# Multiple Fault Location in a Photovoltaic Array Using Bidirectional Hetero-Associative Memory Network in Micro-Distribution Systems

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## Abstract

**:**

## 1. Introduction

_{1}, p

_{2}, p

_{3}, …. Then, the operation state of each PV panel can be identified. The proposed BHAM is designed as a classifier to locate the multiple faults in a PV array that can indicate one or more PV panel faults. In contrast to traditional machine learning methods, the BHAM network can reduce the computation time and memory storage requirements. The proposed model is also easily implemented in an embedded system or a tablet PC. Thus, experimental results show it is capable of detecting multiple faults in a rooftop PV system.

## 2. Methodology

#### 2.1. Maximum Output Power Estimation and Fault Feature Extraction

_{q}, where q is the number of PV panels in parallel, as seen in Figure 2a. The output voltage, V, and current, I, for q PV panels in a parallel or series configuration can be expressed as:

_{L}is the grid rated load current; parameter, a, is the environment modified factor, and a = 7.8–9.0 in Taiwan; η is the output effectiveness; V

_{q}is the rated voltage per PV panel, V

_{q}= 12 or 24 voltage; and s is the number of PV panels in a series. Thus, the output power can be increased, as:

_{q}

_{,est}, and photo-current, I

_{ph}

_{,q}, of each PV panel are as follows:

_{sat}is the reverse saturation current; T is the surface temperature of the cell; n

_{p}and n

_{s}are the number of modules connected in parallel and series, respectively; Q is the electron charge; b is Boltzmann’s constant; A is the p–n junction ideality factor, which is typically in the range of 1 < A < 5 for different manufacturers; T

_{c}is the ambient temperature; T

_{r}is the reference temperature (25 °C); I

_{sc}is the cell short-circuit current at T

_{r}; k

_{sc}is the short-circuit current temperature coefficient; S is the solar radiation; ρ is the temperature compensation coefficient. Temperature and irradiance sensors are required in each PV array (in a parallel or series configuration).

_{q}

_{,est}, and total MOP, P

_{est}, can be estimated as:

_{q}

_{,mea}, of each panel, as seen in the measurement system in Figure 2b.

_{q}, of power degradations is computed in per-unit (pu) quantities with an interval of [0,1] and with an estimated output power, P

_{q},

_{est}, and a measured output power, P

_{q}

_{,mea}, at each PV panel. According to the power degradation of each PV panel, the index can be parameterized with certainty factors as [6,11]

_{q}= 0.10; n the identical PV panels are connected in a parallel or series configuration, q = 1, 2, 3, …, n (n = 8 means 8 PV panels in this study); p

_{q}is the power degradation index. The functions of certainty factors for normal condition and fault types are shown in Figure 3. The operation state of each PV panel can be identified as:

_{1}, s

_{2}, …, s

_{q}, …, s

_{n}] = [0/1, 0/1, …, 0/1, …, 0/1]. Equation (12) is the generalized form to screen the operation state of each PV panel for large PV arrays. For n-digit binary numbers, each bit has two states, {0, 1}, and the total number of the n-digit binary string is 2

^{n}combinations. In this study, with 8 PV panels in a series configuration (n = 8, q’ = 0, 1, 2, …, n), we have 2

^{8}= 256 combinations of different binary patterns, as:

#### 2.2. Bidirectional Associative Memory Network

**Learning stage**

_{k}and R

_{k}, k = 1, 2, 3, …, K, K = 256 binary training patterns, where state vector, S

_{k}= [s

_{k}

_{1}, …, s

_{ki}, …, s

_{kn}]

^{t}, s

_{ki}∈ {0, 1}, and the fault pattern, R

_{k}= [r

_{k}

_{1}, …, r

_{kj}, …, r

_{kn}]

^{t}, R

_{kj}∈ {0, 1}.

_{ij}]

_{n}

_{×n}.

_{i}= w

_{ij}, i = j = 1, 2, 3, …, 8, the weight matrix, W, and the associative matrix, A, for the eight faults as follows:

_{h}, h = 0, 1, 2, …, 8, is the weight value for normal condition and eight faults within the weight matrix, W = [ω

_{hi}]

_{9×8}, ω

_{hi}= ω

_{h}× λ

_{i}, and each element in the associative matrix, A = [a

_{hj}]

_{9×8}, element, a

_{hj}, is encoded as numerical data from value “1” to value “8” to indicate which one is fault in a PV array, and the normal condition is encoded as the value “0.”

**Recalling stage**

_{0}= [s

_{1}, s

_{2}, …, s

_{i}, …, s

_{8}] to the BHAM network;

_{0}= [r

_{1}, r

_{2}, …, r

_{i}, …, r

_{8}]

^{T}, as:

_{0}, to the Gaussian function unit, g

_{h}, and the output of g

_{h}, as:

_{h}) × 0.90; if the pattern, R

_{0}, is similar to any row weight vector of matrix W, the ED

_{h}will be small (ED

_{h}→ 0, argmin||ED

_{h}||, h = 0, 2, 3, …, 8) and the g

_{h}unit will approach 1. The g

_{h}unit is the index that measure the similarity degree among nine row weight vectors.

_{h}units to the r

_{i}unit with nonlinear feedback and compute the output of the r

_{i}unit using the hard limit function with a threshold value of 0.50, as:

_{i}units and g

_{h}units until bidirectional stability is reached. When the patterns, R

_{0}, is not changed, and $\Delta {R}_{0p}=\left|\right|{R}_{0p}-{R}_{0p-1}\left|\right|=0$, where p is the iteration number, then the BHAM algorithm will be terminated.

_{i}= 1, means one or more faults have been detected. Thus, the BHAM network associates the numerical data to locate which PV panel is at fault within the PV array. A flow chart of the BHAM algorithm for multiple fault location is shown in Figure 5.

## 3. Experimental Results and Discussion

^{2}and 30–40 °C, respectively, during the summer season. For various radiation and temperature values, the MPPT algorithm [1,2,3,19,20,21] can be employed to control the DC–DC boost converter until the desired MOP and output voltage is reached. In this study, an ICM-based method [1,3] is used to estimate the desired output and adjust the boost converter’s duty ratio to match the maximum point. The MPPT is used to track the MOP by adjusting the voltage as solar radiation and temperature increase from 0.2 kW/m

^{2}to 1.0 kW/m

^{2}and from 30 °C to 45 °C, respectively. The P–V and the I–V characteristic curves of each PV panel are shown in Figure 6. Hence, when atmospheric conditions change, the MPPT algorithm takes less than 10 switching controls to achieve the desired value. During the summer season, each PV panel had output powers of 199.1 W to 262.2 W, output currents of 9.8 A to 13.6 A, and an output voltage of 19.8 V, as seen in Figure 6a,b. The boost converter adjusts the duty ratio until the desired values of output power and voltage are reached, as seen in Figure 6c. The experimental results confirm that the MPPT can estimate the output power of each panel under various atmospheric conditions, and it can also work during clear day, low solar radiation and at the night-to-day transition.

_{1}= λ

_{2}= … = λ

_{8}= 128, are eigenvalues of matrix C.

^{2}and 37.5 °C; the MPPT algorithm was employed to estimate the MOP, 224.4 W, for each PV panel, and the output power for each faulted panel was 0.0 W. Six of the PV panels in parallel were disconnected, and thus, the string output power degraded 37.5% of the MOP, and an overcurrent was not generated. Hence, 16 power indexes could be estimated using Equation (9). The fault location procedures at the recall stage for two BHAM networks are as follows:

- Step (1)
- String 1#: [p
_{1}, p_{2}, p_{3}, p_{4}, p_{5}, p_{6}, p_{7}, p_{8}] = [0.00, 0.00, 0.00, 0.95, 0.96, 0.95, 0.96, 0.97];String 2#: [p_{1}, p_{2}, p_{3}, p_{4}, p_{5}, p_{6}, p_{7}, p_{8}] = [0.00, 0.00, 0.00, 0.96, 0.97, 0.96, 0.96, 0.95]; - Step (2)
- power indexes were parameterized using Equations (10) to (12). The operation states of 16 PV panels were identified asString 1#: [s1, s2, s3, s4, s5, s6, s7, s8] = [1, 1, 1, 0, 0, 0, 0, 0];String 2#: [s1, s2, s3, s4, s5, s6, s7, s8] = [1, 1, 1, 0, 0, 0, 0, 0];
- Step (3)
- associated the output patterns:String 1#: [r1, r2, r3, r4, r5, r6, r7, r8] = [256, 256, 256, 192, 192, 192, 192, 192];String 2#: [r1, r2, r3, r4, r5, r6, r7, r8] = [256, 256, 256, 192, 192, 192, 192, 192];
- Step (4)
- computed the outputs of Gaussian function units:String 1#: [g1, g2, g3, g4, g5, g6, g7, g8] = [0.0454, 0.2665, 0.5738, 0.4881, 0.2148, 0.0888, 0.0362, 0.0147, 0.0060];String 2#: [g1, g2, g3, g4, g5, g6, g7, g8] = [0.0454, 0.2665, 0.5738, 0.4881, 0.2148, 0.0888, 0.0362, 0.0147, 0.0060];
- Step (5)
- transited the outputs of Gaussian function units to the output units using Equations (22) and (23):String 1#: [r1, r2, r3, r4, r5, r6, r7, r8] = [1, 2, 3, 0, 0, 0, 0, 0];String 2#: [r1, r2, r3, r4, r5, r6, r7, r8] = [1, 2, 3, 0, 0, 0, 0, 0];
- Step (6)
- reached bidirectional stability and terminated the BHAM algorithm.

^{−2}, the iteration computing process took about <100 iterative computations to reach the convergent condition, as seen in Figure 8. Optimal smoothing parameter, 0.1125 and 0.0773, was obtained to minimize the mean squared error, and improve accuracy rate with learning rates, 0.5 and 0.6. However, initial condition assignments, such as initial network parameters, learning rates, and pre-specified tolerance value, can affect the model’s learning outcome performance. For example, a greater learning rate, >0.6, allowed rapid learning stage to reach the convergent condition. However, its computation easily trapped in the local minimum and perturbation around the desired optimal parameters, or tended to the divergent condition. With learning rate, 0.5–0.6, and tolerance value, <10

^{−2}, the learning stage could guarantee to reach the convergent condition in <50 iteration computations. In addition, fill-in with elements in the input and output matrices can increase computing time, memory storage requirements, and iterative computations. Therefore, considering 4 bytes for digital storage, the total memory storage was 16,384 bytes (input matrix: 256 × 8 × 4 bytes and output matrix: 256 × 8 × 4 bytes). PNN also provided a 100% hit rate and provided promising results for detecting multiple fault locations. However, in contrast to the proposed model, the iterative computing processes and memory storage requirements had two limitations.

## 4. Conclusions

^{2}–0.8 kW/m

^{2}and temperatures of 25 °C–40 °C, and indicated a fault location accuracy of 100% under clear days, lower solar radiation conditions, and night-to-day transition. In addition, as the capacity of PV systems will increase when connecting several PV panels in either parallel or series, and this will use a vast amount of space and long-term outdoor operations, the promising technology presented here can be integrated into light, unmanned vehicles and wireless communication. In addition, through an advanced metering infrastructure (AMI), metering power data can be transited to the BHAM-based monitor via WiFi wireless. In each PV array (parallel or series configuration), multiple BHAM-based monitoring system can be further established to identify fault types for each PV panel, including lower/upper grounded faults, open-circuit faults, bridged faults, and mismatch faults. The proposed BHAM algorithm is easy to implement and embed in existing supervisory control and data acquisition (SCADA) systems and AMI system without the need for extra devices.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Schematic diagram of multiple fault location in a PV array using hetero-associative memory network.

**Figure 2.**Schematic diagram of PV array. (

**a**) PV array in a parallel or series configuration, (

**b**) Measurement system of each PV panel.

**Figure 6.**The MPPT estimated results. (

**a**) Output power versus output voltage, (

**b**) Output current versus output voltage, (

**c**) Duty ratio versus switch number.

**Figure 7.**Experimental setup. (

**a**) Schematic diagram of a rooftop PV system, consisting of 2 strings with 16 PV panels; (

**b**) Solar radiation and temperature versus time (from 8:00 a.m. to 18:00 p.m.); (

**c**) Each PV panel and string measurement power and estimation power.

**Figure 8.**Smoothing parameter and mean squared error versus the iteration number for PNN (learning rate = 0.5 or 0.6) and BHAM methods.

Fault Type | Power Degradation Index, p_{q} |
---|---|

1. Normal (Nor) | <0.10 |

2. Lower Grounded Fault (LGF) | 0.10~0.30 |

3. Mismatch Fault/Hot Spot (MF/HS) | 0.30~0.60 |

4. Bridged (line-o-line) Fault (BF) | 0.30~0.50 |

5. Open Circuit Fault (OCF) | 0.00 |

6. Upper Grounded Fault (UGF) | >0.60 |

Specific Parameter | Value |
---|---|

Maximum Power P_{max} | 87.70 (W) |

Short-circuit Current I_{SC} | 4.80 (A) |

Open-circuit Voltage V_{OC} | 21.70 (V) |

Rated Voltage V_{R} | 19.14 (V) |

Rated Current I_{R} | 4.58 (A) |

Number of Modules Connected in Series n_{s} | 36 |

Number of Modules Connected in Parallel n_{p} | 2 |

String | Panel Number | Radiation kW/m^{2} | Temperature °C | Each Panel Power (W) | Total Output Power (kW) and Current (A) |
---|---|---|---|---|---|

1# | 8 | 0.2–1.0 | 30–45 | 199.1–262.2 | 1.6–2.1 kW 78.4–108.8 A |

2# | 8 | 0.2–1.0 | 30–45 | 199.1–262.2 | 1.6–2.1 kW 78.4–108.8 A |

Method | BHAM Network | PNN Method [24,25] | |
---|---|---|---|

Task | |||

Network Configuration | 8-8-9 | 8-256-9-8 | |

Number | 2 BHAM networks for 2 strings | 2 PNNs for 2 strings | |

Training Data | 256 input-output pairs | 256 input-output pairs | |

Storage Matrix | C_{8×8}, W_{9×8}, and A_{9×8} | Input (256 × 8) and output (256 × 8) matrices | |

Memory Storage | 832 bytes | 16,384 bytes | |

Process Unit | Gaussian function and hard limit function | Gaussian function | |

Learning Algorithm | Bidirectional associative memory | Least square algorithm | |

Learning Stage | Establish matrices, C, W, and A (Matrix Operation) | Iteration computing process < 100 | |

Recalling Stage | Iteration computing process ≤2 | - | |

Execution Time | Average time: <0.03 s | Average time: <20 s | |

Testing Pattern | 256 patterns for each BHAM network | 256 patterns for each PNN | |

Accuracy | 100% | 100% | |

Application | Easy to implement in a mobile intelligent vehicle | Average to implement in a mobile intelligent vehicle |

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## Share and Cite

**MDPI and ACS Style**

Chang, L.-Y.; Pai, N.-S.; Chou, M.-H.; Chen, J.-L.; Kuo, C.-L.; Lin, C.-H. Multiple Fault Location in a Photovoltaic Array Using Bidirectional Hetero-Associative Memory Network in Micro-Distribution Systems. *Crystals* **2018**, *8*, 327.
https://doi.org/10.3390/cryst8080327

**AMA Style**

Chang L-Y, Pai N-S, Chou M-H, Chen J-L, Kuo C-L, Lin C-H. Multiple Fault Location in a Photovoltaic Array Using Bidirectional Hetero-Associative Memory Network in Micro-Distribution Systems. *Crystals*. 2018; 8(8):327.
https://doi.org/10.3390/cryst8080327

**Chicago/Turabian Style**

Chang, Long-Yi, Neng-Sheng Pai, Min-Hung Chou, Jian-Liung Chen, Chao-Lin Kuo, and Chia-Hung Lin. 2018. "Multiple Fault Location in a Photovoltaic Array Using Bidirectional Hetero-Associative Memory Network in Micro-Distribution Systems" *Crystals* 8, no. 8: 327.
https://doi.org/10.3390/cryst8080327