## 2 Modelling and Control Organization
### Control Organization Using Energetic Macroscopic Representation  
EMR is a graphical formalism used to highlight the energetic properties of the components of a system to develop control schemes [20]. EMR has already been used in several works on the energy management of vehicles [7; 33]. The EMR of the studied system is represented in Figure 5 with several pictograms (green and orange pictograms--see Appendix A):  
* Four energy sources (green ovals) depict the three voltage sources (FC, SC, and Bat) and an equivalent current source (representing the electric load of the traction subsystem);
* One coupling element (orange overlapping square) depicts the current node between the FC, the battery, the SC branches, and the DC bus (5);
* The smoothing inductors store kinetic energy (2) and are accumulation elements (orange-barred rectangles) with the currents \(i_{\textit{LX}}\) as state variables, i.e., the outputs of the elements. The DC bus is also described as an accumulation element with the voltage \(u_{\textit{bus}}\) as the state variable (4);
* The DC-DC converters are described by conversion elements (orange square) (3).  
EMR is a graphical representation exclusively based on physical integral causality. This property enables a deduction of an inversion-based control scheme that can be implemented directly in real time. This deduction leads to having two control levels: local control and global control. The former is linked to the local control of elements, while the latter is linked to the EMS of the system to coordinate all the elements. The global control gives the control variables (setpoints) that the local control has to track with generally closed-control loops [20].  
The local control level, light blue blocks in Figure 5, manages the system components to track the reference of the DC bus voltage to define the suited modulation ratios \(m_{\textit{fc}}\), \(m_{\textit{b}}\), and \(m_{\textit{sc}}\) of the DC-DC converters. The local control is deduced step-by-step by following the inversion of the EMR of the system. The inversion of accumulation elements (orange-barred rectangular pictograms) is performed using closed-loop controls (light blue crossed parallelograms). Conversion elements (orange square pictograms) are directly inverted with open-loop controls (blue parallelograms). The inversion of coupling elements (orange overlapping pictograms) depicts degrees of freedom that correspond to the output of the EMS. The local control level highlights the fact that four closed-loop controls are required:  
Figure 5: Energetic macroscopic representation and control organization of the system.  
three controllers to manage the currents of each source (\(i_{\mathit{tf}}\), \(i_{\mathit{lb}}\), and \(i_{\mathit{Lsc}}\)) and one controller to track the DC bus voltage (\(u_{bus}\)).  
The global control level (dark blue block in Figure 5) coordinates the different components to achieve a global objective. The EMS is coded at this level and has to ensure the power sharing between the different energy sources. The outputs of the EMS correspond to the control variables (setpoints) of the local control level. They are highlighted by the EMR-based control organization. In this study, the EMS imposes the output current setpoints of the FC chopper \(i_{\mathit{def}\_{\mathit{ref}}}\) and battery chopper \(i_{\mathit{dcb\_{\mathit{ref}}}}\) to minimize the hydrogen consumption and to preserve the battery lifetime, respectively.