Adaptive Neuro-Fuzzy Inference System (ANFIS) Model for Forecasting and Predicting Industrial Electricity Consumption in Nigeria

The main aim of this paper is to model the industrial power consumption in Nigeria with the Adaptive Neuro-Fuzzy Inference System (ANFIS) model and then forecast the industrial power consumed for the next five years beyond the available data. About 45 years (1970 to 2015) dataset was obtained from the Central Bank of Nigeria (CBN), the National Bureau of Statistics (NBS) and other relevant organizations. The data includes population, rainfall, electricity connectivity and temperature which are the explanatory variables. Matlab was used along with the dataset to train and evaluate the ANFIS model which was then used to forecast the industrial power consumption in Nigeria for the years 2016 to 2020.The prediction performance of the ANFIS model was compared to those of Autoregressive Moving Average model and Moving Average model. From the result obtained, ANFIS gave R-square value of 0.9977 (99.77%), SSE value of 395.3674 and RMSE value of 2.9641. The regression coefficient of 99.77% shows that about 99.77% of the variations in the industrial power consumption in Nigeria for the years 1970 to 2015 are explained by the selected explanatory variables. The forecast result showed that the Nigerian industrial power consumption would be about 374.7 MW at the end of 2020 which is about 73.1% increase from the industrial power consumption in 2015. As such, based on the industrial power consumption in 2015, over 73% increment in power supply to the industrial sector will be required to satisfy the industrial sector’s power demand in 2020.


Introduction
Forecasting is the act of making prediction of future events and situations. In different areas of life, forecasting is the basic technique of decision making targeted at minimizing risk in decision making and reducing unanticipated cost [1,2,3]. Accordingly, in the power industry, correct prediction of future load demand enables power utility companies to supply electrical energy to the consumers economically. Particularly, it allows power utilities companies to plan their operations such as unit commitment and generator maintenance beforehand, and thus, serve their customers with more reliable and more economically efficient electric power [4,5,6,7]. This has become important seeing that energy resources are often limited along with challenges emanating from environmental factors [8,9,10,11,12]. Studies have shown that geographical location, population, social factors and weather factors have different impacts on power systems [11,12,13,14,15,16].Therefore, accurate load forecasting model that takes into consideration the essential factors that do affect the power demand pattern is important in power system planning.
Consequently, in this paper Adaptive Neuro-Fuzzy Inference System (ANFIS) technique is used to model and forecast the industrial electricity consumption in Nigeria [16,17,18,19,20]. This has become necessary as Nigerian government is focused on diversifying its economy by facilitating more indigenous technologies, expanding its small and medium scale enterprises and attracts more foreign investments [21,22,23,24,25,26]. ANFIS which is a kind of artificial neural network that is based on Takagi-Sugeno fuzzy inference system was developed in the early 1990s [27,28,29,30,31,32,33]. ANFIS integrates both neural networks and fuzzy logic principles and it has the potential to capture the benefits of both neural networks and fuzzy logic in a single framework [34,35,36,37,38].
One of the advantages of fuzzy systems is that they describe fuzzy rules, which fit the description of the real-world processes to a greater extent [2,39,40,41,42,43,44]. Another advantage of fuzzy systems is their interpretability; it means that it is possible to explain why a particular value appeared at the output of a fuzzy system. In view of its salient attributes, ANFIS has been employed in a number of studies including those concerning load forecasting [45,46,47,48,49].

Collection of Data
In this paper Adaptive Neuro-Fuzzy Inference System (ANFIS) is used in modeling the industrial electricity consumption in Nigeria and then to forecast the industrial electricity consumption in Nigeria from 2016 to 2020. The 45 years (1970The 45 years ( -2015 data used in the study was collected from various publications of the Central Bank of Nigeria (CBN) and the National Bureau of Statistics (NBS). The data collected include: industrial electricity consumption, temperature, connectivity, population and rainfall. The data is given in Table 1.
The raw data is normalized to within the range of 0.1 to 0.9 using the equation.

=
( 1) where is the normalized data of the original values of the explanatory variables, x is the raw values of the explanatory variables (temperature, rainfall, population, connectivity and actual industrial electricity consumption).
is the maximum value of the explanatory variables (temperature, rainfall, population, connectivity and actual industrial power consumption). This normalized form is chosen because it tends to provide a better outcome on the Predicted Industrial Power Consumption (Predicted IPC). About 60 percent (60%) of the original data was used as training dataset whereas 40 percent (40%) of the dataset was used as the validation dataset.

Development of the Adaptive Neuro-Fuzzy Inference System (ANFIS) Model
Four unique inputs namely temperature, rainfall, population and electricity connectivity which were the explanatory variables were used in this work. Also, one output, the industrial power consumption was used in this work. The input data are converted to degrees of memberships and membership values in a process called fuzzification. The triangular membership function was used for the four inputs as well as the output. Each of the four inputs was divided into three triangular membership functions. Also, the output was divided into three triangular membership functions. The input variables (explanatory variables) and the output variables were imported to the ANFIS environment via the workspace key after clicking on load data. The outcome of these commands can be seen in Figure 1. Fuzzification process was performed in the MATLAB FIS editor and the outcome is given in Figure  2.The ANFIS structure is given in Figure 3 which shows the four input neurons with each neuron connected to three membership functions as it is also in the fuzzy part of the system. Membership function for each of the explanatory variables is shown in Figure 4 to Figure 7. The number of fuzzy logic rules used was two hundred and forty-six (246) as shown in Figure 8.       The ANFIS graphic user interface showing the error of the epoch is shown in Figure 9, while Figure 10 shows the checking of the ANIFIS predicted data. According to Figure 9, after simulating the system under 40 epochs (40 iterations), with the normalized dataset the error of the ANFIS system at the 40th iteration was 0.00076577, after checking ( Figure  10), the minimal error was 0.61265. With this minimal error of 0.00076577, it shows that the ANFIS can be used to effectively predict the industrial power consumption in Nigeria.

Other Models Considered
The prediction performance of the ANFIS model was compared to that of two other regression models namely, Autoregressive Moving Average Model and Moving Average Model. The models are developed from the same dataset used for the training of the ANFIS model. The autoregressive moving average model is expressed as follow; The moving average model is expressed as follows; The moving average model for predicting industrial power consumption is given as: Where −1 is −1 Table 2 shows the normalized data for the prediction of industrial electricity consumption in Nigeria with Adaptive-Neuro Fuzzy Inference System (ANFIS) model and the normalized ANFIS model predicted industrial power consumption in Nigeria for the years1970 to 2015. Table 3 and Figure 11 show actual industrial power consumption in Nigeria (MW) and the ANFIS model predicted industrial power consumption in Nigeria for the years1970 to 2015.

Results and Discussions
Based on Table 3 and Figure 11, the regression coefficient between the actual industrial power consumed and the ANFIS model predicted industrial power consumed is 0.9977 (99.77%), the SSE is 395.3674 and RMSE is 2.9641.The regression coefficient of 99.77 % shows that about 99.77% of the variations in industrial power consumption in Nigeria for the years 1970 to 2015 are explained by the selected explanatory variables.   The comparison of the actual industrial power consumed with the Autoregressive moving average model predicted industrial power is shown in Figure 12. Also, the comparison of the actual industrial power consumed with the moving average model predicted industrial power is shown in Figure 13. The prediction performance of the three models considered in this paper is shown in Table 4. The results in Table 4 show that among the three models the ANFIS model has the best prediction performance. In this study, the ANFIS model was developed (trained) using 60% of the dataset which consist of the data from 1970 to 2001. Also, the ANFIS model was validated using 40% of the dataset which consist of the data from 2002 to 2015. Again, Table 4 shows that the prediction performance of the ANFIS model with respect to the training data and also with respect to the validation data are very good. As such, the ANFI model was used to forecast the industrial electricity consumption in Nigeria from 2016 to 2020. The ANFIS forecast result is shown in Figure 14 and Table 5. From Figure 14, Nigeria shall witness the least industrial power consumption in October of 2017 with a total industrial power consumption of about 323.2 MW. The Nigerian industrial power consumption will be about 374.7 MW at the end of 2020. This is about 73.1% increase from the industrial power consumption in 2015. As such, based on the last published industrial power consumption in 2015, over 73% increment in power supply to the industrial sector will be required to satisfy the industrial sector's power demand in 2020.  1970 1975 1980 1985 1990 1995 2000 2005 1970 1975 1980 1985 1990 1995 2000 2005 7 1970 1975 1980 1985 1990 1995 2000 2005 1970 1975 1980 1985 1990 1995 2000 2005

Conclusions
Development and evaluation of Adaptive Neuro-Fuzzy Inference System (ANFIS) model for characterizing the industrial power consumption in Nigeria is presented. About 45 years data on industrial power consumption in Nigeria, population, rainfall, electricity connectivity and temperature was obtained relevant organisations where population, rainfall, electricity connectivity and temperature are the explanatory variables. Matlab was used along with the dataset to train and evaluate the ANFIS model which was then used to forecast the industrial power consumption in Nigeria for the years 2016 to 2020.The prediction performance of the ANFIS model was compared to those of Autoregressive Moving Average Model and Moving Average Model. In all the results obtained, ANFIS gave very high and acceptable R-square value which showed that about 99.77 % of the variations in industrial power consumption in Nigeria for the years 1970 to 2015 are explained by the selected explanatory variables. The forecast result showed that based on the industrial power consumption in 2015, over 73 % increment in power supply to the industrial sector will be required to satisfy the industrial sector's power demand in 2020.