# Ensemble Learning Techniques-Based Monitoring Charts for Fault Detection in Photovoltaic Systems

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## Abstract

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## 1. Introduction

- This paper aims to develop flexible and efficient semi-supervised machine learning-driven methodologies to improve the operation and performance of PV plants. These semi-supervised approaches only employ normal events data without labeling to train the detection models, making them more attractive for detecting faults in practice. This study presents a semi-supervised monitoring approach for anomaly detection in PV plants by combining the advantages of the ensemble learning models and the Double Exponentially Weighted Moving Average (DEWMA) chart. In the last decade, ensemble learning-driven methods (e.g., boosting and bagging models), which combine several single models, have demonstrated a promising solution compared to traditional machine learning methods. Notably, ensemble models are characterized by their ability to reduce the model’s variance while achieving a low bias, making them appealing to improve prediction quality [25]. Overall, an efficient monitoring strategy relies principally on the accuracy of the adopted modeling method and the sensitivity of the anomaly detection technique. Here, we employed ensemble learning methods to exploit their capability to enhance the modeling precision of the PV monitored system. On the other hand, the key characteristic of the DEWMA scheme resides in its capacity to enclose all of the information from past and actual samples in the detection statistic, which makes it sensitive for uncovering anomalies with small magnitudes. In the proposed approach, ensemble learning models are used for residual generation. Essentially, residuals are close to zero in the absence of anomalies, while residuals diverge from zero in the presence of anomalies. The DEWMA detector is employed to check the generated residuals to uncover possible anomalies in the inspected PV array.
- Additionally, in this work, Bayesian optimization (BO) has been adopted to optimally tune hyperparameters of the boosted trees (BS) and bagged trees (BG) models. Specifically, the BO is used to find the optimal parameters of the ensemble models based on training data (anomaly-free data). This enables obtaining more accurate prediction models and improves the detection performance.
- Note that the detection threshold in the DEWMA chart is computed based on the Gaussian assumption of data. Here, to extend further the flexibility of the proposed fault detection method, we employed kernel density estimation (KDE) to compute the detection threshold in a non-parametric way. We assessed the effectiveness of the considered fault detection approaches on real data from a 9.54 kWp photovoltaic system. The detection capacity of the proposed approaches is investigated in the presence of different types of faults. Six statistical scores are computed to judge the fault detection quality. Results revealed the promising performance of the proposed approaches in detecting various types of anomalies in a PV system.

## 2. PV System Description

## 3. Ensemble Learning Methods

#### 3.1. Boosted Trees

#### 3.2. Bagged Regression Trees

Algorithm 1: Bagging trees approach |

## 4. PV System Modeling and Validation

#### 4.1. Data Analysis

#### 4.2. PV Array Modeling Using Ensemble Learning Models

## 5. EWMA and DEWMA Monitoring Schemes

#### 5.1. EWMA Monitoring Scheme

#### DEWMA Monitoring Approach

#### 5.2. Monitoring PV Systems Using Ensemble Learning Techniques Based DEWMA Chart

- Step 1: Computing the DEWMA charting statistic (Equation (18)) for each observation.
- Step 2: Estimating the probability density function for given DEWMA measurements via KDE.
- Step 3: Setting up the detection threshold based on the previously estimated distribution of DEWMA in a non-parametric way as the ($1-\alpha $)-th quantile.
- Step4: Flagging out a fault if the DEWMA statistic is above the detection threshold.

## 6. Results and Discussion

#### 6.1. Scenarios with String Faults

#### 6.2. Scenarios with Inverter Disconnections

#### 6.3. Scenario with Circuit Breaker Faults

#### 6.4. Scenario with Shaded Modules

#### 6.5. Short-Circuit Fault

## 7. Conclusions

- It would be useful to incorporate more data inputs such as open circuit voltage, short circuit current, and fill factor to further enhance the fault detection and diagnosis capabilities of the proposed approach. Moreover, electrical sensors on the AC side of the PV system at the connection point could be added to monitor the energy flow.
- We also plan to develop deep learning-driven monitoring charts by merging the extended capacity of deep learning models (e.g., long short-term memory (LSTM) and gated recurrent unit (GRU) [71,72]) in automatically extracting important features from multivariate data with statistical monitoring charts such as the generalized likelihood ratio test [73,74] to improve fault detection in PV systems.
- We plan also to construct parsimonious ensemble learning models by selecting only the important variables for the prediction by the random forest algorithm. Then, the reduced models can be employed for residuals generation to detect faults.
- Since the DEWMA chart assumes a fixed threshold [75], which may not be suitable to deal with non-stationary (or time-varying) data, adaptive ensemble learning-based DEWMA techniques will be developed in future work by allowing the thresholds of these methods to varying online to account for the changing nature of the data.
- Data from PV systems are usually tainted with noise measurements, which can degrade the performance of the designed fault detection methods by increasing the number of false alarms and masking pertinent features in data. Future works will improve the robustness of the ensemble learning-based-DEWMA model to noisy measurements by developing a wavelet-based DEWMA detector. Noise effects will be reduced using wavelet-based multiscale denoising; hence, the fault detection performance will significantly be improved.
- In addition, it will be interesting to investigate the detection capability of the proposed data-driven anomaly detection methodology in other renewable energy systems, such as wind turbine monitoring.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 8.**Boxplot of residual errors of bagged tree, boosted tree, optimized BG, and optimized BS models.

**Figure 13.**Results of the BG-based schemes in monitoring a string fault: (

**a**) BG-DEWMA scheme, and (

**b**) BG-DEWMA scheme.

**Figure 14.**Results of the BG and BS-based schemes in monitoring inverter disconnections: (

**a**) BG-DEWMA, (

**b**) BG-EWMA, (

**c**) BS-DEWMA, and (

**d**) BS-EWMA schemes.

**Figure 15.**Results of the BG and BS-based schemes in monitoring a circuit breaker fault: (

**a**) BG-DEWMA, (

**b**) BG-EWMA, (

**c**) BS-DEWMA, and (

**d**) BS-EWMA schemes.

**Figure 16.**(

**Top**) PV array with shaded modules due to two communication pylons installed in front of this PV array. (

**Bottom**) Shading of pylon 2 on PV sub-array 2.

**Figure 17.**Results of the BG and BS-based schemes in monitoring partial shading: (

**a**) BG-DEWMA, (

**b**) BG-EWMA, (

**c**) BS-DEWMA, and (

**d**) BS-EWMA schemes.

**Figure 18.**Results of the BG-based schemes in the presence of two short-circuited modules: (

**a**) BG-DEWMA, (

**b**) BG-EWMA, (

**c**) BS-DEWMA, and (

**d**) BS-EWMA schemes.

Parameters | ${\mathit{V}}_{\mathit{OC}}$ (V) | ${\mathit{I}}_{\mathit{SC}}$ (A) | ${\mathit{V}}_{\mathit{MPP}}$ (V) | ${\mathit{I}}_{\mathit{MPP}}$ (A) | ${\mathit{P}}_{\mathit{M}}$ (W) |
---|---|---|---|---|---|

PV Module | 21.6 | 6.54 | 17.4 | 6.1 | 106 |

PV sub-array | 324 | 13.08 | 261 | 12.2 | 3180 |

Parameters | Nominal AC Power (W) | DC Voltage Range (V) | AC Voltage Range (V) | Inverter Efficiency (%) | Frequency Range (Hz) |
---|---|---|---|---|---|

Value | 2500 | 150–400 | 195–253 | 92.7–94.3 | 49.8–50.2 |

Measured Parameters | Sensor N° | Symbol | Sensor Type & Reference | Accuracy |
---|---|---|---|---|

Ambient Temperature (°C) | S1 | T_{amb} | Thermocouple K | 0.5 °C |

Tilted Global Irradiance for 27° (W/m^{2}) | S2 | G_{ic} | Isofoton PV Reference Cell | ±5% |

S3 | G_{ip} | CM 11 Pyranometer | ±2% | |

PV array DC Voltage (V) | S4 | V_{DC} | Voltage Divider | ±0.9% |

Grid AC Voltage (V) | S5 | V_{AC} | Voltage Transformer | 1.5% |

PV array DC Current (A) | S6 | I_{DC} | Hall Effect Sensor | ±0.5% |

Inverter AC Current (A) | S7 | I_{AC} | F.W. BELL CLSM-50S |

Min | Max | STD | Q 0.25 | Q 0.5 | Q 0.75 | Skewness | Kurtosis | |
---|---|---|---|---|---|---|---|---|

Ambient Temp | 14.51 | 37.22 | 4.61 | 22.26 | 26.04 | 29.14 | −0.22 | 2.36 |

Cell Temp | 16.12 | 64.47 | 11.21 | 33.43 | 44.07 | 52.49 | −0.25 | 1.98 |

Irradiance | 42.67 | 1085.10 | 312.30 | 277.07 | 614.26 | 862.42 | −0.21 | 1.65 |

DC voltage | 205.56 | 263.19 | 9.24 | 227.58 | 233.76 | 240.11 | 0.01 | 2.78 |

DC current | 0.50 | 11.78 | 3.22 | 3.22 | 6.57 | 8.96 | −0.22 | 1.76 |

AC voltage | 140.72 | 250.67 | 7.68 | 227.89 | 235.52 | 241.27 | −0.64 | 7.28 |

AC current | 0.38 | 11.83 | 3.00 | 3.24 | 6.45 | 8.49 | −0.33 | 1.81 |

DC power | 104.10 | 2969.84 | 733.36 | 784.03 | 1551.90 | 2034.70 | −0.28 | 1.83 |

AC power | 92.73 | 2857.53 | 703.93 | 764.18 | 1502.86 | 1961.53 | −0.29 | 1.84 |

Model | Hyperparameter Search Range | Optimized Hyperparameters |
---|---|---|

-Number of learners: 10–500 | -Number of learners: 10 | |

Bagged | -Minimum leaf size: 1–1684 | -Minimum leaf size: 2 |

-Number of predictors to sample: 1–7 | -Number of predictors to sample: 7 | |

-Number of learners: 10–500 | -Number of learners: 46 | |

Boosted | -Minimum leaf size: 1–1684 | -Minimum leaf size: 89 |

-Number of predictors to sample: 1–7 | -Number of predictors to sample: 7 |

Methods | RMSE | R2 | MSE | MAPE (%) |
---|---|---|---|---|

BG | 20.03 | 1 | 401.07 | 13.88 |

BS | 53.98 | 0.99 | 2914.1 | 44.94 |

OBG | 11.36 | 1 | 129.11 | 8.31 |

OBS | 14.65 | 1 | 214.59 | 11.53 |

Method | TPR | FPR | Accuracy | AUC | EER |
---|---|---|---|---|---|

BS-EWMA${}^{pa}$ | 1 | 0.0779 | 0.9223 | 0.9610 | 0.0777 |

BS-EWMA${}^{np}$ | 1 | 0.0304 | 0.9697 | 0.9848 | 0.0303 |

BS-DEWMA${}^{pa}$ | 1 | 0.0276 | 0.9725 | 0.9862 | 0.0275 |

BS-DEWMA${}^{np}$ | 1 | 0.0200 | 0.9801 | 0.9900 | 0.0199 |

BG-EWMA${}^{pa}$ | 1 | 0.1511 | 0.8494 | 0.9244 | 0.1506 |

BG-EWMA${}^{np}$ | 1 | 0.0257 | 0.9744 | 0.9872 | 0.0256 |

BG-DEWMA${}^{pa}$ | 1 | 0.0437 | 0.9564 | 0.9781 | 0.0436 |

BG-DEWMA${}^{np}$ | 1 | 0.0238 | 0.9763 | 0.9881 | 0.0237 |

Method | TPR | FPR | Accuracy | AUC | EER |
---|---|---|---|---|---|

BS-EWMA${}^{pa}$ | 0.9815 | 0.0315 | 0.9692 | 0.9750 | 0.0308 |

BS-EWMA${}^{np}$ | 0.9815 | 0.0241 | 0.9762 | 0.9787 | 0.0238 |

BS-DEWMA${}^{pa}$ | 0.9815 | 0.0346 | 0.9662 | 0.9734 | 0.0338 |

BS-DEWMA${}^{np}$ | 0.9815 | 0.0304 | 0.9702 | 0.9755 | 0.0298 |

BG-EWMA${}^{pa}$ | 0.9815 | 0.0063 | 0.9930 | 0.9876 | 0.0070 |

BG-EWMA${}^{np}$ | 0.9815 | 0.0042 | 0.9950 | 0.9886 | 0.0050 |

BG-DEWMA${}^{pa}$ | 0.9815 | 0.0084 | 0.9911 | 0.9865 | 0.0089 |

BG-DEWMA${}^{np}$ | 0.9815 | 0.0042 | 0.9950 | 0.9886 | 0.0050 |

Method | TPR | FPR | Accuracy | AUC | EER |
---|---|---|---|---|---|

BS-EWMA${}^{pa}$ | 0.8182 | 0.0342 | 0.9072 | 0.8920 | 0.0928 |

BS-EWMA${}^{np}$ | 0.8052 | 0.0299 | 0.9046 | 0.8876 | 0.0954 |

BS-DEWMA${}^{pa}$ | 0.8831 | 0.0983 | 0.8943 | 0.8924 | 0.1057 |

BS-DEWMA${}^{np}$ | 0.7727 | 0 | 0.9098 | 0.8864 | 0.0902 |

BG-EWMA${}^{pa}$ | 0.9740 | 0.0214 | 0.9768 | 0.9763 | 0.0232 |

BG-EWMA${}^{np}$ | 0.9675 | 0.0128 | 0.9794 | 0.9774 | 0.0206 |

BG-DEWMA${}^{pa}$ | 0.9935 | 0.0256 | 0.9820 | 0.9839 | 0.0180 |

BG-DEWMA${}^{np}$ | 0.9805 | 0.0043 | 0.9869 | 0.9881 | 0.0103 |

Method | TPR | FPR | Accuracy | AUC | EER |
---|---|---|---|---|---|

BS-EWMA${}^{pa}$ | 0.6230 | 0 | 0.7983 | 0.8115 | 0.2017 |

BS-EWMA${}^{np}$ | 0.6407 | 0 | 0.8078 | 0.8204 | 0.1922 |

BS-DEWMA${}^{pa}$ | 0.6319 | 0 | 0.8030 | 0.8159 | 0.1970 |

BS-DEWMA${}^{np}$ | 0.6832 | 0 | 0.8305 | 0.8416 | 0.1695 |

BG-EWMA${}^{pa}$ | 1 | 0.0122 | 0.9943 | 0.9939 | 0.0057 |

BG-EWMA${}^{np}$ | 0.9876 | 0 | 0.9934 | 0.9938 | 0.0066 |

BG-DEWMA${}^{pa}$ | 0.9965 | 0.0244 | 0.9867 | 0.9860 | 0.0133 |

BG-DEWMA${}^{np}$ | 0.9929 | 0.0041 | 0.9943 | 0.9944 | 0.0057 |

Duration | DC Current Indicator (A) | DC Voltage Indicator | |
---|---|---|---|

PV string Faults (open-circuit) | Permanent | −50% | No change |

Circuit breaker fault | Permanent | Zero energy | Voc (280–300) |

Inverter disconnection | Temporary (1–5 min) | Zero energy | Voc (280–300) |

Partial shading (pylons) | Temporary (0.5–2 h) | −15/35% | 220–260 |

2 PV modules short-circuited | Permanent | No change | −10% |

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## Share and Cite

**MDPI and ACS Style**

Harrou, F.; Taghezouit, B.; Khadraoui, S.; Dairi, A.; Sun, Y.; Hadj Arab, A. Ensemble Learning Techniques-Based Monitoring Charts for Fault Detection in Photovoltaic Systems. *Energies* **2022**, *15*, 6716.
https://doi.org/10.3390/en15186716

**AMA Style**

Harrou F, Taghezouit B, Khadraoui S, Dairi A, Sun Y, Hadj Arab A. Ensemble Learning Techniques-Based Monitoring Charts for Fault Detection in Photovoltaic Systems. *Energies*. 2022; 15(18):6716.
https://doi.org/10.3390/en15186716

**Chicago/Turabian Style**

Harrou, Fouzi, Bilal Taghezouit, Sofiane Khadraoui, Abdelkader Dairi, Ying Sun, and Amar Hadj Arab. 2022. "Ensemble Learning Techniques-Based Monitoring Charts for Fault Detection in Photovoltaic Systems" *Energies* 15, no. 18: 6716.
https://doi.org/10.3390/en15186716