IEEE Electrification Magazine - December 2017 - 76

112

85
80

110

75

108

65

Voltage (V)

Voltage (V)

70

60
55
50

104
102

45

100

40
35

106

0

50

100 150

200 250
Time (s)
(a)

300

350

400

98

0

50

100 150

200 250
Time (s)
(b)

300

350

400

Figure 5. The voltages in (a) a storage device and (b) a fuel cell throughout the mission for the sizing displayed in Table 1.

90
80
70

Voltage (V)

60
50
40
30
20
RUC = 0.02 Ω
RUC = 0.01 Ω
RUC = 0 Ω

10
0
-10

0

10 20

30

40 50 60
Time (s)

70

80

90 100

Figure 6. The ultracapacitor (UC) voltage evolution, taking into
account losses due to internal resistances.

Vmes
V
Storage

-
Vref +

K

Iref

Storage
Figure 7. A control loop for the state of charge of the stored energy.

Impact of System Losses
Now, let us consider some losses in the system, in particular in the stored energy elements (the internal resistance of
the ultracapacitors), as shown in Figure 6. An observation

76

I E E E E l e c t r i f i cati o n M a gaz ine / DECEMBER 2017

can be made that the state of charge of the stored energy is
no longer within its limitations and that it moves toward a
total discharge. In this case, the application quickly
becomes no longer able to operate because all of the energy lost in stored energy losses is never compensated.
The solution put forward to maintain the state of charge
of the stored energy is to add a proportional control loop
coupled with a low-pass filter on the ultracapacitor voltage,
as shown in Figure 7. The difficulty in choosing this corrector lies in choosing the proportional gain value K. With a
gain K that is too low, the corrector will not be able to maintain the stored energy at a state of charge stable enough to
be within its limitations. With a gain K that is too high, the
stored energy voltage undulates at the frequency of the
low-pass filter placed at the ultracapacitor voltage measurement point. Without this low-pass filter, high-frequency variations in the ultracapacitor voltage are carried onto
the current provided by the fuel cell, which we aim to avoid.
In addition, complying with the voltage limitations chosen
for the stored energy is strongly linked to its reference voltage. Additionally, this loop must be included in the control
of the system converter that is current controlled (with
ultracapacitors first and fuel cells second) is because the
converter that controls the bus voltage no longer has any
degrees of freedom (DoF) to perform an additional function,
in which case the bus voltage would be degraded.
Figure 8 shows various choices for the V ref and K
parameters of the control loop for the state of charge of the
stored energy and the importance of the choice of these
values for system stability. With a stored energy reference
voltage that is too low, its mean state of charge cannot fulfill the entire mission. With a reference voltage for the
stored energy that is too high, there is a risk of exceeding
the maximum ultracapacitor voltage values. The choice of
these values can help reduce (or increase, if poorly chosen)



Table of Contents for the Digital Edition of IEEE Electrification Magazine - December 2017

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