Microsoft Word - 17013-Modelling and Forecasting of Residential Electricity Consumption.docx 139 Mathematical and Software Engineering, Vol. 3, No. 1 (2017), 139-148. Varεpsilon Ltd, varepsilon.com Modelling of Nigerian Residential Electricity Consumption Using Multiple Regression Model with One Period Lagged Dependent Variable Runcie Amlabu 1 , Nseobong. I. Okpura 2 , Anthony Mfonobong Umoren 3 corresponding author: umoren_m.anthony@yahoo.com 1,2,3 Department of Electrical/Electronic and Computer Engineering, University of Uyo, Akwa Ibom, Nigeria Abstract This paper presents the modelling and forecasting of residential electricity consumption in Nigeria based on nine years (2006 and 2014) data and multiple regression model with one period lagged dependent variable. A Socio economic parameter (population), and climatic parameter (annual average temperature) are used as explanatory variables in modelling the and forecasting of residential electricity consumption in Nigeria. The results of the multiple regression analysis applied to the data arrived at the model with the least sum of square error as ��� = −36.2458 + 9.7202�� − 12.0265�� + 0.1540���� , where t is the year; ��� is the predicted residential electricity demand in MW/h; �� is the annual population in millions; �� is the average annual temperature in °C and ���� is the residential electricity demand in the year before year t. The error analysis gave coefficient of determinant of 0.913, adjusted coefficient of determination of 0.86 and Root Mean Square Error of 61.86. The forecast results gave 5.11% annual average increase in the electric power demand of the residential sector with respect to the 2014 electricity consumption data. Such results presented in this paper are useful for effective planning of power supply to the residential sector in Nigeria. Keywords: Multiple Regression; Regression Analysis; Error Analysis; Least Square Method; Sum of Square Error; Forecast; Residential Electricity Demand 1. Introduction Across the globe, electricity is one of the most dominant forms of energy. Some of the most common advantages of electricity as a future carrier of energy include its cleanliness, versatility, accessibility and simplicity in distribution. The flexibility of electricity as an energy carrier has contributed to technological innovation and increased industrial productivity in many countries [1]. These advantages have contributed to the increased share of electricity in the total energy consumption in many countries. Accordingly, in advanced economies, the ideal choice for the carrier of energy is electricity. Furthermore, electricity power supply has been identified as the most important commodity for the development of a nation [2,3,4,5,6]. People become easily empowered to work and develop themselves when there is electricity power supply. This 140 development takes place from domestic level to industrial level and can also be transferred from small to medium and to large scale level. Among other things, electricity consumption demand depends on the population and level of industrialization of a country [2,7,8,9,10,11,12]. The increased use of electricity from residential homes to industry has contributed to the increasing demand in electricity consumption worldwide. The growth in demand is even higher in developing countries as the robust economic growth boosts demand for new electrical appliances. Although the rate of growth in electricity consumption may be slower in the industrialized countries, their dependence on electricity may even be higher than the developing countries [12,13,14]. The high demand due to the heavy dependence on electricity requires planning of resources of electricity well in advance to ensure a continuous supply of electricity in the future. In the power industry, proper planning of electric power system requires among other things, modelling of the electric power demand [15,16,17,18]. In this paper, the focus is on modelling of the residential electric power demand in Nigeria. This has become necessary in view of the perennial shortfall in power supply across Nigeria and the sweeping policy changes the government is making to address the challenges in the power sector [3,19,20]. Particularly, multiple regression model with one period lagged dependent variable is considered in the paper for modelling the residential electricity consumption in Nigeria [21,22]. The study is based on nine years (2006 and 2014) data on residential electric power demand in Nigeria. A socio-economic variable is used as parameters along with climatic variable for the modelling of the residential electricity consumption in Nigeria. The socio economic variable is population while the climatic variable is average annual temperature. Finally, performance evaluation of the selected model is conducted using statistical measures such as the Root Mean Square Error(RMSE), coefficient of determination ( �� ) and adjusted coefficient of determination (�����). 2. Methodology 2.1. Sources of data Nine (9) years (2006-2014) data on yearly average residential electricity consumption expressed in megawatt hour (MW/h) are obtained from Central Bank of Nigeria Statistical Bulletin [23] while data on yearly average temperature (in 0C) and population are obtained from the Bulletin of the National Bureau of Statistics [24]. 2.2. Description Of The Models For The Predictor and The Response Variables Multiple regressions with one period lagged of the dependent variable is used to express �� (the yearly average residential electricity consumption) in Nigeria as a linear function of population (�� ), temperature (�� ) and ���� (which is the electricity consumption with one period lagged of the dependent variable). In the model, �� is defined as follows; �� = �(��,��,����) (1) �� = ! + ��� + ��� + "���� + #� (2) where �� is the yearly average residential electricity consumption (in MW/h) estimated at 141 time, t; �� is population at time t; �� is temperature at time t; t is time in years; �, � and " are regression coefficients. A regression coefficient in multiple regressions is the slope of the linear relationship between the dependent variable and the part of a dependent variable that is independent of all other independent variables. Specifically, �, � and " are the contributions of population (P), temperature (T) and ���� respectively and ! is the intercept; #� is a random error or residuals term. Measurement error for the dependent and independent variables, the random nature of human responses and effect of omitted variables are the main sources of the random disturbance [5]. In this study, data for the independent variable, namely, P � and �� are available for the years 2006 to 2014. Mathematical expression for each of the independent variables �� and �� are themselves obtained from models applied to the data sets of these variables over time (t). Particularly, the population for the years beyond 2014 are projected using the mathematical expression; P � = P ���(1 + �)% (3) where n is the number of years, P ��� is previous year population, P � is the population of the year to be estimated and r is the population growth rate of Nigeria which is given as 3.2% according to 2006 population census [4,5]. Also, temperature is predicted using simple linear regression model as follows; �� = &! + &�(') (4) Where β! and β� are the simple linear regression coefficients and t is time in years. The model parameters β! and β� are estimated using MATLAB and the following values are obtained; β! = 34.602 and β� = 0.0613 . Therefore, �� = 34.602 − 0.0613t (5) Where t = time, t= 10,11,…,20. 3. Regression Analysis for the Multiple Regression Model with One Period Lagged Dependent Variable The multiple regression model with one period lagged dependent variable (in Eq. 2) can be written in matrix form as; E = X + ε (6) where • n is the number of sampled points • k is the number of predictor variables. In the given model, the predictors are P*,T* and E*��, hence, k = 3 • E = [E�, . . . , E0] is the n × 1 column vector (or n × 1 matrix) of the response variable which is the electricity consumption • X is an n × (k+ 1) design matrix determined by the regression model predictors whereby the values in the first column of the matrix are all 1. • = [ !, . . . , 1] is k × 1 column vector of parameters (or k × 1 matrix of predictor coefficient) • ε = [ε�, . . . , ε%] is an n × 1 column matrix called the error vector or vector of error terms Let 3 = [ 3�, . . . , 31] be the vector of least squares estimator or predictor coefficient which give the predicted dependent variable E4 that has the least possible value to sum of the squares error. The regression coefficients or least squares 142 estimator, 3 that minimize the sum of the squared errors for the multiple regression are determined by solving the least squares normal equation given as ; X6X( 3) = X6E (7) Then, the least squares estimator β� is given as; 3 = (X6X) �� (78E) (8) Let 9� = X6X and 9��� = (X6X) �� and :� = (78E) , the vector of least squares estimators 3 = (X6X) �� (X8E) = ;9���