# Intelligent Fault Diagnosis Framework for Modular Multilevel Converters in HVDC Transmission

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## Abstract

**:**

## 1. Introduction

- The proposed intelligent fault diagnosis framework utilises only current sensor data for fault diagnosis. This study achieves high accuracy of fault diagnosis using only current sensors and AI-based techniques.
- We combine the measured current data of the AC-side three-phase current and of the upper bridge and lower bridge of each three phases to form a vector of features that represent the current health condition of MMCs.
- Our proposed framework reduces measured current data using PCA that linearly maps the current data into a lower-dimensional space of principal components.
- For fault classification, multiclass SVM based on error-correcting output codes (ECOC) and multinomial logistic regression (MLR) algorithms are used with the learned feature vector to achieve improved classification accuracy and reduced computation time.
- Compared to recently published results that are based on machine learning techniques, our proposed method is faster and yet achieves competitive, if not better, classification accuracies of open-circuit failures of IGBT fault diagnosis in MMC-HVDC transmission.
- The high reduction in the computational time comes from two elements of our proposed method: (i) using a minimum number of only current sensors; (ii) using the PCA method to select fewer features that can be used for training the classification algorithm—i.e., SVM and MLRC algorithms—and for classifying MMC-HVDC health conditions using the trained classification models.
- Being able to obtain high classification accuracy while highly reducing the computational time, our proposed method can be used in real implementations of MMC-HVDC fault diagnosis systems.

## 2. Proposed Framework

#### 2.1. Data Modeling

_{1}is an equivalent voltage source for an AC network. E

_{2}is a wind farm.

_{a}, I

_{b}, I

_{c}) and three-phase circulation current (I

_{diffa}, I

_{diffb}, I

_{diffc}). The circulation current and bridge current can be represented mathematically using the following equations, where k stands for the a, b, and c phase, while p and n separately stand for the upper and lower arms of the MMC. The symbols i

_{kp}and i

_{kn}are respectively the currents of the upper bridge and lower bridge of each three phases.

_{ap}, i

_{bp}, i

_{cp}, i

_{an}, i

_{bn}, and i

_{cn}can be directly measured, we recorded them, instead of I

_{diffa}, I

_{diffb}, and I

_{diffc}. Consequently, we recorded nine parameters, i.e., I

_{a}, I

_{b}, I

_{c}, i

_{ap}, i

_{bp}, i

_{cp}, i

_{an}, i

_{bn}, and i

_{cn}, (see Figure 1). Figure 3 depicts some typical time series plots for seven different health conditions of the MMC as shown in Table 3, based on the values of the nine parameters described above during the seven states of the wind farm side MMC. Depending on the fault conditions, the defects modulate the recorded signals with their own patterns. The plots give an example of every kind of state, in which six types of faults happened at different IGBTs at different times.

#### 2.2. Description of the Proposed Framework

_{a}, I

_{b}, I

_{c}, i

_{ap}, i

_{bp}, i

_{cp}, i

_{an}, i

_{bn}, and i

_{cn}—are recorded. Then, we combine the measured current data of the AC-side three-phase current and three-phase circulation currents to form a vector of features. However, they may not be the best features from a classification point of view. Moreover, in real operating conditions, the size of the acquired and combined data represents a large amount of data to be processed for monitoring of SM health conditions. Therefore, a technique to extract a set of features that achieves superior fault detection and diagnosis, and consequently reduces the computational cost, is needed. Our framework employed PCA [48], often used for feature extraction and dimensionality reduction, to extract principal components from the measured current data.

#### 2.2.1. SVM-Based ECOC

#### 2.2.2. MLR

^{(i)}∈ {0,1} to multi-classification problems that have labels {1, …, c} where c is the number of classes. The LR and MLR have been used in machine fault diagnosis [52,53,54,55]. We briefly describe the simplified multinomial logistic regression model as follows: in multinomial logistic regression with multi-labels c

^{(i)}∈ {1, …, c} the aim is to estimate the probability P(c = c

^{(i)}|x) for each value of c

^{(i)}= 1 to c, such that

## 3. Experimental Study

_{a}, I

_{b}, I

_{c}, i

_{ap}, i

_{bp}, i

_{cp}, i

_{an}, i

_{bn}, and i

_{cn}—were recorded to obtain 5001 time samples. The measurements of these nine parameters were concatenated to form a vector of samples that represent the current health condition of the MMCs. This gave a total of 45,009 (5001 × 9) samples dimension for each vector of health condition. First, experiments were conducted for testing data of sizes 15% to 50% and 20 trials for each experiment with 10-fold cross-validation.

^{−10}of the largest eigenvalue, we obtain 604 principal components, retaining well over 99% of the total variance of the data. With these learned features, SVM-based on the ECOC algorithm and MLR algorithm are used for classification. Classification accuracies are obtained by averaging the results of twenty trials for each classifier and each experiment. Additionally, in each experiment, we have examined the effects of using a normalisation technique in our classification results for both SVM and MLR.

#### 3.1. Results of SVM-Based ECOC without Data Normalisation

#### 3.2. Results of SVM-Based ECOC with Data Normalisation

#### 3.3. Results of MLR without Data Normalisation

#### 3.4. Results of MLR with Data Normalisation

## 4. Comparisons of Results

#### 4.1. Comparisons of Testing Classifications

#### 4.2. Comparisons with Recently Published Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Structure of a three-phase MMC with half-bridge submodules [6].

**Figure 3.**Typical time series plots for seven different conditions as shown in Table 3.

**Figure 6.**Classification results of training and testing data using SVM-based ECOC without data normalisation.

**Figure 7.**Classification results of training and testing data using SVM-based ECOC with data normalisation.

**Figure 10.**Comparisons of testing classification accuracies using our framework with SVM and MLR on normalised and unnormalised data.

**Table 1.**Summary of different techniques that have been used in different studies of IGBT open-circuit fault diagnosis.

Ref. | Approach Used | Detection Threshold Parameters | Localisation Threshold Parameters |
---|---|---|---|

[24] | Fault detection: The comparison between the observed ${\widehat{i}}_{p}$ using Sliding Mode Observer (SMO) and measured the current of the upper arm i _{p}.Fault localisation The comparison between the observed and measured lower arm current, ${\widehat{i}}_{p}$ and i _{p}, and the capacitor voltages, ${\widehat{V}}_{ci}$ and V_{ci} of the assumed faulty SM. | Threshold parameters: I_{th}, and 700 time-steps (2 µs per step) Usage:If $\left|\text{}{\widehat{i}}_{p}-{i}_{p}\right|\ge {I}_{th}$ and it lasts for 700 time-steps (2 µs per step) then an open-circuit fault has occurred. | Threshold parameters: I_{th}, V_{thi}, and 100 ms. Usage:If $\left|\text{}{\widehat{i}}_{p}-{i}_{p}\right|{I}_{th}$ and $\left|\text{}{\widehat{V}}_{ci}-{V}_{ci}\right|{V}_{thi}$ and it lasts for 100 ms, then the SM is faulty. |

[42] | Fault detection: The detection is achieved using a state observer to estimate the ideal circulating current ${\widehat{i}}_{c}$ and the output current ${\widehat{i}}_{o}$ using the state models of the MMC and the variables already available from the main control system. Fault localisation The comparison between the SM capacitor voltage V _{ci} and a threshold value U_{th}. | Threshold parameters: I^{th}, and ΔT_{1}. Usage:If $\left|\text{}{\widehat{i}}_{c}-{i}_{c}\right|{I}_{th}$ and it lasts for ΔT _{1}, then an open-circuit fault has occurred. | Threshold parameters: U^{th}, and ΔT_{2}. Usage:If ${V}_{ci}\ge {U}_{th}$ and it lasts for ΔT _{2}, then this SM is located to be faulty. |

[44] | Fault detection: The comparison between measured inner difference current i _{diff} and the estimated inner difference current ${\widehat{i}}_{diff}$ through Kalman Filter (KF).Fault localisation Each capacitor voltage (V _{c,p,N}) of the upper and lower arms of the targeted phase, i.e., the phase with a detected fault, is compared with the minimum capacitor voltage value (V_{c(t),min}) for a given time instant. | Threshold parameters: Δi_{diff} and Δt_{i}. Usage:If $\left|{\widehat{i}}_{diff}-{i}_{diff}\right|>\Delta {i}_{diff}$ and it lasts for a period of Δt _{i}, then a fault is assumed in this phase of the MMC. | Threshold parameters: ΔV_{c} and Δt_{v}. Usage:If ${V}_{c,p,N}-{V}_{c\left(t\right),min}\Delta {V}_{c}\text{}\Delta {V}_{c}$ and it lasts for a period of Δt _{v}, then it indicates this SM is faulty. |

[45] | Fault detection: The comparison between the measured current of the lower arm current i _{N} and observed arm current ${\widehat{i}}_{N}$, which is based on Sliding Mode Observer (SMO), and one of the capacitor voltages, ${\widehat{V}}_{c}$ and V_{c}.Fault localisation The comparison between the observed and measured lower arm current, ${\widehat{i}}_{N}$ and i _{N}, and the capacitor voltages, ${\widehat{V}}_{ci}$ and V_{ci} of the assumed faulty SM. | Threshold parameters: I_{th} and V_{th}. Usage:If $\left|\text{}{\widehat{i}}_{N}-{i}_{N}\right|\ge {I}_{th}$ and $\left|\text{}{\widehat{V}}_{c}-{V}_{c}\right|\ge ,{V}_{th}$ and it lasts for 500 μs (50 time-steps, 10 μs per step), then an open-circuit fault has occurred. | Threshold parameters: I_{th} and V_{thi}. Usage:If $\left|\text{}{\widehat{i}}_{N}-{i}_{N}\right|{I}_{th}$, and $\left|\text{}{\widehat{V}}_{ci}-{V}_{ci}\right|{V}_{thi}$ and it lasts for 80 ms, then the SM is faulty. |

**Table 2.**Parameters of MMC [6].

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

Number of SMs per arm | 9 |

SM capacitor | 3000 μF |

Arm inductance | 0.05 ohm |

AC frequency | 50 Hz |

**Table 3.**MMC health conditions [6].

Faulty Bridge | Label Value |
---|---|

Normal | 1 |

A-phase lower SMs | 2 |

A-phase upper SMs | 3 |

B-phase lower SMs | 4 |

B-phase upper SMs | 5 |

C-phase lower SMs | 6 |

C-phase upper SMs | 7 |

**Table 4.**Sample confusion matrix of the classification results of SVM-based ECOC without data normalization.

Testing Data = 15%
| |||||||

Normal | A-Phase Lower SMs | A-Phase Upper SMs | B-Phase Lower SMs | B-Phase Upper SMs | C-Phase Lower SMs | C-Phase Upper SMs | |

Normal | 100 | 0 | 0 | 0 | 0 | 0 | 0 |

A-Phase Lower SMs | 0 | 99.7 | 0 | 0 | 0 | 1 | 0 |

A-Phase Upper SMs | 0 | 0 | 100 | 0 | 0 | 0 | 0 |

B-Phase Lower SMs | 0 | 0 | 0 | 100 | 0 | 0 | 0 |

B-Phase Upper SMs | 0 | 0 | 0 | 0 | 100 | 0 | 0 |

C-Phase Lower SMs | 0 | 0.3 | 0 | 0 | 0 | 99.0 | 0 |

C-Phase Upper SMs | 0 | 0 | 0 | 0 | 0 | 0 | 100 |

Testing Data = 40%
| |||||||

Normal | A-Phase Lower SMs | A-Phase Upper SMs | B-Phase Lower SMs | B-Phase Upper SMs | C-Phase Lower SMs | C-Phase Upper SMs | |

Normal | 100 | 0 | 0 | 0 | 0 | 0 | 0 |

A-Phase Lower SMs | 0 | 98.8 | 0 | 0.4 | 1.5 | 1.8 | 0.5 |

A-Phase Upper SMs | 0 | 0 | 98.8 | 0 | 0.8 | 0 | 0 |

B-Phase Lower SMs | 0 | 0.6 | 0 | 99.1 | 0 | 0.4 | 0 |

B-Phase Upper SMs | 0 | 0 | 0.5 | 0 | 96.6 | 0 | 1.9 |

C-Phase Lower SMs | 0 | 0.4 | 0.7 | 0.5 | 0 | 97.4 | 0 |

C-Phase Upper SMs | 0 | 0.2 | 0 | 0 | 1.1 | 0.5 | 97.6 |

**Table 5.**Sample confusion matrix of the classification results of SVM-based ECOC with data normalisation.

Testing Data = 15%
| |||||||

Normal | A-Phase Lower SMs | A-Phase Upper SMs | B-Phase Lower SMs | B-Phase Upper SMs | C-Phase Lower SMs | C-Phase Upper SMs | |

Normal | 100 | 0 | 0 | 0 | 0 | 0 | 0 |

A-Phase Lower SMs | 0 | 99.7 | 0 | 0 | 0 | 0.7 | 0 |

A-Phase Upper SMs | 0 | 0 | 100 | 0 | 0 | 0 | 0 |

B-Phase Lower SMs | 0 | 0 | 0 | 100 | 0 | 0 | 0 |

B-Phase Upper SMs | 0 | 0 | 0 | 0 | 100 | 0 | 0 |

C-Phase Lower SMs | 0 | 0.3 | 0 | 0 | 0 | 99.3 | 0 |

C-Phase Upper SMs | 0 | 0 | 0 | 0 | 0 | 0 | 100 |

Testing Data = 40%
| |||||||

Normal | A-Phase Lower SMs | A-Phase Upper SMs | B-Phase Lower SMs | B-Phase Upper SMs | C-Phase Lower SMs | C-Phase Upper SMs | |

Normal | 100 | 0 | 0 | 0 | 0 | 0 | 0 |

A-Phase Lower SMs | 0 | 98.5 | 0 | 0.8 | 1.5 | 1.5 | 0.6 |

A-Phase Upper SMs | 0 | 0 | 98.9 | 0 | 0.8 | 0 | 0 |

B-Phase Lower SMs | 0 | 0.9 | 0 | 99.1 | 0 | 0.4 | 0 |

B-Phase Upper SMs | 0 | 0 | 0.5 | 0 | 97.0 | 0 | 0.5 |

C-Phase Lower SMs | 0 | 0.4 | 0.6 | 0.1 | 0 | 97.5 | 0 |

C-Phase Upper SMs | 0 | 0.3 | 0 | 0 | 0.8 | 0.6 | 98.9 |

**Table 6.**Sample confusion matrix of the classification results of MLR-based without data normalisation.

Testing Data = 15%
| |||||||

Normal | A-Phase Lower SMs | A-Phase Upper SMs | B-Phase Lower SMs | B-Phase Upper SMs | C-Phase Lower SMs | C-Phase Upper SMs | |

Normal | 100 | 0 | 0 | 0 | 0 | 0 | 0 |

A-Phase Lower SMs | 0 | 99.7 | 0 | 0 | 0 | 1 | 0 |

A-Phase Upper SMs | 0 | 0 | 100 | 0 | 0 | 0 | 0 |

B-Phase Lower SMs | 0 | 0 | 0 | 100 | 0 | 0 | 0 |

B-Phase Upper SMs | 0 | 0 | 0 | 0 | 100 | 0 | 0.3 |

C-Phase Lower SMs | 0 | 0.3 | 0 | 0 | 0 | 99.0 | 0 |

C-Phase Upper SMs | 0 | 0 | 0 | 0 | 0 | 0 | 99.7 |

Testing Data = 40%
| |||||||

Normal | A-Phase Lower SMs | A-Phase Upper SMs | B-Phase Lower SMs | B-Phase Upper SMs | C-Phase Lower SMs | C-Phase Upper SMs | |

Normal | 100 | 0 | 0 | 0 | 0 | 0 | 0 |

A-Phase Lower SMs | 0 | 99.4 | 0 | 0.4 | 0 | 2 | 0.5 |

A-Phase Upper SMs | 0 | 0 | 99.5 | 0 | 0 | 0 | 0 |

B-Phase Lower SMs | 0 | 0 | 0 | 99.1 | 0 | 0.4 | 0 |

B-Phase Upper SMs | 0 | 0 | 0.5 | 0 | 100 | 0 | 0.9 |

C-Phase Lower SMs | 0 | 0.4 | 0 | 0.5 | 0 | 97.1 | 0 |

C-Phase Upper SMs | 0 | 0.2 | 0 | 0 | 0 | 0.5 | 98.6 |

**Table 7.**Sample confusion matrix of the classification results of MLR-based with data normalisation.

Testing Data = 15% | |||||||

Normal | A-Phase Lower SMs | A-Phase Upper SMs | B-Phase Lower SMs | B-Phase Upper SMs | C-Phase Lower SMs | C-Phase Upper SMs | |

Normal | 100 | 0 | 0 | 0 | 0 | 0 | 0 |

A-Phase Lower SMs | 0 | 99.7 | 0 | 0 | 0 | 1 | 0 |

A-Phase Upper SMs | 0 | 0 | 100 | 0 | 0 | 0 | 0 |

B-Phase Lower SMs | 0 | 0 | 0 | 100 | 0 | 0 | 0 |

B-Phase Upper SMs | 0 | 0 | 0 | 0 | 100 | 0 | 0 |

C-Phase Lower SMs | 0 | 0.3 | 0 | 0 | 0 | 99.0 | 0 |

C-Phase Upper SMs | 0 | 0 | 0 | 0 | 0 | 0 | 100 |

Testing Data = 40% | |||||||

Normal | A-Phase Lower SMs | A-Phase Upper SMs | B-Phase Lower SMs | B-Phase Upper SMs | C-Phase Lower SMs | C-Phase Upper SMs | |

Normal | 100 | 0 | 0 | 0 | 0 | 0 | 0 |

A-Phase Lower SMs | 0 | 99.4 | 0 | 0.4 | 0 | 2 | 0.5 |

A-Phase Upper SMs | 0 | 0 | 99.5 | 0 | 0.2 | 0 | 0 |

B-Phase Lower SMs | 0 | 0 | 0 | 99.1 | 0 | 0.4 | 0 |

B-Phase Upper SMs | 0 | 0 | 0.5 | 0 | 99.8 | 0 | 0.4 |

C-Phase Lower SMs | 0 | 0.4 | 0 | 0.5 | 0 | 97.1 | 0 |

C-Phase Upper SMs | 0 | 0.2 | 0 | 0 | 0 | 0.5 | 99.1 |

Ref. | Type of Measurement | No. of Measured Parameters | Classification Accuracy | Testing Time |
---|---|---|---|---|

[27] | Capacitor voltage Circulating current | 5000 × 7 5 × 9 | 98.9% | 80 ms |

[56] | DC current | -- | 92.8% | - |

[57] | Capacitor’s voltages in all SMs | 800 × 72 | 98.2% | -- |

[6] | Current signals CNN AE-DNN | 5001 × 9 40% testing rate | 97.0% 97.5% | 400 ms 1500 ms |

[46] | Current signals LSTM BiLSTM | 5001 × 9 40% testing rate | 97.4% 97.0% | 1290 ms 2630 ms |

Proposed framework at 15% testing rate using PCA in all cases | Current signals and their phases | 5001 × 9 100 × 7 | ||

SVM, no norm | 99.8% | 62 ms | ||

SVM, with norm | 99.9% | 59 ms | ||

MLR, no norm | 99.8% | 4 ms | ||

MLR, with norm | 99.8% | 4 ms | ||

at 40% testing rate using PCA in all cases | SVM, no norm | 98.3% | 106 ms | |

SVM, with norm | 98.6% | 96 ms | ||

MLR, no norm | 99.1% | 8 ms | ||

MLR, with norm | 99.2% | 7 ms |

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**MDPI and ACS Style**

Ahmed, H.O.A.; Yu, Y.; Wang, Q.; Darwish, M.; Nandi, A.K.
Intelligent Fault Diagnosis Framework for Modular Multilevel Converters in HVDC Transmission. *Sensors* **2022**, *22*, 362.
https://doi.org/10.3390/s22010362

**AMA Style**

Ahmed HOA, Yu Y, Wang Q, Darwish M, Nandi AK.
Intelligent Fault Diagnosis Framework for Modular Multilevel Converters in HVDC Transmission. *Sensors*. 2022; 22(1):362.
https://doi.org/10.3390/s22010362

**Chicago/Turabian Style**

Ahmed, Hosameldin O. A., Yuexiao Yu, Qinghua Wang, Mohamed Darwish, and Asoke K. Nandi.
2022. "Intelligent Fault Diagnosis Framework for Modular Multilevel Converters in HVDC Transmission" *Sensors* 22, no. 1: 362.
https://doi.org/10.3390/s22010362