The study area considered in this study is Bamenda in the North West Region of Cameroon, as shown in Figure 2 . Bamenda is the main city of the North West Region, and is located at latitude 5.961˚N and longitude 10.152˚E. The study area was chosen because it is one of the localities in the North West Region targeted in the Renewable Energy Master Plan (REMP) of Cameroon for the deployment of solar PV generation stations [17] .

The dataset for the study incorporates six meteorological variables as input (direct beam irradiance, diffuse irradiance, reflected irradiance, sun height, ambient temperature, and wind speed) and one output variable (PV power). Given the absence of datasets with ground measurements of these input and output variables for the study area, a dataset with a four-year time range (2017-2020) and hourly resolution was downloaded from Photovoltaic Geographical Information Systems (PVGIS); a platform which provides information on solar radiation and solar PV power generation potential for all locations in Europe, Africa, and a large part of

Asia and America. The PVGIS data is obtained from satellite images and very high-quality European Center for Medium-Range Weather Forecasts (ECMWF) Reanalysis version 5 (ERA5) data, which has hourly estimates of a large number of atmospheric, land, and oceanic variables from 1940 up to date [19] . The raw data used in this study was made up of 35,064 records with the above-mentioned input and output variables; and enabled the forecast of the solar PV power generation potential of a 20 kW solar PV system in Bamenda, Cameroon.

The first step in data preparation was feature selection. The six meteorological inputs and PV power output in the downloaded dataset were retained given that they align with the features in previous research reported in [20] . Although other features such as humidity, and precipitation affect solar PV power, they do not show any dominant relationship with solar PV power generation [21] .

The second step in data preparation involved preprocessing. Data preprocessing is essential in Machine Learning (ML) because raw data usually contains duplicates, outliers, and missing values. Preprocessing was used to properly clean and transform the data into a format suitable for ML. The data obtained for this study was preprocessed using Microsoft Excel and MATLAB software. While Microsoft Excel was used to search for and remove duplicates from the dataset, MATLAB was used to remove outliers and missing values. The third and final step in the data preparation was splitting the preprocessed data into training and testing sets. In line with previous research, during the splitting, 80% of the data was retained for training and 20% for testing [20] .

The preprocessed data comprised of six input variables or features (direct beam irradiance, diffuse irradiance, reflected irradiance, sun height, ambient temperature, and wind speed) and one output feature (solar PV power). The dataset used in this study contained more features as compared to two and four features in [21] and [22] , respectively.

Solar PV power generation is dependent on meteorological conditions, implying that different meteorological parameters affect solar PV power generation differently [23] . Therefore, meteorological parameters were considered independent variables, used to forecast generated solar PV power as the dependent variable.

Machine learning techniques (MLTs) also referred to as machine learning algorithms (MLAs) often comprise two or more machine learning models (MLMs). Twenty-four MLMs stemming from six MLTs were trained, validated, and tested. The most accurate and better-yield model was later identified and selected for forecasting solar PV power. The MLMs considered in this study are presented below and summarized in Table 1 .

Linear Regression models are supervised MLMs that use a polynomial slope-intercept form to connect the independent and dependent variables. In this case, the expected output is a continuous number. Linear Regression models learn the best fit of the line between the inputs (independent variable) and the outputs (dependent variable). This is achieved by minimizing the approximated error from the forecasted and actual responses [24] . The relationship between the input/independent variable, X, and the output/dependent variable, Y, is given by Equation (1) [11] .

$Y={\beta }_0+{\beta }_{1}X+\epsilon$ (1)

where:

Y = the dependent variable,

X = the independent variable,

β₀ = the intersection point with the y-axis,

β₁ = regression coefficient, and

ε = error term.

Equation (1) is often referred to as a simple linear regression, where the dependent variable is modeled with one independent variable only. However, if the dependent variable is modeled with two or more independent variables, the relationship is called multivariate linear regression and is given by Equation (2) [11] . In this study, a multivariate regression was used, because the dataset employed, contained six independent variables.

$Y={\beta }_0{\displaystyle {\sum }_{i=1}^n{\beta }_i{X}_i}+\epsilon$ (2)

where,

X_i = independent variables,

β₀ I = a constant

β_i = regression coefficients

ε = error term

Regression trees are MLMs developed using the fast divide and conquer greedy algorithm that recursively partitions the given training data into smaller subsets. Regression trees are well known for their efficiencies. However, Regression trees can also lead to poor decisions in lower levels of the trees, as a result of the unreliability of estimates, based on small samples of cases. Regression trees are also known for their instability. A small change in the training dataset may lead to a different choice when building a node, which may represent a dramatic change in the tree, especially if the change occurs at the top-level nodes. A simple regression tree is essentially the same as a decision tree, used in the context of response prediction. The branches of the tree represent splits on the value of a regressor, creating partitions in the independent data where the dependent data is more homogenous, like a form of clustering. The terminal nodes contain the prediction model for that branch of the tree. In this application, prediction models are constants; specifically, the medians of observations within the partition defined by that branch of the tree [25] [26] .

Support vector machines (SVM) are supervised MLMs, developed to solve problems of classification and regression [2] [24] . The key of support vector machines is to determine a function having n deviations from the actual vectors for training data. For regression problems, the main objective structures of support vector machines are to minimize training errors, and to reduce generalized errors to achieve generalized performance. Support vector machines are used extensively to achieve good performance in regression applications. In such applications, support vector machines use a mathematical function referred to as the cost function for the measurement of the empirical risk to minimize error [24] .

Gaussian process regression is a non-parametric technique used frequently for solving extreme non-linear problems. Gaussian process regression is comprised of random variables. In a Gaussian process regression, all input and output data follow a Gaussian distribution profile. Gaussian process regression provides a distribution of all potential functions that are reliable with the training dataset. Gaussian process regression is then defined as a Gaussian process of the mean function n(x) and kernel function $t\left(x,x^{\prime }\right)$. This can be represented mathematically as shown in Equation (3) [2] .

$F\left(x\right)=GP\left(n\left(x\right),t\left(x,x^{\prime }\right)\right)$ (3)

where n(x) = central tendency of F, x = test input.

Ensembles algorithms are used to develop ensembles of regression trees used for reducing fluctuations in individual trees. This approach as applicable to machine learning, uses the bootstrap aggregation or bagging algorithm for creating similar datasets, tested from the identical source dataset. Ensembles of regression trees are machine learning models developed to overcome overfitting, a common problem with regression trees [2] .

Neural networks are MLM inspired by the way the human brain functions. These networks have interconnected layers of processing units, known as neurons [27] between which information is transmitted through interconnections during operation. Weights characterize each of these connections; and an activation function limits the amplitude of the output neurons. It is worth noting that neural networks are not developed for particular machine learning applications, but are trained to learn patterns from specific datasets. Once trained, neural networks can be used to make predictions or classifications. These networks can learn to recognize patterns in data from physical systems, computer programs, or other source [28] .

Model training is a process that seeks to enable a MLM to learn the trends and relationships in the dataset. Model training involves feeding the MLM with input data [29] . MLM training in this study was performed using a MATLAB built-in application referred to as the Regression Learner. The Regression Learner is a specialized MATLAB application for training regression-based MLM. This application specializes in training MLM to make predictions on data. This application enables users to explore data, select features, specify validation techniques, train models and evaluate performance. With the Regression Learner, users can perform supervised machine learning using labeled data.

To train the MLM in this research, the training dataset of 26,400 records, which represented 80% of the preprocessed data of 33,000 records, was imported into the Regression Learner app in MATLAB, followed by selecting a validation technique. Validation is the process of accessing the ability of a trained MLM to perform on a new and unseen dataset. During validation, the MLM made predictions using the validation dataset. Then the model’s performance was evaluated using different performance evaluation metrics such as RMSE, R², MAE, and MAPE. Validation is crucial in identifying whether or not the MLM is overfitting the training dataset. The validation of all the 24 MLM in this study was performed using the Regression Learner in MATLAB in terms of the RMSE and R². The RMSE and R² are the most widely used performance evaluation metrics [13] . Two validation techniques, namely, hold out and re-substitution validation were employed. These validation techniques are widely used with large datasets [30] . The use of the two validation techniques was to ensure that the most accurate MLM is rightly identified and selected for Solar PV power forecasting applications. With the Hold-out validation technique, 25% of the training dataset was held out (reserved) for accessing the performance of the MLM after training. With the re-substitution validation technique, the entire training dataset was used for assessing the performance of the different MLMs after training.

Validation of MLM was also performed with response plots, which are visual representations of the relationship between actual values and forecasted values.

Testing of MLMs after training and validation is crucial. Just as validation, testing of MLMs involves the evaluation of the model’s performance. Unlike validation which seeks to evaluate the performance of MLMs on new data, testing of MLMs is to evaluate their performance in real-world scenarios. The testing of MLMs was performed using the test data. Testing of all the 24 MLMs in this study was performed with the Regression Learner in MATLAB with a test dataset of 6600 records representing 20% of the preprocessed dataset of 33,000 records. During the testing the test dataset was uploaded into the Regression Learner, followed by running the 24 MLM on the test dataset. Thereafter, the RMSE, and R² values, and actual versus predicted plots generated by the models were observed and recorded.

The 24 MLMs were evaluated through the computation of the coefficient of determination (R²) and Root Mean Squared (RMSE) values of each model, as shown in Equations (4) and (5) respectively [25] [31] [32] .

${\text{R}}^2=1-\frac{{\displaystyle {\sum }_{i=1}^n{\left(y_i-{\hat{y}}_i\right)}^2}}{{\displaystyle {\sum }_{i=1}^n{\left(y_i-{\bar{y}}_i\right)}^2}}$ (4)

$\text{RMSE}=\sqrt{{\displaystyle {\sum }_{i=1}^n\frac{{\left(y_i-{\hat{y}}_i\right)}^2}{n}}}$ (5)

Root Mean Squared Error (RMSE) is a performance evaluation metric widely used in machine learning applications. The RMSE is a measure of the average difference between the forecasted values and the actual values and provides an estimation of how well the trained machine learning model can forecast the target value. Best machine model accuracy is demonstrated by lower RMSE values. The coefficient of determination (R²), is another performance evaluation metric widely used in regression-based machine learning applications. R² is defined as the measure of the variance in the response variable that can be predicted using the predictor variable. R² values lie between 0 and 1, where values close to 1 indicate good model accuracy, while values close to 0 indicate poor model accuracy.

In order to select the most accurate MLM for forecasting solar PV power generation in Bamenda, Cameroon, the RMSE and R² values of all the trained and tested models were compared. Following this evaluation, the model with the lowest RMSE and highest R² value was selected as the most accurate MLM for forecasting solar PV power in the Bamenda, Cameroon.

Additionally, the most accurate MLM was identified visually, with the aid of response plots. By this technique, the model whose data points lie closest to the diagonal line compared to the other models was identified as the most accurate model and consequently selected as the best MLM for forecasting solar PV power in Bamenda, Cameroon.

The identified accurate MLM was used to perform Solar PV power forecasting in Bamenda, Cameroon based on short-term forecasting horizon. Firstly, the selected MLM was exported to the MATLAB workspace. Then, new data was fed into the model in order to perform forecasting. The MATLAB command shown in Equation (6) was used to feed data into the model:

$\text{yfit}=\text{trainedModel}\text{.predictFcn}\left(T\right)$ (6)

where:

yfit contains the forecasted values for each data point,

trained Model = the exported machine learning model,

T = the test dataset in a tabular format.

A dataset made up of both electrical and meteorological data was obtained and used for the training, validation, and testing of MLMs. The raw data acquired was made up of 35,064 records. After preprocessing the acquired raw data was reduced to 33,000 records, representing 94% of the original raw data. Solar PV power generation which was used as the output varied from 0 kW to 18 kW.

Both electrical and meteorological data sets were used for the training, validation, and testing of MLMs. The raw data acquired had 35,064 records. After preprocessing the acquired raw data was reduced to 33,000 records, representing 94% of the original raw data. Solar PV power generation used as the output varied from 0 kW to 18 kW as shown in Figure 3 .

The data acquired revealed that the study area considered has a high solar PV power potential, whose exploitation and use can go a long way to provide households and businesses with sustainable electricity supply.

Direct beam irradiance and ambient temperature influence Solar PV power generation more than other meteorological parameters [23] . Thus, after the data was acquired and preprocessed, the relationship between the direct beam irradiance and ambient temperature and solar PV power generation were studied. The results showed that solar PV power generation is directly proportional to the direct beam irradiance [23] , while the optimum Solar PV power generation of 17 kW occurred when the ambient temperature was somewhere between 24˚C and 28˚C.

As mentioned in Section 2.5, a total of 24 MLMs were trained and validated. The MLMs were first validated using the hold out validation technique, and then using the re-substitution validation technique. The results obtained in terms of RMSE and R² with both validation techniques are shown in Table 2 . The hold-out validation yielded RMSE and R² values of the 24 MLMs ranging from 8.8227 to 477.19 and 0.994 to 0.999 respectively. The re-substitution validation yielded RMSE and R² values ranging from 2.4620 to 352.07 and 0.994 to 0.999 respectively. From Table 2 , the Fine Gaussian SVM MLM was the least accurate with a RMSE value of 477.19 and an R² value of 0.990 after the hold-out validation and also the least accurate with an RMSE value of 352.07 and an R² value of 0.994 after the Re-substitution validation.

After the Hold-out validation, the Wide Neural Network was the most accurate MLM with a RMSE values of 8.8227 and R² value of 0.999 while the Exponential GPR MLM had a RMSE value of 14.450 and R² of 0.999. After the re-substitution validation, Exponential GPR was the most accurate MLM with a RMSE value of 2.4620 and R² value of 0.999 while the Wide Neural Network had a RMSE of 9.2997 and a R² value of 0.999. Also, after the hold-out validation, the Matern 5/2 GPR MLM had a RMSE value of 9.4042 and a R² value of 0.999; and a RMSE value of 8.8580 and an R² value of 0.999 after the re-substitution validation. Therefore, the Wide Neural Network and Matern 5/2 GPR MLMs were potential candidates for the most accurate MLM for forecasting of Solar PV power generation in Bamenda, Cameroon, after training.

Table 3 presents the outcome of the test of the 24 MLMs in terms of RMSE and R². From Table 3 , the Fine Gaussian SVM MLM was the least accurate MLM with a RMSE value of 458.97 and an R² value of 0.990 after the hold-out validation and also the least accurate with a RMSE value of 443.50 and an R² value of 0.991 after the Re-substitution validation.

After the Hold-out validation, the Wide Neural Network was the most accurate MLM with a RMSE value of 9.377 and an R² value of 0.999, the Matern 5/2 GPR had a RMSE value of 9.4522 and R² value of 0.999 while the Exponential GPR MLM had a RMSE value of 10.299 and R² value of 0.999. After the re-substitution validation, the wide neural network was the most accurate MLM with a RMSE value of 9.5279 and R² value of 0.999, the Matern 5/2 GPR had a RMSE value 10.104 and a R² value of 0.999, while the Exponential GPR had a RMSE value of 14.861 and a R² value of 0.999.

Therefore, after testing of the MLMs, the Wide Neural Network and Matern 5/2 GPR MLMs were potential candidates for an accurate MLM for forecasting of Solar PV power generation in Bamenda, Cameroon. Additionally, 62% of the MLMs yielded more accurate results with the hold-out validation technique.

Performance evaluation of the 24 MLM was done by comparing the RMSE and R² values of the models achieved during the testing phase, as well as observing and comparing the actual versus forecasted plots of Solar PV power generation of the models. In the plots of actual versus forecasted Solar PV power generation, the spread of the data points along the diagonal is an indication of the accuracy of the MLM. The more spread the data points, the least accurate the MLM, the less spread the data point, the more accurate the MLM. The most performant MLM is one with the lowest RMSE and highest R² values and less spread of the data points on the plot of the actual vs forecasted Solar PV power generation, while the least performant model is one with highest RMSE and lowest R² values and the more spread the data points on the plot of actual vs forecasted Solar PV power generation. A MLM with lowest RMSE and highest R² values will be the most accurate model for Solar PV power forecasting in Bamenda, Cameroon. From the testing of the 24 MLMs, the Fine Gaussian SVM yielded the least accuracy, while the wide neural network yielded the highest accuracy and was therefore identified as the most accurate model for forecasting Solar PV power generation in Bamenda, Cameroon. Figure 4 is a plot of the actual vs forecasted Solar PV power generation for Fine Gaussian SVM (the least accurate MLM) while Figure 5 is the actual vs predicted plot of Wide Neural Network (the most accurate MLM).

Therefore, the wide neural network MLM, with a RMSE value of 9.377 and R² value of 0.999 from the hold-out validation during the testing, was identified to be the most accurate MLM for forecasting Solar PV power generation in the Bamenda, Cameroon. In terms of R², the wide neural network, identified as the most accurate MLM in this study, yielded higher values, compared to the values obtained by [31] - [35] .

Therefore, the wide neural network MLM, with a RMSE value of 9.377 and R² value of 0.999 from the hold-out validation during the testing, was identified to be the most accurate MLM for forecasting Solar PV power generation in Bamenda, Cameroon. Key hyper-parameters of the wide neural network MLM are shown in Table 4 . In terms of R², the wide neural network, identified as the most accurate MLM in this study, yielded higher values, compared to the values obtained in previous research as reported in [31] - [35] .

The Wide Neural Network MLM was used to forecast the Solar PV power generation in Bamenda, North West Region following the procedure described in Section 2.9. The short-term forecasting results are shown graphically in Figure 6 .

The forecasting results revealed a small variation between the actual values of solar PV power generation and forecasted values of solar PV power generation.