PV array fault DiagnosticTechnique for BIPV systems

Accepted Manuscript Title: PV array Fault DiagnosticTechnique for BIPV Systems Author: Hachana Oussama Giuseppe Marco Tina Kamel Eddine Hemsas PII: DOI: Reference:

S0378-7788(16)30400-5 http://dx.doi.org/doi:10.1016/j.enbuild.2016.05.031 ENB 6666

To appear in:

ENB

Received date: Revised date: Accepted date:

2-7-2015 6-3-2016 13-5-2016

Please cite this article as: Hachana Oussama, Giuseppe Marco Tina, Kamel Eddine Hemsas, PV array Fault DiagnosticTechnique for BIPV Systems, Energy and Buildings http://dx.doi.org/10.1016/j.enbuild.2016.05.031 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

PV array Fault DiagnosticTechnique for BIPV Systems Hachana Oussamaa,1, Giuseppe Marco Tinab, Kamel Eddine Hemsasc a Kasdi Merbah University of Ouargla, Ouargla, Algeria. b University of Catania, Italy. c Ferhat Abbas University Setif1, Setif, Algeria. 1 [email protected], Tel. +213 (0) 699668785. Fax. +213 (0) 36611211.

Abstract—To ensure the cost effectiveness of photovoltaic power plants (PVPPs) it is needed to keep the level of yearly energy production as high as possible. In this context, efficiency and availability of a PVPP have to be checked continuously. The section of a PVPP which deserves more attention is surely the PV array, where many fault conditions can happen (shading, by-pass diode faults, cable interruptions, and so on). A diagnostic tool to detect faults in the PV array is desirable, even if its implementation is critical owing to: the fluctuation of the operating conditions (mainly irradiance), which complicates the instantaneous response investigation and costs and implementation constraints to implement a distributed (at PV module level) or semi-distributed (at string level) monitoring/diagnostic system. Particularly, for BIPV systems, further constraints related to the regular access for inspection and maintenance operations have to be considered. In this paper, the procedure adopted to develop and validate a diagnostic tool can be summarized in four steps: 1) using real data to model the PV array; 2) introducing several fault scenarios on the real PV string and analyzing the relative modifications of the I-V curves; 3) assessment of the meaningful parameters useful to discern the different faults by means of a PV generator (PVG) simulator based on a metaheuristic technique denominated ABC-DE; 4) proposition of several fault signing tables to assess the PV plant fault diagnostic. Keywords—Photovoltaic system; BIPV; Fault diagnostic; One-diode circuit; Metaheuristic model; Bypass diode; Shading. 1. Introduction A total ground floor area over 22,000 km2, 40% of all building roofs and 15% of all facades in the European Union are suited for PV applications. In terms of power and energy, this means that over 1,500 GWp of installed PV plants and about 1,400 TWh of yearly production, it would represent 40% of the total European electricity demand by 2020 [1]. The development of a solar energy planning system to predict the potential of solar technology, specifically photovoltaic, is necessary for the optimization of energy efficiency strategies and its integration in urban and sub-urban areas. Especially Geographic Information Systems (GIS) can be used to exploit the real available rooftop area for PV deployment in specific areas and contexts [2]. Of course, the deployment of favorable conditions across Europe will support a wide BIPV applications extension. From 2012 onwards, all member States will need to adopt the recently approved Energy Performance of Building Directive (EPBD) establishing that by 2020, all new building will need to be Nearly Zero Energy Buildings. Quite often the PV modules are installed on top of the existing building structure and do not provide any additional function. That acknowledges the added effort and the extra cost of integrating PV as part of the building envelope. BIPV systems present significant challenges with respect to energy efficiency, reliability and availability of PV arrays. In such systems, the PV panels replace roof

tops, and other building components such as windows. Due to their diverse locations and orientations, influence of numerous environmental factors can significantly reduce the performance and overall efficiency rendering the BIPV system economically infeasible. On the other hand, a deep performance investigation should be carried out by the manufactures and the researchers to reduce the PV system weak points and to make it strong against the inherent anomaly situations. The feasible solutions to reach an effective integration are very different and technically advanced. As a matter of fact, many research centers and universities are actively involved as stated by the systems proposed in the Solar Decathlon Europe houses [3]. BIPV systems show important differences respect to large ground-mounted PV plants: 

Rated power is usually from some kW to tens of kW.



They differ from one to another by: size, components, orientation and tilt angles and, topology.



They work under different operating conditions that vary from one installation to another, both in space and in time.



Energy output recorded by the energy meter is often the only accurate information available.

This inhomogeneity makes difficult a cost-effective procedure for monitoring, fault detection, performance analyses, operation and maintenance. As a result, many problems affecting BIPV systems go undetected. A recent review of a 10,000 residential PV systems performance in France and Belgium draw the conclusions that, on average, the performance of a PV system is 15% lower than what could be achieved [4,5]. These studies have identified and quantified the main causes explaining the performance losses, and they have drawn a general picture of the state of the art. The PVG power is well known by its fluctuating aspect, because it depends notably on the irradiance level which makes the fault diagnosis process more complicated. Notably to distinguish the causality between the PV system output and the arising defects instantaneously. In addition, the extracted data from the PVG are not quite enough to ensure a precise fault detection and localization since its output similarity at normal and abnormal conditions towards the permanent irradiance variation, and the constraint of obtaining the output of each PV cell separately and simultaneously. Different fault diagnosis techniques were proposed in the literature. Almost all of them are based on a comparison between the measured and the simulated data taking either from a validated simulation model or reference data established by experience. They vary according to: the employed outfit, the required measurement data, the signalized defects, the technique robustness, the implementation feasibility, the computational technique, the equipment cost, and so on. There are some fault diagnosis techniques which use sophisticated tools [6-10], such as: Infrared Thermography (IR) Thermoreflectance Imaging (TR), Electroluminescence (EL) and Photoluminescence (PL) to detect especially the hot spot and the shunts defects. In [11], the authors have proposed a crack detection and analysis procedure by using resonance ultrasonic vibrations. Satellite climatic data were utilized to monitor the PV system to detect some defects owing to the snow [12,13]. Other techniques are not based on sophisticated tools, they use classical or modern evaluation approaches to perform the fault diagnosis procedure such as the proposed technique in [14] to define the number of open and short circuited PV modules in one PV string at normal irradiance incidence, and in the case of shading occurrence [15]. Some procedures of monitoring and fault detection are based on power losses evaluation by including several reference factors [16-19]. In [20] the authors have presented a technique based on the earth capacitance measurement (ECM) to locate the disconnected module, and the time domain reflectometry to detect the degraded module(s). A technique differentiate between the series and parallel

PVG arc faults is proposed [21,22]. Fourier series were also proposed in [23] for the same purposes. In [2426] the developed fault diagnosis procedure is based on the model parameters variation, notably the MPP values (Impp ; Vmpp ; Pmpp) and series resistance (Rs). An extension theory based fault diagnosis method to detect a faulty PV module in several branches developed by a PSIM based model is proposed in [27]. Besides, another technique based on the extension theory to detect the number of failed modules is proposed in [28]. Afterwards, a modified neural network based on Solar Pro software model [29], and other approaches using the artificial neural network (ANN) [30,31] and fuzzy logic [32] are proposed for the same purposes. In [33,34] the authors have suggested a fault detection algorithm based on inferential and robust statistics to locate the defected modules. In [35] the authors propose a technique based on three different outlier rules to perform a fault diagnosis tool. As actually, there are a new generation of PV inverters which allow to get a full or partial I-V curve [3638]. Many diagnostic techniques are based on I-V curve analysis to get more accurate results [39-43]. In this paper the proposed fault diagnosis technique is based on the evaluation of the parameters that characterize the I-V curves of a PVG; the parameter extraction from the measured I-V curves is performed by means of a metaheuristic technique, based on ABC-DE algorithm [44]. From that, it is possible to generate simulated I-V curves at whatever normal conditions or under specific fault conditions, such as:    

total and partial shading; by-pass diode defects; connection line defects; short circuited sub-strings.

The proposed PVG fault diagnosis procedure is based on look-up tables developed experimentally to get more feasible results. This paper is organized as follows: section. II the proposed ABC-DE parameter extraction algorithm is described; section. III, the experimental validation results of the proposed PVG emulator at both normal and abnormal operating conditions are reported; section. IV, the proposed PVG fault diagnosis technique is detailed. Finally, section. V draws the conclusions and the perspectives. 2. PV array modeling and parameter extraction To get jointly meaningful parameters and less computation time, the PVG one-diode model will be adopted, the equivalent electrical circuit is shown in Fig. 1, whereas the relative implicit equation is Eq. (1). . V−I∙Rs

I = Iph − I0 ∙ (exp ( η∙V

tm

) − 1) −

V−I∙Rs Rsh





This model is characterized by five parameters : Iph (light or photo-generated current) represents the charge carrier generation in the semiconductor layer of the PV cell caused by the incident radiation, Rsh (shunt resistance) expresses the losses due to the high-current path through the semiconductor throughout the mechanical defects and the leakage current to the ground, Rs (series resistance) represents the internal losses due to current flow and the connection between cells, I0 or Isat (diode's reverse-bias saturation current) and η (diode ideality factor). Where, the thermal module voltage (Vtm= T . Ns . kb/q), cells temperature (T), electron charge (q= 1.602 10-19 C), Boltzman’s constant (kb = 1.381 10-23 J/K), solar cell number in series (Ns) are known parameters. 2. 1.

PV array modeling and ABC-DE technique

The one diode model requires the extraction of five unknown parameters which vary according to the operating conditions (e.g. incident irradiance and PV cells temperature). Among the different techniques proposed in literature to calculate such parameters, in this paper, the used technique is inspired by the foraging behavior of a bee swarm to search honey sources. Specifically it combines ABCO (Artificial Bee Colony Optimization) technique [45] and DE (Differential Evolution) [46] to find a good comprise between the convergence speed to reach the global optimum and the final result accuracy. Each honey source is considered as a multi-dimensional position. After the first navigation, the bees return to their hive from the discovered honey sources, they share their reports towards the honey sources quality, where the best source is that one with the best honey's quality found [44]. To well cover the D-dimensional search space in way to reach as quick as possible the global optimum and to reduce the possibility of tracing the wrong ways, the bees are initialized by Eq.(2) and Eq.(3) according to the population size (NI), the search range [Xmin, Xmax], and the maximum iterations number (jmax). 𝐵𝑖𝑎 = 𝑋𝑚𝑖𝑛 + 𝑟𝑑 ( 𝑋𝑚𝑎𝑥 − 𝑋𝑚𝑖𝑛 )





𝐵𝑖𝑏 = 𝑋𝑚𝑖𝑛 + ( 𝑋𝑚𝑎𝑥 − 𝐵𝑖𝑎 )





where, 𝐵𝑖𝑎 and 𝐵𝑖𝑏 represent the honey sources discovered by a and b bees group, Eqs.(2,3) are representing two random generations 𝐵𝑖𝑎 a and 𝐵𝑖𝑏 , respectively, they represent a group of a random parameter extracted vector, in order to select the adopted initial generation.𝑟𝑑 is a random number between 0 and 1. After the evaluation of the objective function (J) for both position vector bee's group 𝐵𝑖𝑎 and 𝐵𝑖𝑏 . These vectors will be ranked and selected to get the initial population. After, they will be classified according to the honey sources discovered into two groups, namely, leaders and scouts. Based on the report of the leaders, the scouts abandon their positions and try to discover other honey sources with a better quality. The best quality means the smallest objective function in our optimization problem. Once returning in the hive, the leaders share their reports with the scouts. The role of each bee will be adjusted then based on the probability factor, 𝑃𝑟𝑖 , calculated by using Eq. (4), the bees with smallest probability factor will be considered as leaders, while the rest of swarm as scouts. 𝑃𝑟𝑖 = 𝐹(𝐵𝑖 )/ ∑𝑁𝐼 𝑖=1 𝐹(𝐵𝑖 )



As much the probability factor is small as the 𝑖 th source position is the best one,𝐵𝑖 is the honey source position reached by the 𝑖 th bee and 𝐹(𝐵𝑖 ) is the objective function of the corresponding bee's honey source quality discovered. Afterwards, the new leaders share their reports with the new scouts for leading them to follow their strategy in way to exploit the discovered honey sources, the first leader guides the last scout and so on, this procedure is called the report exchange, Eq. (5). While, k expresses the dimension level selected randomly. 𝑘 𝐵𝑛𝑘 = 𝐵(𝑁𝐼−𝑛)+1 





Inspired from the mutation report of the 𝑖 th bee, Mui , expresses the research strategy of each bee to find hives based on the other bees reports, Eq. (6). 𝑀𝑢𝑖 = 𝐵𝑔 + 𝑄𝑘𝑖 ∙ (𝐵ℎ1 − 𝐵ℎ2 ) + 𝑄𝑘𝑖 ∙ (𝐵ℎ3 − 𝐵ℎ4 )



where, ℎ1 , ℎ2 , ℎ3 and ℎ4 are indices of the swarm bees different from 𝑖. While, 𝐵ℎ1 , 𝐵ℎ2, 𝐵ℎ3 and 𝐵ℎ4 are their corresponding honey sources discovered. 𝑄𝑘𝑖 is a random number between -1 and 1. And, 𝐵𝑔 is the best honey source already found by all the swarm. The mutation report is evaluated according to the best honey source already reached by the 𝑖 th bee, Eq. (7): 𝐵𝑖 = {

𝑀𝑢𝑖 𝑖𝑓 𝐹(𝑀𝑢𝑖 ) < 𝐹(𝐵𝑖 )  𝐵𝑖 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒





Moreover, the best swarm source discovered is selected by Eq. (8): 𝐵𝑔 = { 2. 2.

𝑀𝑢𝑖 𝐵𝑔

𝑖𝑓 𝐹(𝑀𝑢𝑖 ) < 𝐹(𝐵𝑔 )  𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒



ABC-DE based parameter extraction

The 𝐵𝑔 honey source represents the PVG model extracted parameters with D-dimensional position vector. D is equal to five, it refers to the unknown parameter extracted number of one-diode PVG model. The objective function is expressed on RMSE (Root Mean Square Error) calculated by Eq. (9) and Eq. (10), respectively. Where, the best honey source quality is the one with the smallest objective function, its honey source position represents the optimal PVG model extracted parameters. min 𝐽 = √S

1 max

max ∑ss=1 𝑓(θ, Is , Vs )2 

Vs −Is ∙Rs

𝑓(θ, Is , Vs ) = Is − (Iph − I0 ∙ (exp (

η∙Vtm

 ) − 1) −

Vs −Is ∙Rs Rsh

 )



where, smax and are, respectively, the maximum number of curve sample data and the sample data index. The flowchart of the based parameter extraction algorithm is presented in Fig. 2, where nr represents the maximum repeated number of the objective function, it is equal to 15. 3.

PVG Matlab/Simulink modeling and experimental validation

In this study, the PV array is formed by a string with three Polycrystalline PV modules (CLS-220P by CHINALIGHT Solar Co) series connected. Each PV module contains 60 series connected PV cells gathered into three sub-strings, each sub-string is constituted by 20 PV cells and connected in anti-parallel with a bypass diode. The experimental setup (PV string; electronic load and acquisition system) has been installed in the power system laboratory at the DIEEI Department of Catania University (Italy); specifically, the PV string with its sensors, it has been positioned on the terrace of DIEEI laboratory building (Fig. 3) and the data acquisition card, electronic load and PC computer in the laboratory (just above the terrace). The experimental setup used to extract the I-V curves is illustrated in Fig. 4, and it is composed by the following elements: Sensors: 1) Spektron 300 by TRITEC is a silicon sensor (sensor accuracy ±5 % annual mean), it is installed at the side of the PV modules and used for measuring the solar irradiation on the PV modules plane G(W/m2). 2) Pt1000 is the PV module temperature sensor, T(°k). It is installed on the back surface (made by Tedlar) of the central module of the PV string.

NI DAQ-P 6015 is the data acquisition module and it is used to acquire the temperature (T) and the irradiance (G) measures. Then, the electronic load Agilent N3300 is used to acquire the current and voltage values by means of a program developed in LabVIEW environment that controls a DC electronic load in such a way to span the voltage in a given interval, from short circuit (sc) operating point to open circuit (oc) point. Each measurement cycle (time step) lasted 30s by including I–V curve acquisition, modules temperature and irradiance measurement. It is preferable to treat each PV cell or at least each PV sub-string alone to get more efficient measurement, so we allot for each sub-string, each own : current, voltage, temperature and irradiance sensors. However, this is not feasible due to economical constraints. Matlab/Simulink/SPS has been used to emulate the electrical behavior of the used PVG. The model is made by 9 parts (3 sub-strings by 3 modules), each one is connected in anti-parallel with a by-pass diode (Fig. 5). Resistors have been introduced among the sub-strings to model the defect of connection cables. So, the basic element in the proposed numerical model is one sub-string (Fig. 6), and one PV module is made of three sub-strings, see the dashed rectangle in Fig. 5. The PVG emulation procedure is based on measurement data. To get a reasonable accuracy, many I-V curves at several G and T values in normal condition have been measured. The meaningful step is to realize a look-up table containing the model parameter sets at representative PVG normal operating conditions. From practical point of view of the diagnostic algorithm, it is crucial to perform a such I-V curves measurements just after the PVG installation (no aging effects) and under stable and normal operating conditions (no faults), in this way it is pretty sure that the measurements refers to an efficient PVG system. Actually, outdoor I-V curves measurements are affected by some disturbances (e.g. transient shadings), so data filtering process has to be applied. On this respect, only the measured I-V curves characterized by negative current gradients (∂I(V)/∂V<0) are considered as valid data and stored. This condition insures that the I-V curve shape is similar to the one given from the manufacturer at STC. After this filtering process, 690 I-V curves have been considered valid. Fig.7 shows three graphs corresponding respectively to the maximum value of the gradient for each I-V curve (top graph), the correspondent measured irradiance values and the correspondent module temperature values are sorted from the high irradiance value to the low one. The graph on the top of Fig. 7 shows that the max(∂I/∂V) values of the selected I-V curves are always negative. According to the same sorting order, Fig. 8 shows five graphs corresponding to the five extracted parameters of the PV string I-V curves: Iph, Rsh, Rs, Isat and . These parameters will be used in the developed Matlab/Simulink/SPS model at sub-string level to get the simulated I-V curves. In fact, according to the measured value of irradiance and PVG temperature, the developed algorithm will select the closest G and T values from the look-up table. The precision level of the I-V curve parameters selection in this table is related to the installed sensors precision in the PVG, specifically: G is ±5 W/m2 and T is ±2 Kelvin. Table. 1 shows complete sets of information about fifteen I-V curves selected among the 690 I-V curves. They have been selected in such a way to bring more precise idea of the values assumed by the five extracted parameters at different operating conditions. The set of information for each I-V curve is completed with the operating conditions (G and T) and the electrical variables values at maximum power point (MPP), specifically: current (Impp), voltage (Vmpp) and power (Pmpp). To check the adopted model precision for a PV module (one-diode model), the entire set of the I-V curves has been simulated. Specifically, for each I-V curve, the five parameters has been introduced in Eq.(1) and the I-V curve is traced. Fig. 9 shows the absolute error between the measured and the simulated values of

Vmpp, Impp, Pmpp, and Isc sorted according to G values shown in Fig. 7. It is worth noting that for all variables the errors are negligible. Fig. 10 illustrates five measured I-V and P-V curves with the simulated ones of the PV string under normal operating conditions. The five curves refer to low (two curves), medium (one curve) and high (two curves) level of irradiance. The precision of the one diode model parameters evaluation process and the chosen model does not appear affected by the level of irradiance. After this first set of tests, the PVG model has been verified under fault conditions. Fig. 11 and Fig. 12 show different measured and simulated I-V curves at partial shading conditions whose patterns are graphically described in Fig. 13 and defined here in after: “A” :G = 569 W/m2 and T = 318 K, two sub-strings of different PV modules are totally shaded. “B”: G = 827 W/m2 and T = 322 K, three cells of different sub-strings are totally shaded. “C” : G = 684 W/m2 and T = 319 K, the vertical half of each module is totally shaded. “D” :G = 839 W/m2 and T = 326 K, PV string is exposed to a partial shading pattern that resembles the railing which closes the building terrace of the laboratory. “E”: G = 764 W/m2 and T = 329 K, similar shading condition in “D”. Fig. 14 shows two I-V curves in case of connection line defects, these cases were realized by connecting a rheostat in series with the PVG.

The second step of PVG model testing under fault conditions has proved the effectiveness of the simulating approach. As matter of fact, the errors among simulated and measured I-V curves are still low. Of course, in reality, the shading patterns can be different compared to the one reported in Fig. 13. But based on the already obtained results whatever shading scenario can be modeled. So many simulations have been performed; two examples of simulated I-V/P-V curves, corresponding to the shading patterns described in Table. 2 and Table. 3, are reported in Fig. 15. By-pass diodes role is important to protect the PVG against malfunctioning, when the voltage operates near to breakdown value owing to mismatch defect. Meanwhile, during the PVG operation, it is possible that the by-pass diodes crack and so it behaves as a resistive impedance thus causing a critical power reduction according to the resistance values (Rbd). To analyze the impact on peak power of PVG when these kind of defect happens, many simulations have been performed considering Rbd equal to 0.1 Ω, 0.5 Ω, 1 Ω, 2 Ω, 5 Ω, 10 Ω or 20 Ω with different G and T values. The I-V/P-V curves are shown in Fig. 16. Connection lines could train a certain resistance (Rc) owing to the increasing of localized or distributed resistance cables due to for example oxidation at high temperature or loosening of connections. Thus engendering a relevant power reduction as it is illustrated in Fig. 17. The multi faulty scenarios are really difficult to be diagnosed, that is when several defects happen at the same time. Fig. 18 shows some I-V curves and their corresponding P-V curves in case of simultaneously defects appearance (partial shading, connection lines and by-pass diode defects). Fig. 19 shows three scenarios of measured and simulated I-V curves by using ABC-DE extraction technique under the following conditions: "1" : Measured I-V curve at the presence of connection line defect. Where, Rc = 2.4 Ω, under G = 818 W/m2 and T =323 K. The correspondent RMSE is 0.056.

"2" : Measured I-V curve without defect under G = 831 W/m2 and T = 324 K. The correspondent RMSE is 0.0096. "3" : Measured I-V curve at the presence of partial shading defect under G = 748 W/m2 and T = 322 K. The correspondent RMSE is 1.57. 4. PVG Fault Diagnosis Technique The adopted fault diagnosis approach is based on the development of a look-up table containing several reference parameters extracted from measured I-V curves at normal operating conditions. Gradient (∂I/∂V) and hessian (∂2I/∂V2) functions are used not only to check the quality of the extracted I-V curves but also to indicate, mainly, the occurrence of shading defects. The reference I-V curves (based on ABC-DE parameters extraction technique) furnish a precise idea about the presence of shading faults. In fact, at normal operating conditions, the RMSE between measured and simulated I-V curves (in the following, such parameter is named Err) is lower than 0.06 (see Fig. 19), whereas, in case of partial shading scenarios, Err values are higher than 0.2. Among the several shading scenarios that can happen, we have considered four shading events to cover the most likely shading scenarios. These scenarios are defined by the percentage of PV cell(s) area shaded in a sub-string; they are: a) Partial shading of around 25%. b) Partial shading of around 50%. c) Partial shading of around 75%. d) Total or quasi-total shading. For example in case a), partial shading of around 25% , it means that 25% of the surface of one or more PV cells in a sub-string is shaded. In fact, due to the series connection of the PV cells in a sub-string, the effect is the same, that is, a 25% reduction of short circuit current, Isc, of the sub-string. For connectors and by-pass diodes defects, Err is not so meaningful. As it does not exceed 0.1, and this value is close to Err under normal operating conditions. For this reason, other significant parameters have to be used, they are: Redp is the percentage of maximum power point reduction referred to the system under the same operating conditions; Qmax_d2I is the I-V curve maximum hessian value, max(∂2I/∂V2); Qmax_d2P is the P-V curve maximum hessian value, max(∂2P/∂V2); α is the arctan(Err/G). Other parameters are related to the relevant points and parameters in a I-V curve, such as: Vmpp, Impp, Iph, Rs and Rsh. All these parameters are referred to the correspondent reference values. Using the following notation, 𝑋 𝜑𝑥 = 𝑋 , the following list of fault parameters is reported: φmax_d2I, φmax_d2P, φVmpp, φPmpp, φPmpp, φImpp, φPmpp, 𝑟𝑒𝑓

φIph, φRs, φRsh. For by-pass diode defects, the following five scenarios are considered: e) IIn stat of resistance Rbd into [0.5 Ω, 5 Ω]; f) In stat of resistance Rbd< 5 Ω; g) Reverse biased; h) Short circuit.

Where, Rbd represents the resistance value of the by-pass diode under defect. Under the same considerations, when connector defects are considered, Rc takes place of Rbd. After performing several parameters evaluation tests under faults, three fault signing tables S1, S2 and S3 have been built; they are reported, respectively, in Table 4, Table 5 and Table 6. All considered fault cases are reported in the column named scenarios. They contain more than 90 defect scenarios, and they are divided according to the diagnosis parameters similarity. In particular, the fault signing table S4, Table 7, indicates the defects when the power reduction is higher than 90%. In these tables, values smaller than 0.01 are rounded to 0, and a tolerance error of ±2% for the power reduction value is considered. Sbx and Bdx indicate, respectively, how many sub-string and by-pass diode are involved in the fault. Specifically, the indices x, that varies between 1 to 9 indicates the number of defected components; for example, Bd5 means that five by-pass diodes are faulty. The symbols Sbx indicates the number of sub-strings involved; for example, Sb1 indicates one sub-string, Sb2 indicates two sub-strings involved. The sub-strings involved can belong to different modules. Thus, in S1, if the calculated diagnosis parameters belong to the scenario b) Sb2, in Table4, it indicates the presence of 50% partial shading in two sub-strings. Or, the scenario d) Sb4 indicates a total or almost total shading in four sub-strings. In table S2 (Table 5), there are 40 by-pass diode defects, according to the number and resistance of involved by-pass diodes. For example in scenario e), in stat of resistance Rbd is lower than 0.5 Ω, Bb2 indicates two by-pass diodes involved. Therefore, if the calculated diagnosis parameters, for example, fill into the category g) Bd3 or f) Bd7, they indicates, respectively, that three by-pass diodes are in defect, each one of them is in stat of resistance (Rbd) higher than 5 Ω, or seven by-pass diodes are in defect, each one of them is in stat of resistance between 0.5 Ω and 5 Ω. If the parameters fill into the category h) Bd4 or i) Bd7, it means respectively that four by-pass diodes are reverse biased, or seven by-pass diodes are short circuited. In table S3 (Table 6) 23 likely defects are reported, it concerns the sub-strings connection defects, all bypass diodes (Bb9) defect, all sub-strings shading (Sb9) defect and connection lines defect (Cc). For example, if the diagnosis parameters fill into the category g) Cc or i) Sb7. It means that, respectively, connection cable is in defect, and it behaves as a resistance (Rc) higher than 5 Ω, or seven sub-strings are short circuited. According to our tests, at maximum we can get three reverse biased sub-strings, otherwise the power is null. Signal S1 = 1 means that the calculated diagnosis parameters fill in one of the fault signing table S1 categories, and it is equal to 0 otherwise. It is the same for signal S2 and S3. Fig. 20 shows the PVG fault diagnosis flowchart, after calculation of the appropriate diagnosis parameters by using ABC-DE parameter extraction technique, else it is equal to 0. The principle of this technique is to assess the measured I-V curve parameters by looking to the reference ones. So, the first step, after the parameter extraction of the measured I-V curve, is to evaluate the power reduction percentage by referring to the look-up table. When the power reduction is higher than 5%, we have to look if the current and power hessian are higher than 0 or not, in such a way to see if there are several peak points owing to partial shading defect. For that, fault signing table S1 indicates the arising of partial or total shading defect scenario. The most significant parameters in table S1, after the power reduction parameter (Redp), are Err and α because they well express the difference between the reference I-V curve and the shaded one under the same conditions. These parameters are used to locate the shaded parts. Fault signing table S4 describes a certain

defects possibility when Redp is higher than 90% and when the fault signing tables signals S1, S2 and S3 are not true (=0). By-pass diodes disconnection is a critical defect especially at the arising of mismatch or partial shading defect, while it is difficult to detect it because it does not cause any power reduction at normal PVG operation, in contrast we can observe a small power rise (it depends on the output power of the PVG), in our case it is about 1% to 2% due to the by-pass diode resistance absence. It is likely that the cells degradation could be detected by looking to Rs and Rsh diagnosis parameters variation (φRs>1, φRp>1) at similar environmental conditions and for a long time. MPPT defect could be detected by taking the DC power value at the DC/DC power converter bus, then according to the conversion efficiency of the DC/DC converter and the MPPT algorithm implemented we can deduce a possible defect at this level. According to our investigation it is preferable to apply this fault diagnosis technique at an irradiance level higher than 600W/m2, to get an effective results due to the presence of diffuse and reflected irradiance which could distort the reduction power percentage at about 5% when looking to the tables S1, S2 and S3 at low level of irradiance (less than 300W/m2). The tables S1, S2 and S3 could be generated for another PVG configuration by introducing the parts number which is in our case equal to nine. It is possible to detect a partial shading in the case of multiple arising defects simultaneously by looking to the maximum value of current and power hessian (φmax_d2I> 0, φmax_d2P>0), thus the first thing to do is removing the shading defect then restart the fault diagnosis procedure. As the experimental PVG is composed of nine sub-strings, after several investigations, we have made the decision to take 5% of error tolerance at maximum, because of the PVG behavior high fluctuation towards the irradiance variation and the following causes: 

temperature and irradiance sensors tolerance error (at minimum, it is about ±1%);



difference of the intrinsic cells proprieties as given by the manufacturer;



supposition that all the sub-strings have the same electrical behavior under normal operating condition in simulation model.

Indeed, it is difficult to assess the exact shading percentage with only one irradiance sensor, otherwise it becomes costly. In this fault diagnostic technique, in the case of partial shading defect; we consider only four options (25%, 50%, 75% and total shading), due to the high difficulty to assess the exact shading percentage on all the PVG. For example : at an irradiance level of 965W/m2 and PV cells temperature equal to 322K, the maximum power (Pmpp) at normal operating conditions is equal to 554W. In the case of partial shading defect in four sub-strings (Sb4) of approximately 75%, the power reduction is about 48% (266W). Then, we have to admit the possibility to tolerate an error of ±5% owing to the causes mentioned above, so the power could be 288W ±14W. Looking to the simulation development procedure and the lookup tables, it is highly possible to generalize the fault diagnosis technique for other PV systems. Of course, the crucial point is to perform I-V curves measurements at normal operating conditions. Then, the developed simulator has to be modified according to the new PV system configuration (mainly, number of PVG parts related to the number of connected by-pass diodes). Finally, the fault diagnosis parameters have to be set according to the sensors precision we can assess. 5. Conclusion and Perspectives

The diagnostic method, proposed in this paper, is based on the knowledge of PV generator model parameters from measured I-V curves. This method has been checked experimentally on a PV string of three modules series connected. According to the illustrated results, the proposed PVG emulator could be used as a fault diagnosis tool since it is able to generate very precise I-V curves of the string in whatever operating conditions. In fact, the I-V curves measured and simulated, under normal and abnormal operating conditions, have shown very small RMSE values (< 0.02) and absolute Pmpp errors lower than 0.6. The main contribution in this paper is the development of an experimentally validated PV emulator able to simulate the real PVG behavior notably under faulty conditions. Indeed, the development of several fault signing tables based on many tests under different operating conditions. A reliable assessment to exactly evaluate and localize the shading level on the PVG surface is desirable but some problems limit its full development: -

economical, design and installation issues to use distribute irradiance and temperature sensors;

-

quick variation of irradiance, especially in cloudy and wind ambient operating conditions;

-

irradiance and temperature sensors precision;

-

use of a semi-distributed measurement system, at string level.

The proposed method can have a large application due to the fact that, nowadays, the manufacturers of PV inverters are introducing in their inverters new and advanced functions (e.g. sweep function) that allow to trace, periodically or on demand, the I-V curve of the connected PV array. It means that both the initial characterization of the strings and the on-line measurements of the I-V curves under fault conditions are possible. In this paper, the experiments have been done with the PVG connected to an electronic load. On the other hand, in a real situation, when the PVG is connection to a PV inverter, dynamic conditions are involved due to the presence of maximum power point tracking function. So to limit the impact of on line I-V curves measurements, it is possible to use partial I-V curves (from Vmpp/2 to Voc) to model adequately the PVG. To increase the PV systems efficiency, especially for BIPVs, a centralized inverter with separated DC MPPT inputs or string inverters are used. It means that the level of diagnostic analysis can be limited to a single string, that is the approach of this paper. Finally, the proposed fault diagnosis tool could be further developed to include also other defects such as: temperature mismatch and ground faults. References [1]EPIA report : Set for 2020, Solar Photovoltaic Electricity : A mainstream power source in Europe by 2020. 2009. [2]A. Gagliano, F. Patania, F. Nocera, A. Capizzi, A. Galesi, GIS-based decision support for solar photovoltaic planning in urban environment, Sustainability in Energy and Buildings. Smart Innovation, Systems and Technologies. 22 (2013) 865–874. [3]J. Cronemberger, M.A. Corpas, I. Ceron, E.Caamano-Martin, S.V. Sanchez, BIPV technology application: Highlighting advances, tendencies and solutions through Solar Decathlon Europe houses, Energy and Buildings. 83 (2014) 44–56. [4]J. Leloux, L. Narvarte, D. Trebosc, Review of the performance of residential PV systems in Belgium, Renewable and Sustainable Energy Reviews, 16 (2012) 1369– 1376. [5]J. Leloux, L. Narvarte, D. Trebosc, Review of the performance of residential PV systems in France, Renewable and Sustainable Energy Reviews, 16 (2012) 178–184.

[6]M.A. Munoz, M.C. Alonso-Garcia, N. Vela, F. Chenlo, Early degradation of silicon PV modules and guaranty conditions, Solar Energy. 85 (2011) 2264–2274. [7]Cl. Buerhop, D. Schlegel, M. Niess, C. Vodermayer, Reliability of IR-imaging of PV-plants under operating conditions, Solar Energy Material & Solar Cells. 107 (2012) 154–164. [8]Y. Hu, W. Cao, J. Ma, S. J. Finney, and D. Li, Identifying PV module mismatch faults by a thermography-based temperature distribution analysis, IEEE Trans. Device Mater. Rel., vol. 14, no. 4 (2014) 951–960. [9]Y. Hu, W. Cao, J. Wu, B. Ji, and D. Holliday, Thermography-based virtual MPPT scheme for improving PV energy efficiency at partial shading conditions, IEEE Trans. Power Electron., vol. 29, no. 11 (2014) 5667–5672. [10] Z. Zou, Y. Hu, B. Gao, W. L. Woo, and X. Zhao, Study of the gradual change phenomenon in the infrared image when monitoring photovoltaic array, J. Appl. Phys., vol. 115, no. 4 (2014) (043522)1– (043522)11. [11] Belyaev, O. Polupan, W. Dallas, S. Ostapenko, D. Hess,Crack detection and analyses using resonance ultrasonic vibrations in full-size crystalline silicon wafers, Applied Physics Letters. 88 (2006) 11907:1–3. [12] A. Drews, A.C. de Keizer, H.G. Beyer, E. Lorenz, W.G.J.H.M. van Sark, W. Heydenreich, E. Wiemken, P. Toggweiler, S. Bofinger, M. Schneider, G. Heilscher, J. Betcke, S. Stettler, D. Heinemann, Monitoring and remote failure detection of grid-connected PV systems based on satellite observations, Solar Energy. 81 (2007) 548–564. [13] G. Wirth, M. Schroedter-Homscheidt, M. Zehner, G. Becker, atellite-based snow identification and its impact on monitoring photovoltaic systems, Solar Energy. 84, (2010) 215–226. [14] N. Gokmen, E. Karatepe, B. Celik, S. Silvestre, Simple diagnostic approach for determining of faulted PV modules in string based PV arrays,” Solar Energy. 86 (2012) 3364–3377. [15] N. Gokmen, E. Karatepe, S. Silvestre, B. Celik, P. Ortega, An efficient fault diagnosis method for PV systems based on operating voltage-window, Energy Conversion and Management. 73 (2013) 350–360. [16] A. Chouder, S. Silvestre, Automatic supervision and fault detection of PV systems based on power losses analysis, Energy Conversion and Management. 51 (2010) 1929–1937. [17] S.K. Firth, K.J. Lomas, S.J. Rees, A simple model of PV system performance and its use in fault detection, Solar Enery, 84, (2010) 624–635. [18] S. Silvestre, A. Chouder, E. Karatepe, Automatic fault detection in grid connected PV systems, Solar Energy. 94, (2013) 119–127. [19] W. Chine, A. Mellit, A. MassiPavan, S.A. Kalogirou, Fault detection method for gridconnected photovoltaic plants, Renewable Energy. 66, (2014) 99–110. [20] T. Takashima, J. Yamaguchi, K. Otani, T. Oozeki, K. Kato, M. Ishida, Experimental studies of fault location in PV module strings, Solar Energy Material & Solar Cells. 93, (2009) 1079–1082. [21] C. Strobl, P. Meckler, Arc faults in photovoltaic systems, Proceedings of the 56th IEEE Holm Conference on Electrical Contacts. (2010) 1–7. [22] J. Jolmson, M. Montoya, S. McCalmont, G. Katzir, F. Fuks, Differentiating Series and Parallel Photovoltaic Arc-Faults, 38th IEEE Photovoltaic Specialists Conference , Austin, TX. (2012) 720–726. [23] J. Johnson, S. Kuszmaul, W. Bower, D. Schoenwald, Using PV module and line frequency response data to create robust arc fault detectors. In Proceedings of the 26th European Photovoltaic Solar Energy Conference and Exhibition, 05–09 September, Hamburg, Germany. (2011) 3745–50.

[24] Y. Hu, B. Gao, X. Song, G. Y. Tian, K. Li, X. He, Photovoltaic fault detection using a parameter based model, Solar Energy. 96, (2013) 96–102. [25] J. Solórzano, M.A. Egido, Automatic fault diagnosis in PV systems with distributed MPPT, Energy Conversion and Management. 76 (2013) 925–934. [26] J.D. Bastidas-Rodríguez, E. Franco, G. Petrone, C.A. Ramos-Paja, G. Spagnuolo, ModelBased Degradation Analysis of Photovoltaic Modules Through Series Resistance Estimation, IEEE Trans. ON INDUSTRIAL ELECTRONICS. Vol.62, No.11 (2015) 7256–7265. [27] K.H. Chao, S.H. Ho, M.H. Wang, Modeling and fault diagnosis of a photovoltaic system, Electric Power Systems Research. 78, (2008) 97–105. [28] M.H. Wang, A Novel Extension Decision-Making Method for Selecting Solar Power Systems, Hindawi Publishing Corporation International Journal of Photoenergy. ID 108981 (2013) 6. [29] K.H. Chao, C.T. Chen, M.H. Wang, C.F. Wu, A Novel Fault Diagnosis Method Based-on Modified Neural Networks for Photovoltaic Systems, Advances in Swarm Intelligence. Lecture Notes in Computer Science. 6146 (2010) 531–539. [30] S. Syafaruddin, E. Karatepe, T. Hiyama, Controlling of Artificial Neural Network for Fault Diagnosis of Photovoltaic Array, International Conference on Intelligent System Application to Power Systems. (2011) 1–6. [31] Z. Li, Y. Wang, D. Zhou, C. Wu, An Intelligent Method for Fault Diagnosis in Photovoltaic Array, System Simulation and Scientific Computing Communications in Computer and Information Science. (2012) 10–16. [32] P. Ducange, M. Fazzolari, B. Lazzerini, F. Marcelloni, An intelligent system for detecting faults in photovoltaic fields, 11th International Conference on Intelligent Systems Design and Applications. (2011) 1341–1346. [33] S. Buddha, H. Braun, V. Krishnan, C. Tepedelenlioglu, A. Spanias, T. Yeider, T. Takehara, Signal processing for photovoltaic applications, IEEE International Conference on Emerging Signal Processing Applications, Las Vegas, USA. (2012) 115–118. [34] S. Vergura, G. Acciani, V. Amoruso, G. Patrono, F. Vacca, “Descriptive and Inferential Statistics for Supervising and Monitoring the Operation of PV Plants,” IEEE Trans. on Industrial Electronics 56, (2009) 4456–4464. [35] Y. Zhao, J.F. de Palma, J. Mosesian, Member, Jr. R. Lyons, B. Lehman, Line–Line Fault Analysis and Protection Challenges in Solar Photovoltaic Arrays, IEEE Trans. on Industrial Electronics 60 (2013) 3784–3795. [36] A. Swingler, Photovoltaic String Inverters and Shade-Tolerant Maximum Power Point Tracking: Toward Optimal Harvest Efficiency and Maximum ROI. Schneider Electric, Burnaby, Canada (2010). [37] Solar Edge, Performance of PV Topologies under Shaded Conditions, Solar Edge (2013). [38] SMA, Solar Inverters FLX Series Installation Guide SMA Solar Technology AG (2014). [39] G.M. Tina, F. Cosentino, F. Ventura, Monitoring and Diagnostics of Photovoltaic Power Plants. Renewable Energy in the Service of Mankind Vol II, ed. Ali Sayigh, Springer (2016). [40] S. Spataru, D. Sera, T. Kerekes, R. Teodorescu, Diagnostic method for photovoltaic systems based on light I–V measurements, Solar Energy. 119 (2015) 29–44. [41] Y. Hu, J. Zhang, W. Cao, J. Wu, G.Y. Tian, S.J. Finney, J.L. Kirtley, Jr., Online Two-Section PV Array Fault Diagnosis With Optimized Voltage Sensor Locations. IEEE Trans. ON INDUSTRIAL ELECTRONICS. Vol.62, No.11 (2015) 7237– 7246. [42] W. Wang, A.C. Liu, H.S. Chung, R. W. Lau, J. Zhang, A.W. Lo. Fault Diagnosis of Photovoltaic Panels Using Dynamic Current–Voltage Characteristics. IEEE Trans. On POWER ELECTRONICS. Vol. 31, No. 2. (2016) 1588–1599.

[43] S. Silvestre, S. Kichou, A. Chouder, G. Nofuentes, E. Karatepe, Analysis of current and voltage indicators in grid connected PV (photovoltaic) systems working in faulty and partial shading conditions, Energy, vol. 86, (2015) 42–50. [44] O. Hachana, K. E. Hemsas, G. M. Tina, C. Ventura, Comparison of different metaheuristic algorithms for parameter identification of photovoltaic cell/module, Journal of Renewable and Sustainable Energy 5 (2013) 053122:1–18. [45] D. Karaboga, An idea based on honey bee swarm for numerical optimization, Technical ReportTR06, Erciyes University, Engineering Faculty, Computer Engineering Department, 2005. [46] R. Storn, K. Price, Differential Evolution – A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces, Journal of Global Optimization 11 (1997) 341–359.

Fig. 1.One-diode circuit based model of PV module Start

 I-V curve extraction, search range and NI setting.  - Initialization by Eq. 2 and Eq. 3.

 Probability factors ranking and calculation by Eq. 4 to select the leaders and the scouts.

j=j+1  Reports exchange, Eq. 5.  Mutation, Eq. 6.  Evaluation, Eq. 7 and Eq. 8.

If j = jmax or F(Bg) was repeated nr time.

No

Yes Bg represents the PVG model optimal extracted parameters.

Fig. 2. Flowchart of the proposed ABC-DE based parameter extraction technique.

Fig. 3. Experimental set-up: PV module and PV string.

PT 100 String PV

Spektron 300

Transducer

Agilent N3300A

NI DAQPad6015

GPIB USB PC

Fig. 4. I-V curve measurement and extraction setup.

Fig. 5. PVG simulation model by using Matlab/Simulink/SPS.

Fig. 6. PV sub-string simulation model by using Matlab/Simulink/SPS.

Fig. 7. Maximum ∂I/∂V values of the measured I-V curves with the corresponding irradiance and cells temperature values

(a)

Iph (A)

10 7.5 5 2.5 0 0

Isat (A)

3

x 10

-6

100

200

300

400

500

600

700

600

700

(b)

2 1 0 0

100

200

300

400

500

Fig. 8. Extracted parameters by using ABC-DE technique : (a) photo-generater current,(b) reverse-bias saturation current, (c) ideality factor, (d) shunt resistance, (e) series resistence.

Current (A)

0.1

Absolute Impp error

0.05

0 0

100

200

300 400 I-V curve tests number

500

600

700

500

600

700

Current (A)

0.06 Absolute Isc error 0.04 0.02 0 0

100

200

300 400 I-V curve tests number

Power (P)

0.8

Absolute Pmpp error

0.6 0.4 0.2 0 0

100

200

300 400 I-V curve tests number

500

Voltage (V)

600

700

Absolute Vmpp error

1

0.5

0 0

100

200

300 400 I-V curve tests number

500

600

700

Fig. 9. Absolute error between the measured and the simulated Pmpp , Vmpp, Isc and Impp sorted acoording to the incidant irradiance illustrated by Fig. 7

600

10

G = 965 W/m2 , T = 322 K

500

8 7

G = 688 W/m2 , T = 322 K

400

Power (W)

9

G = 800 W/m2 , T = 322 K

450

6

350

G = 474 W/m2 , T = 317 K

300

5

250

4

200

2

G = 432 W/m , T = 318 K

Current (A)

550

3

150 2

100

1

50 0 0

20

40

60

80

100

0

Voltage (V)

Fig. 10. Measured and simulated I-V curves and the corresponding P-V curves under different measured irradiance and PV cells temperature.

Measured I-V curve of the condition "A" Simulated I-V curve of the condition "A" Measured I-V curve of the condition "B" Simulated I-V curve of the condition "B" Measured I-V curve of the condition "C" Simulated I-V curve of the condition "C"

8 7

Current (A)

6 5 4 3 2 1 0 0

10

20

30

40

50 60 Voltage (V)

70

80

90

100

Fig. 11. Measured and simulated I-V curves at “A”, “B” and “C”shading patterns. 8 7

Current (A)

6 5 4 3 2

Measured I-V curve of the condition "D" Simulated I-V curve of the condition "D" Measured I-V curve of the condition "E" Simulated I-V curve of the condition "E"

1 0 0

10

20

30

40

50 Voltage (V)

60

70

80

Fig. 12. Measured and simulated I-V curves “D” and “E” shading patterns. 90

100

Fig. 13. Graphic descriptions of shading patterns : “A”, “B”, “C”, “D”, “E” 8 7

Current (A)

6 5 Measured I-V curve with Rc = 5.2 ohm

4

Simulated I-V curve with Rc = 5.2 ohm

3

Measured I-V curve with Rc = 3.2 ohm

2

Simulated I-V curve with Rc = 3.2 ohm

1 0 0

10

20

30

40

50 60 Voltage (V)

70

80

90

100

Fig. 14. Measured and simulated I-V curves at different cases of connection lines defect.

10 250 9

2

Shaded P-V curve under G = 508 W/m and8 T = 317 K

200

2

Shaded P-V curve under G = 908 W/m and7 T = 323 K 6

150

5 4

100

Current (A)

Power (W)

2

Shaded I-V curve under G = 908 W/m and T = 323 K

3 2

50

1 20

40

60

0 100

80

Fig. 15. I-V andP-V curves under different scenarios of shading defined in Table 2 and Table 3.

Voltage (V)

500

10

450

9

400

8

Power (W)

350 300 250 200 150 100 50

7 6

I-V curve when Rbd = 10 ohm I-V curve when Rbd = 5 ohm P-Vcurve curvewhen whenRbd Rbd===110 10 ohm P-V curve when Rbd ohm I-V ohm P-V curve when when Rbd Rbd == 0.5 510ohm ohm I-V P-Vcurve curve when when Rbd Rbd == 15 ohm ohm P-V curve 5 P-V curve when Rbd = 10 ohm P-V curve when Rbd = 0.5 ohm 11 ohm P-V P-V curve curve when when Rbd Rbd == 5 ohm P-V curve when Rbd = 0.5 ohm 1 ohm P-V curve when Rbd = 0.5 ohm

0 0

20

5 4

Current (A)

0 0

3 2 1

40

60

80

0

100

Voltage (V)

Fig. 16. I-V and P-V curves under different scenarios of by-pass diode defect, where Rbd expresses the bypass diode resistance. 500

400

Power (W)

350 300 250

10

I-V curve P-V curve when when Rc Rc = = 10 10 ohm ohm I-V ohm P-Vcurve curvewhen whenRc Rc==510 ohm P-V curve when Rc ohm I-V ohm P-Vcurve curvewhen whenRc Rc===1510 5ohm ohm I-V P-V curve when Rc ==0.5 10 ohm 5 ohm P-Vcurve curvewhen whenRc Rc== P-V curve when Rc 11 ohm P-V ohm 510.5 ohm P-V curve curve when when Rc Rc == 10 ohm P-V curve when Rc = 5 1 ohm 0.5 ohm P-V curve when Rc = 10.5 ohm ohm I-V P-Vcurve curve when when Rc Rc == 0.5 0.5 ohm ohm

9 8 7 6 5

200

4

150

3

100

2

50 0 0

Current (A)

450

1 20

40

60

80

100

0

Fig. 17. I-V andP-V curves under different scenarios of connexion resistance defects, where Rc expresses the connection resistance. Voltage (V)

400

10 9

350

8 300

50 0 0

4

I-V curve, when Rbd = 1 ohm, Rc = 1 ohm and 2 Sb are totally shaded under G = 823 W/m 2 and T = 3320 K I-V curve, when Rbd = 5 ohm, Rc = 0.5 ohm and 3 Sb are totally shaded under G = 765 W/m 2 and T = 314 K P-V 2 2 P-V curve, curve, when when Rbd Rbd == 15 ohm, ohm, Rc Rc == 10.5 ohm and 3 Sb totally shaded under = 765 W/m and T2320 = 314 P-V ohm and 2 Sb areare totally shaded under GG = 823 W/m and T= KK P-V curve, when Rbd = 1 ohm, Rc = 1 ohm and 2 Sb are totally shaded under G = 823 W/m 2 and T =1 320 K 20

40

60

80

100

0

Voltage (V)

Fig. 18. I-V and P-V curves under twoscenarios of simultaneous faults Current (A)

100

5

10 5 Condition__1

0 0

Current (A)

150

Current (A)

Power (W)

6

200

Current (A)

7 250

10

20

30

40

50 60 Voltage (V)

40

50 60 Voltage (V)

70

80

90

100

70

80

90

100

10 5

Condition__2

0 0

10

20

10

30

Condition__3

5

Measured I-V curve Simulated I-V curve by using ABC-DE

0 0

10

20

30

40

50 60 Voltage (V)

70

80

90

100

Fig. 19. Measured and simulated I-V curves under different conditions.

Measured data (I-V, G, T) and Reference table introduction

No

Yes expected power calculation

IF : Red ≥ 5%

Cells degradation if

ΦRs > 1 & ΦRp < 1 If : max(∂ I/∂V ) > 0 & 2 2 max(∂ P/∂V ) > 0 2

2

IF : Red_mpp ≥ 5%

IF : Red < 0%

No

Possibly bypass diode disconnection

Yes

Table S2 and S3

Diagnosis parameter calculation

Possibly MPPT fault

Table S1

Diagnosis parameter calculation IF : Red > 90% & Signals S1 = 0 & S2 = 0 & S3 = 0

Signal S2 and S3 = 0

False alarm or bad measurment

Signal S2 or S3 = 1

Fault according to table S2 or S3

Signal S1 = 0

False alarm or bad measurment

Signal S1= 1

Fault according to table S1

Fig. 20. PVG fault diagnosis flowchart.

Fault according to table S4

Table 1 An extracted of the look-up table. T Test/Outpu G Pmpp Impp [W/m2 [Kelvin [W] t [A] ] ] 1) 965 322 554 7.6 8 2) 879 323 505 7.0 2 3) 846 324 488.2 6.7 6 4) 833 326 470.5 6.5 9 6 5) 809 330 447.6 6.3 1 5 6) 751 322 444.5 6.0 8 3 7) 727 324 418.8 5.7 4 8) 693 324 405.3 5.5 8 8 9) 683 324 399.9 5.4 2 5 10) 659 321 388.2 5.1 6 6 11) 582 313 358.4 4.5 7 8 12) 529 311 325.3 4.1 9 2 13) 507 318 302.1 3.9 1 6 14) 474 317 271 3.5 2 15) 291 308 155.5 1.9 3 3

Vmpp [V]

Voc [V]

Isc [A]

Iph [A]

I0 [A]

Rs [Ω]

Rsh [Ω]



72.0 7 71.8 6 72.1 4 71.6 8 70.4 1 73.6 9 72.8 9 72.6 5 73.2 8 75.1 2 78.2 0 78.9 0 76.2 1 76.8 6 80.2 9

100.0 9 98.89

8.5 7 7.8 9 7.5 6 7.3 6 7.1 9 6.7 5 6.3 8 6.2 2 6.1 4 5.7 3 5.0 1 4.5 0 4.3 6 4.0 9 2.1 5

8.5 7 7.9 1 7.5 8 7.3 7 7.2 1 6.7 6 6.3 8 6.2 2 6.1 5 5.7 4 5.0 1 4.5 0 4.3 5 4.1 0 2.1 5

1.59e -6 1.27e -6 1.17e -6 1.14e -6 2.16e -6 8.37e -7 1.09e -6 6.57e -7 5.93e -7 4.54e -7 1.08e -7 1.44e -7 6.43e -7 5.17e -7 7.39e -8

1.71 4 1.73

1.43e 3 484.2 4 778.8 9 659.1 4 612.9 3 776.7 7 1.14e 3 687.8 2 579.8 1 964.5 4 1.28e 3 1.48e 3 1.52e 3 314.6 3 1.14e 3

1.2 9 1.2 6 1.2 5 1.2 3 1.2 5 1.2 4 1.2 5 1.2 0 1.1 9 1.2 1 1.1 7 1.2 1 1.2 7 1.2 6 1.2 0

98.37 97.74 96.01 98.69 97.63 97.29 97.28 98.85 101.1 2 101.1 5 98.55 98.54 98.72

1.71 1.74 1.75 1.71 1.71 1.75 1.76 1.74 1.73 1.69 1.64 1.68 1.72

\ Table 2 Shading level onthe PV sub-strings surface, under G = 508 W/m2 and T = 317 K. Module ‘‘1’’ Module ‘‘2’’ Module ‘‘3’’ Sb Sb Sb Sb Sb Sb‘ Sb Sb Sb ‘1’ ‘2’ ‘3’ ‘4’ ‘5’ 6’ ‘7’ ‘8’ ‘9’ 50 30 45 16 80 25 90 68 22 % % % % % % % % %

Table 3 Shading level on the PV sub-strings surface, under G = 908 W/m2 and T = 323 K. Module ‘‘1’’ Module ‘‘2’’ Module ‘‘3’’ Sb Sb Sb Sb Sb Sb‘6’ Sb Sb Sb ‘1’ ‘2’ ‘3’ ‘4’ ‘5’ ‘7’ ‘8’ ‘9’ 50% 30% 0% 15% 80% 25% 90% 0% 40%

Table 4 Fault signing table S1. Diagn Scen osis a1 2 para rios meter [10 , a) [13 , 15] 12] b) 24 12 𝑹𝒆𝒅𝒑 c) 24 12 d) 24 12 [0.15 , [0.22 , 0.24] 0.35] a) [0.33 , [0.49 , b) 0.55] 0.76] Err c) [0.55 , [0.76 , d) 0.93] 1.27] [0.70 , [1.06 , 1.59] 1.50] [0.05 , [0.07 , 0.10] 0.11] a) [0.10 , [0.12 , b) 0.12] 0.18] 𝝋𝒎𝒂𝒙𝒅𝟐 𝑰 c) [0.12 , [0.15 , d) 0.20] 0.18] [0.12 , [0.16 , 0.20] 0.22] [4.8 , [4.8 , 7.1] 7.1] a) [8.1 , [8.1 , b) 12.1] 𝝋𝒎𝒂𝒙𝒅𝟐 𝑷 12.1] c) [13 , [13 , 19] d) 19] [13.6 , [13 , 24] 28] 0.02 0.01 a) 0.04 0.03 b) [0.06 , 0.05  c) 0.09] [0.05 , d) [0.08 , 0.09] 0.13]

Number of faulty Sub-string (Sb) 3

4

5

6

7

8

[15 , 17] 36 36 36

[17 , 18] [41 , 44] 48 48

[18 , 20] [43 , 45] 60 60

[20, 21] [45, 47] [67 , 72] 72

24 [47 , 49] [73 , 75] 85

[23, 24] [45 , 49] [74 , 76] > 93

[0.26 , 0.43] [0.53 , 1.07] [1.19 , 1.32] [1.09 , 1.83] [0.10 , 0.20] [0.21 , 0.33] [0.23 , 0.43] [0.31 , 0.47] [3.7 , 7.7] [10 , 13.6] [9.4 , 14.7] [11.4 , 21.1] 0.02 [0.04 , 0.07] [0.07 , 0.11] [0.10 ,

[0.03 , 0.48] [0.61 , 0.96] [0.96 , 1.59] [1.24 , 2.03] [0.15 , 0.23] [0.26 , 0.37] [0.37 , 0.47] [0.37 , 0.48]

[0.28 , 0.41] [0.60 , 0.86] [1 , 1.91] [1.27 , 2.26]

[0.17 , 0.24] [0.42 , 0.58] [0.65 , 1] [0.82 , 1.28]

[0.15 , 0.33] [0.28 , 0.50] [0.50 , 0.67] [0.51 , 0.72]

[0.25 , 0.59] [1.05 , 1.71] [1.02 , 1.33] [0.91 , 1.22]

[3.3 , 7] [8.9 , 12.4] [10.3 , 13.9] [10.2 , 17.7]

[1.3 , 2.6] [3.1 , 4.9] [6.2 , 12] [7.1 , 12.1]

[0.5 , 1] [1.7 , 3.2] [4 , 5] [2.8 , 4.9]

0.02 [0.05 , 0.06] [0.09 , 0.12] [0.11 ,

0.02 0.05 [0.09 , 0.11] [0.11 , 0.15]

0.01 [0.03 , 0.04] [0.05 , 0.06] [0.07 ,

[0.24 , 0.38] [0.50 , 1.03] [0.77 , 1.14] [1.15 , 1.56] [0.09 , 0.17] [0.16 , 0.21] [0.17 , 0.28] [0.22 , 0.30] [4.7 , 8.7] [8.7 , 12] [9.9 , 15] [14.3 , 22] 0.02 [0.04 , 0.07] [0.06 , 0.07] [0.08 ,

[0.24 , 0.39] [0.50 , 1] [0.75 , 1.16] [1 , 1.67] [0.10 , 0.18] [0.17 , 0.33] [0.27 , 0.34] [0.31 , 0.42] [4.1 , 8.3] [7.7 , 15.8] [12.5 , 17.3] [16.8 , 22.3] 0.02 [0.04 , 0.07] [0.07 , 0.08] 0.09

0.11]

𝝋𝑽𝒎𝒑𝒑

𝝋𝑷𝒎𝒑𝒑

𝝋𝑰𝒎𝒑𝒑

a) b) c) d)

a) b) c) d)

a) b) c) d)

𝝋𝑰𝒑𝒉

a) b) c) d)

𝝋𝑹𝒔

a) b) c) d)

𝝋𝑹𝒑

a) b) c) d)

[0.87 , 1] 0.87 0.87 0.87 [0.87 , 0.89] 0.87 0,87 0,87

[0.8 , 1] 1 1 1

[1.02 , 1.03] [1.03 , 1.07] [1.08 , 1.12] [1.12 , 1.37] [0.53 , 0.77] [1.15 , 1.17] [1.15 , 1.17] 0 [0.06 , 0.23] [0.04 , 0.15] [0.02 , 0.09] [0 , 0.05]

1.06 0.75 0.75 0.75

[0.84 , 0.86] 0.75 0.75 0.75

0.11]

0.12] 1.02 [1.01 , 1.05] [0.26 , 1.07] 0.27 [0.78 , 0.79] [0.52 , 0.62] [0.26 , 0.32] 0.27

1.05 0.63 0.63 0.63

1.04 [1.07 , 1.10] 0.51 0.51

1.03 [1.05 , 1.08] 0.39 0.39

[0.82 , 0.84] 0.63 0.63 0.63

[0.81 , 0.82] [0.55 , 0.58] 0.51 0.51

[0.79 , 0.81] [0.54 , 0.56] 0.39 0.39

[0.76 , 0.77] [0.5 , 0.61] [0.25 , 1.01] 1

0.09] 1 1 [1.01 , 1.04] 0.15

1 1 1 [1.01 , 1.07]

[0.75 , 0.76] [0.50 , 0.51] [0.24 , 0.25] [0.92 , 0.96] [0.86 , 0.87] [0.71 , 0.74] [0.65 , 0.87] [0.53 , 0.84]

0.75 [0.5 , 0.54] [0.23 , 0.25] [0.04 , 0.06] [0.74 , 0.75] [0.50 , 0.54] [0.24 , 0.25] [0.04 , 0.06] [0.78 , 0.79] [0.56 , 0.64] [0.36 , 0.37] [0.18 , 0.22]

0.75 [0.5 , 0.52] [0.24 , 0.26] 0.15

[0.79 , 0.81] 1 1 1

[0.78 , 0.79] 1 1 1

[0.77 , 0.78] 0.51 1 1

[0.77 , 0.78] [0.5 , 0.52] 1 1

[1.05 , 1.07] [1.11 , 1.13] [1.17 , 1.42] [1.21 , 1.73]

[1.05 , 1.07] [1.12 , 1.54] [1.20 , 1.21] [1.16 , 1.58]

1.04 [1.10 , 1.48] [1.12 , 1.45] [1.04 , 1.19]

1 [1.02 , 1.38] [1.04 , 1.49] [0.94 , 1.18]

1 [0.91 , 1.08] [0.88 , 1.25] [0.82 , 0.95]

[0.15 , 0.53] 0 [0 , 0.16] [0 , 1]

[0 , 0.19] [0 , 1.17] 0 [0 , 0.70]

0 [0 , 1.17] [0 , 0.94] 0

0 [0 , 1.16] [0 , 1.16] 0

[0 , 1.14] 0 [0 , 1] 0

[1.16 , 1.17] 0 0 0

[1.12 , 1.17] 0 0 0

[0.02 , 0.07] [0 , 0.03] [0 , 0.03] [0 , 0.01]

[0.01 , 0.06] [0 , 0.03] [0 , 0.01] [0 , 0.01]

[0.01 , 0.06] [0 , 0.03] [0 , 0.01] [0 , 0.01]

[0.02 , 0.07] [0.01 , 0.03] [0 , 0.01] [0 , 0.02]

[0.04 , 0.11] [0.02 , 0.06] [0 , 0.03] [0 , 0.03]

[0.11 , 0.29] [0.05 , 0.15] [0.03 , 0.1] [0.03 , 0.11]

[0.02 , 0.09] [0.01 , 0.04] [0 , 0.03] [0 , 0.02]

Table 5 Fault signing table S2.

Diagno sis param eter 𝑹𝒆𝒅𝒑

𝝋𝑽𝒎𝒑𝒑

𝝋𝑷𝒎𝒑𝒑

𝝋𝑰𝒎𝒑𝒑

𝝋𝑹𝒔

𝝋𝑹𝒑

𝝋𝜼

Scen a1 rios

Number of faulty by-pass diodes (Bd) 5

6

7

8

22 33 44 [6 , 20] [8 , 32] [12 , 42] <6 <8 < 12 20 30 40 22 33 44 < 0.78 < 0.7 < 0.58 [0.78 , [0.7 , [0.58 , 0.92] 0.95] 0.7] [0.92 , 1] [0.95 , 1] [0.7 , 1] 0.8 0.7 0.6 0.77 0.66 0.55 < 0.9 < 0.78 < 0.7 < 0.58 [0.9 , [0.78 , [0.7 , [0.58 , 0.95] 0.92] 0.95] 0.63] [0.95 , [0.92 , 1] [0.95 , 1] [0.63 , 1] 1] 0.8 0.7 0.6 0.9 0.77 0.66 0.55 0.88 1 1 1 1 [0.94 , [0.9 , 1] [0.84 , 1] [0.89 , 1] 1] [0.9 , 1] [0.84 , 1] [0.78 , [0.94 , 1 1 0.89] 1] 1 1 1 1 1 1

55 [14 , 53] < 14 50 55 < 0.47 [0.47 , 0.64] [0.64 , 1] 0.5 0.44 < 0.47 [0.47 , 0.55] [0.55 , 1] 0.5 0.44

66 [16 , 65] < 16 60 66 < 0.36 [0.36 , 0.6] [0.6 , 1] 0.4 0.33 < 0.34 [0.34 , 0.46] [0.46 , 1] 0.4 0.33

77 [18 , 76] < 18 70 77 < 0.23 [0.23 , 0.56] [0.56 , 1] 0.3 0.22 < 0.23 [0.23 , 0.39] [0.39 , 1] 0.3 0.22

88 [20 , 86] < 20 80 88 < 0.12 [0.13 , 0.5] [0.5 , 1] 0.2 0.11 < 0.12 [0.13 , 0.34] [0.34 , 1] 0.2 0.11

1 [0.85 , 1] [0.74 , 0.85] 1 1

1 [0.77 , 1] [0.7 , 0.84] 1 1

1 [0.7 , 1] [0.6 , 0.84] 1 1

e) f) g) h) i)

0.88 0.88

0.77 0.77

0.66 0.66

0.55 0.55

0.44 0.44

e) f) g) h) i)

0.88 0.88

0.77 0.77

0.66 0.66

0.55 0.55

e) f) g)

0.88 0.77 [1.16 , [1.28 1.52] 1.36]

e) f) g) h) i) e) f) g) h) i) e) f) g) h) i) e) f) g) h) i)

2

3

4

11 [4 , 10] <4 10 11 < 0.9 [0.9 , 1] 1 0.9 0.88

0.66 , [0.67 1.28]

0.55 , [0.67 1.28]

[0.87 , 1] [0.61 , 0.85] [0.61 , 0.85] 1 [0.94 , 1.03] , [0 , 0.12] -

[0.13 0.3] [0.11 , 0.33] 0.44 [0.33 , [0.21 0.44 0.35] 0.24] [0.12 , 0 0.33] 0.45 [0.39 , [0.39 , [1 , 1.23] 0.42] 0.43] [1.3 , [0.63 , [0.63

, 0.01 0

, [0.39 0.42] , [0.4

, ,

𝝋𝑽𝒐𝒄

h) i)

[1 , [1 , 1.54] 1.52] 0.77 0.88 0.77 0.88

e) f) g) h) i)

< 0.93 < 0.79 [0.93 , [0.89 , 1] 1] 1 1 0.8 0.9 0.77 0.88

[1.2 1.5] 0.66 0.66

, [1.3 1.7] 0.55 0.55

, 1.7] 0.44 0,44

1.22] 1.19] 1.16] [1.22 , [1.21 , [1.16 , 1.68] 1.68] 1.68] [0.39 , [0.39 , [0.39 , 0.43] 0.43] 0.43] [0.39 , [0.39 , [0.39 , 0.43] 0.43] 0.43] < 0.69 < 0.58 < 0.48 < 0.38 < 0.28 < 0,17 [0.79 , 1] [0.58 , [0.48 , [0.38 , [0.28 , [0.17 , 1 0.89] 0.84] 0.8] 0.8] 0.73] 0.7 1 [0.84 , 1] [0.8 , 1] [0.8 , 1] [0.73 , 1] 0.66 0.6 0.5 0.4 0.3 0.2 0.55 0.44 0.33 0.22 0.11

Table 6 Fault signing table S3. Sc Faul en𝝋𝑷𝒎𝒑𝒑 𝑹𝒆𝒅𝒑 𝝋𝑽𝒎𝒑𝒑 t ari os [27, [0.71 , i) 0.74 Sb 1 28] 0.72] h) 0.88 11 0.88 [53, [0.43 , i) 0.48 Sb 2 56] 0.46] h) 0.77 22 0.77 [78, [0.18 , i) 0.25 Sb 3 81] 0.21] h) 0.66 33 0.66 [0.07 i) 97 0.02 Sb 4 ,0.08] h) 44 0.55 0.55 Sb 5 i) 55 0.44 0.44

𝝋𝑰𝒎𝒑𝒑

𝝋𝑰𝒔𝒄

𝝋𝑽𝒐𝒄

𝝋𝑰𝒑𝒉

1 1

1 1

0.77 0.88

1 1

1 1

0.55 0.77

1 1

1 1

0.33 0.66

[0.89 , 0.94] 1 [0.70 , 0.82] 1 [0.27 , 0.36] 1 1

[0.5 , 0.65] 1 1

0.44

[1.08 , 1.25] 1 [0.30 , 0.43] 1 1 1

0.11 0.55

Sb 6

i)

66

0.33

0.33

1

1

0.33

Sb 7

i)

77

0.22

0.22

1

1

0.22

Sb 8

i)

88

0.11

0.11

1

0.11

Sb 9

a) b) c) d)

25 50 75 < 93

1 1 1 1

e) f) g) h)

> 94 [20, 94] < 20 90

e) f) g)

<6 [6 , 45] < 45

Bd 9

Cc

0.75 0.5 [0.22 0.25] [0.04 0.06] [0.1 , [0.05 0.47] 0.26] [0.47 , [0.26 1] 1] 0.1 0.1

, ,

, ,

[0.94 , 1.03] 0.75 0.5 [0.23 0.25] [0.04 0.06] [0.54 0.56] [0.56 0.84] 1

0.75 0.98 0.5 0.95 , 0.25 0.91 [0.04 , [0.91, , 0.07] 0.93] , 1 1 , 1 1

[0.95 , [0.95 , 1 1] 1] 1 [0.75 , [0.75, [0.55 , 1 1] 0.95] 0.94] < 0.92 < 0.75 < 0.75 < 0.55

[1, 1.13] [0.83 , 1.17]

𝝋𝑹𝒔

𝝋𝑹𝒑

[1.04 , 1.07] 0.88 [1.1 , 1.14] 0.77 [1.16 , 1.17] 0.66

[0.76 , 0.86] 0.88 [0.35 , 0.65] 0.77 [0 , 0.02] 0.66

0 0.55 0.44 [0.11 , 0.33] [0 , 0.12] 0

1 1 1

1 [1 , 1.5] [0.4 , 1]

0.87 0.88

[0.73, 0.74] 0.77 [0.41, 0.51] 0.66 [0.38, 0 , 0.01] 0.40] 0.55 0.55 0.44 0.44 [0.11 , [0.39, 0.33] 0.43] [0.39, 0 0.43] [0.39, 0 0.43]

0.75 1 1 0.5 1 1 0.25 1 1 [0.04 , [1.16 , [0.81 0.07] 1.17] 1.89]

1 [0.16 , 1 0.7] 1 [0.71, [0 , 0.94] 0 0.46] 0.10

𝝋𝜼

1 1 1 , [0.86, 0.92]

[0.41, 1.13] 0.96 [0.39, 0.43] [1 , + [1 , [1.05 , ∞] 1.16] 1.17] [0.02 , [1.16, 1.17 0.27] 1.54] 0 [0 , [1.56, 0.04] 1.63] 0.01

Table 7 Fault signing table S4. Possibly defects All by-pass diodes are in short circuit. All by-pass diodes are reverse biased. All sub-strings are totally shaded. All sub-strings are in short circuit. One or more sub-string is disconnected. More than three cascade connected sub-strings are reverse biased.