Analysis of Single-Diode PV Model and Optimized MPPT Model for Different Environmental Conditions

S. Senthilkumar; V. Mohan; S. P. Mangaiyarkarasi; M. Karthikeyan

doi:10.1155/2022/4980843

Analysis of Single-Diode PV Model and Optimized MPPT Model for Different Environmental Conditions

Senthilkumar, S.;Mohan, V.;Mangaiyarkarasi, S. P.;Karthikeyan, M. 2022-01-31 00:00:00 Hindawi International Transactions on Electrical Energy Systems Volume 2022, Article ID 4980843, 17 pages https://doi.org/10.1155/2022/4980843 Research Article Analysis of Single-Diode PV Model and Optimized MPPT Model for Different Environmental Conditions 1 2 3 4 S. Senthilkumar , V. Mohan , S. P. Mangaiyarkarasi , and M. Karthikeyan Department of Electronics and Communication Engineering, E.G.S. Pillay Engineering College (Autonomous), Nagapattinam, Tamilnadu, India Department of Electrical and Electronics Engineering, E.G.S. Pillay Engineering College (Autonomous), Nagapattinam, Tamilnadu, India Department of Electrical and Electronics Engineering, University College of Engineering, Panruti Campus, Panruti, Tamilnadu, India Department of Electrical and Electronics Engineering, University College of Engineering, Pattukkottai Campus, Pattukkottai, Tamilnadu, India Correspondence should be addressed to S. Senthilkumar; senthil.lanthiri@gmail.com Received 30 September 2021; Revised 4 November 2021; Accepted 23 November 2021; Published 31 January 2022 Academic Editor: Sudhakar babu T Copyright © 2022 S. Senthilkumar et al. &is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. &e performance of photovoltaic (PV) systems must be predicted through accurate simulation designs before proceeding to a real- time application to avoid errors. However, predicting the cohesive relationship between current and voltage and estimating the parameters of a single diode model become a perplexing task due to insuﬃcient data in the datasheet of PV panels. &is research work presents single-diode solar PV system simulation analysis under diﬀerent conditions, and the performance is improved by introducing an optimization-based maximum power point tracking (MPPT) strategy. Before simulation, a mathematical model for a single diode and optimization approaches are presented in this research work. Particle swarm optimization (PSO), genetic algorithm (GA), BAT optimization, and grey wolf optimization (GWO) model-based MPPT circuits are designed, and the performances are comparatively analyzed. &e simulation results identify the nonlinear relationship between current and voltage and between power and voltage as characteristic curves for diﬀerent temperature and irradiance values. For maximum power (P ), the maximum peak point tracking power and eﬃciency are analyzed to verify the optimization-based MPPTsystem. &e max simulation results demonstrate that the GWO model obtains a maximum tracking eﬃciency (TE) of 98%, which is much better than that of other optimization techniques. energy at a particular time [2]. But the abundant availability 1. Introduction and seasonal-independent characteristics of solar energy- Among all renewable energy sources, solar-based power based systems make them perform better than wind energy- generation gains more attention due to its inexhaustible and based systems [3]. High-quality ac output with reduced clean energy characteristics. &e conversion of energy, i.e., lower order harmonics and total harmonic distortion can be sunlight to electricity, can be obtained directly using PV cells synthesized from the PV modules using multilevel inverters or a combination of concentrated solar power systems. Solar [4–7]. &e power generated by solar PV systems can be power generation prominently helps to minimize the transferred through grids, which is equal to the power emissions from fossil fuel-based power generation [1]. Wind generated through thermal power plants [8, 9]. &ough the energy-based power generation systems also contribute power generation of solar power systems is better, their better energy and reduce fossil fuel requirements. Wind implementation cost is quite high. So, it is essential to energy is seasonally dependent, and it can produce more measure the reliability and power generation accuracy of the 2 International Transactions on Electrical Energy Systems detailed mathematical formulations are presented for the solar power systems before installation. Simulation envi- ronments are used to measure the performance so that proposed solar PV model and MPPT. In Section 4, exper- imental results and their observations are presented. Finally, errors can be avoided and performance can be improved upon implementing in real time. in Section 5, the conclusion and future scope are presented. In the design procedure of solar PV cells, a thin wafer of semiconductors and a p-n junction diode are used. Electricity 2. Related Works has been generated by converting solar radiation by fabricating the diode into the cell wafers [10]. Characteristics of semi- A vast survey of existing research works on solar PV systems conductors are the key feature of the PV process. &e photons and their feature merits, demerits, and applications is dis- fromsunlight have higher energythan the semiconductor band cussed in detail in this section. Researchers pay more at- gap energy. Due to this, electron-hole pairs are created in the tention to analyze the performance of single-diode solar PV cell. &e pair generation is directly proportional to solar ir- models in various research works. &e parameters are es- radiance, and it is isolated by the p-n junction internal electric timated through characteristic equations, and extracting ﬁeld. Due to this process, photocurrent is generated and solar relevant optimal parameters from the manufacturer’s radiation acts as the most important part of the energy gen- datasheet is quite complex [23]. Also, it is diﬃcult to obtain eration process. &e dc power generated from solar panels is the parameters of a PV model from the current-voltage converted into ac power as load using novel control strategies characteristics due to its implicit nature. &e power-law [11, 12]. &e characteristics of PV cells such as I-V and P-V are system characterizes the PV module’s I-V properties. Dif- nonlinear due to cell temperature, solar radiation, and other ferent operating incidences are considered to predict the parameters. Typically, solar cells are assembled using silicon, electrical characteristics, which do not require any iterative and due to low conversion eﬃciency, the generated power will or nonelementary functions. Reduced computational be inadequate [13, 14]. So, it is essential to analyze and improve complexity and cost are the major features of the power-law the conversion eﬃciency of the PV systems through eﬃcient model [24]. &e parameters such as irradiance and tem- cell modeling. perature are considered, and the parameters of the single- Cell modeling is directly related to accuracy, which diode, double-diode, and triple-diode PV systems are represents the PV system characteristics [15]. To obtain a evaluated for diﬀerent conditions [25–27]. Combining the desired current and voltage from a solar panel, a series or analytical equations and pattern search algorithm, the I-V parallel combination of cells is generally used. However, the characteristics are analyzed with maximum accuracy, which performance can be aﬀected by temperature, solar radiation, is the feature merit of research work. However, the com- etc.; due to this, simulation of solar panels becomes crucial. putational complexity is quite high due to the long training Generally, a comprehensive investigation is followed to process. measure the performance of solar PV models [16, 17]. &e reduced space search approach eﬃciently estimates Diﬀerent parametric models are presented by researchers the parameters of the single-diode model [28]. &e no such as the single-diode model and two-diode model [18]. convex nature of the optimization problem is eliminated Among all, the single-diode model is widely preferred as the through the space search approach. Due to this, the com- performance matches the real-time solar cell performance putational complexity in parameter estimation is reduced [19–21]. &e single-diode model is alternatively called the and high-quality solutions are obtained without user in- ﬁve-parameter model, and its design includes a parallel tervention. &e performance of parameter estimation of PV connection of ideal diode and current source with bypassed modules is improved by converting no convex optimization shunt resistance. Single-diode model solar cell parameters problems into convex optimization problems using a can be eﬃciently analyzed to improve the performance of PV modiﬁed barrier function [29]. &e optimal values are ob- systems. &e single-diode model has more beneﬁts in terms tained using an adaptive identiﬁcation technique, which of parameters such as minimum error I-V and P-V curves, provide a unique solution to improve the precision of and a simple and easy implementation provides better re- electrical parameters. &e relationship between operating sults similar to manufacturer’s results [22]. conditions and electrical parameters utilizes the thermal &e major contributions of this research work are as coeﬃcient of power to evaluate the performance of the PV follows: cell [30]. &e impact of energy production due to changes in (i) A single-diode model is developed for solar PV the operating point and the disconnected array is reduced, systems under diﬀerent environmental conditions which obtains P for the temperature and irradiance. max Shunt resistance was evaluated from a mathematical (ii) For the achieved single-diode solar PV model, model based on the manufacturer’s datasheet information diﬀerent optimization techniques are presented for [31]. &e balance between computation time and accuracy is MPPT demonstrated to validate the shunt PV module. Evaluation (iii) Comparative analysis of diﬀerent optimization of series resistance for a single-diode PV module presents a models is performed to ﬁnd an appropriate tech- comparative analysis of diﬀerent techniques [32]. &e sys- nique for MPPT tematic analysis describes the feature merits and demerits of &is research work is structured as follows. In Section 2, series resistance parameter estimation techniques in terms of a review of existing research works is presented. In Section 3, accuracy and reliability. A voltage-dependent temperature International Transactions on Electrical Energy Systems 3 performance for the MPPT methods. &e perturb and ob- coeﬃcient is considered for I-V parameter estimation of a single-diode model [33]. Series resistance is obtained to get serve method utilizes the local irradiance data to determine the oﬄine conditions [44]. &e perturbation step size is improved accuracy for diﬀerent temperature ranges. Ac- curate estimation of the solar PV parameters for single diode optimized based on the analysis results of the support vector and double diode models depends on solar irradiance, machine model. &is process improves the system perfor- temperature, and values from solar PV datasheet. Improved mance without any complex control circuits. An adaptive precision is obtained for diﬀerent irradiance and tempera- neurofuzzy inference system and PSO methods are com- tures that increase the voltage range as well as P point bined as a hybrid MPPT model to obtain maximum PV max extraction. power [45]. &e hybrid approach provides maximum TE &e explicit nonlinear model presents a generalized per- with zero oscillations, and it does not require any extra unit-single-diode model for a PV system to extract the I-V sensor arrangements to measure the temperature and ir- radiance parameters. An adaptive fuzzy logic-based MPPT characteristics [34]. &e nonlinear least-square ﬁt technique utilized in this research work extracts the three parameters, model improves the adaptive skills of conventional fuzzy logic-based techniques [46]. &e operating point of existing and it is reﬁned using the per-unit-single-diode model to extract ﬁve parameters. After MATLAB programming is methods varies due to temperature and irradiance in real- over and done with, the demonstration is presented to depict time conditions, which introduces slow convergence and the minimum computational cost. A data-driven model poor accuracy in the results. &e adaptive method eliminates includes feature extraction techniques to extract essential such practical limitations and improves accuracy with faster information from a large volume of I-V data [35]. &ree convergence under dynamic conditions. diﬀerent sources are considered with diﬀerent data point Recently, various optimization models are introduced densities to generate the single-diode PV module’s I-V for MPPT. Among all, PSO gains more attention, and nu- characteristics, which make the approach suitable for time- merous research works are evolved to enhance the tracking performance of PV systems [47]. However, conventional series performance evaluation. RStudio is used to demon- strate the feature extraction process and power degradation PSO-based MPPT methods’ eﬃciency decreases because of several peaks in the PV curves that occur due to partially mechanisms in the PV module [36]. Computation of the average cell temperature of PV shaded conditions. Modiﬁed PSO is used to eliminate this modules is reported, which discusses the limitations in the limitation and to improve eﬃciency, which increase the temperature measurement process [37]. Conventional output power under nonuniform irradiation level and partial computational models ignore the sensor temperatures, shading conditions [48, 49]. &e dynamic PSO model which are from the backside of the PV module. However, considers the converter topology and solar panel conﬁgu- they will establish a temperature gradient that aﬀects the rations to select the parameters for the PSO model, which provides optimal sampling time for MPPT [50]. parameter evaluation performance. Using standard test conditions and translational formulas, the factors that aﬀect &ough PSO-based MPPT techniques are evolved for eﬃciency improvement, they face diﬃculties while the performance are identiﬁed. Diﬀerent temperature and irradiation levels are considered to deﬁne the high degree of extracting global parameters. Other than PSO, few other optimization models are introduced such as the ﬂower accuracy in the evaluation process. In solar-based power generation, another important pollination algorithm [51], the Lipschitz optimization MPPT factor that must be considered to improve the conversion algorithm [52], artiﬁcial bee colony optimization [53], and eﬃciency and power generation is MPPT. MPPT is used to the perturb and observe algorithm [54] for MPPT. From the track solar irradiance, and various MPPT techniques are literature analysis, it could be observed that the single-diode introduced by researchers in the recent era [38]. &e liter- model is widely used for solar PV modules. &e performance ature analysis presents a detailed analysis of MPPT tech- of the single-diode model is more reliable and accurate than that of other models. For MPPT, the PSO model is widely niques [39]. &e nonuniform solar irradiance condition is considered to analyze hybrid techniques, and online, uni- used. However, it faces issues while extracting global pa- rameters that aﬀect the accuracy. Considering these ob- form irradiance is considered for oﬄine conditions. &e electrical characteristics of the PV system and MPPT esti- servations, this research work presents an analysis of a single-diode model under diﬀerent conditions and an op- mation process utilize a series of analytical equations under partial and uniform shading conditions [40–42]. Research timization model for MPPT. &e performance of the overall work accurately evaluates the I-V characteristics and im- system is veriﬁed under diﬀerent environmental conditions proves the MPPTeﬃciency. Similarly, the MPPTestimation for better results. model processes the PV current and voltage characteristics and eliminates oscillations in the power point tracking 3. Proposed Work process [43]. &e estimation loss is reduced and estimation speed is increased for the evaluation procedure of the single- Solar PV cells are made from semiconducting materials. diode model. Diﬀerent manufacturing processes are followed to design the &e major factor that needs to be considered for MPPT PV cells. &e working of PV cells is based on the PV eﬀect models is their tracking accuracy and tracking speed. It is that generates a potential diﬀerence in the junction of p-n in essential to introduce a better tradeoﬀ between cost and response to radiation or visible light. &e basic structure of 4 International Transactions on Electrical Energy Systems silicon-based PV cells includes a thin layer of bulk silicon or R a thin ﬁlm of Si that is connected to electric terminals. Also, a I I d sh metallic grid is connected to the semiconductor top surface, while a thin semiconductor layer is specially treated to D R I V obtain a p-n junction. Depending on the necessity, a series or pg sh parallel combination of PV models is used. When the module is exposed to light, the charge carriers are generated, while the semiconductor absorbs the photons from the light. Figure 1: Single-diode solar cell equivalent circuit. &e electric ﬁeld in the p-n junction separates the carriers so that an electric current will start to ﬂow through the external circuit. &e working procedure is similar to the p-n junction Mathematically, the above circuit output current is obtained diode if the PV eﬀect is removed. Based on this, the current from equation (2) as ﬂow of the PV module is obtained from the diode current equation, and it is given as I � I − I − , (5) pg d sh V /nN V d s t I � I 􏼐e − 1􏼑, (1) d o where the diode voltage (V ) is obtained from the sum- where V is the potential diﬀerence, I is the reverse mation of actual input voltage (V) and the voltage across the d o saturation current, V is the thermal voltage, and N is the series resistance as V � V + IR . However, the shunt and t s d s number of series-connected cells. &e diode ideality series resistance will introduce an impact on the I-V factor is represented as n. &e thermal voltage is obtained characteristics of the PV device. Series resistance has an from the Boltzmann constant and electron charge as impact on the output voltage, and shunt resistance has an V � kT/q, where k is the Boltzmann constant and q impact on current. So, the above equation is modiﬁed to represents the electron charge whose values are obtain a single-diode model, and the current is expressed as − 23 − 19 1.380650 ×10 J/K and 1.602176 ×10 C, respectively, V + IR qV /nkT s and T is the temperature. I � I − I e − 1 − . 􏼐 􏼑 (6) pg s sh &e characteristics of ideal solar PV cells are represented based on current generation. However, the generated cur- &e I-V and P-V characteristics of the single-diode rent gets diverted from its ideal characteristics due to optical model are depicted in Figures 2(a) and 2(b), respectively. and electrical losses. &e ideal model does not consider the To calculate the values of series and shunt resistance, the eﬀects of resistance, and its output is represented as current I from equation (5) is reformulated as follows: pg I � I − I , (2) pg d R + R s sh I � I 􏼠 􏼡. (7) pg s sh where I is the current generated by the PV eﬀect and I is pg d the diode current. For ideal analysis, the diode current By substituting the above equation in (6), the shunt equation is represented using the Shockley equation, and it is resistance can be obtained as a function of series resistance as given as follows: V /nV d t I � I e − 1 , (3) 􏼐 􏼑 I R − V − I R d s s s m m s R � , (8) sh V /nkT I + I 􏼐e − 1􏼑 − I m sat s where V is the potential diﬀerence of the diode, I is the d s diode saturation current, and V is the thermal voltage, where V and I are the voltage and current at the max- m m which is given as V � kT/q, and the ideal solar PV ﬁnal imum power point. From the above equation, the maximum current is given as series resistance value can be obtained by neglecting the qV /nkT denominator terms, and the series resistance is expressed as I � I − I 􏼐e − 1􏼑. (4) pg s nkTln I − I 􏼁 /I − 1􏼁 − V s m sat m R � . (9) However, ideal models fail to establish a better and accurate relationship between voltage and current of the cells. &is happens because the analysis does not consider the In the parameter estimation process, the details of solar internal resistance eﬀects. &e practical single-diode PV cell I-V characteristics are analyzed under diﬀerent tem- model consists of series resistance and shunt resistance to get peratures and irradiation. &e iterative procedure obtains a better relationship among the cell parameters. Single-diode the parameters on every iteration. &e proposed model does models are simple and eﬃcient, but they have constraints for not utilize any optimization techniques and other extraction temperature variations. Figure 1 depicts an illustration of a techniques to obtain the parameters that are the novelty of single-diode PV circuit. this research work. From equation (6), the load current is &e current ﬂow due to metal-semiconductor contact obtained as and resistance due to impurity concentration are observed as V + IR q V+I R /nkT s ( l s) series resistance. &e shunt resistance indicates the leakage � I − I 􏼒e − 1􏼓 − . (10) l pg s sh current across the junction that is parallel to the diode. International Transactions on Electrical Energy Systems 5 9 4.5 sc Maximum Power max 8 4 3.5 6 3 2.5 4 2 3 1.5 1 0.5 V V p oc 0 0.2 0.4 0.6 0 0.2 0.4 0.6 Voltage (V) Voltage (V) (a) (b) Figure 2: Characteristics of the PV cell: (a) I-V characteristics; (b) P-V characteristics. Assume the voltage is ﬁxed at the load side and the zV 1 zI l q V+I R /nkT l ( ) l s � 􏼔I + I 􏼒1 − e 􏼓 − I 􏼕 . (19) derivative of current I with respect to PV current is given as pg s l zR R zI sh sh pg zI qR I zI R zI l s s q V+IR /nkT l s l ( s) � 1 − 􏼒e 􏼓 − . (11) &e current and voltage points in the curve can be moved zI nkT zI R zI pg pg sh pg vertically using the approximation process, and the change in current and voltage points is given as ΔI (i) and ΔV (i), &e above expression can be expressed ﬁnally as l l respectively. However, the nonlinear output voltage and − 1 zI qR I R zI q V+IR /nkT current characteristics are directly proportional to irradi- l s s ( ) s l � 􏼢1 + 􏼒e 􏼓 + 􏼣 . (12) zI nkT R zI ance, load current, and temperature. So, it is essential to pg sh pg introduce an MPPT system for the solar PV module. From &e other parameters are obtained in the same manner, the I-V and P-V characteristics of a PV system, it can be and they are given in the following equations: observed that maximum current is obtained in the absence of shunt and series resistance. By short circuiting the re- zI zI q V+IR /nkT l ( ) l � 􏼔1 − 􏼒e 􏼓􏼕 , (13) sistance, the maximum current is obtained as I , whereas the sc zI zI s pg voltage is zero when the PV module is short circuited. If there is a break in the circuit, an open-circuit voltage (V ) oc zI q V + I R 􏼁 zI q V+I R /nkT l l s ( ) l l s will occur and resistance will become high, which reduces � 􏼢I 􏼒e 􏼓􏼣 , (14) zn zI n kT pg the current. &e knee point where P is obtained is given as max the P point, and the voltage and current at this point are max zI q I􏼁 I zI given as V and I . In the proposed work, four optimization p p q V+I R /nkT l l ( ) l l l s � − 􏼢I 􏼒e 􏼓 + 􏼣 . (15) models are introduced for MPPT, and the performances are zR nkT R zI s sh pg compared to obtain a better model. Existing techniques acquire the maximum power point or obtain the diode Similar to the above process, the output voltage pa- rameters are obtained from equation (7) by assuming the model parameters using optimization techniques or the mathematical model. In the case of proposed work, the load current is ﬁxed, and they are expressed as parameters are extracted without any special optimization − 1 zV qR I l sh s q V+IR /nkT ( ) techniques; instead, the optimization model is used to attain � R 􏼔1 + 􏼒e 􏼓􏼕 , (16) sh zI nkT pg better performances in terms of tracking eﬃciency, maxi- mum power, and maximum power point tracking. A short zV zV description of optimization models is presented in the l q V+IR /nkT l ( s) � 1 − e , 􏼔 􏼒 􏼓􏼕 (17) zI zI following section. s pg zV q V + I R 􏼁 zV l l s q(V+I R )/nkT l l s � 􏼢I 􏼒e 􏼓􏼣 , 3.1. Particle Swarm Optimization. &e PSO is a stochastic (18) zn zI pg technique that is formulated based on the bird’s ﬂocking Current (A) Power (W) 6 International Transactions on Electrical Energy Systems characteristics when it searches for food. Initially, a random current P. On successive evolution, the optimal solution is population is initiated as particles, and each particle carries obtained in the GA. Objective functions that are stochastic, some information about the search space, which is ex- discontinuous, nonlinear, and nondiﬀerentiable can be ef- changed with other particles in P. &e best solution is ﬁciently solved by a GA. Genetic algorithm-based MPPT considered the global best, and other particles are starting to identiﬁes the optimal parameter based on the survival of move towards the best particle solution. &e trajectory of ﬁttest principle. &ree basic operators considered in the GA movement will be based on the best solution, and this are selection, crossover, and mutation. In this, the selection process is repeated until it meets the stopping criteria. &e operator deﬁnes the selection of materials from the present current and previous velocity values are held by each particle generation that is suitable for the next generation. Generally, so that the next best position can be obtained on every it- the ﬁtness parameter is used to select the materials. &e eration. &e velocity and position vectors of each particle are crossover operator produces new materials by combining updated as follows: two chromosomes, and the mutation operator helps to maintain the genetic diversity of each generation. To get t+1 t t+1 x � x + v , (20) ij ij ij better convergence, the ﬁrst P is reset into the initial con- dition when there is a variation in irradiance and temper- t th where x is the position vector of the i particle at iteration t ij ature. &e reinitialization is obtained based on the following t+1 th and x is the position vector of the i particle at iteration ij two conditions: t + 1, while the velocity is given as |v(k + 1) − v(k)| < Δv, (25) t+1 t t t t t v � ωv + c r pbest − x + c r gbest − x , 􏼐 􏼑 􏼐 􏼑 (21) ij ij 1 1 ij ij 2 2 ij 􏼌 􏼌 􏼌 􏼌 􏼌 􏼌 t+1 th 􏼌􏼐p (k + 1) − p (k)􏼑􏼌 where v is the velocity vector of the i particle at iteration pv pv 􏼌 􏼌 ij 􏼌 􏼌 > Δp, (26) 􏼌 􏼌 􏼌 􏼌 t + 1 and c and c are the coeﬃcients. &e random numbers 􏼌 􏼌 p (k) 1 2 􏼌 pv 􏼌 that are distributed uniformly in the range [0,1] are rep- resented as r and r . &e best ﬁtness values for the particle 1 2 where v is the output voltage and p is the power of the PV pv are considered pbest, and gbest represents the ﬁtness value system. For each iteration, the initial P and their individuals for all the particles. &e position of each particle has been are applied, and the initial position of P is given as evaluated based on this ﬁtness function, and it is given as 􏼂P , P , P , P , P 􏼃 � [1.0,0.8,0.6,0.4,0.2]V . (27) 1 2 3 4 5 oc 2 2 t t (22) f � 􏼐x − v 􏼑 + 􏼐x − i 􏼑 . ij max ij max &e generated power p (k) at the kth iteration is pv considered the ﬁtness function. &e crossover operator To update the pbest and gbest positions, the ﬁtness function of each particle is compared. If the present position function combines the two chromosomes to obtain a new child, and it is given as is comparatively better than the previous position, then the present position is considered the best value, and the overall c(k) � rp(r) − ((1 − r)p(k + 1)), (28) ﬁtness function is also updated based on that. Mathemati- cally, it is formulated as c(k + 1) � ((r − 1)p(k)) − ((r)p(k + 1)), (29) t t t ⎧ ⎪ x , if f􏼐x 􏼑 < pbest , ij ij ij pbest � (23) where c(k) is the next-generation solution and r is the ij ⎪ pbest , otherwise, ij random number. To obtain the relationship between the duty cycle (D) and the output voltage, the ratio of next- t t t t generation solution and open-circuit voltage is considered. gbest � min pbest , pbest , . . . , pbest . 􏼐 􏼑 (24) ij j j+1 s Due to the sequential aspect of chromosomes, the dynamic To update the position and velocity of all the particles, response and mutation impact on convergence are con- the above equations are used and the same procedure is sidered in the genetic model. c(k) and the random number r implemented to obtain the MPPT process. &e position of are selected in the range [0,1], and the position values are the panel is adjusted for every iteration, and the best position taken in the range [0.2,1.0]. is updated so that P can be tracked during the power max generation process. In the proposed work, the values of c 3.3. BAT Optimization. BAT optimization is a nature-in- and c are considered 2 and 1.5, respectively. &e weight spired optimization algorithm that is formulated based on factor ω is taken as 1.2, and the values of r and r are taken 1 2 the echolocation features of bats’ food-searching process. in the range of [0,1]. Using echolocation, the insects are identiﬁed by bats so that the food sources are identiﬁed. &e intensity of the return 3.2. Genetic Algorithm Optimization. &e GA was intro- signal and its direction are the major factors to locate the duced to solve constrained and unconstrained optimization prey in the optimization model. &e ultrasonic pulses are issues. Based on natural selection and biological evolution, emitted at a certain amplitude and rate, and a bat receives its the problems are solved in the GA. &e individual solutions own signal as feedback in between the pulse trains to in- in the GA are modiﬁed continuously, and next generations terpret the prey location. Depending on the feedback in- are produced by selecting a random individual from the tensity, the distance is measured. If the intensity is high, the International Transactions on Electrical Energy Systems 7 prey is near the bat and it moves towards the prey by in- optimization model, the search agents are limited, and the tensifying the pulse amount to capture the prey. &e ﬂying encircling behavior is formulated as 􏼌 􏼌 characteristics of bats are random with velocity (v ), and its → 􏼌→ 􏼌 → → 􏼌 􏼌 􏼌 􏼌 (36) D � C x (t) − x (t) , 􏼌 p sg 􏼌 position and loudness are given as x and l . &e emission i i rate of bats is considered in the range [0,1] depending on the → → → → target proximity. &e velocity and position of the bat at each x (t + 1) � x (t) − A . D , (37) sg p step are formulated as → → where A and C are the coeﬃcients that balance the ex- t+1 t t+1 (30) x � x + v , i i i ploitation and exploration factors and are given as A � → → → → (2 a ∗ r ) − (a) and C � 2 r , in which the factors r and 1 2 1 t+1 t t ∗ v � v + 􏼐x − x 􏼑f , (31) ij i i i r are random numbers whose range is [0,1]. &e range of coeﬃcient (a) gradually decreased from 2 to 0 for every where f is the randomly assigned frequency that is given as iteration, which indicates the wolves approach the prey. &e position of best search agents is used to update the position f � f + f − f 􏼁φ, (32) i min max min of all agents for every iteration, and it is given as 􏼌 􏼌 where φ is the random vector for uniform distribution that is → 􏼌 􏼌 → → → 􏼌 􏼌 ∗ 􏼌 􏼌 D � c x − x , (38) 􏼌 􏼌 in the range [0,1] and x is the global best position that is α 1 α sg obtained by comparing all the solutions at each iteration. In 􏼌 􏼌 􏼌 􏼌 → → → 􏼌 􏼌 the position update process, the pulse emission rate is 􏼌 􏼌 (39) D � c x − x , 􏼌 􏼌 β 2 β sg considered. If the random vector is greater than the emis- sion, then the exploitation stage is selected. &e current → → → → (40) x � x − A ∗ D , 1 α 1 α position is replaced based on the solution obtained in the local search process, and it is given as → → → → (41) x � x − A ∗ D , ∗ t 2 β 1 β (33) x � x + l , → → where the random number is obtained from Gaussian x + x 􏼁 → 1 2 (42) x (t + 1) � . sg distribution or uniform distribution in the range [− 1,1] and l is the average loudness at this timestamp. &e ﬁtness &e hunting process is stopped if the prey has stopped its function is further improved if the generated random movement and the search agents have ﬁnished the attacking number is smaller than loudness. A new solution is obtained process. &e position update and attacking procedure of grey during the exploration process, and the parameters such as wolves are depicted in Figure 3. emission rates and loudness are updated. Mathematically, &e proposed optimization model is used to maximize the parameter update is formulated as the output power of PV array considering its D as the de- t+1 t l � ρl , (34) cision variable. In the initialization process, the population is i i limited in the range of 0.1 to 0.9 of D, and it is expressed as t+1 (− αt) (35) r � r 􏼐1 − e 􏼑, i i d � rand􏼐n ,1􏼑 d − d 􏼁 + d , (43) i p max min min where ρ is constant whose range is deﬁned as [0,1] and α is where d is the D and n is the initial population, which i p the positive constant. &e bat’s food-searching behavior is refers to the number of PV systems. related to energy tracking to obtain the P point in the max &e position of the prey is obtained by calculating the solar PV model. ﬁtness function. In the proposed model, the values d and d α β are considered the ﬁrst- and second-best solutions with the highest PV power. To update the position of search agents 3.4. Grey Wolf Optimization. GWO is a metaheuristic op- based on the position of d and d , the population position α β timization algorithm that is derived based on the hunting and D are updated, and they are given as nature of grey wolves. It is a type of swarm intelligence 􏼌 􏼌 􏼌 􏼌 → → 􏼌 􏼌 algorithm that eﬃciently solves nonlinear optimization is- 􏼌 􏼌 D � 􏼌 c d − d 􏼌, (44) α 1 α i 􏼌 􏼌 sues. &e structure of grey wolves includes an alpha (α) that 􏼌 􏼌 􏼌 􏼌 → → → is the leader of the group, beta (β) that is the subordinates of 􏼌→ 􏼌 􏼌 􏼌 D � c d − d , (45) 􏼌 􏼌 β 2 β i 􏼌 􏼌 α, and the reaming delta (δ) and omega (ω) that are the third- and fourth-class supporting wolves. Alpha wolves are → → → → (46) d � d − A ∗ D , the leaders and provide the best ﬁtness solution for the given 1 α 1 α optimization problem. &e hunting steps of grey wolves → → → → (47) include the following: (1) prey search, (2) encircling the prey, d � d − A ∗ D , 2 β 1 β and (3) attacking the prey. GWO has high convergence → → speed and provides better accuracy than other optimization 􏼒 d + d 􏼓 1 2 (48) algorithms as it has a better balance between exploitation d (t + 1) � . and exploration phases. To improve the performance of the 8 International Transactions on Electrical Energy Systems temperature of 25 C. &e maximum current is obtained for 1000W/m , and the lowest current is obtained for 200W/ 1 m . 2 In the next analysis, the irradiance is kept constant and ° ° ° 2 the temperature is varied in the range [10 C, 30 C, 60 C], and the P-V characteristics are observed and depicted in Fig- ure 9. When the voltage increases, the power generation alfa increases linearly, reaches the maximum for minimum temperature, and exhibits a lower power for a maximum beta temperature of 60 C. &is indicates the eﬀect of temperature on power generation. Move &e I-V characteristics depicted in Figure 10 are ob- served by holding the irradiance at a constant value, and the ° ° ° temperature is varied in the range [10 C, 30 C, 60 C]. When delta the voltage increases, the power generation decreases and reaches a minimum value. However, the minimum tem- perature does not introduce much eﬀect on the results, whereas the maximum temperature of 60 C reduces quickly than others, which indicates the eﬀect of temperature on Figure 3: Position update and hunting of grey wolves. current characteristics. Furthermore, to analyze and improve the performance &e powers are calculated, and the process needs to be of the PV model, optimization-based MPPTis introduced in terminated when P is obtained. &e maximum iteration max the proposed work. Four optimization models are included and maximum output power are the termination criteria for for the analysis, and based on the performance, the best the process, and they can be reinitialized if the power is model is selected. Five PV arrays are connected in series, and reduced, and the process is given as a partial shading condition is considered for the analysis. &e 􏼌 􏼌 􏼌 􏼌 experimentation is performed under three cases for better 􏼌 􏼌 􏼌 􏼌 p − p 􏼌 pv pv,l􏼌 validation, and the cases are given as follows: (49) ≥ ΔP, pv,l 2 Case 1: uniform irradiance of 1000W/m is applied in G3, G4, and G5, and nonuniform irradiance is applied where ΔP represents the last operating point and p pv,l in remaining panels G1 and G2 represents the power at the global P point. &e process max ﬂow of GWO-based MPPT is given in Figure 4. Case 2: uniform irradiance of 1000W/m is applied in G4 and G5, and nonuniform irradiance is applied in remaining panels G1, G2, and G3 4. Results and Discussion Case 3: uniform irradiance of 1000W/m is applied in &e proposed model performance is veriﬁed through a G5, and nonuniform irradiance is applied in remaining simulation designed in the MATLAB Simulink tool. &e PV panels G1, G2, G3, and G4 cell speciﬁcations are given in Table 1, and Figure 5 depicts For each case, ﬁve simulation tests are conducted and the the arrangement of the single-diode solar PV model. &e performances are measured in terms of P , MPPT power max performances are measured under diﬀerent irradiance and (MPPTP), and TE. &e tracking eﬃciency (TE) is obtained temperature values, and the observations are discussed in based on the ratio between maximum power and MPPT this section. power, and it is formulated as &e Simulink model for the proposed single-diode model is given in Figure 6. Initially, the parameters are P MPPT η � × 100. (50) extracted, and the performance of the single-diode PV max model is analyzed under diﬀerent irradiance and temper- &e optimized MPPT model for the proposed work is ature conditions. depicted in Figure 11. &e Simulink model includes the PSO- &e P-V characteristics of the single-diode PV model are based MPPT model, and the same model is used for all the analyzed under diﬀerent irradiance values in the range [1000, 800, 600, 400, 200] W/m optimization by replacing respective optimization units for , and the 25 C reference GA optimization, BAToptimization, and GWO in the design. temperature is ﬁxed for the analysis shown in Figure 7. It could be observed from the analysis that P is obtained for &e rest of the elements are similar for all the optimization max models. &e performance of the PSO-based MPPT model is the irradiance value 1000, whereas for others, the power gets analyzed for all three cases and listed in Tables 2–4 for cases decreased gradually and irradiance of 200W/m exhibits the 1–3, respectively. It is observed from the analysis the PSO- lowest power among all others. based MPPT process obtains an average TE of 96%. &e I-V characteristics of the single-diode PV model are &e performance of the GA-based MPPT model is an- depicted in Figure 8 for diﬀerent irradiance values in the alyzed for all three cases and listed in Tables 5–7, range [1000, 800, 600, 400, 200] W/m with a reference International Transactions on Electrical Energy Systems 9 Start Initialize GWO parameters Initialize D and population Sense V , I from PV panel pv pv Calculate power, D Check p (i)>p (i-1) Yes No D =D -δd D =D +δd n i n i Update P , optimal D and GWO parameters max No All agents evaluated? Yes No Reached Convergence? Yes End Figure 4: Process ﬂow of GWO-based MPPT. Table 1: Solar PV cell speciﬁcation. S. no. Parameter Range 1 Input power 260W 2 Short circuit current (I ) 8.67A sc 3 Open-circuit voltage (V ) 37.92V oc 4 Temperature coeﬃcient of I 0.06% per C sc 5 Temperature coeﬃcient of V − 0.33% per C oc 6 Reference temperature 25 C respectively. It is observed from the analysis the GA-based respectively. It is observed from the analysis the BAT op- MPPTprocess obtains an average TE of 93%, which is much timization-based MPPT process obtains an average TE of less than that of the PSO-based MPPT model. 97%, which is 4% higher than that of the GA-based MPPT &e performance of the BAT optimization-based MPPT model and 1% higher than that of the PSO-based MPPT model is analyzed for all three cases and listed in Tables 8–10, model. 10 International Transactions on Electrical Energy Systems [1×5] Bypass Diode 1 Solar Radiation PV Module 1 Bypass Diode 2 [1×5] PV Module 2 Module Temperature Bypass Diode 3 PV Module 3 Bypass Diode 4 PV Module 4 Bypass Diode 5 PV Module 5 Figure 5: Proposed single-diode PV array model. Power Power2 [Ipv] RL I i Connection Port c v [Vpv] M + Connection Port1 PV array1 Figure 6: Simulink model of the proposed single-diode PV array. g International Transactions on Electrical Energy Systems 11 P-V Characteristics with various Irradiance –20 0 2 468 10 12 Voltage (V) G4 = 400 W/m2 G1 = 1000 W/m2 G5 = 200 W/m2 G2 = 800 W/m2 G3 = 600 W/m2 Figure 7: P-V characteristics under various irradiances in the range [1000, 800, 600, 400, 200] W/m . V-I Characteristics with various Irradiance 02468 10 12 Voltage (V) G4 = 400 W/m2 G1 = 1000 W/m2 G5 = 200 W/m2 G2 = 800 W/m2 G3 = 600 W/m2 Figure 8: I-V characteristics under various irradiances in the range [1000, 800, 600, 400, 200] W/m . P-V Characteristics with Various Temperature –20 02 4 6 8 10 12 Voltage (V) Temp1 = 10 C Temp2 = 30 C Temp3 = 60 C Figure 9: P-V characteristics at various temperatures. &e performance of the GWO-based MPPT model is be observed from the analysis the TE of the GWO model is analyzed for all three cases and listed in Tables 11–13, re- higher than that of other optimization models in all the three spectively. It is observed from the analysis the GWO-based cases. &e fast convergence and accuracy of GWO have MPPT process obtains an average TE of 98%, which is 5% obtained maximum TE compared to those of other opti- higher than that of the GA-based MPPT model, 2% higher mization models. For case 1, for all the ﬁve test conditions, than that of the PSO-based MPPT model, and 1% greater the tracking eﬃciency obtained by GWO is above 98%, than that of the BAT optimization-based MPPT model. whereas the tracking eﬃciency of BAToptimization obtains &e TE of all the optimization models is compared and an average of 97% and PSO attains 96% tracking eﬃciency. &e least performance is attained by the genetic algorithm, depicted in Figures 12–14 for cases 1–3, respectively. It could Power (W) Power (W) Current (A) 12 International Transactions on Electrical Energy Systems V-I Characteristics with Various Temperature −2 0 2 4 6 810 12 Voltage (V) Temp1 = 10 C Temp2 = 30 C Temp3 = 60 C Figure 10: I-V characteristics at various temperatures. 761.9 752.2 Power1 [Vpv] Vpv Power DD P Power2 PSO Saturation [Ipv] Ipv [0...1] [Ipv] RL i Connection Port [Vpv] c v Connection Port1 PV array1 Figure 11: Simulink design-optimized MPPT model. Table 2: PSO-based MPPT performance for case 1. Test G1 G2 G3 G4 G5 P MPPTP TE (%) max 1 900 950 1000 1000 1000 974.1 936.7 96.16 2 810 860 1000 1000 1000 910.2 879.5 96.63 3 720 770 1000 1000 1000 857.7 826.1 96.32 4 610 680 1000 1000 1000 712.6 689.9 96.81 5 550 580 1000 1000 1000 621.1 596.3 96.01 Table 3: PSO-based MPPT performance for case 2. Test G1 G2 G3 G4 G5 P MPPTP TE (%) max 1 910 940 970 1000 1000 937.3 908.2 96.90 2 800 850 890 1000 1000 876.1 844.6 96.40 3 710 750 780 1000 1000 756.7 731.2 96.63 4 620 660 690 1000 1000 670.6 643.7 95.99 5 500 550 590 1000 1000 579.5 559.3 96.51 Current (A) g International Transactions on Electrical Energy Systems 13 Table 4: PSO-based MPPT performance for case 3. Test G1 G2 G3 G4 G5 P MPPTP TE (%) max 1 900 930 960 890 1000 934.5 902.3 96.55 2 800 840 870 780 1000 856.7 824.4 96.23 3 700 730 760 670 1000 736.2 704.3 95.67 4 600 670 640 570 1000 646.9 619.8 95.81 5 500 540 580 490 1000 549.7 527.2 95.91 Table 5: GA-based MPPT performance for case 1. Test G1 G2 G3 G4 G5 P MPPTP TE (%) max 1 900 950 1000 1000 1000 971.3 909.4 93.63 2 810 860 1000 1000 1000 912.4 857.3 93.96 3 720 770 1000 1000 1000 862.1 798.1 92.58 4 610 680 1000 1000 1000 710.8 663.7 93.37 5 550 580 1000 1000 1000 598.8 552.4 92.25 Table 6: GA-based MPPT performance for case 2. Test G1 G2 G3 G4 G5 P MPPTP TE (%) max 1 910 940 970 1000 1000 942.1 876.8 93.07 2 800 850 890 1000 1000 883.7 827.4 93.63 3 710 750 780 1000 1000 763.5 712.3 93.29 4 620 660 690 1000 1000 664.9 623.7 93.80 5 500 550 590 1000 1000 569.3 527.8 92.71 Table 7: GA-based MPPT performance for case 3. Test G1 G2 G3 G4 G5 P MPPTP TE (%) max 1 900 930 960 890 1000 941.8 880.2 93.46 2 800 840 870 780 1000 864.6 812.4 93.96 3 700 730 760 670 1000 743.1 694.7 93.49 4 600 670 640 570 1000 652.7 607.9 93.14 5 500 540 580 490 1000 543.2 504.2 92.82 Table 8: BAT optimization-based MPPT performance for case 1. Test G1 G2 G3 G4 G5 P MPPTP TE (%) max 1 900 950 1000 1000 1000 963.2 937.2 97.30 2 810 860 1000 1000 1000 907.8 883.2 97.29 3 720 770 1000 1000 1000 859.9 837.1 97.35 4 610 680 1000 1000 1000 720.1 702.4 97.54 5 550 580 1000 1000 1000 610.2 591.2 96.89 Table 9: BAT optimization-based MPPT performance for case 2. Test G1 G2 G3 G4 G5 P MPPTP TE (%) max 1 910 940 970 1000 1000 937.8 916.7 97.75 2 800 850 890 1000 1000 894.8 873.5 97.62 3 710 750 780 1000 1000 780.9 764.5 97.90 4 620 660 690 1000 1000 678.1 659.8 97.30 5 500 550 590 1000 1000 579.4 563.8 97.31 which attains 93% tracking eﬃciency. For case 2, the optimization, and GWO is 93.374%, 96.034%, 96.974%, and tracking eﬃciency of GA, PSO, BAT optimization, and 98.284%, respectively. &e average tracking eﬃciency con- GWO is 93.3%, 96.486%, 97.576%, and 98.164%, respec- sidering all the three cases attained by the optimization tively. For case 3, the tracking eﬃciency of GA, PSO, BAT models is 93.3% for GA, 96.3% for PSO, 97.3% for BAT 14 International Transactions on Electrical Energy Systems Table 10: BAT optimization-based MPPT performance for case 3. Test G1 G2 G3 G4 G5 P MPPTP TE (%) max 1 900 930 960 890 1000 936.7 910.4 97.19 2 800 840 870 780 1000 875.2 847.9 96.88 3 700 730 760 670 1000 751.1 725.7 96.62 4 600 670 640 570 1000 674.9 654.9 97.04 5 500 540 580 490 1000 549.8 534.1 97.14 Table 11: GWO-based MPPT performance for case 1. Test G1 G2 G3 G4 G5 P MPPTP TE (%) max 1 900 950 1000 1000 1000 957.8 942.7 98.42 2 810 860 1000 1000 1000 910.7 896.2 98.41 3 720 770 1000 1000 1000 849.3 829.4 97.66 4 610 680 1000 1000 1000 728.8 716.1 98.26 5 550 580 1000 1000 1000 623.4 612.8 98.30 Table 12: GWO-based MPPT performance for case 2. Test G1 G2 G3 G4 G5 P MPPTP TE (%) max 1 910 940 970 1000 1000 920.4 907.8 98.63 2 800 850 890 1000 1000 884.7 867.1 98.01 3 710 750 780 1000 1000 772.9 759.5 98.27 4 620 660 690 1000 1000 684.5 669.9 97.87 5 500 550 590 1000 1000 571.2 560 98.04 Table 13: GWO-based MPPT performance for case 3. Test G1 G2 G3 G4 G5 P MPPTP TE (%) max 1 900 930 960 890 1000 927.9 916.2 98.74 2 800 840 870 780 1000 873.8 857.3 98.11 3 700 730 760 670 1000 763.3 751.7 98.48 4 600 670 640 570 1000 680.1 668.4 98.28 5 500 540 580 490 1000 551.8 539.7 97.81 Case 1 Test number BAT GA PSO GWO Figure 12: TE comparisons for case 1. optimization, and 98.2% for GWO. It is observed that single-diode PV model can be improved with the GWO- maximum performance is attained by the GWO model, based MPPT strategy. Compared to other optimization which increases the performance of PV systems. models, GWO has a much better convergence rate and From the analysis, it could be observed that GWO ex- provides maximum power tracking, which increases the hibits maximum TE and power in all the cases compared to total power, whereas the convergence rate of PSO is better other optimization algorithms. &e performance of the than that of GA but less than that of GWO, and in the case of TE (%) International Transactions on Electrical Energy Systems 15 Case 2 Symbols V : Potential diﬀerence I : Reverse saturation current V : &ermal voltage N : Series-connected cells − 23 k: Boltzmann constant (1.380650 ×10 J/K) − 19 q: Electron charge (1.602176 ×10 C) T: Temperature I : &e current generated by photovoltaic eﬀect 88 pg I : Diode current Test number I : Diode saturation current GA BAT R : Series resistance PSO GWO R : Shunt resistance sh Figure 13: TE comparisons for case 2. ΔI (i): Change in current point ΔV (i): Change in voltage point V : Open-circuit voltage oc Case 3 V : Maximum power point voltage th x : Position vector of the i particle at iteration t ij th t+1 x : Position vector of the i particle at iteration t+1 ij c and c : Coeﬃcients 1 2 r and Random numbers distributed uniformly in the 94 → r : range [0,1] 92 P : Power of the photovoltaic system pv V: Output voltage C(k): Next-generation solution V : Random bat’s velocity X : &e position of bats Test number i L : &e loudness of bats GA BAT F : Randomly assigned frequency GWO i PSO φ: Random vector for uniform distribution Figure 14: TE comparisons for case 3. ρ: Constant α: Positive constant → → A and C: Coeﬃcients in grey wolf optimization BAToptimization, the convergence rate is better than that of β: Beta-subordinates of α PSO and GA but less than that of the GWO model. &is δ and ω: Delta and omega-third- and fourth-class indicates that, with minimum time, the GWO model attains supporting wolves maximum performance so that it can be selected as the best D : Duty cycle optimization model among other optimization algorithms. i N : Initial population ΔP: Last operating point. 5. Conclusion &is research work presents an analysis of a single-diode PV Data Availability model and MPPT using optimization techniques to improve &e reference articles data used to support the ﬁndings of the performance of solar PV systems. &e parameters of the this study are included within this article. single-diode model are derived, and the I-V and P-V char- acteristics are analyzed under diﬀerent conditions. Irradiance and temperature are varied to measure the characteristics. Additional Points Furthermore, four optimization models such as PSO, GA, BAToptimization, and GWO are introduced to obtain MPPT of the proposed system. &e performance is analyzed under Highlights. (1) A mathematical model for a single-diode PV three diﬀerent cases by varying the irradiance levels. Among system and four optimization approaches for MPPT under all four optimization techniques, the GWO-based MPPT diﬀerent environmental conditions are presented in this model attains approximately 98% TE, which is much better research work. (2) &e simulation results demonstrate that than that of other optimization techniques. Furthermore, this the grey wolf optimization model achieves a maximum research work can be improved by integrating Internet of power tracking eﬃciency of 98%, which is better than that of things models for fault detection so that the factors that aﬀect other competing optimization techniques such as BAT the TE can be identiﬁed and replaced immediately. optimization (97%), PSO (96%), and GA (93%). TE (%) TE (%) 16 International Transactions on Electrical Energy Systems [15] A. Mohanty, P. K. Ray, M. Viswavandya, S. Mohanty, and Conflicts of Interest P. P. 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Publisher: Hindawi Publishing Corporation
Copyright: Copyright © 2022 S. Senthilkumar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
eISSN: 2050-7038
DOI: 10.1155/2022/4980843
Publisher site: See Article on Publisher Site

Abstract

Hindawi International Transactions on Electrical Energy Systems Volume 2022, Article ID 4980843, 17 pages https://doi.org/10.1155/2022/4980843 Research Article Analysis of Single-Diode PV Model and Optimized MPPT Model for Different Environmental Conditions 1 2 3 4 S. Senthilkumar , V. Mohan , S. P. Mangaiyarkarasi , and M. Karthikeyan Department of Electronics and Communication Engineering, E.G.S. Pillay Engineering College (Autonomous), Nagapattinam, Tamilnadu, India Department of Electrical and Electronics Engineering, E.G.S. Pillay Engineering College (Autonomous), Nagapattinam, Tamilnadu, India Department of Electrical and Electronics Engineering, University College of Engineering, Panruti Campus, Panruti, Tamilnadu, India Department of Electrical and Electronics Engineering, University College of Engineering, Pattukkottai Campus, Pattukkottai, Tamilnadu, India Correspondence should be addressed to S. Senthilkumar; senthil.lanthiri@gmail.com Received 30 September 2021; Revised 4 November 2021; Accepted 23 November 2021; Published 31 January 2022 Academic Editor: Sudhakar babu T Copyright © 2022 S. Senthilkumar et al. &is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. &e performance of photovoltaic (PV) systems must be predicted through accurate simulation designs before proceeding to a real- time application to avoid errors. However, predicting the cohesive relationship between current and voltage and estimating the parameters of a single diode model become a perplexing task due to insuﬃcient data in the datasheet of PV panels. &is research work presents single-diode solar PV system simulation analysis under diﬀerent conditions, and the performance is improved by introducing an optimization-based maximum power point tracking (MPPT) strategy. Before simulation, a mathematical model for a single diode and optimization approaches are presented in this research work. Particle swarm optimization (PSO), genetic algorithm (GA), BAT optimization, and grey wolf optimization (GWO) model-based MPPT circuits are designed, and the performances are comparatively analyzed. &e simulation results identify the nonlinear relationship between current and voltage and between power and voltage as characteristic curves for diﬀerent temperature and irradiance values. For maximum power (P ), the maximum peak point tracking power and eﬃciency are analyzed to verify the optimization-based MPPTsystem. &e max simulation results demonstrate that the GWO model obtains a maximum tracking eﬃciency (TE) of 98%, which is much better than that of other optimization techniques. energy at a particular time [2]. But the abundant availability 1. Introduction and seasonal-independent characteristics of solar energy- Among all renewable energy sources, solar-based power based systems make them perform better than wind energy- generation gains more attention due to its inexhaustible and based systems [3]. High-quality ac output with reduced clean energy characteristics. &e conversion of energy, i.e., lower order harmonics and total harmonic distortion can be sunlight to electricity, can be obtained directly using PV cells synthesized from the PV modules using multilevel inverters or a combination of concentrated solar power systems. Solar [4–7]. &e power generated by solar PV systems can be power generation prominently helps to minimize the transferred through grids, which is equal to the power emissions from fossil fuel-based power generation [1]. Wind generated through thermal power plants [8, 9]. &ough the energy-based power generation systems also contribute power generation of solar power systems is better, their better energy and reduce fossil fuel requirements. Wind implementation cost is quite high. So, it is essential to energy is seasonally dependent, and it can produce more measure the reliability and power generation accuracy of the 2 International Transactions on Electrical Energy Systems detailed mathematical formulations are presented for the solar power systems before installation. Simulation envi- ronments are used to measure the performance so that proposed solar PV model and MPPT. In Section 4, exper- imental results and their observations are presented. Finally, errors can be avoided and performance can be improved upon implementing in real time. in Section 5, the conclusion and future scope are presented. In the design procedure of solar PV cells, a thin wafer of semiconductors and a p-n junction diode are used. Electricity 2. Related Works has been generated by converting solar radiation by fabricating the diode into the cell wafers [10]. Characteristics of semi- A vast survey of existing research works on solar PV systems conductors are the key feature of the PV process. &e photons and their feature merits, demerits, and applications is dis- fromsunlight have higher energythan the semiconductor band cussed in detail in this section. Researchers pay more at- gap energy. Due to this, electron-hole pairs are created in the tention to analyze the performance of single-diode solar PV cell. &e pair generation is directly proportional to solar ir- models in various research works. &e parameters are es- radiance, and it is isolated by the p-n junction internal electric timated through characteristic equations, and extracting ﬁeld. Due to this process, photocurrent is generated and solar relevant optimal parameters from the manufacturer’s radiation acts as the most important part of the energy gen- datasheet is quite complex [23]. Also, it is diﬃcult to obtain eration process. &e dc power generated from solar panels is the parameters of a PV model from the current-voltage converted into ac power as load using novel control strategies characteristics due to its implicit nature. &e power-law [11, 12]. &e characteristics of PV cells such as I-V and P-V are system characterizes the PV module’s I-V properties. Dif- nonlinear due to cell temperature, solar radiation, and other ferent operating incidences are considered to predict the parameters. Typically, solar cells are assembled using silicon, electrical characteristics, which do not require any iterative and due to low conversion eﬃciency, the generated power will or nonelementary functions. Reduced computational be inadequate [13, 14]. So, it is essential to analyze and improve complexity and cost are the major features of the power-law the conversion eﬃciency of the PV systems through eﬃcient model [24]. &e parameters such as irradiance and tem- cell modeling. perature are considered, and the parameters of the single- Cell modeling is directly related to accuracy, which diode, double-diode, and triple-diode PV systems are represents the PV system characteristics [15]. To obtain a evaluated for diﬀerent conditions [25–27]. Combining the desired current and voltage from a solar panel, a series or analytical equations and pattern search algorithm, the I-V parallel combination of cells is generally used. However, the characteristics are analyzed with maximum accuracy, which performance can be aﬀected by temperature, solar radiation, is the feature merit of research work. However, the com- etc.; due to this, simulation of solar panels becomes crucial. putational complexity is quite high due to the long training Generally, a comprehensive investigation is followed to process. measure the performance of solar PV models [16, 17]. &e reduced space search approach eﬃciently estimates Diﬀerent parametric models are presented by researchers the parameters of the single-diode model [28]. &e no such as the single-diode model and two-diode model [18]. convex nature of the optimization problem is eliminated Among all, the single-diode model is widely preferred as the through the space search approach. Due to this, the com- performance matches the real-time solar cell performance putational complexity in parameter estimation is reduced [19–21]. &e single-diode model is alternatively called the and high-quality solutions are obtained without user in- ﬁve-parameter model, and its design includes a parallel tervention. &e performance of parameter estimation of PV connection of ideal diode and current source with bypassed modules is improved by converting no convex optimization shunt resistance. Single-diode model solar cell parameters problems into convex optimization problems using a can be eﬃciently analyzed to improve the performance of PV modiﬁed barrier function [29]. &e optimal values are ob- systems. &e single-diode model has more beneﬁts in terms tained using an adaptive identiﬁcation technique, which of parameters such as minimum error I-V and P-V curves, provide a unique solution to improve the precision of and a simple and easy implementation provides better re- electrical parameters. &e relationship between operating sults similar to manufacturer’s results [22]. conditions and electrical parameters utilizes the thermal &e major contributions of this research work are as coeﬃcient of power to evaluate the performance of the PV follows: cell [30]. &e impact of energy production due to changes in (i) A single-diode model is developed for solar PV the operating point and the disconnected array is reduced, systems under diﬀerent environmental conditions which obtains P for the temperature and irradiance. max Shunt resistance was evaluated from a mathematical (ii) For the achieved single-diode solar PV model, model based on the manufacturer’s datasheet information diﬀerent optimization techniques are presented for [31]. &e balance between computation time and accuracy is MPPT demonstrated to validate the shunt PV module. Evaluation (iii) Comparative analysis of diﬀerent optimization of series resistance for a single-diode PV module presents a models is performed to ﬁnd an appropriate tech- comparative analysis of diﬀerent techniques [32]. &e sys- nique for MPPT tematic analysis describes the feature merits and demerits of &is research work is structured as follows. In Section 2, series resistance parameter estimation techniques in terms of a review of existing research works is presented. In Section 3, accuracy and reliability. A voltage-dependent temperature International Transactions on Electrical Energy Systems 3 performance for the MPPT methods. &e perturb and ob- coeﬃcient is considered for I-V parameter estimation of a single-diode model [33]. Series resistance is obtained to get serve method utilizes the local irradiance data to determine the oﬄine conditions [44]. &e perturbation step size is improved accuracy for diﬀerent temperature ranges. Ac- curate estimation of the solar PV parameters for single diode optimized based on the analysis results of the support vector and double diode models depends on solar irradiance, machine model. &is process improves the system perfor- temperature, and values from solar PV datasheet. Improved mance without any complex control circuits. An adaptive precision is obtained for diﬀerent irradiance and tempera- neurofuzzy inference system and PSO methods are com- tures that increase the voltage range as well as P point bined as a hybrid MPPT model to obtain maximum PV max extraction. power [45]. &e hybrid approach provides maximum TE &e explicit nonlinear model presents a generalized per- with zero oscillations, and it does not require any extra unit-single-diode model for a PV system to extract the I-V sensor arrangements to measure the temperature and ir- radiance parameters. An adaptive fuzzy logic-based MPPT characteristics [34]. &e nonlinear least-square ﬁt technique utilized in this research work extracts the three parameters, model improves the adaptive skills of conventional fuzzy logic-based techniques [46]. &e operating point of existing and it is reﬁned using the per-unit-single-diode model to extract ﬁve parameters. After MATLAB programming is methods varies due to temperature and irradiance in real- over and done with, the demonstration is presented to depict time conditions, which introduces slow convergence and the minimum computational cost. A data-driven model poor accuracy in the results. &e adaptive method eliminates includes feature extraction techniques to extract essential such practical limitations and improves accuracy with faster information from a large volume of I-V data [35]. &ree convergence under dynamic conditions. diﬀerent sources are considered with diﬀerent data point Recently, various optimization models are introduced densities to generate the single-diode PV module’s I-V for MPPT. Among all, PSO gains more attention, and nu- characteristics, which make the approach suitable for time- merous research works are evolved to enhance the tracking performance of PV systems [47]. However, conventional series performance evaluation. RStudio is used to demon- strate the feature extraction process and power degradation PSO-based MPPT methods’ eﬃciency decreases because of several peaks in the PV curves that occur due to partially mechanisms in the PV module [36]. Computation of the average cell temperature of PV shaded conditions. Modiﬁed PSO is used to eliminate this modules is reported, which discusses the limitations in the limitation and to improve eﬃciency, which increase the temperature measurement process [37]. Conventional output power under nonuniform irradiation level and partial computational models ignore the sensor temperatures, shading conditions [48, 49]. &e dynamic PSO model which are from the backside of the PV module. However, considers the converter topology and solar panel conﬁgu- they will establish a temperature gradient that aﬀects the rations to select the parameters for the PSO model, which provides optimal sampling time for MPPT [50]. parameter evaluation performance. Using standard test conditions and translational formulas, the factors that aﬀect &ough PSO-based MPPT techniques are evolved for eﬃciency improvement, they face diﬃculties while the performance are identiﬁed. Diﬀerent temperature and irradiation levels are considered to deﬁne the high degree of extracting global parameters. Other than PSO, few other optimization models are introduced such as the ﬂower accuracy in the evaluation process. In solar-based power generation, another important pollination algorithm [51], the Lipschitz optimization MPPT factor that must be considered to improve the conversion algorithm [52], artiﬁcial bee colony optimization [53], and eﬃciency and power generation is MPPT. MPPT is used to the perturb and observe algorithm [54] for MPPT. From the track solar irradiance, and various MPPT techniques are literature analysis, it could be observed that the single-diode introduced by researchers in the recent era [38]. &e liter- model is widely used for solar PV modules. &e performance ature analysis presents a detailed analysis of MPPT tech- of the single-diode model is more reliable and accurate than that of other models. For MPPT, the PSO model is widely niques [39]. &e nonuniform solar irradiance condition is considered to analyze hybrid techniques, and online, uni- used. However, it faces issues while extracting global pa- rameters that aﬀect the accuracy. Considering these ob- form irradiance is considered for oﬄine conditions. &e electrical characteristics of the PV system and MPPT esti- servations, this research work presents an analysis of a single-diode model under diﬀerent conditions and an op- mation process utilize a series of analytical equations under partial and uniform shading conditions [40–42]. Research timization model for MPPT. &e performance of the overall work accurately evaluates the I-V characteristics and im- system is veriﬁed under diﬀerent environmental conditions proves the MPPTeﬃciency. Similarly, the MPPTestimation for better results. model processes the PV current and voltage characteristics and eliminates oscillations in the power point tracking 3. Proposed Work process [43]. &e estimation loss is reduced and estimation speed is increased for the evaluation procedure of the single- Solar PV cells are made from semiconducting materials. diode model. Diﬀerent manufacturing processes are followed to design the &e major factor that needs to be considered for MPPT PV cells. &e working of PV cells is based on the PV eﬀect models is their tracking accuracy and tracking speed. It is that generates a potential diﬀerence in the junction of p-n in essential to introduce a better tradeoﬀ between cost and response to radiation or visible light. &e basic structure of 4 International Transactions on Electrical Energy Systems silicon-based PV cells includes a thin layer of bulk silicon or R a thin ﬁlm of Si that is connected to electric terminals. Also, a I I d sh metallic grid is connected to the semiconductor top surface, while a thin semiconductor layer is specially treated to D R I V obtain a p-n junction. Depending on the necessity, a series or pg sh parallel combination of PV models is used. When the module is exposed to light, the charge carriers are generated, while the semiconductor absorbs the photons from the light. Figure 1: Single-diode solar cell equivalent circuit. &e electric ﬁeld in the p-n junction separates the carriers so that an electric current will start to ﬂow through the external circuit. &e working procedure is similar to the p-n junction Mathematically, the above circuit output current is obtained diode if the PV eﬀect is removed. Based on this, the current from equation (2) as ﬂow of the PV module is obtained from the diode current equation, and it is given as I � I − I − , (5) pg d sh V /nN V d s t I � I 􏼐e − 1􏼑, (1) d o where the diode voltage (V ) is obtained from the sum- where V is the potential diﬀerence, I is the reverse mation of actual input voltage (V) and the voltage across the d o saturation current, V is the thermal voltage, and N is the series resistance as V � V + IR . However, the shunt and t s d s number of series-connected cells. &e diode ideality series resistance will introduce an impact on the I-V factor is represented as n. &e thermal voltage is obtained characteristics of the PV device. Series resistance has an from the Boltzmann constant and electron charge as impact on the output voltage, and shunt resistance has an V � kT/q, where k is the Boltzmann constant and q impact on current. So, the above equation is modiﬁed to represents the electron charge whose values are obtain a single-diode model, and the current is expressed as − 23 − 19 1.380650 ×10 J/K and 1.602176 ×10 C, respectively, V + IR qV /nkT s and T is the temperature. I � I − I e − 1 − . 􏼐 􏼑 (6) pg s sh &e characteristics of ideal solar PV cells are represented based on current generation. However, the generated cur- &e I-V and P-V characteristics of the single-diode rent gets diverted from its ideal characteristics due to optical model are depicted in Figures 2(a) and 2(b), respectively. and electrical losses. &e ideal model does not consider the To calculate the values of series and shunt resistance, the eﬀects of resistance, and its output is represented as current I from equation (5) is reformulated as follows: pg I � I − I , (2) pg d R + R s sh I � I 􏼠 􏼡. (7) pg s sh where I is the current generated by the PV eﬀect and I is pg d the diode current. For ideal analysis, the diode current By substituting the above equation in (6), the shunt equation is represented using the Shockley equation, and it is resistance can be obtained as a function of series resistance as given as follows: V /nV d t I � I e − 1 , (3) 􏼐 􏼑 I R − V − I R d s s s m m s R � , (8) sh V /nkT I + I 􏼐e − 1􏼑 − I m sat s where V is the potential diﬀerence of the diode, I is the d s diode saturation current, and V is the thermal voltage, where V and I are the voltage and current at the max- m m which is given as V � kT/q, and the ideal solar PV ﬁnal imum power point. From the above equation, the maximum current is given as series resistance value can be obtained by neglecting the qV /nkT denominator terms, and the series resistance is expressed as I � I − I 􏼐e − 1􏼑. (4) pg s nkTln I − I 􏼁 /I − 1􏼁 − V s m sat m R � . (9) However, ideal models fail to establish a better and accurate relationship between voltage and current of the cells. &is happens because the analysis does not consider the In the parameter estimation process, the details of solar internal resistance eﬀects. &e practical single-diode PV cell I-V characteristics are analyzed under diﬀerent tem- model consists of series resistance and shunt resistance to get peratures and irradiation. &e iterative procedure obtains a better relationship among the cell parameters. Single-diode the parameters on every iteration. &e proposed model does models are simple and eﬃcient, but they have constraints for not utilize any optimization techniques and other extraction temperature variations. Figure 1 depicts an illustration of a techniques to obtain the parameters that are the novelty of single-diode PV circuit. this research work. From equation (6), the load current is &e current ﬂow due to metal-semiconductor contact obtained as and resistance due to impurity concentration are observed as V + IR q V+I R /nkT s ( l s) series resistance. &e shunt resistance indicates the leakage � I − I 􏼒e − 1􏼓 − . (10) l pg s sh current across the junction that is parallel to the diode. International Transactions on Electrical Energy Systems 5 9 4.5 sc Maximum Power max 8 4 3.5 6 3 2.5 4 2 3 1.5 1 0.5 V V p oc 0 0.2 0.4 0.6 0 0.2 0.4 0.6 Voltage (V) Voltage (V) (a) (b) Figure 2: Characteristics of the PV cell: (a) I-V characteristics; (b) P-V characteristics. Assume the voltage is ﬁxed at the load side and the zV 1 zI l q V+I R /nkT l ( ) l s � 􏼔I + I 􏼒1 − e 􏼓 − I 􏼕 . (19) derivative of current I with respect to PV current is given as pg s l zR R zI sh sh pg zI qR I zI R zI l s s q V+IR /nkT l s l ( s) � 1 − 􏼒e 􏼓 − . (11) &e current and voltage points in the curve can be moved zI nkT zI R zI pg pg sh pg vertically using the approximation process, and the change in current and voltage points is given as ΔI (i) and ΔV (i), &e above expression can be expressed ﬁnally as l l respectively. However, the nonlinear output voltage and − 1 zI qR I R zI q V+IR /nkT current characteristics are directly proportional to irradi- l s s ( ) s l � 􏼢1 + 􏼒e 􏼓 + 􏼣 . (12) zI nkT R zI ance, load current, and temperature. So, it is essential to pg sh pg introduce an MPPT system for the solar PV module. From &e other parameters are obtained in the same manner, the I-V and P-V characteristics of a PV system, it can be and they are given in the following equations: observed that maximum current is obtained in the absence of shunt and series resistance. By short circuiting the re- zI zI q V+IR /nkT l ( ) l � 􏼔1 − 􏼒e 􏼓􏼕 , (13) sistance, the maximum current is obtained as I , whereas the sc zI zI s pg voltage is zero when the PV module is short circuited. If there is a break in the circuit, an open-circuit voltage (V ) oc zI q V + I R 􏼁 zI q V+I R /nkT l l s ( ) l l s will occur and resistance will become high, which reduces � 􏼢I 􏼒e 􏼓􏼣 , (14) zn zI n kT pg the current. &e knee point where P is obtained is given as max the P point, and the voltage and current at this point are max zI q I􏼁 I zI given as V and I . In the proposed work, four optimization p p q V+I R /nkT l l ( ) l l l s � − 􏼢I 􏼒e 􏼓 + 􏼣 . (15) models are introduced for MPPT, and the performances are zR nkT R zI s sh pg compared to obtain a better model. Existing techniques acquire the maximum power point or obtain the diode Similar to the above process, the output voltage pa- rameters are obtained from equation (7) by assuming the model parameters using optimization techniques or the mathematical model. In the case of proposed work, the load current is ﬁxed, and they are expressed as parameters are extracted without any special optimization − 1 zV qR I l sh s q V+IR /nkT ( ) techniques; instead, the optimization model is used to attain � R 􏼔1 + 􏼒e 􏼓􏼕 , (16) sh zI nkT pg better performances in terms of tracking eﬃciency, maxi- mum power, and maximum power point tracking. A short zV zV description of optimization models is presented in the l q V+IR /nkT l ( s) � 1 − e , 􏼔 􏼒 􏼓􏼕 (17) zI zI following section. s pg zV q V + I R 􏼁 zV l l s q(V+I R )/nkT l l s � 􏼢I 􏼒e 􏼓􏼣 , 3.1. Particle Swarm Optimization. &e PSO is a stochastic (18) zn zI pg technique that is formulated based on the bird’s ﬂocking Current (A) Power (W) 6 International Transactions on Electrical Energy Systems characteristics when it searches for food. Initially, a random current P. On successive evolution, the optimal solution is population is initiated as particles, and each particle carries obtained in the GA. Objective functions that are stochastic, some information about the search space, which is ex- discontinuous, nonlinear, and nondiﬀerentiable can be ef- changed with other particles in P. &e best solution is ﬁciently solved by a GA. Genetic algorithm-based MPPT considered the global best, and other particles are starting to identiﬁes the optimal parameter based on the survival of move towards the best particle solution. &e trajectory of ﬁttest principle. &ree basic operators considered in the GA movement will be based on the best solution, and this are selection, crossover, and mutation. In this, the selection process is repeated until it meets the stopping criteria. &e operator deﬁnes the selection of materials from the present current and previous velocity values are held by each particle generation that is suitable for the next generation. Generally, so that the next best position can be obtained on every it- the ﬁtness parameter is used to select the materials. &e eration. &e velocity and position vectors of each particle are crossover operator produces new materials by combining updated as follows: two chromosomes, and the mutation operator helps to maintain the genetic diversity of each generation. To get t+1 t t+1 x � x + v , (20) ij ij ij better convergence, the ﬁrst P is reset into the initial con- dition when there is a variation in irradiance and temper- t th where x is the position vector of the i particle at iteration t ij ature. &e reinitialization is obtained based on the following t+1 th and x is the position vector of the i particle at iteration ij two conditions: t + 1, while the velocity is given as |v(k + 1) − v(k)| < Δv, (25) t+1 t t t t t v � ωv + c r pbest − x + c r gbest − x , 􏼐 􏼑 􏼐 􏼑 (21) ij ij 1 1 ij ij 2 2 ij 􏼌 􏼌 􏼌 􏼌 􏼌 􏼌 t+1 th 􏼌􏼐p (k + 1) − p (k)􏼑􏼌 where v is the velocity vector of the i particle at iteration pv pv 􏼌 􏼌 ij 􏼌 􏼌 > Δp, (26) 􏼌 􏼌 􏼌 􏼌 t + 1 and c and c are the coeﬃcients. &e random numbers 􏼌 􏼌 p (k) 1 2 􏼌 pv 􏼌 that are distributed uniformly in the range [0,1] are rep- resented as r and r . &e best ﬁtness values for the particle 1 2 where v is the output voltage and p is the power of the PV pv are considered pbest, and gbest represents the ﬁtness value system. For each iteration, the initial P and their individuals for all the particles. &e position of each particle has been are applied, and the initial position of P is given as evaluated based on this ﬁtness function, and it is given as 􏼂P , P , P , P , P 􏼃 � [1.0,0.8,0.6,0.4,0.2]V . (27) 1 2 3 4 5 oc 2 2 t t (22) f � 􏼐x − v 􏼑 + 􏼐x − i 􏼑 . ij max ij max &e generated power p (k) at the kth iteration is pv considered the ﬁtness function. &e crossover operator To update the pbest and gbest positions, the ﬁtness function of each particle is compared. If the present position function combines the two chromosomes to obtain a new child, and it is given as is comparatively better than the previous position, then the present position is considered the best value, and the overall c(k) � rp(r) − ((1 − r)p(k + 1)), (28) ﬁtness function is also updated based on that. Mathemati- cally, it is formulated as c(k + 1) � ((r − 1)p(k)) − ((r)p(k + 1)), (29) t t t ⎧ ⎪ x , if f􏼐x 􏼑 < pbest , ij ij ij pbest � (23) where c(k) is the next-generation solution and r is the ij ⎪ pbest , otherwise, ij random number. To obtain the relationship between the duty cycle (D) and the output voltage, the ratio of next- t t t t generation solution and open-circuit voltage is considered. gbest � min pbest , pbest , . . . , pbest . 􏼐 􏼑 (24) ij j j+1 s Due to the sequential aspect of chromosomes, the dynamic To update the position and velocity of all the particles, response and mutation impact on convergence are con- the above equations are used and the same procedure is sidered in the genetic model. c(k) and the random number r implemented to obtain the MPPT process. &e position of are selected in the range [0,1], and the position values are the panel is adjusted for every iteration, and the best position taken in the range [0.2,1.0]. is updated so that P can be tracked during the power max generation process. In the proposed work, the values of c 3.3. BAT Optimization. BAT optimization is a nature-in- and c are considered 2 and 1.5, respectively. &e weight spired optimization algorithm that is formulated based on factor ω is taken as 1.2, and the values of r and r are taken 1 2 the echolocation features of bats’ food-searching process. in the range of [0,1]. Using echolocation, the insects are identiﬁed by bats so that the food sources are identiﬁed. &e intensity of the return 3.2. Genetic Algorithm Optimization. &e GA was intro- signal and its direction are the major factors to locate the duced to solve constrained and unconstrained optimization prey in the optimization model. &e ultrasonic pulses are issues. Based on natural selection and biological evolution, emitted at a certain amplitude and rate, and a bat receives its the problems are solved in the GA. &e individual solutions own signal as feedback in between the pulse trains to in- in the GA are modiﬁed continuously, and next generations terpret the prey location. Depending on the feedback in- are produced by selecting a random individual from the tensity, the distance is measured. If the intensity is high, the International Transactions on Electrical Energy Systems 7 prey is near the bat and it moves towards the prey by in- optimization model, the search agents are limited, and the tensifying the pulse amount to capture the prey. &e ﬂying encircling behavior is formulated as 􏼌 􏼌 characteristics of bats are random with velocity (v ), and its → 􏼌→ 􏼌 → → 􏼌 􏼌 􏼌 􏼌 (36) D � C x (t) − x (t) , 􏼌 p sg 􏼌 position and loudness are given as x and l . &e emission i i rate of bats is considered in the range [0,1] depending on the → → → → target proximity. &e velocity and position of the bat at each x (t + 1) � x (t) − A . D , (37) sg p step are formulated as → → where A and C are the coeﬃcients that balance the ex- t+1 t t+1 (30) x � x + v , i i i ploitation and exploration factors and are given as A � → → → → (2 a ∗ r ) − (a) and C � 2 r , in which the factors r and 1 2 1 t+1 t t ∗ v � v + 􏼐x − x 􏼑f , (31) ij i i i r are random numbers whose range is [0,1]. &e range of coeﬃcient (a) gradually decreased from 2 to 0 for every where f is the randomly assigned frequency that is given as iteration, which indicates the wolves approach the prey. &e position of best search agents is used to update the position f � f + f − f 􏼁φ, (32) i min max min of all agents for every iteration, and it is given as 􏼌 􏼌 where φ is the random vector for uniform distribution that is → 􏼌 􏼌 → → → 􏼌 􏼌 ∗ 􏼌 􏼌 D � c x − x , (38) 􏼌 􏼌 in the range [0,1] and x is the global best position that is α 1 α sg obtained by comparing all the solutions at each iteration. In 􏼌 􏼌 􏼌 􏼌 → → → 􏼌 􏼌 the position update process, the pulse emission rate is 􏼌 􏼌 (39) D � c x − x , 􏼌 􏼌 β 2 β sg considered. If the random vector is greater than the emis- sion, then the exploitation stage is selected. &e current → → → → (40) x � x − A ∗ D , 1 α 1 α position is replaced based on the solution obtained in the local search process, and it is given as → → → → (41) x � x − A ∗ D , ∗ t 2 β 1 β (33) x � x + l , → → where the random number is obtained from Gaussian x + x 􏼁 → 1 2 (42) x (t + 1) � . sg distribution or uniform distribution in the range [− 1,1] and l is the average loudness at this timestamp. &e ﬁtness &e hunting process is stopped if the prey has stopped its function is further improved if the generated random movement and the search agents have ﬁnished the attacking number is smaller than loudness. A new solution is obtained process. &e position update and attacking procedure of grey during the exploration process, and the parameters such as wolves are depicted in Figure 3. emission rates and loudness are updated. Mathematically, &e proposed optimization model is used to maximize the parameter update is formulated as the output power of PV array considering its D as the de- t+1 t l � ρl , (34) cision variable. In the initialization process, the population is i i limited in the range of 0.1 to 0.9 of D, and it is expressed as t+1 (− αt) (35) r � r 􏼐1 − e 􏼑, i i d � rand􏼐n ,1􏼑 d − d 􏼁 + d , (43) i p max min min where ρ is constant whose range is deﬁned as [0,1] and α is where d is the D and n is the initial population, which i p the positive constant. &e bat’s food-searching behavior is refers to the number of PV systems. related to energy tracking to obtain the P point in the max &e position of the prey is obtained by calculating the solar PV model. ﬁtness function. In the proposed model, the values d and d α β are considered the ﬁrst- and second-best solutions with the highest PV power. To update the position of search agents 3.4. Grey Wolf Optimization. GWO is a metaheuristic op- based on the position of d and d , the population position α β timization algorithm that is derived based on the hunting and D are updated, and they are given as nature of grey wolves. It is a type of swarm intelligence 􏼌 􏼌 􏼌 􏼌 → → 􏼌 􏼌 algorithm that eﬃciently solves nonlinear optimization is- 􏼌 􏼌 D � 􏼌 c d − d 􏼌, (44) α 1 α i 􏼌 􏼌 sues. &e structure of grey wolves includes an alpha (α) that 􏼌 􏼌 􏼌 􏼌 → → → is the leader of the group, beta (β) that is the subordinates of 􏼌→ 􏼌 􏼌 􏼌 D � c d − d , (45) 􏼌 􏼌 β 2 β i 􏼌 􏼌 α, and the reaming delta (δ) and omega (ω) that are the third- and fourth-class supporting wolves. Alpha wolves are → → → → (46) d � d − A ∗ D , the leaders and provide the best ﬁtness solution for the given 1 α 1 α optimization problem. &e hunting steps of grey wolves → → → → (47) include the following: (1) prey search, (2) encircling the prey, d � d − A ∗ D , 2 β 1 β and (3) attacking the prey. GWO has high convergence → → speed and provides better accuracy than other optimization 􏼒 d + d 􏼓 1 2 (48) algorithms as it has a better balance between exploitation d (t + 1) � . and exploration phases. To improve the performance of the 8 International Transactions on Electrical Energy Systems temperature of 25 C. &e maximum current is obtained for 1000W/m , and the lowest current is obtained for 200W/ 1 m . 2 In the next analysis, the irradiance is kept constant and ° ° ° 2 the temperature is varied in the range [10 C, 30 C, 60 C], and the P-V characteristics are observed and depicted in Fig- ure 9. When the voltage increases, the power generation alfa increases linearly, reaches the maximum for minimum temperature, and exhibits a lower power for a maximum beta temperature of 60 C. &is indicates the eﬀect of temperature on power generation. Move &e I-V characteristics depicted in Figure 10 are ob- served by holding the irradiance at a constant value, and the ° ° ° temperature is varied in the range [10 C, 30 C, 60 C]. When delta the voltage increases, the power generation decreases and reaches a minimum value. However, the minimum tem- perature does not introduce much eﬀect on the results, whereas the maximum temperature of 60 C reduces quickly than others, which indicates the eﬀect of temperature on Figure 3: Position update and hunting of grey wolves. current characteristics. Furthermore, to analyze and improve the performance &e powers are calculated, and the process needs to be of the PV model, optimization-based MPPTis introduced in terminated when P is obtained. &e maximum iteration max the proposed work. Four optimization models are included and maximum output power are the termination criteria for for the analysis, and based on the performance, the best the process, and they can be reinitialized if the power is model is selected. Five PV arrays are connected in series, and reduced, and the process is given as a partial shading condition is considered for the analysis. &e 􏼌 􏼌 􏼌 􏼌 experimentation is performed under three cases for better 􏼌 􏼌 􏼌 􏼌 p − p 􏼌 pv pv,l􏼌 validation, and the cases are given as follows: (49) ≥ ΔP, pv,l 2 Case 1: uniform irradiance of 1000W/m is applied in G3, G4, and G5, and nonuniform irradiance is applied where ΔP represents the last operating point and p pv,l in remaining panels G1 and G2 represents the power at the global P point. &e process max ﬂow of GWO-based MPPT is given in Figure 4. Case 2: uniform irradiance of 1000W/m is applied in G4 and G5, and nonuniform irradiance is applied in remaining panels G1, G2, and G3 4. Results and Discussion Case 3: uniform irradiance of 1000W/m is applied in &e proposed model performance is veriﬁed through a G5, and nonuniform irradiance is applied in remaining simulation designed in the MATLAB Simulink tool. &e PV panels G1, G2, G3, and G4 cell speciﬁcations are given in Table 1, and Figure 5 depicts For each case, ﬁve simulation tests are conducted and the the arrangement of the single-diode solar PV model. &e performances are measured in terms of P , MPPT power max performances are measured under diﬀerent irradiance and (MPPTP), and TE. &e tracking eﬃciency (TE) is obtained temperature values, and the observations are discussed in based on the ratio between maximum power and MPPT this section. power, and it is formulated as &e Simulink model for the proposed single-diode model is given in Figure 6. Initially, the parameters are P MPPT η � × 100. (50) extracted, and the performance of the single-diode PV max model is analyzed under diﬀerent irradiance and temper- &e optimized MPPT model for the proposed work is ature conditions. depicted in Figure 11. &e Simulink model includes the PSO- &e P-V characteristics of the single-diode PV model are based MPPT model, and the same model is used for all the analyzed under diﬀerent irradiance values in the range [1000, 800, 600, 400, 200] W/m optimization by replacing respective optimization units for , and the 25 C reference GA optimization, BAToptimization, and GWO in the design. temperature is ﬁxed for the analysis shown in Figure 7. It could be observed from the analysis that P is obtained for &e rest of the elements are similar for all the optimization max models. &e performance of the PSO-based MPPT model is the irradiance value 1000, whereas for others, the power gets analyzed for all three cases and listed in Tables 2–4 for cases decreased gradually and irradiance of 200W/m exhibits the 1–3, respectively. It is observed from the analysis the PSO- lowest power among all others. based MPPT process obtains an average TE of 96%. &e I-V characteristics of the single-diode PV model are &e performance of the GA-based MPPT model is an- depicted in Figure 8 for diﬀerent irradiance values in the alyzed for all three cases and listed in Tables 5–7, range [1000, 800, 600, 400, 200] W/m with a reference International Transactions on Electrical Energy Systems 9 Start Initialize GWO parameters Initialize D and population Sense V , I from PV panel pv pv Calculate power, D Check p (i)>p (i-1) Yes No D =D -δd D =D +δd n i n i Update P , optimal D and GWO parameters max No All agents evaluated? Yes No Reached Convergence? Yes End Figure 4: Process ﬂow of GWO-based MPPT. Table 1: Solar PV cell speciﬁcation. S. no. Parameter Range 1 Input power 260W 2 Short circuit current (I ) 8.67A sc 3 Open-circuit voltage (V ) 37.92V oc 4 Temperature coeﬃcient of I 0.06% per C sc 5 Temperature coeﬃcient of V − 0.33% per C oc 6 Reference temperature 25 C respectively. It is observed from the analysis the GA-based respectively. It is observed from the analysis the BAT op- MPPTprocess obtains an average TE of 93%, which is much timization-based MPPT process obtains an average TE of less than that of the PSO-based MPPT model. 97%, which is 4% higher than that of the GA-based MPPT &e performance of the BAT optimization-based MPPT model and 1% higher than that of the PSO-based MPPT model is analyzed for all three cases and listed in Tables 8–10, model. 10 International Transactions on Electrical Energy Systems [1×5] Bypass Diode 1 Solar Radiation PV Module 1 Bypass Diode 2 [1×5] PV Module 2 Module Temperature Bypass Diode 3 PV Module 3 Bypass Diode 4 PV Module 4 Bypass Diode 5 PV Module 5 Figure 5: Proposed single-diode PV array model. Power Power2 [Ipv] RL I i Connection Port c v [Vpv] M + Connection Port1 PV array1 Figure 6: Simulink model of the proposed single-diode PV array. g International Transactions on Electrical Energy Systems 11 P-V Characteristics with various Irradiance –20 0 2 468 10 12 Voltage (V) G4 = 400 W/m2 G1 = 1000 W/m2 G5 = 200 W/m2 G2 = 800 W/m2 G3 = 600 W/m2 Figure 7: P-V characteristics under various irradiances in the range [1000, 800, 600, 400, 200] W/m . V-I Characteristics with various Irradiance 02468 10 12 Voltage (V) G4 = 400 W/m2 G1 = 1000 W/m2 G5 = 200 W/m2 G2 = 800 W/m2 G3 = 600 W/m2 Figure 8: I-V characteristics under various irradiances in the range [1000, 800, 600, 400, 200] W/m . P-V Characteristics with Various Temperature –20 02 4 6 8 10 12 Voltage (V) Temp1 = 10 C Temp2 = 30 C Temp3 = 60 C Figure 9: P-V characteristics at various temperatures. &e performance of the GWO-based MPPT model is be observed from the analysis the TE of the GWO model is analyzed for all three cases and listed in Tables 11–13, re- higher than that of other optimization models in all the three spectively. It is observed from the analysis the GWO-based cases. &e fast convergence and accuracy of GWO have MPPT process obtains an average TE of 98%, which is 5% obtained maximum TE compared to those of other opti- higher than that of the GA-based MPPT model, 2% higher mization models. For case 1, for all the ﬁve test conditions, than that of the PSO-based MPPT model, and 1% greater the tracking eﬃciency obtained by GWO is above 98%, than that of the BAT optimization-based MPPT model. whereas the tracking eﬃciency of BAToptimization obtains &e TE of all the optimization models is compared and an average of 97% and PSO attains 96% tracking eﬃciency. &e least performance is attained by the genetic algorithm, depicted in Figures 12–14 for cases 1–3, respectively. It could Power (W) Power (W) Current (A) 12 International Transactions on Electrical Energy Systems V-I Characteristics with Various Temperature −2 0 2 4 6 810 12 Voltage (V) Temp1 = 10 C Temp2 = 30 C Temp3 = 60 C Figure 10: I-V characteristics at various temperatures. 761.9 752.2 Power1 [Vpv] Vpv Power DD P Power2 PSO Saturation [Ipv] Ipv [0...1] [Ipv] RL i Connection Port [Vpv] c v Connection Port1 PV array1 Figure 11: Simulink design-optimized MPPT model. Table 2: PSO-based MPPT performance for case 1. Test G1 G2 G3 G4 G5 P MPPTP TE (%) max 1 900 950 1000 1000 1000 974.1 936.7 96.16 2 810 860 1000 1000 1000 910.2 879.5 96.63 3 720 770 1000 1000 1000 857.7 826.1 96.32 4 610 680 1000 1000 1000 712.6 689.9 96.81 5 550 580 1000 1000 1000 621.1 596.3 96.01 Table 3: PSO-based MPPT performance for case 2. Test G1 G2 G3 G4 G5 P MPPTP TE (%) max 1 910 940 970 1000 1000 937.3 908.2 96.90 2 800 850 890 1000 1000 876.1 844.6 96.40 3 710 750 780 1000 1000 756.7 731.2 96.63 4 620 660 690 1000 1000 670.6 643.7 95.99 5 500 550 590 1000 1000 579.5 559.3 96.51 Current (A) g International Transactions on Electrical Energy Systems 13 Table 4: PSO-based MPPT performance for case 3. Test G1 G2 G3 G4 G5 P MPPTP TE (%) max 1 900 930 960 890 1000 934.5 902.3 96.55 2 800 840 870 780 1000 856.7 824.4 96.23 3 700 730 760 670 1000 736.2 704.3 95.67 4 600 670 640 570 1000 646.9 619.8 95.81 5 500 540 580 490 1000 549.7 527.2 95.91 Table 5: GA-based MPPT performance for case 1. Test G1 G2 G3 G4 G5 P MPPTP TE (%) max 1 900 950 1000 1000 1000 971.3 909.4 93.63 2 810 860 1000 1000 1000 912.4 857.3 93.96 3 720 770 1000 1000 1000 862.1 798.1 92.58 4 610 680 1000 1000 1000 710.8 663.7 93.37 5 550 580 1000 1000 1000 598.8 552.4 92.25 Table 6: GA-based MPPT performance for case 2. Test G1 G2 G3 G4 G5 P MPPTP TE (%) max 1 910 940 970 1000 1000 942.1 876.8 93.07 2 800 850 890 1000 1000 883.7 827.4 93.63 3 710 750 780 1000 1000 763.5 712.3 93.29 4 620 660 690 1000 1000 664.9 623.7 93.80 5 500 550 590 1000 1000 569.3 527.8 92.71 Table 7: GA-based MPPT performance for case 3. Test G1 G2 G3 G4 G5 P MPPTP TE (%) max 1 900 930 960 890 1000 941.8 880.2 93.46 2 800 840 870 780 1000 864.6 812.4 93.96 3 700 730 760 670 1000 743.1 694.7 93.49 4 600 670 640 570 1000 652.7 607.9 93.14 5 500 540 580 490 1000 543.2 504.2 92.82 Table 8: BAT optimization-based MPPT performance for case 1. Test G1 G2 G3 G4 G5 P MPPTP TE (%) max 1 900 950 1000 1000 1000 963.2 937.2 97.30 2 810 860 1000 1000 1000 907.8 883.2 97.29 3 720 770 1000 1000 1000 859.9 837.1 97.35 4 610 680 1000 1000 1000 720.1 702.4 97.54 5 550 580 1000 1000 1000 610.2 591.2 96.89 Table 9: BAT optimization-based MPPT performance for case 2. Test G1 G2 G3 G4 G5 P MPPTP TE (%) max 1 910 940 970 1000 1000 937.8 916.7 97.75 2 800 850 890 1000 1000 894.8 873.5 97.62 3 710 750 780 1000 1000 780.9 764.5 97.90 4 620 660 690 1000 1000 678.1 659.8 97.30 5 500 550 590 1000 1000 579.4 563.8 97.31 which attains 93% tracking eﬃciency. For case 2, the optimization, and GWO is 93.374%, 96.034%, 96.974%, and tracking eﬃciency of GA, PSO, BAT optimization, and 98.284%, respectively. &e average tracking eﬃciency con- GWO is 93.3%, 96.486%, 97.576%, and 98.164%, respec- sidering all the three cases attained by the optimization tively. For case 3, the tracking eﬃciency of GA, PSO, BAT models is 93.3% for GA, 96.3% for PSO, 97.3% for BAT 14 International Transactions on Electrical Energy Systems Table 10: BAT optimization-based MPPT performance for case 3. Test G1 G2 G3 G4 G5 P MPPTP TE (%) max 1 900 930 960 890 1000 936.7 910.4 97.19 2 800 840 870 780 1000 875.2 847.9 96.88 3 700 730 760 670 1000 751.1 725.7 96.62 4 600 670 640 570 1000 674.9 654.9 97.04 5 500 540 580 490 1000 549.8 534.1 97.14 Table 11: GWO-based MPPT performance for case 1. Test G1 G2 G3 G4 G5 P MPPTP TE (%) max 1 900 950 1000 1000 1000 957.8 942.7 98.42 2 810 860 1000 1000 1000 910.7 896.2 98.41 3 720 770 1000 1000 1000 849.3 829.4 97.66 4 610 680 1000 1000 1000 728.8 716.1 98.26 5 550 580 1000 1000 1000 623.4 612.8 98.30 Table 12: GWO-based MPPT performance for case 2. Test G1 G2 G3 G4 G5 P MPPTP TE (%) max 1 910 940 970 1000 1000 920.4 907.8 98.63 2 800 850 890 1000 1000 884.7 867.1 98.01 3 710 750 780 1000 1000 772.9 759.5 98.27 4 620 660 690 1000 1000 684.5 669.9 97.87 5 500 550 590 1000 1000 571.2 560 98.04 Table 13: GWO-based MPPT performance for case 3. Test G1 G2 G3 G4 G5 P MPPTP TE (%) max 1 900 930 960 890 1000 927.9 916.2 98.74 2 800 840 870 780 1000 873.8 857.3 98.11 3 700 730 760 670 1000 763.3 751.7 98.48 4 600 670 640 570 1000 680.1 668.4 98.28 5 500 540 580 490 1000 551.8 539.7 97.81 Case 1 Test number BAT GA PSO GWO Figure 12: TE comparisons for case 1. optimization, and 98.2% for GWO. It is observed that single-diode PV model can be improved with the GWO- maximum performance is attained by the GWO model, based MPPT strategy. Compared to other optimization which increases the performance of PV systems. models, GWO has a much better convergence rate and From the analysis, it could be observed that GWO ex- provides maximum power tracking, which increases the hibits maximum TE and power in all the cases compared to total power, whereas the convergence rate of PSO is better other optimization algorithms. &e performance of the than that of GA but less than that of GWO, and in the case of TE (%) International Transactions on Electrical Energy Systems 15 Case 2 Symbols V : Potential diﬀerence I : Reverse saturation current V : &ermal voltage N : Series-connected cells − 23 k: Boltzmann constant (1.380650 ×10 J/K) − 19 q: Electron charge (1.602176 ×10 C) T: Temperature I : &e current generated by photovoltaic eﬀect 88 pg I : Diode current Test number I : Diode saturation current GA BAT R : Series resistance PSO GWO R : Shunt resistance sh Figure 13: TE comparisons for case 2. ΔI (i): Change in current point ΔV (i): Change in voltage point V : Open-circuit voltage oc Case 3 V : Maximum power point voltage th x : Position vector of the i particle at iteration t ij th t+1 x : Position vector of the i particle at iteration t+1 ij c and c : Coeﬃcients 1 2 r and Random numbers distributed uniformly in the 94 → r : range [0,1] 92 P : Power of the photovoltaic system pv V: Output voltage C(k): Next-generation solution V : Random bat’s velocity X : &e position of bats Test number i L : &e loudness of bats GA BAT F : Randomly assigned frequency GWO i PSO φ: Random vector for uniform distribution Figure 14: TE comparisons for case 3. ρ: Constant α: Positive constant → → A and C: Coeﬃcients in grey wolf optimization BAToptimization, the convergence rate is better than that of β: Beta-subordinates of α PSO and GA but less than that of the GWO model. &is δ and ω: Delta and omega-third- and fourth-class indicates that, with minimum time, the GWO model attains supporting wolves maximum performance so that it can be selected as the best D : Duty cycle optimization model among other optimization algorithms. i N : Initial population ΔP: Last operating point. 5. Conclusion &is research work presents an analysis of a single-diode PV Data Availability model and MPPT using optimization techniques to improve &e reference articles data used to support the ﬁndings of the performance of solar PV systems. &e parameters of the this study are included within this article. single-diode model are derived, and the I-V and P-V char- acteristics are analyzed under diﬀerent conditions. Irradiance and temperature are varied to measure the characteristics. Additional Points Furthermore, four optimization models such as PSO, GA, BAToptimization, and GWO are introduced to obtain MPPT of the proposed system. &e performance is analyzed under Highlights. (1) A mathematical model for a single-diode PV three diﬀerent cases by varying the irradiance levels. Among system and four optimization approaches for MPPT under all four optimization techniques, the GWO-based MPPT diﬀerent environmental conditions are presented in this model attains approximately 98% TE, which is much better research work. (2) &e simulation results demonstrate that than that of other optimization techniques. Furthermore, this the grey wolf optimization model achieves a maximum research work can be improved by integrating Internet of power tracking eﬃciency of 98%, which is better than that of things models for fault detection so that the factors that aﬀect other competing optimization techniques such as BAT the TE can be identiﬁed and replaced immediately. optimization (97%), PSO (96%), and GA (93%). TE (%) TE (%) 16 International Transactions on Electrical Energy Systems [15] A. Mohanty, P. K. Ray, M. Viswavandya, S. Mohanty, and Conflicts of Interest P. P. 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Analysis of Single-Diode PV Model and Optimized MPPT Model for Different Environmental Conditions

Analysis of Single-Diode PV Model and Optimized MPPT Model for Different Environmental Conditions

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Analysis of Single-Diode PV Model and Optimized MPPT Model for Different Environmental Conditions

Analysis of Single-Diode PV Model and Optimized MPPT Model for Different Environmental Conditions

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