\%$), i.e., Scenario 1 gave a better forecasting accuracy for working days from simple OLS methods; Saturday and Sunday from Scenario 2. However, Scenario 3 showed the worst accuracy from both the models for holidays. Therefore, it is better to choose Scenario 4 (all the data together) rather than Scenario 3 (holidays data) to forecast the holidays.