Electricity is a vector of development for countries. However, there is a major challenge in optimizing its production due to its integration of intermittent renewable energy sources. On the other hand, the most pressing concern is the efficient management of electrical load demands. Many studies have been carried out on the subject of more efficient and optimized energy management [10]. In this context, Izquierdo-Monge et al. proposed, in their paper, a methodology for optimizing electrical energy consumption in a distribution network that involved equipping the network with intelligence [11]; in [12], the authors proposed microgrid optimization based on a hybridized system of renewable energy resources; Mah et al. presented an optimization of the design and operation of an autonomous microgrid with electric and hydrogen loads, showing a significant reduction in load costs [13]; moreover, a strategy for controlling and managing the energy supply of a microgrid in order to achieve higher efficiency, reliability and economy was proposed in [14] with demand optimization by advanced algorithms such as particle swarm optimization [15].

All of these studies propose scientific methods and approaches with the aim of improving the management of renewable energy systems for the efficient exploitation of these resources to generate balance between supply and demand. To study the response to disruptions caused by the reduction of systems using non-renewable fossil resources in favor of renewable resources in microgrids, a robustness improvement study based on variable-shape LADRC technology for the electrical load interface was conducted [16]. A study on the dynamic analysis of microgrid systems for powering sailboat electrical loads using renewable energy was conducted [17]. Rajamand's objective in [18] is to manage energy consumption by adjusting demand based on supply conditions, often through incentives for consumption during peak periods. Amado et al. improve microgrid efficiency by integrating renewable energy [19].

Developing countries have conducted many studies on electricity to further their development [20] and explores the challenges and strategies for improving electricity access and affordability in these countries [21]. However, the growth of the population at present, causes on the one hand, an increase in electrical energy demand [22] with the modelling of the optimal electricity at long term [23]. The lack of electricity in rural areas then leads to a number of challenges in mobilizing the resources needed for optimal electrification planning [24] taking into account, the techno-economic assessment integrating renewable sources [25]. It is important to electrify rural areas and areas on the outskirts of cities, using power plants not far from these areas, to mobilize local natural resources [26] and to develop integrated energy systems for off-grid [27], in order to minimize distances and electrical losses. These available natural resources can thus be exploited by microgrids [28] with a necessary to optimize their design, operation and integration into conventional power systems [29]. At present, the management of these microgrids and all of electrical network management, are often robust [30] and a robust coordination framework of these microgrids is proposed in [31], because of the daily variation of short- and long-term loads due to the ever-increasing energy needs of the population. This difficulty in pairing the real-time adaptation of electricity production to the demand for electrical energy is explained by the lack of an efficient management program for these microgrids. The lack of a modernized predictive model for the management of these mini-grids in most sub-Saharan countries is a difficulty in the operational planning of these power generation systems. It is therefore necessary to develop optimized prediction models for managing the evolution of microgrid loads.

Thus, machine learning techniques [32] and its importance for forecasting electrical energy consumption (load) [33], used to solve societal problems via different regression methods. In particular, prediction work based on neural network methods [34] for short term loads forecasting in microgrids environment [35] and with his radial basis functions [36] for modelling nonlinear and complex relationships in times series data [37]. Multilayer perceptron (MLPs) approach, and his convolution neural networks (CNNs) have also been presented in [10] and in [38]. Now, artificial neural network has the capacity to imitate biological neural systems [39] and to incorporate fuzzy logic principles to handle uncertainty and imprecision data [40]; so, their applications in science and engineering are presented in [41] and can be tested on real-world data under varying weather conditions such as for example, photovoltaic data [42]. Other models have also been developed, such as the LSTM (Long Short-Term Memory) technique [43] where authors propose and test a CNN and LSTM models reveal that the models behave differently when the number of layers changed over the different configurations; in [44], a short term load forecasting model that integrates a multi-scale CNN-LSTM hybrid approach neural network is proposed; for support vector regression : a proposition of algorithms, has been trained and tested with a significant encouraging result show an accuracy improvement from 20% to 23.4% in [45], and in [46], authors used support vector machine for the forecasting and recommended a combination of this approach with algorithms like artificial neural network (ANN) model and clustering; fuzzy polynomial regression methods is discussed in [47] showing how a fuzzy logic approach can be applied to predict electrical load during holidays; multiple regression in [48] with the aims to improve the accuracy of electric load forecasting by a boosting-based approach; deep learning in [49] advanced in short term load forecasting by combining deep learning with socioeconomic and infrastructural data, offering a practical solution for sustainable management in geographically or economically constrained environments; authors explore in [50], the application of neural networks in wind resource assessment and forecasting; probabilistic methods: in [51], the study likely aims to enhance the accuracy and reliability of industrial load forecasting by adopting a multivariate probabilistic approach involving characterizing the uncertainty in load predictions which is crucial for managing industrial energy systems effectively and an improvement of quantile regression neural network architecture can better capture complex patterns in load data and provide more accurate probabilistic forecasts [52].

Other authors such as, Yasameen et al. [53], have used the Structural Equations Modeling to forecast the impact of the environmental and energy factor to improve urban sustainability; for Afshin Balal et al. [54], it is possible to use the Random forest regression and the LSTM to forecast solar power generation; an application is being carried out in Lubbock, Texas. Meryem El Alaoui et al. [55] have used ARIMA and statistical methods for the prediction of energy consumption of an administrative building. Other works have been carried out to propose also, a model based on LSTM for enhancing power load forecasting accuracy [56] and in [57], a hybrid model based on Gated Recurrent Unit (GRU) and CNN.

Each of these methods has its own specificities; the number of hyperparameters to be defined, according to the model, is often high and the forecasting time is sometimes long.

Table 1 provides an overview of the various methods used to forecast short- and long-term expenses.

Forecasting is the study of a given quantity, whose future evolution can be estimated by calculation [62]. Let there be a training set D containing T pairs of input vectors x and scalars y according to relation eq. (1):

where y_t is a time series and x_t is a vector of dimension d, defined by relation eq. (2):

All input vectors are often combined into matrix X, and the output values into output vector Y, relation eq. (3):

The general model of a time series is given by relation eq. (4):

where f is a function; x_t is the independent variables (or features) at time t; θ is the parameter vector, it represents the parameters of the model that define the relationship between x_t and y_t and are typically estimated from historical data during the model training process; and ϵ_t is a Gaussian noise. The forecast at a future time T+h is obtained by evaluating the function f at the test point x_T+h according to relation eq. (5):

where θ ^ is the vector of parameters from the training data set D. It represents the estimated parameters of the model. Indeed, f( x T+h , θ ^ ) is a function that models the relationship between the explanatory variables and the target variable we want to predict. x T+h represents the explanatory variables at the future time T+h. f is the function that can be linear, nonlinear, a regression odel, or any other type of function that describes the relationship between x and y. The choice of f, depends on the model used.

The regression ensemble method is a collection of regression models used to make prediction much faster and more efficient. It is defined by the following: the space of hypothesis H; a method for combining prediction elements h_t, such as h_{t = 1...T} ∈ H. Part of the regression ensemble method is the adaboost regression method, which is a set of machine learning procedures that consist of combining several sub-predictors to optimize better, prediction. Figure 1 shows the flowchart of the adaboost regressor approach.

Figure 1.

Flowchart of the adaboost regressor approach

The ensemble method thus provides a predictor H(x), such that equations eqs. (6) - (8) [60]:

The goal is to find a sequence of predictor elements h_t and weights α_t such that the previous global predictor achieves a small error.

The proposed algorithm is given:

1. As a given sample (x₁, y₁), (x_i, y_i), …., (x_N, y_N): N training samples set;

2. Initialize the weights vector of the sample: D 1 =( α 1 1 ,… α i 1 ,… α N 1 )), D=1/N. N is the number of training samples;

3. While t < T, T the iteration numbers;

4. Under the probability distribution of training samples:

   the weak learner h_t(x) are trained;

5. The probability P= α t Σ i=1 N α i t;

6. Update weight distribution

   D t+1 =( α 1 t+1 ,… α i t+1 ,… α N t+1 );

   α i t+1 = α i t β 1−| h t ( x i )− y i | ,i=1,2,…,N;

   With weak learner weight α t = 1 2 ln( 1 β t ); β t = ε t 1− ε t

7. Calculate the combination of learners: H(x)= ∑ t=1 T α t h t (x).

The statistical analyses of the data presented in the rest of this study are based on the minimum and maximum values of the data used and the mean, standard deviation and median of these data (eqs. (9), (10), (11)):

where X ¯, x and σ represent the mean, the variable and the standard deviation, respectively. The calculation of the errors inspired in [63] and [64], contained within the model, allowing to appreciate the difference between the predicted model and the real curve, is formulated as follows.

The mean square error by eq. (12):

The average of the absolute errors by eq. (13):

The square root of the mean square error by eq. (14):

The coefficient of determination by eq. (15):

All of these regression metrics are calculated in order to evaluate the error, which is assumed to be minimal.

Electrical load consumption data are presented and averaged over a population of more than 500 households. These data were collected from a renewable energy source photovoltaic solar energy and were obtained from the Electrical Energy Company of Togo. These are the data on which the forecasts were based and, in fact, represent only 0.87 % of the total consumption data for the electrical loads used during this period. The total dataset is around 4100 to 4300.

Figure 2.

General flowchart used for electrical load forecasting and optimal model selection

To perform simulations using Machine Learning techniques, a considerable quantity of datasets is required. In fact, this data represents the consumption of electrical loads over several days by months. Figure 3 shows a part of the global datasets:

Figure 3.

Presentation of a part of load data for simulation

The results are presented and discussed in the next section.

This section presents a study based on forecasting results. The studies present the statistical indicators of the data, then, the various prediction results and the correlation results between the predicted and the real value.

The forecasting results obtained were based on load data recorded on a monthly basis, the statistical indicators of which are presented in Table 2.

Table 2 shows the minimum, maximum, mean, standard deviation and median values of the electrical load data. The number of data analyzed per month is about 4100 to 4300. The maximum value recorded during these half months is 71.974. The overall mean was 16.2, with a standard deviation of around 15.7, showing the non-homogeneity of the consumption load each month and the variance in the data: the load of the installed microgrid therefore varies dynamically.

The results of the electrical loads forecasting, are presented.

The statistical indicators are presented in Table 2.

The following figure, Figure 4, shows the variation over time (by step of 5 min) of the electrical consumption loads (in kW). The forecast results over time are also shown.

Figure 4.

Real curve for the month of January (a); real and forecast curves for January (b)

Figure 4a and Figure 4b, respectively show the actual and predicted electrical loads for the month of January. During this month, the electrical consumption loads recorded are to the order of 70 kW. These loads vary over the course of the month. The results of the learning and test model are shown in Table 3.

The same results are shown for the others months : February, March, April, May, June, July, August, September, October, November and December, respectively in Figure 5a and Figure 5b, Figure 6a and Figure 6b, Figure 7a and Figure 7b, Figure 8a and Figure 8b, Figure 9a and Figure 9b, Figure 10a and Figure 10b, Figure 11a and Figure 11b, Figure 12a and Figure 12b, Figure 13a and Figure 13b, Figure 14a and Figure 14b, and Figure 15a and Figure 15b.

Figure 5a and Figure 5b show respectively the real curve and the forecast curve for the month of February.

Figure 5.

Real curve for the month of February (a); real and forecast curves for February (b)

The real curve and the forecast curve are shown respectively in Figure 6a and Figure 6b for the month of March.

Figure 6.

Real curve for the month of March (a); real and forecast curves for March (b)

The variation of the curves depends on the variation of the data for each month. Figure 7 shows the results of the real (a) and the forecast (b) curves for the month of April.

Figure 7.

Real curve for the month of April (a); real and forecast curves for April (b)

The real curves and the forecast curves for the month of May are presented respectively in Figure 8a and Figure 8b.

Figure 8.

Real curve for the month of May (a); real and forecast curves for May (b)

Figure 9a and Figure 9b show respectively the real curve and the forecast curve for the month of June.

Figure 9.

Real curve for the month of June (a); real and forecast curves for June (b)

However, Figure 10a and Figure 10b show respectively the real curve and the forecast curve for the month of July.

Figure 10.

Real curve for the month of July (a); real and forecast curves for July (b)

Figure 11a and Figure 11b show respectively the real curve and the forecast curve for the month of August.

Figure 11.

Real curve for the month of August (a); real and forecast curves for August (b)

In Figure 12a and Figure 12b, the real curve and forecast curve of the month of September are presented.

Figure 12.

Real curve for the month of September (a); real and forecast curves for September (b)

Figure 13a and Figure 13b show respectively the real curve and the forecast curve for the month of October.

Figure 13.

Real curve for the month of October (a); real and forecast curves for October (b)

Figure 14a and Figure 14b show respectively the real curve and the forecast curve for the month of November.

Figure 14.

Real curve for the month of November (a); real and forecast curves for November (b)

Figure 15a and Figure 15b show respectively the real curve and the forecast curve for the month of December.

Figure 15.

Real curve for the month of December (a); real and forecast curves for December (b)

The results obtained for the various months show the variance in electrical load demands. In fact, these loads are dynamic and show a good correlation with the predicted data.

The results of the forecasting model's performance indicators, in relation to the actual loads, are shown in Table 3, and the model's learning and test results are thus obtained.

The analysis of the various indicators of the model’s performance in Table 3 demonstrates the level of variation present in the data compared to the model, as seen in all the real and forecast curves. In fact, these results show a fairly significant coefficient of determination, indicating that the model is representing real data with a low MAE, MSE and RMSE. This reflects the minimal nature of the errors made by the model, showing that the errors are much smaller than the variance present in the data, which explains the model's performance.

The correlation results between the microgrid-generated consumption loads and predicted consumption loads for all months, are shown respectively in Figure 16a and Figure 16b, Figure 17a and Figure 17b, Figure 18a and Figure 18b, Figure 19a and Figure 19b, Figure 20a and Figure 20b, Figure 21a and Figure 21b.

Figure 16a and Figure 16b show respectively correlation curve for January and February.

Figure 16.

Correlation curve for January (a); correlation curve for February (b)

Figure 17a and Figure 17b show respectively correlation curve for March and April.

Figure 17.

Correlation curve for March (a); correlation curve for April (b)

Figure 18a and Figure 18b show respectively correlation curve for May and June.

Figure 18.

Correlation curve for May (a); correlation curve for June (b)

Figure 19a and Figure 19b show respectively correlation curve for July and August.

Figure 19.

Correlation curve for July (a); correlation curve for August (b)

Figure 20a and Figure 20b show respectively correlation curve for September and October.

Figure 20.

Correlation curve for September (a); correlation curve for October (b)

Figure 21a and Figure 21b show respectively correlation curve for November and December.

Figure 21.

Correlation curve for November (a); correlation curve for December (b)

In the previous figures R-squared denotes R².

These figures show the test results of the developed model by month. The more points nearer the line, means the better the prediction performance. However, it should be noted that the model is not actually fitted directly to the test data, as the latter have the effect of minimizing the model's overfitting for testing purposes. These results therefore show the good correlation between the measured and predicted values. The dynamic variation in load by month, shown in the figures above, demonstrates the usefulness of this study and the accuracy with which a model should forecast trends. The initial results from the forecasting tests in this study are conclusive, with satisfactory performance indicators.

The forecasting results obtained and the calculated performance indices MAPE, MSE, RMSE and R² have allowed to evaluate the proposed model. In fact, these different indicators, by month, reflect the minimization of the error between the actual electrical load consumption data and those predicted. The first MAE results, according to the different months studied (January, February, March, April, May, June, July, August, September, November and December) have values ranging from 1.38 to 2.9. These differences can be explained by the variances in the data for each month, as there were variations in the dynamic loads recorded. Although these values are low, it provides information on the difference between the actual values and those predicted. The results obtained for the MAE therefore show the minimum variation between the actual and predicted data. In addition, the values recorded for the MSE and RMSE of the forecasting model enabled to determine whether deviating values would interfere with the forecasting data. These values being relatively low indicates that the accuracy of the model is high. Finally, the R² coefficient, which expresses the correlation between actual and predicted data, shows that, on average, over 90% of the actual load data is represented by the proposed model. This indicates the accuracy of the predictive model in relation to the electrical consumption data.

In general, the minimization of performance indicators reflects the optimal forecasting of electricity demand, necessary to minimize the cost of energy supply or production. Indeed, if the deviations (errors) between actual and predicted data are significant, this would mean that the model would be less efficient and, consequently, could lead to significant financial losses; hence the importance of developing models that minimize errors as much as possible. In addition, these studies contribute to the management of the electrical load and are necessary for any study contributing to the optimization, for example, of the electrical network installation (microgrids): previous studies carried out by Kabe et al. [65].

Indeed, the model of adaboost regressor proposed, learns better and minimize significant errors. It is therefore recommended that network managers opt for more accurate models with minimized errors, such as the one proposed in this article. The proposed model demonstrates its excellent performance in forecasting electrical loads. The minimization of its performance coefficients such as MAPE, MSE, RMSE and R² show the accuracy of the proposed model.

However, a more extensive study with other approaches of forecasting electrical loads consumption could be envisaged in order to appreciate the limitations of the model.