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. 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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. 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