Chaotic Extension Neural Network-Based Fault Diagnosis Method for Solar Photovoltaic Systems

At present, the solar photovoltaic system is extensively used. However, once a fault occurs, it is inspected manually, which is not economical. In order to remedy the defect of unavailable fault diagnosis at any irradiance and temperature in the literature with chaos synchronization based intelligent fault diagnosis for photovoltaic systems proposed by Hsieh et al., this study proposed a chaotic extension fault diagnosis method combined with error back propagation neural network to overcome this problem. It used the nn toolbox of matlab 2010 for simulation and comparison, measured current irradiance and temperature, and used the maximum power point tracking (MPPT) for chaotic extraction of eigenvalue. The range of extension field was determined by neural network. Finally, the voltage eigenvalue obtained from current temperature and irradiance was used for the fault diagnosis. Comparing the diagnostic rates with the results by Hsieh et al., this scheme can obtain better diagnostic rates when the irradiances or the temperatures are changed.


Introduction
This study focused on solar photovoltaic fault diagnosis.Solar energy is generated from the sunlight, which is an inexhaustible renewable energy, as compared to other green energies.At present, the solar photovoltaic system has been used in many fields, and current research focuses are the use of this technology, such as efficient storage, environmental issues, and subsequent maintenance.The analysis based on fault diagnosis technology can save labor cost greatly.
Many studies have proposed fault diagnosis technologies for photovoltaic system.Most of traditional fault diagnosis technologies are based on intelligent algorithms including neural network [1][2][3].For example, in 2009, Wu et al. used BP neural network for fault diagnosis, the diagnostic rate was very high, but a large amount of data was required for learning and training.The convergence of samples was time consuming [4].In 2011, Syafaruddin et al. used threelayer artificial neural network for fault diagnosis and provided more accurate diagnostic result than one-layer fault diagnosis.However, this method was also time consuming [5].In 2011, Shimakage et al. discussed photovoltaic system fault diagnosis and used measurement and observation for diagnosis.They recorded the power generated by the faulted photovoltaic system and compared it with the presently measured power.However, the data for comparison were required and time was required to create the database [6].In 2012, Zhao et al. proposed a decision tree-based diagnostic method for photovoltaic cell.The diagnostic rate of this method was as high as 99.8%, but more than 1,000 times of intercomparison were required in the course of diagnosis [7].In 2014, Tadj et al. proposed a GISTEL (gisement solaire par télédetection: solar radiation by teledetection) model to improve the photovoltaic cell diagnosis on fuzzy logic estimated satellite image.The method was difficult to be implemented [8].In 2014, Hsieh et al. used chaotic extension theory for diagnosis, and the accuracy rate was very high.However, due to the limitation of extension theory, the diagnostic rate decreased greatly when the temperature and irradiance changed.This study aims to remedy the defects in the literature [9].
In the literature [9], 10-series 2-parallel solar photovoltaic array was used as the model of fault diagnosis.Chaotic synchronization system was combined with extenics for fault diagnosis.However, the classical domain cannot identify  3 .0 V Short-circuit current ( SC ) 0.8 A the fault state accurately as long as the irradiance and temperature have changed.This study uses BP neural network, so as to remedy the defect of unavailable diagnosis when the irradiance and temperature change, and uses the center of error dynamic trajectories of two chaotic subsystems as eigenvalue, to overcome the decrease in diagnostic rate that resulted from undervoltage at low light level.

Architecture of Solar Power System
The fault diagnosis module used in this paper is 10-series 2parallel photovoltaic, as shown in Figure 1, and MPPT, the system architecture, is shown in Figure 2; the matlab 2010 is used for simulation.The specifications of SM1611 photovoltaic cell are shown in Table 1 [9].The photovoltaic cell is set as short circuit to simulate nine fault states to be illustrated by Table 2, and the I-V and P-V characteristic curves at different irradiances and temperatures are observed.

Research Method
3.1.Chaos Synchronization Theory.The chaos synchronization theory designs a slave system to synchronize a master system.The chaos synchronization system consists of two subsystems, a master system and a slave system, representing the relation between master and servant.This paper uses Lorenz chaos synchronization system, which is highly sensitive to parametric variation, to capture the voltage signal of photovoltaic system and extract the kinematic trajectory of dynamic error.The center of this kinematic trajectory is used

Fault category
Fault condition (short circuit set in faulted solar cell)

Case 1 (C1)
There is no fault in two-series connected photovoltaic cells.Case 2 (C2) One solar cell fault occurs in any series branch of two-series branch photovoltaic system.Case 3 (C3) Two solar cells have faults in any series branch of two-series branch photovoltaic system.Case 4 (C4) Three solar cells have faults in any series branch of two-series branch photovoltaic system.Case 5 (C5) One solar cell fault occurs in both of the two-series branches of two-series branch photovoltaic system.Case 6 (C6) Two solar cells have faults in both of the two-series branches of two-series branch photovoltaic system.

Case 7 (C7)
In the two-series branch photovoltaic system, one solar cell has fault in one-series branch and two solar cells have faults in the other branch.

Case 8 (C8)
In the two-series branch photovoltaic system, one solar cell has fault in one-series branch and four solar cells have faults in the other branch.

Case 9 (C9)
In the two-series branch photovoltaic system, two solar cells have faults in one-series branch and three solar cells have faults in the other branch.
as the eigenvalue of fault.The architecture of Lorenz chaos synchronization system is expressed as follows [10]: where , , and  are system parameters and  and  are the state variables.The master-slave system error state can be expressed as  1 =  1 −  1 ,  2 =  2 −  2 , and  3 =  3 −  3 ; the dynamic error system is expressed as follows [10]: This paper uses the final dynamic errors ė 1 , ė 2 , and ė 3 to draw the dynamic error trajectory diagram for observation.

Extension Theory.
The extension theory solves contradiction problem quantitatively and qualitatively to change it into compatibility problem.The difference between extension theory and fuzzy theory is that the range of fuzzy set is ⟨0, 1⟩, whereas the extension is a real number extended from ⟨0, 1⟩ to ⟨−∞, ∞⟩ [11].The extension theory is characterized by a small amount of calculation and simplicity, and it has high accuracy rate in evaluating multiple parameters and complex construction.This paper uses this feature to judge  the eigenvalue captured by Lorenz chaos synchronization system to identify the fault category of photovoltaic system.

Matter-Element Theory.
In the extension theory, the matter-element is the basic element describing things.The general matter-element model is the mathematical model applied to extension, defined as follows [12]: where  is the matter-element,  is the name of the matterelement,  is the eigenvector, and  is the magnitude vector corresponding to .

Extension Set.
The extension set means the range of set is extended from −∞ to ∞ to represent the extensibility of thing characteristics, the correlation function is defined as (4), and the correlation grade of extension set can be expressed as Figure 3  The neural network consists of multiple layers of neurons; the input end is called input layer and the output end is called output layer.The hidden layer is between the output layer and input layer.The input layer and the output layer are the basic structures forming the neural network; the hidden layer is dispensable.The basic structure is shown in Figure 4 [14].network system to obtain the extension classical domain range of chaos center eigenvalue at current irradiance and temperature, and then the recorded voltage is imported into the chaos synchronization system to obtain a kinematic trajectory of chaotic dynamic system.The center point of kinematic trajectory is taken as the basis of diagnosis.Finally, the fault category of photovoltaic system can be identified as long as the obtained signal is imported into the diagnostic system of chaotic extension neural network.

Simulation Results and Comparison
This study aims to remedy the defect of unavailable diagnosis at varying irradiance and temperature in the literature [9], so the BP neural network is adopted.Figure 6 is the schematic diagram of system diagnosis.

Simulation Results
. This study uses matlab 2010 and nn toolbox for simulation.The fault category is the short circuit in the solar panel of photovoltaic array, so as to simulate one normal state and eight fault states (i.e., C1∼C9), as shown in Table 2.
The P-V and I-V characteristic curves are different in different states.The additional noise makes the kinematic trajectory of chaos system easier to be identified.Figure 7 is the three-dimensional diagram of chaotic dynamic error in the normal state of 500 W/m 2 40 ∘ C; the chaos center points in various states are taken as the range of extension classical domain, and the BP neural network is used to decide the chaos center points at different temperatures and irradiances.The sunshine intensity is about 400 W/m 2 ∼ 1000 W/m 2 during 8:00∼16:00 in Taiwan, as shown in Table 3 [15], and the temperature is about 25 ∘ C∼50 ∘ C; the simulation is based on the conditions [9].  4 shows the center point values at various irradiances and temperatures.The data are imported into the BP neural network of nn tool for training to calculate the center point of chaotic kinematic trajectory generated in different conditions.In Table 3, the center point adds ±0.5 as the range of extension classical domain, and then the fault voltage signal is imported for fault diagnosis.Table 8 compares the diagnostic rates and shows the diagnostic method of the literature [9].When the irradiance is unchanged and the temperature rises by 5 ∘ C, the diagnostic   rate decreases to 22.23% as the range of chaotic kinematic trajectory is changed.When the irradiance decreases to 1000 W/m 2 and the temperature is unchanged, the diagnostic rate is only 11.11%.The diagnostic rate will decrease greatly if the temperature or irradiance changes.

Conclusion
The chaotic extension neural network diagnosis proposed in this paper is integrated with error backpropagation neural network.It can remedy the defect of large decrease in diagnostic rate when the irradiance and temperature have changed in the original literature effectively.The defect in the original literature is remedied, and the high diagnostic rate in the original literature is maintained.In comparison to the original neural network diagnosis, the addition of extension theory reduces the time of repeated training.In addition, as the chaos synchronization theory is used, when the diagnosis is difficult due to undervoltage caused by the environment, the signal can be amplified by using the advantages of chaos theory for diagnosis.

Figure 6 : 3 Figure 7 :
Figure 6: Schematic diagram of system diagnosis of chaotic extension neural network.
Figures 8(a), 8(b), 9(a), and 9(b) show the P-V and I-V characteristic curves at 1000 W/m 2 25 ∘ C and 500 W/m 2 40 ∘ C. First, the irradiance of 400 W/m 2 ∼ 1000 W/m 2 is divided into intervals of 100 irradiance; the temperature is divided into 25 ∘ C, 30 ∘ C, 40 ∘ C, and 50 ∘ C intervals as the input ends of BP neural network.The voltage of each interval is taken for chaos signal extraction; the obtained signal center point is used as the output end of neural network.Figures 10 and 11 show the ė 1 − ė 3 dynamic error plane and center of different faults at 1000 W/m 2 25 ∘ C and 500 W/m 2 40 ∘ C. The data of ė 3 center point of each interval are obtained.Table

Table 1 :
Solar panel model and specifications.

Table 2 :
Solar photovoltaic system fault category.

Table 3 :
Sunshine intensity in different time intervals.

Table 4 :
Center point values at different irradiances and temperatures.

Table 8 :
Comparison of diagnostic rates.