## 4 Devised Configuration for the Integrated WT-ACO-FFANN Based ML Forecast Model
### Feedforward Artificial Neural Network (FFANN)
The chosen FFANN model configuration for the proposed WPP task in this paper is depicted schematically in Figure 4. The corresponding parameter values of the model are presented in Table 2.  
The mathematical modeling depiction of the \(i\)th neuron in the FFANN is illustrated in Figure 5 [19]. In Figure 5, the \(x\)s are the inputs to the \(i\)th neuron, \(y_{i}\) is the result, \(w_{ij}\) is a connecting weight, \(b_{i}\) is a bias quantity (usually constant), and \(f_{i}\) is called the activation function. The activation function carries out a major task during the FFANN model training. It controls the behavior of the neurons' output. Based on Figure 5, the FFANN neuron output can be formulated as follows. \[y_{i}=f_{\text{i}}\left(\sum_{j=1}^{n}w_{ij}.x_{j}+b_{i}\right) \tag{9}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Configuration & Feedforward with 3 layers \\ Hidden layer size & 1 \\ Hidden neuron quantity & 20 \\ Hidden layer neurons activation & Tangent sigmoid (tansig) \\ Output layer size & 1 \\ Output neuron quantity & 1 \\ Output layer neurons activation & Pure linear (purelin) \\ Training ratio & 0.01 \\ Epochs & 1000 \\ Training target error & 0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of FFANN. Figure 4: Structure of FFANN. Figure 5: Mathematical model of a neuron of FFANN. Normally, FFANN is developed using the back propagation (BP) training technique. In the BP learning of the FFANN, the neuron connecting weights are adjusted by employing the BP algorithm over the given input/output dataset. This greatly helps the FFANN model to learn the behavior of the data very quickly. While running to find the values of the FFANN weight parameters during the training process, the BP executes a gradient descent inside the solution domain in the direction of the global least value. Although the BP training technique needs less computation time, it may be stuck by suboptimal (local) solutions and is therefore not capable of reaching a global (system-level) optimal solution. Hence, the BP training of the FFANN model does not guarantee reliable wind power forecasting accuracy throughout the entire forecasting horizon and scenario. This paper uses the ACO algorithm for the FFANN training. Hence, the ACO training of the FFANN model results in global optimal values for the FFANN connection weights, which correspond to a higher wind power forecasting accuracy. The ACO optimization technique is computationally simple and convergent for a given configuration of the FFANN model. In this work, the FFANN model weights are implemented as parameters of the ACO. The mean squared error (MSE) between the FFANN result and the real observation is formulated as the cost (fitness) function of the ACO algorithm. The goal of the devised strategy is to obtain the smallest value of this fitness function. This procedure iterates until the prediction error achieves the intended level. The dual-step integrated ML algorithm employed to implement the devised WPP is discussed stepwise in Appendix A.