1. Introduction
Permanent magnet synchronous motors (PMSMs) have some attractive characteristics, such as their high reliability and efficiency, robustness and compactness, which make them very popular machines in the industry and in power systems [
1,
2]. To obtain these attractive features of PMSMs, the driving system must be as reliable as possible. Thus, inverters are essential players in driving these motors [
3,
4]. However, the reliable operation of these inverters improves the reliability of the power grid and the PMSMs [
5].
In smart grids, inverters are used for various reasons [
6]. When an inverter is operated at high frequencies for an extended period of time, it is vulnerable to serious heat generation and loss issues, which can result in switching device failures such as short-circuit and open-circuit faults, which account for the majority of motor drive system failures [
7]. Open-circuit faults have less of an effect on the motor itself and can be detected easily using different techniques. Short-circuit faults are rapid and hard to detect, meaning a protection circuit is required to avoid their impact on the motor drivers. Hence, the motor should be stopped when a short-circuit fault occurs and repair will be needed. The detection of these faults is covered in many papers with different techniques, such as in [
8,
9]. Fault diagnosis in PMSM driving systems has been paid more attention in recent years. Different methods have been proposed for this purpose in recent years. For instance, the signal-based open switch fault detection method was proposed in [
10,
11]. In these two studies, due to the use of a complex mathematical model, they employed more hardware devices (in addition to voltage and current measuring systems), such as FPGAs in [
10] and magnetic coupling elements in [
11]. Therefore, their systems cost more, which means these methods are not preferable for the industry. Another current-signal-based method was proposed in [
12]. This method can effectively detect a fault if the inverter current is not balanced (detecting the neutral current of the three-phase inverter). However, this method becomes more complex when using a high multilevel inverter (e.g., above seven levels). In [
13,
14], new systems were proposed to detect both mechanical and electrical faults (open-circuit faults in PMSM driving systems). The proposed systems are sensors-based. Both systems have a degree of complexity, even during hardware installation or software implementation. However, neither method involves any driving system recovery techniques.
In [
15,
16], machine learning techniques were applied to detect abnormalities in a power system, such as symmetric and asymmetric faults. In these studies, a real power system dataset was collected and divided into training and testing datasets with different percentages. The accuracy of the proposed system was high, and it was compared with different artificial intelligence (AI) techniques. However, in order to reduce the complexity and number of malfunctions and failures due to the use of large measuring systems with the conventional fault diagnosis methods, AI methods were introduced for driving system fault diagnosis. In recent years, various AI algorithms have been applied to detect faults, and they have shown their usefulness in fault detection and identification. For instance, the authors in [
9] proposed a method to detect open-circuit faults using Park’s vector average current method; then, they applied a fuzzy logic technique to obtain information regarding faulty VSI switches. The results for this method were compared with open-circuit detection methods. In [
17], a combinational logic-based and fuzzy logic system was proposed for fault diagnosis. This method has some merits; it is simple to apply and it has good accuracy in the diagnosis procedure, but it must be combined with an intelligence redundancy engagement system. Moreover, the presented method is limited to detecting only open switch faults.
In [
18], a neural network algorithm was generated for fault diagnosis and fault placement detection. The paper proposed a multiclass neural network algorithm in which a very careful design for input/output spaces was considered. Moreover, the torque, voltage, and current signals were used in this algorithm. The results revealed that the fault diagnosis methods integrated with ANNs are very effective and useful. However, a very complicated mathematical model is required to deal with the proposed methods, making them very complex and limited their applications. Moreover, the authors in [
19,
20] used a neural network algorithm based on stator current sensors. The main advantage of the proposed algorithm is that it is very fast compared to the conventional current sensors that are used in such applications. However, the system has two algorithms: the first for PMSM control and the second for the NN algorithm for fault detection.
Additionally, in contrast to the method proposed in this paper, the proposed fault detection algorithms in the literature are not able to recover the driving system to its normal operating conditions.
AI methods are among the advanced methods used for processing data and deriving special rules between datapoints [
21]. They are utilized for demand response [
22], generation control [
23], and frequency stabilization purposes [
24], as well as for fault diagnosis for PMSMS drives [
25]. However, to date, the literature lacks studies on the use of other methods. Recently, fault diagnosis in PMSM driving systems has been paid more attention. When an inverter is operated at high frequencies for an extended period of time, it is vulnerable to serious heat generation and loss issues, which can result in switching device failures such as short-circuit and open-circuit faults. Open- and short-circuit faults have severe impacts on the system. Thus, detecting and solving these problems reduces the stop periods for the inverter-fed PMSM system and the repair costs. Under open-circuit fault conditions, the PMSM driving system is operated from a backup inverter. This increases the cost and volume of the driving system.
The inverter and motor winding are connected in series. An open-circuit fault will result in a large torque ripple or even braking torque because the motor output will produce a serious torque gap. On the other hand, a short-circuit fault will cause the power supply voltage to act directly on both ends of the winding, forcing the fault phase current to increase at an extremely high speed. In order to preserve the safety and dependability of the complete motor drive system, it is crucial to diagnose inverter problems and develop the necessary fault-tolerant solutions accurately.
The proposed fault detection algorithms in the literature are not able to recover the driving system to its normal operating conditions. Therefore, a novel and universal voltage compensation method is proposed in this study to recover the drive system to its typical working conditions. The proposed recovery system is very simple to apply and can eliminate the use of the current protection systems.
The use of artificial intelligence greatly contributes to finding the hidden relationships between the states of the inverted switch and the condition associated with the failure. Such relationships can only be known using artificial intelligence algorithms that are able to discover the hidden relationships and links between inputs and outputs.
AI algorithms are used in driving fault diagnosis, such as naïve Bayes, support vector machine (SVM), and decision tree (DT) algorithms. Thus, this paper applies different AI machine learning techniques to detect and classify the faults that may occur in three-phase VSI switches. The artificial intelligence system classifier is implemented based on measured switches voltages, PWM signals, and phase angles. Then, the measured data are processed using the AI technique to detect the faulty switch and determine whether it is an open- or short-circuit fault. When an open fault switch has occurred, a portion of the DC voltage is lost during the open switch malfunction. Therefore, a novel and universal voltage compensation method is proposed in this study to recover the drive system to its typical working conditions. Its universal nature means it is applicable to any type of inverter. This method makes use of AI to identify the facts about the malfunctioning switch. Then, this decision is used with a voltage compensation loop to trigger the selector switch to be connected to the right phase. The proposed recovery system is very simple to apply and can eliminate the use of the current protection systems.
This paper proceeds as follows.
Section 1 discusses the literature review of the PMSM, its driving system, and the inverter fault detection methods.
Section 2 discusses and simulates the proposed system.
Section 3 presents the use of different AIs methods in fault detection and outlines the accuracy of each method.
Section 4 presents the proposed voltage compensation method to recover the driving system to its normal operating conditions. Finally,
Section 5 concludes the paper.
3. AI Methods and System Classifiers
The proposed system shown in
Figure 9 consists of the three-phase VSI-fed PMSM, AI system classifier, and measuring units for the switches voltages, PWM signals (high (logic 1)/low (logic 0)), and phase angle.
Figure 10 illustrates the system under testing. It shows the inverter block containing a built-in measuring unit. This unit is able to measure the three-phase output voltages, line currents, power factor, and total harmonics distortion (THD). The measured data are recorded using a data logger and then the data acquisition system is used to analyze it. The drain-to-source voltage of each switch is not directly measured because Kirchhoff’s voltage loop can simply estimate it. In more detail, the current loop should contain a DC supply, one upper switch (M1, M3, M5), one lower switch (M4, M6, M2), and the stator impedance. Therefore, The AI system can decide if there is a faulty switch during the voltage loop. These measuring devices detect the phase voltage of the inverter output. Therefore, from the difference between the two-phase voltages, it is easy to detect the switch voltage based on the voltage loop. Regarding the PWM signals, the FPGA performs this job. It senses the width, peak, and shift between the pulses of the different switches. The sensed values are used for AI training using interfacing between the AI and FPGA systems.
In this system, the data for switch voltages Vds1 to Vds6, PWM signals p1 to p6, and the phase angle theta are collected and input using an AI technique to detect the faulty switch and determine whether it is an open- or short-circuit fault. The output for each technique is collected. The accuracy of each technique is measured to decide the best AI method for the proposed system.
3.1. Naïve Bayes Classifier
The Bayesian classifier model assumes separated properties with different values, so changing any property value does not affect the other values. This method is considered a very fast algorithm for classifications, which can be used for real-time classifications. The Bayesian algorithm starts by detecting one class out of N classes, and then the maximum probability for a given set of m data inputs for all possible values in the class is selected.
Step 1 involves selecting the class number
N using Equation (1):
where the data d have m variables
d =
d1,
d2,
d3, …,
dm, which are given by:
where
P(.) is also called the class probability and
P (|) is called the conditional probability. By dropping the denominator, as the denominator remains constant for a given input, we can remove that term:
3.2. Support Vector Machine (SVM)
A SVM is a linear classifier that depends on choosing an optimal hyperplane, such that the distance between the closest vectors of two classes and the suggested hyperplane is the maximum. This method is highly recommended over feedforward artificial neural networks for solving complex problems consisting of high dimensions and large data without overfitting.
3.3. Artificial Neural Network
This method consists of multiple layers with a set of neurons. It has three main layers, the input, hidden, and output layers. The connection between any two layers has a weight value, and the output layer uses a linear or non-linear function based on the problem’s complexity. In this method, the designer can increase the number of hidden layers for fast and more accurate models.
3.4. Decision Tree
A decision tree divides an input space into a group of mutually exclusive regions by giving each region its own label. A decision tree is made up of root nodes and inner nodes. To perform the classification, one way of separating the data for the different categories is to measure the percentage of impurities in the root nodes. The most famous of these methods is the entropy measure:
where
The entropy measures the homogeneity of a node. The maximum entropy value (log nc) is obtained when the records are evenly distributed.
Similarly, the impurity measure of a tree
T can be expressed as:
where
Ψ is the set of terminal nodes in the tree
T,
nt is the number of records at child
t, and
n is the number of records at the terminal node. The information gain is calculated as in Equation (6):
where the parent node
P (non-leaf node, node with partition) is split into
k partitions (children),
ni is the number of records in the partition
i, and
n is the number of records at the terminal node.
Figure 11 shows the developed decision tree model based on the data from
Table 2. It is important to mention that H means healthy and NH means non-healthy.
Table 2 is created based on the possible stator current loops of the PMSM, or in other words the possible combinations between VSI switches that form the current loop. It consists of the pulse width modulation signals for all switches, switch statuses (drain–source voltage
Vds values for all switches), and operation time periods. For example, when the theta is between 0 and 60°, then line a is in positive polarity, while both lines b and c provide the return bath of the stator current. Based on the normal operation of the VSI,
Table 2 is filled out. Moreover, the
P,
Vds, and theta columns are the input parameters for the different AI methods. The AI algorithm provides the monitor with the expected decision, as clarified in the last column (green column).
The developed model has been clarified in the manuscript as requested. The data used in the system development process are divided into three groups, a training group, a testing group, and a validation group. The data are processed at an initial stage to extract features and reduce the dimensions of these features after identifying a set of influencing factors.
The resulting features are then used to train the system to obtain the basic attributes of the phase model, which is the backbone of the classification system. The ability of the proposed system to classify the data with high efficiency and accuracy is ensured. If the required accuracy is not obtained, the features and influence factors are indicated, and the factors are re-defined until the best ready-to-use model is reached.
Here, the used symbols in
Table 2 P
1–P
6 are the PWM signals for all switches; NZ is not zero; Z is zero; OC means the open-circuit fault; the included number relates to the switch number from
Figure 1; L
1–L
3 are positive half periods of phases A, B, and C; and L
5–L
6 are negative half periods of phases A, B, and C, respectively.
Table 3 shows a comparison between the different AI classifier methods. The decision tree (DT) provides the best evidence among the other methods. It achieves 99% accuracy, making it the most accurate method. Moreover, it has the lowest possible classification time as compared with other methods. Additionally, this method has the lowest training time as compared with other methods. In contrast, the lowest accuracy is recorded for the naïve Bayes method (25%), with the slowest classification time (0.03 s).
The artificial neural network (ANN) is the fastest method for classifying the data. This can be seen from its classification time of 0.01 s. However, it has relatively low accuracy of about 37.5%. In addition, the training time of this method is in the middle, between the other classification methods. Finally, the SVM method achieves the highest training time as compared to other methods. At the same time, it has a good accuracy rate of about 75% and has the fastest classification time of 0.01 s, the same as the ANN method.
4. The Proposed Voltage Compensation Method for Inverter Fault Recovery
The inverter and motor winding are connected in series. The open-circuit fault will result in a large torque ripple or even braking torque because the motor output will produce a serious torque gap. On the other hand, the short-circuit fault will cause the power supply voltage to act directly on both ends of the winding, forcing the fault phase current to rise at an extremely high speed. In order to preserve the safety and dependability of the complete motor drive system, it is crucial to diagnose inverter problems and develop the necessary fault-tolerant solutions accurately. There are several methods that can be used to detect inverter switch faults. One of them involves using AI methods [
26,
27,
28,
29]. This section presents the proposed method that can be used to overcome the inverter faults and recover normal system operation.
Previous studies presented a fault-tolerant control technique for cascaded, two-level, inverter-driven, open-end winding permanent magnet synchronous motors [
26,
27,
28] as a fault treatment method. Under open-circuit faults, the PMSM driving system is operated from a backup inverter. This increases the cost and volume of the driving system. In [
26,
27,
28,
29], during the open-circuit fault, the topology can be changed to operate as a two-phase H-bridge inverter. Assuming phase A is under open-circuit fault conditions, the controller can disable the switch on the phase a bridge leg. In order to maintain the fault-tolerant topology, the topology can be changed to a two-phase H-bridge inverter, then the circular flux linkage trajectory can be rebuilt by altering the PWM modulation mode during the motor’s operation. Due to its higher redundancy, the multiphase motor driver is a popular topic of discussion in fault-tolerant control.
Figure 12 introduces a method for fault diagnosis and treatment. It shows the flow chart of the fault detection steps, determines the fault type, and then decides whether the situation requires a voltage compensation loop. The two types of faults can be treated as follows:
Short Circuit Fault of the Inverter Switch: To overcome a short-circuit fault of any switch inverter, it is possible to connect fuses at the coupling point between the inverter legs and the PMSM stator windings. Thus, the fuse will burn out in case of a short-circuit current and the motor operation will stop immediately.
Open-Circuit Fault of the Inverter Switch: If any switch is opened, a part of the current line is missed. Therefore, part of the DC voltage is lost. This section proposes a voltage compensation method to recover the driving system to its normal operating conditions. In this method, the faulty switch’s information is determined using AI. Then, this signal is processed by sending a trigger signal to a selector switch. The selector switch is shifted to a position to compensate for the missing part of the voltage supply. This voltage is chopped using a voltage-controlled oscillator (VCO). The oscillation frequency is set as the switching frequency.
The voltage compensation method is illustrated in
Figure 13. When the open-circuit fault attacks any inverter switch, the decision comes from the AI method. The decision is used to trigger the selector switch to connect the compensation voltage loop instead of the faulty phase path. Meanwhile, the sawtooth signal has a switching frequency equal to the inverter switching frequency and is compared with a constant value to generate a chopped voltage compatible with the missing voltage. Then, this signal is connected to the stator terminal, which suffers from an open switch fault.
To verify the voltage compensation loop, it is assumed that switch M
1 is a faulty switch. To simulate the open-circuit fault, the MOSFET is replaced by a 100 kΩ resistance, then the compensated voltage is connected to replace the faulty switch. The decision is made by the AI classifier. The normalized output of the voltage compensation loop is shown in
Figure 14, whereas the three-phase stator currents of the PMSM are shown in
Figure 15.
The output of the voltage compensation loop has the same pattern as the M
1 switch’s drain–source voltage during normal operating conditions (see
Figure 4). Moreover, as seen in
Figure 15, the stator current of the faulty phase has a lower peak current, which is related to the use of the 100 kΩ resistance. This resistance causes a voltage drop, which reduces the peak of the stator current. However, the voltage compensation loop shows its effectiveness in open-circuit fault recovery.