# Fault tolerant operation of a three-level boost converter with minimal input current ripple in both healthy and faulty conditions

Merlin Limon, Arnaud Gaillard, Philippe Poure

► To cite this version:

Merlin Limon, Arnaud Gaillard, Philippe Poure. Fault tolerant operation of a three-level boost converter with minimal input current ripple in both healthy and faulty conditions. International Conference on Environment and Electrical Engineering - EEEIC 2025, Jul 2025, Platanias-Chania, Crete, Greece. hal-05175545

HAL Id: hal-05175545

https://hal.science/hal-05175545v1

Submitted on 22 Jul 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Fault tolerant operation of a three-level boost converter with minimal input current ripple in both healthy and faulty conditions

Merlin Limon

Université de Lorraine, CNRS, IJL,
F-54000 Nancy, France

merlin.limon@univ-lorraine.fr

Arnaud Gaillard

Université Marie et Louis Pasteur,
UTBM, CNRS, Institut FEMTO-ST
F-90000 Belfort, France

arnaud.gaillard@utbm.fr

Philippe Poure

Université de Lorraine, CNRS, IJL,
F-54000 Nancy, France

philippe.poure@univ-lorraine.fr

**Abstract**— This paper investigates the fault tolerant operation of a two-phase three-level boost converter, used in renewable energy systems based on fuel cell, thermoelectric generator or photovoltaic cells. Firstly, the study focusses on healthy operation. Then, service continuity under open circuit switch fault conditions is studied. By optimizing carriers' phase shifts, the converter can maintain operation in post-fault mode while minimizing input current ripple. The analysis highlights the benefits of this topology in terms of current ripple through the duty cycle range. Nevertheless, the post-fault mode strategy results in a reduced power mode, that could limit its applicability in some cases.

**Keywords**—Two-Phase Interleaved Three-Level Boost Converter, renewable energies, fuel cell-based heavy-duty applications, fault tolerant operation, continuity of service.

## I. INTRODUCTION

DC-DC converters are fundamental components of embedded energy systems, enabling voltage level adaptation and ensuring DC bus voltage regulation. More specifically, non-isolated boost topologies play a central role in the power conversion chains of hybrid transportation systems (including hydrogen-based fuel cells and batteries). Indeed, they provide significant voltage step-up capabilities, which are particularly necessary for the DC bus of heavy-duty transport vehicles [1].

Minimizing the input current ripple through the converter is a key challenge in fuel cell power application. The ripple generated by the switching operation must be kept as low as possible to ensure a prolonged fuel cell stack lifespan [2], [3]. The Three-Level Boost Converter (TLBC) presented in Fig. 1(a) has been proposed to reduce this input current ripple [4], [5]. The interleaved topologies also features this advantages [6], [7].

In addition, heavy duty vehicles require continuity of service for the user's comfort and make the transport reliable. In this context, the fault tolerant capability of DC/DC converters remain major concerns. Many fault tolerant converters have been studied in the literature [8], [9], [10]. The main catalectic failures are switches faults [11] that can be an Open Circuit or Short Circuit Fault (OCF, SCF).

Some topologies including several parallel phases feature active redundancy. In this case, the additional phase add a degree of freedom for the structure when a fault occurs [12], [13]. The two-phase Three-Level Boost Converter (2ph-TLBC) presented in Fig. 1(b) has both advantages of

fault tolerant capability and input current ripple reduction. This structure has an internal phase shift associated with each phase and an external phase shift between the two phases. These two parameters have an impact on the input current ripple and need to be optimized to minimize the ripple [14].

The fault tolerant operation needs to take this parameter into account to keep the converter at its best performance in both healthy and post-fault conditions.

The next section is related to the context of this study and the targeted applications. In section III, the TLBC is studied in healthy operation, under nominal condition. First, the optimization of the internal phase shift is discussed. Then, the structure behavior under OCF has been studied. In section IV, the 2ph-TLBC is studied during nominal and healthy operation modes. The needs to select the optimal phase shift between each phase is demonstrated. Each converter state has been studied to obtain input current ripples formulas. The fault tolerance reconfiguration after an OCF has been addressed in section V. Finally, conclusion and future works are proposed.

## II. CONTEXT OF THE STUDY AND APPLICATIONS

This study is a part of a research project founded by the French program "France 2030". It aims to improve PEMFC fuel cell systems for high-power mobility applications with fault tolerant operation. The targeted power is about 1MW. To reach this power level, several elementary submodules must be combined. These submodules consist of 63.4kW fuel cells (@360A,176V), typically FCgen-LCS from Ballard company, associated with fault tolerant DC-DC converters. The studied converters are 2ph-TLBC, with an output voltage regulated at 400V. The association of elementary submodules allows to reach an output voltage level in the range of 1kV to 1.5kV. In this study, SiC MOSFET are used to increase the converter efficiency and to withstand the high voltages. In addition, the SiC technology allows high switching frequency, which contributes to reduce the passive components size. The switching frequency can be up to 75kHz. This value is chosen in this study.

The 2ph-TLBC structure is not widely analyzed in the current state of the art, which justifies a detailed analysis for operations in healthy and faulty conditions. Moreover, it is of particular interest to evaluate the capability of the converter to perform service continuity under open-circuit switch fault.

<footnote>The authors acknowledge support from the French Nation Research Agency (ANR) under France 2030 program and reference ANR-22-PEHY-0018 (project PEPRH2-HYSySPEM)</footnote>
<figure><img src="image_2.png" /><figcaption>Figure 1: (a) Three level boost converter (b) Two-phase Three-level boost converter</figcaption></figure>

### III. STUDY OF THE TLBC

In this section, the TLBC topology is analyzed in two key operating modes: healthy condition with minimal input current ripple and faulty condition under OCF.

#### A. Input current ripple minimisation

The TLBC topology includes two switches leading to four operating modes described in Table I.

<table><caption>TABLE I. STATE OF THE SWITCHES FOR EACH MODE</caption><thead><tr><th>Mode</th><th>1</th><th>2</th><th>3</th><th>4</th></tr></thead><tbody><tr><td>St</td><td>ON</td><td>ON</td><td>OFF</td><td>OFF</td></tr><tr><td>Sb</td><td>ON</td><td>OFF</td><td>ON</td><td>OFF</td></tr></tbody></table>

For each mode, the equivalent circuit given in Fig 2.

<figure><img src="image_3.png" /><figcaption>Figure 2: TLBC equivalent electrical circuits for each modes</figcaption></figure>

Based on the equivalent electrical circuits, the analytical expression for the derivative of the input current for each mode is given in Table II.

<table><caption>TABLE II. ANALYTICAL EXPRESSIONS OF THE CURRENTS' DERIVATIVES OF THE TLBC</caption><thead><tr><th>Mode</th><th>1</th><th>2</th><th>3</th><th>4</th></tr></thead><tbody><tr><td>di(t)/dt</td><td>V<sub>fc</sub>/L</td><td>(V<sub>fc</sub> - V<sub>c2</sub>)/L</td><td>(V<sub>fc</sub> - V<sub>c1</sub>)/L</td><td>(V<sub>fc</sub> - V<sub>o</sub>)/L</td></tr></tbody></table>

The analysis of the TLBC over one switching period, considering variations of the duty cycle D, enables the calculations of the analytical expressions for the input current ripple. The methodology employed follows the same approach detailed in Section IV.C. In this paper, a symmetrical control is considered, where both switches operate with the same duty cycle. To generate the control signals, the duty cycle is compared to the two triangular carrier signals generated in the PWM modules. The choice of the carrier phase shift $\phi_{TLBC}$, between the two triangular carriers, is crucial to minimize the input current ripple of the converter [15].

Table III presents the analytical expressions of the input current ripple, depending on the duty cycle D and the

carrier phase shift $\phi_{TLBC}$. The phase shift $\phi_{TLBC}$ is expressed by: $\phi_{TLBC} = T * X$, with T the switching period and $0 \le X \le 1$.

<table><caption>TABLE III. INPUT CURRENT RIPPLE ACCORDING TO THE DUTY CYCLE D AND THE CARRIER PHASE SHIFT T*X</caption><thead><tr><th>ΔI<sub>fc,TLBC</sub></th><th>0 ≤ D < 1/2</th><th>1/2 ≤ D ≤ 1</th></tr></thead><tbody><tr><td>0 ≤ X < 1/2</td><td>V<sub>fc</sub> D (1 - X - D) / L f</td><td>V<sub>fc</sub> / L f (D - X)</td></tr><tr><td>1/2 ≤ X < 1</td><td>V<sub>fc</sub> D (X - D) / L f</td><td>V<sub>fc</sub> / L f (D + (X - 1))</td></tr></tbody></table>

Based on the analytical study of the minima of the expressions given in Table III, it can be demonstrated that the optimal carrier phase shift is $\phi_{TLBC} = T/2$ (for $X = 1/2$), regardless of the D value ($0 \le D \le 1$).

The conventional Boost Converter (BC) serves as a useful reference for normalizing the analytical results presented in this paper. Indeed, the well-known expression for the current ripple in a BC is given by [12]:

$$ \Delta I_{fc,CB} = \frac{V_{fc}}{L f} D \quad (1) $$

The ripple for the TLBC is always lower than that of the conventional boost converter. Its theoretical value is zero when the duty cycle is equal to 1/2.

#### B. TLBC fault tolerance capability

In this sub-section, the TLBC fault tolerance capability is studied under OCF, resulting from a driver malfunction or a catastrophic switch failure [11]. Some selected simulation results are presented hereafter, specifications are provided in Table IV. The parameters have been chosen to have an input current ripple equal to 10% of its average value and an output voltage ripple equal to 1% of its average value. According to the voltage gain formula for a TLBC converter [7], the theoretical duty cycle is calculated.

<table><caption>TABLE IV. SPECIFICATIONS FOR SIMULATION</caption><thead><tr><th>Parameters</th><th>Values</th><th>Parameters</th><th>Values</th></tr></thead><tbody><tr><td>V<sub>fc</sub>, V<sub>o</sub></td><td>176V,400V</td><td>Resistive charge R</td><td>2.52Ω</td></tr><tr><td>P<sub>in</sub></td><td>63.4kW</td><td>C1=C2</td><td>63.4μF</td></tr><tr><td>D (duty cycle)</td><td>0.56</td><td>L</td><td>3.9μH</td></tr><tr><td>Switching frequency f</td><td>75kHz</td><td>φ<sub>TLBC</sub></td><td>T/2</td></tr></tbody></table>

A closed-loop control is applied, based on the double loop control strategy for voltage and current, presented in [15] and performing a voltage balancing between the output capacitors' voltages.

In Fig. 3, simulation results obtained in the Matlab/Simulink and Simscape environment are presented. An OCF is applied to the TLBC, at t = 4 ms, by forcing to '0' the switching order of $S_{11}$. After the fault occurrence, the output voltage cannot be maintained to its nominal value, as well as the voltage balancing between capacitors' voltages. The controller is unable to compensate the fault, as there is no redundancy to maintain operational functionality. To guarantee normal operation after an OCF, it is necessary to make the TLBC fault-tolerant, by modifying the circuit and/or the applied control.
<figure><img src="image_4.png" /><figcaption>Figure 3: TLBC behavior under OCF on $S_{1t}$ at $t = 4$ms</figcaption></figure>

A possible approach based on redundancy consists in adding a second phase to the converter, to form a 2ph-TLBC, as illustrated in Fig. 1(b). In this study, both interleaved phases of the 2ph-TLBC operates in healthy conditions. As a result, after an OCF fault detection, the 2ph-TLBC operates as TLBC structure (Fig 1(a)), based on the single healthy phase.

In addition to its contribution to fault tolerance, the introduction of the additional phase could also contribute to reduce input current ripple in healthy conditions, as demonstrated in the case of a conventional 2-phase boost converter [8]. In the next section, the analytical study of the current ripple is presented.

# IV. STUDY OF THE TWO-PHASE TLBC

## A. Introduction

In two-phase converter structures, the PWM carrier signals for each phase must be appropriately shifted to take advantage of the interleaving effect and to reduce the input current ripple. For the classical 2-phase interleaved BC, the optimal phase shift, so called $\phi_{ITL}$, is $T/2$ [16]. To our best knowledge, the value of the optimal phase shifts has not be studied and defined for a 2ph-TLBC. Thus, based on the classical two-phase BC, the value of the phase shift $\phi_{ITL}$ is firstly set to $T/2$, Fig. 4 compares the input current ripples for the three converters when this phase shift $\phi_{ITL} = T/2$ is applied to the 2ph-TLBC (Simulation parameters in Table IV with $L_1 = L_2 = L_3 = L_4 = L/2$ and $\phi_{TLBC} = T/2$).

<figure><img src="image_5.png" /><figcaption>Figure 4: Input currents waveforms of the BC, TLBC and 2ph-TLBC</figcaption></figure>

The input current ripples for both TLBC and 2ph-TLBC remain lower than the one for the BC. The current ripple in the 2ph-TLBC is higher than of the TLBC, whereas a decrease was expected. Thus, in the next section, a more detailed analysis determines the optimal values of the phase shifts $\phi_{ITL}$ and $\phi_{TLBC}$ for the 2ph-TLBC.

## B. Analysis of the 2ph-TLBC operation and inductors' current slopes analytical expressions

The 2ph-TLBC converter includes four switches, resulting in 16 possible operating modes. By analyzing the slope of the inductors' current over each mode and integrating the different consecutive slopes over a switching period, the input current ripple can be obtained.

The modes are detailed in Table V. The switches ($S_{1t}$ and $S_{1b}$) and ($S_{2t}$ and $S_{2b}$) are the top and bottom switches of the phase 1 and the phase 2 of the 2ph-TLBC, respectively.

<table><caption>TABLE V. STATE OF THE SWITCHES FOR EACH MODE</caption><thead><tr><th>Mode</th><th>S<sub>1t</sub></th><th>S<sub>2t</sub></th><th>S<sub>1b</sub></th><th>S<sub>2b</sub></th><th>Mode</th><th>S<sub>1t</sub></th><th>S<sub>2t</sub></th><th>S<sub>1b</sub></th><th>S<sub>2b</sub></th></tr></thead><tbody><tr><td>1</td><td>OFF</td><td>OFF</td><td>OFF</td><td>OFF</td><td>9</td><td>ON</td><td>OFF</td><td>OFF</td><td>OFF</td></tr><tr><td>2</td><td>OFF</td><td>OFF</td><td>OFF</td><td>ON</td><td>10</td><td>ON</td><td>OFF</td><td>OFF</td><td>ON</td></tr><tr><td>3</td><td>OFF</td><td>OFF</td><td>ON</td><td>OFF</td><td>11</td><td>ON</td><td>OFF</td><td>ON</td><td>OFF</td></tr><tr><td>4</td><td>OFF</td><td>OFF</td><td>ON</td><td>ON</td><td>12</td><td>ON</td><td>OFF</td><td>ON</td><td>ON</td></tr><tr><td>5</td><td>OFF</td><td>ON</td><td>OFF</td><td>OFF</td><td>13</td><td>ON</td><td>ON</td><td>OFF</td><td>OFF</td></tr><tr><td>6</td><td>OFF</td><td>ON</td><td>OFF</td><td>ON</td><td>14</td><td>ON</td><td>ON</td><td>OFF</td><td>ON</td></tr><tr><td>7</td><td>OFF</td><td>ON</td><td>ON</td><td>OFF</td><td>15</td><td>ON</td><td>ON</td><td>ON</td><td>OFF</td></tr><tr><td>8</td><td>OFF</td><td>ON</td><td>ON</td><td>ON</td><td>16</td><td>ON</td><td>ON</td><td>ON</td><td>ON</td></tr></tbody></table>

The equivalent electrical circuits for the 16 possible modes are drawn in Fig. 5. Regardless of the mode, the inductors' currents satisfy the following equations:

$$i_1(t) + i_2(t) + i_3(t) + i_4(t) = 0 \quad (2)$$

Thus, the currents' slopes verify:

$$\frac{di_1(t)}{dt} + \frac{di_2(t)}{dt} + \frac{di_3(t)}{dt} + \frac{di_4(t)}{dt} = 0 \quad (3)$$

In the following, the case of the mode 2 is detailed. The same solving approach can be used for each mode to find the analytical expressions of the inductors' current slopes. In Mode 2, applying Kirchhoff's voltage laws leads to the following equations:

$$L_1 \frac{di_1(t)}{dt} - L_2 \frac{di_2(t)}{dt} = 0 \quad (4)$$

$$L_3 \frac{di_3(t)}{dt} - L_4 \frac{di_4(t)}{dt} = V_{C2} \quad (5)$$

$$L_2 \frac{di_2(t)}{dt} - L_3 \frac{di_3(t)}{dt} = V_{fc} - V_{C1} - V_{C2} \quad (6)$$

The equations (3) to (6) can be expressed by the system of equations $A * X = B$ where:

$$X^T = \left( \frac{di_1(t)}{dt} \quad \frac{di_2(t)}{dt} \quad \frac{di_3(t)}{dt} \quad \frac{di_4(t)}{dt} \right) \quad (7)$$

And, in the case of the Mode 2:

$$A = \begin{pmatrix} 1 & 1 & 1 & 1 \\ L_1 & -L_2 & 0 & 0 \\ 0 & 0 & L_3 & -L_4 \\ 0 & L_2 & -L_3 & 0 \end{pmatrix} \quad B = \begin{pmatrix} 0 \\ 0 \\ V_{C2} \\ V_{fc} - V_{C1} - V_{C2} \end{pmatrix} \quad (8)$$

In this study, $L_1 = L_2 = L_3 = L_4 = L/2$ and $V_{c1} = V_{c2} = V_o/2$. The results of the system's resolution in Mode
2 can be found in Fig. 6, as well as the analytical expressions for the other modes. The input current slopes have been obtained by summing $\frac{di_1(t)}{dt}$ and $\frac{di_2(t)}{dt}$.

<figure><img src="image_6.png" /><figcaption>Figure 5: Equivalent circuits for the 16 modes</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Figure 6: Analytical expressions of the currents' slopes for the 2ph-TLBC</figcaption></figure>

### C. Input current ripple calculation

By analyzing the succession of the modes over one switching period and considering their respective durations, the instants corresponding to the maximum and minimum current values can be determined. By integrating the current variations between these two instants and using the analytical expressions provided in Fig. 6 for the concerned modes, the input current ripple analytical expressions can be obtained.

In Fig. 7, an example of calculation is performed for $\phi_{ITL} = \frac{T}{2}$, $\phi_{TLBC} = \frac{T}{4}$ and $D = 0.56$. The control signals for the four switching cells are first determined and then translated into operating modes in order to obtain the derivative of the targeted signal, here $I_{fc}$.

This method can be applied for other parameter values. In the considered case, the four inductor currents, not shown here, follow the same mode and duration, resulting in identical current waveforms, phase-shifted in time. This observation validates the assumption $V_{c1} = V_{c2} = V_o/2$ and shows balanced current between both phases. However, this balance is not guaranteed under all phase-shift configurations.

<figure><img src="image_8.png" /><figcaption>Figure 7: Mode succession at an operating point</figcaption></figure>

As seen in Fig. 6, $I_{fc}(t)$ reaches the minimum at $t=0s$ and the maximum at $t=T(D-1/2)$. The input courant ripple is obtained as follows.

$$ \Delta I_{fc} = I_{fc,max} - I_{fc,min} \qquad (9) $$

$$ \Delta I_{fc} = \int_{tmin}^{tmax} \frac{di_{fc}(t)}{dt} dt \qquad (10) $$

$$ \Delta I_{fc} = \int_{0}^{T(D-1/2)} (Mode 14) dt \qquad (11) $$

$$ \Delta I_{fc} = \int_{0}^{T(D-1/2)} \frac{4V_{fc}-V_{o}}{2L} dt \qquad (12) $$

With $V_o$ considered as constant, $V_o = V_{fc}/(1-D)$

$$ \Delta I_{fc} = \frac{V_{fc}}{L_f} * 2(D - \frac{1}{2}) * \frac{\frac{3}{4} - D}{1 - D} \qquad (13) $$

The obtained expression for current ripple is valid within the operating intervals where the switching modes remain unchanged between the minimum and maximum current points. For instance, when both phase shifts are fixed, the interval is $D \in [\frac{1}{2}; \frac{3}{4}]$. By repeating the method, the current ripple in the inductors or the fuel cell can be determined,
through the full range of the desired variables. Furthermore, by considering the phase shifts as variables, the approach can be extended, thereby introducing additional intervals that require detailed analysis.

### D. Phase shift optimisation

In the case of the 2ph-TLBC, the choice of two phase shifts impact the input current ripple. In the following, we have fixed $\phi_{ITL} = T/2$. This choice is based on open loop simulations conducted for various couples of phase shift values ($\phi_{TLBC}, \phi_{ITL}$): if $\phi_{ITL} = T/2$, a symmetrical duty cycles is obtained, with equal mean current values for the 2 phases and balanced voltages across the capacitors $C_1$ and $C_2$.

The theoretical expressions of the input current ripple have been established for all duty cycles and all $\phi_{TLBC}$. Based on this analysis and the 16 equations obtained (not provided in this abstract to limit paper length), Fig. 8 is computed. The results indicate that the optimal values for $\phi_{TLBC} = X * T$ (for all duty cycles) are T/4 and 3T/4. These two values give identical ripple reduction due to the symmetry of the two-phase converter.

Conversely, the worst-case $\phi_{TLBC}$ value is T/2, which results in the highest input current ripple. With $\phi_{TLBC} = \phi_{ITL} = T/2$, the current ripple is the same as the one obtained for an interleaved conventional boost converter, studied in [12]. If the optimal value for the two phase shifts $\phi_{ITL} = T/2$ and $\phi_{TLBC} = T/4$ are applied, the theoretical expressions of the input current ripples are expressed hereafter, depending on the duty cycle range:

$$ 
\left\{
\begin{array}{ll}
\Delta I_{fc,2ph-TLBC} = 2 \frac{V_{fc}}{L_f} * D \left(\frac{1}{4}-\frac{D}{1-D}\right) & \text{for } D \in \left[0; \frac{1}{4}\right] \\
\\
\Delta I_{fc,2ph-TLBC} = 2 \frac{V_{fc}}{L_f} * \left(D-\frac{1}{4}\right) \left(\frac{1}{2}-\frac{D}{1-D}\right) & \text{for } D \in \left[\frac{1}{4}; \frac{1}{2}\right] \\
\\
\Delta I_{fc,2ph-TLBC} = 2 \frac{V_{fc}}{L_f} * \left(D-\frac{1}{2}\right) \left(\frac{3}{4}-\frac{D}{1-D}\right) & \text{for } D \in \left[\frac{1}{2}; \frac{3}{4}\right] \\
\\
\Delta I_{fc,2ph-TLBC} = 2 \frac{V_{fc}}{L_f} * \left(D-\frac{3}{4}\right) & \text{for } D \in \left[\frac{3}{4}; 1\right]
\end{array}
\right.
\quad (14) $$

<figure><img src="image_9.png" /><figcaption>Figure 8: Normalized input current ripple for different $\phi_{TLBC} = X * T$</figcaption></figure>

Based on Table III and equation (14), the input current ripple for both TLBC and 2ph-TLBC topologies, versus the

duty cycle D, is plotted in Fig. 9. In this figure, the current ripple is normalized to the input current ripple for a CB (Eq. 1). Additionally, simulation results are included in Fig. 9, as circular markers, for selected duty cycle values ranging from 0 to 1. Simulation results validate the theoretical expressions.

<figure><img src="image_10.png" /><figcaption>Figure 9: Input current ripple normalized for both structure</figcaption></figure>

Seen from the inductances of the 2ph-TLBC, the 2 phases cannot be considered as acting independently; this is illustrated by the equivalent electrical circuits for the operating modes, in Fig. 5. Consequently, the waveforms of the currents crossing the four inductances are not similar to the ones that are obtained for a TLBC.

## V. FAULT TOLERANT OPERATION OF THE 2PH-TLBC

### A. Post fault operation and remedial actions

When an open-circuit switch fault occurs, the faulty phase is isolated and the converter operates with the remaining healthy phase only. However, the control strategy must be modified by adjusting the internal phase shift of the healthy phase between PWM carriers for top and bottom switches control ($\phi_{TLBC}$) to minimize the input current ripple in post-fault operation ($\phi_{TLBC} = T/2$, instead of $\phi_{TLBC} = T/4$). Thus, the TLBC control orders with $\phi_{TLBC} = T/2$ are computed in parallel of the ones for the 2ph-TLBC. When an OCF is detected and localized, the applied commands will change and the TLBC command will be applied to the healthy phase, leading to the optimal situation. Since the post-fault input current is no longer shared between the two phases, the full current now crosses a single inductor, instead of two. This inductor was initially sized and optimized for healthy operation (2ph-TLBC structure). To prevent any damage, the maximum current in the inductor must remain within the limits defined in healthy conditions; thus, the post-fault operation will be a degraded one. Another approach would consist in oversizing the inductances of the 2ph-TLBC in healthy conditions, so that the nominal post fault operation can be performed after the fault occurrence; this approach has not been chosen in this paper. In the chosen degraded operation, the post-fault power must be reduced. However, since the current waveforms in the inductors change after the fault, the nominal power is not reduced by half.
## B. Simulation results

Some selected simulation results for the 2ph-TLBC are presented in Fig. 10. They have been obtained with Matlab/Simulink and Simscape Specialized Power Systems, for the parameters provided in Table IV, in closed loop control [15]. An open circuit switch fault is applied to the top switch in one of the two phases, at time $t = 4$ ms. After three switching periods, the OCF is supposed to be detected and localized; then remedial actions are applied to the converter.

As observed in Fig. 10, the converter successfully maintains the output voltage across the capacitors, but at a reduced power level. As expected, the post-fault input current ripple is slightly higher. However, this increase remains acceptable, considering that the faulty operation is assumed to be temporary.

<figure><img src="image_11.png" /><figcaption>Figure 10: Voltage and current waveforms before and after fault occurrence: From top to bottom: Inductors' currents, Input current and Capacitors voltages</figcaption></figure>

# VI. CONCLUSION

This study demonstrates the fault-tolerant capability of the 2ph-TLBC in the presence of an OCF. By redesigning the phase shift value to stay in the best configuration, the topology maintains a minimal input current ripple, even after a fault occurs. The implemented fault tolerant strategy results in a degraded operating mode after a fault but only at 85% of the maximum power, based on the proposed reconfiguration strategy.

## REFERENCES

[1] V. F. Pires, A. Cordeiro, D. Foito, and J. F. Silva, 'High Step-Up DC-DC Converter for Fuel Cell Vehicles Based on Merged Quadratic Boost-Cuk', *IEEE Trans. Veh. Technol.*, vol. 68, no. 8, pp. 7521-7530, Aug. 2019, doi: 10.1109/TVT.2019.2921851.

[2] Y. Zhan, Y. Guo, J. Zhu, and L. Li, 'Input current ripple reduction and high efficiency for PEM fuel cell power conditioning system',

in 2017 20th International Conference on Electrical Machines and Systems (ICEMS), Sydney, Australia: IEEE, Aug. 2017.

[3] M. V. Naik and P. Samuel, 'Design and analysis of ripple current reduction in fuel cell generating systems', in *2015 International Conference on Power and Advanced Control Engineering (ICPACE)*, Bengaluru, India: IEEE, Aug. 2015, pp. 200-204.

[4] M. Afkar, P. Karimi, R. Gavagsaz-Ghoachani, M. Phattanasak, and S. Pierfederici, 'Effect of fault in output capacitor due to its parasitic resistance in modular DC-DC three-level converter', in *2022 9th Iranian Conference on Renewable Energy & Distributed Generation (ICREDG)*, Mashhad, Iran, Islamic Republic of: IEEE, Feb. 2022, pp. 1-6. doi: 10.1109/ICREDG54199.2022.9804561.

[5] S. Dusmez, A. Hasanzadeh, and A. Khaligh, 'Comparative Analysis of Bidirectional Three-Level DC-DC Converter for Automotive Applications', *IEEE Trans. Ind. Electron.*, vol. 62, no. 5, May 2015.

[6] Z. Yao, X. He, M. Liu, K. Zhang, and Y. Tang, 'Soft-Switching Control Method of Interleaved Three-Level Boost Converter in near-CRM for Fuel Cells', in *2024 IEEE 10th International Power Electronics and Motion Control Conference (IPEMC2024-ECCE Asia)*, Chengdu, China: IEEE, May 2024, pp. 1685-1690.

[7] H. Mehida, M. Y. Ayad, R. Saadi, O. Kraa, and A. Aboubou, 'Multi-Stack Fuel Cells and Interleaved DC/DC Converters Interactions for Embedded Applications', in *2018 International Conference on Electrical Sciences and Technologies in Maghreb (CISTEM)*, Algiers: IEEE, Oct. 2018, pp. 1-6.

[8] X. Hao, S. Laghrouche, Y. A. Amirat, and A. Djerdir, 'Super-Twisting Based Fault-Tolerant Control of Multiple-input Three-Phase Interleaved Boost Converter', in *IECON 2020 The 46th Annual Conference of the IEEE Industrial Electronics Society*, Singapore, Singapore: IEEE, Oct. 2020, pp. 2868-2873.

[9] R. Yahyaoui, A. De Bernardinis, A. Gaillard, and D. Hissel, 'Switch short-circuit fault detection algorithm based on drain-to-source voltage monitoring for a fault tolerant DC/DC converter', in *IECON 2016 - 42nd Annual Conference of the IEEE Industrial Electronics Society*, Florence, Italy: IEEE, Oct. 2016, pp. 2212-2217.

[10] Q. Li, Y. Huangfu, J. Zhao, S. Zhuo, and F. Chen, 'Controller design and fault tolerance analysis of 4-phase floating interleaved boost converter for fuel cell electric vehicles', in *IECON 2017 - 43rd Annual Conference of the IEEE Industrial Electronics Society*, Beijing: IEEE, Oct. 2017, pp. 7753-7758.

[11] Shaoyong Yang, A. Bryant, P. Mawby, Dawei Xiang, Li Ran, and P. Tavner, 'An Industry-Based Survey of Reliability in Power Electronic Converters', *IEEE Trans. Ind. Appl.*, vol. 47, no. 3, pp. 1441-1451, May 2011, doi: 10.1109/TIA.2011.2124436.

[12] M. Gleissner and M. Bakran, 'Design and control of fault-tolerant non-isolated multiphase multilevel dc-dc converters for automotive power systems', *IEEE Trans. Ind. Appl.*, pp. 1-1, 2015.

[13] S. Kim, S. Jo, S. Kim, C.-S. Shin, C.-H. Jo, and D.-H. Kim, 'Advanced Ripple Reduction in Interleaved Boost Converter for Fuel Cell Application', in *2024 IEEE Energy Conversion Congress and Exposition (ECCE)*, Phoenix, AZ, USA: IEEE, Oct. 2024.

[14] X. Liu, S. Zhuo, Y. Huangfu, S. Wang, H. Bai, and R. Ma, 'Ripple Suppression of Multi-Phase Converter under Switch Fault for Fuel Cell Application Based on Phase Shift Reconfiguration', in *2024 IEEE Transportation Electrification Conference and Expo (ITEC)*, Chicago, IL, USA: IEEE, Jun. 2024.

[15] K.-M. Lee and I.-S. Kim, 'Unified Modeling and Double-Loop Controller Design of Three-Level Boost Converter', *Sustainability*, vol. 15, no. 2, p. 1597, Jan. 2023, doi: 10.3390/su15021597.

[16] P. M. Preethiraj, 'Design of novel DC-DC interleaved boost converter for BLDC application', *Heliyon*, vol. 10, Issue 22, 2024, e40041, https://doi.org/10.1016/j.heliyon.2024.e40041.