A Diagnostic Method for Switch Faults Applied to an Asymmetric Half-Bridge Converter

Fault diagnosis of switching devices is crucial for improving the reliability of power converters. In this paper, a current-slope-based fault diagnosis scheme is proposed for power switches in asymmetric half-bridge converters. First, a new current sensor installation scheme is proposed to obtain more current information for fault diagnosis while using fewer power devices and current sensors. In addition, a simple algebraic expression for the phase current under normal conditions is derived. Second, the principles of the fault diagnosis scheme are presented, enabling effective fault diagnosis of switches by digitizing the current slope. Finally, experiments are carried out on a four-phase switched reluctance motor system to verify the effectiveness of the proposed fault diagnosis scheme.

SECTION I. Introduction

Asymmetric half bridge power converters (AHPC) have been applied to motor drive, smart grid, and energy storage systems [1], [2]. In particular, AHPC can effectively enhance the control performance of switched reluctance motors (SRMs). To date, SRMs have received much attention because of their good robustness, high reliability and excellent fault tolerance. Moreover, the absence of windings in the rotor, no need for per-manent magnets, and simple fabrication process all lead SRMs to a low cost advantage [3], [4]. In addition, SRMs do not use brushes, enabling their use in harsh environments. However, changes in the operating environment can easily lead to motor drive system failures [5], [6], which greatly limits the application of SRMs.

Electrical faults including stator winding and power converter faults, account for the largest portion of fault cases [7]. Among them, power converter faults account for 35% of the total faults and have received considerable attention from researchers. Existing fault diagnosis algorithms for power converters can be broadly classified into two types: voltage-based methods and cur-rent-based methods. In general, voltage-based fault diagnosis methods have good diagnostic speed and diagnostic accuracy, but additional hardware circuits or voltage sensors are required. Power switch faults are detected via drive signals and a neutral-point voltage in microseconds [8]. However, this method requires additional diagnostic circuits designed separately for odd and even phase branches, which increases the cost of the SRM system. It has also shown that location information is needed to diagnose and distinguish all typical position signal faults of each position sensor rapidly and independently [9]. A switch fault diagnosis method is proposed which uses the inductor voltage as the diag-nostic quantity [10], but the method cannot identify the fault types. Similarly, faulty transistors can be identified by measuring the output voltage and comparing with the expected voltage, but the proposed fault diagnosis method is limited to open-circuit faults [11].

In general, voltage-based fault diagnosis methods require additional voltage sensors and specially designed logic judgment circuits. Current-based fault diagnosis methods, as their name implies, extract di-agnostic parameters from current information. This information is already measured for control algorithms. Therefore, these methods have received more attention than voltage-based ones because the cost of diagnosis does not increase. To date, current-based fault diagnosis methods can be subdivided into three types: phase, bus, and predictive current-based methods. Despite the high diagnostic accuracy of the phase method, it faces dif-ficulties in increased system cost and restricted application range. Two examples in [12] and [13] require the installation of additional current sensors to obtain more phase information and develop fault diagnosis, which increases the cost of the system. Other examples de-velop fault diagnosis for power transistors by reconstructing the current sensors based on phase current slopes [14] and by calculating the error between the reference and the measured phase currents [15]. How-ever, the above two approaches are only applicable to the current chopping control (CCC) strategy.

Bus current-based diagnostic methods require more current information than phase methods. In addition, more measured information require more complex di-agnostic methods. A fault diagnosis method calculates the error between the estimated and the actual bus cur-rents [16]. Although it can diagnose a wide range of fault types, it is very computationally intensive. Reference [17] studies effectively identifies faults by digitally analyzing the measured currents from the sensors and the reconstructed auxiliary currents from the DC bus, though it is limited to the soft chopping method. In addition, two fault diagnosis methods are proposed by monitoring currents at different locations within the converter via one or two current sensors [18]. However, both are limited to the voltage pulse width modulation (VPWM) strategy.

The predictive current-based methods do not increase the cost of the system, but computation demand increases significantly, which can affect the diagnostic accuracy. A current prediction method is proposed to detect and identify switch faults based on the error between the predicted and actual currents [19]. A virtual current coefficient model is developed to obtain the predicted current and to identify the fault type [20], while [21] shows that predictive current can be used to diagnose switch faults effectively. The above-ground current prediction methods cause large bias in the di-agnosis results, while model parameter interference affects diagnostic accuracy [22]. In addition, intelligent diagnostic algorithms can also improve diagnostic performance, but most of them can only be done offline [23]. In summary, research on the fault diagnosis of power switches is still in progress.

In this paper, a current-slope-based fault diagnosis scheme is proposed for AHPC. The main features of this paper are summarized as follows: 1) A new current sen-sor layout scheme based on the traditional AHPC is proposed; 2) The proposed four-phase SRM diagnosis method uses only three current sensors, which reduces the cost of the SRM system; 3) The proposed fault di-agnosis method can directly use the measured current information instead of the predicted current information, reducing the computational complexity.

The reminder of the paper is organized as follows. In Section II, the implementation principles of the proposed phase current detection scheme are presented, while the fault diagnosis scheme is proposed in Section III. Section IV analyzes the misdiagnosis moment of the proposed diagnosis method and its solution. In Section V, the proposed scheme is verified via simulations and prototype experiments. Finally, Section VI concludes the paper.

SECTION II. Proposed Phase Current Detection Scheme

A. Working States of AHPC

The topology of the four-phase AHPC is shown in Fig. 1, with four semiconductor devices in each phase. Taking phase A as an example, the four semiconductor devices are the upper switch S 1, the lower switch S2, the lower diode D 1, and the upper diode D2. There is one current sensor in each phase because of the inde-pendence of the phases. The control strategies that can be implemented include the CCC, the VPWM, and the angle position control (APC). In the soft chopping operation mode, each phase of the power converter has two MOSFET tubes as the chopper tubes and position tubes, in which S 1, S3, S5, and S7 are the chopper tubes, while S2, S4, S6, and S8 are the position tubes. $G_{\mathrm{s}\iota}-G_{\mathrm{s}\sigma}$ represent the gate signals of S I-S8. Notably, for $k$ being 1–8, $G_{\mathrm{S}k}=1$ indicates that a high-level gate signal is applied, and $G_{\mathrm{S}k}=0$ indicates that a low-level one is applied.

Fig. 1.

The topology of traditional AHPC.

The phase currents of the AHPC are defined as $i_{\mathrm{a}}, i_{\mathrm{b}}, i_{\mathrm{c}}$, and $i_{\mathrm{d}}$. The different operation states of the AHPC are shown in Fig. 2. In phase A, there are three basic operation states. As shown in Fig. 2(a), the first operation state is the excitation state (State E). In State E, $G_{\mathrm{s}1}$ and $G_{\mathrm{S}2}$ are set at high levels to turn on the chopper tube SI and position tube S2, which increases the ex-citation current. The zero-voltage freewheeling state (State Z) is shown in Fig. 2(b). In State $\mathrm{Z}, G_{\mathrm{S}1}$ is set to a low level, and $G_{\mathrm{S}2}$ is set to a high level. The third operation state is the demagnetization state (State D) as shown in Fig. 2(c), in which both $G_{\mathrm{s}1}$ and $G_{\mathrm{S}2}$ are set at low levels to demagnetize the phase current.

Fig. 2.

AHPC operating states. (a) Excitation state. (b) Zero-voltage freewheeling state. (c) Demagnetization state.

B. Current Detection

As shown in Fig. 3, the currents flowing through the phase A chopper tube S 1, position tube S2, lower diode D 1, and upper diode D2 are denoted by $i_{\mathrm{S}1}, i_{\mathrm{S}2}, i_{\mathrm{D}1}$, and $i_{\mathrm{D}2}$, respectively. The total currents of phase A flowing through the lower and upper parts of the bridge arm are defined as $i_{\mathrm{K}1}$ and $i_{\mathrm{K}2}$, respectively, presented as: $$\begin{align*} & i_{\mathrm{K} 1}=i_{\mathrm{S} 2}+i_{\mathrm{D} 1} \tag{1}\\ & i_{\mathrm{K} 2}=i_{\mathrm{S} 1}+i_{\mathrm{D} 2}\tag{2}\end{align*}$$

Fig. 3.

Description of current path.

According to the operation principles of the SRM, the total current and slope of the upper and lower bridge arms in State E, State Z, and State D are analyzed as follows. In State E, the chopping tube S 1 and position tube S2 are turned on. At this time, the current flows through S 1 and S2, and the total current of the lower part of the bridge arm only contains the $i_{\mathrm{S}2}$ component, whereas the total current of the upper part of the bridge arm only contains the $i_{\mathrm{S}1}$ component. Therefore, the winding excitation phase current increases continuously. The current slope in State E is defined as: $$\begin{equation*} \xi_{\mathrm{E}}=(U_{\mathrm{s}}-i\times R_{\mathrm{E}}-i\times\frac{\mathrm{d}L}{\mathrm{d}t})\div L\tag{3}\end{equation*}$$ where $U_{\mathrm{s}}$ is the bus voltage; $i$ is the phase current; $L$ is the winding inductance; and $R_{\mathrm{E}}$ is the equivalent resistance of the excitation loop.

In State Z, the lower diode D 1 and position tube S2 are turned on. It can be seen that $i_{\mathrm{D}1}$ is equal to $i_{\mathrm{S}2}$. The current slope in State Z is: $$\begin{equation*} \xi_{\mathrm{z}}=(-i\times R_{\mathrm{z}}-i\times\frac{\mathrm{d}L}{\mathrm{d}t})\div L\tag{4}\end{equation*}$$ where $R_{\mathrm{Z}}$ is the equivalent resistance of the ze-ro-voltage continuing loop.

In State D, the current flows through the lower diode D 1 and upper diode D2. The total current of the lower half of the bridge arm contains only the $i_{\mathrm{D}1}$ component, and the total current of the upper half of the bridge arm contains only the $i_{\mathrm{D}2}$ component. The current slope in State D is defined as: $$\begin{equation*} \xi_{\mathrm{N}}=(-U_{\mathrm{s}}-i\times R_{\mathrm{N}}-i\times\frac{\mathrm{d}L}{\mathrm{d}t})\div L\tag{5}\end{equation*}$$ where $R_{\mathrm{N}}$ is the equivalent resistance of the demag-netization circuit.

The current slope relationship differs for different current paths and operation states in the CCC strategy, and this feature can also be applied to the VPWM. For the APC, the on-state has State E and State D, and Eqs. (1) and (3) are also applicable. The current analysis under different states is summarized in Table I.

Table I Current analysis under different states

C. Reconstruction of Current Sensors

A placement scheme for current sensors is proposed to reduce the diagnostic cost, which is shown as Fig. 4. Compared with the traditional current detection scheme in Fig. 1, the number of current sensors can be reduced to 3. The currents measured by the sensors LEM 1, LEM 2, and LEM 3 are denoted by $i_{1}, i_{2}$ and $i_{3}$, respectively.

Fig. 4.

New position of the current sensor.

Taking phase A as an example, the working interval of each phase is shown in Fig. 5.

Fig. 5.

CCC schematic diagram of the four-phase working interval under control.

Next, the relationship between the phase current and measurement current is shown in (6). In State E, the phase-A current $(i_{\mathrm{a}})$ is equal to $i_{2}$; in State Z, com-bined with Table I, $j_{\mathrm{a}}$ is equal to $0.5i_{2}$; and in State D, $j_{\mathrm{a}}$ is equal to $i_{2}$. $$\begin{equation*} i_{\mathrm{a}}=\begin{cases} i_{2},\ \text{when}\ G_{\mathrm{s}\iota}=1\ \text{and}\ G_{\mathrm{S}2}=1\\ 0.5i_{2},\ \text{when}\ G_{\mathrm{S}1}=0\ \text{and}\ G_{\mathrm{S}2}=1\\ i_{2},\ \text{when}\ G_{\mathrm{S}2}=0,\ G_{\mathrm{S}4}=1,\ \text{and}\ G_{\mathrm{S}6}=0\end{cases}\tag{6}\end{equation*}$$

Then, $j_{\mathrm{a}}$ can be derived as: $$\begin{equation*} i_{\mathrm{a}}=G_{\mathrm{S} 1} i_2+\frac{1}{2} \overline{G_{\mathrm{S} 1}} G_{\mathrm{S} 2} i_2+\overline{G_{\mathrm{S} 2}} \overline{G_{\mathrm{S} 6}} G_{\mathrm{S} 4} i_2\tag{7}\end{equation*}$$

Similarly, the phase-B current $(i_{\mathrm{b}})$, phase-C current $(i_{\mathrm{c}})$ and phase-D current $(i_{\mathrm{d}})$ are presented as: $$\begin{equation*}\left\{\begin{array}{l} i_{\mathrm{b}}=G_{\mathrm{S} 3} i_3+\frac{1}{2} \overline{G_{\mathrm{S} 3}} G_{\mathrm{S} 4} i_3+\overline{G_{\mathrm{S} 4}} \overline{G_{\mathrm{S} 8}} G_{\mathrm{S} 6} i_3 \\ i_{\mathrm{c}}=G_{\mathrm{S} 5} i_2+\frac{1}{2} \overline{G_{\mathrm{S} 5}} G_{\mathrm{S} 6} i_2+\overline{G_{\mathrm{S} 2}} \overline{G_{\mathrm{S} 6}} G_{\mathrm{S} 8} i_2 \\ i_{\mathrm{d}}=G_{\mathrm{S} 7} i_3+\frac{1}{2} \overline{G_{\mathrm{S} 7}} G_{\mathrm{S} 8} i_3+\overline{G_{\mathrm{S} 4}} \overline{G_{\mathrm{S} 8}} G_{\mathrm{S} 2} i_3\end{array}\right.\tag{8}\end{equation*}$$

The current of each phase in normal operation can be obtained by combining (7) and (8).

SECTION III. Proposed Fault Diagnostic Scheme

As shown in Fig. 4, current sensor LEM 1 collects the current flowing through the chopper tube and the upper diode. Current sensor LEM 2 collects the relevant cur-rents crossing over position tubes and the lower diode of phase A and phase C, while LEM 3 collects the relevant currents crossing over position tubes and the lower diode of phase B and phase D. As shown in Fig. 5, phase A may work in phase A alone, in phases AD and in phases AB at the same time. The phase A working interval is completely separated from that in phase C, so LEM 2 will not be affected by the working current of the other phases in the phase A working interval. The cur-rent collected by LEM 2 in the phase A operating interval is completely dependent on the different states of phase A, and this property is also applicable in the case of transistor failure.

Combined with the analysis in Section II.B, the total current flowing through $i_{\text{Kl}}$ and $i_{\mathrm{K}2}$ of the upper and lower bridge arms related to phase A are extracted for phase A fault diagnosis. The obtained $j_{\mathrm{a}}$ is equal to $i_{\mathrm{K}1}$, shown as: $$\begin{equation*} i_{\mathrm{K} 1}=G_{\mathrm{S} 1} i_2+\frac{1}{2} \overline{G_{\mathrm{S} 1}} G_{\mathrm{S} 2} i_2+\overline{G_{\mathrm{S} 2}} \overline{G_{\mathrm{S} 6}} G_{\mathrm{S} 4} i_2=i_{\mathrm{a}}\tag{9}\end{equation*}$$

$i_{\mathrm{K}2}$ refers to the current component related to phase A flowing through LEM 1, and other phase current components should be removed. When phase A is in operation, if the other phases are not in the excitation or de-magnetization interval, $i_{\mathrm{K}2}$ is equal to $i_{s2}$. If phase D is in the excitation and demagnetization intervals, $i_{\mathrm{K}_{2}}$. is equal to the difference between $i_{1}$ and $j_{\mathrm{d}}$. If phase B is in the exciting interval, $i_{\mathrm{K}2}$ is equal to the difference between $i_{1}$ and $i_{\mathrm{b}}$. Taking the gate signal expressions into consideration, the expression of $i_{\mathrm{K}2}$ is shown as: $$\begin{gather*} i_{\mathrm{K} 2}=\left(G_{\mathrm{S} 2}+\overline{G_{\mathrm{S} 2}} \overline{G_{\mathrm{S} 6}} G_{\mathrm{S} 4}\right) i_1-G_{\mathrm{S} 2} G_{\mathrm{S} 7} i_{\mathrm{d}}-\\\overline{G_{\mathrm{S} 4}} \frac{G_{\mathrm{S} 8}}{G_{\mathrm{S} 2} i_{\mathrm{d}}}-\left(G_{\mathrm{S} 2}+\overline{G_{\mathrm{S} 2}} \frac{G_{\mathrm{S} 6}}{\left.G_{\mathrm{S} 4}\right) G_{\mathrm{S} 3} i_{\mathrm{b}}}. \right.\tag{10}\end{gather*}$$

To enhance the immunity of fault diagnosis, digital processing of $i_{\mathrm{K}1}$ and $i_{\mathrm{K}2}$ is explored to determine the digitization values $P_{1}$ and $P_{2}$, as shown in (11). The digitization values $P_{1}$ and $P_{2}$ are set as the diagnosis indices to detect the switch faults. $$\begin{equation*} P_{i(i=1,2)}=\begin{cases} 1,\ i_{Ki} > 0\\ 0,\ i_{Ki}=0\end{cases}\tag{11}\end{equation*}$$

A. Analysis of Patient Characteristics Under Normal Operation Conditions

Under normal operation, there are three working conditions: State E, State Z, and State D. In State E, the chopper and the position tubes are turned on, so the values of $P_{1}$ and $P_{2}$ are both high. In State Z, the diode and the position tube work in the conduction state, so the current does not pass through LEM 1, and the cur-rent of LEM 2 decreases with time, which leads to $P_{1}$ being 1 and $P_{2}$ being 0. In State D, the upper and lower diodes conduct continuous current, and the current simultaneously passes through LEM 1 and LEM 2, which increases $P_{1}$ and $P_{2}$.

B. Analysis of the Characteristics of Faulty Operation

A diagram of the current paths under different fault states is shown in Fig. 6. The proposed fault detection criteria are summarized as follows.

OUM and OLM faults can be detected in the excitation interval of A. As shown in Fig. 6(a), when an OUM fault occurs, the phase A winding cannot be excited normally, and the winding current continues to flow through the position tube and the lower diode without passing through LEM 1. Therefore, when $P_{1}$ is detected as 1 and $P_{2}$ is detected as 0, an OUM fault can be de-tected. As shown in Fig. 6(b), when an OLM fault oc-curs, the winding current continues to flow through the chopper tube and the upper diode. As the continuous current does not pass through LEM 2, $P_{1}$ is equal to 0 and $P_{2}$ is equal to 1, indicating the identification of an OLM fault.

OLM and SUM faults can also be detected in state Z.

When an OLM fault occurs, as shown in Fig. 6(b), the phase A winding cannot have a normal zero-voltage continuous current, so the winding current continues through the chopper tube and the upper diode rather than through LEM 2. Consequently, $P_{1}$ is equal to 0 and $P_{2}$ is equal to 1, indicating that an OLM fault can be identified. When an SUM fault occurs, as shown in Fig. 6(c), the winding current is channeled through the chopper and position tubes, and the channeling process passes through LEM 1 and LEM 2. Thus, $P_{1}$ and $P_{2}$ are equal to 1, indicating that an SUM fault can be detected.

Moreover, a negative voltage demagnetizing range can be applied to detect the SUM and SLM faults. When an SUM fault occurs, the phase-A winding cannot undergo normal negative voltage demagnetization. At this time, the winding current is channeled through the chopper tube and the upper diode without LEM 2, so $P_{1}$ is equal to 0 and $P_{2}$ is equal to 1 (Fig. 6(d)). When an SLM fault occurs (Fig. 6(e)), the winding current is channeled through the position tube and lower diode, and the current flowing through LEM 2 decreases with time, so $P_{1}$ and $P_{2}$ are equal to 1, indicating that an SLM fault can be detected.

The diagnostic indices of patients in phase A are presented in Table II according to the above analysis.

Fig. 6.

Diagram of current paths in different fault states. (a) OUM fault. (b) OLM fault. (c) SUM fault. (d) SUM fault. (e) SLM fault.

Table II Diagnosis index of phase A

SECTION IV. Misdiagnosis Moment and Solution

The possible misdiagnosis moments and mitigating solutions are analyzed in this section to enhance the diagnostic reliability of the proposed fault diagnosis method.

There are two possible misdiagnosis moments, de-noted by moment A and moment B. Moment A is the moment of state transition. Ideally, if the sampling frequency of analog-to-digital conversion is extremely high, the driving signal can be approximated such that it is consistent with the change in the current state. However, it is impossible to achieve such a condition in real systems. The sampling time interval affects the calculation of the diagnosis index, and the update time of the driving signal is earlier than the calculation time of the diagnosis index, which is unfavorable for diag-nosis and may lead to misdiagnosis.

As shown in Fig. 7(a), the two adjacent sampling moments are $t_{1}$ and $t_{2}$, and the gate signal change moment is $t_{\mathrm{s}}$. At time $r_{1}$, the gate signals $G_{\text{sl}}$ and $G_{\mathrm{S}2}$ are both high. At moment $t_{2}$, the gate signals $G_{\text{sl}}$ and $G_{\mathrm{S}2}$ are low and high, respectively. During time from $r_{1}$ to $t_{2}$, the values of $P_{1}$ and $P_{2}$ depend on the value at $t_{1}$. After the $t_{\mathrm{s}}$ moment, $P_{1}$ and $P_{2}$ should be equal to 1 and 0, respectively. However, the next sampling point has not yet arrived. $P_{1}$ and $P_{2}$ maintain their values at $t_{1}$. According to Table I, SUM faults are detected, re-sulting in misdiagnosis. After the diagnosis index is updated, phase A is normal. Therefore, the possible misdiagnosis range is from the gate signal change moment $t_{\mathrm{s}}$ to $t_{2}$ in the two sampling moments.

It is generally considered that the diagnostic time $(T_{\mathrm{d}})$ refers to the time when a fault affects system operation until the fault is confirmed. Now, the diagnostic time at phase A is quantified. From the analysis of the actual diagnosis process, because the update time of the driving signal is inevitably smaller than the update time of the feature quantities $P_{1}$ and $P_{2}$, even if a fault does not occur at the state transition, the sampling and cal-culation times of the feature quantities must be consid-ered to ensure that the driving signal and diagnosis indices are the same for accurate comparison. Only in this way can the diagnosis be truly convincing.

As shown in Fig. 7(b), taking $G_{\mathrm{S}1}=1$ and $G_{\mathrm{S}2}=1$ as examples, when a fault occurs in a non-turning state, the diagnostic time only depends on a single sampling time, namely $T_{s}$, and in this case, $T_{\mathrm{d}}=T_{\mathrm{s}}$. The possible so-lution to misdiagnosis at time A may lead to an increase in the actual diagnostic time. Taking the SUM fault occurring at $G_{\mathrm{S}1}=1$ and $G_{\mathrm{S}2}=1$ as an example, the worst-case scenario is shown in Fig. 7(c). The first sampling is carried out at the moment of state transition, and the driving signal and feature quantities are compared at time $t_{2}$ after the first $T_{s}$ interval. At this time, $P_{1}=1$ and $P_{2}=1$, so the fault will not be detected. In-stead, the fault can be identified only at time $t_{3}$ after the second $T_{s}$ interval, in which case $T_{\mathrm{d}}=2T_{\mathrm{s}}$.

Fig. 7.

Fault situation time analysis. (a) State transition moment. (b) OUM occurs in non-transitional states. (c) OUM occurs in transitional states.

Therefore, in addition to the criteria in Section III, some supplementary principles are needed to avoid misdiagnosis. Misdiagnosis may occur at moment A, and its root cause is the non-synchronized times at which the gate signal and fault characteristic quantities are obtained. The solution is to use the gate signal in each inspection at the latest current signal collection, i.e., the gate signal at $t$ l in Fig. 7. The advantage of this approach is that in the event of a state transition occur-rence, the gate signal used in the false diagnosis interval is still the gate signal before the transition, which can avoid possible misdiagnosis at the state transition moment. However, the diagnostic time is related to the sampling time of the current sensor.

1. The moment B is the time when other phase faults occur. In Section III, the currents of $i_{\text{KJ}}$ and $i_{\mathrm{K}2}$ which are related to the upper and lower bridge arms of phase A are extracted, and the value of the fault characteristic quantity is determined by whether there is current in $i_{\mathrm{K}1}$ and $i_{\mathrm{K}2}$. The extracted current is calculated by the joint action of the current sensor and the gate signal. The derivation process considers that ABCD phases work normally. In fact, when the BCD phases are faulty, $i_{\mathrm{K}1}$ and $i_{\mathrm{K}2}$ may be affected, and phase A misjudgment may occur. The following describes the impact of the oc-currence time of other phase faults on phase A fault diagnosis.

2. It can be seen from the phase A operating interval shown in Fig. 4 that the phase C of the AHPC cannot work at the same time as the phase A, and the operating interval of the phases BD partially overlaps with the phase A. However, the phases Band D do not work at the same time, so it is only necessary to consider the phase B and phase D when other phase faults occur. $i_{\text{KJ}}$ is calcu-lated by the current $i_{2}$ collected by LEM 2, and the value of $i_{\mathrm{K}2}$ is related to the current $i_{1}$ collected by LEM 1. Therefore, it is only necessary to consider the influence of the phase B and phase D faults on the value of $i_{\mathrm{K}2}$.

The chopper tube is analyzed. For example, if the phase B chopper tube is short-circuited shown as Fig. 8(a), the corresponding gate signal $G_{\mathrm{S}3}$ is at a low level, and the phase B cannot enter State Z. At this time, if $G_{\mathrm{S}1}=0$ and $G_{\mathrm{S}2}=1$, the actual $i_{\mathrm{K}2}$ increases according to (10), $i_{\mathrm{K}2}=i_{\mathrm{J}}$, resulting in $P_{2}=1$. Phase A may be misdiagnosed as an SUM fault. This analysis is also applicable to short circuits in the phase D chopper tubes. If the phase B chopper tube is open as shown as Fig. 8(b), the corresponding gate signal $G_{\mathrm{S}3}$ is at a high level, and if $G_{\mathrm{S}1}=1$ and $G_{\mathrm{S}2}=1$, the actual $i_{\mathrm{K}2}$ decreases according to (10) and $i_{\mathrm{K}2}=i_{1}-i_{\mathrm{b}}$, which may cause $P_{2}=0$. When $G_{\mathrm{S}1}=1$ and $G_{\mathrm{S}2}=1$, phase A is misdi-agnosed as an OUM fault. This analysis is also appli-cable to the phase D chopper open circuit.

3. Analyze the position tube. If the phase D position tube is short-circuited as shown in Fig. 8(c), in the de-magnetization interval (only State D of the phase D is considered at this time, and phase B cannot be in the demagnetization state when phase A works), if $G_{\mathrm{S}1}=1$ and $G_{\mathrm{S}2}=1$, the actual $i_{\mathrm{K}2}$ decreases according to (10) and $i_{\mathrm{K}2}=i_{1}-i_{\mathrm{d}}$, which may result in $P_{2}=0$. When $G_{\mathrm{S}1}=1$ and $G_{\mathrm{S}2}=1$, phase A is misdiagnosed as an OUM fault. If the phase B position tube is open, the corresponding gate signal $G_{\mathrm{S}3}$ is at the high level, and the calculated values of $i_{\mathrm{b}}$ are all zero, which is increased according to (10), resulting in $P_{2}=1$. When $G_{\mathrm{S}1}=0$ and $G_{\mathrm{S}2}=1$, phase A may be misdiagnosed as an SUM fault. This analysis is also applicable to an open phase D position tube.

The misdiagnosis of phase A due to other phase faults is shown in Table III.

Fig. 8.

Phases B or D fault current path. (a) phase B SUM. (b) phase B OUM. (c) phase D SLM. (d) phase B OLM.

Table III Influence of other phase faults on phase a diagnosis

Therefore, in addition to the criteria in Section III, some supplementary principles are needed to avoid misdiagnosis.

For time B, other phase faults may cause incorrect di-agnoses of phase A OUM and SUM faults. The root cause of this problem is that the fault characteristic quantity $P_{2}$ is related to $i_{\mathrm{K}2}$, and the value of $i_{\mathrm{K}_{2}}$. changes when there is a fault in other phases. The solution is to identified $i_{\mathrm{K}1}$ after the diagnosis of the OUM and SUM faults. If the $i_{\mathrm{K}1}$ waveform deviates from the normal operating track, the OUM and SUM faults are identified; however, if the $i_{\mathrm{K}1}$ waveform is normal, this diagnosis is considered a mis-diagnosis of the OUM and SUM faults. Notably, this is not a misdiagnosis in the traditional sense. If this type of misdiagnosis occurs, it is bound to be a fault in phases B or D, and it is necessary to conduct relevant investigations on phases B or D. The flow chart of the online implementation is shown in Fig. 9.

Fig. 9.

Online execution flow chart.

SECTION V. Simulation and Experimental Verification

A. Simulation Results

The software Matlab/Simulink is used to build the simulation model of a four-phase 8/6 SRM. The CCC is adopted with a turn-on angle of 0° and a turn-off angle of 16°. The current sampling time is 50 $\mu \mathrm{s}$, the SRM operates at 1000 r/min, and $U$ is 24 V. Short-circuit and open-circuit faults are simulated by a constant on signal and a constant off signal, respectively.

Figure 10(a) shows the simulation waveforms of the phase A current quantities $i_{\mathrm{K}1}$ and $i_{\mathrm{K}2}$, and the characteristic quantities $P_{1}$ and $P_{2}$ when the motor is running normally in CCC mode. In State E, both $i_{\mathrm{K}1}$ and $i_{\mathrm{K}2}$ increase, and the characteristic quantities $P_{1}=1$ and $P_{2}=1$. In State $\mathrm{Z}, i_{\mathrm{K}1}$ decreases, the value of $i_{\mathrm{K}2}$ is 0, and the characteristic quantities $P_{1}=]$ and $P_{2}=0$. In State D, the phase current $i_{\mathrm{a}}$ is nonzero, $i_{\mathrm{K}1}$ and $i_{\mathrm{K}2}$ decrease, and the characteristic quantities $P_{1}=1$ and $P_{2}=1$. The simulation results agree with the theoretical analysis.

Figure 10(b) shows the simulation results of the phase A OLM fault under the CCC mode operation of the motor. When a fault occurs, the winding current continues to flow through the chopping tube and upper diode without passing through LEM 2, and the current flows twice through LEM 1, so $i_{\mathrm{K}1}$ is $0, P_{1}=0, i_{\mathrm{K}2}$ increases suddenly, and $P_{2}=1$.

Figure 10(c) shows the simulation results of the phase A SLM fault under the CCC mode operation of the motor. When a fault occurs, the phase A winding cannot undergo normal negative voltage demagnetization. At this time, the winding current is channeled through the position tube and the lower diode without passing through LEM 1, and the current flows twice through LEM 2. Therefore, $i_{\mathrm{K}1}$ increases suddenly, $P_{1}=1, i_{\mathrm{K}2}$ is 0, and $P_{2}=0$.

Fig. 10.

Simulation results. (a) Normal operation. (b) OLM fault of phase A. (c) SLM fault of phase A.

B. Experimental Verification

A low-power 8/6 SRM prototype is designed according to the above analysis to verify the proposed transformer reconstruction method and diagnostic strategy. As shown in Fig. 11(a), TMS320F28335 is used as the control core to develop the control strategy and generate the driving signals. After the driving sig-nals passing through the optically coupled isolators, the driving signals are amplified by TLP250. At the same time, analog-to-digital sampling and digital-to-analog conversion are carried out by AD7606 and DA5344, respectively. As shown in Fig. 11(b), a dynamic torque sensor, magnetic powder brake, and encoder are se-lected for torque measurement, load simulation and position detection, respectively. The sampling frequency in the experiment is set to 20 kHz, which is consistent with the simulation.

Fig. 11.

Control platform. (a) Prototype SRM. (b) Experimental setup.

The CCC experiments are conducted under different loads and speeds, and the corresponding results are shown in Fig. 12. As seen, the currents of the four phases current are symmetrical.

Fig. 12.

The calculated phase current under different loads and speeds. (a) 0 Nm and 500 r/min. (b) 0 Nm and 1000 r/min. (c) 0.5 Nm and 500 r/min. (d) 0.5 Nm and 1000 r/min.

The measured phase current is defined as $j_{\text{am}}$. and the current error is defined as $\Delta i_{\mathrm{a}}$. Figure 13 shows that $\Delta i_{\mathrm{a}}$ has small fluctuations and low amplitudes, and the calculated phase current agrees with the actual phase current. The difference between the calculated current and the actual current $\Delta i_{\mathrm{a}}$ is 0.2 A and is within the allowable error range, indicating the validity of current detection.

Fig. 13.

Error of currents. (a) 0.2 Nm and 500 r/min. (b) 0.2 Nm and 1000 r/min.

The reconstruction method of the current transformer is also suitable for the VPWM and APC. The conduction states of the VPWM and CCC are the same, so no VPWM results are presented here. Compared with the on-state of the CCC, the APC lacks State Z. The experimental results of the APC experiments are shown in Fig. 14.

Fig. 14.

The calculated phase current in the APC strategy. (a) 0.2 Nm and 1000 r/min. (b) Comparison of the phase current at 0.2 Nm and 1500 r/min.

The diagnosis situation of the OUM fault is shown in Fig. 15. In this case, the phase A winding cannot be excited normally, and the winding current continues to flow through the position tube and the lower diode, while only passing through LEM 2. Therefore, $i_{\mathrm{K}1}$ has a current value but continues to decrease, and $i_{\mathrm{K}_{2}}$. is zero. When the OUM fault occurs, $P_{1}$ is equal to 1, and $P_{2}$ is equal to O. The abnormal situation of the $i_{\mathrm{K}1}$ value for a period of time after the fault occurred is due to the fact that $i_{\text{KI}}$ cannot maintain the original rule after the fault occurrence. Because the experiment uses a constant on signal and constant off signal to simulate the short-circuit fault and open-circuit fault, respectively, the sampling time may be less than the specified cal-culation time of TMS320F28335 for a period of time after the fault occurs, resulting in violent jitter of the calculated current value for a period of time.

Fig. 15.

OUM fault experiment results. (a) Operating at 500 r/min. (b) Operating at 1000 r/min.

Moreover, Fig. 15 shows the phenomenon of regular movement within a certain range. This situation does not affect the diagnosis. First, even though the precise current cannot be calculated within a short time after the fault, the fault diagnosis strategy is based on detecting a current, while severe current jitter only occurs when a current is present. Therefore, when the current is zero, current instability will not occur, and the value of the characteristic quantity will not be affected. Second, the general change law of the current can still be seen in the case of unstable current calculations. The current change trend clearly decreases after the fault occurrence. Therefore, this situation does not affect fault diagnosis.

The SUM fault is shown in Fig. 16. In this case, the phase A winding cannot have a normal zero-voltage continuous current, the winding current flows through the chopping and the position tubes, and the conduction process passes through LEM 1 and LEM 2. Therefore, $i_{\mathrm{K}1}$ and $i_{\mathrm{K}_{2}}$. have current values and continue to increase.

Fig. 16.

SUM fault experiment results. (a) Operating at 500 r/min. (b) Operating at 1000 r/min.

The OLM fault is shown in Fig. 17. In this case, the phase A winding cannot be properly excited and can continue at zero voltage. At this time, the winding cur-rent continues to flow through the chopping tube and the upper diode while only passing through LEM 1. Therefore, $i_{\mathrm{K}2}$ has a current value but continues to de-crease, but $i_{\mathrm{K}1}$ is zero. For a period of time after the fault occurrence, $i_{\mathrm{K}1}$ is negative, which does not affect diagnosis, but the winding phase current cannot be considered as negative.

Fig. 17.

OLM fault experiment results. (a) Operating at 500 r/min. (b) Operating at 1000 r/min.

The SLM fault is shown in Fig. 18. In this case, the phase A winding cannot undergo normal negative voltage demagnetization. At this time, the winding current is conducted through the position tube and the lower diode without passing through LEM 1 during the conduction process. The current flowing through LEM 2 decreases with time, so $i_{\mathrm{K}1}$ continues to decrease and $i_{\mathrm{K}2}$ becomes zero.

Fig. 18.

SLM fault experiment results. (a) Operating at 500 r/min. (b) Operating at 1000 r/min.

Dynamic situations can be added to fault diagnosis through simulation and experimentation to avoid mis-diagnosis in experimental verification. If the fault can still be diagnosed under dynamic conditions, the proposed fault diagnosis method has a strong ability to avoid misdiagnosis. As shown in Fig. 19(a), when the load torque increases from 0.1 Nm to 0.5 Nm, if an OUM fault occurs, the fault can be effectively diag-nosed, and the load transformation process is not mis-diagnosed. As shown in Fig. 19(b), when the speed changes from 500 r/min to 1000 r/min, if an OUM fault occurs, the fault can be effectively diagnosed, and the speed change process is not misdiagnosed. Therefore, the proposed fault diagnosis method has good robustness to dynamic changes in speed and load torque mu-tations.

Fig. 19.

Robustness verification of the fault diagnosis scheme. (a) Load mutation causes the OUM fault. (b) Speed mutation causes the OUM fault.

The feasibility of the reconstruction and diagnosis methods for the current transformers is verified via experiments. The new position of the current trans-former can realize various control modes for the CCC, VPWM, and APC. Moreover, the proposed diagnosis method can identify OUM, SUM, OLM, and SLM faults.

C. Comparison with Existing Methods

A comparison of the fault diagnosis methods is shown in Table IV. $T_{\mathrm{s}}$ and $T_{\mathrm{p}}$ are the sampling time and phase current period, respectively. Compared with other schemes, the proposed method has the following advantages: 1) fast diagnostic speed; 2) ability to reduce the number of current sensors and cost of power con-verters; and 3) suitability for various control strategies.

Table IV Comparison with existing methods

To more intuitively reflect the comparison effect, a radar chart is presented in Fig. 20 with a score of 0–10 points. Figure 20(a) compares the proposed method and voltage-based fault diagnosis methods, while Fig. 20(b) shows a comparison of the proposed method and cur-rent-based fault diagnosis methods. Several indicators related to the radar chart are defined as follows: 1) Di-agnosis time. The shorter the diagnostic time is, the greater the scores are. 2) Cost. Higher scores are obtained when the number of current sensors is reduced. 3) Control measures. Higher scores are obtained when the method is suitable for multiple control strategies. 4) Multiple fault detection. The potential to detect multiple faults is awarded with higher scores. 5) Ability to pre-vent misdiagnosis. A greater ability to prevent misdi-agnosis under various working conditions is associated with higher scores. Notably, for the phase current-based fault diagnosis method, each phase requires a current sensor. Thus, for the prototype four-phase SRM, the number of current sensors is four. However, the proposed method requires three current sensors. Therefore, in comparison with phase current-based methods, the proposed fault diagnosis method is more cost-effective.

Figure 20 shows that the prominent advantages of the proposed method in this paper are cost effective, have wide applicability, strong anti-misdiagnosis ability, and rapid diagnosis speed.

Fig. 20.

Comparison of fault diagnosis methods. (a) Comparison with voltage-based fault diagnosis methods. (b) Comparison with current-based fault diagnosis methods.

SECTION VI. Conclusion

According to the fault type and location of switches in an SRM system, a new fault diagnosis scheme based on the current slope is proposed. The proposed AHPC-based current detection scheme can effectively obtain the phase current and additional current information before and after a fault while reduce the number of current sensors used. According to the obtained cur-rent information, the digital characteristic value of the current slope is defined to diagnose the fault of the switches. The experimental results verify the effectiveness of the proposed fault diagnosis scheme. The main contributions of this study can be summarized as follows: 1) a new current sensor layout scheme based on AHPC is proposed; 2) the proposed four-phase SRM diagnosis method uses only three current sensors, which reduces the cost of the SRM system; and 3) the fault diagnosis method proposed in this paper can directly use the measured current information instead of the predicted one, thus reducing the computational complexity and accelerating the diagnosis speed.

Availability of Data and Materials

Not applicable.

ACKNOWLEDGMENT

Not applicable.