# An Efficient Neural Network-Based Method for Diagnosing Faults of PV Array

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## Abstract

**:**

## 1. Introduction

- The data feeding (
**first step**) uses the real measured data: array’s temperature, solar irradiance, PV voltage, and PV current at the maximum power point (MPP). - The
**second step**consists of modeling the healthy system and fault detection. According to input data, two networks of artificial neural networks (NANNs), NANN1 and NANN2, are used to predict the current and voltage output values for healthy or default operation. - The
**third step**provides PV system diagnosis by combining the outputs from two PNNs. The respective output values (currents and voltages) from NANNs are used as input for two probabilistic neural networks (PNNs), called PNN1 and PNN2. PNN1 and PNN2 classify the current and voltage values from the NANN1 and NANN2 models by comparing them with actual measured values. PNN1 classifies the existing data into two classes (healthy and faulty), while PNN2 classifies the voltage data into five categories (one healthy and four default alternatives).

- Modeling healthy system operation and separate detection of one current and four voltage short-circuit defaults using two networks of artificial neural networks (NANNs).
- Diagnosis of one healthy and five faulty short-circuits operation conditions using real current and voltage data variation in time. The classification and decision use probabilistic neural networks (PNNs) fueled by NANNs simulations.
- The robustness of the proposed method is tested in the presence of noise from the inverter.

## 2. Modeling and Diagnosis of PV Faults

- ▪
- Collection of real meteorological data (G and T) with sensors, and their injection to NANNs.
- ▪
- Production of classes from NANNs.
- ▪
- Acquisition of real data from the PV array (I
_{mpp}and V_{mpp}) and their injection to PNNs. - ▪
- Classification of the later measured data to their convenient classes by PNNs.
- ▪
- Decision about the health state of the PV array.

#### 2.1. Feeding with Real Data

_{mpp}, V

_{mpp}), are fed to the created NANNs and PNNs for learning. The time variation of these parameters is summarized in Figure 6. The experimental setup of the PV plant, located at the Renewable Energies Development Centre (CDER) of Algiers, Algeria [33,34], is detailed at the beginning of this section. The measurements in Figure 6 were taken in March 2018 with a sampling period of one minute, equivalent to 220 data points for each parameter.

^{2}. For the electrical parameters, the PV current varies in the range (6–12 A), while the PV voltage varies in the range (20–30 V).

#### 2.2. Modeling and Detection of Faults Using NANNs

_{mpp}and V

_{mpp}). The approach consists of modeling a healthy mode and five defective modes. The first NANN is used to model current outputs, while the second NANN is used to model voltage outputs under variable operating conditions, as shown in Figure 8 and Figure 9.

- -
- The first graph (in blue line) represents Class 1, which models the MPP current at the healthy state.
- -
- The second graph (in black line) represents Class 6, which models the MPP current at a faulty state with a short-circuited string.
- -
- -
- The first graph (in green line) represents Class 1, which stands for the healthy voltage model at MPP.
- -
- The second graph (in blue line) represents Class 2, which stands for the faulty voltage model at MPP for one short-circuited panel.
- -
- The third graph (in magenta line) represents Class 3, which stands for the faulty voltage model at MPP for two short-circuited panels.
- -
- The fourth graph (in cyan line) represents Class 4, which stands for the faulty voltage model at MPP for four short-circuited panels.
- -
- The fifth graph (in black line) represents Class 5, which stands for the faulty voltage at MPP for six short-circuited panels.

- -
- -
- -
- The faulty model one short-circuited panel (V
_{mpp1sc}with blue Figure 12). - -
- The faulty model two short-circuited panels (V
_{mpp2sc}with magenta Figure 12). - -
- The faulty model four short-circuited panels (V
_{mpp4sc}with cyan Figure 12). - -
- The faulty model six short-circuited panels (V
_{mpp6sc}with black Figure 12).

#### 2.3. Diagnosis, Classification and Decision Using PNNs

_{mpp}and V

_{mpp}of each output, along with measured data in real operating conditions, leads to the identification and isolation of failures.

- ▪
- A PNN uses the probabilistic model, Bayesian classifiers.
- ▪
- A PNN is guaranteed to converge to a Bayesian classifier when enough training data are provided.
- ▪
- No learning process is required in PNNs.
- ▪
- No need to initialize the weights of the PNN.
- ▪
- There is no relationship between the learning and recall process.

_{mpp}. It shows that a string fault directly impacts the output current of the PV array.

_{mpp}.

- $P({C}_{i}/x)$ is the conditional probability density function of x given ${C}_{i}$.
- $P({C}_{j})$ is the probability of choosing a sample from the class ${C}_{j}$.

## 3. Details about the Elaboration of NANNS

- -
- The collection of real measured data (T, G, I
_{mpp}, V_{mpp}), reserved for learning and validating NANNs. - -
- The choice of the type of ANNs (multi-layer perceptron (MLP)) and their architectures.
- -
- The choice of the learning type (supervised learning).
- -
- The validation of NANNs.
- -
- The exploitation of the results.

#### 3.1. Collection of Real Measured Data

#### 3.2. Choice of Type of ANNs and Their Architectures

_{mpp}(supervised following real healthy and real faulty) and V

_{mpp}(supervised following real healthy and real faulty) as described in Figure 17. Besides, faults are introduced in the real PV system to obtain real current and voltage data for each faulty mode.

#### 3.3. Choice of Learning Type

#### 3.4. Validation of ANNs

- (a)
- Validation of model from ANN1 of NANN1 (I
_{mpp}of the healthy system, Figure 22):The following Figure 23 shows the error between real and modeled currents data. The following equation gives the error:$$Error={I}_{MPP-\mathrm{Re}al}-{I}_{MPP-Model}$$ - (b)
- Validation of model from ANN1 of NANN2 (V
_{mpp}of the healthy system, Figure 24).

#### 3.5. Exploitation of Results

- N: number of data points.

- Data
_{Mean}: Mean of real data points.

## 4. Test of Robustness

#### 4.1. Presence of Noise from the Inverter

#### 4.2. Effect of Detection Time

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Nomenclature

PV | Photovoltaic |

BBD | Blocking and bypassing diode |

OC | Open circuit |

SC | Short circuit |

GF | Ground fault |

LLF | Line-to-line |

AF | Arc fault |

FDD | Fault detection and diagnosis |

IR | Infrared |

AI | Artificial intelligence |

ANN | Artificial neural network |

MLP | Multi-layer perceptron |

RBN | Radial basis network |

FF | Feed-forward |

RNN | Recurrent neural network |

NN | Neural network |

MPP | Maximum power point |

ANNs | Artificial neural networks |

NANNs | Networks of artificial neural networks |

NANN1 | Network of artificial neural network 1 |

NANN2 | Network of artificial neural network 2 |

PNNs | Probabilistic neural networks |

I-V | Current–voltage curve |

CDER | Renewable Energies Development Centre |

G | Solar irradiance |

T | Panel’s temperature |

P_{mpp} | Maximum power |

I_{sc} | Short circuit current |

V_{oc} | Open circuit voltage |

α | Coefficient of temperature at I_{sc} |

β | Coefficient of temperature at V_{oc} |

I_{mpp} | Maximum current |

V_{mpp} | Maximum voltage |

I_{mpp_h} | Healthy current at the maximal power point |

V_{mpp_h} | Healthy voltage at the maximal power point |

V_{mpp1sc} | Voltage at maximum power point of one short-circuited panel |

V_{mpp2sc} | Voltage at maximum power point of two short-circuited panels |

V_{mpp4sc} | Voltage at maximum power point of four short-circuited panels |

V_{mpp6sc} | Voltage at maximum power point of six short-circuited panels |

I_{mpp_s} | Current at maximal power point of string fault |

Probability density function | |

RBF | Radial basis functions |

LM | Levenberg–Marquardt |

RMSE | Root mean square error |

MRE | Mean relative error |

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**Figure 6.**Real data of (

**a**) array’s temperature; (

**b**) solar irradiance; (

**c**) PV current; (

**d**) PV voltage.

**Figure 7.**A generic neural network-based multiple-model fault detection and isolation scheme [36].

**Figure 18.**Data provided to the ANN1 from NANN1 in a healthy system for the current learning process.

**Figure 19.**Data provided to the ANN1 from NANN2 in a healthy system for the voltage learning process.

**Figure 30.**Classification of current at maximum power point in the presence of noise from the inverter.

**Figure 31.**Classification of voltage at maximum power point in the presence of noise from the inverter.

**Figure 32.**Classification of current at maximum power point in the presence of noise from an inverter, over 10 data points.

**Figure 33.**Classification of voltage at maximum power point in the presence of noise from the inverter, over 10 data points.

Parameters | Values |
---|---|

Maximum power (P_{mpp}) | 106 W |

Short circuit current (I_{sc}) | 6.54 A |

Open circuit voltage (V_{oc}) | 21.6 V |

Coefficient of temperature at I_{sc} (α) | 0.060 %/°C |

Coefficient of temperature at V_{oc} (β) | −0.36 %/°C |

Maximum current (I_{mpp}) | 6.1 A |

Maximum voltage (V_{mpp}) | 17.4 V |

Name of Faults | Symbols |
---|---|

Healthy model | C1 |

Fault detection due to voltage of one short-circuited panel | C2 |

Fault detection due to voltage of two short-circuited panels | C3 |

Fault detection due to voltage of four short-circuited panels | C4 |

Fault detection due to voltage of six short-circuited panels | C5 |

Fault detection due to current of short-circuited string | C6 |

Numbers | ANNs of NANN1 | Input Layer | Hidden Layer | Output Layer |
---|---|---|---|---|

ANN1 | Healthy current | 2 | 40 | 1 (I_{mpp_healthy}) |

ANN2 | Fault in the current of string short circuited | 2 | 40 | 1 (I_{mpp_string}) |

Numbers | ANNs of NANN2 | Input Layer | Hidden Layer | Output Layer |
---|---|---|---|---|

ANN1 | Healthy voltage model | 2 | 40 | 1 (V_{mpp_healthy}) |

ANN2 | Fault in voltage of one panel SC | 2 | 40 | 1 (V_{mpp_1SC}) |

ANN3 | Fault in voltage of two panels SC | 2 | 40 | 1 (V_{mpp_2SC}) |

ANN4 | Fault in voltage of four panels SC | 2 | 40 | 1 (V_{mpp_4SC}) |

ANN5 | Fault in voltage of six panels SC | 2 | 40 | 1 (V_{mpp_6SC}) |

Symbols | Parameters | Classes |
---|---|---|

I_{mpp_h} | Healthy current at the maximal power point | Class 1 |

V_{mpp_h} | Healthy voltage at the maximal power point | Class 1 |

V_{mpp1sc} | Voltage at maximum power point of one short-circuited panel | Class 2 |

V_{mpp2sc} | Voltage at maximum power point of two short-circuited panels | Class 3 |

V_{mpp4sc} | Voltage at maximum power point of four short-circuited panels | Class 4 |

V_{mpp6sc} | Voltage at maximum power point of six short-circuited panels | Class 5 |

I_{mpp_s} | Current at maximal power point of string fault | Class 6 |

I_{mpp} | V_{mpp} | Decision about PV System |
---|---|---|

I_{mpph} | V_{mpph} | 2Healthy system |

I_{mpph} | V_{mpp1sc} | Fault detection due to one short-circuited panel |

I_{mpph} | V_{mpp2sc} | Fault detection due to two short-circuited panels |

I_{mpph} | V_{mpp4sc} | Fault detection due to four short-circuited panels |

I_{mpph} | V_{mpp6sc} | Fault detection due to six short-circuited panels |

I_{mppstring} | V_{mpph} | Fault detection due to string |

Current Healthy System | Current String Fault | Voltage Healthy System | Voltage 1 Panel SC | Voltage 2 Panels SC | Voltage 4 Panels SC | Voltage 6 Panels SC | |
---|---|---|---|---|---|---|---|

RMSE | 0.5737 | 0.8264 | 2.4928 | 2.4493 | 1.1601 | 1.7280 | 0.8201 |

MRE (%) | 3.21 | 1.62 | 1.78 | 1.02 | 1.51 | 1.54 | 1.67 |

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**MDPI and ACS Style**

Tchoketch Kebir, S.; Cheggaga, N.; Ilinca, A.; Boulouma, S.
An Efficient Neural Network-Based Method for Diagnosing Faults of PV Array. *Sustainability* **2021**, *13*, 6194.
https://doi.org/10.3390/su13116194

**AMA Style**

Tchoketch Kebir S, Cheggaga N, Ilinca A, Boulouma S.
An Efficient Neural Network-Based Method for Diagnosing Faults of PV Array. *Sustainability*. 2021; 13(11):6194.
https://doi.org/10.3390/su13116194

**Chicago/Turabian Style**

Tchoketch Kebir, Selma, Nawal Cheggaga, Adrian Ilinca, and Sabri Boulouma.
2021. "An Efficient Neural Network-Based Method for Diagnosing Faults of PV Array" *Sustainability* 13, no. 11: 6194.
https://doi.org/10.3390/su13116194