**3. Auxiliary power source based on the fuel cell**

The proposed auxiliary power source contains the following energy sources: Proton Exchange Membrane (PEM) fuel cells, battery system, DC to DC boost converter connected to the PEMFC output terminals, DC to DC boost converter connected to the battery package, DC to DC Buck converter used for providing the charging/discharging path between the PEMFC and battery, as in **Figure 4**.

The dynamic characteristics of the two types of power sources make the hybrid power system more complicated. Therefore, it is essential, very important, and necessary to ensure efficient energy management. Energy management strategies determine the allocation of power between different energy sources and promote the energy efficiency and life of the hybrid power system. The energy stored in the battery systems offers a double benefit, keeping the life of the fuel cell and obtaining a better dynamic response to load variation. The goals of this hybrid configuration are presented in detail in [15].

#### **3.1 Modeling of PEMFC**

A PEM fuel cell stack model was chosen from the MATLAB/Simulink, SimPowerSystems (SPS) Toolbox library. The MATLAB/Simulink model implements a generic hydrogen fuel cell stack. The model has two options: a simplified model and a detailed model.

*Modeling and Simulation of APU Based on PEMFC for More Electric Aircraft DOI: http://dx.doi.org/10.5772/intechopen.105597*

#### **Figure 4.**

*Block diagram of hybrid fuel cell/battery.*

**Figure 5.** *The dynamic behavior of a PEMFC.*

The simplified model shows a particular fuel cell stack operating at nominal conditions of temperature and pressure. **Figure 5** presents the dynamic behavior of a PEMFC and **Table 2** shows fuel cell model parameters. The stack is supplied by liquid hydrogen and compressed air [15].

#### **3.2 Modeling of batteries**

The batteries chosen in order to realize this study are lithium-ion types as they have proved to exhibit a high energy density and efficiency in comparison to other battery types like lead-acid, NiCd, or NiMH. This makes them more attractive for aircraft applications. The battery output voltage is given by [15].

$$V\_{\text{bart}} = E\_0 - K \frac{Q}{Q - \frac{\gamma}{\beta} idt} - R \cdot i + A \exp\left(-B\left[idt\right]\right) \tag{2}$$

where *i* is the battery current [A], *E*0 is the battery constant voltage [V], *K* is the polarization voltage [V], *A* is the exponential zone amplitude [V], *Q* is the battery capacity [Ah], *B* is the exponential zone time constant inverse [Ah]−1, ∫idt is the actual battery charge [Ah], *R* is the internal resistance [Ω], and *V*batt is the battery no load voltage [V].


#### **Table 2.**

*Fuel cell parameters.*

The characteristics of the chosen battery are presented in **Figure 6** and the parameters of the above model are shown in **Table 3**. The state-of-charge (*SOC*) of the battery is between 0 and 100%. The *SOC* is calculated as

$$SOC = 100 \left( 1 - \frac{Q \cdot 1.05}{\int idt} \right) \tag{3}$$

#### **3.3 Modeling of a DC-to-DC converter**

Relying on load profile, APU consists of the following: 12.5 kW (peak), 30–60 V PEM (Proton Exchange Membrane) FCPM – Fuel Cell Power Module, with nominal power of 10 kW; 48 V, 40 Ah, lithium-ion battery system; 12.5 kW fuel cell DC to DC boost converter, with regulated output voltage and input current limitation; two DC

**Figure 6.** *The dynamic behavior of a battery.*

*Modeling and Simulation of APU Based on PEMFC for More Electric Aircraft DOI: http://dx.doi.org/10.5772/intechopen.105597*


**Table 3.**

*Battery parameters.*

to DC converters for discharging (4 kW boost converter) and charging (1.2 kW buck converter) the battery system.

Two classical types of DC-to-DC converters are selected for the proposed hybrid battery/fuel cell system (**Figure 4**) to stabilize the output profile of the auxiliary power source system. During transient conditions, the battery supplies electric power for the essential loads on the aircraft electric network until PEM-FC warms up. Moreover, the fuel cell is the one that provides all requested power for the essential loads when the synchronous generator is shut down. Therefore, the DC-to-DC converter of the battery must ensure a bidirectional flow. The battery system during transitional periods provides electric power to the emergency loads, so the converter operates in the boost mode, increasing the output voltage to its standard value at 270 VDC using a feedback control system.

The DC-to-DC boost converter controls the fuel cell. Bi-directional DC to DC boost converter controls the battery. These converters are also output voltage regulated with current limitations. The fuel cell DC to DC converter system is 30–60 V DC input, 270 V DC, 9.2 A output. The battery DC to DC converter system includes 2, 40–58.4 V DC input, 270 V DC, 7 A output, and these DC to DC isolated boost converters are connected in parallel. Alongside 1, 240–297 V DC input, 48 V DC, 20 A output, DC to DC isolated buck converter. The converters used in this study contain the average value model.

**Figure 7** shows DC to DC boost converter model realized in Simulink/ SimPowerSystems (SPS) [15].

#### **3.4 Power management strategy of APU based on fuel cell**

The most common schemes presented in the literature include the following techniques: the state machine control strategy, the rule-based fuzzy strategy, the classical PI control strategy, and the equivalent consumption strategy ECMS [18–25].

The energy management strategy is designed based on: keeping the fuel cell lifetime by avoiding an insufficient supply of reactants (fuel cell starvation); the fuel cell current slope of 40A/s; fuel cell power: *Pfcmin* = 1 kW and *Pfcmax* = 10 kW; battery power: *PBattmin* = 1.2 kW and *PBattmax* = 4 kW [15]; also, in order to operate the battery system efficiently, it is requested always keeping the battery SOC above 40%. The fuel cell power is caused by the battery state of charge and the required load power (*Pload)*. The bus voltage is stabilized through the battery converters for energy management system strategies. The output of the algorithm is the reference for the

#### **Figure 7.** *DC to DC converter model in Simulink/SimPowerSystems (SPS).*

#### **Figure 8.**

*Schematic of the power management strategies [15, 26].*

fuel cell power, as it can be seen in **Figure 8**. This quantity relative to the fuel cell voltage and from the efficiency of the DC-to-DC converter has resulted in the value of the fuel cell reference current [15, 26]. A detailed description of the controller based on fuzzy logic is presented in [15, 26].
