## 4 Simulation Results  
We evaluate our proposed DLF model (m(MI + ANN)) by comparing it with an existing MI + ANN model in [12]. We choose the existing MI + ANN model in [12] for comparison, because its architecture has a close resemblance to our proposed model. In our simulations, historical load time series data from November (2014) to January (2015) are taken from the publicly-available PJM electricity market for two SGs in the United States of America; DAYTOWN and EKPC [19]. November to December (2014)data are used for training and validation purposes, and January (2015) data are used for testing purposes. Simulation parameters are shown in Table 1, and their justification can be found in [9,12,17,18]. In this paper, we have considered two performance metrics; % error and execution time (convergence rate). * Error performance: This is the difference between the actual and the forecast signal/curve and is measured in \(\%\). * Convergence rate or execution time: This is the simulation time taken by the system to execute a specific forecast model. Forecast models for which the execution time is small are said to converge quickly as compared to the opposite case. In this paper, execution time is measured in seconds. Figures (a)a and (a)a are the graphical illustrations of how well our proposed ANN-based DALF model predicts the target values of an SG. In these figures, the proposed m(MI + ANN)-based forecast curve more tightly follows the target curve as compared to the existing MI + ANN-based forecast curve, which is justification of the theoretical discussion of our proposed methodology in terms of non-linear forecast ability. Not only the sigmoid \(f_{act}^{AN}\) (refer to equation), but also the multivariate auto-regressive training algorithm enable the day-ahead ANN-based forecast methodology to capture non-linearity(ies) in historical load data. Figure (b)b shows the % forecast error when tests are conducted on the DAYTOWN grid; our m(MI + ANN) forecasts with \(2.9\%\) and the existing MI + ANN forecasts with \(3.84\%\) relative errors, respectively. Similarly, Figure (b)b shows the \(\%\) forecast error when tests are conducted on the EKPC grid; our m(MI + ANN) forecasts with \(2.88\%\) and the existing MI + ANN forecasts with \(3.88\%\) relative errors, respectively. This improvement in terms of relative % error performance by our proposed DALF model is due to the following two reasons: (i) the modified feature selection technique in our proposed DALF model; and (ii) multi-variate auto-regressive training algorithm. The first reason accounts for the removal of redundant, as well as irrelevant features from the input data in a more efficient way as compared to the existing DALF model. By a more efficient way, we mean that as our proposal considers the average sample in the feature selection process, as well in addition to the last sample and the target sample. Thus, the margin of outliers that cause significant relative % error is down-sized. The second reason deals with the selection of an efficient training algorithm, as our proposition trains the \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Number of forecasters & \(24\) \\ Number of hidden layers & \(1\) \\ Number of neurons in the hidden & \(5\) \\ unit & \\ Number of iterations & \(100\) \\ Momentum & \(0\) \\ Initial weights & \(0.1\) \\ Historical load data & \(26\) days \\ Bias value & \(0\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. ANN via the multi-variate auto-regressive algorithm and the existing DALF model trains the ANN via Levenberg-Marquardt algorithm. As discussed in Sections 1, 2 and 3 that there exist a trade-off between forecast accuracy and execution time. However, Figures 6b,c and 7b,c show that our proposed DALF model not only results in relatively less % error but also less execution time.