# A Deep Learning Method for Short-Term Dynamic Positioning Load Forecasting in Maritime Microgrids
## 3 The Proposed Method  
As we mentioned in Section 2, to justify the NARX equations as the proposed method and its computational procedure in (15), the following dynamic load values are used for one-day ahead prediction, where y(\(n\),\(t\)) = {y(\(n\),\(t\)) \(\in\)\(t\) = 1, 2,..., 24} as the present DP load demand at day \(n\), time \(t\), \(\overset{\wedge}{y}(n,t)\) = {\(\overset{\wedge}{y}(n,t)\) \(\in\)\(t\) = 1, 2,..., 24} as the predicted DP load demand at day \(n\), time \(t\) by the NARX network, \(w\)(\(n\),\(t\)); is the weight vector at day \(n\), time \(t\) and the \(F\)(\(U\)) is the nonlinear vector function representing ANN. Furthermore, the Table 1 shows the environmental disturbances according to Figure 6 where the \(W_{h1}(n,t)\), \(W_{V2}(n,t)\), \(W_{S3}(n,t)\), \(W_{D4}(n,t)\), \(D(n,t)\), \(H(n,t)\) are determined as wave height (m), wave swing (deg), wind speed(m/s), wind swing (deg), head swing (deg), and ship displacement (deg) as external inputs in \(x\)(\(n\),\(t\)) = {x(\(n\),\(t\)) \(\in\) \(t\) = 1, 2,..., 24} in (15) and (16) respectively. Also tapped delay lines (TDL) values \(Tdy\) and \(Tdx\) for the NARX inputs which we have used for training the weights in (13)-(17) as shown in Figure 7 with daily DP load forecasting as 24, 48, 72, hourly from 1 to 24, and weekly 168 have been selected, respectively. Figure 5: The typical structural design of NN-NARX series-parallel modes with error back-propagation computing method with TDL values \(Tdy\) and \(Tdx\) as network output and input memory respectively. To train, validate, and test the proposed RNN method for DP load forecasting, we used real-time data from the noon report of IFDC [69]. The data noon has collected from the actual DP load profile for January 2020. The dataset also includes weather information of the sea state of the Caspian Sea, such as wave height, wind speed, wave, and wind directions, which are shown in Figure 6 and Table 1. The sea state parameters affect the thrusting power demand as a dynamic load profile, which changes with the vessel motion. To define the DP load-forecasting problem and optimal dispatching between generators \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Description** & **Range** \\ \hline \(DP_{L}\) & \(DP\) power (MW) & \(y(n,t)\) & 0–7 \\ \(W_{\text{H}1}(n,t)\) & wave height (m) & \(x_{1}(n,t)\) & 0–8 \\ \(W_{V2}(n,t)\) & wave deg (\(\Theta\)) & \(x_{2}(n,t)\) & 0–360 \\ \(W_{\text{S3}}(n,t)\) & wind Speed (m/s) & \(x_{3}(n,t)\) & 0–20 \\ \(W_{\text{D4}}(n,t)\) & wind deg (\(\Theta\)) & \(x_{4}(n,t)\) & 0–360 \\ \(D(n,t)\) & Displacement deg (\(\Theta\)) & \(x_{5}(n,t)\) & 0–360 \\ \(H(n,t)\) & heading deg (\(\Theta\)) & \(x_{6}(n,t)\) & 0–360 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters used in NARX-NN. Figure 6: Historical data patterns of weather parameters, and Vessel displacement for the period one month of offshore operation. Figure 7: Schematic diagram of NARX-NN based LM-BP that used in training procedure by considering environmental disturbances, and vessel motion. in various sea conditions, we used an hourly sea state and DP load data to train the proposed NN model. The hourly data is the average of the 'thirty' 2 min dataset, which we collected each 2-min data set during the DP operation. For that reason, a precise range of input parameters increases the DP demand forecasting in sea state more accuracy. Furthermore, we used the correspondence study on the historical data of thrust power consumption that determines the nonlinear and dynamic dataset of historical data, contains hourly, daily, and weekly in the DP load predicting model. The DP load demand dataset is analyzed and the load profiles are classified according to weather conditions in Table 2. The past DP load demands and the profiles, which are the current DP load, the weather condition, and ship displacement are included affect the current load.