1. Introduction
Due to high efficiency and wide flux-weakening capability, a permanent magnet synchronous generator (PMSG) has been widely employed in many industrial applications such as a wind energy system (WS). These applications have always demanded service continuity, reliability, and availability. In practice, although PMSG as one of the mature technologies in WS has been widely adopted, its accidents due to some factors such as friction [
1,
2], high temperature [
3], and an operation process, have inevitably occurred [
4,
5]. Various faults may have occurred in rotor bar [
6,
7], engine [
8], bearing [
9,
10], wind turbine gearboxes [
11], and more. Faulty events may have damaged electrical energy, threatened the safety of the power system, and even harmed human lives and environments [
4].
Currently, the diagnostic technique topic is very large [
12,
13]. In view of the fault parts, various approaches have been proposed to monitor and detect many kinds of faults. For instance, the methods in References [
1,
2] have been proposed for detecting the faults in the brake system. In Reference [
6], motor current signals analysis by the tooth-fast fourier transform (FFT) has been used to detect both incipient and consolidated broken rotor bars conditions. In addition, for the detection of the half broken rotor bar fault, the other method known as the motor square current MUSIC analysis has been presented in Reference [
7]. The manuscript [
8] has focused on wall conveyor engines diagnosis. On the basis of these three models (signal correlation, extreme vibration, and RMS intensity), monitoring RMS and extreme values has served as a leading indicator for early detection of faults [
9]. Bearing faults has been diagnosed by the extended park vector approach [
11]. The open-circuit fault (OCF) causes that the phase winding has been disconnected from or one leg of the inverter bridge has failed have been researched in Reference [
14].
The fact that electronics faults in WS has accounted to about 1% of the total cost only, which was indicated in Reference [
4]. Power converter failures have been generally categorized into two types of faulty, short-circuit faults (SCF) together with OCF. When an SCF has occurred, drive systems have been immediately stopped or transformed into OCF by the emergency control schedule for alleviating or isolating the fatal damage by SCF. While OCFs are associated with slow responses and less danger, it is still connected with gird for the economy and safety [
15]. Yet, the potential safety problems could not have been ignored by the public [
4]. Many articles have focused on reliability issues of power electronics monitoring methods [
4,
5,
16]. Generally, these fault diagnosis methods are achieved by the output current or voltage signals such as current-based methods or voltage-based methods [
17].
Current-based methods often have depended on arm current. In order to simplify the application and improve diagnostic speed, the normalized way using three-phase currents has been developed for multiple OCF in insulated gate bipolar transistors (IGBTs) for the power inverter in electric vehicles [
18]. By the measurement of the output inverter currents, a fuzzy technique has detected intermittent loss of firing pulses in the inverter power switches to diagnosis [
19]. The manuscript [
20] has presented an OCF diagnostic method of inverters in closed-loop controlled PMSG drive systems based on the current residual vector (CRV). For detection and discrimination of OCF in a five-leg voltage source inverter feeding a five-phase biharmonic PMSG, the investigation into real-time faults diagnosis has been conducted [
21]. The method by using adaptive thresholds has been proposed for multiple IGBTs OCF and current sensor faults detection [
22]. The method proposed in Reference [
23] was achieved by analyzing and combining the information provided with the line current shapes in the
frame and their normalized mean values under both healthy and faulty operating conditions. These methods have had a major drawback, which involves sensitivity to transients. The current signals have been load dependent [
24]. For instance, literature [
25] has indicated that current measurement noises and inverter dead-time harmonics have resulted in the distortion on DQ currents, which limits fault detection performance [
26].
Aiming to dissolve this drawback, the data-driven methods have been used to detect faults. For instance, the Bayesian network in Reference [
24] has been adopted for diagnosis. On the basis of FFT, the relative principle component analysis (RPCA) and the support vector machine (SVM), which is a fault diagnosis method, has been proposed for detecting OCFs in an H-bridge multilevel inverter [
27]. By analyzing the output currents of normal and fault states, a fault diagnosis algorithm has been designed and achieved by a multistate data processing (MSDP) block, a subsection fluctuation analysis (SSFA) block, and the artificial neural network (ANN) block [
28]. The paper [
29] attempted to develop a novel method of training the ANN for a fault diagnosis technique of the OCF in converters of the PMSGWS. However, these data-driven methods take a long time to record data and to train the network [
30].
Voltage-based methods have decreased sensitivity to transients and are achieved with a shorter detection time in comparison with that of current-based methods [
25] even though additional sensors or other hardware devices have been required. On the basis of the output line-to-line voltage model, a novel diagnostic technique developed and proposed in Reference [
31] has allowed a fast detection time and a good performance. A voltage-based detection method realized by the principle component analysis and the multiclass relevance vector machine (PCA-m RVM) has designed for the cascaded H-bridge multilevel inverter system (CHMLIS) [
32]. On the aim of avoiding additional sensors, the three-phase voltages calculated by the DC link voltage and switching times contributed toward detection in Reference [
25]. The calculated amount increased and was very time-consuming. Observer-based approaches have also been addressed in References [
33,
34,
35]. In Reference [
34], both IGBTs OCF and current sensor faults in three-phase PMSG drives have been distinguished. The proposed diagnosis method in Reference [
35] has been successful in the detection of multiple OCF. However, an adaptive threshold has been necessary for these observer-based approaches.
In practice, each switch is composed of a power switch and a parallel freewheel diode (PFD). The power switch is more sensitive than the PFD. References [
15,
16] have indicated the fact that an OCF may have occurred in the power switch only [
15,
16]. This kind of OCF is named the open switch fault (OSF). The OSFs have remained undetected and led to potential secondary faults [
17,
30]. After an OSF occurred in a back-to-back converter using NPC topology for wind turbine systems [
36] or a three-phase pulse-width modulating (PWM) voltage source rectifier (VSR) system [
37], these converters have been open to a two-way traffic for faulty current. In addition, it has two different characteristics during the zero-crossing and non-zero-crossing section. In fact, this phenomenon also has produced in the event of OSF in PMSG drives, which we verify in the next sections. If the faulty currents have gone through the converter unidirectionally, the faulty characteristics of current, harmonic, temperature distribution and more have been shown clearly [
38]. However, to a bi-directional faulty current, the distortions have been found difficult due to the small residuals [
37]. The performance of the method achieved by residuals may have been reduced [
39]. Therefore, for distinguishing between the OSF and the normal commutation operation, the threshold has been necessary, according to Reference [
37]. The dissatisfaction with reliability issues of power electronic voltage-based monitoring methods has been exposed [
5].
This paper analyzes the faulty behaviors of PMSG drives in WS and proposes a new OSF detection and faulty switch identification algorithm. This proposed fault diagnosis scheme is implemented on the basis of the faulty behavior analysis. In consideration of fault-mode behavior during the zero-crossing and non-zero-crossing faulty current section, the detection method without a threshold setting comes from the feature of lower tube voltage. Due to the criteria in a lower tube voltage, a special RMS voltage is obtained in a certain period. The detection time and the robustness are also achieved by this certain period. All authors of this paper are devoted to the simple implementation of the detection method.
Section 1 investigates OSF in PMSG drives of WS. The effects on current and voltage are also discussed in this section by presenting the detail fault-mode behavior. In
Section 2, the identification method for OSF is proposed. The simulation and experimental results are presented in order to evaluate the fault diagnosis performance in
Section 3. Lastly, the concluding remarks are provided in
Section 4.
3. The Proposed Open-Circuit Fault Diagnosis
Too many factors are influenced on arm current in the event of an OSF in MSC. The wide range of values
is too complex to detect. Fortunately, we find the criteria that is summarized in
Table 3 as a very helpful key for the OSF detection problem. The fault diagnostic formula is studied below.
3.1. Method of Fault Diagnose
Figure 8 illustrates the proposed fault diagnosis algorithm for detecting the OSF condition and identifying the faulty switch. This algorithm contains three steps including measurement, comparison, and classification.
Measurement is the most important process of the proposed fault diagnosis algorithm. After this process, we can obtain a special RMS voltage
, which is the key for deciding fault localization variables. In addition, the details of this process are explained in
Section 2.3.
The second step is a comparison between
and
. Let DC-Link reference voltage
equal
. By this step, fault localization variables
appear. If
is equal to 0 or 1, the fault show time would appear. It can also deduce that an OSF happens. We collect the values of
after all possible single switch faults occurred in MSC as
Table 4 lists.
Classification is designed as the last step of the detection method.
Table 4 shows different faulty switches come with different fault localization variables
. So the faulty switch can be detected according to these variables.
In this fault diagnosis method, the setting of threshold is unnecessary. Only the values in the fault show time are considered. The misjudgment during the faulty current cutting off would should be avoided. In the detection process, we only monitor the lower tube voltage and sample with a certain period. The implementation of the detection method for OSF in MSC is very simple. The fault feature is obtained from the lower tube voltage directly in which it is easier to distinguish faulty switches in comparison to residuals. Surely, influences on the detection speed and the cost of the detection method.
3.2. Fault Detection Time
PWM frequency is several hundred times bigger than grid frequency and is not proper for sampling because of the high cost of the sensors. To shorten this cost, we choose other frequencies to sample. As the above proposed method, is the one we use to monitor lower tube voltage. is the major parts of fault detection time. The shorter detection time, the less the period . The other problem is choosing . which may affect the reliability of the detection method. In detail, if is too large, the fault show time may not be detected and if it is too small, the possibility of false detection increases. Therefore, this part introduces many problems such as how to choose the proper period , how long the fault detection time takes, and so on.
(A) Choosing the Proper Period
Several methods such as intelligent methods and empirical selection are effective and available to obtain . Considering the merit and disadvantage of experimental conditions and each method, one of the most reliable choice methods known as the empirical selection is employed in this paper.
is bigger than the time of the maximum pulse width ratio (MPR) and shorter than the fault show time, according to
Section 2.1. The work [
42] indicates the pulse width ratios are derived from the reference curve for the PWM. During the pre-delivery test, we can change the wind between cut-in and cut-out speed in different modes such as steady speed, random wind, ad step wind. Then, MPR of all wind modes can be recorded. So
can be chosen according to MPR.
(B) The Calculation of Fault Detection Time
If an OSF occurs, the fault show time as analyzed in
Section 2.3.1 would appear. Once the fault occurs at the beginning of the fault blank time, the detection time is the longest. It has to wait more than half of the current fundamental period for the fault show time.
Let us suppose the fault occurs at
. The period of the fault blank time
and
are not proportional as seen in Equation (16).
where
;
is a positive integer. Therefore, assuming
as the telecommunication and calculation time, the detection time
is equal to the longest one
as seen in
Figure 9a.
If the fault occurs at the beginning of the fault show time, the detection time is the shortest one
. Assuming the fault occurred at
, the detection time
as seen in
Figure 9b shown can be expressed.
In conclusion, the values of detection time are less than one current fundamental period. In addition, the shortest detection time is nearly equal to the sampling time.
3.3. Measurement of Electrical Signal
The key of the fault diagnosis algorithm is the measurement process. Its principle is shown in
Figure 10, which we also realize in the next simulation part. In this process, the special RMS voltage
is calculated. Before the calculation of
, the period
should be obtained after the pulse width measurement. The detail expatiation about
is listed in
Section 2.2.
The calculation of
is shown below.
Assume
is proper and take T1 fault as an example. If the measurement is conducted during the positive cycle of faulty current.
are equal to 0 due to
according to
Table 3. Once faulty current turns to a negative cycle,
can be expressed by Equation (20) below.
are unequal to 0. In addition, when faulty current is under the zero-crossing section, may be not equal to 0 as . That means only when the fault show time comes out, is 0.
4. Simulation and Experimental Results
The model of PMSGWS as illustrated in
Figure 6 is built on the basis of the PSCAD environment. The main system parameters of PMSG for simulation are given in
Table 1 and
Table 2. The parameters are set the same as expressed in
Section 2.2.2.
Figure 4 gives the photos of experiment devices. Dynamic responses of voltage are shown in this section.
Figure 11 is the experimental responses of the lower tube voltage. The results of the simulations are illustrated by
Figure 12 and
Figure 13.
Comparing
Figure 11a with
Figure 11b, it is visible that, under different operating conditions, although the similar feature that all
skip on 0 and 0.65 Kv is revealed in the fault blank time, different characteristics of
are shown during the fault show time.
We also assume T1 and T4 are the top and lower switch of MSC in phase A, respectively.
Figure 12 and
Figure 13 present the simulation results during T1 fault occurrence with an imposed reference wind speed of 10.5 m/s. The time-domain waveforms of lower tube voltage are similar to that obtained by experiments.
change with the fault show time when OSF occurs in T1. During
,
shows different features in comparison with that during
. Comparing
Figure 12 with
Figure 11, it is visible that
is more complex than
. There are several values of
.
is smaller than 0 during
.
These simulation results indicate a similar phenomenon as obtained by experiments. In details,
does not skip on 0 and 1.5 Kv during the fault show time.
is more complex than
. As shown in
Figure 13,
with a high frequency are discrete most of the time. During the zero-crossing section,
obtains some values not as the non-zero-crossing section. The responses in
Figure 12 and
Figure 13 are consistent with experiments as well as analyses in
Section 1.
The effectivity and availability of the simulation model are verified according to the above analysis of faulty behaviors. Considering the damage to devices, we test the diagnosis method in simulation surroundings. Six cases including the normal condition with 7 m/s, the normal condition with 10.5 m/s, OSF in T1 with 7 m/s, OSF in T4 with 7 m/s, OSF in T1 with 10.5 m/s, and OSF in T4 with 10.5 m/s are demonstrated for verifying the performance of the proposed method. All faults occur at the 0.02 st second. Setting sample time as a 0.003 s, we can obtain the values of .
These values of localization variables in
Figure 14 can be obviously categorized into three main types: normal case between 0 and 1, T1 fault case reducing to 0, and T4 fault case up to 1. The OSF in T4 with 7 m/s is detected in the shortest time of about 0.003 s. The longest detection time is about 0.015 s showing in the event of T1 fault with 7 m/s. These responses prove that the proposed diagnosis algorithm with a certain period can distinguish a faulty switch in different wind speeds. It also proves that the proposed diagnosis algorithm can achieve fault detection in this paper.
Moreover, we also take these results to compare with other previous methods, as presented in
Table 5. The proposed method with similar detection speed as that in Reference [
18] even though the faulty current in Reference [
18] is considered as a unidirectional one. Absolutely, the robust and accuracy proven by the results can meet the requirements of grid stability.