Concerning the most recent KB solution ^[7][47], Yao et al. develop a fault-diagnosis method for five-phase marine current generators. On the one hand, empirical mode decomposition and Hilbert transform is applied for fault detection. On the other hand, variable-parameter particle swarm optimization is employed for fault-type identification and location, with the parameters being adapted by a support vector machine. The input signal is the projection of the alpha-beta current onto the direct axis of the synchronous reference frame, that is, d1. The kind of fault is identified based on the pattern of this current. Addressing the robustness for different operating conditions (i.e., R5) is left for future work. As a significant advantage, this technique also diagnoses current-sensor faults.

SB fault-detection methods have been widely carried out using vector space decomposition (VSD) components ^{[9][10][4][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]}[15,18,44,53,54,55,56,57,58,59,60,61,62,71,72,73,74,75], although monitoring just the phase currents has also been suggested for this purpose ^{[26][27][28][29][30][31][32][33][34]}[48,49,50,51,52,67,68,69,70], especially in older papers. In a 2012 publication ^[26][48], Meinguet et al. propose the localization of open-phase faults by quantifying the imbalance of the phase currents, exploiting the fact that these signals are more affected by the occurrence of a fault than the main (alpha-beta) VSD subspace. The fault is identified after several fundamental cycles. Alternatively, since an open-phase failure is characterized by null current in the damaged phase, a trivial solution to diagnose a phase OC is to check if the average during a certain period of any phase-current absolute [70] or squared [49,50,67,68,69] value is approximately zero. Unfortunately, this technique could also be relatively slow, because the detection takes at least as much time as the interval that is necessary for computing the average (e.g., a fundamental cycle). Moreover, false alarms can be triggered when the machine operates with small current magnitudes [48], especially near zero crossings if one attempts to set a short averaging time. Another method based on averaging current values was recently proposed by Mesai-Ahmed et al. [51] for asymmetrical six-phase IM drives. This technique calculates the average absolute values and the average values of the measured currents over a fundamental period, and provides a set of normalized numerical signatures to detect and localize the faulty devices. It is capable of identifying up to 54 different fault scenarios, involving multiple phase/switch OC faults, with no need for detection thresholds or tuning. However, R2 is not fulfilled either. Although phase currents can exhibit these limitations when monitored, Wen et al. recently proposed in [52] a fault-detection method based on them for identifying the sector affected by an OC fault, in a three-sector nine-phase PMSM. The alarm is set when the instantaneous (not average) absolute value of a phase current is lower than a threshold while the current error of said phase (with respect to its control reference) is large. Simulation and experimental results confirm its effectiveness for detecting single- or three-phase OC faults in one or two sectors. However, the current-measurement ripple, which depends on the drive and operating conditions, needs to be considered in the design to avoid false alarms (R4 and R5 are not met). Moreover, it is not suitable if it is desired to keep using the healthy phases of a sector with a single-phase OC, because the particular faulty phase within the sector is not found.

In spite of the low sensitivity of the main VSD subspace identified in ^[26][48], the analysis of the VSD components has been in fact the most popular option for the diagnosis of OC failures in multiphase systems. Many of these methods take advantage of the high sensitivity offered by the x-y subspaces.

Meinguet et al. ^[11][53] proposed a fault-detection method where the ratio between the negative and positive sequences of the alpha-beta fundamental currents is employed to detect open-phase faults. The criterion to identify a phase OC is defined using a cumulative sum control chart algorithm. Unfortunately, the performance of the fault-detection index is affected by the machine speed and the controller gains, and as a consequence, the requirements R4 and R5 are not fulfilled. Moreover, other faults that cause alpha-beta imbalance, such as eccentricity [289,290] or stator SCs [291,292], may lead to misdiagnosis. The secondary VSD subspaces, which could be useful for preventing this problem and finding clearer symptoms, are not exploited.

Taking advantage of the inherent secondary (x-y) subspaces of multiphase machines, Duran et al. ^[12][54] introduce an open-phase detection method for an asymmetrical six-phase induction machine (IM) driven by rotor field-oriented control (RFOC). The fault indices are derived considering the phase-OC condition (null current through the damaged phase) and the six-phase VSD transformation. Monitoring the x-y currents instead of the per-phase ones facilitates attaining fast and robust detection. This fault-detection method can be extended to different multiphase drives and control strategies, as illustrated in ^[21][71] for a five-phase IM driven by current FCS-MPC. Moreover, the developed fault indices allow the detection of open-switch faults as well ^[21][71]. In fact, these same fault locators may be employed to identify the specific OC switch, by just carrying out some additional non-complex analysis/operations ^[13][14][55,56]. For example, Kong et al. ^[13][55] reformulate the fault indices proposed in ^[21][71] and study the polarity of the secondary VSD components to obtain this extra information about the fault in a five-phase PMSM drive. Farag et al. ^[14][56] applied analogous fault-detection indices to a symmetrical six-phase IM, and additionally proposed the estimation of the average phase current after the fault detection to distinguish between phase/switch OCs and to achieve the location of the specific faulty switch. Consequently, although the fault detection time is short, its location takes more than one fundamental cycle. This technique ^[14][56] is able to diagnose broken rotor bars and high-resistance connections as well. It is also worth noting that the SB procedure proposed in ^[4][44] as an alternative to an MB one (see Section 2.1) also relies on the x-y currents and detects high-resistance connections, but the transient response has not been assessed so far.

Other publications present methods developed on the basis of the so-called symmetrical component theory ^[15][16][57,58], which is actually equivalent to distinguishing between the positive and negative sequences within the VSD subspaces ^[35][293]. In particular, in ^[15][16][57,58] the pattern of the symmetrical components of the stator current is employed to identify single and double OC faults in five-phase PMSMs. Arafat et al. ^[15][57] defined two fault indices as a function of the amplitude of the current symmetrical components. However, the measured currents need to be filtered to extract the fundamental component and its sequences, and no information about fault detection time is provided in the paper. In the case of Chen et al. ^[16][58], the diagnosis is performed based on the phase angle of the alpha-beta current space vector (SV) over a fundamental period; namely, on the deviation from its expected value. This deviation is oscillating in the case of OC fault. Given that a fundamental cycle is required, R2 is not fulfilled.

However, many of these SB procedures assume that the current in the x-y plane(s) is nearly zero in healthy conditions. In contrast, some authors devised phase/switch-OC diagnosis SB methods that exploit the x-y current symptoms with robustness to harmonics (e.g., third) in the current references ^[18][20][60,62] or in the PMSM back-EMF ^{[17][18][19][20]}[59,60,61,62]. These techniques satisfy the five requirements R1–R5. Trabelsi et al. ^[17][59] proposed to calculate the centroid of the x-y current trajectory during a fundamental period, and locate a single-switch OC by means of its phase angle. Phase OCs are found by checking whether the mean absolute value of the phase current is zero during a certain interval, similarly to other aforementioned papers ^{[27][28][31][32][33][34]}[49,50,67,68,69,70]. In spite of the averaging, the faults are detected in a brief time; this implies that the phase-current mean is computed over a short interval, which could aggravate the risk of false alarms at zero crossings when the current is low ^[26][48]. The signals are normalized by the two-norm of the VSD currents, to achieve independence from operating conditions. Later, the same authors presented another technique in ^[18][60], with greater robustness to the third harmonic in the back-EMF and in the current references (for increasing torque). New indices are derived for detecting single-switch OCs based on the VSD components of not only the measured currents, but also of their control references. Phase OCs are identified analogously to the preceding work ^[17][59]. To ensure R4, suitable normalization is applied, and the ratio between the first two back-EMF harmonics is considered for selecting the thresholds. More recently, Gonçalves et al. ^[19][61] implemented fault indices based on the mean value and the amplitude of the second current harmonic with respect to a rotor-oriented frame within the x-y plane. Integration of VSD variables is performed during half a fundamental cycle, avoiding the averaging of phase currents and the associated risks. Simulation results have demonstrated the ability of the method to detect open-phase faults in asymmetrical six-phase PMSMs. Although fifth and seventh back-EMF/deadtime harmonics are considered, null current references are assumed in the x-y plane. In this regard, the same authors improve this method in ^[20][62], where the non-zero current references are taken into account, and high-resistance connections are also diagnosed. Later, it is further enhanced in ^[4][44] so that the values of increased resistance are estimated, and smaller resistance imbalance can be detected. The potential of the x-y signals of multiphase machines to be employed in OC-detection indices has also been confirmed in particular topologies such as series-connected six-phase PMSMs (two-motor drive) ^[25][75] or T-type three-level VSCs ^[9][15], and even under specific scenarios such as stator SCs ^[10][18]. In ^[25][75], Moraes et al. carry out the fault diagnosis for the two-PMSM drive in two stages. In the first one, the fault is detected using a single index, and in the second one, the fault is classified according to three fault indices. The method developed by Wang et al. in ^[9][15] allows the detection of switch OCs, phase OCs, and switch SCs in a T-Type three-phase VSC driving an asymmetrical six-phase PMSM. First, an SB approach using two fault indices is applied. For this purpose, different postfault features of the x-y currents are recognized. Then, an intervention-based diagnostic method (exciting the affected leg) is employed to additionally distinguish between the various kinds of faults. Since an invasive technique is necessary for this goal, the requirement R1 is not achieved. Finally, the strategy proposed by Guo et al. ^[10][18] for the identification of single open-switch failures has been specifically designed for the scenario of a symmetrical six-phase drive with two isolated neutral points under stator SC or OC. For this purpose, the four VSD currents are employed as inputs to a look-up table (LUT), in which the different fault situations are classified. Wang et al. ^[22][72] have suggested a fault diagnosis approach considering five types of failures, including those in the speed sensor, dc-link voltage sensor, or current sensor (discussed in Part 1), as well as switch and stator OCs. MB strategies are designed to detect failures in the speed and dc-link voltage sensors, whereas the other faults are localized using an SB method. A three-step procedure has been designed to diagnose the problems related to current, that is, open-phase, open-switch, and current-sensor faults. In the first step, the amplitude of the x-y current SV is compared with a predefined threshold in order to detect abnormal behavior caused by any of these faults. In the second step, the mean values over a fundamental period of the current projection onto six axes within the x-y plane are computed, and the lowest one permits discarding all fault scenarios except four. These six axes correspond with the potential x-y current trajectories under these faults. Finally, among the four possible scenarios obtained from the second step, the fault type and location are established in the third step using twelve average absolute currents. These indices are calculated with the positive and negative parts of each phase current. Thus, the identification and location requires one fundamental cycle after the failure occurs. Resistance dissymmetry due to high-resistance connections, already surveyed in Part 1, can be considered as incipient OC faults. In fact, an open-phase failure could be understood as an extreme case of resistance dissymmetry. The appearance of this type of faults causes certain imbalance in the phase currents, as it occurs in open-phase scenarios. This fact has promoted the use of some diagnosis methods that are able to identify either OC faults or high-resistance connections ^{[4][14][15][20][24]}[44,56,57,62,74], most of which have just been discussed. In the case of Salas-Biedma et al. ^[24][74], the proposed localization method, based on the current imbalance, permits the identification of stator resistance dissymmetry and OCs with the same fault indices. Namely, the distinction between both kinds of faults is performed by analyzing the values obtained with the indices that were proposed for phase OCs in ^[21][71]. However, the technique should only be applied without x-y closed-loop control, as in natural (reconfigurationless) fault-tolerant strategies; otherwise, the symptoms of high-resistance connections may be canceled by the controller. In control schemes without postfault reconfiguration, the localization of the specific OC phases is no longer a mandatory requirement, and it can therefore be omitted. Nevertheless, the OC fault situation needs to be identified to some extent in order to apply the corresponding derating (reduction of maximum values) to the control references. In this regard, Entrambasaguas et al. ^[23][73] develop a simple fault-detection method where a single index distinguishes, while using natural fault-tolerant control, between three potential fault scenarios (with single or double OC faults) that need different derating.

4. Concluding Remarks about Detection of Phase/Switch OC Faults

Three main types of fault diagnosis approaches (MB, KB, and SB) have been explored in the literature to detect phase/switch OC faults. Nevertheless, in agreement with a number of publications, SB strategies may be considered the preferred alternative in multiphase drives. This solution generally avoids the dependence on model parameters of MB techniques, as well as the complexity of KB ones. Focusing on the existing SB methods, they are all based on the current signals, which are typically available in the drive without installing extra sensors. Two principal trends can be identified in the state of art. In the first one, it is checked whether the absolute/squared value of each phase current is close to zero during a certain period. However, the detection time is normally long due to the need to set a minimum interval for the averaging (e.g., a fundamental period) ^{[27][28][31][32][33][34]}[49,50,67,68,69,70], and false alarms may easily be triggered. The second trend, more recent, involves monitoring the VSD currents (or current control errors). The suitability of these components to be employed in the design of fault indices has been confirmed for multiple multiphase electric drives and control strategies ^{[9][10][4][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]}[15,18,44,53,54,55,56,57,58,59,60,61,62,71,72,73,74,75]. In this regard, a special role is played by the x-y currents, since their values are decoupled from the alpha-beta fundamental in healthy drives without filtering, and they normally change to a great extent after the OC fault occurrence. In this manner, simple, fast, and robust (to control type, parameters, and operating conditions) identification of OC faults can be attained. Performing suitable normalization of the monitored signals is often important for ensuring robustness for different operating conditions, as with other solutions. Nonetheless, although the detection time is commonly shorter when VSD components are employed, a certain moving average is still necessary, giving rise to a trade-off situation. On the one hand, the selection of a long interval of integration avoids false alarms, but on the other hand, the detection time is increased. Even though this situation is much less relevant for reconfigurationless fault-tolerant strategies, in the case of standard postfault reconfiguration, a fast identification of the OC failure is conventionally a mandatory requirement for avoiding the detrimental fault effects as soon as possible. Moreover, most of the reported approaches have not been tested under other failures, with the main exception, in several instances, of high-resistance connections [44,56,57,62,74], which can be regarded as incipient OC faults. In particular, the detection of failures in the freewheeling diodes [294], such as OC ones, has been largely ignored in multiphase drives. Furthermore, diagnosing switch OCs in VSC topologies other than half-bridge (HB) ones has barely been addressed so far either, aside from T-type and diode NPC VSCs in [15,46], respectively. Therefore, future research of multiphase methods for identifying OC failures could be targeted at further reducing the required time without compromising robustness. Detection of switch OC faults in other attractive VSC topologies such as full-bridge (FB) and multilevel ones is also of substantial interest. In addition, the design of comprehensive fault diagnosis techniques, where numerous kinds of faults besides phase/switch OCs could be distinguished by means of a unified procedure, may become a significant milestone in the years to come.