Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx Contents lists available at ScienceDirect Renewable and Sustainable Energy Reviews journal homepage: www.elsevier.com/locate/rser Metaheuristic algorithms for PV parameter identification: A comprehensive review with an application to threshold setting for fault detection in PV systems Dhanup S. Pillai, N. Rajasekar ⁎ Solar Energy Research Cell (SERC), School of Electrical Engineering (SELECT), VIT University, Vellore, India A R T I C L E I N F O A B S T R A C T Keywords: Parameter extraction Fault detection PV Metaheuristic algorithms Optimization techniques Precise model parameters being the prerequisite for realizing accurate PV models, parameter identification techniques have gained immense interest over the years among the researchers specializing in PV systems. The application of various promising metaheuristic algorithms to optimize the model parameters have lightened up the scope of further enhancements in this field. Ever since, numerous metaheuristic algorithms have deployed for this purpose. With handful of techniques available in this regard, this paper takes up an initiative to review the existing metaheuristic algorithms based parameter extraction techniques with an emphasis on their compatibility, accuracy, convergence speed, range of parameters set and their validating environment. Based on the analysis conducted, accurate models available for 17 different industrial solar cells/modules are identified. Inspired by this review, an unidentified gateway between parameter extraction and fault detection in PV systems have been identified; and has further extended this review to differentiate some models that can help the researchers to achieve accurate, efficient and rapid fault detection. This review is a valuable gathering of statistics from the various researches carried out in PV parameter extraction which can assist enhanced researches for fault detection in PV systems as well. 1. Introduction Over the decades, efforts have been made to efficiently harness the abundant renewable energy resources like Sun, Wind, Tides, and Geothermal Heat to meet the extended energy needs of the mankind. The contained humungous energy capability and copious availability irrespective of global locations makes solar energy the foremost among all resources. However, this unmatched energy resource in real time, encounters difficulties in the form of PV non-linearity, low PV panel efficiency and unavailability of standard models for PV performance assessment. Moreover, constraints in real time data acquisition add to its complexity. Besides, recent power quality issues due to the penetration of large roof top PV power plants in low voltage distribution systems necessitates critical simulation tool. Further, the prediction of PV panel performance is vital in design, optimization, and simulation analysis of PV systems. Therefore, the need for simulation modeling of real PV power plants remains indispensable in both academic and industrial point of view. Unfortunately, till date, no exact model for PV characteristic prediction has been made available. Moreover, the existing single and double diode model prediction is vulnerable to the model parameter variations; especially under the context of low irradiance. Further, poor model prediction sometimes lead to erroneous Abbreviations: ABCO, Artificial Bee Colony Optimization; AE, Absolute Error; AGA, Adaptive Genetic Algorithm; APSO, Particle Swarm Optimization with Adaptive Inertia Weight Control; BBO-M, Bio-Geography Based Optimization with Mutation Strategies; BMO, Bird Mating Optimization; CPSO, Chaos Particle Swarm Optimization; DD, Double Diode; DEIM, Differential Evolution with Integral Mutation; GGHS, Grouping Based Global Harmony Search; HS, Harmony Search; IADE, Improved Adaptive Differential Evolution; IBCPSO, PSO with Inverse Barrier Constraints; IP, Interior Point; JADE, Adaptive Differential Evolution; LS, Least Square; MPP, Maximum Power Point; N.A, Not Applicable; NMS, Nelder-Mead Algorithm; NR, Newton-Raphson; P-DE, Penalty Based Differential Evolution; PSA, Parallel Swarm algorithm; PV, Photovoltaic; RMSE, Root Mean Squared Error; SBMO, Simplified Bird Mating Optimization; SIV, Suitability Index Variable; STLBO, Simplified Teaching Learning Based Optimization; TVIWAC-PSO, Particle Swarm Optimization with Time Varying Inertia Weight and Acceleration Coefficients; ABSO, Artificial Bee Swarm Optimization; AIS, Artificial Immune System; ANN, Artificial Neural Network; BBO, Bio-Geography Based Optimization; BFA, Bacterial Foraging Algorithm; BPFPA, Bee Pollinated Flower Pollination Algorithm; CPU, Central Processing Unit; DE, Differential Evolution; GA, Genetic Algorithm; GPU, Graphical Processing unit; HSI, Habitat Suitability Index; IAE, Individual Absolute Error; IGHS, Innovative Global Harmony Search; IPSO, Improved Particle Swarm Optimization; LM, LevenbergMarquardt; MPCOA, Mutative-Scale Parallel Chaos Optimization; MSE, Mean Squared Error; N.E, Not Extracting; NOCT, Nominal Operating Cell Temperature; N.S, Not Specified; PS, Pattern Search; PSO, Particle Swarm Optimization; R-JADE, Repaired Adaptive Differential Evolution; SA, Simulated Annealing; SD, Single Diode; STC, Standard Test Conditions; TLBO, Teaching Learning Based Optimization; VC-PSO, Particle Swarm Optimization with Velocity Clamping ⁎ Correspondence to: School of Electrical Engineering, VIT University, Vellore, Tamil Nadu 632014, India. E-mail addresses: [email protected] (D.S. Pillai), [email protected] (N. Rajasekar). http://dx.doi.org/10.1016/j.rser.2017.10.107 Received 23 January 2017; Received in revised form 19 August 2017; Accepted 28 October 2017 1364-0321/ © 2017 Elsevier Ltd. All rights reserved. Please cite this article as: Pillai, D.S., Renewable and Sustainable Energy Reviews (2017), http://dx.doi.org/10.1016/j.rser.2017.10.107 Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx D.S. Pillai, N. Rajasekar Nomenclature V VMP VPV W W .L Wmin XB XW BP C1 CG D F fmin Gb Id IMP IPV ISC K Ki KV mcf Me NP PAR Pb PMi q ri rm RP RPO Tbest TF Tnew Vd VOC VT We Wmax Ws Xe Z Greek symbols α λS σ0 γ ε2 L (λ ) β σG μS ε μm Cross over rate Immigration rate Standard deviation of initial generation Scaling factor for FPA Switching operator in DEIM Levy factor Mutation rate Standard deviation of current generation Emigration rate Switching factor Mutation probability English symbols a Diode ideality factor Bandwidth of generation BW C2 Social coefficient Cr Cross over rate E Energy state fmax Maximum fitness value G Irradiance (W/m2) HM Harmony memory Reverse saturation current (A) I0 Photon current (A) IPh IPVn Photon current (A) Random index j Iteration index k k max Maximum number of iterations M Number of mutant vectors Md Classic Mutation mu Mutation variable NS Number of cells in series parent 1, 2 Current solutions in GA Pm Mutation rate PMP Power at maximum power point (W) r Random number between 0 and 1 Rank of the Vector Ri RS Series resistance (Ω) RSO Reciprocal of the slope at open circuit point (Ω) T Temperature (K) Temperature control parameter TC Told Old teacher Velocity of particle Voltage at maximum power point (V) Output PV voltage (V) Inertia weight Worst learner Final inertia weight Best vector Worst vector Base point Cognitive coefficient Current generation Search space Scaling factor Minimum fitness value Global best solution Diode current (A) Current at maximum power point (A) Output PV current (A) Short circuit current (A) Boltzmann constant (J/K) Temperature coefficient of short circuit current (A/K) Temperature coefficient at open circuit voltage (V/K) Mutation control factor Electromagnetism based mutation Population size Pitch adjusting rate Current best solution Probability of selection Charge of one electron (C) Random number between 0 and 1 Random number between 0 and 1 Shunt resistance (Ω) Reciprocal of the slope at short circuit point (Ω) Best teacher Teaching factor New teacher Diode voltage (V) Open circuit voltage (V) Thermal voltage (V) End weight in TVIWAC-PSO Initial inertia weight Start weight in TVIWAC-PSO Elite vector Chaotic variable parameters since the data varies and are not available in the datasheet provided by the manufacturers either. Making the scenario even worse, these parameters are to be processed from the minimal data provided in the datasheet. Therefore, to build an accurate and reliable PV model, precise model parameters are mandatory. The scope for an authentic parameter extraction technique further widens and transforms into an optimization problem since most of the parameter extraction techniques are carried out using optimization techniques. Many optimization techniques have been deployed to handle the multimodal parameter optimization problem. Inspired by the significance of PV cell modeling techniques, even reviews were made available based on the analysis of different optimization techniques [11–14]. In [11], a survey has been conducted on the various analytical methods and different soft computing techniques available for PV parameter extraction. A review on various analytical methods in terms of number of parameters extracted and the effect of each parameter on model characteristics is discussed in [12]. Comparative analysis of specific six different bio inspired triggering of protection circuits under normal operating conditions as well. Hence, the subject of PV parameter estimation assumes surmount importance even in the context of PV fault detection due to the fact that most of the fault prediction is based on the estimated I-V curves. Overall, the requirement of accurate PV model is always on high demand. Researches on PV panel model prediction remains as an agile field due to: 1) Non-linear PV characteristics and 2) its colossal dependency on insolation level and panel temperature. Among many models that exist, the noteworthy PV models to be mentioned are 1) Single Diode (SD) model and 2) Double Diode (DD) model [1–3]. Apart from these, the other models detailed in literature are three diode model [4], single diode model with parasitic capacitor [5], improved two diode model [6,7], reverse two diode model, generalized three diode model [8], diffusion based model [9] and multi diode model [10]. However, model accuracy varies based on the estimated model parameters. Unfortunately, it is hardly possible to set global values for these 2 Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx D.S. Pillai, N. Rajasekar 2.2. Double diode PV model metaheuristic techniques and its scopes for improvement are elaborated in [13]. While in [14], the author has outlined a detailed review on the accuracy of the metaheuristic algorithms and its hybrid variants used for parameter identification. However, none of these researches have produced an assessment of metaheuristic algorithms based on their error evaluation and its application towards PV fault diagnostics. Moreover, a critical performance evaluation over a wide range of metaheuristic algorithms used for parameter extraction problem has not been studied either. On the other hand, for rapid detection and mitigation of faults, various fault detection techniques often compare the real time entities with the threshold ones. Undoubtedly, accuracy of the threshold limits set by the PV model decides the reliability of a fault detection technique. Hence, there exists a colossal dependency of PV parameter extraction for PV fault diagnosis. With handful of literature available, the paper aims to provide an authentic document that reviews the various parameter extraction techniques. Further, this review is extended to differentiate some PV models that can guide researchers/ PV manufacturers to achieve accurate, efficient and rapid fault detection. All available previous literatures lack this effort. The subsections provide details regarding: 1) PV modeling, 2) different PV parameter extraction techniques and its applicability towards parameter identification, 3) fault detection in PV systems and its application towards parameter identification. The sole difference between DD model and SD model is the presence of an additional diode, ‘D2’ as depicted in Fig. 3. The presence of second diode imparts a better accuracy to the model especially at low irradiance levels when compared to the SD model. The diode D2 is in cooperated in the model to represent the recombination losses occurring in the depletion layer during low irradiance levels. Here the output current, Ipv is given by [1–3] as; Ipv = Ipvn − Id1 − Id2 − Vpv + Ipv Rs Rp (5) The diode currents Id1 and Id2 are given as Id1 = IO1 ⎡exp ⎛ ⎢ ⎝ ⎣ q (Vpv + Ipv RS ) ⎞ Id2 = IO2 ⎡exp ⎛ ⎢ ⎝ ⎣ q (Vpv + Ipv RS ) ⎞ ⎜ ⎜ a1 NS Vt a2 NS Vt ⎟ ⎠ ⎟ ⎠ − 1⎤ ⎥ ⎦ (6) − 1⎤ ⎥ ⎦ (7) Hence, for a PV cell (NS = 1), the output current equation can be derived as: q (Vpv + Ipv RS ) ⎞ ⎧ Ipv = Ipvn − IO1 ⎡exp ⎛ − 1⎤ ⎢ ⎥ ⎨ a1 Vt ⎝ ⎠ ⎣ ⎦ ⎩ ⎜ 2. PV modeling − IO2 ⎡exp ⎛ ⎢ ⎝ ⎣ ⎜ The two basic PV modeling techniques convenient to represent a PV module are SD modeling and DD modeling. Sometimes, the ideal PV models presented in [15,16] are also used for the theoretical understanding of PV concepts. Most methods in literature prefer the SD model due to its simplicity and lesser number of parameters. However, the lack of accuracy of SD model makes the DD model preferable for certain applications where precise I-V and P-V characteristics are required. At the same time, the DD model has the disadvantage of high computational burden due to more number of model parameters. The steps involved in realizing a PV model for a PV cell is depicted in Fig. 1. − Id − (1) From literature [1–3], the diode current can be expressed as, Id = { I0 [exp (Vd/ aVT )] − 1} (2) Now VT is given by the equation Vt = NS KT q ⎜ (3) Embedding (1)–(3), the current equation for a single PV cell (NS = 1) can be obtained as Ipv = Ipvn − Io ⎧exp ⎛ ⎨ ⎝ ⎩ ⎜ q (Vpv + Ipv Rs ) ⎞ aKT Vpv + Rs Ipv − 1⎫ − ⎬ Rp ⎠ ⎭ ⎟ (8) PV model plays an inevitable role in simulation analysis, design optimization and fault diagnosis of any PV system. Further, the ability of the PV model to replicate accurate I-V characteristics under all insolation and temperature profiles is of extreme significance. However, the accurate I-V curve emulation entirely depends on the precision of the unknown model parameters deermined. Moreover, these values are neither readily available in manufacturer datasheet nor it can be found using simple calculations. In addition, the presence of noise in the extracted synthetic data adds to the difficulty. With manufacturers only providing experimental I-V curve for Standard Test Conditions (1000 W/m2 and 25 °C), the process of identifying model parameters utilizing a suitable strategy becomes extremely indispensable. This high potential research area is commonly referred as “PV parameter identification problem”. Here, the term parameter identification refers to the process of finding out the unknown model parameters indicated in Eqs. (4) and (8). The complete cycle of parameter extraction process and the commonly identified parameters along with the manufacturer data is illustrated in Fig. 4 and Table 1 respectively. As mentioned earlier, estimating PV model parameters is a strenuous and difficult assignment due to: 1) Minimal amount of data available, 2) Ample number of unknowns and 3) Complex mathematical VPV + Ipv Rs Rp Vpv + Ipv RS ⎞ ⎫ − 1⎤ − ⎛ ⎥⎬ RP ⎠ ⎠ ⎦⎭ ⎝ ⎟ a2 Vt 3. PV parameter extraction The SD model of a solar PV cell is shown in Fig. 2. It comprises of an illuminated current source, ‘IPVn ’ or ‘IPh ’, diode, ‘D’ that represents the optical and recombination losses at the surface of the semiconductor, series resistance, ‘RS ’ and shunt resistance, ‘RP ’ that account for the leakage losses. From figure, by node analysis, n q (Vpv + Ipv RS ) ⎞ From (8) it is clear that the DD model has seven unknown parameters namely IPVn , I01, I02 , RS , RP , a1 and a2 . As explained above each parameter is highly dependent to Irradiation levels and temperature [17]. 2.1. Single diode PV model Ipv = IPV ⎟ ⎟ (4) From (4), SD model has five unknown parameters; IPVn , I0 , RS , RP and a . Fig. 1. PV modeling. 3 Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx D.S. Pillai, N. Rajasekar + I pv Rs Ipvn (Iph) Rp Vpv D Id Mathematical Equations Analytical Method Objective Function [ Error ] PV Model - Extracted Parameters to Model Metaheuristic Optimization Fig. 2. Single diode model. I pv Rs + Fig. 5. Steps for parameter identification. I d2 I d1 Rp D1 I pvn (I ph ) Objective Function [ MPP ] superior to analytical methods. At the same time, it should be emphasized that analytical methods are handy if there are only a few unknown parameters. Sometimes, to reduce the computational burden, merging an analytical method with a metaheuristic algorithm proved to be advantageous. Similarly, combining two optimization algorithms have also led to improvement in accuracy. Thus the solutions to the broad PV parameter extraction problem can be categorized into three: 1) Analytical methods, 2) Metaheuristic optimization and 3) Hybrid methods. The steps involved in solving parameter identification problem can be illustrated using Fig. 5. To handle the voluminous data's of the methods involved, this paper focuses on briefing the different metaheuristic algorithms and its hybrid versions; while only a short description about the analytical methods is added for the basic understanding. V pv D2 Fig. 3. Double diode model. Data from Manufacturer Sheet Parameter Identification Method 3.1. Analytical approach for PV parameter extraction Model Parameters Analytical methods rely on deriving necessary mathematical equations in order to realize PV characteristics. In a mathematical sense, for solving an equation with ‘n’ number of unknowns, at least ‘n’ equations are necessary. For instance, identifying SD model and DD model parameters require at least five and seven equations accordingly. The idea behind formulating these equations can be explained with the help of a single diode ‘RS ’ model. Further, the same can be extended to conventional SD and DD models as well. A single diode ‘RS ’ model is a simplified form of conventional SD model where the parameter ‘RP ’ in the SD model tends to infinity. Hence, the current through the parallel RP branch in the current Eqs. (1) and (4) are eliminated for this model. The modified output current equation now reduces to; Initialization Fig. 4. Cycle of parameter extraction. Table 1 Model parameters and its availability. Parameters Manufacturer Data Sheet PV Model Parameters VOC IPVn (Iph) ISC I01 IMP I02 VMP a1 PMP a2 Ki RS Kv RP Ipv = Ipvn − Io ⎧exp ⎜⎛ ⎨ ⎝ ⎩ computations. Hence, over the decades, to resolve the problem of parameter identification, researchers have made use of several approaches. Initially, analytical methods were used to extract model parameters by utilizing a series of interdependent mathematical equations to co-relate between different model parameters [18–40]. Most of them use: 1) short-circuit current, 2) open-circuit voltage and 3) maximum power point voltage and current along with the manufacturer data to derive suitable equations. However, solving these equations mathematically consumes monumental time and effort. On the other hand, introduction of metaheuristic algorithms brought a radical change in the way researchers approached the PV model parameter estimation problem. These metaheuristic algorithms transformed the difficult model parameter identification problem to a simple non-linear constrained optimization problem. The colossal benefits of using metaheuristic algorithms are: 1) Superior accuracy, 2) Flexibility to adopt. The additional advantage of these methods in case of parameter identification is its capability to match the actual curve with minimal error via curve fitting technique. This approach made the method extremely q (Vpv + Ipv Rs ) ⎞ ⎟ aKT ⎠ − 1⎫ ⎬ ⎭ (9) There are four unknown parameters in a single diode ‘RS ’ model is; ‘IPVn ’, ‘I0 ’, ‘RS ’ and ‘a ’. To solve for these unknown parameters at least four equations are necessary. From the maximum power point in the I-V curve, Ipv = IMP, Vpv = VMP, IMP = Ipvn − Io ⎧exp ⎛ ⎨ ⎝ ⎩ q (VMP + IMP Rs ) ⎞ − 1⎫ ⎬ aKT ⎠ ⎭ (10) With the help of the short-circuit point; Ipv = ISC , Vpv = 0 qR I ISC = Ipvn − Io ⎧exp ⎛ S SC ⎞ − 1⎫ ⎬ ⎨ aKT ⎠ ⎝ ⎭ ⎩ (11) From the open circuit point in the I-V curve; Ipv = 0, Vpv = VOC ; 0 = Ipvn − Io ⎧exp ⎜⎛ ⎨ ⎝ ⎩ q (VOC + Ipv Rs ) ⎞ aKT ⎟ ⎠ − 1⎫ ⎬ ⎭ Combining (10) and (11), (13) and (14) can be derived as 4 (12) Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx D.S. Pillai, N. Rajasekar ISC IO = exp 3.2. Metaheuristic algorithms for PV parameter Identification ( ) − exp ( qVOC aKT qRS ISC aKT ( ( ) ) (13) qRS ISC aKT ) ( ⎡ − 1⎤ ⎤ ISC ⎡exp ⎣ ⎦ ⎥ IPVn = ISC ⎢1 + qV qR OC S ISC ⎥ ⎢ exp aKT − exp aKT ⎢ ⎥ ⎣ ⎦ ) Metaheuristic algorithms, in last few decades, have gained immense momentum for solving complex multi objective optimization problems in various engineering disciplines [41–44]. The enormous capability in finding potential solutions provoked its importance towards PV parameter identification problem. The evolution of metaheuristic algorithms started with Genetic Algorithm (GA) followed by Differential Evolution (DE) and Particle Swarm Optimization (PSO). Inspired by these basic algorithms, several new and hybrid metaheuristic algorithms were developed in recent years [45–81]. Some prominent objective functions utilized by various metaheuristic algorithms for PV parameter optimization are: 1) Root Mean Squared Error (RMSE) [48,51–57,60,62–71,73,74], 2) Mean Squared Error (MSE) [45,59,72], 3) Absolute Error (A.E) [46,58,75,76] and 4) Derivative at maximum power point (MPP) [60,67]. In this section, basic theory of every metaheuristic algorithm and its improved variants are outlined for fundamental understanding. Further, the performance of each algorithm is reviewed based on: 1) Type of approach, 2) Compatibility towards parameter identification, 3) Accuracy, 4) Convergence speed and 5) Range of parameters set. In literature, as shown in Table 2, it can be observed that each algorithm has used numerous solar cells/modules to validate their results. However, for brevity, the ranges set and the identified parameters are shown only for either one of the cells/modules used by each algorithm and the inferences discussed are identical for other cells/modules as well. Moreover, a detailed analysis based on all the cells/modules used for parameter identification is presented in Section 4. The validating conditions of each method have also been taken into account for a better evaluation on the performance various algorithms. (14) At MPP, the derivative of the output power with respect to the voltage must be zero. Hence, at the maximum power point; d (VMP IMP ) dP dI = = VMP + IMP = 0 dV dV dV i. e. (15) dI −IMP = dV VMP (16) Combining (16) and the derivative of (9) with respect to Vpv, −IMP = VMP qIO aKT qIO aKT exp ⎡ ⎣ exp ⎡ ⎣ q (VMP + RS IMP ) ⎤ aKT ⎦ q (VMP + RS IMP ) ⎤ aKT ⎦ −1 (17) Thus, by analytical approach, the parameter extraction of a single diode ‘RS ’ model can be executed by solving the four Eqs. (12)–(14) and (17) [30–32]. It is noteworthy to mention that, instead of Eq. (17), either one of the two slope equations derived at the open circuit point or the short circuit point in the I-V curve can also be used to extract the model parameters [33]. The same procedure can be adopted for SD and DD models except that it requires some additional equations to extract the parameters. For instance, for the conventional SD model, both the slope equations (RSO , RPO ) are used along with the equations at the open circuit, short circuit and maximum power points [19–21,34–40]. While, to extract the model parameters for a DD model, an additional equation is derived using the assumption that the sum of the ideality factors of the two diodes D1 and D2 is 3 [23–27]. For a detailed study on analytical methods readers can refer to [14]. To conclude, the following disadvantages limit the adaptability of analytical methods towards parameter identification problem. 3.2.1. Genetic algorithm (GA) GA is a bio-inspired population-based algorithm which replicates the phenomenon of ‘survival of the fittest’ [82]. The formulation of objective function involves expressing the decision variables that are encoded as chromosomes. An iteration based control strategy is followed to improve the quality of each chromosome (solution). Based on the fitness value of an off spring, the quality of the solutions is evaluated and off springs for further iterations is chosen. Several works on GA for the non-linear optimization of PV parameter estimation problem is presented in [83,84]. GA follows three main steps; selection, crossover and mutation ➣ ➣ ➣ ➣ Involved complex mathematical expressions and computations. Monumental time consumption in solving the equations. Convergence is not always guaranteed. Assumptions made for simplification significantly affect the accuracy of the parameters extracted. ➣ Difficult to apply for improved PV models as the mathematical formulations will be highly complex. 1. Selection: Initially, solutions are randomly generated and the fitness of each solution is evaluated. After selection, only fitter chromosomes are selected for the next generation. Table 2 Cells/modules used for parameter identification. Refs. Tested cells/Modules [46] [47] [48,51,60,63,65,66,68,73–75,77] [49] [51,59,64,72,75] [52] [53] [55] [56] [61] [67] [70] [71] [73] [79] [80] Sanyo HIT215, KC200 GT and ST40 PV Modules KC 200GT, ST40 and E20/333 PV Modules 57 mm dia RTC France Solar Cell SM 55 PV Module, Thin film ST40 PV Module, S75 Solar Module 57 mm dia RTC France Solar Cell, Photo watt PWP201 PV Module SL80CE Solar Cell, Photo watt PWP201 PV Module S75, SM55, S115, SQ150 PC, ST36 and ST40 PV Modules 57 mm dia RTC France Solar Cell, KC200GT and PWP201 PV Modules 5 W CuInSe2 Solar Cell, 50 W mono-Si and 50 W multi-Si PV Modules Kyocera KD210GH-2PU, Shell SP-70, Shell SQ-85 and ST-40 Thin Film PV Modules S36, SM55 and ST40 PV Modules 57 mm dia RTC France Solar Cell, Photo watt PWP201, S75, SM40, SM55, KC200 GT and ST40 PV Modules. 57 mm dia RTC France Solar Cell, KC200GT, SM55 and ST-40 Thin Film PV Modules Kyocera KC120 PV Module OST 80 Solar Cell, SM55 PV Module S36 PV Module, SP 70 PV Module, SM55 PV Module, KC200 GT PV Module 5 Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx D.S. Pillai, N. Rajasekar the diversity factor of the algorithm. In AGA + LS method, the typical LS operator initially performs a local search at the start point and is used to adjust the population to enhance the performance of GA. A detailed analysis on AGA + LS method proposed in [48] gives the following inferences: 1) The initial setting of parameters are based on the short circuit and open circuit points in the IV curve to eliminate the trial run, 2) In validation, AGA + LS method outperformed the conventional Newton method and conductance method, 3) No validations were done in the context of varying irradiation and temperature levels and 4) Even though the accuracy was slightly improved, AGA + LS have slow convergence characteristics. A critical comparison of all these methods is presented in Table 3 while the results obtained via optimization are consolidated in Table 4. 2. Crossover: Generates the off springs for the upcoming generation as α . parent 1 + (1 − α ) . parent 2 ⎫ offspring = ⎧ ⎨ ⎩ (1 − α ) . parent 1 + α . parent 2 ⎬ ⎭ (18) 3. Mutation: Helps to achieve better off springs which the crossover operation might have missed. A user defined mutation rate, β is used for mutation operation. offspring = ± β . offspring + offspring (19) For a better understanding, the flowchart of GA method is also presented in Fig. 6. 3.2.2. Differential evolution (DE) Rather than GA, DE treats solutions as real numbers called particles and hence, no encoding is required [86]. The algorithm is formulated by having four operations namely initialization, mutation, crossover and selection. 3.2.1.1. Hybrid and adaptive versions of GA. To further enhance the performance of conventional GA, several hybrid and adaptive variants of GA were also proposed in literature [46–48]. To reduce the computational burden of GA, Newton Raphson technique was used to extract two model parameters in a hybrid strategy (GA + NR) proposed in [46]. In another hybrid approach, GA was used along with an interior point method to determine the MPP of a given I-V curve which has been formulated as a sub problem of the parameter identification problem to match the NOCT and STC MPP data of the manufacturer data sheet [47]. Adaptive genetic algorithm (AGA) is an adaptive variant of GA with an improved selection routine and an adaptive control of crossover and mutation factors. In [48], AGA was merged with the Least Square algorithm (AGA + LS) to build a hybrid strategy for parameter identification as well. 1. Initialization: A target vector representing the solutions is randomly set. i.e. for the ith particle, Xi CG : i → {1, 2, 3........ NP } (20) 2. Mutation: Two vectors are randomly selected and their weighted difference is utilized to mutate the ith vector. Mi, CG = Xi, CG + F . (Xr 2, CG − Xr 3, CG ) (21) Where ‘Mi, CG’ is the resultant vector, ‘Xr2, CG’ and ‘Xr3, CG’ are two vectors randomly selected from the current generation i.e. r1, r2 are in the range {1,2,3……NP}. 3. Crossover: Generates trial vectors using the resultant mutated vectors for the next generation by a non-uniform operation. 3.2.1.2. Application towards PV parameter extraction. Compared to the analytical methods, when GA is applied for parameter identification; the mutation phase efficiently explores new dimensions in the search space to search for potential solutions while the cross over operation intends to improve the diversity among the population. In the proposed work in [45], crossover operation has been applied to all chromosomes and a mutation rate of 4% was utilized to extract the SD model parameters of a 50 W solar panel. The comparison was made with Pasan CT 801 software model and found that the parameter values estimated by GA for the solar cell possess significant error particularly for the values of ‘I0’ and ‘Rp’. However, validations on different irradiance and temperature levels were not assessed. In GA + NR hybrid strategy employed in [46], GA was used to extract three parameters, ‘RS’, ‘RP’ and ‘a’ whereas ‘Iph’ and ‘I0’ were extracted analytically using NR method. NR is an effective iterative technique, when initialized to solve for only less number of parameters. Hence, GA + NR hybrid parameter identification reduces the computational burden of GA. In validation, the hybrid version outperformed the ANN model and the conventional analytical ‘RS’ model in terms of accuracy. The algorithm was validated using both MATLAB tool box and MATLAB coding. The results of the former were used for comparisons. Interestingly, the method is one of the very few which have considered the shading effects on a PV panel and has successfully validated KC200GT PV module under partial shading conditions. In [47], a multi objective based optimization [85] considering the standard and nominal operating cell temperature (NOCT) conditions of a PV was carried out to extract the model parameters of an SD model using GA + IP hybrid strategy. The IP method in contrast with other optimization techniques can traverse a set of internal points inside the boundaries to reach the global best solution This undoubtedly has increased the accuracy particularly for the nominal operating conditions of a PV. Furthermore, in validation, the method has outperformed the conventional NR method and PSO with barrier constraints in terms of accuracy. However, poor convergence persists even though the modifications have improved Mi . CG , if ri ≤ Cr or j = rni ⎫ UJ i, CG = ⎧ ⎨ ⎭ ⎩ Xi, CG , if ri > Cr or j ≠ rni ⎬ (22) 4. Selection: Regardless of the fitness value, parent vectors emerges to the next generation while the trial vectors are selected according to their fitness values as, Start YES Reinitialization Condition satisfied ?? Initialization Generate the first population of the chromosomes Evaluate the populations fitness Next iteration reinitialization NO NO All chromosomes finished Perform selection and produce the parents YES Perform cross over and generate off springs Output the offspring End Mutate the chromosomes according to mutation rate Fig. 6. Flowchart for GA method. 6 Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx D.S. Pillai, N. Rajasekar vector. The binomial crossover operation in R-JADE can be mathematically represented as Table 3 GA and its variants used for parameter identification. Method utilization of search space due to mutation and crossover • Better operations. in exploration but poor in exploitation. • Good computational burden. • High technique converges fast when number of unknowns is low. • NR computational burden. • Low depends on the parameters optimized by GA. • Accuracy objective based optimization. • Multi in real-time operating conditions. • Accurate convergence. • Slow stage selection routine using tournament and roulette• Two wheel selection. local search. • Improved tuning of control parameters. • Adaptive • Slow convergence. GA GA + NR GA + IP AGA + LS Xi . CG + 1 Uji, CG = bij Mi, CG + (1 − bij ). Xi, CG Specific comments Ui . CG, if f (Ui .(CG + 1) ) ≥ f (Xi . CG ) ⎫ =⎧ ⎨ ⎭ ⎩ x i . CG , if f (Ui .(CG + 1) ) < f (Xi . CG ) ⎬ (24) In addition, a ranking based mutation was also proposed to ensure that high quality vectors are selected for the mutation process. R 2 PMi = ⎛ i ⎞ ⎝M⎠ (25) Similarly in [52], an improved adaptive DE (IADE) method was proposed; which is an extended adaptation of conventional DE method in which the choice of scaling factor (F) and crossover rate (Cr) is wisely done by utilizing the memory of the particles. The control parameter ‘A’ used in this method links the current and previous fitness values of a particle and ‘A’ is defined as A= fitness. best (i) fitness. best (i − 1) (26) In penalty based differential evolution (P-DE) presented in [53], boundary limits are checked when a mutant parameter is selected as the trial vector. A new penalty function was introduced in the control structure to make sure that all the trial vectors lie within the specified range. Any control variable violating the solution space during particle update will be replaced by the penalty based function to lie within the constraints defined as follows; (23) For a better understanding, the flowchart for DE method is depicted in Fig. 7. Related works on DE based optimization are presented in [87,88]. Ui (CG) − r (x iH − x iL), Ui (CG) > XiH ⎫ Ui (CG) = ⎧ U ⎨ ⎭ ⎩ i (CG) + r (XiH − XiL ), Ui (CG) < XiL ⎬ 3.2.2.1. Hybrid and adaptive versions of DE. In a vision to achieve an enhanced trade-off between exploration and exploitation capability; researchers have applied many adaptive variants of DE and its improved versions for PV parameter identification. Among them, adaptive differential evolution (JADE) is an improved variant which employ adaptive mutation and crossover rates rather than using user defined ones [50]. To further improve JADE method; repaired adaptive differential evolution (R-JADE) was proposed in [51]. This method introduced an automatic repairing technique for crossover rate which improves the randomness in control variable. The repaired crossover rate is obtained by using a binary string, ‘bij ’ generated for each target (27) where ‘Ui (CG) ’ is the recombined vector, ‘ XiH ’ and ‘ XiL ’ are the upper and lower bounds of ‘ Xi ’ respectively and ‘r’ is a random number in the range {0, 1}. DEIM is a hybrid version of DE proposed in [54,55] which uses hybrid mutation operation per iteration. The type of mutation to be used depends on the current standard deviation (σ) of the vectors and can be expressed as; M , if σ G < ε2 σ 0||⎫ M=⎧ e ⎨ M otherwise ⎬ ⎭ ⎩ d, (28) Table 4 Parameter identification using GA and its variants. Method GA [45] AGA + NR [46] GA + IP [47] GA + LS [48] Approach Metaheuristic Hybrid Hybrid Hybrid RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – Cell/Module 0.01–1.2 0.331 N. S 99,050 N. S 0.136 N. S 1.0196 N. S 12,170 – – – – 50 W panel (Make N.S) RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – KC200GT PV Module 0.01–1.2 0.331 50–1000 883.925 N. E N-R Method 1–2 1.106 N. E N-R Method – – – – RS (Ω) 0.01–1.2 0.29 RP (Ω) 50–1000 480.496 Iph (A) N. E N-R Method a1 1–2 1.112 I01 (µA) N. S 0.00423 a2 1–2 1.377 I02 (µA) N. S 0.0091 PV Model SD Range Set Extracted Parameters RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – 0.001–1 0.214 50–1100 1060.66 N. E A.M 1–2 1.348 N. E A.M – – – – PV Model SD Range Set RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – W.R.T Slope at Voc 0.0364 W.R.T Slope at Isc 52.7293 1–5% of Isc 0.5–2 0–10% of Isc – – 0.7607 1.4804 0.3198 – – PV Model SD Range Set Extracted Parameters PV Model SD Range Set Extracted Parameters DD Range Set Extracted Parameters Extracted Parameters N.S: Not Specified, N.E: Not Extracting, A.M: Analytical Method W.R.T: With Respect To. 7 KC200 GT PV Module 57 mm RTC France Solar Cell Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx D.S. Pillai, N. Rajasekar Fig. 7. Flowchart for differential evolution. Re -initialization Start NO DE Initialization Re - Any improvement in the fitness of trial vectors compare to target vectors?? initialization Condition satisfied ?? YES Select the target vectors and perform YES DE operation NO Update target vectors Mutation to obtain the mutant vector NO Is objective function Crossover to obtain the obtained ?? YES trial vector Display the best target vector Calculate objective funcion stop Next iteration Multi crystalline S75 PV module was carried out in [53]. In agreement to the control strategies adopted, the method has shown good accuracy and a satisfactory convergence. The validations presented in this work shows good agreement with the experimental values especially under varying irradiation levels. Moreover, it outperforms GA, SA, DE and PSO algorithms as well. In a more critical perspective, the extracted values of ‘RS’ and ‘RP’ were found to be unsound at particularly low irradiance profiles. Unlike all other DE variants, DEIM does not perform of a local search. Instead, the two mutation steps incorporated per iteration improves the search ability and reduces the number of assessments required to reach the optimum solution. Furthermore, DEIM uses a sigmoid logistic function which can significantly improve the convergence speed. The application is discussed in [54,55] where the hybrid DEIM technique was used to extract the model parameters of SD and DD models. In the validations presented, the method has outperformed all conventional DE methods in terms of accuracy and convergence speed. The algorithm was also tested to analyze its performance under different irradiance levels and the results obtained were in good agreement with the experimental curves. However, in SD model, the range of ‘RP’ is chosen so high compared to the extracted parameter value. Furthermore, in the DD model, the extracted parameters ‘a1’ and ‘a2’ shows the same value which may induce false emulation under varying irradiation levels. Some key points on the peculiarity of each DE variant is illustrated in Table 5 and Table 6 represents the results obtained for each DE variant when applied for parameter extraction. 3.2.2.2. Application towards PV parameter extraction. Unlike GA, DE primarily utilizes the mutation operation rather than the cross-over operation as an initial search. The mutation operation is based on the weighted difference of two vectors which can substantially improve the search space. Hence, the recombination phase will be more effective to achieve feasible parameters. Authors in [49] employed the DE based optimization technique to extract the SD model parameters of three different solar cells/modules. In this work, three industrial PV modules were considered for validation. The proposed method extracted different parameter values for ‘a’, ‘Rs’ and ‘Rp’ at different temperature and irradiance levels with a mutation and crossover rate of 0.4. The ideality factor was found decreasing with increase in temperature. Furthermore, the method outperformed ABC, ABSO, AIS and ANN based SD models in validation. The application of R-JADE algorithm towards PV parameter extraction (both SD and DD model) for a 57 mm dia RTC France PV cell is presented in [51]. The proposed ranking based mutation ensures that the best vectors are selected for mutation operation while the cross-over repairing technique based on the average number of components taken from the mutant gives an improved exploitation. The method shows improved RMSE but suffers from poor convergence speed. However, in validation, R-JADE has outperformed ABC, ABSO, AIS and conventional DE algorithms. The advantage of IADE when applied for parameter extraction is that the memory based adaptive control makes sure that the search space is better exploited while updating the particles. Hence, the resultant vectors are expected to be potentially more feasible solutions. The application of IADE for PV parameter extraction is presented in [52] where the model parameters for an 80 W PV module were estimated. The experimental validations were done for both the PV cell and the PV module. As shown in Table 6, IADE extracted different parameters for different irradiance levels. At several instances, parameter values obtained for ‘RS’, ‘RP’ and ‘a’ were erroneous with respect to the change in irradiation levels. However, in the validations presented, IADE outperforms GA, PSO and SA. When P-DE is used to optimize model parameters, the effect of penalty function is that it ensures that all particles reach the global optimum by continuously shifting the violated parameters towards the feasible region. However, the increased search space in penalty based DE method can reduce the convergence speed and hence a large mutation factor is usually used to account for it. The application of P-DE for the parameter extraction of a 3.2.3. Particle Swarm Optimization Algorithm (PSO) PSO is a bio inspired algorithm evolved from the bird flocking phenomenon [89–91]. The method defines a solution space where the target vectors are treated as particles. These particles move along the solution space with a velocity, ‘V’ to reach the optimal position. PSO method has three phases, initialization, exploration and evaluation. ■ Initialization: Defines the population size and starts from a random particle. ■ Exploration: The current position of the particles, ‘Xi’ updates as they move along the search space with velocity, ‘Vi’. During the evaluation process, the current best position of the particle, ‘Pbi’ and the global best position ‘Gb’ are recorded. The position of each particle is 8 Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx D.S. Pillai, N. Rajasekar Pbi = Xik , Gb = Pbi , Table 5 DE and its variants used for parameter identification. Method if f (x ik ) ≥ f (Pi ) if f (Pbi ) ≥ f (Gb) (31) Specific comments operation is used for initial exploration. • Mutation recombination phase compared to GA. • Effective fitness evaluation for parent vectors. • No mutation and crossover operations. • Adaptive diversity among populations. • Better crossover rate repairing. • Automatic for vectors. • Ranking selection of mutant vector. • Probabilistic based cross over and mutation phases. • Memory diversity • Improved premature convergence. • No trial vectors. • Penalizes exploitation. • Better mutation operations. • Hybrid initial local search. • No • Good convergence speed. DE JADE R-JADE IADE P-DE DEIM The continuous evaluation of the global best solution makes PSO best suited for parameter extraction and maximum power point tracking applications [92–98]. For a better understanding of the algorithm, a flowchart is presented in Fig. 8. 3.2.3.1. Hybrid and adaptive versions of PSO. Inspired by the flexibility and adaptability of PSO towards any difficult optimization problem, researchers have proposed many variants of PSO to solve PV model parameter identification problem. In [56], an adaptive PSO (APSO) based on linearly decreasing inertia weight function is proposed. The linearly decreasing inertia weight function used in APSO method is given by; W (t ) = Wmax − (Wmax − Wmin ) k / k max updated using the following strategy; Xik + 1 = Xik + Vik + 1 (29) Vik + 1 = W . Vik + [r1 C1 (Pbi − Xik )] + [r2 C2 (Gb − Xik )] (30) (32) Alternatively in [57], the authors proposed an improved PSO (IPSO) using dynamic inertia weight function to control the velocity of the particle. The modified inertia weight function used in IPSO is; (33) W ′ = Wu−k where Xik + 1 represents the updated position of the ith particle, Xik is the current position of the ith particle, Vik + 1 is the updated velocity and Vik is the current velocity. ■ Evaluation: The fitness value of the particles is evaluated in this phase to update the recorded data for ‘Pbi ’ and ‘Gb ’. where ‘W ′’ is the user defined inertia weight in the range {0, 1}, ‘u’ uses a value between 1.001 and 1.005 and ‘K’ is the iteration number. PSO with velocity clamping (VC-PSO) is a finely tuned version of APSO which employs a velocity clamping function to update the particles [58]. The velocity update in VC-PSO for the jth particle is defined as; Table 6 Parameter identification using DE and its variants. Method DE [49] R-JADE [51] IADE [52] P-DE [53] DEIM [54,55] Approach Analytical Metaheuristic Metaheuristic Metaheuristic Hybrid RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – Cell/Module 0.1–1 Varies with G&T 100–3000 Varies with G&T N. E N. E 1–2 Varies with G&T N. E N. E – – – – Multi Crystalline S 75 RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – 57 mm dia RTC France Solar Cell 0–0.5 0.03638 0–100 53.7185 0–1 0.76078 1–2 1.4812 0–1 0.32302 – – – – RS (Ω) 0–0.5 0.03674 RP (Ω) 0–100 54.4854 Iph (A) 0–1 0.76078 a1 1–2 1.451 I01 (µA) 0–1 0.22597 a2 1–2 2 I02 (µA) 0–1 0.7494 PV Model SD Range Set Extracted Parameters RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – 0–2 Varies with G&T 50–5000 Varies with G&T 0–5 Varies with G&T 0–10 Varies with G&T 0–1 Varies with G&T – – – – PV Model DD Range Set Extracted Parameters RS (Ω) RP (Ω) Iph (A) a1 I01 (µA) a2 I02 (µA) 0–1 Varies with G 50–1000 Varies with G 0–7.6 Varies with G 0.5–4 Varies with G 0–1 Varies with G 0.5–4 Varies with G 0–1 Varies with G PV Model SD Range Set RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – 0.1–2 100–5000 1–8 1–2 – – Extracted Parameters DD Range Set Extracted Parameters 0.5533 115.211 4.4412 1.376 1E− 12 to 1E −5 1.01 – – RS (Ω) N. S 0.59 RP (Ω) N. S 541.368 Iph (A) N. S 3.5556 a1 N. S 1.3971 I01 (µA) N. S 4.33 a2 N. S 1.3971 I02 (µA) N. S 4.67 PV Model SD Range Set Extracted Parameters PV Model SD Range Set Extracted Parameters DD Range Set Extracted Parameters G: Irradiance, T: Temperature, N.S: Not Specified, N.E: Not Extracting. 9 SL80 CE Multi Crystalline S 75 KC120 PV Module Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx D.S. Pillai, N. Rajasekar Fig. 8. Flowchart for PSO algorithm. Vj, if Vj < Vmax ⎫ Vj + 1 = ⎧ Vmax . j, otherwise ⎬ ⎨ ⎩ ⎭ accuracy. The authors identified that the accuracy is highly dependent on the initial setting of parameter values for ‘RS’ and ‘RP’ since it directly affects ‘a2’ and ‘I02’. Hence, a global approach was used to set the initial ranges for these parameters and is expressed Table 8. However, the extracted parameter values show significant error with respect to the theoretical concepts of a PV. The compatibility of IPSO towards parameter extraction is that the dynamic inertia weight function reduces the velocity accordingly to make use of the positions that a conventional PSO might have missed to achieve a better curve fit. In the validations presented in [57], IPSO outperformed the conventional GA algorithm. However, a close examination on the results presented in Table 8 indicates that the parameter ‘Iph’ was extracted out of the range selected. Furthermore, the convergence characteristics were not analyzed. At the same time, high values of velocity can sometimes tempt the particles to move away from their solution ranges in PSO and APSO. Hence, to compensate this draw back; velocity clamping approach was proposed in [58] for achieving an efficient trade-off between the local search and the global search ability of the algorithm [101,102]. A review on the performance of VC-PSO based parameter identification gives the following observations: 1) The extracted value for a1 is > 1 and a2 is > 2; which are not in fit with theoretical concepts, 2) In optimization, assuming value for one parameter can affect the quality of other parameters as well, 3) Wrongly extracted value for parameter ‘RP’ might be affecting a1 and a2 since the value of ‘RP’ has a direct effect on the ideality factor [56] and 4) A three-diode model was proposed for PV modeling and the model parameters were extracted to show its superiority when compared with the conventional SD and DD models. While, in CPSO, when there is stagnation in solutions; a chaotic search is performed to produce ‘D’ neighboring points around the stagnated particle to update its position and thereby eliminating the local minima. After critically reviewing the CPSO technique in [59], following observations have been made: 1) The global search performance and the local convergence of conventional PSO are improved by embedding a chaotic search, 2) It does not require any trial runs to set the initial ranges of the PV parameters and instead, a mathematical formulation indicated in Table 8 has been used, 3) In validation, the method outperformed [103–106]; viz. the conventional Newton method, fivepoint method and the conductance method. However, control (34) where ‘Vmax . j ’ is the maximum allowable velocity, ‘Vj ’ is the current velocity of the jth particle and ‘Vj+1’ is the new velocity. By introducing a chaotic based principle [99], a new chaos particle swarm optimization (CPSO) was proposed in [59]. Apart from conventional and adaptive versions; PSO with time varying inertia weight and acceleration coefficients (TVIWAC-PSO) proposed in [60]. TVIWAC-PSO adaptively controls both inertia weight and acceleration coefficients in the conventional PSO. The control of these parameters can be expressed as; For inertia weight control, W = We + k max − k (We − Ws ) k max − 1 (35) For acceleration coefficient control, C1n = C1e + k max − k (C1e − C1s ) k max − 1 (36) C2n = C2e + k max − k (C2e − C2s ) k max − 1 (37) where ‘C1n’ and ‘C2n’ are the updated values of C1 and C2 respectively, ‘C1s’, ‘C2s’, ‘C1e’ and ‘C2e’ represents the start values and end values of C1 and C2 respectively. For optimal solution, ‘C1’ tends to vary from 2.5 to 0.5 and ‘C2’ varies from 0.5 to 2.5. In a hybrid PSO version proposed in [61], PSO with inverse barrier constraints (IBCPSO) was merged with an analytical method for optimization. Compared to other PSO methods, IBCPSO used an Inverse Barrier Constraints (IBC) based objective function to optimize model parameters. 3.2.3.2. Application towards PV parameter extraction. Improper selection of control parameters in conventional PSO can make the algorithm to get trapped at a local optimum [100]. To attenuate the aforementioned drawback, adaptive selection of inertia weight was found beneficial in [56]. In this regard, a better global search during the initial runs and an efficient local search during the final runs were achieved. Hence, when used for parameter identification APSO safeguards the best solutions until the end. The experimental results of the proposed work indicated the superiority of the DD model with respect to the SD model in terms of 10 Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx D.S. Pillai, N. Rajasekar parameters play a crucial rule in any PSO variant and hence, finding optimal control parameters using trial runs is computationally very expensive [107–109]. Hence, in TVIWAC-PSO, all the three control parameters are adaptively controlled throughout the iterations. Furthermore, it facilitates better exploitation and faster convergence. From the proposed research work in [60], it is evident that time varying values of inertia weight and acceleration coefficients enhanced both the convergence speed and the accuracy of the algorithm compared to all other PSO versions. Furthermore, in validation, TVIWAC-PSO outperformed ABSO, SA and PSO based methods. However, the performance of the algorithm in varying irradiation and temperature levels were not assessed. Rather than conducting field tests to determine the ranges of the initial parameters; IBCPSO incorporates these constraints in the objective function itself. This will heavily penalize the objective function when solutions reach near to their boundaries. Due to this heavily constrained objective function evaluation, [61] adopted an analytical method along with IBCPSO to extract two parameters of a SD model. The consolidated data is illustrated in Table 8 and the following inferences on the method are likely to be suggested: 1) A new objective function based on the barrier constant, irradiance and temperature was proposed, 2) In validation, IBCPSO outperformed all the conventional direct methods used for parameter extraction, 3) The change in series resistance with respect to diode ideality factor was monitored and 4) Time varying model parameters were suggested to account for the time varying temperature levels. A critical comparison of all the PSO variants are presented in Table 7 and the parameters identification results are illustrated in Table 8. Readers can also refer [110–112] where reviews on metaheuristic algorithms are presented with an application to maximum power point tracking. 3.2.5.2. Application towards PV parameter extraction. In ABCO, to further improve a stagnated solution, scout bees are used perform random searches. This exploration significantly improves the quality of the solutions when used for parameter identification. In the validations presented in [63], ABC outperformed HS, PSO, GA and BFA in terms of accuracy as well as convergence speed. However, all comparisons were made for same irradiance levels. Inspired by the effectiveness of ABCO, the authors in this research suggested harmony search algorithms as an effective alternative to solve parameter identification problem. On the other hand, in ABC + NMS hybrid technique, a three-stage strategy is used to reach the optimal solution: 1) ABC is used for initial exploration, 2) NMS is used to perform exploitation and 3) Adaptive NMS is used for a fine search to reach the global best. In [64], ABC + NMS algorithm was used to extract both the SD and DD model parameters. In validation, ABC + NMS strategy outperformed ABSO, STLBO and R-JADE algorithms. Furthermore, the method was successfully validated in varying environmental conditions for a PWP 201 PV module. However, the method suffers from slow convergence and there are a number of control parameters to be manually tuned. The consolidated data is illustrated in Table 10. 3.2.6. Artificial Bee Swarm Algorithm Optimization (ABSO) ABSO is a similar algorithm to PSO but it follows the bee algorithm approach [118]. Similar to ABCO, bees having low quality food sources (solutions) are treated as scout bees which explore the search space. However, a notable procedure followed in ABSO is that among the onlooker bees; some bees are selected as elite bees [65]. Elite bees encourage the onlooker bees to find the best solution obtained so far. Using the tournament selection approach, each onlooker bee selects an elite bee to update their position as follows; j Xnew = X j + Wb rb (Xbj − X j ) + We re (Xej − X j ) 3.2.4. Mutative Scale Parallel Chaos Optimization Algorithm (MPCOA) Unlike swarm optimization, [113,114] proposed a population based pure chaotic optimization technique (COA) with multiple chaotic mapping on each decision variable. MPCOA is an improved version of COA which utilizes the cross over and merging operations between two randomly selected parallel variables along with a mutative scale search space to achieve a wider search space for the particles [62]. (38) ‘Xe’ is the elite bee, ‘Xb’ is the best achievement by onlooker bee and ‘rb’ and ‘re’ are random numbers in the range {0, 1}. ‘Wb ’, ‘We ’ are control parameters which are linearly decreasing functions defined as 3.2.4.1. Application towards PV parameter extraction. Since PV parameters are to be very precise, MPCOA utilizes two additional strategies: 1) The solutions obtained by chaotic search are further updated using recombination and merging operations, 2) When parallel solutions are gathered, a mutative scale search space is used to exploit the exact solution. MPCOA based PV model realized in [62] was validated in different irradiation levels for two different PV modules. In the validations carried out, the method outperformed GA, CPSO, ABSO, PS, SA and HS techniques; both in terms of accuracy and convergence speed. The results obtained are consolidated in Table 9. Regardless of its computational burden, it is worth to mention that MPCOA has shown prodigious capability in handling the parameter identification problem. Wb = Wb , max − (Wb max − Wb min ) k / k max (39) We = We , max − (We max − We min ) k / k max (40) 3.2.6.1. Application towards PV parameter extraction. In ABSO, to balance between local and global search; the control parameters, ‘Wb ’ and ‘We ’ are adaptively tuned during the runs. Further, the elite strategy adopted in ABSO improves the quality of potential solutions through Table 7 PSO and its variants used for parameter identification. Method PSO APSO 3.2.5. Artificial Bee Colony Optimization (ABCO) ABCO algorithm has been evolved from the food search behavior of honey bees [115]. In ABCO, three types of bees continuously search for food and their food sources are treated as the solutions [116,117]. Among the bees, scout bees explore the search space while employed bees and onlooker bees perform exploitation. IPSO VC-PSO CPSO TVIWAC-PSO 3.2.5.1. Hybrid variant of ABCO. In [64], Nelder-Mead algorithm (NMS) was fused with ABCO to further enhance the performance of the algorithm. In the proposed hybrid strategy (ABC + NMS), ABC was used to perform the initial global search while the NMS algorithm performs the local search during the final runs. IBCPSO 11 Specific comments exploration and exploitation. • Good memory requirement. • Large depends upon user defined values for control • Performance parameters. control of inertia weight function • Adaptive best solutions until the end. • Preserves dynamic inertia weight function. • Uses exploitation of search space. • Improved control of velocity of particles. • Optimal decreasing inertia weight. • Linearly chaotic search. • Embedded exploitation. • Excellent complex. • Computationally control of all control variables. • Adaptive tradeoff between exploration and exploitation. • Enhanced convergence speed. • Good function based on barrier constraints. • Objective initial ranges to be set. • No • High computational burden. Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx D.S. Pillai, N. Rajasekar Table 8 Parameter identification using PSO and its variants. Method APSO [56] IPSO [57] VCPSO [58] CPSO [59] TVIWACPSO [60] IBCPSO [61] Approach Metaheuristic Metaheuristic Metaheuristic Metaheuristic Metaheuristic Hybrid PV Model DD Range Set Extracted Parameters RS (Ω) RP (Ω) Iph (A) a1 I01 (µA) a2 I02 (µA) Cell/Module ± 70% of Slope at Isc 0.02386 ± 70% of Slope at Voc 4.04 N. S 4.21 1–5 1.74 0–1 121 1–5 4.78 0–1 0.0005 50 W Multi-Silicon Module. Make N. S RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – N.S 0–0.05 0.02334 10–500 100.13 1.5–1.6 1.6928 1–5 1.6961 0–100 56.3 – – – – PV Model DD Range Set Extracted Parameters RS (Ω) RP (Ω) Iph (A) a1 I01 (µA) a2 I02 (µA) N. S 0.01515 N. S 33.704 Isc Isc N. S 1.233 N. S 0.0084 N. S 2.57 N. S 15.29 PV Model SD Range Set Extracted Parameters RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – w.r.t Slope at Isc 0.0354 w.r.t Slope at Voc 59.012 1–5% of Isc 0.7607 0.5–2 1.5033 0–10% of Isc 0.4 – – – – PV Model SD Range Set Extracted Parameters RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – N. A 0.03638 N. A 53.6894 N. A 0.76078 N. A 1.4811 N. A 0.32267 – – – – PV Model SD Range Set Extracted Parameters RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – IBC Varies with G & T IBC Varies with G & T N. E A.M IBC Varies with G & T N. E A.M – – – – PV Model SD Range Set Extracted Parameters N.S 57 mm RTC France Solar Cell 57 mm RTC France Solar Cell KD210 GH-2PU G: Irradiance, T: Temperature, N.S: Not Specified, N.E: Not Extracting, N.A: Not Applicable, w.r.t: with respect to. Also, it is important to note that the value of I and E is usually chosen as 1. The value of ‘λ’ decides whether to modify SIV or not while ‘µ’ decides which solution should migrate. A good solution indicates that high HSI islands have large number of species while a low HSI island with small number of species indicates a poor solution. better exploitation. In the research work proposed in [65], a similar objective function to that of ABCO was employed to extract both the SD and DD model parameters; and the results are illustrated in Table 11. Compared to ABCO, ABSO shows a better performance in the DD model but lacked rapid convergence. In the validations presented, ABSO outperforms PSO, GA, PS, HS, CPSO and SA. However, the validations were based on only for one irradiance level. Furthermore, the optimal performance of ABSO depends on the user defined control parameter ‘ne’ (number of elite bees). 3.2.7.1. Adaptive variant of BBO. To overcome the disadvantages of the conventional BBO algorithm [120], hybrid mutation and hybrid migration is proposed in BBO-M [66]. Hybrid migration in this method replicates the mutation phase in DE algorithm. Furthermore, a chaotic search is also introduced in BBO-M. In an essence; BBO-M integrates new advantages into the conventional BBO keeping its advantages intact. 3.2.7. Biogeography Based Optimization (BBO) BBO method works on the theory of island Bio-Geography [119]. Each Island is considered to have a habitat suitability index (HSI) and each variable in the island is called as suitability index variable (SIV). In BBO method, immigration with an immigration rate, ‘λ’ and emigration with an emigration rate, ‘µ’ are the two fundamental phases of the algorithm. The immigration and emigration of the Sth individual can be mathematically represented as s λs = I ⎛1 − ⎞ n⎠ ⎝ (41) s μs = E ⎛ ⎞ ⎝n⎠ (42) 3.2.7.2. Application towards PV parameter extraction. When used for parameter identification, the hybrid migration replicating the mutation phase of DE provides diversity among the generations and makes the algorithm robust. Furthermore, the chaotic variable is used to find the optimal solution once the solution reaches close to the optimal value. The parameter identification using BBO-M proposed in [66] has been reviewed and the following inferences are made: 1) BBO-M is computationally expensive since the number of parameters to be controlled through the runs is high, 2) In model parameter extraction, Table 9 Parameter identification using MPCOA. Ref. [62] Approach Numerical PV Model SD √ Range Set Extracted Parameters DD √ Range Set Extracted Parameters RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – Cell/Module 0–0.5 0.03635 RS (Ω) 0–0.5 0.03635 0–100 54.6328 RP (Ω) 0–100 54.2531 0–1 0.76073 Iph (A) 0–1 0.76078 1–2 1.48168 a1 1–2 1.47844 0–1 0.32655 I01 (µA) 0–1 0.31259 – – a2 1–2 1.78459 – – I02 (µA) 0–1 0.04528 57 mm dia RTC France Solar Cell 12 Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx D.S. Pillai, N. Rajasekar Table 10 Parameter identification using ABC and its hybrid variant. Method ABCO [63] Approach Metaheuristic ABC + NMS [64] Hybrid PV Model SD Range Set Extracted Parameters DD Range Set Extracted Parameters PV Model SD Range Set Extracted Parameters RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – 0–0.5 0.0364 RS (Ω) 0–0.5 0.0364 0–100 53.6433 RP (Ω) 0–100 53.7804 0–1 0.7608 Iph (A) 0–1 0.7608 1–2 1.4817 a1 1–2 1.4495 0–1 0.3251 I01 (µA) 0–1 0.0407 – – a2 1–2 1.4885 – – I02 (µA) 0–1 0.2874 RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – 0–2 1.20127 0–2000 981.982 0–2 1.03051 1–2 48.643 0–50 3.48226 – – – – Cell/Module 57 mm RTC France Solar Cell PWP 201 PV Module Table 11 Parameter identification using ABSO. Method ABSO [65] Approach Metaheuristic PV Model SD Range Set Extracted Parameters DD Range Set Extracted Parameters RS (Ω) RP (Ω) Iph (A) a I0(µA) – – Cell/Module 0–0.5 0.03659 RS(Ω) 0–5 0.03657 0–100 52.2903 RP (Ω) 0–100 54.6219 0–1 0.7608 Iph (A) 0–1 0.76078 1–2 1.47583 a1 1–2 1.46512 0–1 0.30623 I01 (µA) 0–1 0.26713 – – a2 1–2 1.98152 – – I02 (µA) 0–1 0.38191 57 mm dia RTC France Solar Cell method showed good accuracy particularly in low irradiance profiles. Furthermore, it outperformed AIS and GA methods in terms of accuracy and convergence speed. It is noteworthy that the parameters extracted using BFA will be helpful in characterization of partially shaded PV modules. However, the model parameters; ‘RS’ and ‘a’ obtained for an irradiation of G = 200 W/m2 were erroneous. BBO-M dominates PSO, BBO, ABSO, HS, PS, DE and SA algorithms in terms of accuracy, 3) ABSO is poor in convergence and 4) Validations were not done in varying irradiation and temperature profiles. Table 12 indicates the resultant parameters obtained via optimization. 3.2.8. Bacterial Foraging Algorithm (BFA) BFA is an evolutionary algorithm evolved from the food search behavior of Escherichia coli bacteria (E-coli) [121]. BFA optimization is performed with the help of four processes; chemotaxis, swarming, reproduction and elimination-dispersion [67]. In chemotaxis phase, E-coli swim or tumble towards a food source while in swarming, all bacteria follows the bacterium which is at the optimum path with the help of a suitable communication strategy. In reproduction phase; the healthier bacteria split into two according to their fitness function in such a way that the swarm size remains constant. In elimination-dispersion step; to reduce the likelihood of bacteria converging to local optima, some bacteria get eliminated and some get dispersed according to a predefined elimination-dispersion probability. 3.2.9. Bird Mating Optimization Algorithm (BMO) BMO deals with a society of four different types of birds; polyandrous, monogamous, polygynous, and promiscuous [68]. To search for potential solutions in the search space, BMO uses several mating strategies: 1) Among many, monogamous birds select one elite female bird using a roulette wheel probability to produce a brood, 2) Polygynous birds mate with more than one female bird to produce a brood having multiple combinations of female genes and 3) The polyandrous birds adopt a probabilistic approach to select an elite male bird to generate their brood. Furthermore, the worst birds in the society are replaced by promiscuous birds which are more feasible solutions. The initial generation of promiscuous birds is generated using a chaotic sequence and is updated as the algorithm proceeds. 3.2.8.1. Application towards PV parameter extraction. In BFA, to efficiently explore the search space from all dimensions, swimming movement explores directional search spaces and the tumble movement explores random spaces. The reproduction and elimination phases provide an excellent exploitation with less computational effort as well. In addition, BFA does not require any initial guess on the parameters to be extracted. BFA based parameter identification proposed in [67] has been reviewed and the obtained results are illustrated in Table 13. As illustrated in the reviewed data, BFA extracted different parameters for different environmental conditions. ‘IPh’ and ‘Id’ were mathematically calculated whereas the extracted parameters are ‘RS’, ‘RP’ and ‘a’ . The validations were done for constant irradiance, varying temperature and vice versa. In validations, the 3.2.9.1. Simplified BMO variant. Compared to BMO, simplified BMO (SBMO) proposed in [69] has the following peculiarities: 1) SBMO has an improved breeding concept similar to the reproduction in [122–124], 2) A ranking based strategy is adopted to classify the birds in the society. In SBMO birds are classified into three groups according to their fitness value as; Type I: Female birds (N1). N N1 = round ⎛ ⎞ ⎝ 10 ⎠ (43) Type II: Male birds mate with one female bird (N2). Table 12 Parameter identification using BBO-M. Method BBO-M [66] Approach Metaheuristic PV Model SD Range Set Extracted Parameters DD Range Set Extracted Parameters RS(Ω) RP (Ω) Iph (A) a I0 (µA) – – Cell/Module 0–0.5 0.03642 RS(Ω) 0–0.5 0.03664 0–100 53.3623 RP(Ω) 0–100 55.0494 0–1 0.76078 Iph (A) 0–1 0.76083 1–2 1.47984 a1 1–2 2 0–1E-6 0.31874 I01 (µA) 0–1E-6 0.59115 – – a2 1–2 1.45798 – – I02 (µA) 0–1E-6 0.24523 57 mm dia RTC France Solar Cell 13 Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx D.S. Pillai, N. Rajasekar Table 13 Parameter identification using BFA. Method BFA [67] Approach Metaheuristic PV Model SD Range Set Extracted Parameters RS (Ω) RP(Ω) Iph (A) a I0(µA) Cell/Module 0–2 Varies with G & T 50–500 Varies with G & T N. E A.M 1–2 Varies with G & T N. E A.M SM55 N.E: Not Extracting, G: Irradiance, T: Temperature, A.M: Analytical Method. 7 ⎞ N2 = round N ⎛ ⎝ 10 ⎠ GGHS and IGHS algorithms. The consolidated results of [68,69] is presented in Table 14. (44) Type III: Male birds mate with two female birds (N3) 3.2.10. Flower Pollination Algorithm (FPA) FPA is a nature inspired algorithm that resembles the pollination process of flowers [125]. Two types of pollination processes are used in FPA method to search for new solutions [70]: 1) Biotic pollination accomplished using insects; 2) Abiotic pollination, where wind acts as the pollinator. Cross-pollination/biotic pollination takes place between different species of different plants; accompanied by levy flights, bees, birds and bats as pollinators represents the global search of the algorithm which can be mathematically represented as; (45) N3 = N − N1 − N2 where ‘N” is the total number birds in the society set by the user. 3.2.9.2. Application towards PV parameter extraction. The probability based selection approach and elite strategy proposed in BMO ensure that the best birds are selected for mating and hence, the broods will be more feasible solutions. At the same time mutation control factor (mcf) maintains diversity among the population and avoids premature convergence. Since chaotic sequence can discover potential solutions in the untested regions of search space; BMO easily escapes from the local optima. On the other hand, in SBMO; type II and type III birds move randomly towards the elite birds from all dimensions of the search space for a better exploration while type I birds are high quality solutions which exploit the search space by self-breeding. The prime advantage of SBMO is that it is more user-friendly as it doesn't need real time control of any parameters after initialization. In [68] the SD model parameters for a 57 mm dia RTC France commercial solar cell were extracted using BMO algorithm. A critical review of BMO based parameter identification gives the following observations: 1) The algorithm with its enhanced ability to search for global optimum via various sleeking patterns has outperformed CPSO, GA, PS, SA, HS, GGHS, IGHS and ABSO techniques in terms of accuracy, 2) In validation, the algorithm has also proved successful in tracking the MPP co-ordinates accurately, 3) BMO has excellent convergence characteristics and 4) The accuracy of model parameters in varying irradiation and temperature levels were not assessed. In SBMO based parameter identification proposed in [69], the value of ideality factor, ‘a’ was found varying in the range of 1.99–2 with respect to a corresponding change in irradiation levels from 1000 W/m2 to 200 W/m2. Sticking to the basic concepts of PV, this can induce false emulation particularly in varying irradiation levels. The initial range set for parameter ‘RP’ was too low for a configuration of 160 PV cells connected in series. Hence, he extracted value of ‘RP’ was in the range of 5–10 Ω which is very low. This might have affected the optimization of parameter ‘a ’ as well. However, in validation, SBMO outperformed PSO, x it + 1 = x it + γ L (λ )(gbest − x it ) (46) ‘ x it + 1’ ‘ x it ’ is the resultant pollen and represents the current pollen. With wind as pollinator, self-pollination/abiotic pollination between different species of the same plant represents the local search of the algorithm. x it + 1 = x it + ε (xkt − x tj ) ‘ xkt ’, (47) ‘ x tj ’ represent pollens of the same species. The ε (epsilon) is of uniform distribution ε∈{0, 1}. 3.2.10.1. Hybrid version of FPA. Improving the pollen exploitation capability, a new Bee Pollinated Flower Pollination Algorithm (BPFPA) was proposed recently in literature by fusing the bee colony properties to the basic FPA [71]. Compared to FPA, a simplex method making use of the discard solution operator used in the ABC algorithm was incorporated in the basic FPA to build the BPFPA structure. 3.2.10.2. Application towards PV parameter extraction. Rather than using computationally expensive specific strategies, FPA uses a probability switch function to switch between global pollination and local pollination between the runs. The balance between exploration and exploitation is effectively laid by the utilization of global pollination during initial runs and local pollination during final runs. Hence the computational burden of FPA is very low. In the application discussed in [70], 1) FPA outperformed ABCO, ABSO, AIS, P-DE, BBO and SBMO in terms of accuracy and convergence time, 2) Initial range of the parameters was selected globally for all the modules used, 3) FPA Table 14 Parameter Identification using BMO and SBMO. Method BMO [68] SBMO [69] Approach Metaheuristic Metaheuristic PV Model SD Range Set Extracted Parameters DD Range Set Extracted Parameters PV Model SD Range Set Extracted Parameters RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – 0–0.5 0.03636 0–100 53.8716 0–1 0.76077 1–2 1.4817 0–1 0.32479 – – – – RS (Ω) 0–0.5 0.03682 RP (Ω) 0–100 55.8081 Iph (A) 0–1 0.76078 a1 1–2 1.4453 I01 (µA) 0–1 0.2111 a2 1–2 2 I02 (µA) 0–1 0.8769 RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – 0–0.5 Varies with G&T 0–100 Varies with G&T 0–1 Varies with G&T 1–2 Varies with G&T 0–1 Varies with G&T – – – – G: Irradiance, T: Temperature. 14 Cell/Module 57 mm RTC France Solar Cell Amorphous Silicon PV module Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx D.S. Pillai, N. Rajasekar minimum is high. SA was applied for parameter identification problem in [72]. In the proposed work, the validations were done based on an assumption that irradiation has no effect on the cell parameters which eventually is wrong. Further in validations presented, SA outperformed the conventional microcomputer based parameter extraction technique [128] and Pattern Search (PS) algorithm in terms of accuracy in an SD model. However, the performance of SA can be significantly improved if the control parameter ‘T’ is adaptively controlled. In LM + SA algorithm, SA based control of damping factor enhances the search ability of LM algorithm to achieve a global solution by improving the search routine during every Iteration [129]. When LM + SA algorithm was used for parameter identification in [73], SA based damping control increased the accuracy of all the model parameters extracted. In the validations presented, LM + SA algorithm outperformed GA, SA, PS, DE, CPSO, ABSO, GGHS and Newton methods. The results of parameter identification using SA and its hybrid variant are illustrated in Table 16. performed better in all conditions of temperature and irradiance with low RMSE error, 4) FPA has only two control parameters to be tuned in real time and 5) The probability switch function needs optimal control for satisfactory performance. On the other hand, the ABC discard operator employed in BPFPA generates diversity among the bee population to strengthen the pollens for a better exploration. This strategy further strengthens the exploitation process in FPA to achieve more accurate solutions. In BPFPA based parameter identification presented in [71], the model parameters, ‘IPh’ and ‘I0’ were calculated mathematically while ‘RS’, ‘RP’ and ‘a’ were extracted. In this research, the innovation of incorporating discard pollen strategy in BPFPA has remarkably increased the quality of extracted parameters. In validation, BPFPA outperformed PSO, GA, FPA, ABSO, HS, PS, SA and CPSO based parameter identification techniques. It is worth to mention that the method has shown terrific promise towards parameter extraction and can be considered as one of the most reliable extraction techniques. Furthermore, BPFPA shows good convergence characteristics as well. The extracted parameters are elucidated in Table 15. 3.2.12. Harmony Search Algorithm (HS) HS algorithm replicates the adjustment of pitch in musical instruments for achieving a pleasing harmony. In HS, a harmony memory (HM) is used to store a set of randomly generated harmony vectors. For updating each variable, either one of the following three rules is utilized: 1) Update by a value in the memory, 2) Update by choosing a value closer to HM, 3) Update using a random value. Through successive iterations, the worst harmonies in the memory are updated with better harmonies generated, yielding an optimal solution. 3.2.11. Simulated Annealing Algorithm (SA) Inspired by the process of production of crystals using annealing, SA algorithm was proposed in [126,127]. SA algorithm has two main processes: 1) Change over between states and 2) Control of temperature to obtain the lowest energy state. SA method starts at an initial solid state, ‘Xi’ with an energy level, ‘E i’. The next state ‘X2’ with an energy level ‘E2’ will be accepted only if the following equation is satisfied. (48) E1 − E2 ≤ 0 If E1 − E2 > 0 , the state is accepted according to the probability function given by E −E ⎛ 1 2⎞ P (E , TC ) = e⎝ KB TC ⎠ 3.2.12.1. Other variants of HS algorithm. Grouping based global harmony search (GGHS) is an improved variant of HS which wisely uses the harmonies in the harmony memory. In GGHS, HM is classified into groups based on their fitness quality and the improvisation is done using the following rules: 1) Select the interesting group using tournament selection, 2) Using roulette wheel selection, select an elite harmony from the interesting group to improvise the current harmony. Another adaptive variant; innovative global harmony search (IGHS) uses predefined high quality elite harmonies for improvisation. The high quality elite harmonies are selected from HM using a roulette wheel approach to update the current harmony. The conventional HS and all its improved versions were used for parameter identification in [74]. (49) The control parameter, ‘TC ’ is controlled during the whole search of the algorithm until the lowest energy state is obtained. 3.2.11.1. Hybrid variant of SA. In [73], a hybrid strategy (LM + SA) was proposed where SA algorithm was used to control the damping factor of Levenberg-Marquardt (LM) algorithm. LM algorithm has the complimentary features of two methods: 1) The steepest descent and 2) Gauss-Newton method. The switching between the two methods is ensured by its damping factor that has to be controlled during each iteration step. In LM + SA algorithm, SA optimization is used to optimize the value of damping factor in each iteration step. 3.2.12.2. Application towards PV parameter extraction. In HS, using the pre-defined and range specific harmonies in HM to update current solutions provide randomness in exploration of the search space. The two control parameters; pitch adjustment rate (PAR) and band width of generations (B.W) balances between exploration and exploitation capabilities of the algorithm [130,131]. After reviewing HS based 3.2.11.2. Application towards PV parameter extraction. In SA algorithm, even if there is randomness while exploring new solutions, the accuracy is low since the memory of the solutions is not used for updating the crystals. Hence, probability of solutions to get trapped at local Table 15 Parameter identification using FPA and BPFPA. Method FPA [70] BPFPA [71] Approach Metaheuristic Hybrid PV Model SD Range Set Extracted Parameters DD Range Set Extracted Parameters PV Model SD Range Set Extracted Parameters DD Range Set Extracted Parameters RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – Cell/Module 0–1 0.03655 RS (Ω) 0–1 0.03633 0–5000 52.8771 RP (Ω) 0–5000 52.3475 0–2 0.76079 Iph (A) 0–2 0.7608 1–4 1.47707 a1 1–4 1.47477 0–1 0.31068 I01 (µA) 0–1 0.30009 – – a2 1–4 2 – – I02 (µA) 0–1 0.16616 57 mm dia RTC France Solar Cell RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – 57 mm dia RTC France Solar Cell 0–2 0.0366 RS (Ω) 0–2 0.0364 50–900 57.7151 RP (Ω) 50–900 59.624 N.E A.M Iph (A) N.E A.M 0.5–2 1.4774 a1 0.1–2 1.4793 N.E A.M I01 (µA) N.E A.M – – a2 1.2–4 2 – – I02 (µA) N.E A.M N.E: Not Extracting, A.M: Analytical Method. 15 Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx D.S. Pillai, N. Rajasekar Table 16 Parameter identification using SA and its hybrid variant. Method SA [72] LM + SA [73] Approach Metaheuristic Hybrid PV Model SD √ Range Set Extracted Parameters DD Range Set Extracted Parameters PV Model SD Range Set Extracted Parameters RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – Cell/Module N. A 0.0313 RS (Ω) N. A 0.0345 N. A 64.1026 RP (Ω) N. A 43.1034 N. A 0.7617 Iph (A) N. A 0.7623 N. A 1.6 a1 N. A 1.5172 N. A 0.998 I01 (µA) N. A 0.4767 – – a2 N. A 2 – – I02 (µA) N. A 0.01 KC200GT PV Module RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – 57 mm RTC France Solar Cell N. S 0.03463 N. S 53.3264 N. S 0.76078 N. S 0.31849 N. S 1.47976 – – – – N.A: Not Applicable, N.S: Not Specified. routine steps: 1) Exploratory search and 2) Pattern move. Exploratory search starts at an arbitrary random point called base point (BP) and with BP as center, the initial search generates a mesh of 2n points by spanning 2n coordinate directions. In pattern move, the base point is updated to a new point in the current direction by harnessing the memory of the last two BPs and is expressed as; parameter identification carried out in [74], the following inferences are likely to be presented: 1) The parameter setting of all HS based algorithms are based on an initial trial, 2) In validations, HS outperformed PSO, SA, PS and GA algorithms in terms of accuracy, 3) HS is poor in convergence and 4) Performance of HS in varying irradiation and temperature levels were not assessed. Since accuracy is the uncompromised feature of any parameter extraction technique, GGHS adopts tournament selection to select the best group for updating the harmony while roulette wheel selection is adopted to enhance the probability of selecting a quality harmony from HM. When used for parameter extraction, with the same range of parameters as HS used, GGHS extracted quality model parameters especially for ‘Rp’ and ‘a’. In further validations, GGHS outperformed PSO, SA, PS and GA algorithms as well. However, similar to HS, GGHS shows slow convergence characteristics. On the other hand, compared to HS and GGHS, since the predefined harmonies are of high quality, the improvisation process in IGHS provides better solutions. While reviewing IGHS based parameter identification, following observations were made: 1) For DD model, the value of a2 is less than a1 which is not a theoretical fit, 2) IGHS is outperformed by GGHS in terms of accuracy in the SD model, 3) For a DD model IGHS extracted accurate parameters when compared with HS, GGHS, GA, PSO, SA and PS methods. The consolidated parameter identification data obtained for HS algorithm and its improved versions is shown in Table 17. k+ k k k−1 XBp = XBp + [XBp − XBp ] (50) If this move deemed successful, i.e. the objective function has imk+ ’ and if proved, the next exploratory search starts from the new BP, ‘ XBp the pattern move is unsuccessful, then the exploratory search again k ’. starts from the old BP, ‘ XBp 3.2.13.1. Application towards PV parameter extraction. Incase of parameter identification, the unique advantages of PS algorithm are: 1) it is insensitive to the initial starting point and 2) it uses its own search history to determine the search direction for forthcoming iterations. The exploratory search in PS searches for all possible solutions in a wider dimension around the starting base point. However, PS algorithm is weak in exploiting best solutions. Refs. [75,76] used PS algorithm to extract the PV parameters and the refined data is presented in Table 18. In the proposed work: 1) A new objective function based on the IAE (Individual absolute Error) was used for optimization, 2) In IAE analysis, PS outperformed the conventional Newton method and GA, 3) Based on IAEs obtained for DD and SD models, the authors commented that SD model is quite sufficient for PV analysis, 4) The value of a1 > a2 in DD parameters is unusual with respect to the theoretical concepts and 5) The 3.2.13. Pattern Search algorithm (PS) Pattern Search is a metaheuristic algorithm which does not require any derivative data for optimization [132]. The method includes two Table 17 Parameter identification using HS and its variants. Method HS [74] GGHS [74] IGHS [74] Approach Metaheuristic Metaheuristic Metaheuristic RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – Cell/Module 0–0.5 0.03663 RS(Ω) 0–0.5 0.03545 0–100 53.5946 RP (Ω) 0–100 46.827 0–1 0.7607 Iph (A) 0–1 0.76176 1–2 1.47538 a1 1–2 1.49439 0–1 0.30495 I01 (µA) 0–1 0.12545 – – a2 1–2 1.49989 – – I02 (µA) 0–1 0.2547 57 mm dia RTC France Solar Cell PV Model SD Range Set Extracted Parameters DD Range Set Extracted Parameters RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – 57 mm dia RTC France Solar Cell 0–0.5 0.03631 RS (Ω) 0–0.5 0.03562 0–100 53.0647 RP (Ω) 0–100 62.7899 0–1 0.76092 Iph (A) 0–1 0.76056 1–2 1.48217 a1 1–2 1.49638 0–1 0.3262 I01 (µA) 0–1 0.37014 – – a2 1–2 1.92998 – – I02 (µA) 0–1 0.13504 PV Model SD Range Set Extracted Parameters DD Range Set Extracted Parameters RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – 0–0.5 0.03613 RS(Ω) 0–0.5 0.0369 0–100 53.2845 RP (Ω) 0–100 56.8368 0–1 0.76077 Iph (A) 0–1 0.76079 1–2 1.4874 a1 1–2 1.92126 0–1 0.34351 I01 (µA) 0–1 0.9731 – – a2 1–2 1.42814 – – I02 (µA) 0–1 0.16791 PV Model SD Range Set Extracted Parameters DD Range Set Extracted Parameters 16 57 mm dia RTC France Solar Cell Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx D.S. Pillai, N. Rajasekar Table 18 Parameter identification using PS. Method PS [75,76] Approach Metaheuristic PV Model SD Range Set Extracted Parameters DD Range Set Extracted Parameters RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – Cell/Module N. S 0.0313 RS (Ω) N. S 0.032 N. S 64.1026 RP (Ω) N. S 81.3008 N. S 0.7617 Iph (A) N. S 0.7602 N. S 1.6 a1 N. S 1.6 N. S 0.998 I01 (µA) N. S 0.9889 – – a2 N. S 1.192 – – I02 (µA) N. S 0.0001 57 mm dia RTC France Solar Cell N.S: Not Specified. Table 19 Parameter identification using STLBO. Method STLBO [77] Approach Metaheuristic PV Model SD Range Set Extracted Parameters DD Range Set Extracted Parameters RS (Ω) RP (Ω) Iph (A) a I0 (µA) – – Cell/Module 0–0.5 0.03638 RS (Ω) 0–0.5 0.03674 0–100 53.7187 RP (Ω) 0–100 55.492 0–1 0.76078 Iph (A) 0–1 0.76078 1–2 1.48114 a1 1–2 1.4505 0–1 0.32302 Id0 (µA) 0–1 0.22566 – – a2 1–2 0.75217 – – Id0 (µA) 0–1 2 57 mm dia RTC France Solar Cell Table 20 Analysis of 57 mm dia RTC France solar cell. Sl. no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 SD Model Sl. no. Algorithm RMSE BPFPA FPA MPCOA STLBO R-JADE TVIWAC PSO BMO ABC + NMS ABC BBO-M LM + SA PSA IADE GGHS ABSO IGHS HS SA CPSO AGA + LS PS 7.27E 7.84E 9.45E 9.86E 9.86E 9.86E 9.86E 9.86E 9.86E 9.86E 9.86E 9.87E 9.89E 9.91E 9.91E 9.93E 9.95E 1.70E 2.65E 2.75E 2.86E Convergence − − − − − − − − − − − − − − − − − − − − − 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 04 03 01 01 01 Fast Fast Fast N. S Slow Fast Fast Slow Fast Slow Fast Fast N. S Slow Slow Slow Slow N. S N. S Slow N. S 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 – – – – – – DD Model Algorithm RMSE BPFPA FPA MPCOA STLBO R-JADE ABC + NMS BMO BB0-M ABSO ABC IGHS GGHS HS SA PS – – – – – – 7.23E 7.73E 9.22E 9.82E 9.82E 9.82E 9.83E 9.83E 9.83E 9.86E 9.86E 1.07E 1.26E N. S N. S – – – – – – Convergence − − − − − − − − − − − − − 04 04 04 04 04 04 04 04 04 04 04 03 03 Fast Fast Fast N. S Slow Slow Fast Slow Slow Fast Slow Slow Slow N. S N. S – – – – – – N. S: Not Specified. in the population and is given by (52). environmental factors were not considered for validating the model. N . S, if f (N . S ) < f (W . L) ⎫ W. L = ⎧ ⎬ ⎨ W ⎭ ⎩ . L, else 3.2.14. Teaching Learning Based Optimization (TLBO) TLBO replicates the teaching learning process between teachers and learners. TLBO has two main phases; 1) Teaching phase: The quality of the teacher is improved with the help of a user defined teaching factor, ‘TF’ such that the quality of learners also increases; 2) Learning phase: The learners try to improve their own quality by the interacting with randomly selected learners. 3.2.14.2. Application towards PV parameter extraction. When TLBO is used for parameter identification; the randomness in the teaching factor, ‘TF’ significantly affects the accuracy of the extracted parameters; while in the case of STLBO, the redefined teacher phase performs a local search to find the near optimum with the help of a mutation variable. Furthermore, introduction of chaotic variable enriches the mutation operation with a good random uniformity. The reduction in number of function evaluations (FES) reduces the FES cost of the algorithm and increases the convergence speed as well [133]. Parameters estimated and ranges selected by STLBO method for extracting PV parameters are illustrated in Table 19. A critical review on STLBO based parameter identification [77] gives the following observations: 1) The enhanced search capability of STLBO has 3.2.14.1. Simplified version. In simplified TLBO (STLBO) proposed in [77]; teaching phase has an improved concept while the learning phase is similar to that of TLBO. The best teacher obtained in TLBO is further improved in STLBO using a local search operation. Tnew + mu, if rm < μ ⎫ (Tnew )* = ⎧ otherwise ⎬ ⎨ ⎭ ⎩Tnew, (52) (51) In addition, an elite strategy is also used to update the worst learner 17 Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx D.S. Pillai, N. Rajasekar Table 21 Accurate models for different PV cells/modules. Sl. no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Cell/Module Accurate model 57 mm dia RTC France Solar cell Photo watt PWP-201 Solar Module Polycrystalline S36 Solar Module Shell SP70 Solar Module Shell SM55 PV Module Kyocera KC200GT PV Module Kyocera KC210 PV Module Thin Film ST40 PV Module Polycrystalline S75 PV Module Sanyo HIT15 PV Module SL80CE PV Module Multi crystalline S115 PV Module Thin Film ST36 PV Module Mono crystalline SQ150PC PV Module Sun power E20/333 Mono crystalline PV Module Shell SM40 Mono crystalline PV Module Shell SQ85 Mono crystalline PV Module DD RMSE/AE Convergence SD RMSE/AE Convergence BPFPA based N. A BPFPA based AIS based BPFPA based BPFPA based DEIM based BPFPA based FPA based N. A N. A P-DE based P-DE based P-DE based N. A FPA based N. A 7.23E − 04 – 5.87 E − 04 N. S 4.58E − 04 2.20E − 04 0.0606 (AE) 3.65E − 04 2.34890E − 03 – – N. S N. S N. S – 2.21152E − 03 – Fast – Fast Fast Fast Fast Fast Fast Fast – – Fast Fast Fast – Fast – BPFPA based FPA based BFA based IBCPSO based FPA based FPA based N. A FPA based DE based GA + NR based IADE based N. A N. A MPCOA based GA + IP based FPA based IBCPSO based 7.270E − 04 2.05467E − 03 N. S N. S 1.5020E − 04 9.9985E − 04 – 8.50040E − 04 N. S 0.01608 (AE) 1.15000E − 02 – – 2.60000E − 02 2.60000E − 02 2.00000E − 03 N. S Fast Fast Fast Slow Fast Fast – Fast N. S Fast N. S – – Fast N. S Fast Slow N.S: Not specified, N.A: Not Available. Parameter Extraction Single/double diode model Prediction of I-V and P-Vcurves V& I sensors Real time Values/ Curves obtained from [135]. In validation, ANN outperformed the conventional direct extraction technique. The authors in [82] employed AIS to predict the DD model parameters of four different PV modules. The parameter ‘IPh’ for all the modules was computed using a direct analytical method. In the validations presented, AIS outperformed conventional PSO and GA. However, all validations are corresponding to STC only. When PSA was used for parameter identification in [81], for the same work load of PSO, the method improved the convergence time significantly even for a very large swarm size. However the complexity of the system and requirement of additional components limits its use for parameter identification. Setting Threshold values /curves Fault detection Comparison PV array Fig. 9. Fault detection in PV systems. succeeded in extracting highly accurate model parameters for both SD and DD models, 2) The algorithm outperformed ABSO, HS, PS, SA, GGHS, CPSO, IADE and TLBO in terms of accuracy and 3) The algorithm was validated only for standard test conditions. 4. Overall review on accuracy and convergence speed of metaheuristic algorithms based parameter identification for various PV cells/modules 3.3. Other techniques for parameter identification This section analyzes the performance of each metaheuristic algorithm deployed for parameter extraction. The analysis of accuracy and convergence speed has been done based on how low the objective function value is and how many iterations an algorithm takes to reach the lowest fitness value respectively. In this work, those algorithms which can rapidly converge to the best fitness value with in 400 iterations are treated to be fast while others are considered to be slow. Furthermore, a comparative evaluation on the accuracy of each method is carried out to identify the best PV model available for each cell/ module specified with a viewpoint to set benchmarks for further research advancements. Seventeen different PV cells/modules mentioned in Table 3 are considered in this regard. In literature, 57 mm dia RTC France solar cell was found to be the most commonly used solar cell for parameter identification. The detailed analysis conducted on the various models realized by different metaheuristic algorithms and their hybrid versions for 57 mm dia RTC France solar cell is illustrated in Table 20. From Table 20, it is evident that, out of the 21 metaheuristic algorithms, 15 metaheuristic techniques have extracted the DD model parameters for RTC France solar cell whereas all the techniques extracted the SD model parameters. The analysis clearly confirms: 1) BPFPA based model surpasses all the other models in terms of accuracy and convergence speed; both in SD and DD models, 2) The RMSE error values are significantly low for the BPFPA and FPA based models when compared to the MPCOA model; which is the third lowest in terms of RMSE, 3) In the case of DD model, BPFPA, FPA, MPCOA, STLBO, RJADE and TVIWAC PSO methods extracted fairly accurate parameters and are found reliable to work with and 4) Out of the six, R-JADE is In literature, Artificial Neural Networks (ANN) which resembles the nervous system of human beings [79]; Artificial Immune System (AIS) which is inspired by the defense mechanism of the human body against pathogens [80] and Parallel Swarm Algorithm (PSA) which utilizes the computational power of a central processing unit (CPU) and a graphical processing unit (GPU) [81] were also used for parameter identification. It should be appreciated that all these methods have taken up a novel initiative to solve the parameter identification problem; but all these methods are still unproven and unclear. However, a very brief review on these methods is also presented in this section. Artificial Neural Network is a computational model which replicates the biological neural network. Once the network is trained with accurate data, ANN can predict the output corresponding to the input data. On the other hand AIS employ a multipoint cross over and mutation strategy for attaining a global maximum solution. Inspired by [134], PSA incorporates a CPU and GPU based parallel computing system with the conventional PSO for fitness value evaluation. 3.3.1. Application towards PV parameter extraction The accuracy of ANN completely relies on its initial training and getting accurate data for training is in fact a very difficult task. Furthermore, as the number of training test increases, the error also exceeds. This limits the use of ANN for PV parameter identification. In [79], a trained ANN was used to extract the model parameters of an SD model. The training sets and the validating data for the network were 18 Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx D.S. Pillai, N. Rajasekar Table 22 Validating environment of various realized models for different cells/modules. (a) Kyocera KC200GT PV Module DD Model SD Model Algorithm Validating Environment Algorithm Validating Environment BPFPA MPCOA GA + NR AIS Varying temperature and Irradiation Levels Varying Irradiation Levels Varying temperature and Irradiation Levels Standard Test Conditions FPA MPCOA GA + NR GA + P Varying Varying Varying Varying temperature and Irradiation Levels Irradiation Levels temperature and Irradiation Levels temperature and Irradiation Levels (b) RTC France Solar Cell DD Model SD Model Algorithm Validating Environment Algorithm Validating Environment All algorithms Standard Test Conditions All algorithms Standard Test Conditions (c) Shell SM55 PV Module DD Model SD Model Algorithm Validating Environment Algorithm Validating Environment BPFPA FPA P-DE AIS Varying temperature and Irradiation Levels Varying temperature and Irradiation Levels Varying Irradiation Levels Standard Test Conditions FPA BFA DE Varying temperature and Irradiation Levels Varying temperature and Irradiation Levels Varying temperature and Irradiation Levels (d) Thin Film ST40 PV Module DD Model SD Model Algorithm Validating Environment Algorithm Validating Environment BPFPA FPA P-DE – – Varying temperature and Irradiation Levels Varying temperature and Irradiation Levels Varying Irradiation Levels – – FPA GA + NR GA + IP BFA DE Varying Varying Varying Varying Varying temperature and Irradiation Irradiation Levels temperature and Irradiation temperature and Irradiation temperature and Irradiation Levels Levels Levels Levels bound to cause catastrophic failures in PV arrays and are the prime underlying cause for panel degradation as well. Even though many protection devices are available, faults occurring at low irradiance levels may remain even undetected in the PV system. With immense investment on land to acquire the huge area required for the installation of PV systems, even a small reduction of power due to a fault cannot be tolerated. Indeed, instant detection of faults and its mitigation is highly demanded irrespective of its type and location. In this regard, accurate PV models are extremely useful to predict the faulty electrical characteristics of a PV array in prior and will guide the user to rapidly detect the fault. Usually fault detection is performed by employing either one of the following techniques [136–156]: poor in convergence speed. The analysis is same in the case with SD model as well. Apart from RTC France solar cell, similar analysis as performed in Table 20 has been carried out for all other PV cells/modules specified in Table 2 to identify the accurate PV model available for each cell/ module. However, for brevity, each case is not shown. Further, an overall consolidated analysis for all 17 PV cells/modules is exhibited in Table 21. For the analysis presented in Table 21, it is worth to mention that, while comparing an RMSE error evaluation method with an AE based technique, the RMSE method is usually considered to be better because RMSE is probably the most accurately interpreted statistic available for curve fitting. For uniformity, the analyzed data for RMSE and AE given in Table 21 are all taken for the standard test conditions. Furthermore, while analyzing some models as specified in [47], the absolute error for both STC and NOCT were available. In those cases, the overall AE was assumed to be the average of the two. ○ Comparison of real time outputs with threshold values. ○ Analyzing real time I-V and P-V curves with threshold curves. ○ By defining new parameters depending on irradiation and temperature [152]. ○ Detecting change in MPPT voltage [153]. ○ Using satellite image or infrared thermography [154,155]. 5. Application of parameter extraction to fault detection in PV systems Among the various fault detection techniques proposed over the years, the first two techniques are most commonly adopted; for which an accurate PV model is indispensable to emulate the PV Inspired by the review on various PV models; an unidentified gateway of interest between parameter extraction and fault detection in PV systems has been noticed. Uninterrupted and unnoticed faults are 19 Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx – – – N. A FPA Based Model N. A Yes Yes FPA Based Model IBCPSO Based Model BPFPA Based Model – – – – – N. A – – GA + NR Based Model – N. A N. A – – BPFPA Based Model N. A – AIS Based Model – – DEIM Based Model – – N. A N. A – – – N. A N. A N. A BPFPA Based Model N. A BPFPA Based Model BPFPA Based Model N. A BPFPA Based Model FPA Based Model N. A N. A P-DE Based Model P-DE Based Model P-DE Based Model N. A No Yes Yes Yes Yes Yes No Yes Yes No Yes No No Yes Yes N. A ABC-NMS Based Model BFA Based Model IBC-PSO Based Model FPA Based Model FPA Based Model N. A FPA Based Model DE Based Model N. A IADE Based Model N. A N. A MPCOA Based Model GA + IP Based Model SD Model DD Model SD Model DD Model SD Model This paper has reviewed handful of parameter extraction techniques using metaheuristic algorithms with an emphasis on its compatibility, approach, range of parameters set, accuracy and convergence speed. Some key inferences on the performance of each algorithm when applied for parameter identification problem were discussed. Among all the algorithms used for parameter identification, BPFPA was found to be the superior in terms of accuracy and convergence speed. Furthermore, 17 different cells/modules used for parameter identification were analyzed and the accurate model available for each cell/ module was identified. A brief review regarding the analytical methods for parameter extraction was also presented. Above all, the application of parameter extraction towards threshold setting for fault detection in PV systems has been explained in detail and the models capable for predicting accurate thresholds were identified for each cell/module. After reviewing metaheuristic algorithms and its hybrid variants employed so far for parameter identification, the following points are likely to be suggested. 16 17 N.A: Not Available. Yes No No No Yes No Yes Yes No Yes Yes No No Yes Yes Yes No 57 mm dia RTC France Solar cell Photo watt PWP-201 Solar Module Polycrystalline S36 Solar Module Shell SP70 Solar Module Shell SM55 PV Module Kyocera KC200GT PV Module Kyocera KC210 PV Module Thin Film ST40 PV Module Polycrystalline S75 PV Module Sanyo HIT15 PV Module SL80CE PV Module Multi crystalline S115 PV Module Thin Film ST36 PV Module Mono crystalline SQ150PC PV Module Sun power E20/333 Mono crystalline PV Module Shell SM40 Mono crystalline PV Module Shell SQ85 Mono crystalline PV Module 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 DD Model Solar Cell/Module Whether accurate model is available for Threshold Setting in Fault Detection Systems? characteristics. This scheme of detecting PV fault is depicted in Fig. 9. In literature, PSO based parameter identification and fault detection by analyzing the change in the parameters extracted is illustrated in [136]. A similar approach using LS based parameter identification is proposed in [150]. IV curves were simulated to set the thresholds for detecting the fault in [138,140,142,143,148]. Authors in [144,147] trained ANN with model predicted threshold curves to identify the fault; while in [137,139,141,145,156] faults are detected by comparing real time output power with the threshold values. Similar approaches are followed in [146,149,151] to detect the fault. From the survey, it is evident that all these fault detection techniques need threshold values predicted by a suitable PV model to detect the fault. Moreover, a PV model selected for predicting these threshold limits must be capable to accurately emulate the PV characteristics in all temperature and irradiation profiles. In addition to the environmental effect on a PV, partial shading is a very common and intense issue which can drastically change the electrical characteristics of a PV. Hence, a PV model which is tested only for STC might not be sensitive enough to accurately emulate the PV characteristics in real-time operating conditions. Using these models for fault detection can cause erroneous detection of faults due to the wrongly set threshold limits. Hence, identifying PV models which are efficient to set accurate threshold limits for fault detection under all working environments is of massive importance. This indeed necessitates that, while selecting a PV model for the fault detection of a particular cell/module, extreme care must be given to identify the model that has been validated for all environmental conditions. Hence, an attempt has been made in this paper to identify those models available for 17 different solar cells/modules; which will guide researchers/manufacturers to set accurate thresholds for achieving rapid fault detection. As shown in Table 22, for each PV cell/module, the testing conditions of their respective models have been evaluated. A careful examination on Table 22 indicates that no PV models realized for RTC France solar cell was validated for varying irradiation and temperature levels. Hence, for fault detection of an RTC France solar cell, no reliable models are available. However, among all the models used for the particular cell, FPA based model possesses the highest accuracy. The same analysis presented in Table 22 has been conducted for all the cells/modules used for parameter extraction. Furthermore, an overall consolidated analysis is presented in Table 23 where the most accurate model available for each solar cell/module; which can help PV manufacturers/researchers to achieve rapid fault detection is identified. 6. Summary Sl. n Table 23 Models available for threshold setting for fault detection in PV systems. If Yes, Name of the Model If No, the most accurate model available for Fault Detection D.S. Pillai, N. Rajasekar ➣ Algorithms can perform better if accurate range for each unknown parameter is initialized. Most algorithms rely on a trial run to determine the range to be set. Indeed, this is not reliable as the noise levels may substantially affect the trial run. Hence, a global concept 20 Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx D.S. Pillai, N. Rajasekar ➣ ➣ ➣ ➣ ➣ ➣ [8] Castro F, Laudani A, Fulginei FR, Salvini A. An in-depth analysis of the modelling of organic solar cells using multiple-diode circuits. Sol Energy 2016;135:590–7. [9] Lumb MP, Bailey CG, Adams JG, Hillier G, Tuminello F, Elarde VC, et al. Analytical drift-diffusion modeling of GaAs solar cells incorporating a back mirror. In: Proceedings of the photovoltaic specialists conference (PVSC), 2013 IEEE 39th; 2013, p. 1063–8. [10] Soon JJ, Low KS, Goh ST. Multi-dimension diode photovoltaic (PV) model for different PV cell technologies. In: Proceedings of the industrial electronics (ISIE), 2014 IEEE 23rd international symposium on; 2014, p. 2496–501. [11] Chin VJ, Salam Z, Ishaque K. Cell modelling and model parameters estimation techniques for photovoltaic simulator application: a review. Appl Energy 2015;154:500–19. [12] Humada AM, Hojabri M, Mekhilef S, Hamada HM. Solar cell parameters extraction based on single and double-diode models: a review. Renew Sustain Energy Rev 2016;56:494–509. [13] Ma J, Bi Z, Ting TO, Hao S, Hao W. Comparative performance on photovoltaic model parameter identification via bio-inspired algorithms. Sol Energy 2016;132:606–16. [14] Jordehi AR. Parameter estimation of solar photovoltaic (PV) cells: a review. Renew Sustain Energy Rev 2016;61:354–71. [15] Ciulla G, Brano VL, Di Dio V, Cipriani G. A comparison of different one-diode models for the representation of I–V characteristic of a PV cell. Renew Sustain Energy Rev 2014;32:684–96. [16] Lim LH, Ye Z, Ye J, Yang D, Du H. A linear method to extract diode model parameters of solar panels from a single I–V curve. Renew Energy 2015;76:135–42. [17] Di Piazza MC, Vitale G. Photovoltaic sources: modeling and emulation. Springer Science & Business Media; 2012. [18] Villalva MG, Gazoli JR, Ruppert Filho E. Comprehensive approach to modeling and simulation of photovoltaic arrays. IEEE Trans Power Electron 2009;24(5):1198–208. [19] Arab AH, Chenlo F, Benghanem M. Loss-of-load probability of photovoltaic water pumping systems. Sol Energy 2004;76(6):713–23. [20] De Blas MA, Torres JL, Prieto E, Garcıa A. Selecting a suitable model for characterizing photovoltaic devices. Renew Energy 2002;25(3):371–80. [21] Brano VL, Orioli A, Ciulla G, Di Gangi A. An improved five-parameter model for photovoltaic modules. Sol Energy Mater Sol Cells 2010;94(8):1358–70. [22] De Soto W, Klein SA, Beckman WA. Improvement and validation of a model for photovoltaic array performance. Sol Energy 2006;80(1):78–88. [23] Elbaset AA, Ali H, Abd-El Sattar M. Novel seven-parameter model for photovoltaic modules. Sol Energy Mater Sol Cells 2014;130:442–55. [24] Belhaouas AN, Cheikh MA, Larbes C. Suitable MATLAB-simulink simulator for PV system based on a two-diode model under shading conditions. In: Proceedings of the systems and control (ICSC), 2013 3rd international conference on; 2013, p. 72–6. [25] Ahmed J, Salam Z. A Maximum Power Point Tracking (MPPT) for PV system using Cuckoo Search with partial shading capability. Appl Energy 2014;119:118–30. [26] Ishaque K, Salam Z. A comprehensive MATLAB simulink PV system simulator with partial shading capability based on two-diode model. Sol Energy 2011;85(9):2217–27. [27] Ishaque K, Salam Z, Taheri H. Modeling and simulation of photovoltaic (PV) system during partial shading based on a two-diode model. Simul Model Pract Theory 2011;19(7):1613–26. [28] Ayodele TR, Ogunjuyigbe AS, Ekoh EE. Evaluation of numerical algorithms used in extracting the parameters of a single-diode photovoltaic model. Sustain Energy Technol Assess 2016;13:51–9. [29] Cubas J, Pindado S, de Manuel C. Explicit expressions for solar panel equivalent circuit parameters based on analytical formulation and the Lambert W-function. Energies 2014;7(7):4098–115. [30] Ulapane NN, Dhanapala CH, Wickramasinghe SM, Abeyratne SG, Rathnayake N, Binduhewa PJ. Extraction of parameters for simulating photovoltaic panels. In: Proceedings of the industrial and information systems (ICIIS), 2011 6th IEEE international conference on; 2011, p. 539–44. [31] Xiao W, Dunford WG, Capel A. A novel modeling method for photovoltaic cells. In: Proceedings of the power electronics specialists conference. PESC 04. 2004 IEEE 35th annual, Vol. 3; 2004, p. 1950–6. [32] Ding K, Bian X, Liu H, Peng T. A MATLAB-Simulink-based PV module model and its application under conditions of nonuniform irradiance. IEEE Trans Energy Convers 2012;27(4):864–72. [33] Walker G. Evaluating MPPT converter topologies using a MATLAB PV model. J Electr Electron Eng, Aust 2001;21(1):49. [34] Chouder A, Silvestre S, Sadaoui N, Rahmani L. Modeling and simulation of a grid connected PV system based on the evaluation of main PV module parameters. Simul Model Pract Theory 2012;20(1):46–58. [35] Mares O, Paulescu M, Badescu V. A simple but accurate procedure for solving the five-parameter model. Energy Convers Manag 2015;105:139–48. [36] Orioli A, Di Gangi A. A procedure to calculate the five-parameter model of crystalline silicon photovoltaic modules on the basis of the tabular performance data. Appl Energy 2013;102:1160–77. [37] Bai J, Liu S, Hao Y, Zhang Z, Jiang M, Zhang Y. Development of a new compound method to extract the five parameters of PV modules. Energy Convers Manag 2014;79:294–303. [38] Sera D, Teodorescu R, Rodriguez P. PV panel model based on datasheet values. In: Proceedings of the industrial electronics. ISIE 2007. IEEE international symposium on; 2007. p. 2392–6. [39] Adamo F, Attivissimo F, Di Nisio A, Lanzolla AM, Spadavecchia M. Parameters estimation for a model of photovoltaic panels. In: Proceedings of the XIX IMEKO or a mathematical formulation with the help of the data available in the data sheet must be proposed; which will remarkably help the algorithms to perform better irrespective of the type of PV cells or modules they use. Even though accurate parameters can be identified for standard test conditions, those parameters may not be accurate enough in nominal operating conditions. Considering the fact that STC conditions are globally not available, for an opinion about the accuracy and performance of the algorithm, the realized models must be tested for all operating conditions. Even though DD model is slightly sophisticated with higher number of unknown parameters when compared to SD model, it can efficiently predict the I-V and P-V characteristics in varying irradiance and temperature levels. Hence for environment sensitive applications, particularly for fault detection in PV systems, DD model must be used. When parameter extraction techniques are used to define thresholds for fault detection in PV systems, apart from the accuracy of the technique, the convergence speed must also be considered for achieving rapid fault detection. In this regard, the computational speed of the algorithm has high dependency on the number of fitness evaluations in each iteration step. Hence when used for applications like fault deduction and maximum power point tracking which demands high speed computation, care should be given to select an accurate algorithm with less number of fitness evaluations. Considering the promise that metaheuristic algorithms has shown, the parameter identification can be extended to much improved PV models other than the conventional SD and DD models such that the models realized can be applied to highly sensitive applications too. Application of new and improved metaheuristic algorithms like Prey Predator algorithm, Radial Movement optimization, Grey Wolf, Fire Fly optimization algorithm etc. for parameter identification, is expected to further enhance the quality of the model parameters extracted. As a future work, an assessment on the performance of each parameter identification technique with respect to various irradiance and temperature profiles is suggested. Acknowledgments The authors would like to thank the Management, VIT University, Vellore, India for providing the support to carry out research work. This work is carried out at Solar Energy Research Cell (SERC), School of Electrical Engineering, VIT University, Vellore. Further, the authors also would like to thank the reviewers for their valuable comments and recommendations to improve the quality of the paper. References [1] Ram JP, Manghani H, Pillai DS, Babu TS, Miyatake M, Rajasekar N. Analysis on solar PV emulators: a review. Renew Sustain Energy Rev 2018;81:149–60. [2] Chowdhury S, Taylor GA, Chowdhury SP, Saha AK, Song YH. Modelling, simulation and performance analysis of a PV array in an embedded environment. In: Proceedings of the universities power engineering conference. 42nd international; 2007, p. 781–5. [3] Gupta S, Tiwari H, Fozdar M, Chandna V. Development of a two-diode model for photovoltaic modules suitable for use in simulation studies. In: Proceedings of the power and energy engineering conference (APPEEC). 2012 Asia-Pacific; 2012, p. 1–4. [4] Nishioka K, Sakitani N, Uraoka Y, Fuyuki T. Analysis of multi crystalline silicon solar cells by modified 3-diode equivalent circuit model taking leakage current through periphery into consideration. Sol Energy Mater Sol Cells 2007;91(13):1222–7. [5] Suskis P, Galkin I. Enhanced photovoltaic panel model for MATLAB-simulink environment considering solar cell junction capacitance. In: Proceedings of the Industrial electronics society, IECON 2013-39th annual conference of the IEEE; 2013, p. 1613–8. [6] Kurobe KI, Matsunami H. New two-diode model for detailed analysis of multi crystalline silicon solar cells. Jpn J Appl Phys 2005;44(12R):8314. [7] Mazhari B. An improved solar cell circuit model for organic solar cells. Sol Energy Mater Sol Cells 2006;90(7):1021–33. 21 Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx D.S. Pillai, N. Rajasekar Energy Convers Manag 2017;135:463–76. [72] El-Naggar KM, AlRashidi MR, AlHajri MF, Al-Othman AK. Simulated annealing algorithm for photovoltaic parameters identification. Sol Energy 2012;86(1):266–74. [73] Dkhichi F, Oukarfi B, Fakkar A, Belbounaguia N. Parameter identification of solar cell model using Levenberg–Marquardt algorithm combined with simulated annealing. Sol Energy 2014;110:781–8. [74] Askarzadeh A, Rezazadeh A. Parameter identification for solar cell models using harmony search-based algorithms. Sol Energy 2012;86(11):3241–9. [75] AlRashidi MR, AlHajri MF, El-Naggar KM, Al-Othman AK. A new estimation approach for determining the I–V characteristics of solar cells. Sol Energy 2011;85(7):1543–50. [76] AlHajri MF, El-Naggar KM, AlRashidi MR, Al-Othman AK. Optimal extraction of solar cell parameters using pattern search. Renew Energy 2012;44:238–45. [77] Niu Q, Zhang H, Li K. An improved TLBO with elite strategy for parameters identification of PEM fuel cell and solar cell models. Int J Hydrog Energy 2014 6;39(8):3837–54. [78] Lourakis MI. A brief description of the Levenberg-Marquardt algorithm implemented by levmar. Found Res Technol 2005;4(1). [79] Karatepe E, Boztepe M, Colak M. Neural network based solar cell model. Energy Convers Manag 2006;47(9):1159–78. [80] Jacob B, Balasubramanian K, Azharuddin SM, Rajasekar N. Solar PV modelling and parameter extraction using artificial Immune system. Energy Procedia 2015;75:331–6. [81] Ting TO, Ma J, Kim KS, Huang K. Multicores and GPU utilization in parallel swarm algorithm for parameter estimation of photovoltaic cell model. Appl Soft Comput 2016;40:58–63. [82] Davis L. A genetic algorithms tutorial. Handbook of genetic algorithms. 1991. [1-01]. [83] Sellami A, Bouaïcha M. Application of the genetic algorithms for identifying the electrical parameters of PV solar generators. INTECH Open Access Publisher; 2011. [84] Jervase JA, Bourdoucen H, Al-Lawati A. Solar cell parameter extraction using genetic algorithms. Meas Sci Technol 2001;12(11):1922. [85] Marler RT, Arora JS. Survey of multi-objective optimization methods for engineering. Struct Multidiscip Optim 2004;26(6):369–95. [86] Storn R, Price K. Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 1997;11(4):341–59. [87] da Costa WT, Fardin JF, Simonetti DS, de VBM Neto L. Identification of photovoltaic model parameters by differential evolution. In: Proceedings of the industrial technology (ICIT), 2010 IEEE international conference on; 2010, p. 931–6. [88] Ishaque K, Salam Z, Taheri H, Shamsudin A. A critical evaluation of EA computational methods for Photovoltaic cell parameter extraction based on two diode model. Sol Energy 2011;85(9):1768–79. [89] Eberhart R, Kennedy J. A new optimizer using particle swarm theory. In: Micro machine and human science. MHS'95, proceedings of the sixth international symposium on; 1995, p. 39–43. [90] Eberhart RC, Shi Y, Kennedy J. Swarm intelligence. Elsevier; 2001. [91] Eberchart RC, Kennedy J. Particle swarm optimization. In: Proceedings of the IEEE, international conference on neural networks. Perth, Australia; 1995. [92] Liu YH, Huang SC, Huang JW, Liang WC. A particle swarm optimization-based maximum power point tracking algorithm for PV systems operating under partially shaded conditions. IEEE Trans Energy Convers 2012;27(4):1027–35. [93] Kamarzaman NA, Tan CW. A comprehensive review of maximum power point tracking algorithms for photovoltaic systems. Renew Sustain Energy Rev 2014;37:585–98. [94] Phimmasone V, Endo T, Kondo Y, Miyatake M. Improvement of the maximum power point tracker for photovoltaic generators with particle swarm optimization technique by adding repulsive force among agents. In: Proceedings of the electrical machines and systems. ICEMS 2009. International conference on; 2009, p. 1–6. [95] Miyatake M, Veerachary M, Toriumi F, Fujii N, Ko H. Maximum power point tracking of multiple photovoltaic arrays: a PSO approach. IEEE Trans Aerosp Electron Syst 2011;47(1):367–80. [96] Seyedmahmoudian M, Mekhilef S, Rahmani R, Yusof R, Asghar Shojaei A. Maximum power point tracking of partial shaded photovoltaic array using an evolutionary algorithm: a particle swarm optimization technique. J Renew Sustain Energy 2014;6(2):023102. [97] Ishaque K, Salam Z, Amjad M, Mekhilef S. An improved particle swarm optimization (PSO)-based MPPT for PV with reduced steady-state oscillation. IEEE Trans Power Electron 2012;27(8):3627–38. [98] Ishaque K, Salam Z. A deterministic particle swarm optimization maximum power point tracker for photovoltaic system under partial shading condition. IEEE Trans Ind Electron 2013;60(8):3195–206. [99] Chen RQ, Yu JS. Study and application of chaos-particle swarm optimization-based hybrid optimization algorithm. J Syst Simul 2008;20(3):685–8. [100] Kaewkamnerdpong B, Bentley PJ. Perceptive particle swarm optimization: an investigation. In: Shojaei swarm intelligence symposium. SIS 2005. Proceedings; 2005, p. 169–76. [101] Shahzad F, Baig AR, Masood S, Kamran M, Naveed N. Opposition-based particle swarm optimization with velocity clamping (OVCPSO). In: Advances in computational intelligence. Berlin, Heidelberg: Springer; 2009, p. 339–48. [102] Engelbrecht AP. Computational intelligence: an introduction. John Wiley & Sons; 2007. [103] Easwarakhanthan T, Bottin J, Bouhouch I, Boutrit C. Nonlinear minimization algorithm for determining the solar cell parameters with microcomputers. Int J Sol Energy 1986 1;4(1):1–2. [104] Chegaar M, Nehaoua N, Bouhemadou A. Organic and inorganic solar cells world congress fundamental applied metrology. Lisbon, Portugal; 2009, p. 6–11. [40] Peng L, Sun Y, Meng Z. An improved model and parameters extraction for photovoltaic cells using only three state points at standard test condition. J Power Sources 2014;248:621–31. [41] Nesmachnow S. An overview of metaheuristics: accurate and efficient methods for optimization. Int J Metaheuristics 2014;3(4):320–47. [42] Gharravi HG, Farham MS. Applying metaheuristic approaches on the single facility location problem with polygonal barriers. Int J Metaheuristics 2014;3(4):348–70. [43] Sambariya DK, Prasad R. Robust tuning of power system stabilizer for small signal stability enhancement using metaheuristic bat algorithm. Int J Electr Power Energy Syst 2014;61:229–38. [44] Fidanova S, Marinov P, Paparzycki M. Multi-objective ACO algorithm for WSN layout: performance according to number of ants. Int J Metaheuristics 2014;3(2):149–61. [45] Zagrouba M, Sellami A, Bouaicha M, Ksouri M. Identification of PV solar cells and modules parameters using the genetic algorithms: application to maximum power extraction. Sol Energy 2010;84(5):860–6. [46] Ismail MS, Moghavvemi M, Mahlia TM. Characterization of PV panel and global optimization of its model parameters using genetic algorithm. Energy Convers Manag 2013;73:10–25. [47] Dizqah AM, Maheri A, Busawon K. An accurate method for the PV model identification based on a genetic algorithm and the interior-point method. Renew Energy 2014;72:212–22. [48] Lingyun X, Lefei S, Wei H, Cong J. Solar cells parameter extraction using a hybrid genetic algorithm. In: Proceedings of the measuring technology and mechatronics automation (ICMTMA), 2011 third international conference on, Vol. 3; 2011, p. 306–9. [49] Ishaque K, Salam Z. An improved modeling method to determine the model parameters of photovoltaic (PV) modules using differential evolution (DE). Sol Energy 2011;85(9):2349–59. [50] Zhang J, Sanderson AC. JADE: adaptive differential evolution with optional external archive. IEEE Trans Evolut Comput 2009;13(5):945–58. [51] Gong W, Cai Z. Parameter extraction of solar cell models using repaired adaptive differential evolution. Sol Energy 2013;94:209–20. [52] Jiang LL, Maskell DL, Patra JC. Parameter estimation of solar cells and modules using an improved adaptive differential evolution algorithm. Appl Energy 2013;112:185–93. [53] Ishaque K, Salam Z, Mekhilef S, Shamsudin A. Parameter extraction of solar photovoltaic modules using penalty-based differential evolution. Appl Energy 2012;99:297–308. [54] Muhsen DH, Ghazali AB, Khatib T, Abed IA. Extraction of photovoltaic module model's parameters using an improved hybrid differential evolution/electromagnetism-like algorithm. Sol Energy 2015;119:286–97. [55] Muhsen DH, Ghazali AB, Khatib T, Abed IA. Parameters extraction of double diode photovoltaic module's model based on hybrid evolutionary algorithm. Energy Convers Manag 2015;105:552–61. [56] Macabebe EQ, Sheppard CJ, van Dyk EE. Parameter extraction from I–V characteristics of PV devices. Sol Energy 2011;85(1):12–8. [57] Ye M, Zeng S, Xu Y. An extraction method of solar cell parameters with improved particle swarm optimization. ECS Trans 2010;27(1):1099–104. [58] Khanna V, Das BK, Bisht D, Singh PK. A three diode model for industrial solar cells and estimation of solar cell parameters using PSO algorithm. Renew Energy 2015;78:105–13. [59] Wei H, Cong J, Lingyun X, Deyun S. Extracting solar cell model parameters based on chaos particle swarm algorithm. In: Proceedings of the electric information and control engineering (ICEICE), 2011 international conference on; 2011, p. 398–402. [60] Hamid NF, Rahim NA, Selvaraj J. Solar cell parameters extraction using particle swarm optimization algorithm. In: Proceedings of the clean energy and technology (CEAT), 2013 IEEE conference on; 2013, p. 461–5. [61] Soon JJ, Low KS. Photovoltaic model identification using particle swarm optimization with inverse barrier constraint. IEEE Trans Power Electron 2012;27(9):3975–83. [62] Yuan X, Xiang Y, He Y. Parameter extraction of solar cell models using mutativescale parallel chaos optimization algorithm. Sol Energy 2014;108:238–51. [63] Oliva D, Cuevas E, Pajares G. Parameter identification of solar cells using artificial bee colony optimization. Energy 2014;72:93–102. [64] Chen Z, Wu L, Lin P, Wu Y, Cheng S. Parameters identification of photovoltaic models using hybrid adaptive Nelder-Mead simplex algorithm based on eagle strategy. Appl Energy 2016;182:47–57. [65] Askarzadeh A, Rezazadeh A. Artificial bee swarm optimization algorithm for parameters identification of solar cell models. Appl Energy 2013;102:943–9. [66] Niu Q, Zhang L, Li K. A biogeography-based optimization algorithm with mutation strategies for model parameter estimation of solar and fuel cells. Energy Convers Manag 2014;86:1173–85. [67] Rajasekar N, Kumar NK, Venugopalan R. Bacterial foraging algorithm based solar PV parameter estimation. Sol Energy 2013;97:255–65. [68] Askarzadeh A, Rezazadeh A. Extraction of maximum power point in solar cells using bird mating optimizer-based parameters identification approach. Sol Energy 2013;90:123–33. [69] Askarzadeh A, dos Santos Coelho L. Determination of photovoltaic modules parameters at different operating conditions using a novel bird mating optimizer approach. Energy Convers Manag 2015;89:608–14. [70] Alam DF, Yousri DA, Eteiba MB. Flower pollination algorithm based solar PV parameter estimation. Energy Convers Manag 2015;101:410–22. [71] Prasanth Ram J, Sudhakar Babu T, Dragicevic Tomislav, Rajasekar N. A new hybrid bee pollinator flower pollination algorithm for solar parameter estimation. 22 Renewable and Sustainable Energy Reviews xxx (xxxx) xxx–xxx D.S. Pillai, N. Rajasekar [105] [106] [107] [108] [109] [110] [111] [112] [113] [114] [115] [116] [117] [118] [119] [120] [121] [122] [123] [124] [125] [126] [127] [128] [129] [130] [131] [132] [133] Črepinšek M, Liu SH, Mernik L. A note on teaching–learning-based optimization algorithm. Inf Sci 2012;212:79–93. [134] Schutte JF, Reinbolt JA, Fregly BJ, Haftka RT, George AD. Parallel global optimization with the particle swarm algorithm. Int J Numer Methods Eng 2004;61(13):2296. [135] King DL. Sandia’s PV module electrical performance model (version, 2000). Albuquerque, NM: Sandia National Laboratories; 2000. [136] Wang W, Liu AC, Chung HS, Lau RW, Zhang J, Lo AW. Fault diagnosis of photovoltaic panels using dynamic current–voltage characteristics. IEEE Trans Power Electron 2016;31(2):1588–99. [137] Bressan M, El-Basri Y, Alonso C. A new method for fault detection and identification of shadows based on electrical signature of defects. In: Proceedings of the power electronics and applications (EPE'15 ECCE-Europe), 2015 17th European conference on; 2015. p. 1–8. [138] Chine W, Mellit A, Pavan AM, Lughi V. Fault diagnosis in photovoltaic arrays. In: Proceedings of the clean electrical power (ICCEP), 2015 international conference on; 2015. p. 67–72. [139] Platon R, Martel J, Woodruff N, Chau TY. Online fault detection in PV systems. IEEE Trans Sustain Energy 2015;6(4):1200–7. [140] Zhao Y, de Palma JF, Mosesian J, Lyons R, Lehman B. Line–line fault analysis and protection challenges in solar photovoltaic arrays. IEEE Trans Ind Electron 2013;60(9):3784–95. [141] Shimakage T, Nishioka K, Yamane H, Nagura M, Kudo M. Development of fault detection system in PV system. In: Proceedings of the telecommunications energy conference (INTELEC), 2011 IEEE 33rd international; 2011, p. 1–5. [142] Zhao Y, Lehman B, de Palma JF, Mosesian J, Lyons R. Fault analysis in solar PV arrays under: low irradiance conditions and reverse connections. In: Proceedings of the photovoltaic specialists conference (PVSC), 2011 37th IEEE; 2011, p. 002000–5. [143] Bressan M, El Basri Y, Galeano AG, Alonso C. A shadow fault detection method based on the standard error analysis of IV curves. Renew Energy 2016;99:1181–90. [144] Mekki H, Mellit A, Salhi H. Artificial neural network-based modelling and fault detection of partial shaded photovoltaic modules. Simul Model Pract Theory 2016;67:1–3. [145] Dhimish M, Holmes V. Fault detection algorithm for grid-connected photovoltaic plants. Sol Energy 2016;137:236–45. [146] Chine W, Mellit A, Lughi V, Malek A, Sulligoi G, Pavan AM. A novel fault diagnosis technique for photovoltaic systems based on artificial neural networks. Renew Energy 2016;90:501–12. [147] Hosseinzadeh M, Salmasi FR. Determination of maximum solar power under shading and converter faults—a prerequisite for failure-tolerant power management systems. Simul Model Pract Theory 2016;62:14–30. [148] Silvestre S, da Silva MA, Chouder A, Guasch D, Karatepe E. New procedure for fault detection in grid connected PV systems based on the evaluation of current and voltage indicators. Energy Convers Manag 2014;86:241–9. [149] Silvestre S, Chouder A, Karatepe E. Automatic fault detection in grid connected PV systems. Sol Energy 2013;94:119–27. [150] Chine W, Mellit A, Pavan AM, Kalogirou SA. Fault detection method for gridconnected photovoltaic plants. Renew Energy 2014;66:99–110. [151] Georgijevic NL, Jankovic MV, Srdic S, Radakovic Z. The detection of series arc fault in photovoltaic systems based on the arc current entropy. IEEE Trans Power Electron 2016;31(8):5917–30. [152] Hariharan R, Chakkarapani M, Ilango GS, Nagamani C. A method to detect photovoltaic array faults and partial shading in PV systems. IEEE J Photovolt 2016;6(5):1278–85. [153] Omana M, Rossi D, Collepalumbo G, Metra C, Lombardi F. Faults affecting the control blocks of PV arrays and techniques for their concurrent detection. In: Proceedings of the defect and fault tolerance in VLSI and nanotechnology systems (DFT), 2012 IEEE international symposium on; 2012, p. 199–204. [154] Tadj M, Benmouiza K, Cheknane A, Silvestre S. Improving the performance of PV systems by faults detection using GISTEL approach. Energy Convers Manag 2014;80:298–304. [155] Ancuta F, Cepisca C. Fault analysis possibilities for PV panels. In: Energetics (IYCE), Proceedings of the 2011 3rd international youth conference on; 2011, p. 1–5. [156] Garoudja E, Harrou F, Sun Y, Kara K, Chouder A, Silvestre S. Statistical fault detection in photovoltaic systems. Sol Energy 2017;150:485–99. parameters evaluation from single I–V plot. Energy Convers Manag 2008;49(6):1376–9. Ouennoughi Z, Chegaar M. A simpler method for extracting solar cell parameters using the conductance method. Solid-State Electron 1999;43(11):1985–8. Chegaar M, Ouennoughi Z, Guechi F. Extracting dc parameters of solar cells under illumination. Vacuum 2004;75(4):367–72. Del Valle Y, Venayagamoorthy GK, Mohagheghi S, Hernandez JC, Harley RG. Particle swarm optimization: basic concepts, variants and applications in power systems. IEEE Trans Evolut Comput 2008;12(2):171–95. Khare A, Rangnekar S. A review of particle swarm optimization and its applications in solar photovoltaic system. Appl Soft Comput 2013;13(5):2997–3006. Shi Y, Eberhart R. A modified particle swarm optimizer. In: Evolutionary computation proceedings. IEEE world congress on computational intelligence. The 1998 IEEE international conference on; 1998, p. 69–73. Seyedmahmoudian M, Horan B, Soon TK, Rahmani R, Oo AM, Mekhilef S, et al. State of the art artificial intelligence-based MPPT techniques for mitigating partial shading effects on PV systems – a review. Renew Sustain Energy Rev 2016;64:435–55. Ram JP, Babu TS, Rajasekar N. A comprehensive review on solar PV maximum power point tracking techniques. Renew Sustain Energy Rev 2017;67:826–47. Ram JP, Rajasekar N, Miyatake M. Design and overview of maximum power point tracking techniques in wind and solar photovoltaic systems: a review. Renew Sustain Energy Rev 2017;73:1138–59. Yuan X, Yang Y, Wang H. Improved parallel chaos optimization algorithm. Appl Math Comput 2012;219(8):3590–9. Yuan X, Zhao J, Yang Y, Wang Y. Hybrid parallel chaos optimization algorithm with harmony search algorithm. Appl Soft Comput 2014;17:12–22. Karaboga D, Basturk B. On the performance of artificial bee colony (ABC) algorithm. Appl soft Comput 2008;8(1):687–97. Karaboga D. An idea based on honey bee swarm for numerical optimization. Technical report-tr06. Erciyes university, engineering faculty, computer engineering department; 2005. Karaboga D, Akay B. A comparative study of artificial bee colony algorithm. Appl Math Comput 2009;214(1):108–32. Askarzadeh A, Rezazadeh A. A new artificial bee swarm algorithm for optimization of proton exchange membrane fuel cell model parameters. J Zhejiang Univ Sci. C 2011;12(8):638–46. Simon D. Biogeography-based optimization. IEEE Trans Evolut Comput 2008;12(6):702–13. Ammu PK, Sivakumar KC, Rejimoan R. Biogeography-based optimization—a survey. Int J Electron Comput Sci Eng 2013;2(1):154–60. Passino KM. Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Syst 2002;22(3):52–67. Katayama K, Narihisa H. On fundamental design of parthenogenetic algorithm for the binary quadratic programming problem. In: Evolutionary computation. Proceedings of the 2001 congress on, Vol. 1; 2001, p. 356–63. Barukčić M, Nikolovski S, Jović F. Hybrid evolutionary-heuristic algorithm for capacitor banks allocation. J Electr Eng 2010;61(6):332–40. Wu J, Wang H. A parthenogenetic algorithm for the founder sequence reconstruction problem. JCP 2013;8(11):2934–41. Yang XS. Flower pollination algorithm for global optimization. In: Proceedings of the international conference on unconventional computing and natural computation. Berlin Heidelberg: Springer; 2012, p. 240–9. Černý V. Thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm. J Optim Theory Appl 1985;45(1):41–51. Kirkpatrick S, Gelatt CD, Vecchi MP. Optimization by simulated annealing. Science 1983;220(4598):671–80. Easwarakhanthan T, Bottin J, Bouhouch I, Boutrit C. Nonlinear minimization algorithm for determining the solar cell parameters with microcomputers. Int J Sol Energy 1986;4(1):1–2. Lampton M. Damping–undamping strategies for the Levenberg–Marquardt nonlinear least-squares method. Comput Phys 1997;11(1):110–5. Mahdavi M, Fesanghary M, Damangir E. An improved harmony search algorithm for solving optimization problems. Appl Math Comput 2007;188(2):1567–79. Geem ZW, Sim KB. Parameter-setting-free harmony search algorithm. Appl Math Comput 2010;217(8):3881–9. Kolda TG, Lewis RM, Torczon V. Optimization by direct search: new perspectives on some classical and modern methods. SIAM Rev 2003;45(3):385–482. 23