## 3 Energy Management Strategy
### Proposed EMS
#### 3.2.2 Low-Level Control  
From the determined PEMFC reference power in the high-level control, the corresponding PEMFC reference current (\(\text{I}_{\text{FC\_ref}}\)) can be systematically deduced for low-level control implementation. As the PEMFC characteristic of slow dynamic, a slope constraint must be applied to regulate the changing rate of this command signal. For instance, the PEMFC takes less than 2 s to increase its output from 10% to 90% of the power rating [18]; hence, the slope constraint is considered to practically realize the PEMFC behavior. For the BAT behavior, the reference current is defined based on the reference power obtained in the high-level control and a SOC regulator scheme that is installed to maintain the SOC level of BAT within the desired range (\(\text{SOC}_{\text{BAT\_min}}<\text{SOC}_{\text{BAT}}<\text{SOC}_{\text{BAT\_ max}}\)), as presented in Figure 6. Because the tramway systems usually operate under high power for a long period, BAT conditions should be handled to deal with the SOC variation or prevent the degradation of BAT capacity. Hence, the reference BAT current is calculated based on the SOC status as follows [46]:  
\[\text{I}_{\text{BAT\_ref}}=\left\{\begin{array}{l}\alpha\Big{|}\frac{\text{P} _{\text{BAT\_ref}}}{\text{V}_{\text{BAT}}}\Big{|}\quad\text{if}\quad\quad \quad\quad\text{SOC}_{\text{BAT}}\leq\text{SOC}_{\text{BAT\_min}}\\ \frac{\text{P}_{\text{BAT\_ref}}}{\text{V}_{\text{BAT}}}\quad\text{if}\quad \text{SOC}_{\text{BAT\_min}}<\text{SOC}_{\text{BAT\_max}}<\text{SOC}_{\text{BAT\_ max}}\\ \beta\Big{|}\frac{\text{P}_{\text{BAT\_ref}}}{\text{V}_{\text{BAT}}}\Big{|} \quad\text{if}\quad\quad\quad\text{SOC}_{\text{BAT}}\geq\text{SOC}_{\text{BAT\_ max}}\end{array}\right. \tag{21}\]  
where \(\text{I}_{\text{BAT\_ref}}\) is the reference BAT current (A), \(\text{P}_{\text{BAT\_ref}}\) denotes the reference BAT power (W), \(\text{V}_{\text{BAT}}\) depicts the measured BAT voltage (V), \(\text{SOC}_{\text{BAT}}\) is the SOC level of the BAT (%), \(\alpha\) and \(\beta\) are the tuning parameters, \(\text{SOC}_{\text{BAT\_min}}\) and \(\text{SOC}_{\text{BAT\_max}}\) are the minimum and maximum allowable SOC of the BAT (%), respectively.  
Figure 8: DC bus voltage control.  
Based on the SOC level of the BAT, the above tuning parameters are described as [38]  
\[\alpha=-\frac{\kappa|\text{SOC}_{\text{BAT}}-\text{SOC}_{\text{BAT},\text{min}}|}{ \text{SOC}_{\text{BAT},\text{min}}} \tag{22}\]  
\[\beta=\frac{\varepsilon|\text{SOC}_{\text{BAT}}-\text{SOC}_{\text{BAT},\text{ max}}|}{\text{SOC}_{\text{BAT},\text{max}}} \tag{23}\]  
where \(\kappa\) and \(\varepsilon\) are positive constants depending on charging or discharging characteristics of the BAT.  
Duty cycles of the DC/DC converters are generated by using the PI controllers as in Figure 6. In detail, the PI-1 controller produces the duty cycle D1 to control the DC/DC converter of the PEMFC source. Similarly, the PI-2 controller is employed to generate duty cycles for the bidirectional DC/DC converter of the BAT source, in which duty cycle D2 handles the buck mode and duty cycle D3 realizes the boost mode operation.