Journal of Applied Engineering and Technological Science Vol 3(1) 2021 : 1-9 1 FORECASTING ELECTRICITY DEMAND IN GHANA WITH THE SARIMA MODEL P. Y. Andoh1*, C. K. K. Sekyere1, L. D. Mensah1,2, D. E.K. Dzebre1,2 Department of Mechanical Engineering, Kwame Nkrumah University of Science and Technology (KNUST), Kumasi, Ghana1 The Brew Hammond Energy Centre, KNUST, Kumasi, Ghana.2 *pyandoh.coe@gmail.com Received : 27 October 2021, Revised: 04 December 2021 , Accepted : 16 December 2021 *Coresponding Author ABSTRACT Demand forecasting is a challenging subject of interest to many organizations whose main focus is to improve their steady growing customer request/demand, and help in increasing their revenue generation. The story is no different in the power industry. It is quite difficult for power or electrical producers to store high quantum of the energy produced, hence this poses a challenge in estimating precisely the quantum of electrical energy in order to equate demand and supply of powers as well as reducing or eliminating the rising transmission losses. This study explores potential time series models in electricity demand prediction or forecasting for the Western Regions of Ghana. Secondary data was sourced formally from the regional headquarters of ECG to aid in research design to be able to estimate the quantum of electricity needed by consumers in the region. This was done using time series data analysis toolpak software. Results show that the models formulated are viable for future consumption forecasts and other investment in alternative power source projects in meeting these future demands. Since there are up-surging energy demand patterns in the region, the flexibility of the formulated models can be very useful and supplementary to framing effective and efficient energy policies. Keywords : Electricity demand, Forecasting SARIMA, Ghana 1. Introduction Accurately modeling and forecasting electricity demand is a very important issue for decision making in deregulated electricity markets. For the efficient management of day-to-day operations of a power system, short term forecasts are very important (Jain et al., 2009), whereas for generator maintenance, acquiring energy resources, balance sheet calculations, new structural investment based on the anticipation of future demand or for long term bilateral contracts to ensure low financial risk, medium and long term forecasts are usually utilized. Efficient and reliable electricity generation, transmission and distribution are critical to achieving accelerated growth in all sectors of Ghana’s economy. As Ghana’s industry base started growing rapidly in the early 2000s, there was a commensurate increase in the country’s national electric energy consumption from approximately 364 kilowatt-hours per capita (kWh/capita) in 2000 to 534 kWh/capita in 2020 (Asumadu-Sarkodie and Owusu, 2016a; Energy Commission of Ghana, 2021). Even with increases in generating capacity over the years arising from public and private sector participation, there are still severe challenges with reliable supply due to growing demand and network instabilities emanating from technical challenges with thermal generation which now constitutes over 64% of Ghana’s gross generating capacity (Energy Commission of Ghana, 2021. Electricity forecasting can be employed for demand side management. In demand side management, customers are cautioned on energy saving tips in conserving electricity during the high demand periods called the peak hours and utilize it during the low peak hours. Statistical models such as regression models, exponential smoothing and time series models are widely used for electricity pricing and demand forecasting problems. These models generally perform better in cases of short-term forecasting and are extensively studied (Cheng et al, 2015; Trindade, 2002; Kim et al., 2002; Kyriakides and Polycarpou, 2007; Taylor and McSharry, 2007; mailto:*pyandoh.coe@gmail.com Andoh, et. al… Vol 3(1) 2021 : 1-9 2 Weron and Misiorek 2005; Baki et al, 2005; Abdel-Aal et al, 1997). Exponential smoothing method uses a weighting factor known as the smoothing constant (parameter) that reflects the weight given to the most recent data values. Smoothing constant value lies between 0 and 1 and it determines the degree of smoothening and consequently, how responsive the model is to the fluctuations in the data (Bosq, 2015). In the electricity context, these techniques have been widely used to model and predict electricity demand and prices. In the short term forecast the techniques generally produce better results as greater weights are given to more recent observations. However, the forecast is relatively sensitive to the specification of the smoothing constant. In general, these methods are capable of accounting for both the time correlation and random nature existing in the underlying phenomenon. To account for the possible correlation among different load periods, vector autoregressive (VAR) models are also used to forecast demand series (Sulugodu & Deka 2019; Ang, 2005). Proper demand management facilitates the planning and use of resources for positive and profitable results, and may involve marketing programs designed to increase or reduce demand in a relatively short time (Feinberg and Genethliou, 2005; Louie, 2017). The ability to estimate demand depends on a medium of unearthing the values for demand in future crises. This explains the critical role of demand forecasting in managing every business entity. The decision of an organization to invest and/ or expand an existing or new infrastructure, increase human resource capacity and process/procedure depend on what the future depicts, (Boisseleau, 2004). The key roles or benefits of forecasting in demand management are in: stabilizing employment and production, taking management decisions, evaluating performance, planning of facilities and an optimal day-to-day operation of the plants. (Feinberg and Genethliou, 2005; Kyriakides and Polycarpou, 2007; Hahn and Nieberg, 2009; Sarkodie, 2017; Adom and Bekoe, 2012). Hahn and Nieberg (2009), in their extensive review of methods and models for load demand forecasting found that, though may suffer from numerical instabilities, time-series methods such as the Autoregressive Integrated Moving Average Model (ARIMA) model, are commonly used in load forecasting. The ARIMA model is a special kind of a regression model which comprises an Autoregressive (AR) component and a Moving Average (MA) component that are dependent on past values and past errors, respectively. ARIMA models are comparatively good in modeling and forecasting as compared to other linear time series models. However, these models are not capable of capturing both seasonal and non-seasonal patterns in a time series. An extension of these models to capture seasonality is the Seasonal Autoregressive Integrated Moving Average (SARIMA) model. A time series is described as exhibiting seasonality if there exists a regular pattern in changes that repeats over several time intervals until the patterns repeat again. SARIMA models are well known for statistical modeling and forecasting but are, however, unable to extract nonlinear relationships within the time series data (Box and Jenkins, 1976; Meese and Geweke, 1984; Harvey, 1990; Marcellino, 2007; Atilla et al, 2007; Shitan and Peiris, 2011; Stock and Watson, 1996; Stock and Watson 2003; N.B Ahmed, 2018; Asumadu-Sarkodie and Owusu, 2016d; Box et al, 1987; Jiang et al, 2018). A significant amount historical demand data exists for the Western regions of Ghana, however, this data which is generated within a 24-hour base has only been used for monthly billing of customers rather than gathering other insights from it to help improve on customer satisfaction and facilitate strategic decision making. The SARIMA model is touted as having the capability to predict more accurately than traditional forecasting techniques. This study therefore seeks to evaluating the effectiveness of SARIMA in predicting electricity demand using data from the Western Region of Ghana 2. Research Methods 2.1. Case Study Area The Western (i.e. Western and Western-North) Regions of Ghana are located at the southern part of the country, along the Atlantic Ocean. The area is regarded as one of the agro- based regions in the country due to its fertile soil and favorable rainfall pattern. The area has a projected population of almost three million, one hundred thousand (3, 100, 000) (Ghana Statistical Service, 2021). Andoh, et. al… Vol 3(1) 2021 : 1-9 3 The area covers a total land area of approximately twenty-four thousand square kilometers (24, 000 sq. kms). The area is blessed with abundant natural resources like gold, bauxite, diamond, manganese, as well as the commercial discovery of oil and gas known as the black gold. The presence of these mineral resources makes the regions view themselves as some of the most tax resourceful regions to the government in executing its mandate to the area and the country as a whole. Over the past decade, more than 58% of electricity generated or produced in Ghana has been utilized by the non-residential and industrial sectors (Energy Commission of Ghana, 2020), of which the quantities consumed by mining companies in the Western Region of Ghana cannot be ignored. 2.2. Data Collected Electricity cannot be stored in large quantum, hence, one can describe its demand and utilization as just in time; that is, once produced, electricity must be transmitted and distributed promptly for its usage. The continuous usage of this electrical power allows metering and billing to be done from seconds to years, as appropriate, by the distributing company. This monitoring and metering are done through the usage of advanced smart meters, some of which are prepaid meters, whilst others are postpaid meters. Postpaid or prepaid advanced smart meters are installed at noticeable and readable points by the distribution companies in the region to capture the inflow and usage of electrical power by customers. The meters are calibrated to record electricity usage by every customer for billing purposes. The daily usage of electricity is collated into months, and then translated into financial terms to be paid by the customers. Domestic electrical connectivity ensures that electrical power is stepped down to a safe voltage level of about 250 volts using a transformer. Industrial or commercial users demand higher amounts of connectivity to power their high consuming electrical gadgets. It is in this vein that the distribution company decided to segregate its customers into three specialized categories to facilitate determining the connectivity quantum, decide on the appropriate connectivity apparatus, as well as, estimating the right billings for revenue generation. The Special Load Tariff group of customers is made of high consuming industries who demand a minimum of 100 KVA of electricity, the Non-Special Load Tariff customers are electricity consumer groups consuming below the one hundred kilo voltages (˂100 KVA) and due to inefficiencies and unreliability of electricity consumption data as well as the alarming rate of electricity theft among the Non-Special Tariff customers, an advanced metering device that allow customers to purchase credits before accessing electricity other than the using power before payment system (Prepaid Tariff Customers) was also introduced. The monthly consumption of electricity by the three groups of customers from January 2008 to December 2013 was used as historical data for forecasting 2.3. Data Analysis and Modelling The Seasonal ARIMA forecasting technique is adopted for this study. The Seasonal ARIMA model is usually denoted in the form ARIMA (p, d, q) ∗ (P, D, Q)s where: p is the number of non-seasonal Autoregressive component; q is the number of non-seasonal Moving Average component; d is the order of non-seasonal differencing; P is the number of seasonal AR component; Q is the number of seasonal MA component; D is order of seasonal differencing and s is time span of repeating seasonal pattern and can be represented monthly as s = 12. (Shi et al, 2011). The seasonal ARIMA model incorporates both non-seasonal and seasonal factors in a multiplicative model. It can be written as: ARIMA (p, d, q) X (P, D, Q) S The general form of seasonal model SARIMA (p, d, q) (P, D, Q) s is given by: 𝝓(𝑩)𝜱(𝑩)𝒔(𝟏 − 𝑩)𝒅(𝟏 − 𝑩)𝒔𝒚𝒕 = 𝜽(𝑩)𝜣(𝑩 𝒔)𝜺𝒕…………………………………….… 2.1 where ∅(𝑩) = 𝟏 − ∅𝟏𝑩 − ∅𝟐𝑩 𝟐 − ⋯− ∅𝒑𝑩 𝒑………………………………………………….. 2.2 𝜱(𝑩𝒔) = 𝟏 − 𝜱𝟏𝑩 𝒔 − 𝜱𝟐𝑩 𝟐𝒔 − ⋯− ∅𝒑𝑩 𝒑𝒔…………………………………..…………. 2.3 Andoh, et. al… Vol 3(1) 2021 : 1-9 4 𝜽(𝑩) = 𝟏 + 𝜽𝟏𝑩 + 𝜽𝟐𝑩 𝟐 + ⋯+ 𝜽𝒑𝑩 𝒑…………………………………………………… 2.4 𝜽(𝑩𝒔) = 𝟏 + 𝜽𝟏𝑩 𝒔 + 𝜽𝟐𝑩 𝟐𝒔 + ⋯+ 𝜽𝒑𝑩 𝒑𝒔…………………………………………..…… 2.5 and yt is the time series observation at time period (t), B is the backward shift operator, εt is a sequence of error term with mean zero and constant variance (σ 2), ϕ(i) and Φj are the non- seasonal and seasonal AR components respectively, θi and Θj are the non- seasonal and seasonal MA components respectively. The non-seasonal components are: AR: ∅(𝑩) = 𝟏 − ∅𝟏𝑩 − ⋯− ∅𝒑𝑩 𝒑……………………………………………………...… 2.6 MA: 𝜽(𝑩) = 𝟏 + 𝜽𝟏𝑩 + ⋯+ 𝜽𝒒𝑩 𝒒……………………………………………………..… 2.7 The seasonal components are: Seasonal AR: 𝝋(𝑩𝑺) = 𝟏 − 𝝋𝟏𝑩 𝑺 − ⋯− 𝝋𝑷𝑩 𝑷𝑺…………………………………....…… 2.8 Seasonal MA: 𝝑(𝑩𝑺) = 𝟏 + 𝝑𝟏𝑩 𝑺 + ⋯+ 𝝑𝑸𝑩 𝑸𝑺………………………………………… 2.9 The preliminary values of autoregressive order p, the order of differencing d, the moving average order q and their corresponding seasonal parameters P, D and Q were estimated with the help of anomalies identified from a time plot of the data. When preliminary values of D and d have been fixed, the Autocorrelation Function (ACF) and the Partial Autocorrelation Function (PACF) were checked to confirm that the values of P, Q, P and q were acceptable stating parameters for the model (Stoffer and Dhumway, 2010). The model was then tentatively generated with the estimated parameters and the corresponding standard errors. The predicted models were validated using historical data from January 2014 - December, 2020. 3. Results and Discussions 3.1 Result The model for the three Load Tariff monthly time series was based on the ideas of the Box-Jenkins methodology. This methodology seeks to fit a Seasonal Auto Regressive Integrated Moving Average Model to the given series. The data was decomposed into its trend, seasonal and random components as presented in Figures 3.1 to 3.3 Fig. 1. Decomposition of additive time series for the Special Load Tariff Customer Andoh, et. al… Vol 3(1) 2021 : 1-9 5 Fig. 2. Decomposition of additive time series for the Non-Special Load Tariff Customer Andoh, et. al… Vol 3(1) 2021 : 1-9 6 Fig. 3. Decomposition of additive time series for the Prepaid Load Tariff Customer The results obtained by following the modeling procedure outlined in Section 2.3 are shown in Tables 1 and 2. Three distinct models were produced for each load tariff and the entire region. The adequate model for each load tariff was obtained using the F-criterion (the least or minimum sum of squared estimate of error). Table 1 - Model for three Load Tariff Data Type of Customer Parameters Models SARIMA (0,1,1)×(0,0,2) SARIMA (1,1,0)×(0,0,2) SARIMA (1,1,1)×(0,0,2) Special Load Tariff Data φ1 -0.4808 ± 0.20 -0.0118±0.33 ψ1 -0.6991 ± 0.17 -0.6930± 0.24 Ψ1 0.1245 ± 0.27 0.1212 ± 0.26 0.1240±0.27 Ψ2 0.4338± 0.38 0.4294± 0.40 0.4331±0.38 SSE 606.64 699.96 606.74 Non-Special Load Tariff Data φ1 -0.4318 ± 0.208 -0.0692 ± 0.281 ψ1 -0.8044 ± 0.148 -0.0818 ± 0.160 SSE 1671.518 2144.627 1666.005 Prepaid Load Tariff Data δ 0.2187 ± 0.275 φ1 -0.3957 ± 0.653 -0.4158 ± 0.225 ψ1 -0.3589 ± 0.205 -0.0035 ± 0.208 Φ1 0.3328 ± 0.232 -0.3661 ± 0.235 0.3490 ± 0.231 SSE 93.66789 91.47522 88.54043 Table 2 - Models for the Regional Load Tariff Data Parameters Models SARIMA (1,1,3) SARIMA (2,1,0) SARIMA (2,1,1) φ1 -0.1516 ±0.710304 -0.4275 ± 0.200704 0.0276 ± 0.380632 φ2 -0.4874 ± 0.197568 -0.3259 ± 0.288708 ψ1 -0.3973 ± 0.689528 -0.6291 ± 0.398076 ψ2 -0.5061 ± 0.148372 ψ3 0.1959 ± 0.312228 SSE 3607.437 3956.292 3726.168 3.2 Generation and Validated of the Predicted Model From Table 1, the SARIMA (0,1,1) × (0,0,2) model was chosen for the special load tariff data because it has the least or minimum sum of squared estimate of error (SSE) which yields the least square of data regression line and the corresponding best model is written out as Xt− Xt−1 = εt+0.6991εt−1−0.087037εt−2−0.4338εt−24−0.3032696εt−25 ………...……… 3.1 The SARIMA (1,1,1) model was chosen for the non-special load tariff data because it has the least/minimum sum of squared estimate of error (SSE) which yields the least square of data regression line with the best model. This is expressed as, Xt− Xt−1 = εt−0.8044εt−1…………………………………………………………………. 3.2 The SARIMA (1,1,0) × (1,0,0) model was chosen for the prepaid load tariff data because it has the least/minimum sum of squared estimate of error (SSE) which yields the least square of data regression line and its best model is written out as Xt−0.5842Xt−1−0.4158Xt−2−0.3490Xt−12+0.2039Xt−13+0.1451Xt−14 = εt+0.2187…...…. 3.3 Finally, the SARIMA (0,1, 1) × (1,1,3) model was chosen for the regional load tariff data because it has the least/minimum sum of squared estimate of error (SSE) which yields the least square of data regression line. The best model is written out as Xt−0.8484Xt−1−0.1516Xt−2 = εt−0.3973εt−1−0.5061εt−2+0.1959εt−3……………….…. 3.4 Andoh, et. al… Vol 3(1) 2021 : 1-9 7 The models obtained were then validated by comparing the predicted result and the recorded results for the 84months period from January, 2014 to December, 2020 and the results for the four customers are presented in Figure 4. NOTE: SLT for Special Load Tariff; NSLT for Non-Special Load Tariff; PLT for Prepaid load Tariff; RLT for Regional Load Tariff Fig. 4. The percentage Error for the four Customers For the purpose of this study, an error of ≤1 GW/was chosen as a criterion to determine the relative difference in results between actual electricity consumption data and predicted data. From Figure 3.4, the results indicate that the predicted values of the model are close to the true value, ranging from -6.00% to 6.00%. The predicted electricity consumption for the Special Load Tariff group of customers resulted in 53.36±1.02 GW/HR @ 95% confidence level whilst the predicted electricity consumption for the Non-Special Load Tariff group of customers resulted in 25.65±0.34 GW/HR @ 95% confidence level. Also, the predicted electricity consumption for the Prepaid customers had an average use of 14.95±0.67GW/HR @ 95% confidence level as a monthly amount of 101.09±0.23 GW/HR @ 95% confidence level was used for the whole region. The models obtained are, therefore, adequate to be used to forecast monthly electricity consumption for all the three Load Tariff Customers. In conclusion, it can be summarized that, with a confidence level of 95%, models developed produced a reliable result that can help guide in the future estimation of electricity to be used by the various categories of customers as well as a means of revenue projection and expansion of the company’s customer network base. 5. 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