# Diagnosis of Power Switch Faults in Three-Phase Permanent Magnet Synchronous Motors via Current-Signature Technique

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions, abating thermal signatures, mitigating noise emissions, and enhancing thrust efficiency [1,2,3]. However, flight endurance and reliability still remain open issues. Endurance is currently limited by the capability of the energy storage devices, which is much lower than ICEs (the capacity of Li-Ion batteries is typically about 0.3 MJ/kg, approximately 100 times lower than gasoline [1]). In addition, due to the novelty of this application, the reliability and safety are still questionable. The failure rate of three-phase Permanent Magnet Synchronous Motors (PMSMs) with conventional three-leg converters is typically around 200 per million flight hours [4,5], which is far from the required levels for airworthiness certification [6]. Specifically, a relevant amount (from 50% to 70%) of PMSMs fault modes originate from motor phases (open-phase [5], inter-turn [7], phase-to-phase [8] and phase-to-ground [9]) and power converters. Among the latter ones, faults of the supply voltage stabilizing capacitor and faults of the power switches are predominant [10,11].

- Model-based methods;
- Signal-based methods;
- Data-driven methods.

- The developed method relies on online ellipse fittings of the current phasor trajectory in the Clarke plane during constant speed operations of the motor, using the geometrical characteristics of the reconstructed ellipse as fault symptoms. The FDI algorithm elaborates the minimum number of measurements that permits the detection and isolation of the fault within a fraction of the electric period;
- The algorithm, formerly adopted in a previous work by the authors, for the FDI of inter-turn short-circuits of PMSM phases [42] is here extended to power switch faults;
- As a relevant case study, the FDI performances are assessed by simulating the failure transients related to power switch faults in a high-speed PMSM employed for the propulsion of a modern lightweight fixed-wing UAV.

## 2. Materials and Methods

#### 2.1. PMSM Electrical Modelling

#### 2.2. Current Signature in Clarke Plane in Case of Open-Circuit Power Switches

#### 2.2.1. Behaviour with Open-Circuit of a Motor Phase

#### 2.2.2. Behaviour with Open-Circuit of a Power Switch

#### 2.3. Fault Diagnosis

#### 2.4. Application to a PMSM for Lightweight Fixed-Wing UAV Propulsion

- ◦
- A control/monitoring electronic box, for the implementation of the closed-loop control and health-monitoring functions;
- ◦
- A four-leg converter;
- ◦
- Three current sensors, one per motor phase;
- ◦
- An angular position sensor, measuring the motor angle;
- ◦
- A power supply unit;
- ◦
- Two connectors for the data and power supply interfaces, related to the UAV flight control computer and the UAV electrical power system, respectively.

#### 2.4.1. Electronic Control Unit

#### 2.4.2. Aero-Mechanical Modelling

## 3. Results

^{−7}s integration step.

- Starting (t = 0 s) with the PMSM delivering 1.7 Nm torque at 5800 rpm speed, corresponding to the FEPS operation during the UAV cruise;
- Commanding, when applicable, a motor speed increase (Event 0, E0) up to 6800 rpm, corresponding to a UAV transition from cruise to climb;
- Injecting an open-circuit fault in the MOSFET CL (Event 1, E1);
- Detecting an open-circuit fault (Event 2, E2), when the difference between the lengths of major and minor axes of the reconstructed ellipse is greater than 10% of their mean value (${\epsilon}_{s}=0.05\left({s}_{M}+{s}_{m}\right)$ in Figure 3b);
- Isolating the open-circuit fault (Event 3, E3), when the coordinates of the reconstructed ellipse centre satisfy one of the conditions defined in the FDI logic flow chart in Figure 3b.

#### 3.1. Simulation in Cruise Conditions

#### 3.2. Simulation of Transition between Cruise and Climb

#### 3.3. Impact of Number of Samples on the Algorithm Performances

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Definition | Symbol | Value | Unit |
---|---|---|---|

Stator phase resistance | $R$ | 0.025 | Ω |

Stator phase inductance | $L$ | 2 × 10^{−5} | H |

Pole pairs number | ${n}_{d}$ | 5 | - |

Motor speed constant | ${k}_{m}$ | 0.0152 | V/(rad/s) |

Voltage supply | ${V}_{DC}$ | 48 | V |

Rotor inertia | ${J}_{m}$ | 2.2 × 10^{−2} | kg·m^{2} |

Propeller diameter | ${D}_{p}$ | 0.5588 | m |

Propeller inertia | ${J}_{p}$ | 1.186 × 10^{−3} | kg·m^{2} |

Coupling joint stiffness | ${K}_{gb}$ | 1.598 × 10^{3} | Nm/rad |

Coupling joint damping | ${C}_{gb}$ | 0.2545 | Nm/(rad/s) |

Rated power | ${P}_{em}^{max}$ | 3200 | W |

Sampling frequency | ${f}_{s}$ | 20 | kHz |

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**Figure 2.**Current phasor trajectory in the Clarke plane in normal conditions and with open-circuit faults: (

**a**) phase fault; (

**b**) low-side power switch fault; (

**c**) high-side power switch fault.

**Figure 3.**Fault diagnosis conceptualisation: (

**a**) ellipse fitting for the current phasor trajectory in the Clarke plane in case of open-circuit fault on MOSFET BH; (

**b**) flow chart of the FDI logic.

**Figure 4.**Architecture of the electronic control unit of the reference FEPS (FCC: Flight Control Computer; EPGDS: Electrical Power Generation and Distribution System; CBCS FDI: Current-Based/Current-Signature FDI).

**Figure 6.**Torque coefficient (

**a**) and thrust coefficient (

**b**) as functions of propeller speed and advance ratio for the APC 18 × 22E propeller.

**Figure 7.**Failure transient due to an open-circuit of MOSFET CL (low-side, phase C) during cruise: motor speed.

**Figure 8.**Failure transient due to an open-circuit of MOSFET CL (low-side, phase C) during cruise: (

**a**) phase currents; (

**b**) direct and quadrature voltages.

**Figure 9.**Failure transient due to an open-circuit of MOSFET CL (low-side, phase C) during cruise: (

**a**) axes lengths of the fitted ellipse; (

**b**) location of the centre of the fitted ellipse.

**Figure 10.**Failure transient due to an open-circuit of MOSFET CL (low-side, phase C) during cruise, with results obtained one electrical period before and two electrical periods after the fault injection: (

**a**) axes lengths of the fitted ellipse (

**top**), location of the centre of the fitted ellipse (

**middle**), phase currents (

**bottom**); (

**b**) current phasor trajectory in Clarke plane.

**Figure 11.**Failure transient due to an open-circuit of MOSFET CL (low-side, phase C) during transition from cruise to climb: motor speed.

**Figure 12.**Failure transient due to an open-circuit of MOSFET CL (low-side, phase C) during transition from cruise to climb: (

**a**) phase currents; (

**b**) direct and quadrature voltages.

**Figure 13.**Failure transient due to an open-circuit of MOSFET CL (low-side, phase C) during transition from cruise to climb: (

**a**) axes lengths of the fitted ellipse; (

**b**) location of the centre of the fitted ellipse.

**Figure 14.**Failure transient due to an open-circuit of MOSFET CL (low-side, phase C) during transition from cruise to climb, with results obtained one electrical period before and two electrical periods after the fault injection: (

**a**) axes lengths of the fitted ellipse (

**top**), location of the centre of the fitted ellipse (

**middle**), phase currents (

**bottom**); (

**b**) current phasor trajectory in Clarke plane.

**Figure 15.**Failure transient due to an open-circuit of MOSFET CL (low-side, phase C) during cruise with a different number of current samples ($n=30,36,40$): (

**a**) axes lengths of the fitted ellipse; (

**b**) location of the centre of the fitted ellipse.

**Figure 16.**Failure transient due to an open-circuit of MOSFET CL (low-side, phase C) during cruise with different number of current samples ($n=30,36,40$): current phasor trajectories in Clarke plane for $n=30$ (

**a**); $n=36$ (

**b**); and $n=40$ (

**c**). The results are obtained one electrical period before and two electrical periods after the fault injection.

**Figure 17.**Failure transient due to an open-circuit of MOSFET CL (low-side, phase C) during cruise with different number of current samples ($n=30,36,40$): (axes lengths of the fitted ellipse (

**top**); location of the centre of the fitted ellipse (

**middle**); phase currents (

**bottom**). The results are obtained one electrical period before and two electrical periods after the fault injection.

Method | Approach | Advantages | Drawbacks |
---|---|---|---|

Model-based | Accurate modelling of system with faults starting from physical first-principles | Detailed information on condition monitoring | Model uncertainties |

Signal-based | Characterisation of behaviour with faults to identify measurements representing fault symptoms | Detailed modelling is not required | Uncertainties regarding fault symptoms, disturbances in measurements |

Data-driven | Collection of experimental databases related to behaviour with faults and faults identification via artificial intelligence | No explicit modelling is required | Dependence on training database, testing costs |

Failed MOSFET (Fault Effect) | Trajectory Equation with Respect to Command |
---|---|

AH (${i}_{a}\le 0$) or AL (${i}_{a}\ge 0$) | $\left\{\begin{array}{c}\mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\left(7\right)\mathrm{i}\mathrm{f}\mathrm{O}\mathrm{n}\\ \mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\left(6\right)\mathrm{i}\mathrm{f}\mathrm{O}\mathrm{f}\mathrm{f}\end{array}\right.$ |

BH (${i}_{b}\le 0$) or BL (${i}_{b}\ge 0$) | $\left\{\begin{array}{c}\mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\left(8\right)\mathrm{i}\mathrm{f}\mathrm{O}\mathrm{n}\\ \mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\left(6\right)\mathrm{i}\mathrm{f}\mathrm{O}\mathrm{f}\mathrm{f}\end{array}\right.$ |

CH (${i}_{c}\le 0$) or CL (${i}_{c}\ge 0$) | $\left\{\begin{array}{c}\mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\left(9\right)\mathrm{i}\mathrm{f}\mathrm{O}\mathrm{n}\\ \mathrm{E}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\left(6\right)\mathrm{i}\mathrm{f}\mathrm{O}\mathrm{f}\mathrm{f}\end{array}\right.$ |

Method | Isolation Time [×Electric Cycle] | Sampling to Electric Frequency | Robustness | Sensitivity to Parameters | Sensitivity to Work Conditions | Computational Effort | Simplicity |
---|---|---|---|---|---|---|---|

Model predictive control [31] | >1 | 20000/80 = 250 | Medium | High | Medium | Medium | Medium |

Average value [32] | >0.5 | Not available | High | Medium | Medium | Medium | Medium |

Two-phase current trajectory [35] | >1 | 3000/50 = 60 | Low | Medium | Low | Medium | Medium |

Current phasor trajectory slope [36] | >1 | 1000/50 = 20 | Medium | Medium | Medium | Medium | High |

Adjacent slope [37] | <0.4 | 500/50 = 10 | Medium | Low | Medium | Low | High |

Current phasor trajectory fitting (this work) | <0.5 | 20000/600 = 33 | High | Low | Medium | Low | High |

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**MDPI and ACS Style**

Suti, A.; Di Rito, G.
Diagnosis of Power Switch Faults in Three-Phase Permanent Magnet Synchronous Motors via Current-Signature Technique. *Actuators* **2024**, *13*, 25.
https://doi.org/10.3390/act13010025

**AMA Style**

Suti A, Di Rito G.
Diagnosis of Power Switch Faults in Three-Phase Permanent Magnet Synchronous Motors via Current-Signature Technique. *Actuators*. 2024; 13(1):25.
https://doi.org/10.3390/act13010025

**Chicago/Turabian Style**

Suti, Aleksander, and Gianpietro Di Rito.
2024. "Diagnosis of Power Switch Faults in Three-Phase Permanent Magnet Synchronous Motors via Current-Signature Technique" *Actuators* 13, no. 1: 25.
https://doi.org/10.3390/act13010025