# A Robust Fault Diagnosis Scheme for Converter in Wind Turbine Systems

^{*}

## Abstract

**:**

## 1. Introduction

- EEMD realizes the adaptive processing of nonlinear and non-stationary signals, and its application mitigates mode mixing and the effects of noise interference;
- The complexity measure of PE enhances the robustness against variations in the operating conditions and signal noise;
- IMF-PE highlights the signal local characteristics;
- The effects of the embedding dimension on the fault diagnosis results are studied, and the optimal value is selected;
- The scheme has high reliability and robustness and low time consumption. It also has a stable diagnostic performance.

## 2. Fault Analysis and Diagnostic Requirements for Wind Power Converter

#### 2.1. Fault Analysis

_{ab}, U

_{bc}, and U

_{ca}are constant with the load variation, while the current signals i

_{a}, i

_{b}, and i

_{c}are easily affected. Therefore, the three-phase voltage signals are selected as the input to the diagnosis method.

#### 2.2. Diagnostic Requirements

## 3. Fault Diagnosis Method

#### 3.1. The Proposed Fault Diagnosis Method

- Acquiring three-phase line-to-line voltages U
_{abcg}(U_{ab}, U_{bc}, U_{ca}) from simulation under both healthy and faulty operating condition, then using them as fault signals to train and test the proposed fault diagnosis method; - Decomposing each fault signal into a group of IMFs using EEMD;
- Obtain the minimum number of all IMFs of all fault signals and noted as $\ell $;
- Calculating the PE of each IMF as a fault feature to reflect the complexity of the signal. The IMF-PE feature is expressed as:$$\begin{array}{ll}{H}_{PE}=& [{H}_{PE}(\mathrm{IMF}1{/}_{{U}_{\mathrm{ab}}}),{H}_{PE}(\mathrm{IMF}2{/}_{{U}_{\mathrm{ab}}}),\dots ,{H}_{PE}(\mathrm{IMF}\ell {/}_{{U}_{\mathrm{ab}}}),\\ & {H}_{PE}(\mathrm{IMF}1{/}_{{U}_{\mathrm{bc}}}),{H}_{PE}(\mathrm{IMF}2{/}_{{U}_{\mathrm{bc}}}),\dots ,{H}_{PE}(\mathrm{IMF}\ell {/}_{{U}_{\mathrm{bc}}}),\\ & {H}_{PE}(\mathrm{IMF}1{/}_{{U}_{\mathrm{ca}}}),{H}_{PE}(\mathrm{IMF}2{/}_{{U}_{\mathrm{ca}}}),\dots ,{H}_{PE}(\mathrm{IMF}\ell {/}_{{U}_{\mathrm{ca}}})]\end{array}$$
- Diagnosing the faults using SVM. The fault features are marked as fault labels and further randomly divided into training samples and testing samples, and the ratio of training samples to testing samples is set as 3:2.

#### 3.2. Signal Decomposition Using EEMD

#### 3.3. Feature Extraction Using PE

- Step 1.
- Reconstruct the phase space of the signal, and each subsequence is represented as $X(i)\hspace{0.17em}$, then the results can be obtained:$$\begin{array}{l}X(i)\hspace{0.17em}=\{u(i),u(i+\tau ),\dots ,u(i+(m-1)\tau )\}\\ i=1,\hspace{0.17em}2\hspace{0.17em},\hspace{0.17em}\dots ,\hspace{0.17em}N-(m-1)\tau \end{array}$$
- Step 2.
- Rearrange each $X(i)\hspace{0.17em}$ in ascending order:$$u(i+({j}_{1}-1)\tau )\le u(i+({j}_{2}-1)\tau )\le \dots \le u(i+({j}_{m}-1)\tau )$$$$\lambda (s)=({j}_{1},\hspace{0.17em}{j}_{2}\hspace{0.17em},\dots ,\hspace{0.17em}{j}_{m})$$
- Step 3.
- The probability distribution of all the symbol sequences is expressed as ${P}_{1},\hspace{0.17em}{P}_{2}\hspace{0.17em},\hspace{0.17em}\dots ,\hspace{0.17em}{P}_{k}$, and ${P}_{k}$ is defined as:$${P}_{k}=\frac{f(k)}{N-(m-1)\tau}$$
- Step 4.
- PE is defined as:$$H(m,\tau )=-{\displaystyle \sum _{j=1}^{k}{P}_{j}\mathrm{ln}{P}_{j}}$$

## 4. Simulation Results and Discussion

#### 4.1. Simulation Platform

_{1}to 0. Measure the three-phase line-to-line voltage U

_{abcg}(U

_{ab}, U

_{bc}, U

_{ca}) of the converter under different fault states; the results are shown in Figure 5, and it can be seen that the OC fault in the switch can cause the distortion of the U

_{ab}, U

_{bc}, and U

_{ca}signals, so the converter fault modes can be identified by analyzing the U

_{ab}, U

_{bc}, and U

_{ca}signals.

_{ab}, U

_{bc}, and U

_{ca}of the converter are measured when the wind speed changes from 10 m/s to 15 m/s with the interval of 0.0625 m/s. Thus, there are 81∗3∗22 = 5346 samples in 22 fault modes.

#### 4.2. Results of EEMD-IMF-PE Feature

#### 4.3. Results of Classification

_{ab}of a normal state, so the time consumption for all samples 22∗3∗81 = 5346 is extremely heavy in m = 9; thus, m = 9 is uneconomical. Similarly, the diagnostic accuracy under m = 7 is only 0.13% higher than that under m = 6, while the calculation time is increased by about 5 times.

#### 4.4. Analysis of Robustness

#### 4.5. Comparison of Different Methods

_{ab}of a normal state, so CEEMDAN and ICEEMDAN are time-consumption heavy for all 5346 samples. The results show that the EEMD-PE method not only has the highest diagnostic accuracy, but also consumes less time. Thus, the EEMD-PE method is optimal.

_{ab}of a normal state, so the calculation speed of the IMFs-PE feature and IMFs-NE feature is perfect for all 5346 samples. Therefore, the performance of the EEMD-PE method and EEMD-NE method is better than that of the EEMD-AE method, EEMD-SE method and EEMD-FE method. In addition, the diagnostic accuracy of the EEMD-PE method (75%) is higher than that of the EEMD-NE method (70%) for the signal-to-noise ratio of 5 dB. Therefore, the EEMD-PE method is more suitable for the high-noisy environment than the EEMD-NE method.

#### 4.6. Comparison with Previous Schemes

#### 4.7. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Worldwide wind power share of global electricity production in 2021 [4].

**Figure 5.**Simulated line-to-line voltage U

_{abcg}(U

_{ab}, U

_{bc}, U

_{ca}). (

**a**) Normal state; (

**b**) OC fault in T1.

**Figure 8.**Comparation of different methods to highlight EEMD. (

**a**) Comparation of average diagnostic accuracy; (

**b**) Comparation of calculation time.

**Figure 9.**Comparation of different methods to highlight PE. (

**a**) Comparation of average diagnostic accuracy; (

**b**) Comparation of calculation time.

Steps | EMD Decomposition |
---|---|

Step 1 | Initialization: ${r}^{0}=x(t)$, $i=1$ |

Step 2 | Calculate the $i$th oscillation mode $IM{F}_{i}$ |

Step 2 (a) | Set ${c}^{i(q-1)}(t)={r}^{i-1}(t)$, $q=1$ |

Step 2 (b) | Calculate the local extremum of ${c}^{i(q-1)}(t)$ |

Step 2 (c) | Use cubic spline to interpolate the local extremum to obtain the lower envelope ${e}_{\mathrm{min}}(t)$ and upper envelope ${e}_{\mathrm{max}}(t)$ |

Step 2 (d) | Average the lower and upper envelopes: ${\psi}^{i(q-1)}(t)=({e}_{\mathrm{max}}(t)+{e}_{\mathrm{min}}(t))/2$ |

Step 2 (e) | Calculate the detailed component: ${c}^{iq}(t)={c}^{i(q-1)}(t)-{\psi}^{i(q-1)}(t)$. If ${c}^{iq}(t)$ satisfies IMF conditions, then set ${d}^{i}(t)={c}^{iq}(t)$, that is $IM{F}_{i}$; else go to step 2 (b) and $q=q+1$ |

Step 3 | Obtain residue: ${r}^{i+1}(t)={r}^{i}(t)-{d}^{i}(t)$. If ${r}^{i+1}(t)$ has more than one extreme, then go to Step 2 and $i=i+1$; else the procedure is ended and ${r}^{i+1}(t)$ is residue |

Steps | EEMD Decomposition |
---|---|

Step 1 | Add white noise to the original signal to obtain a new signal: ${x}^{\delta}(t)=x(t)+{w}^{\delta}(t)$$,\delta =1,2,\dots ,\rho $, where $\rho $ is the number of ensemble realizations, ${w}^{\delta}(t)$ is the $\delta $th independent white noise |

Step 2 | $\mathrm{Decompose}{x}^{\delta}(t)$ by EMD and obtain a group of IMFs: ${d}^{i,\delta}$$,i=1,2,\dots ,I$, where $I$ is the number of IMFs, ${d}^{i,\delta}$ is the $i$th IMF of the $\delta $th realization |

Step 3 | Average all realizations to obtain final $\overline{IMF}$$:\overline{{d}^{i}}=\frac{1}{\rho}{\displaystyle {\sum}_{\delta =1}^{\rho}{d}^{i,\delta}}$, where $i=1,2,\dots ,I$ and $\delta =1,2,\dots ,\rho $ |

Quantity | Value | Quantity | Value |
---|---|---|---|

Rated voltage | 575 V | Stator leak inductance | 0.18 pu |

Rated power | 1.5 MW | Rotor leak inductance | 0.16 pu |

Pole pairs number | 3 | Stator resistance | 0.023 pu |

Magnetizing inductance | 2.9 pu | Rotor resistance | 0.016 pu |

Fault Mode | Accuracy (%) | ||||||
---|---|---|---|---|---|---|---|

m = 3 | m = 4 | m = 5 | m = 6 | m = 7 | m = 8 | m = 9 | |

Normal | 96.8750 | 100 | 100 | 100 | 100 | 100 | 100 |

T1 | 90.6250 | 90.6250 | 93.7500 | 100 | 93.7500 | 96.8750 | 96.8750 |

T2 | 100 | 100 | 100 | 96.8750 | 100 | 100 | 100 |

T3 | 90.6250 | 90.6250 | 100 | 93.7500 | 96.8750 | 96.8750 | 100 |

T4 | 81.2500 | 84.3750 | 90.6250 | 93.7500 | 93.7500 | 96.8750 | 96.8750 |

T5 | 93.7500 | 93.7500 | 100 | 100 | 100 | 100 | 100 |

T6 | 100 | 90.6250 | 100 | 100 | 96.8750 | 100 | 100 |

T1T2 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |

T3T4 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |

T5T6 | 96.8750 | 96.8750 | 100 | 100 | 100 | 100 | 100 |

T1T3 | 87.5000 | 90.6250 | 87.5000 | 96.8750 | 100 | 100 | 93.7500 |

T1T5 | 96.8750 | 84.3750 | 96.8750 | 100 | 100 | 96.8750 | 100 |

T3T5 | 93.7500 | 100 | 90.6250 | 100 | 96.8750 | 96.8750 | 96.8750 |

T2T4 | 93.7500 | 96.8750 | 100 | 96.8750 | 100 | 96.8750 | 100 |

T2T6 | 96.8750 | 96.8750 | 100 | 96.8750 | 96.8750 | 96.8750 | 96.8750 |

T4T6 | 96.8750 | 100 | 100 | 100 | 100 | 100 | 100 |

T1T4 | 100 | 100 | 100 | 96.8750 | 100 | 96.8750 | 100 |

T1T6 | 93.7500 | 100 | 100 | 96.8750 | 96.8750 | 100 | 100 |

T3T2 | 71.8750 | 90.6250 | 93.7500 | 100 | 96.8750 | 93.7500 | 96.8750 |

T3T6 | 100 | 100 | 100 | 96.8750 | 100 | 100 | 100 |

T5T2 | 93.7500 | 100 | 100 | 96.8750 | 96.8750 | 100 | 96.8750 |

T5T4 | 93.7500 | 96.8750 | 100 | 100 | 100 | 100 | 100 |

Average | 94.0341 | 95.5966 | 97.8693 | 98.2955 | 98.4375 | 98.5795 | 98.8636 |

Standard deviation | 6.8131 | 5.2521 | 3.9039 | 2.0968 | 2.1019 | 1.8619 | 1.8159 |

Noise Conditions | Stability | Evaluation Indicators (%) | ||||||
---|---|---|---|---|---|---|---|---|

Accuracy | Precision | Recall | F1-Score | Specificity | FAR | MAR | ||

20 dB | Minimum | 96.8750 | 96.9758 | 96.8750 | 96.8654 | 99.8512 | 0.0541 | 1.1364 |

Maximum | 98.8636 | 98.8965 | 98.8636 | 98.8629 | 99.9459 | 0.1488 | 3.1250 | |

Average | 97.8220 | 97.9108 | 97.8220 | 97.8186 | 99.8963 | 0.1037 | 2.1780 | |

Standard deviation | 0.5735 | 0.5387 | 0.5735 | 0.5756 | 0.0273 | 0.0273 | 0.5735 | |

15 dB | Minimum | 94.3182 | 94.5155 | 94.3182 | 94.3085 | 99.7294 | 0.0947 | 1.9886 |

Maximum | 98.0114 | 98.0806 | 98.0114 | 98.0086 | 99.9053 | 0.2706 | 5.6818 | |

Average | 96.3021 | 96.4387 | 96.3021 | 96.2939 | 99.8239 | 0.1761 | 3.6979 | |

Standard deviation | 0.8616 | 0.8381 | 0.8616 | 0.8660 | 0.0410 | 0.0410 | 0.8616 | |

10 dB | Minimum | 85.7955 | 86.2573 | 85.7955 | 85.8105 | 99.3236 | 0.4532 | 9.5170 |

Maximum | 90.4830 | 90.7074 | 90.4830 | 90.4658 | 99.5468 | 0.6764 | 14.2045 | |

Average | 88.1203 | 88.5073 | 88.1203 | 88.0924 | 99.4343 | 0.5657 | 11.8797 | |

Standard deviation | 1.0354 | 1.0319 | 1.0354 | 1.0320 | 0.0493 | 0.0493 | 1.0354 | |

5 dB | Minimum | 72.3011 | 72.6030 | 72.3011 | 72.2741 | 98.6810 | 1.0011 | 21.0227 |

Maximum | 78.9773 | 79.5929 | 78.9773 | 78.9605 | 98.9989 | 1.3190 | 27.6989 | |

Average | 75.9375 | 76.4467 | 75.9375 | 75.8553 | 98.8542 | 1.1458 | 24.0625 | |

Standard deviation | 1.6764 | 1.7411 | 1.6764 | 1.6651 | 0.0798 | 0.0798 | 1.6764 |

Scheme | Fault Types | Training to Testing Ratio | Number of Runs | Noise Conditions | Average Accuracy (%) | Standard Deviation of Accuracy (%) |
---|---|---|---|---|---|---|

EEMD-PE | 22 OC faults | 3:2 | 30 | 20 dB | 97.8220 | 0.5735 |

15 dB | 96.3021 | 0.8616 | ||||

10 dB | 88.1203 | 1.0354 | ||||

5 dB | 75.9375 | 1.6764 | ||||

MEMD-FE [12] | 22 OC faults | 3:2 | 30 | 30 dB | 95.5758 | 1.9344 |

20 dB | 92.1477 | 1.3312 | ||||

10 dB | 84.2338 | 1.7167 | ||||

EEMD-NE [11] | 22 OC faults | 3:2 | 30 | 20 dB | 99.2756 | - |

15 dB | 97.8598 | - | ||||

10 dB | 90.0758 | - | ||||

5 dB | 71.8040 | - |

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**MDPI and ACS Style**

Liang, J.; Zhang, K. A Robust Fault Diagnosis Scheme for Converter in Wind Turbine Systems. *Electronics* **2023**, *12*, 1597.
https://doi.org/10.3390/electronics12071597

**AMA Style**

Liang J, Zhang K. A Robust Fault Diagnosis Scheme for Converter in Wind Turbine Systems. *Electronics*. 2023; 12(7):1597.
https://doi.org/10.3390/electronics12071597

**Chicago/Turabian Style**

Liang, Jinping, and Ke Zhang. 2023. "A Robust Fault Diagnosis Scheme for Converter in Wind Turbine Systems" *Electronics* 12, no. 7: 1597.
https://doi.org/10.3390/electronics12071597