An Open-Circuit Fault Diagnosis Method for LLC Converters

Abstract

In electrified transportation systems, power system failures can lead to greater disasters. Therefore, the reliability of converters in transportation systems has been a concern. Fault-tolerant techniques are widely applied to ensure that converters can continue to supply loads under fault conditions. Fault diagnosis as a prerequisite for fault tolerance has also become a research hotspot. This paper proposes a fast method for fault diagnosis of high-frequency LLC converters. The proposed fault diagnosis method is based on the observation of the voltage across the resonant capacitor to determine and locate the faulty power switch, providing a basis for fault tolerance. This diagnosis method requires a voltage sensor, which is also necessary for some control methods. When applying these control methods, the proposed fault diagnosis method can be used without additional sensors, beneficial for cost reduction. A full-bridge LLC converter controlled by a digital signal processor was used as an experimental platform to verify the effectiveness and speed of the proposed diagnostic method. The results show that the proposed fault diagnosis method can achieve the fast diagnosis of high-frequency LLC converters in a short time and with only minimal computational resources.

1. Introduction

As electrification in transportation advances, the significance of DC–DC converters escalates. While a conservative design enhances reliability, it is impractical due to power density and cost constraints. Redundancy, both at the module and switch levels, although effective, compromises power density and incurs high costs due to parallel connections. A more viable solution is fault-tolerant operation, particularly for systems with stringent cost, volume, and weight limitations [1]. This operation encompasses fault diagnosis and isolation [2,3], with the former being a prerequisite for the latter and crucial for practical implementation [2,3]. Hence, this paper concentrates on the fault diagnosis of DC–DC converters.

Power devices, susceptible to electrical and thermal stresses [4], are prone to failures, primarily open-circuit faults (OCF) and short-circuit faults (SCF) [5,6]. SCFs can induce destructive overcurrents, necessitating immediate isolation to prevent system paralysis or destruction. Mature techniques for handling SCFs are integrated into the gate driver’s standard features for practical applications [7,8]. Additionally, hardware protection circuits, such as fuses, convert SCFs into OCFs to prevent converter damage [9]. OCFs, however, overstrain healthy devices and cause pulsating current. In MOSFETs, switch failures primarily result from gate-oxide degradation, bond wire degradation, and die attach solder cracks and delamination [10,11,12]. Given their concealed nature compared to SCFs, there is a demand for rapid and accurate OCF diagnosis methods.

Open-Circuit Fault (OCF) diagnosis methods are generally classified into three categories: signal-based, model-based, and data-based methods [13]. Signal-based fault diagnosis methods measure specific signals containing fault information and extract features for diagnosis. Typical signals include inductor currents [14], inductor voltages [15], and DC bus currents [16]. In [14], faulty switches were localized within 0.4 ms by monitoring the PWM pulses’ rising and falling edges for each phase inductor current. In [15], faults in switches and diodes of Boost converters were diagnosed using inductor voltage polarity and drive signals. In [16], OCF was diagnosed utilizing DC bus current derivatives.

Model-based fault diagnosis methods substitute hardware redundancy with computational redundancy. Various observers, including sliding mode observers [13], state estimators [17], and adaptive gradient descent algorithms [18], are applied to fault diagnosis. In [13], a sliding mode observer-based fault diagnosis method for power switch OCFs was proposed. In [17], a generalized fault diagnosis method was proposed after analyzing, designing, and experimentally verifying various types of converters using a model-based state estimator method.

Data-based fault diagnosis methods leverage artificial intelligence techniques and large volumes of historical data to train expert diagnosis systems. With advancements in machine learning algorithms and computational power, various deep learning network algorithms, such as back-propagation neural networks [19] and extreme learning machines [20], have been applied to the fault diagnosis of power electronic converters. These methods do not require modeling, fault analysis, or rule formulation, but they necessitate substantial training data and computation. Most data-based fault diagnosis methods are challenging to apply to real-time fast fault diagnosis.

The rising switching frequency enhances the appeal of the LLC converter, renowned for its high efficiency, power density, electrical isolation, low electromagnetic interference, and high operational frequency. Despite its widespread application, research on LLC converter fault diagnosis is sparse. Typical OCF diagnostic strategies utilize the bridge arm midpoint voltage as the fault signal for detection. However, this approach necessitates the installation of a voltage sensor at each converter bridge arm’s midpoint and tends to have a relatively complex computation [21]. This study introduces a two-step, signal-based OCF diagnostic method for LLC converters, suitable for high-frequency applications due to its minimal computational and sampling resource requirements. The method involves sensing the resonant capacitor voltage, comparing it with a reference value for a general fault indication, and employing a fault injection strategy to pinpoint the faulty switch. Fault injection is achieved by temporarily modifying the modulation module’s switching signals. The method’s advantages include low cost, simple circuit design, and high reliability, requiring minimal sensors and components, some of which are already present in certain control methods.

This paper is organized as follows. The structure and operation principles of the LLC converter are introduced in Section 2. The operation process under fault condition is analyzed, and the feature extraction is illustrated in Section 3, and the fault injection strategy is given to locate the faulty switch. The experimental results are presented to verify the feasibility of the proposed method in Section 4, and a conclusion is drawn in Section 5.

2. System Overview

2.1. Basic Operation of the LLC Converter

The conventional full-bridge LLC converter is shown as Figure 1. The converter consists of power switches $S_{1-4}$, freewheeling diodes $D_{1-4}$, a resonant tank, and rectifier diodes $D_{5-8}$. The resonant tank includes a resonant inductor $L_r$, a resonant capacitor $C_r$, and a magnetizing inductor $L_m$. The output capacitor $C_o$ filters the rectified current and stabilizes output voltage for the load $R_o$. The LLC converter is usually designed to be operated lower and near the resonant frequency. The waveforms can be obtained as Figure 2, and the operation waveforms can be divided into six stages in a switching period. Stage 1, 4 show resonance with $L_r$ and $C_r$. Stage 2, 5show resonance with $L_m$, $L_r$ and $C_r$. Stage 3, 6 represent dead-time durations.

Stage 1 [$t_0<t<t_1$]: Since resonant current $i_r$ is lower than 0 before $t=t_0$, $i_r$ flows through diodes $D_{1,4}$, which makes the drain-source voltage $V_{ds}$ of $S_{1,4}$ clamped at $-V_F$, where $V_F$ is the forward conduction voltage drop of the freewheeling diode. Therefore, ZVS for $S_{1,4}$ is achieved at $t=t_0$. During this stage, power is transferred to the secondary side through the transformer. On the secondary side, $D_5$ is forward conducting and $D_6$ is reversely biased. The voltage across the transformer secondary side is clamped at the output voltage $V_o$, so the voltage across the magnetizing inductor $L_m$ remains $N{V}_o$. Magnetizing current $i_m$ increases linearly with the slope rate of $N{V}_o/L_m$. Resonant current $i_r$ flows through MOSFETs $S_1$ and $S_4$, fluctuating in sinusoidal form. Therefore, the resonant current $i_r\left(t\right)$, the resonant capacitors voltage $V_{cr}\left(t\right)$, the magnetizing current $i_m\left(t\right)$, and the secondary current $i_{d5}\left(t\right)$ can be given as follows:

$$\begin{array}{c}\hfill i_r\left(t\right)=C_r{\omega }_{r1}(V_{in}-V_{1,ini}-N{V}_o)sin\left({\omega }_{r1}t\right)\\ \hfill +I_{1,ini}cos\left({\omega }_{r1}t\right)\end{array}$$

(1)

$$\begin{array}{c}\hfill V_{cr}\left(t\right)=V_{in}-N{V}_o-\left(V_{in}-N{V}_o-V_{1,ini}\right)cos\left({\omega }_{r1}t\right)\\ \hfill +\frac{I_{1,ini}}{C_r{\omega }_{r1}}sin\left({\omega }_{r1}t\right)\end{array}$$

(2)

$$i_m\left(t\right)=\frac{N{V}_o(t-t_0)}{L_m}+I_{1,ini}$$

(3)

$$i_{d5}\left(t\right)=N[i_r\left(t\right)-i_m\left(t\right)]$$

(4)

where $I_{1,ini}$ and $V_{1,ini}$ is the initial value of resonant current $i_r$ and resonant capacitor voltage $V_{cr}$ at $t=t_0$, ${\omega }_{r1}=2\pi f_{r1}=\frac{1}{2\pi \sqrt{L_r{C}_r}}$.

Stage 2 [$t_1<t<t_2$]: At $t=t_1$, $i_r\left(t\right)$ and $i_m\left(t\right)$ become equal, while the energy transmission between the primary side and the secondary side is terminated. Diode current $i_{d5}$ drops to zero, so ZCS for $D_{5,8}$ is achieved. Magnetizing inductance $L_m$ participates in the resonance between $L_r$ and $C_r$. Due to $L_m$ is much larger than $L_r$, resonance angular velocity ${\omega }_{r2}$ in Stage 2 is much less than ${\omega }_{r1}$ in Stage 1. Therefore, $i_m$ and $i_r$ are approximately unchanged at this time. The resonant capacitor is charged by the approximately constant current and $V_{cr}$ rises approximately linearly. Therefore, the resonant current $i_r\left(t\right)$, the resonant capacitors voltage $V_{cr}\left(t\right)$, the magnetizing current $i_m\left(t\right)$, and the secondary current $i_{d5}\left(t\right)$ can be derived as follows:

$$\begin{array}{c}\hfill i_r\left(t\right)=i_m\left(t\right)=\sqrt{\frac{C_r}{L_m+L_r}}(V_{in}-V_{2,ini})sin\left[{\omega }_{r2}\left(t-t_1\right)\right]\\ \hfill +I_{2,ini}cos\left[{\omega }_{r2}\left(t-t_1\right)\right]\end{array}$$

(5)

$$\begin{array}{c}\hfill V_{cr}\left(t\right)=V_{in}+\left(V_{2,ini}-V_{in}\right)cos\left[{\omega }_{r2}\left(t-t_1\right)\right]\\ \hfill +\sqrt{\frac{L_m+L_r}{C_r}}{I}_{2,ini}sin\left[{\omega }_{r2}\left(t-t_1\right)\right]\end{array}$$

(6)

$${\omega }_{r2}=2\pi f_{r2}=\frac{1}{\sqrt{(L_r+L_m)C_r}}$$

(7)

$$i_{d5}\left(t\right)=N[i_r\left(t\right)-i_m\left(t\right)]=0$$

(8)

where $I_{2,ini}$ and $V_{2,ini}$ is the initial value of resonant current $i_r$ and resonant capacitor voltage $V_{cr}$ at $t=t_1$. Due to the waveforms of $i_r$, $i_m$ and $V_{cr}$ are symmetrical, it can be derived as follows:

$$I_{1,ini}=-I_{2,ini}=-\frac{N{V}_o{T}_r}{4L_m}$$

(9)

where $T_r$ is the resonance period of $L_r$ and $C_r$ and equals $1/f_{r1}$.

Stage 3 [$t_2<t<t_3$]: At $t=t_2$, $S_{1,4}$ are turned off. The current of resonant tank $i_r$ cannot drop to zero immediately because of the inductance. So, $D_{2,3}$ start freewheeling. There is still no energy transmission from the primary side to the secondary side, so $i_r$ and $i_m$ remain equal. The conducting of $D_{2,3}$ making $S_{2,3}$ clamped, ready to be turned on with ZVS.

Stage 4–6 [$t_3<t<t_6$]: During these stages, $S_{1-4}$ respectively perform the opposite operation of Stage 1–3. Resonant current $i_r$, magnetizing current $i_m$ and resonant capacitor voltage $V_{cr}$ are equal to those in Stage 1–3, but in opposite directions. Diode current $i_{d6}$ repeats the change during Stage 1–3 of $i_{d5}$.

Through the above analysis about steady-state operating process, it can be seen that during the Stage 4–6, energy transmission only happens in the Stage 1,4. The average value of the rectifier output current $i_o$ in a cycle $T_s$ ($T_s=1/f_s$) is equal to $I_{oa}$, which can be expressed as

$${\int }_{t_0}^{t_1}{i}_o\left(t\right)dt={\int }_{t_0}^{t_1}N[i_r\left(t\right)-i_m\left(t\right)]dt=\frac{T_s{I}_{oa}}{2}$$

(10)

when the load is determined. $V_{1,ini}$ in (1) can be derived based on (10), which is as follows:

$$V_{1,ini}=-{\displaystyle \frac{I_{oa}}{4N{f}_l{C}_r}}-{\displaystyle \frac{N{V}_o(f_l-f_{r1})}{16L_m{f}_{r1}{C}_r}}$$

(11)

2.2. The LLC Converter after an OCF

In fact, the full-bridge LLC converter can continue to output power with an OCF on a power switch. As shown in Figure 3, the converter is still operating with an OCF on $S_4$. Therefore, $V_{gs4}$ is always pulled down to simulate the OCF. It is imperative to highlight that the symmetrical architecture of the LLC converter implies that a comparable event would transpire if any power device were to malfunction. For the purpose of this discussion, we exemplify this scenario by pulling down $V_{gs4}$. However, there are differences between before and after the OCF. A operating cycle after the OCF can be divided into seven stages. Some stages are similar to those before the OCF.

Stage 1 [$t_0<t<t_1$]: At $t=t_0$, $S_{2,3}$ are turned on with ZVS. $L_r$ and $C_r$ begin resonance. The transformer primary side is clamped, and the magnetizing current $i_m$ drops linearly, as normal.

Stage 2 [$t_1<t<t_2$]: $i_m$ drops until $i_m$ equals $i_r$ at $t=t_1$. Then the energy transmission is interrupted. $i_m$ and $i_r$ drop slowly due to the resonance of $L_r$, $L_m$, and $C_r$. $V_{cr}$ drops almost linearly.

Stage 3 [$t_2<t<t_3$]: At $t=t_2$, all power switches are off. $i_r$ starts to discharge $C_{oss1,4}$ and charge $C_{oss2,3}$, where $C_{ossx}$ is the parasitic capacitor of $S_x$. When the charge on $C_{oss1,4}$ is released, the current begins to flow through the freewheeling diodes.

Stage 4 [$t_3<t<t_4$]: At $t=t_3$, $V_{gs1,4}$ is pulled up. However, $S_4$ cannot be turned on because of the OCF. Therefore, $i_r$ flows through $D_4$ and feeds back energy to the power supply $V_{in}$, which results in $i_r$ rising sharply. Due to the recovery of energy transmission, $V_p=N{V}_o$ and $i_m$ rises linearly.

Stage 5 [$t_4<t<t_5$]: The primary side continues to supply energy to the secondary side until $i_r$ drops to 0 at $t=t_4$. Then the direction of $i_r$ is reversed. $C_r$ releases the stored charge, and together with $V_{bus}$ discharges $C_{oss5}$ and charges $C_{oss6}$. This process continues until $C_{oss5}$ releases the charge, then $D_5$ is conducted, and the resonant tank continues to supply energy to the secondary side through the $S_3$ and $D_5$.

Stage 6 [$t_5<t<t_6$]: At $t=t_5$, $i_r$ equals $i_m$, and energy the transmission ends. $L_r$, $L_m$ and $C_r$ begin to resonate together.

Stage 7 [$t_6<t<t_7$]: At $t=t_6$, $V_{gs1,4}$ are pulled down, and the converter enters the dead zone again. $i_r$ starts to charge or discharge $C_{oss1-4}$.

It can be seen that the faulty converter behaves like a half-bridge LLC converter. About half of input voltage become the bias voltage on $C_r$, and output voltage $V_o$ drops by half. This once again demonstrates the concealment of OCF and the importance of timely discovery. However, these are the waveforms after the converter is stabilized again after an OCF occurs. When the OCF occurs, the system will enter a transient state until $V_o$ drops. As shown in Figure 4, the time $t_f$ when the OCF occurs is marked with red dotted lines. Since the faulty converter cannot maintain the original output voltage, the converter can hardly output energy for the secondary side, and the load only relies on the output capacitor $C_o$ to supply energy until $V_o$ drops to half. During this period, a bias voltage is generated on $C_r$, and $V_{cr}$ is no longer reversed.

3. Fault Diagnose Strategy of The LLC Converter

3.1. Diagnostic Signal Selection

$V_{cr}$ is the integral of $i_r$, and $V_{cr}$ change periodically with $i_r$ in steady state. Therefore, when $i_r$ crosses zero, $V_{cr}$ reaches the maximum or minimum value. However, when the load is different, the time of $i_r$ zero crossing is also different. The output current depends on the difference between $i_m$ and $i_r$, as shown in the gray line filled part in Figure 5. $i_m$ is not affected by the load and always crosses zero at the middle of the pulse $t_{mid}$. When the load is extremely light, the curve of $i_r$ is infinitely close to that of $i_m$, and the zero-crossing time $t_{zeo}$ of $i_r$ is close to $t_{mid}$. Therefore, $V_{cr}\left(t_{beg}\right)$ is approximately equal to 0 in light load due to the symmetry. And the heavier the load, the faster the $i_r$ will cross zero. Therefore, $V_{cr}\left(t_{beg}\right)$ is close to $V_{cr}\left(t_{zeo}\right)$ in heavy load.

To locate the faulty switch of a high-frequency converter, the signal $V_{cr}\left(t_{beg}\right)$ with adequate information is selected. This can effectively reduce the number of samples per cycle and relieve the pressure of DSP sampling and calculation. If an OCF occurs, it will be reflected in $V_{cr}$ soon. This helps to find the OCF faster. It is worth noting that many control methods take $V_{cr}$ as a control variable [22,23]. Therefore, the proposed method has little cost for these control methods.

3.2. Fault Diagnose Strategy

The proposed fault diagnosis strategy shown in Figure 6 will be illustrated based on the LLC converter with parameters as shown in

Table 1. Converter parameters.

Input Voltage $V_{in}$	36 V
Output Voltage $V_o$	24 V
Output Power $P_o$	160 W
Switching Frequency of LLC $f_l$	200 kHz
Transformer Turns Ratio N	3:2
Magnetizing Inductance $L_m$	12.5 µH ± 10%
Resonant Inductance $L_r$	1.8 µH ± 10%
Resonant Capacitance $C_r$	300 nF ± 5%
MOSFET $S_1-S_4$	BSC070N10NS3G

. It should be noted, however, that this strategy is not limited to these specific parameters and can be adapted to LLC converters with different characteristics. As the load increases, the amplitude of $V_{cr}\left(t_{beg}\right)$ increases from about 0. However, no matter how heavy the load is, $V_{cr}\left(t_{beg1}\right)$ at the pulse starting time of $V_{gs1}$ is always negative, while $V_{cr}\left(t_{beg2}\right)$ at the pulse starting time of $V_{gs2}$ is always positive. This conclusion can also be derived from (11). When the OCF occurs, $V_{cr}\left(t_{beg}\right)$ no longer fluctuates around zero point, but changes to fluctuate around $+\frac{V_{in}}{2}$ or $-\frac{V_{in}}{2}$. Therefore, the OCF can be diagnosed by monitoring the direction of $V_{cr}\left(t_{beg}\right)$ shown in Figure 7. $V_{cr}$ is sampled twice per cycle, at the beginning of two driver signal pulses respectively, and converted into a logical signal $S_{vcr}$

$$\left\{\begin{array}{cc}{V}_{cr}\left(t_{beg}\right)>+V_{thd},\hfill & S_{vcr}=1\hfill \\ V_{cr}\left(t_{beg}\right)<-V_{thd},\hfill & S_{vcr}=-1\hfill \\ -V_{thd}<V_{cr}\left(t_{beg}\right)<+V_{thd},\hfill & S_{vcr}=0\hfill \end{array}\right.$$

(12)

where the threshold voltage $V_{thd}$ is set to prevent misdiagnosis caused by zero crossing oscillation, sampling error and other factors during light load. Therefore, in normal operation, the sampled $V_{cr}\left(t_{beg}\right)$ of each cycle can as shown in the

Table 2. The value of $S_{vcr}$ with the system in condition.

${\mathit{V}}_{\mathit{cr}}$	${\mathit{S}}_{\mathit{vcr}}$
$V_{cr}\left(t_{beg1}\right)$	−1 or 0
$V_{cr}\left(t_{beg2}\right)$	1 or 0

.

When $V_{cr}\left(t_{beg1}\right)$ and $V_{cr}\left(t_{beg2}\right)$ are both 1 or −1, it is deemed that an OCF happens and the fault signal $fla{g}_{vcr}$ changes from 0 to 1 or −1. Therefore, all cases of $S_{vcr}$ can be summarized as

Table 3. The relationship between system condition and $S_{vcr}$.

${\mathit{S}}_{\mathit{vcr}1}\&{\mathit{S}}_{\mathit{vcr}2}$	${\mathit{flag}}_{\mathit{vcr}}$	Location of the Fault
1, 1	1	$S_2$ or $S_3$
−1, −1	−1	$S_1$ or $S_4$
else	0	none

. This process may take 1 or 2 cycles to detect the OCF.

However, it is not enough just to detect the OCF, but also to be able to locate the faulty device in some applications such as fault-tolerant methods. Therefore, the operation principles after the OCF should be modified. As shown in Table 3, when $fla{g}_{vcr}$ becomes −1, it can only be determined that the OCF is on $S_1$ or $S_4$. Therefore, assuming the OCF on $S_1$ or $S_4$ is detected in the $k\_th$ cycle, $V_{gs1,4}$ are pulled down and $V_{gs2,3}$ are pulled up in the first half of the $(k+1)\_th$ cycle to charge the $C_r$. In the second half cycle, all driver signals are pulled down and $i_r$ rapidly drops to 0. Then, $V_{gs2,4}$ are pulled up and $V_{gs1,3}$ are pulled down from the $(k+2)\_th$ cycle to determine whether the OCF is on $S_4$ or not. In this case, if the faulty device is $S_4$, only $S_2$ can be turned on. $V_{cr}$ will remain negative and $i_r$ will remain 0. On the contrary, if the faulty device is $S_1$, then the resonant tank starts resonance through $S_{2,4}$, and $V_{cr}$ will cross zero point in a few cycles. The number of cycles depends on the ratio of $L_m$ to $L_r$. The resonant period $T_{rf}$ becomes $\sqrt{(L_r+L_m)C_r}$. Assuming $h=L_m/L_r$, $T_{rf}$ is $\sqrt{1+h}$ times of $T_s$, which is $T_{rf}=\sqrt{1+h}{T}_s$. Therefore, $V_{cr}$ will reverse in half a resonant period $T_{rf}$. Suppose $k_c$ is the rounded up value of $\sqrt{1+h}/2$. According to Table 1, $h=12.5/1.8=6.94$, so $k_c=2$. From the $(k+2)\_th$ cycle, the system still samples $V_{cr}$ twice every cycle, with a maximum of $k_c$ cycles taken. Therefore, during the $(k+2)\_th$ to $(k+4)\_th$ cycle, once $S_{vcr1}$ or $S_{vcr2}$ changes from −1 to 0 or 1, the faulty device can be proved to be $S_1$. As shown in Figure 8a, $V_{cr}$ crosses zero and reverses within one switching cycle as analyzed. On the other hand, $S_{vcr}$ remains −1 until $(k+4)\_th$ cycle as shown in Figure 8b, locating the faulty device at $S_4$.

When $fla{g}_{vcr}$ is 1, the operation principles are the opposite. The OCF on $S_2$ or $S_3$ is detected in the $k\_th$ cycle. $V_{gs2,3}$ are pulled up and $V_{gs1,4}$ are pulled down in the first half of the $(k+1)\_th$ cycle to charge the $C_r$. In the second half cycle, all driver signals are pulled down to reduce the amplitude of $i_r$. Then, $V_{gs2,4}$ are pulled up and $V_{gs1,3}$ are pulled down from the $(k+2)\_th$ cycle to determine whether the OCF is on $S_2$ or not. From the $(k+2)\_th$ cycle, the system still samples $V_{cr}$ twice every cycle until $k_c$ times. If $S_{vcr}$ is always 1 until $(k+4)\_th$ cycle as shown in Figure 9a, the faulty device is $S_2$. On the other hand, if $S_{vcr}$ changes from 1 to 0 or −1 as shown in Figure 9b, which proves the faulty device is $S_3$. In this way, the faulty device can be located and subsequent fault-tolerant methods can be implemented.

In some applications, the switching frequency of the converter may be further increased, when the controller may have difficulty maintaining sampling per cycle. In this case, the sampling period can be increased to a multiple of the switching period to save resources. As shown in Figure 10, when the system operates in condition, $V_{cr}$ is sampled every two cycles to save resources for the control method. When an OCF is detected, the control method is stopped and resources are used to locate the OCF as soon as possible.

4. Experiment Result

To verify the effectiveness of the proposed fault diagnosis method, an LLC converter with parameters shown in Table 1 is built and shown in Figure 11a. The proposed fault diagnosis method is implemented on the DSP TMS320F28377D, a product of Texas Instruments, headquartered in Dallas, TX, USA. The TCPA300 current probe, a Tektronix product based in Beaverton, OR, USA, is utilized for current measurements. The waveforms are monitored using the ZDL6000 wavescope platform, a product of Guangzhou Zhiyuan Electronics Co., Ltd., based in Guangzhou, China.

The relationship between $V_{cr}$ and the sampling time in different loads is shown in Figure 11b,c. The red dotted line next to the solid green line representing $i_r$ is the estimated $i_m$. The gray dashed lines represent the rising edge moments of $V_{gs1}$ and $V_{gs2}$. As analyzed, when the load is lighter, $i_r$ and $i_m$ are closer, and $V_{cr}$ at the rising edge of the pulses is closer to 0. On the contrary, when the load is heavy, $i_r$ will quickly cross zero, and $V_{cr}$ at the rising edge will be close to the maximum value of $V_{cr}$.

The process of detecting and locating OCFs in every power device of the converter is shown Figure 12, Figure 13 and Figure 14. Among them, the signal $T_{ocf}$ is generated by GPIO, which is used to indicate the time of fault occurrence and diagnosis process. To avoid misjudgment of OCFs, the voltage threshold $V_{th}$ is set to 0.5V. Take the power device $S_1$ as an example to illustrate. As shown in Figure 12a,b, an OCF occurs on $S_1$ at $t=t_0$, and $T_{ocf}$ is pulled up. In the process of $t_0-t_1$, the system detects that $fla{g}_{vcr}$ is −1, judges that there is an OCF on $S_1$ or $S_4$, and starts to locate the faulty device. At $t=t_1$, $V_{gs2}$ and $V_{gs3}$ are pulled up, the power supply charges $C_r$ through $S_2$ and $S_3$, which make the amplitude of $V_{cr}$ rises rapidly. At $t=t_2$, $V_{gs2}$ and $V_{gs3}$ are pulled down, $S_{1-4}$ are all turned off, the resonant current ir quickly drops to 0, and $V_{cr}$ also remains stable, preparing for the subsequent $i_r$ direction reversal to make $V_{cr}$ quickly cross zero. From $t=t_3$, $V_{gs2}$ and $V_{gs4}$ are pulled up, and $V_{cr}$ is continuously sampled to determine whether $V_{cr}$ will be close to zero or cross zero within kc cycles, that is, before time $t_4$. $S_2$ and $S_4$ are healthy and form a resonant circuit, and $i_r$ has dropped to 0 before $t=t_3$. After $t=t_3$, $i_r$ rises rapidly, causing $V_{cr}$ to rise rapidly, and crosses zero after about half a cycle, which makes the system locate the faulty device $S_1$.

The detection and location process of $S_2$ is shown in Figure 12c and Figure 13a. At $t=t_0$, the power device $S_2$ has an OCF. The system detects that $fla{g}_{vcr}$ is 1, and judges that $S_2$ or $S_3$ is faulty. Therefore, the system pulls up $V_{gs1}$ and $V_{gs4}$ at $t=t_1$, uses $S_1$ and $S_4$ to charge $C_r$, and turns off all power devices at $t=t_2$, so that the resonant current $i_r$ drops to 0 until $t=t_3$. At $t=t_3$, $S_2$ and $S_4$ are turned on and $V_{cr}$ is continuously detected. However, due to the OCF of $S_2$, the resonant circuit cannot be formed, and $V_{cr}$ hardly changes. Until $t=t_4$, $V_{cr}$ is still not close to zero or crosses zero, so the faulty device is located as $S_2$.

The diagnosis processes of $S_3$ and $S_4$ are similar to the above and are shown in Figure 13 and Figure 14. According to the fault diagnosis processes of various power devices, the detection process of the proposed fault diagnosis method needs 1–2 switching cycles, and locates the faulty device within a maximum of 3 switching cycles.

5. Conclusions

In this paper, an OCF diagnosis method for LLC converters is proposed. The proposed diagnosis method can locate the faulty switch within the system in 30 µs, and can be extended to high-frequency applications. The direction of $V_{cr}$ is utilized to detect the OCF. Then, the fault injection strategy is adopted to locate the faulty device. The proposed diagnostic technique requires only a single voltage sensor, a component already incorporated in numerous control method converters. This represents a reduction from the 2–3 sensors typically required. Furthermore, it outperforms conventional methods by reducing the number of samples to 1–2 per switch cycle. The diagnostic time has been reduced from over 70 µs to less than 30 µs, thereby facilitating swift OCF detection.