Influence of Climate and Nonclimate Parameters on Monthly Electricity Consumption in Niger

This study examines the impacts of relevant factors (climatic and nonclimatic) on the monthly electricity consumption (MEC) in four major cities in Niger using simple multiple linear regressions (MLRs). Parameters such GDP/capita, air temperature (Tmean), relative humidity (RH), wind speed (WSP), solar radiation (SR), precipitation, and clearness index (K) are used. In addition, two heat indices, heat index (HI) and discomfort index (DI) are calculated to take into account the impacts of high humidity in conjunction with high ambient temperature. Hence, three different models were derived from the aforementioned variables. The three models have been tested using the k-folds cross-validation. Results show that the model with primitive variables such GDP per capita, Tmean, RH, SR, and WSP perform better than the other two models with a coefficient determination R2 equal to 0.87, 0.854, 0.833, and 0.551 for Niamey, Maradi, Zinder, and Agadez, respectively. According to the month considered, the mean absolute percentage error can give a small error for specific combinations of climate variables. The variables such as precipitation and clearness index are found to be not statistically significant.


Introduction
Investigating the influence of relevant factors on the electricity consumption is very important to derive a model that can predict the future energy consumption under changing climate. Indeed, one of the most vulnerable sectors to climate change and variability is the energy sector especially the electricity demand owing to the observed correlation between electricity demand and climate variables during hot periods. Hence, for a sustainable management of the energy sector under changing climate, there is a need to understand the factors that affect the electricity consumption. For instance, the electricity produced needs to be instantly consumed, as it cannot be stored. So, understanding the influence of climate and nonclimatic factors on electricity consumption will help to derive a robust model to face this challenge.
Previous studies have found that the relationship between the electricity demand and the ambient temperature by using the temperature-derived parameters such the cooling degree days (CDD) and the heating degree days (HDD) to solve the problem of nonlinearity between the electricity demand and ambient temperature [14][15][16][17][18]. However, in addition to temperature variable, other primitive climate variables such as relative humidity, solar radiation, and wind speed may also influence the electricity consumption.
Moreover, socioeconomic factors including the gross domestic product, the population, the income, and the consumer behavior have also been found to influence the energy demand but at different timescales [5,19,20].
Nevertheless, there is no study in Niger regarding the influence of climate and nonclimate factors on monthly electricity consumption. Hence, due to the fact that both the influence of climate and nonclimate factors on consumption depend on the specific location, there is a need to carry out such a study in order to help the policymakers in the energy sector to take informed decision in a context of continuous population growth and climate change.
In recent years, many models have been used to study both the influence of climate and socioeconomic parameters on electricity throughout the world. These models include the multiple linear regression (MLR) model, the artificial neural network (ANN), the principal component analysis (PCA), and the autoregressive integrated moving average (ARIMA) [21][22][23][24][25]. Among these models, the MLR presents advantages because it is easy to use and also easy to control since the inputs can be adjusted for each analysis [17,26]. Hence, in this work, the impacts of climate variables and GDP per capita on the monthly electricity consumption in four major cities in Niger (Niamey, Maradi, Zinder, and Agadez) will be investigated using the MLR model. The climate data used include variables such as temperature, RH, WSP, SR, HI, and DI.

Electricity Data.
A time series of monthly electricity consumption (MEC) in kWh, from January 2003 to October 2016 for the four cities in Niger (Niamey, Maradi, Zinder, and Agadez), have been used in this study. The data was obtained from the national agency for electricity (NIGELEC) [27]. The data comprise the aggregated electricity consumption for all the sectors including the residential, the commercial, and the industrial sectors as disaggregated data for individual sectors are not available. Figure 1 presents the electricity share of the different sectors in Niger in 2011. It is worth noting that the residential (household) sector presents the largest share (74.98%) of the total electricity consumption in Niger ( Figure 1).
The monthly electricity of each month is derived by the number of days within this month in order to remove the calendar effect.
The electricity consumption in the four cities depicts seasonal variation and an increasing trend ( Figure 2). The latter could be attributed to the socioeconomic development while the former could be a result of weather fluctuations. The seasonal variation of electricity consumption can be examined with the monthly seasonal variation index defined in equation (1).
where MSVI ij is the index value for month i in year j, E ij is the energy consumption for month i in year j, and the Ej is the average electricity consumption in year j. The MSVI of the electricity consumption for the four cities is shown in Figure 3. From this figure, peaks and valleys can be noticed. For example, the MSVI for Niamey shows two distinct peaks in April-May and October corresponding to the hot months according to the climatology of the city. The high electricity consumption in these months is due to high cooling requirement and refrigeration. Minimum values of the consumption are obtained in December-February for all the four cities. This corresponds to the winter period where low solar radiation is obtained.

Weather
Variables. The weather variables used in this study consist of daily values of ambient temperature, relative humidity, wind speed, solar radiation, and clearness index. The ambient temperature and relative humidity data were obtained from the meteorological service in Niger while the solar radiation data were from the National Center for Solar Energy (CNES), Niamey. In addition to these variables, clearness index was computed using the following formula: where GH is the horizontal global radiation and the G0 is the radiation at the top of the atmosphere. The G0 data were obtained from the NASA power agro climatology website [28]. In addition to these weather variables, two humiditytemperature indices, the heat index (HI) developed by Steadman [29] and the discomfort index (DI), are also calculated using equations (2) and (3), respectively.
where HI is the heat index, T is the temperature in Fahrenheit, H is the relative humidity in %, and C n is the constants

Journal of Energy
In addition to these variables, the socioeconomic parameter such as GDP/capita data has been also considered. Figure 4 shows the annual cycle of the various climate variables considered in this study. For all the cities, high temperature values are observed in summer (March-May) with peaks in May while low values are in winter (December-February). Regarding the relative humidity, the maximum value is observed in August. This is due to the fact that the intertropical discontinuity (ITD) reaches its north most position in August. Looking at solar radiation, the same pattern of variation is obtained compared to temperature variable. Low values are obtained for December-February and August. The low values in December-February are a result of the winter season while in August, it is due to high cloudy conditions that blocks the incoming solar radiation [30]. Table 1 summarizes the relevant statistics for these weather variables. Prior to this, the influence of the population data has been removed by considering energy consumption per capita. Then, all the parameters were considered to build the MLR models.   The general MLR model is formulated using the equation below: where EC is the monthly energy consumption; β 0 , β 1 , …β n are the regression constants which are determined by the ordinary least squares method (OLS); X 1 , X 2 , …X n are the independent variables; and ε is the error term. From this equation, we derive three different models given by the following.
The first model comprises all the primitive weather variables given by eq. (4) where Temp, RH, WSP, SR, K, and GDP are the independent variables considered in this study.
In both model 2 and model 3, the combined effect of temperature and RH has been taken into account by introducing DI and HI, respectively.
1.3.2. Model Validation. The MLR models are validated by using k-folds cross-validation. The k-fold cross-validation is mainly used to overcome the issues of overfitting in predictive modeling [31]. The k-folds cross-validation is performed by dividing the data into k subsets (folds). Then, k − 1 subsets corresponding to 9 subsets in this case were used to train the model and the last subset is left for testing.
The accuracy of the model was verified through the use of mean absolute percentage error (MAPE), and the coefficient of determination R 2 given by equations (9) and (10).
The t test is also used to find out how significant each independent variable is in the regression model. The level of significance is set to 0.05. In other words, all the variables with a p value of less than 0.05 will be considered statistically significant.

Correlations between Per Capita Electricity Consumption
and Parameters. The coefficients of determination R 2 between the energy consumption and the various parameters considered in this study are given in Table 2. From this table, GDP and temperature are the most influential parameters to the MEC. However, their relative contribution depends on the city. Indeed, the highest coefficient of determination (R 2 ) between the MEC and GDP is found for the city of Maradi while the lowest is for the city of Agadez. This might due the ambient temperature which contributes more to MEC in Niamey than in the other cities. This can be attributed to the level of development of each area. Indeed, the electricity consumption in Niamey is more   Figure 5 shows the comparison between the actual and predicted per capita MEC for the four cities for model 1, model 2, and model 3. It can be noted that a close correspondence between the real and predicted MEC values, except for Agadez where a strong difference between the real predicted values of MEC, can be observed. This might be due to the fact that in this city, the electricity is more influenced by the mining activities that were not taken into consideration in any of the 3 models.

Multiple Linear Regression Results.
Based on the coefficient of determination R 2 and mean absolute percentage error (MAPE), model 1 performs better than models 2 and 3. Indeed, for Niamey, 87% of variability in MEC is explained by model 1 while models 2 and 3 explain, respectively, 85.4% and 78% of the variation in MEC. This is confirmed by the MAPEs, which are, respectively, 7 Tables 3-5 show the regression results for model 1, model 2, and model 3, respectively. The different regression coefficients defined in equations (6)- (8) and their corresponding p values were presented in these tables. Model 1 for Niamey shows that all the variables except the precipitation and clearness index are statistically significant at 95% confidence level. However, for Maradi and Zinder, in addition to precipitation and clearness index, the wind speed is also found to be not statistically significant at 95% confidence level. These values are above the significant level set earlier. In contrast, only GDP and temperature are statistically significant at 95% confidence level in Agadez. All the other variables have p values greater than 0.05.
The residual error from the fitted regression models is the difference between the actual and predicted MECs as defined earlier in equations (6)- (8). The residual plot should be normally distributed to comply with the basic assumptions of regression models. The plots of residual errors obtained from the best MLR model for the four cities are shown in Figure 6. The plots show that there is no significance curvature and no major outliers for all the cities except Agadez where some outliers are observed. This confirms that there are not specific patterns between the residuals and observed independent variables. Therefore, we can conclude that the models comply with the multiple linear regression assumptions.   Journal of Energy    Figure 7 shows the monthly MAPE values for the three models. From a general point of view, model 1 performs better than the two other models. In addition, the MAPEs differ from the month and the city considered. For instance, for Niamey, all the models perform well compared to the other cities. The models show very low values of MAPEs (<2%) for February, March, April, July, September, October, and December. In other words, in these months, any of the combination of variables can be successfully used to predict the electricity consumption in Niamey. Conversely, for May, June, and November, the models depict high values of MAPEs (>3%). It is also worth noting that the use of HI or DI instead of Tmean and RH could yield to a good estimate in some months. This is the case for May and August where the use of heat indices resulted to a minimum MAPE than that of Tmean and RH.
For the other cities, the MAPEs are relatively higher than that of Niamey, suggesting the impacts of climate variables are more pronounced in Niamey than the other cities. This could be explained by the fact that Niamey is the largest city in Niger accounting about 40% of the urban population. Indeed, according to Valor et al. [13], climate influences electricity consumption through the response of people to weather. That is, depending on the weather condition, people will increase or decrease the use of electric heating or cooling devices. Consequently, the higher the population, the higher the influence of climate on electricity consumption.

Conclusion
As part of the efforts to anticipate the impact of climate change on the energy sector in Niger, this study examines the influence of weather variables on electricity consumption in four major cities in Niger using the multiple linear regression models and a set of weather parameters. Three different regression models are derived for the weather parameters. Finally, the accuracy of the model is evaluated using the coefficient of determination R 2 and the mean absolute percentage errors. The results obtained are summarized below: (i) The electricity consumption in Niger varies both seasonally and year to year. The former is attributed to the socioeconomic development while the former is due to prevailing weather conditions (ii) Temperature and GDP/capita are the most influential factors that influence the electricity consumption of the four cities (iii) Model 1 was found to be the best model with R 2 equals to 0.87, 0.854, 0.833, and 0.551 for Niamey,  (iv) Precipitation and clearness index are found to be not statistically significant at 95% confidence level for all the cities. However, in addition to these variables, the wind speed and radiation are also not significant for cities Maradi, Zinder, and Agadez In order to improve the ability of this study, future work could also include the influence of urbanization, electricity price, and energy efficiency in the models.

Data Availability
The data will be made available upon request.

Conflicts of Interest
The author declares that he has no conflicts of interest.