Online Fault Detection of Open-Circuit Faults in a DTP-PMSM Using Double DQ Current Prediction

: This research proposes a strategy to diagnose open-phase faults (OPF) and open-switching faults (OSF) in dual three-phase permanent magnet synchronous motor (DTP-PMSM) inverters. The method is based on the dual d–q predictive current model and involves establishing a mathematical model and utilizing the finite control set model predictive current extraction technique to predict the motor current. It then analyzes the characteristics of the switching-tube current under both normal and fault conditions. Finally, a fault predictive current model is introduced and the residual is calculated based on the predicted fault current value and the actual measured current value to diagnose the inverter fault. The proposed method effectively overcomes misjudgment issues encountered in traditional open-circuit fault diagnosis of inverters. It enhances the system’s response speed during dynamic processes and strengthens the robustness of diagnosis algorithm parameters. The experimental results demonstrate that the proposed method can rapidly, effectively, and accurately diagnose open-circuit faults presented in this paper fastest within one-fifth of a current cycle. It achieves a diagnostic accuracy rate of 97% in the dual three-phase permanent magnet synchronous motor drive system.


Introduction
The development of AC transmission has led to increasing research on high-power control systems.One area of interest for scholars is multiphase motors, which are characterized by low voltage, high power, small torque ripple, and strong fault tolerance [1][2][3].Dual three-phase permanent magnet synchronous motors have been extensively studied among multiphase motors.These motors have several advantages over ordinary threephase motors, including reduced torque ripple and improved fault tolerance.As a result, dual three-phase permanent magnet synchronous motors are an excellent choice for applications requiring high power and high reliability, meeting the demanding performance requirements of the current engineering field [4,5].
The power switching devices in motor drive systems play a crucial role, but they often experience frequent switching states over long periods o, leading to switching losses and heat build-up.In addition, these devices are susceptible to environmental factors, transient conditions during operation, and overload situations that increase the risk of failure.Short-circuit faults are particularly serious as they can quickly propagate throughout the system [6].Currently, hardware circuits such as fast fuses are used to protect powerswitching devices from short-circuit faults by converting them to open-circuit faults once they occur.This helps to prevent further damage to the system.However, unlike shortcircuit faults, which immediately stop the operation of the system, open-circuit faults do not necessarily lead to an immediate shutdown but can affect the performance of the motor.If open-circuit faults are not recognized and rectified immediately, they can lead to secondary faults in the system and cause major damage [7].Therefore, the effective diagnosis of open-circuit faults in inverter switchgear is of great importance to ensure the reliability and safety of the system.
The core of fault detection and localization technology lies in extracting key signal features and comparing them with benchmark parameters to evaluate deviations during equipment operation [8], providing data support for fault diagnosis and localization.Opencircuit faults can significantly affect the system's output current and voltage in inverter applications.Current signals, as essential monitoring indicators in motor control systems, are often selected for open-circuit fault diagnosis using methods such as phase current average value [9], radius [10], angle [11], Park vector [12], zero crossing (ZC) feature [13,14], and similarity feature [15].
To simplify fault detection, a method based on the unique x-y plane current of multiphase motors was proposed in reference [16].This method utilizes VSD to detect openphase faults in six-phase induction motors.Similarly, reference [17] proposes a fault diagnosis method for a single switch open-circuit fault in a six-phase fault-tolerant permanent magnet synchronous motor system.This method is based on the average current Park's vector and compares the modulus of the average current Park's vector before and after the switch fault in two orthogonal subspaces to determine whether a switch fault has occurred.On the other hand, voltage-based open-circuit fault diagnosis methods typically require additional voltage sensors in the system.These methods diagnose faults by measuring the phase voltage, line voltage, or voltage values at key points output by the inverter, as discussed in references [18][19][20][21][22].After considering factors such as neutral point voltage imbalance and time-offset injection, references [23] proposed an assumption-based method for T-type three-level inverter OC fault diagnosis based on the output phase voltage model.The method established a phase voltage model and determined the fault location based on the amplitude and angle of the residual vector.The proposed method in [24] presents a technique for rapid open-circuit fault diagnosis on an induction motor drive system by calculating the common-mode voltage, enabling diagnosis within five control cycles.However, this approach necessitates the design of a complex observer to estimate the motor back-EMF.
In summary, due to their similar characteristics, previous fault diagnosis methods have faced difficulties in achieving simultaneous rapid detection of OPF and OSF.Therefore, this article proposes an online fault diagnosis scheme based on dual dq current prediction by combining model-based and signal-based diagnosis.The proposed strategy can be divided into three steps: first, detecting differences between normal and faulty models of permanent magnet synchronous motors to determine when faults occur; secondly, using different OPF models to predict general deviations between current and dq axis feedback currents for identifying faulty phases; finally, utilizing harmonic currents' trajectory angles for specific fault diagnosis and localization.By employing this method, quick diagnoses of OSF and OPF in PMSM drivers can be achieved within one-fifth of a current cycle.
First, the topological structure and the basic principle of the DTP-PMSM are presented and a mathematical model of the DTP-PMSM is derived.Subsequently, the characteristics of the current at open fault are analyzed and the basic principle and methodology of the fault current model are explained in more detail.Furthermore, the use of the fault current model for the diagnosis of open faults in PMSMs is presented.Finally, the effectiveness of the proposed methodology is validated by experiments, and its feasibility in practice is discussed.

Mathematical Model of Dual Three-Phase PMSM
The main circuit topology of the dual three-phase PMSM driving system is shown in Figure 1.The stator consists of two groups of three-phase, symmetrical windings that are connected in a Y-shape.The two groups of windings are spatially separated by an electrical angle of 30 • and are fed by a six-phase voltage source inverter.To simplify research and analysis, it is assumed that the back EMF of the motor is sinusoidally distributed.
World Electr.Veh.J. 2024, 15, x FOR PEER REVIEW 3 of 14 connected in a Y-shape.The two groups of windings are spatially separated by an electrical angle of 30° and are fed by a six-phase voltage source inverter.To simplify research and analysis, it is assumed that the back EMF of the motor is sinusoidally distributed.The expression for the stator voltage of a dual three-phase PMSM is The U6s, I6s, ψ6s, and R6s, respectively, denote the stator voltage vector, phase current vector, magnetic flux vector, and stator resistance.
The vector space decoupling of the dual three-phase PMSM model in the d-q, x-y, o1-o2 coordinate systems for the continuous-time-domain voltage state equation In the equation, Ld and Lq represent the dq-axis inductances, respectively; LZ denotes the stator side leakage inductance; id and iq are the dq-axis stator currents; ix and iy are the current components in the harmonic plane; io1 and io2 are the zero-sequence sub-plane currents; Rs is the stator resistance; ω is the angular frequency, and ψf is the magnitude of the magnetic flux linkage.The widely used forward Euler method is chosen to discretize the current in Equation (2), as the influence of zero sequence subspace can be neglected due to center point isolation.The predicted values of current in each subspace are obtained accordingly.

Fault Analysis
Figure 2 illustrates the voltage and current distortion caused by inverter bridge arm faults, using the W-phase current as an example.
Following the T61 switch fault, the positive W-phase current is forced to zero within several switching cycles, as shown in Figure 2. The duration of these few cycles is The expression for the stator voltage of a dual three-phase PMSM is The U 6s, I 6s , ψ 6s, and R 6s , respectively, denote the stator voltage vector, phase current vector, magnetic flux vector, and stator resistance.
The vector space decoupling of the dual three-phase PMSM model in the d-q, x-y, o1-o2 coordinate systems for the continuous-time-domain voltage state equation In the equation, L d and L q represent the dq-axis inductances, respectively; L Z denotes the stator side leakage inductance; i d and i q are the dq-axis stator currents; i x and i y are the current components in the harmonic plane; i o1 and i o2 are the zero-sequence sub-plane currents; R s is the stator resistance; ω is the angular frequency, and ψ f is the magnitude of the magnetic flux linkage.The widely used forward Euler method is chosen to discretize the current in Equation (2), as the influence of zero sequence subspace can be neglected due to center point isolation.The predicted values of current in each subspace are obtained accordingly.

Fault Analysis
Figure 2 illustrates the voltage and current distortion caused by inverter bridge arm faults, using the W-phase current as an example.
Following the T 61 switch fault, the positive W-phase current is forced to zero within several switching cycles, as shown in Figure 2. The duration of these few cycles is negligible when compared to a full period.Consequently, the T 61-O SF fault exhibits similar fault characteristics to the W-phase OPF in the positive half cycle, and the PMSM model with W-phase OPF applies to the T 61-O SF.During the negative half-cycle of the W-phase current, it does not pass through T 61 ; hence, the T 61-O SF does not affect the W-phase current in the negative half-cycle.Analysis results can be obtained when an open-circuit fault occurs at T 61 .In addition, as shown in Figure 3, the trajectory of harmonic current can be observed in the case of OPF and OSF.
fault characteristics to the W-phase OPF in the positive half cycle, and the PMSM mo with W-phase OPF applies to the T61-oSF.During the negative half-cycle of the W-ph current, it does not pass through T61; hence, the T61-oSF does not affect the W-phase curr in the negative half-cycle.Analysis results can be obtained when an open-circuit fault curs at T61.In addition, as shown in Figure 3, the trajectory of harmonic current can observed in the case of OPF and OSF.negligible when compared to a full period.Consequently, the T61-oSF fault exhibits similar fault characteristics to the W-phase OPF in the positive half cycle, and the PMSM model with W-phase OPF applies to the T61-oSF.During the negative half-cycle of the W-phase current, it does not pass through T61; hence, the T61-oSF does not affect the W-phase current in the negative half-cycle.Analysis results can be obtained when an open-circuit fault occurs at T61.In addition, as shown in Figure 3, the trajectory of harmonic current can be observed in the case of OPF and OSF.negligible when compared to a full period.Consequently, the T61-oSF fault exhibits similar fault characteristics to the W-phase OPF in the positive half cycle, and the PMSM model with W-phase OPF applies to the T61-oSF.During the negative half-cycle of the W-phase current, it does not pass through T61; hence, the T61-oSF does not affect the W-phase current in the negative half-cycle.Analysis results can be obtained when an open-circuit fault occurs at T61.In addition, as shown in Figure 3, the trajectory of harmonic current can be observed in the case of OPF and OSF.

Proposed Fault Diagnosis Method
In this section, we propose a novel method for diagnosing multiple open-circuit faults in the OPF system based on the dual d-q predicted current model, as depicted in Figure 5.In this paper's electrical fault diagnosis, we present a two-step diagnostic scheme.Firstly,

Proposed Fault Diagnosis Method
In this section, we propose a novel method for diagnosing multiple open-cir faults in the OPF system based on the dual d-q predicted current model, as depicte Figure 5.In this paper's electrical fault diagnosis, we present a two-step diagn scheme.

Fault Current Model
Under normal operation, the predicted current in the (k + 1)th sampling interval be derived from the current in the kth sampling interval according to Equation (3).If t is a fault, the predicted current in the (k + 1)th sampling interval predicted by the nor model will deviate from the feedback current.First, the correct predicted current in fault operation needs to be calculated for fault diagnosis.
The stator voltage of a dual three-phase permanent magnet synchronous mot expressed as U6s, I6s, ψ6s, and R6s represent the six-phase stator voltage vector, phase current ve magnetic flux linkage, and stator resistance, respectively.Because of the neutral isolation, each winding can be treated as an indepen winding.The phase-current relation can be changed as follows Assuming that the A-phase current will be forced to zero in case of an open-cir fault in the A phase.According to Kirchhoff's law, the relationship between the B-p current and the C-phase current can be expressed as follows According to Equations ( 6) and (8), the line voltage between phases B and C un A-phase OPF can be expressed as Through the discretization processing of Equation ( 3), it can be obtained that

Fault Current Model
Under normal operation, the predicted current in the (k + 1)th sampling interval can be derived from the current in the kth sampling interval according to Equation (3).If there is a fault, the predicted current in the (k + 1)th sampling interval predicted by the normal model will deviate from the feedback current.First, the correct predicted current in the fault operation needs to be calculated for fault diagnosis.
The stator voltage of a dual three-phase permanent magnet synchronous motor is expressed as U 6s , I 6s , ψ 6s , and R 6s represent the six-phase stator voltage vector, phase current vector, magnetic flux linkage, and stator resistance, respectively.Because of the neutral isolation, each winding can be treated as an independent winding.The phase-current relation can be changed as follows Assuming that the A-phase current will be forced to zero in case of an open-circuit fault in the A phase.According to Kirchhoff's law, the relationship between the B-phase current and the C-phase current can be expressed as follows According to Equations ( 6) and (8), the line voltage between phases B and C under A-phase OPF can be expressed as Through the discretization processing of Equation ( 3), it can be obtained that According to Equation (10), the predicted B-phase current during the (k + 1)th sampling interval under A-phase OPF operation can be represented as Thus, using Park transformation, the predictive current in the d1q1 axis of the OPF model under the A-phase OPF constraint can be derived from Equations ( 7) and (11), expressed as Similarly, when an open-circuit fault occurs in the U phase, the fault current constraint can be expressed as i V_OU = −i W_OU (13) Under the constraint of the U-phase fault current, the predictive current in the d2-q2 axis of the OPF model under the U-phase OPF constraint can be derived Due to the spatial symmetry of the windings in a dual three-phase permanent magnet synchronous motor, the dual dq-axis predictive current model under the other phase's OPF constraints can be obtained by adjusting the angles according to Equations ( 12) and ( 14).In summary, the fault current model can be represented by the formulas (15) and ( 16) In the equation, the variables are as follows: n = (A, B, C); n* = (B, A, A); ω = (0, 1, −1); m = (U, V, W); m* = (V, U, U); λ = (−1, 1, 0).

Determination of Fault Occurrence
According to the analysis of fault current in Section 3, the current trajectories of OPF and OSF have the same trajectory characteristics in the harmonic plane, so they can be used for fault determination.The harmonic predicted current vector mode is defined as Define f n as an intermediate variable for fault detection.Under normal conditions, i x and i y are nearly zero, keeping f n close to zero.In the event of various open-circuit faults, the harmonic currents exhibit a predictable distribution, causing the magnitude of the vector to significantly deviate from zero.Consequently, monitoring changes in f n can enable rapid fault detection.
To reduce the effects of random noise in time series data, a moving average filter is used to smooth the signal waveform.Post-filtering, the filtered value f n_mean is assigned to f n as a basis for fault detection in the algorithm.
In the experiment described in this paper, the index f n has a maximum error of about 0.2 A during normal operation.To avoid misdiagnosis and ensure sufficient safety margin, the threshold of the index f n_th is set to 0.3 A. When f n_mean is greater than the threshold, the system is determined to be in fault and the fault index F n = 1 is output.

Identification of Faulty Phase
As shown in Figure 5, the first step of the fault diagnosis process, F n , determines whether the system is at fault.The second step of the fault diagnosis process narrows the fault search range to specific faults, such as single inverter OSF and single-phase OPF.
Under fault, the feedback currents of the fault model of axis d1-q1 in the (k + 1)th sampling interval are almost the same as the predicted currents of axis d1-q1 of the normal model, which can be expressed as.
According to Equation ( 20) the equation of residual currents of planar fault prediction current and health prediction current under the constraint of A-and U-phase OPF is obtained as follows Take the residual current vector mode and construct the intermediate variables d A and d U for phase diagnosis The A-phase fault can be analyzed using Formula (21) to define two intermediate variables for phase location of winding faults, denoted as d N (f = A, B, C; s = U, V, W).
The intermediate variables of fault phase location of two sets of windings are processed by sliding average filtering, respectively, and the filter d N_mean is assigned to d N in the algorithm.
In the fault state, the residual model of the fault-predicted current is close to equal, and the residual vector modulus d A and d U under the fault is close to zero.In the healthy state of the system, d A will be greater than zero, and they are constant positive half-wave functions.Therefore, by observing the changes of d N and d N_th , the fault phase can be quickly positioned, and the waveforms of the intermediate variables f n and d N under different faults are shown in Table 1.The reference angle of the harmonic current vector at each phase fault can be de-   The reference angle of the harmonic current vector at each phase fault can be de-   The reference angle of the harmonic current vector at each phase fault can be de-   The reference angle of the harmonic current vector at each phase fault can be de-   The reference angle of the harmonic current vector at each phase fault can be de-   The reference angle of the harmonic current vector at each phase fault can be de- The reference angle of the harmonic current vector at each phase fault can be described as follows

Intermediate
The analysis in Section 3 reveals that the harmonic plane current trajectories undergo systematic variations when an OSF occurs, depending on the position of the faulty switch tube.Figure 6 presents a diagram illustrating the segmentation of current vector trajectories under a single-tube fault, (where A + denotes the upper switch of phase A and A − represents the lower switch of phase A).

Experiment System
The diagnostic strategy's efficacy was validated through experiments conducted on a DTP-PMSM.The experimental platform is shown in Figure 7 The experimental platform demonstrates the functions and interrelationships of the various parts of the system.Key motor parameters include: rated power of 4 kW; peak current of 3.5 A; rated speed of 1000 r/min; and stator resistance Rs 1.45 Ω.The control system's core is constructed using TI TMS320F28379 DSP of USA and Intel's FPGA MAX-V chip of USA.During the experiment, a switching frequency of 10 kHz was employed, with load provided by the PMSM while vector control and fault diagnosis algorithms were implemented through DSP technology.Fault simulation was achieved by blocking corresponding pulse drive signals.

Transient Performance Analysis
Experimental validations were conducted to assess the robustness of the proposed fault diagnosis scheme during transient operations, specifically evaluating speed and load response.Figure 8a depicts an acceleration experiment where a constant torque of 5 N•m To overcome the effects of non-ideal factors during the actual operation of the system, a safety threshold θ* is added to the ideal position of the current trajectory.This ensures that once the diagnosis method calculates the current trajectory position as satisfying Equation ( 24), the position of the faulty switch can be determined.The selection of θ* should be based on the actual operation of the system, and in this experiment, θ* is chosen to be 5 As shown in Figure 6, the faulty tube position can be accurately identified by determining the position angle t M of the harmonic current trajectory within the corresponding error interval.

Experimental Verification 5.1. Experiment System
The diagnostic strategy's efficacy was validated through experiments conducted on a DTP-PMSM.The experimental platform is shown in Figure 7 The experimental platform demonstrates the functions and interrelationships of the various parts of the system.
Key motor parameters include: rated power of 4 kW; peak current of 3.5 A; rated speed of 1000 r/min; and stator resistance R s 1.45 Ω.The control system's core is constructed using TI TMS320F28379 DSP of USA and Intel's FPGA MAX-V chip of USA.During the experiment, a switching frequency of 10 kHz was employed, with load provided by the PMSM while vector control and fault diagnosis algorithms were implemented through DSP technology.Fault simulation was achieved by blocking corresponding pulse drive signals.

Experiment System
The diagnostic strategy's efficacy was validated through experiments conducted on a DTP-PMSM.The experimental platform is shown in Figure 7 The experimental platform demonstrates the functions and interrelationships of the various parts of the system.Key motor parameters include: rated power of 4 kW; peak current of 3.5 A; rated speed of 1000 r/min; and stator resistance Rs 1.45 Ω.The control system's core is constructed using TI TMS320F28379 DSP of USA and Intel's FPGA MAX-V chip of USA.During the experiment, a switching frequency of 10 kHz was employed, with load provided by the PMSM while vector control and fault diagnosis algorithms were implemented through DSP technology.Fault simulation was achieved by blocking corresponding pulse drive signals.

Transient Performance Analysis
Experimental validations were conducted to assess the robustness of the proposed fault diagnosis scheme during transient operations, specifically evaluating speed and load response.Figure 8a depicts an acceleration experiment where a constant torque of 5 N•m was applied, increasing the speed from 400 r/min to 800 r/min within 0.5 s after achieving stable operation for a certain duration.Throughout the variable-speed process, transient step phenomena were observed in the intermediate variables.In the load variation experiment shown in Figure 8b, after accelerating and maintaining a stable speed of 800 r/min for a specific period, the load was abruptly increased to 8 N•m within 0.5 s due to loading effects.This led to an increase in phase current amplitude and intermediate variables, resulting in changes in motor speed and load; however, these variations did not affect fault diagnosis as protection strategies employed an undershoot threshold setting method.During the testing period, all intermediate variables consistently remained above their

Transient Performance Analysis
Experimental validations were conducted to assess the robustness of the proposed fault diagnosis scheme during transient operations, specifically evaluating speed and load response.Figure 8a depicts an acceleration experiment where a constant torque of 5 N•m was applied, increasing the speed from 400 r/min to 800 r/min within 0.5 s after achieving stable operation for a certain duration.Throughout the variable-speed process, transient step phenomena were observed in the intermediate variables.In the load variation experiment shown in Figure 8b, after accelerating and maintaining a stable speed of 800 r/min for a specific period, the load was abruptly increased to 8 N•m within 0.5 s due to loading effects.This led to an increase in phase current amplitude and intermediate variables, resulting in changes in motor speed and load; however, these variations did not affect fault diagnosis as protection strategies employed an undershoot threshold setting method.During the testing period, all intermediate variables consistently remained above their thresholds while the fault detection index D N consistently maintained a zero value, thereby validating both the effectiveness and stability of this diagnostic approach during transient operations.World Electr.Veh.J. 2024, 15, x FOR PEER REVIEW 11 The fault diagnosis experiment of the open-circuit fault in the PMSM drive syste illustrated in Figure 11, focusing on the A-phase switching tube T12.Under normal op tion, the A-phase current exhibits a sinusoidal waveform with an occurrence index fn nificantly below the threshold fn_th.However, when T12 experiences an open-circuit f the A-phase current drops to zero during the negative half cycle and approximates a waveform during the positive half cycle.Simultaneously, there is a momentary incr in the fault occurrence index fn above its threshold fn_th value, leading to a transitio fault flag Fn from 0 to 1 indicating completion of the initial diagnostic step.Furtherm as evidenced by the phase positioning index dN surpassing its threshold value, it ca determined that this is a single inverter fault with the identified position.Upon confirm T12 open-circuit fault condition, TM fault flag changes from 0 to 7 within 28 ms signif the completion of the diagnostic process and determination of the seventh pin (i.e., lo bridge arm of A-phase) as a faulty location.The fault diagnosis experiment of the open-circuit fault in the PMSM drive system is illustrated in Figure 11, focusing on the A-phase switching tube T 12 .Under normal operation, the A-phase current exhibits a sinusoidal waveform with an occurrence index f n significantly below the threshold f n_th .However, when T 12 experiences an open-circuit fault, the A-phase current drops to zero during the negative half cycle and approximates a sine waveform during the positive half cycle.Simultaneously, there is a momentary increase in the fault occurrence index f n above its threshold f n_th value, leading to a transition of fault flag F n from 0 to 1 indicating completion of the initial diagnostic step.Furthermore, as evidenced by the phase positioning index d N surpassing its threshold value, it can be determined that this is a single inverter fault with the identified position.Upon confirming T 12 open-circuit fault condition, T M fault flag changes from 0 to 7 within 28 ms signifying the completion of the diagnostic process and determination of the seventh pin (i.e., lower bridge arm of A-phase) as a faulty location.

Parametric Disturbance Analysis
The stability of the diagnostic strategy is verified by introducing a 20% error s rately in the d-q axis inductance and stator resistance and observing its impact on diagnostic results.As depicted in Figure 12, parameter deviations cause minimal fluc tion in the waveform of intermediate variables during fault occurrence, which is sig

Parametric Disturbance Analysis
The stability of the diagnostic strategy is verified by introducing a 20% error separately in the d-q axis inductance and stator resistance and observing its impact on the diagnostic results.As depicted in Figure 12, parameter deviations cause minimal fluctuation in the waveform of intermediate variables during fault occurrence, which is significantly smaller than the maximum error of 0.1 A under normal conditions.The diagnostic intermediate variables f n are much smaller than the threshold f n_th , while the phase diagnostic intermediate variables d n are much larger than the threshold d N_th .Based on this analysis, it can be concluded that when parameter errors are introduced during healthy motor operation, the diagnostic algorithm performs well, and intermediate variable values remain considerably lower than their preset thresholds f n_th and d N_th .This demonstrates that parameter disturbances do not affect diagnosis.

Parametric Disturbance Analysis
The stability of the diagnostic strategy is verified by introducing a 20% erro rately in the d-q axis inductance and stator resistance and observing its impact diagnostic results.As depicted in Figure 12, parameter deviations cause minimal fl tion in the waveform of intermediate variables during fault occurrence, which is cantly smaller than the maximum error of 0.1 A under normal conditions.The dia intermediate variables fn are much smaller than the threshold fn_th, while the phas nostic intermediate variables dn are much larger than the threshold dN_th.Based analysis, it can be concluded that when parameter errors are introduced during motor operation, the diagnostic algorithm performs well, and intermediate varia ues remain considerably lower than their preset thresholds fn_th and dN_th.This d strates that parameter disturbances do not affect diagnosis.

Conclusions
This study addresses the problem of incorrect fault diagnoses that frequentl in a dual three-phase permanent magnet synchronous motor during load steps, id at low load.An open-circuit fault diagnosis strategy is proposed to improve robu The theoretical analysis and experimental validation confirm the results:

Conclusions
This study addresses the problem of incorrect fault diagnoses that frequently occur in a dual three-phase permanent magnet synchronous motor during load steps, idling, or at low load.An open-circuit fault diagnosis strategy is proposed to improve robustness.The theoretical analysis and experimental validation confirm the results:

Figure 3 .
Figure 3. x-y plane current trajectories: (a) different open-circuit faults; (b) different switching t of an inverter.

Figure 4 .
Figure 4. Current waveform under the same conditions.(a) Health; (b) single pipe open circuit single-phase open circuit.

Figure 3 .
Figure 3. x-y plane current trajectories: (a) different open-circuit faults; (b) different switching tube of an inverter.Similarly, this method can be applied to analyze various open-circuit fault scenarios.Figure 4. illustrates the fault phase currents for three types of faults: a single inverter open circuit, a single-phase open circuit, and a two-phase open circuit, when the drive system experiences a failure.

Figure 4 .
illustrates the fault phase currents for three types of faults: a single inverter open circuit, a single-phase open circuit, and a two-phase open circuit, when the drive system experiences a failure.

Figure 4 .
Figure 4. Current waveform under the same conditions.(a) Health; (b) single pipe open circuit; (c) single-phase open circuit.

Figure 3 .
Figure 3. x-y plane current trajectories: (a) different open-circuit faults; (b) different switching tube of an inverter.Similarly, this method can be applied to analyze various open-circuit fault scenarios.Figure 4. illustrates the fault phase currents for three types of faults: a single inverter open circuit, a single-phase open circuit, and a two-phase open circuit, when the drive system experiences a failure.

Figure 4 .
illustrates the fault phase currents for three types of faults: a single inverter open circuit, a single-phase open circuit, and a two-phase open circuit, when the drive system experiences a failure.

Figure 3 .
Figure 3. x-y plane current trajectories: (a) different open-circuit faults; (b) different switching tube of an inverter.Similarly, this method can be applied to analyze various open-circuit fault scenarios.Figure 4. illustrates the fault phase currents for three types of faults: a single inverter open circuit, a single-phase open circuit, and a two-phase open circuit, when the drive system experiences a failure.

Figure 4 .
illustrates the fault phase currents for three types of faults: a single inverter open circuit, a single-phase open circuit, and a two-phase open circuit, when the drive system experiences a failure.

Figure 4 .
Figure 4. Current waveform under the same conditions.(a) Health; (b) single pipe open circuit; (c) single-phase open circuit.

Figure 4 .
Figure 4. Current waveform under the same conditions.(a) Health; (b) single pipe open circuit; (c) single-phase open circuit.
system faults are identified by monitoring the fault indicator F n .Secondly, the phase sequence of open-circuit faults is determined through the fault phase indicator D N .It is possible to locate the specific faulty transistor by evaluating the magnitude of the inverter fault indicator T M corresponding to inverter PINs 1 to 12.
Firstly, system faults are identified by monitoring the fault indicator Fn.Secon the phase sequence of open-circuit faults is determined through the fault phase indic DN.It is possible to locate the specific faulty transistor by evaluating the magnitude o inverter fault indicator TM corresponding to inverter PINs 1 to 12.

Figure 5 .
Figure 5. Flowchart of the diagnosis process.

Figure 5 .
Figure 5. Flowchart of the diagnosis process.

dN 4 . 4 .
Determination of Specific Fault TypeWhen the judgment condition satisfies the constraint conditions of fn > fn_th and dN < dN_th, according to the judgment of the condition statement, the model will move to the positioning stage of the switch tube fault location.Here, "fn > fn_th" refers to the first diagnostic variable indicator indicating that the system has a fault, while "dN < dN_th" indicates that the phase fault indicator does not change and there is no open-circuit fault.At this point, it indicates that the system has a fault but not an open-circuit fault, that is the switch tube open-circuit fault.The model will execute the switch tube positioning program to determine the specific fault tube position.

dN 4 . 4 .
Determination of Specific Fault TypeWhen the judgment condition satisfies the constraint conditions of fn > fn_th and dN < dN_th, according to the judgment of the condition statement, the model will move to the positioning stage of the switch tube fault location.Here, "fn > fn_th" refers to the first diagnostic variable indicator indicating that the system has a fault, while "dN < dN_th" indicates that the phase fault indicator does not change and there is no open-circuit fault.At this point, it indicates that the system has a fault but not an open-circuit fault, that is the switch tube open-circuit fault.The model will execute the switch tube positioning program to determine the specific fault tube position.

dN 4 . 4 .
Determination of Specific Fault TypeWhen the judgment condition satisfies the constraint conditions of fn > fn_th and dN < dN_th, according to the judgment of the condition statement, the model will move to the positioning stage of the switch tube fault location.Here, "fn > fn_th" refers to the first diagnostic variable indicator indicating that the system has a fault, while "dN < dN_th" indicates that the phase fault indicator does not change and there is no open-circuit fault.At this point, it indicates that the system has a fault but not an open-circuit fault, that is the switch tube open-circuit fault.The model will execute the switch tube positioning program to determine the specific fault tube position.

4 .
Determination of Specific Fault TypeWhen the judgment condition satisfies the constraint conditions of fn > fn_th and dN < dN_th, according to the judgment of the condition statement, the model will move to the positioning stage of the switch tube fault location.Here, "fn > fn_th" refers to the first diagnostic variable indicator indicating that the system has a fault, while "dN < dN_th" indicates that the phase fault indicator does not change and there is no open-circuit fault.At this point, it indicates that the system has a fault but not an open-circuit fault, that is the switch tube open-circuit fault.The model will execute the switch tube positioning program to determine the specific fault tube position.

4 .
Determination of Specific Fault TypeWhen the judgment condition satisfies the constraint conditions of fn > fn_th and dN < dN_th, according to the judgment of the condition statement, the model will move to the positioning stage of the switch tube fault location.Here, "fn > fn_th" refers to the first diagnostic variable indicator indicating that the system has a fault, while "dN < dN_th" indicates that the phase fault indicator does not change and there is no open-circuit fault.At this point, it indicates that the system has a fault but not an open-circuit fault, that is the switch tube open-circuit fault.The model will execute the switch tube positioning program to determine the specific fault tube position.

4 .
Determination of Specific Fault TypeWhen the judgment condition satisfies the constraint conditions of fn > fn_th and dN < dN_th, according to the judgment of the condition statement, the model will move to the positioning stage of the switch tube fault location.Here, "fn > fn_th" refers to the first diagnostic variable indicator indicating that the system has a fault, while "dN < dN_th" indicates that the phase fault indicator does not change and there is no open-circuit fault.At this point, it indicates that the system has a fault but not an open-circuit fault, that is the switch tube open-circuit fault.The model will execute the switch tube positioning program to determine the specific fault tube position.

4. 4 .
Determination of Specific Fault TypeWhen the judgment condition satisfies the constraint conditions of f n > f n_th and d N < d N_th , according to the judgment of the condition statement, the model will move to the positioning stage of the switch tube fault location.Here, "f n > f n_th " refers to the first diagnostic variable indicator indicating that the system has a fault, while "d N < d N_th "indicates that the phase fault indicator does not change and there is no open-circuit fault.At this point, it indicates that the system has a fault but not an open-circuit fault, that is the switch tube open-circuit fault.The model will execute the switch tube positioning program to determine the specific fault tube position.

14 Figure 6 .
Figure 6.Position angle of ix-iy current track corresponding to inverter open-circuit fault.

Figure 6 .
Figure 6.Position angle of ix-iy current track corresponding to inverter open-circuit fault.
World Electr.Veh.J. 2024, 15, x FOR PEER REVIEW 10 of 14 thresholds while the fault detection index DN consistently maintained a zero value, thereby validating both the effectiveness and stability of this diagnostic approach during transient operations.

Figure 9
Figure 9 depicts the experiment of fault diagnosis in the PMSM drive system under open-circuit fault conditions in phase A. During normal operation, the phase A current exhibits a sinusoidal waveform with the fault occurrence index fn significantly below its threshold fn_th.However, when an open-circuit fault occurs in phase A, the current drops to zero and remains constant.At this point, the fault occurrence index briefly exceeds its

Figure 9
Figure 9 depicts the experiment of fault diagnosis in the PMSM drive system under open-circuit fault conditions in phase A. During normal operation, the phase A current exhibits a sinusoidal waveform with the fault occurrence index f n significantly below its threshold f n_th .However, when an open-circuit fault occurs in phase A, the current drops to zero and remains constant.At this point, the fault occurrence index briefly exceeds its threshold f n_th , resulting in the transition of the fault flag F n from 0 to 1 within 5 ms, indicating that a fault has occurred and completing the first diagnostic step.After an open-circuit fault occurs in phase A, intermediate variable d A rapidly decreases below its threshold and causes a surge of D A from 0 to 1 within 10 ms signifying the completion of the diagnostic process.Additionally, all five intermediate variables d A −d V remain above their thresholds confirming no false positives during diagnosis.

Figure 10 .
Figure 10.Fault diagnosis of phase-A and U OPF.

Figure 9 .
Figure 9. Fault diagnosis of phase-A OPF.The fault diagnosis experiment of loading a U-phase open-circuit PMSM drive with an A-phase open-circuit fault is depicted in Figure 10.Under normal operating conditions, the fault occurrence index f n remains significantly lower than its threshold value f n_th .However, when the U-phase experiences OPF following the A-phase, throughout the entire process, the fault occurrence index f n consistently exceeds the threshold value f n_th , indicating that the initial step of diagnosis is always responsive.Before the U-phase fault, the phase indicator DA consistently remains at 1; after the fault occurs, d U rapidly decreases.Within 7 ms, the fault phase indicator D U transitions from 0 to 1, signifying completion of the diagnostic process.Throughout this process, four additional intermediate variables d B ~dC and d V ~dW all surpass their thresholds while indicators d B ~dC and d V ~dW remain zero; thus ensuring no misjudgment in this procedure.The fault diagnosis experiment of the open-circuit fault in the PMSM drive system is illustrated in Figure11, focusing on the A-phase switching tube T 12 .Under normal operation, the A-phase current exhibits a sinusoidal waveform with an occurrence index f n significantly below the threshold f n_th .However, when T 12 experiences an open-circuit fault, the A-phase current drops to zero during the negative half cycle and approximates a sine waveform during the positive half cycle.Simultaneously, there is a momentary increase in the fault occurrence index f n above its threshold f n_th value, leading to a transition of

Figure 9 .
Fault diagnosis of phase-A OPF.

Figure 10 .
Figure 10.Fault diagnosis of phase-A and U OPF.

( 1 )
This strategy can diagnose three types of open-circuit faults in the DTP-PMSM drive system, including 12 fault types for OSF and 21 fault types for single-phase and twophase OPF, making a total of 33 fault types.And, it can also diagnose single-phase open faults and two-phase open faults simultaneously.(2) The strategy effectively overcomes the issue of misjudgment in load mutation encountered by traditional methods, The empirical verification has confirmed the demonstrating high reliability and robustness in diagnosing open-circuit faults.The diagnosis time for OPF and OSF in the system is within 10 ms and 30 ms, respectively.(3) After simplifying the calculation process, the strategy of this paper achieves that there is no interference between the different diagnostic variables in the compatible diagnosis of multiphase open-circuit faults.Furthermore, this strategy does not require additional hardware support and can perform fault diagnosis quickly and accurately even when operating points, control strategies or drive parameters change.(4) This strategy employs the approach of utilizing predicted current extraction to construct fault models, which acts as a link between fault diagnosis and fault-tolerant control based on predicted current, providing certain support for future research on a dual three-phase permanent magnet synchronous motor's fault-tolerant control and laying part of the foundation.

Table 1 .
Time-domain fault variable waveform under different faults.

Table 1 .
Time-domain fault variable waveform under different faults.

Table 1 .
Time-domain fault variable waveform under different faults.

Table 1 .
Time-domain fault variable waveform under different faults.

Table 1 .
Time-domain fault variable waveform under different faults.

Table 1 .
Time-domain fault variable waveform under different faults.

Table 1 .
Time-domain fault variable waveform under different faults.