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Electrical power is a major factor for the social and economic development of the countries. The consumption of electrical energy will reportedly be doubled in 2040 (IEA, 2018), where comes the need to install new electrical infrastructure.
In Morocco, electricity demand (ED) is experiencing an average increase of 6-7% annually, and the expected electricity consumption in 2030 is 95 TWh. Currently, Morocco consumes 37 TWh for an installed capacity of 9GW. The electricity production field has made it possible to meet 86% of the national ED, and the difference is compensated via the Moroccan Algerian (MA) and Moroccan Spanish (MS) interconnection ().
In Morocco, where air conditioning is very widespread, the seasonal peak takes place in summer. Electricity consumption also varies significantly on the scale of a day: As we can see from the data collected for the ED, there are two-peak consumption per day; Midday peak: this one reflects the launch of the economic and industrial works. Evening peak: begins at around 19h, corresponds to the increase in household consumption and coincides with the end of economic activity.
The main contribution made in this paper is to consolidate a low-carbon energy mix by promoting renewable energies integration into the power grid by:
Modeling and predicting monthly ED in Morocco by 2025
Propose a flexible and low carbon demand model by promoting the contribution of renewable energies within the power grid by 48% in 2025
The remainder of this paper is organized as follows: section 2 describes the problem and presents the data. In section 3, the regression model was studied and a 2025 ED forecasting scenario was elaborated. The proposed algorithm is analyzed in section 4, and the results are presented in section 5. The last section summarizes the results and draws conclusions.
Figure 1 presents the evolution of ED in Morocco from 2000 until 2017. First, the figure shows a slight increase during the first seven years. Then a strong increase is observed since 2007. This may be due to several factors, direct and indirect, such as the increase in the exploitation rate of electronic equipment, climate change, and the acceleration of growth dynamics and modernization.
Monthly ED in Morocco (2000-2017)
Modelling monthly electricity demand
Annual ED in Morocco (1971-2017)
In the literature, several prediction methods are available according to prediction horizons. Every method has its strengths, weaknesses, and changes according to the context and environment of prediction. It is often difficult to identify a prediction method that differs widely from others (Doucouré 2015).
Forecasting techniques are ranging from time series to hybrid models. Reviews research is presented by Bohi and Zimmerman (1984), and by Suganthi and Samuel (2012). In this study, a regression-based model has been used to predict electricity consumption in Morocco in the long-term.
The main objective of multiple regression is to learn more about the relationship between several independent or predictive variables and a dependent or criterion variable. A straight line in a two-dimensional space is defined by the equation (1)
where Y is the variable described by a constant ''a'' and slope ''b'' multiplied by the variable X. Multiple regression is where a dependent variable is described by several parameters, as is shown in equation (2):
Where (b, c, d , n) are the coefficients of the regression
R2 describe the model fit goodness. If R2 adjusted is close to one, it indicates that the model has managed to explain almost all the dispersion thanks to the independent''s variables.
In this paper, a regression-based model has been used introducing gross national product (GNP), population, and 11monthly dummy variables as explanatory variables. The model development was done in excel, and the results are summarized in Table 1.
The P value designates the probability that measures certainty with which it is possible to invalidate the null hypothesis. The more P valued tends to one, the more the null hypothesis is invalidated with more certainty. Table 1 reports that the intercept coefficient with GNP and population are all highly significant with a confidence level of 99%. The coefficient for May is not significant which indicates that ED this month is similar to that of December. All the other dummy variables for the other months are significant, which means that more or less electricity is consumed during the corresponding months than in December.
However, the model still contains a large serial correlation despite its high predictive power. Autocorrelation occurs when the error term observations in regression are correlated. If those values follow a pattern, it means that the model contains autocorrelation. The Durbin-Watson (D-W) is widely used to test the first-order residues independence. The D-W statistic is calculated as follow:
Where ei describe the residuals and n is the number of elements in the sample. D-W statistic value varies between zero and 4. If it is equal 2, it means that the model has no autocorrelation. If''d'' is less than 2, especially a value less than 1, means that the data is positively autocorrelated. If''d'' is substantially above 2 means that the data is negatively autocorrelated. The D-W statistic calculated in this model is estimated at 0.79730711, indicating the presence of positive autocorrelation.
In theory, if the residuals are serially correlated, then the estimate of the coefficients may be unstable. In this study, all the independent variables are statistically significant at a 1% error level. However, autocorrelation could be affecting the results, making it appear significant when it is not.
Back in reviews, two approaches can be used to deal with serial autocorrelation. The first method is eliminating the symptoms of autocorrelation by using another estimation method. Otherwise, preventing autocorrelation from occurring in the first place by adding relevant missing independent variables. There are situations in which autocorrelation cannot be eliminated if the omitted independent variable is not available or cannot be found. To reduce autocorrelation, several methods are presented in reviews, such as the AR (1) method used by (Mirasgedis et al. 2006), and Henley and Pierson (1994). Cochrane-Orcutt Method, feasible generalized least squares (FGLS) or estimated generalized least squares (EGLS).
Cochrane-Orcutt regression is an iterative version of the FGLS method for addressing autocorrelation. This approach uses the following steps for estimating rho.
Step 1: Run Ordinary Least Square (OLS) regression on eq (2) and calculate the residualse1, e2 en
Step 2: Using these sample residuals ei, find an estimate for ρ using OLS regression on
Step 3: Substitute this estimate for ρ in the generalized difference equation
Step 4: Based on step 3, new residuals can be calculated. Go to Step 2.
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