The document describes the experimental validation of a 4-phase floating-interleaving boost converter (FIBC) for fuel cell applications. The FIBC exhibits low input current ripple and distributed power losses. A 100W prototype was constructed using an Arduino microcontroller to generate gate signals. Experimental results validated the operation of the 4-phase FIBC, showing tight voltage regulation under load changes and low fuel cell current ripple that is 1/4 of the inductor ripple currents. The FIBC provides advantages over conventional converters for fuel cell applications by reducing component ratings and increasing reliability.
2. Fig.1. 4-phases-FIBC
1. Increasing the overall converter efficiency;
2. Increasing the input and output ripple frequency without
increasing the switching frequency;
3. Decreasing the input ripple current;
4. Enhancing the system reliability by paralleling phases and
not by paralleling multiple devices;
5. Decreasing current and voltage ratings of power electronic
devices;
6. Reducing the size and weight of the passive components.
III. STEADY STATE ANALYSIS DESIGN
Table I shows that the current and voltage ratings of the power
electronic devices of FIBC are smaller than their of the basic boost
converters.
TABLEAU IIII:
CURRENT AND VOLTAGE RATINGS OF POWER ELECTRONIC DEVICES
Voltage ratings Current ratings
4-phase
FIBC 1 2 1
The voltages of the two condensers are given by the following
relation:
2
1
The Voltage Gain of the presented converter is expressed as
follows:
1
1
2
On the other hand, the basic boost converter Voltage Gain is
given by
1
1
3
Fig. 2 shows the plot of Voltage Gain various Duty Cycle for
FIBC and basic boost converter.
Fig.2 Voltage Gain Plot Various Duty Cycle for FIBC and basic boost
converter.
For the input current ripple the mathematical expressions are
derived under six assumptions.
1. The resistances of inductor and capacitor are negligible.
2. Stray inductor and capacitor are negligible.
3. Switches are ideal.
4. Passive components are identical.
5. Switches in parallel operate (360/N)° out of phase.
6. The converters operate in continuous conduction mode.
The ratio of the input current ripple to the inductor current
ripple is given by
4
For basic boost converter
5
The input current slope of the N-phase FIBC is expressed as
follows:
6
The generalized expression of the ratio of the input current
ripple to the inductor current ripple of the N-phase FIBC as a
function of duty cycle MN(D) is
1
1
7
Where n is the interval between two duty cycles values,
resulting in zero current ripple.
The ratio of the input current ripple to the inductor current
ripple of a four-phase FIBC as a function of duty cycle M4(D) is:
0.3 0.4 0.5 0.6 0.7 0.8 0.9
0
1
2
3
4
5
6
7
8
9
10
Duty Cycle(D)
VoltageGain(G)
basic boost
topology of FIBC
3. 1 4
1
0
1
4
4 1 2 4
4 1
1
4
1
2
4 2 3 4
4 1
1
2
3
4
4 3
3
4
1
8
The variation of the ratio of input current ripple to inductor
current ripple as a function of duty cycle is shown in Fig. 3.
Fig.3 Ratio between the input current ripple and the inductor current ripple
versus duty cycle
On the one hand, by studying Fig. 3, it can be observed that
input current ripple cancelation occurs at specific duty cycles,
which are multiple duties of 1/N, such as 0.25, 0.5, and 0.75 in a
4-phase FIBC. On the other hand, it is clear that the input current
ripple is always less than the inductor current ripple.
IV. 4-PHASES-FIBC: MODELING AND CONTROL LOOP DESIGN
The equations relating to the converter are given for the two
sequences of operation represented Fig 4. In order to simplify the
analysis, we take into account only resistance parasitizes r of
inductor.
(a) 0 < t < DT (b) DT < t < T
Fig.4. Equivalent electric diagram of topology 4-phase FIBC
For the sequence of operation (0<t<DT), the equations are
given below:
9
For the sequence of operation (DT<t<T), the equations are
given below:
10
The averaged-circuit model is:
1
1
1
1
1 1
1 1
11
By admitting the assumption that the duty cycles (D1, D2, D3
and D4) are identical, the equations of this converter with a
resistive load R are given below.
1
2 1
1
12
From the equation (1) we find:
2 1 2 1
4 1
2
13
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Duty Cycles(D)
RatioM(D)
4. The averaged small signal model is:
2
̃
1 2 ̃ 1
4 1 ̃
2
14
In permanent mode:
1
1 1
1
2 1
15
In variable mode with the first order:
̃
1 2 ̃ 1
4 1 ̃ 4
2
16
By applying the transform of Laplace, we obtain:
1 1 2 ̃
2 1
1 1
2
4 1 ̃
2
1
17
The different transfer functions of this converter are given
below
̃ 1 1 3
2 4 1 4
̃
1 4 1 4
1 1 3
18
The diagram of control integrating the two control loops in loop
closed for a phase is shown
Fig.5. Diagram of control integrating the two control loops
The parameters of two correctors PI (C1 and C2) were
determined by the Sisotool®
available in the Matlab/Simulink
software.
V. SIMULATION RESULTS
The design specifications are input voltage Vfc=20V, output
voltage Vdc=40V, output Power P=100W and switching frequency
f=10 kHz.
By using our preceding results we can determine the inductor
value of 4-phase FIBC.
. . .
4 1 1 2
2 1
19
The critical value of capacitance is obtained by:
Fig.6. Photograph of the emulator.
2
20
The validation of the performances of control is given through
the following results of simulation:
Fig. 7 illustrates the behavior of controlled system with an
output voltage reference Vdc=40V (which represents the DC bus
voltage) and successive load step changes, the resistance can
change between 16Ω and 32Ω yielding variation of 50% of the
power of the DC bus. As it can be seen, despite the load resistor
uncertainty, the controller behavior is satisfactory.
The curve in blue shows a tight voltage regulation under step
load changes.
The curve in red shows the change of operation point of the fuel
cell voltage, showing its high dependence on the current.
The curve in green shows the load current.
Fig. 8 shows the FC current, and inductor currents of the 4-
phase FIBC. One can observe that the FC ripple current is 1/4 the
individual inductor ripple currents. So, the FC ripple current of the
4-phase FIBC converter is nearly zero. It means that the FC mean
current is close to the FC RMS current. In addition, it can be seen
the FC ripple frequency is 4 times the switching frequency of 10-
kHz.
Fig. 7. Controller behavior in response to a step reference and changes in the
load resistance.
Fig.8. Waveform of inductor currents and input current.
0 1 2 3 4 5
0
5
10
15
20
25
30
35
40
45
50
Temps(s)
Tension(V)
2.48 2.49 2.5 2.51 2.52 2.53 2.54
0
5
10
15
20
25
30
35
40
45
50
Temps(s)
Tension(V)
Vdc
Vfc
Ich
0 0.5 1 1.5 2
0
1
2
3
4
5
6
7
Temps(s)
Courant(A)
0.9999 1 1.0001 1.0002
0
1
2
3
4
5
6
7
Temps(s)
Courant(A)
Ifc
IL1
IL2
IL3
IL4
5. VI. EXPERIMENTAL VALIDATION
A 100W, 20V/40V prototype was constructed to validate the
operation of the 4-phase FIBC converter. An Arduino card was
suitably programmed to generate the gate pulse at a frequency of
10 kHz.
Because of the non-availability of a fuel cell on the level of the
Laboratory, we realized an emulator of its characteristic.
The emulator is a buck converter controlled in voltage and
which reproduces the same characteristic voltage-current of the
FC. The output current of this buck is measured to obtain a
reference voltage using a model of the FC is developed and stored
previously in the memory of an Arduino card DUE. The regulation
of this voltage gives the control signal of the buck.
Figure 8: Photograph of the emulator.
To evaluate the performances of the control, an experimental
set up of an emulator of PEMFC associated to a 4-phase FIBC
converter was applied. The experimental tests have been carried
out by connecting the DC bus to an adjustable resistor. The
Arduino DUE card is used to create and ensured a shift of the
PWM signals generated. Fig. 9 shows an example of four shifted
control signals of a quarter of period for 4-phase-FIBC
Fig. 10 shows The DC bus voltage regulation under load
changes.
The curve in green shows the load current [1A/Div].
Fig.9. Four shifted control signals of a quarter of period.
Fig. 10. The DC bus voltage regulation under load changes.
Fig. 11. Inductor currents and PEMFC emulator current.
On the basis of the figure Fig.10, it can be observed that the
controller of the converter offers good performances in terms of
stability and precision. Concerning the response time, it can be
observed that the DC bus voltage follows its reference perfectly
Fig. 11 shows the experimental results of the PEMFC emulator
current and the inductor currents waveforms [1A/Div].
During the permanent mode represented by Fig.11, we can
observe on the one hand that the currents of phase are perfectly
shifted as wished by the objectives of the control and on the other
hand, it can be observed that the ripple of the current of the FC is
very weak, which confirms the advantage of this topology.
The experimental results are in agreement with those obtained
with theoretically simulation.
VII. CONCLUSION
In this paper the four-phase FIBC has been designed,
simulated and experimentally verified. This is an interesting
alternative dc-dc structure to the IBC basic converter because it’s
provides significant part count reduction, size and eventually
converter cost without penalizing performance.
Converter design guidelines have been provided and
implementation of 100 W 4-phase FIBC has also been performed,
including the power converter and the Arduino card based control
system. Experimental validation has also been reported showing
the most interesting converter features, gate driving scheme, main
inductor and input currents, dynamic response and efficiency
measurements.
Finally, because of its interesting features, such as low input
current ripple, high current capabilities, modularity, power losses
distribution and high efficiency, this converter could adapt
attractively for medium and high power fuel cell dc-dc converters.
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