IEEE Electrification Magazine - December 2017 - 75

50% of its voltage (i.e., 75% of its state of charge). The maximum voltage of the stored energy is used to determine
the number of elements to be connected in series. Its
capacity indicates how many branches of these elements
are to be connected in parallel, with the elements being
selected from ultracapacitor manufacturers' catalogues.
Table 1 contains an example of sizing, with an arbitrary choice of criteria to set some general figures. Subsequently, the following criteria remain variable
to optimize the weight of the overall system and its
gas consumption:
xx
fuel cell minimal voltage (V) = 100
xx
ultracapacitor maximal voltage (V) = 80
xx
ultracapacitor maximal discharge (%) = 50
xx
cutoff frequency (Hz) = 0.05
xx
fuel cell maximal current density (A/cm2) = 0.5
xx
switching frequency (Hz) = 20,000
xx
number of parallel converter branches = four.

TABLE 1. An example of ideal hybrid system

sizing (with no losses).
Fuel Cell
Surface (cm2)

Fuel Cell
Number

C (F)

V0 (V)

627.2

154

9.83

61.16

C: equivalent capacitance of ultracapacitors; V0: Initial ultracapacitor voltage.

P

Power-Sharing
Frequency

Theoretical Energy Management
for the Studied Hybrid System

f
Power to Be
Supplied by the Main
Energy Source

Frequency Sharing Principle

Figure 3. The principle of hybridization by frequency filtering, illustrated in a power-frequency drawing.

80

Load
Storage Device Power
Fuel Cell Power

70
60
50
Power (kW)

Hybridization in terms of power is defined as the association of various complementary sources. In our case, this
association is achieved with a source of high specific
energy (the fuel cell), which poorly withstands rapid variations in power (Schindele et al. 2005, Thounthong and
Sethakul 2007), and a source of high specific power (ultracapacitors), which can only supply or absorb the mean
power of zero (excluding losses). The idea of this power
hybridization is to assign low variations in power to the
fuel cell and zero mean power to the ultracapacitors. Several methods are available for this, including the distribution of frequency powers band and slope limitation. The
method chosen for this study is power frequency sharing
(Chapoulie and Astier 1998, Garcia-Arregui 2007) and is
shown in Figure 3.
The desired filtering frequency will play a significant
role in sizing the solution because, for a specific stored
energy capacity, a lower frequency will cause the energy
level of the ultracapacitors to fluctuate more. In other
words, given the ultracapacitors' limitations (the maximum voltage level not to be exceeded and the minimum
power reserve to be retained), at a given filtering frequency, a minimum stored energy capacity must be used for
the system to be able to operate. In our case, this filtering
frequency enabled us to size the stored energy capacity
and its reference voltage. This frequency was recommended by a fuel cell manufacturer as the fastest frequency enabling the auxiliaries to correctly control the
gas supply (the pressure and flow rate), despite the variations in fuel cell consumption.
An example of power frequency sharing is simulated in
Figure 4. The presented case is an ideal scenario, taking
into account neither the losses in the components nor the

Power to Be
Provided by
the Storage

40
30
20
10
0

-10
-20

0

50

100 150

200 250
Time (s)

300

350 400

Figure 4. The use of frequency sharing for a frequency of 50 mHz.

auxiliary consumption used to demonstrate frequency
sharing. The mission profile is given in Figure 1, and the
filtering frequency is 50 mHz.
Figure 5 shows the changes in voltage for stored energy
and fuel cells throughout the mission for the sizing proposed in Table 1. Using an ideal model, the state of charge
of the stored energy and the limitation voltage of the fuel
cell are within their limitations.
IEEE Elec trific ation Magazine / D EC EM BE R 2 0 1 7

75



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