# A New Fault Diagnosis Algorithm for PMSG Wind Turbine Power Converters under Variable Wind Speed Conditions

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## Abstract

**:**

## 1. Introduction

## 2. PMSG Wind Turbine System Simulation

#### 2.1. Wind Speed Simulation

_{m}, wind speed ramp v

_{r}, wind gust v

_{g}and turbulence v

_{t}[15]:

_{r}(m/h), wind ramp starting time T

_{sr}(s), wind ramp maximum time T

_{er}(s) in Equation (3):

_{g}(m/h), wind gust starting time T

_{sg}(s), wind gust end time T

_{eg}(s) as shown in Equation (4):

_{g}is the wind gust duration.

_{0}is the roughness length (m).

#### 2.2. PMSG Wind Turbine Simulation

^{3}), R is turbine radius (m), V is wind speed (m/s), C

_{p}(β,λ) is the turbine power coefficient that describes the WT power extraction efficiency and it is a function of tip-speed-ratio and the blade pitch angle. It can be calculated using the equation below [17]:

_{p}value where the tip-speed-ratio reaches the optimal value for each wind speed. This is the principle of the MPPT control strategy for WTs. The resulting optimal power delivered by the WT has a relationship with the rotor speed, which can be described by:

_{opt}is the optimal tip-speed-ratio that is often provided by the wind turbine manufacturers and c

_{popt}is optimal wind energy utilization coefficient.

#### 2.3. PMSG Control Logic

_{f}is the flux of the permanent magnets; ω

_{e}is the electrical angular speed which can be expressed as follows:

_{opt}is determined by optimal tip-speed-ratio and the wind speed V as shown in Equation (14):

_{d}, i

_{q}). By controlling the q-axis stator current the rotational speed of the generator can be controlled, while the d-axis stator current is kept at zero in order to ensure reactive power control. Their coupling effects are considered through voltage compensation, so the measured generator torque is compared to the optimal rotational speed to generate suitable SVPWM signals for the generator-side converter in order to realize the MPPT control strategy. Once a fault occurs in the generator-side converter, the generator speed will become unstable and the resultant stator currents deviate from the desired value. In addition, as the wind speed varies simultaneously the converter fault diagnosis needs to distinguish between abnormal symptoms from the nonlinear response of control system and wind speed fluctuations.

#### 2.4. Generator-Side Converter SVPWM Control Strategy

_{m}is the amplitude and ω is the space vector’s frequency. Park transformation (or abc/dq) is applied to transform the three phase voltage into two phase frame vector u

_{d}, u

_{q}with Equation (16). The desired vector u

_{d}, u

_{q}are given by the PI controller. Then the voltage vector can be determined by Equation (17). PWM signals for the converter are generated [9] based on the space vector as illustrated in Figure 3 [20]. The resulted vector is obtained by adjusting the eight basic vectors from u

_{0}to u

_{7}that are adjacent to the desired voltage vector with Equation (18).

## 3. Fault Diagnostic Method

#### 3.1. Direct Current Detection Method

_{a}, i

_{b}, i

_{c}) can be transferred to the d-q axis as shown in Equation (19):

_{n}is the characteristic parameter of each phase (index as n). It is defined to detect and localize switch failures. Its capability for wind turbine converter open-circuit fault detection is investigated in a later section.

#### 3.2. Current Vector/Trajectory Pattern Recognition

#### 3.3. Comparison of the Two Diagnostic Methods

_{n}/|i

_{s}|| and normalized phase current average value <|i

_{n}/|i

_{s}||> respectively for constant wind and step wind situations. They are two critical fault diagnostic parameters in the ENCAAV method. From Figure 6, it can be confirmed that with these two parameters, converter faults can be detected for a constant wind situation while it is not valid for step winds. It clearly shows that under step wind conditions the diagnostic parameters of the ENCAAV method deviate from zero under heathy situation. Such a deviation is actually caused by wind speed variation and may lead to false alarms. Figure 6c,d show the diagnostic result of using the CVTPR method for step wind and turbulent wind, respectively. Wind speed variation also leads to untraceable pattern when faults occur. The comparison shows that current pattern recognition methods become invalid for step wind and turbulent wind situations.

#### 3.4. Wind Speed Based Normalized Current Trajectory Detection

_{3}= 0.0309, k

_{2}= 20842, k

_{1}= 2.677 and k

_{0}= −4.718 obtained by fitting to the relationship between current magnitudes to wind speeds. For different WT model, the values of the four parameters may vary correspondingly. The park vector currents in d-q axis are then normalized to the benchmark current magnitude calculated for each measured wind speed in Equation (23):

## 4. Experimental Results

_{d}-I

_{q}vector pattern. This is compared to Figure 10d which shows that the step wind has caused a corresponding rotational speed variation and then the phase currents’ magnitude changes. It shows that without wind speed normalization operation, the fault feature of converters with open-circuited T1 switches generates multiple concentric semicircles that are mainly due to the step wind situation, while with operation of WSBNCT, Figure 10e shows that wind speed-induced disturbance is eliminated and the current’s park vector pattern converges to a single semicircle. Therefore, the corresponding fault feature is easily identified. For the failure of T2 to T6 switches, the operation is similar and the fault detection is also effective. This proves that WSBNCT method is capable and effective to identify converter open-switch faults for WT applications.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 5.**Three phase currents for the three wind speed situations: (

**a**) Constant wind; (

**b**) Step wind; (

**c**) Turbulent wind.

**Figure 6.**Diagnostic parameters: (

**a**) Normalized phase currents for constant and step wind situations; (

**b**) Normalized phase current average value for constant and step wind situations; (

**c**) I

_{d}-I

_{q}pattern for step wind situation; (

**d**) I

_{d}-I

_{q}pattern for turbulent wind situation.

**Figure 8.**Result of using WSBNCT fault detection method for: (

**a**) Step wind and (

**b**) Turbulent wind situations.

**Figure 10.**Experimental results: (

**a**) Time domain phase currents of healthy situation (constant rotational speed); (

**b**) Time domain phase currents of faulty situation (variable rotational speed); (

**c**) I

_{d}-I

_{q}pattern before T1 failure (constant rotational speed); (

**d**) I

_{d}-I

_{q}pattern before WSBNCT implementation (variable rotational speed); (

**e**) I

_{d}-I

_{q}pattern after WSBNCT implementation.

Parameters | Value |
---|---|

Rated Power | 30 kW |

Cut in/out Wind Speed | 3 m/s & 25 m/s |

Rated Wind Speed | 7.2 m/s |

Power Control Mode | Pitch control |

Stator Resistance (ohm) | 0.362 |

Inductance L (H) | 0.0015 |

Flux ψ (Wb) | 2.34 |

Pole Pairs P | 10 |

Damping F (N·M·S) | 0.000139 |

Inertia J (kg·m^{2}) | 1.2 |

Asynchronous Motor | |

Rated Power (kW) | 4 |

Rated Frequency (Hz) | 50 |

Rated Voltage and Current | 380 V & 7.9 A |

Rotational Speed (rpm) | 0–1460 |

Control Mode | V/F |

PMSG | |

Rated Power (kW) | 3 |

Rated Frequency (Hz) | 50 |

Rated Voltage and Current | 380 V & 5 A |

Rotational Speed (rpm) | 0–1500 |

Converter (Mitsubishi IPM) | |

Rated Voltage and Current | 600 V & 50 A |

Rated Power | 3.7 kW/220 VAC |

Load | |

Power (kW) | 3kW |

Resistance (ohm) | 100 |

Methods | Constant Wind | Step Wind | Turbulent Wind |
---|---|---|---|

ENCAAV | √ | × | × |

CVTPR | √ | × | × |

WSBNCT | √ | √ | √ |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Qiu, Y.; Jiang, H.; Feng, Y.; Cao, M.; Zhao, Y.; Li, D.
A New Fault Diagnosis Algorithm for PMSG Wind Turbine Power Converters under Variable Wind Speed Conditions. *Energies* **2016**, *9*, 548.
https://doi.org/10.3390/en9070548

**AMA Style**

Qiu Y, Jiang H, Feng Y, Cao M, Zhao Y, Li D.
A New Fault Diagnosis Algorithm for PMSG Wind Turbine Power Converters under Variable Wind Speed Conditions. *Energies*. 2016; 9(7):548.
https://doi.org/10.3390/en9070548

**Chicago/Turabian Style**

Qiu, Yingning, Hongxin Jiang, Yanhui Feng, Mengnan Cao, Yong Zhao, and Dan Li.
2016. "A New Fault Diagnosis Algorithm for PMSG Wind Turbine Power Converters under Variable Wind Speed Conditions" *Energies* 9, no. 7: 548.
https://doi.org/10.3390/en9070548