1

ASYMMETRICAL FUZZY LOGIC CONTROL BASED MPPT ALGORITHM FOR STAND-ALONE 1 PHOTOVOLTAIC SYSTEM UNDER PARTIALLY SHADED CONDITIONS 2

Pallavi Verma*a, Rachana Gargb, Priya Mahajanc 3 apallaviverma@live.com, brachana16100@yahoo.co.in, cpriyamahajan.eed@gmail.com 4

a,b,c Electrical Engineering Department, Delhi Technological University, Bawana Road, Delhi, India-110042 5 (*Mobile No. +91-9910348910) 6

7

ABSTRACT 8 Partial shading conditions (PSCs) in Photovoltaic (PV) system is an inevasible situation which 9 curtails the PV array output by exhibiting multiple peaks in its Power-Voltage (P-V) curve. The 10 multiple peaks consist of a single global maximum power point (GMPP) and many local maximum 11 power points (LMPP). The presence of multiple peaks makes tracking of maximum power point 12 more difficult and demands an efficient controller to track the global peak of the P-V curve. 13 In the present work, a novel intelligent asymmetrical Fuzzy Logic Control (AFLC) based maximum 14 power point tracking (MPPT) algorithm has been proposed for tracking GMPP. The fuzzy 15 membership functions of the proposed algorithm have been optimized using a heuristic approach. 16 The algorithm has been designed, developed and analyzed using MATLAB/Simulink. Furthermore, 17 to establish the superiority of proposed AFLC algorithm, it has been compared with conventional 18 perturb & observe (P&O) algorithm and intelligent Fuzzy Logic Control (FLC) based algorithm for 19 GMPP tracking and shading losses under standard test condition (STC) and partially shaded 20 conditions. 21

Keywords: Solar Photovoltaic system; Maximum Power Point Tracking; Perturb and Observation 22 algorithm; Fuzzy and Asymmetrical Fuzzy algorithm; Shading loss; DC-DC Boost Converter. 23

1. Introduction 24

Energy is required at every step of life, and due to depletion of fossil fuels, this demand may not be 25 fulfilled by conventional power generation system only. To overcome this major concern, 26 renewable resources such as solar, hydro, wind, hydrogen fuel cell, biogas, etc. has taken the center 27 stage of emerging technology. Amongst these non-conventional energy resources, photovoltaic 28 energy conversion is gaining widespread acceptance due to its being green, abundant in nature and 29 continuous reduction in the prices of PV modules [1]. Sun is a huge source of energy that can be 30 converted into utilizable form with the help of solar PV (SPV) cell. 31 32 The performance of a solar PV system highly depends on varying meteorological conditions like 33 insolation, temperature, etc. The PV panel gives optimum output under STC (irradiation 1kW/m2 34 and temperature 25°C), and its output is negatively affected by partial shading. Shading is the 35 condition when PV array is not uniformly irradiated. The shading on solar PV array can be caused 36 because of dense clouds, nearby building, big trees, towers, dust and panel aging or cracking. A 37 major consequence of shading is that it exhibits multiple peaks in Power-Voltage and Current-38 Voltage (I-V) curve of PV array, which may account for the conventional MPPT algorithms 39 converging in LMPP instead of GMPP, resulting in power loss. Hence, mitigating the effect of partial 40 shading is a major practical challenge. 41

Several conventional MPPT techniques viz. perturb & observation, incremental conductance (INC), 42 fractional open circuit voltage (FCOV), etc. have been reviewed and addressed in [2,3]. Among these 43

2

conventional MPPT methods, P&O is most widely used because of its simplicity and ease of 44 implementation. But its reliability is low under PSCs because the perturbation process makes the 45 operating point lurch around the maximum power point, resulting in wastage of power. This 46 challenge can be met by reducing the step size of perturbation, but small perturbation size delays 47 the MPP tracking [4,5]. Sadeq D. Al-Majidi et al. have proposed a novel MPPT algorithm in [6] where 48 they have compared the performance of P&O and FLC based MPPT for grid connected PV system. 49 The proposed algorithm accurately tracks maximum power with no drift problem. 50

The INC algorithm offers improved tracking accuracy under steady-state and variable 51 environmental conditions. The main compensations provided by INC algorithm over the P&O 52 algorithm have been dissected by Liu C. et al. [7]. The INC algorithm is founded on the fact that 53 the rise of the PV module power curve is zero at the MPP, positive on the left side and negative on 54 the right position of the MPP. It uses the derivative algorithm to find the MPP. This 55 method takes more computation in the controller because the differentiation process involves a 56 relatively complex decision-making procedure [8,9]. So, implementing INC algorithm increases the 57 cost and complexity of the system, and it may give unsatisfactory results at low insolation level. 58 Further, Reisi A.R. et al. [10] distinguished MPPT algorithms into two categories: direct and 59 indirect method. The indirect MPPT algorithms such as fractional open circuit voltage and short 60 circuit current cannot trace MPP at any given environmental condition, as these methods require 61 prior behavior of P-V characteristics. On the other side, direct method [11] based algorithms do not 62 require prior knowledge of P-V characteristics and can track MPP under any weather conditions. 63 Authors in [12] have compared the effect of different membership functions of FLC. Triangular 64 membership function shows the best result and Guassian membership function has poor 65 performance under the considered cases. Asim N. et al. [13], has done performance analysis for 66 maximum power point tracking by different controllers such as P&O, FLC, neural network, ripple 67 correction control current sweep, DC-Link capacitor droop control, etc. Ripple Correction Control 68 by Esram T. et al. [14] has higher tracking efficiency at uniform shading condition, and its efficiency 69 significantly reduces under PSC as it takes more time to search GMPP. 70

Recently distinguished work done includes deployment of P&O under partial shading condition by 71 R. Balasankar et al in [15]. In [16] adaptive neuro fuzzy inference system based MPPT algorithm is 72 presented. ANFIS model for tracking MPP takes temperature and irradiation as input and duty cycle 73 is the output. In [17], Sahoo S.K detected the presence of PSC by examining the voltage at each PV 74 module, but this technique requires an equal number of voltage sensors as the PV module in the 75 array. Ishaque et al. [18] presented an impressive method based on particle swarm optimization 76 (PSO) algorithm, but it is too complicated to be commercially applied as some parameters need to 77 be set by the user. Karami N et al. [19] applied artificial neural network (ANN). The problem faced 78 by ANN based algorithm is that it is dependent on available training data under the different 79 environmental conditions, so the data needs to be revised again when array configuration changes. 80 Authors in [20-22] reviewed algorithms such as an artificial bee, ant colony, particle swarm 81 optimization, flashing fireflies, grey wolf algorithms. Though, the genetic algorithm has better 82 stability; its implementation is a significant challenge as it involves complicated calculation, 83 equations, and some data need to be set by the user. 84

In [23], the proposed system tracks maximum power utilizing differential evolution (DE). The 85 proposed technique comes out to have a better response regarding fast convergence during both 86 uniform and non-uniform shading condition. It also eliminates fluctuation around MPP. Inputs like 87 insolation level, the temperature to SPV are ephemeral. So, control algorithms need to be 88

3

implemented to meet the uncertainties in the quantities of interest. FLC technique, a soft computing 89 tool meets these uncertainties [24]. FLC can incorporate a conventional design to track MPP under 90 ambient conditions as suggested by K. Sundareswarm et al. [25]. Pallavi Verma et al. [26] have 91 compared P&O and intelligent FLC algorithm under the partially shaded condition for stand-alone 92 PV system and simulation results shows that FLC can track maximum power with better tracking 93 efficiency. Results also shows that under dynamic condition conventional MPPT may track LMPP 94 instead of GMPP. 95

The present work focuses on the tracking of global peak out of multiple peaks under PSC’s. Solar 96 photovoltaic panels under partial shading condition are not uniformly irradiated, which makes P-V 97 characteristic to exhibit more than one peak. Out of these multiple peaks, there is only one peak 98 exhibiting maximum power i.e. GMPP. The conventional algorithm may not be able to track GMPP, 99 and may lurch around LMPP. To overcome these drawbacks of a conventional algorithm, FLC have 100 been implemented which enhances the performance of MPPT by tracking GMPP. The MPPT 101 tracking efficiency is further enhanced using novel, intelligent asymmetrical Fuzzy Logic Controller 102 based algorithm. For asymmetrical FLC, the authors have optimized the universe of discourse by 103 fine-tuning them at the center for an effective implementation of maximum power point tracking. 104 The proposed asymmetrical FLC MPPT algorithm distinguishes between GMPP & LMPP and 105 contributes towards the global peak tracking. By implementing asymmetrical fuzzy controller, the 106 tracked power is more in comparison with other conventional algorithms which establishes the 107 superiority of proposed algorithm. Also, with AFLC algorithm shading losses are reduced. The 108 proposed MPPT algorithm showed enhanced performance under both steady state and dynamic 109 conditions. This relatively new idea of asymmetrical FLC based MPPT algorithm under PSC’s for 110 stand-alone PV system can be implemented for large solar farms also. These studies shall be helpful 111 for system designers. 112

1.1 System Configuration 113

Figure 1 presents the block diagram of a stand-alone PV system. To track maximum available power 114 at a given environmental condition MPPT technique is utilized by adjusting the duty ratio of a boost 115 converter. The proposed asymmetrical FLC based MPPT algorithm has been designed, developed 116 and validated to track the global peak from multiple peaks of the P-V curve under partially shaded 117 condition which may not be efficiently traced by other conventional approaches. The components 118 of the proposed system are explained in the following sections. 119 120

2. Solar Photovoltaic Cell 121

Solar cell works on the principle of Photovoltaic effect. It is an active transducer which converts 122 energy from sunlight (photons) into electricity (current). The voltage produced by the solar cell is 123 minimal (0.5V to 0.8V), so to get desired output they need to be connected in series. Solar cell 124 connected in series makes PV module and PV module connected in a series-parallel configuration, 125 as per power requirement, makes PV array [27]. Figure 2 presents the ideal and practical 126 equivalent circuit of single diode model used in the proposed system. 127

128 The output current Io/p of PV cell is given as equation 1: 129

𝐼𝑜/𝑝 = 𝐼𝑐𝑠 − 𝐼𝑠𝑎𝑡 ∗ [𝑒𝑥𝑝 (𝑞(𝑉𝑜/𝑝+ 𝐼𝑜/𝑝∗𝑅𝑠 )

𝑁𝑠 𝐴𝑘𝑇𝑎𝑐 ) − 1] −

𝑉𝑜/𝑝+𝐼𝑜/𝑝𝑅𝑠

𝑅𝑠ℎ (1) 130

4

where, Io/p is the output current of PV cell, Ics is the photon current, Isat is the diode saturation 131 current, q is the elementary charge (1.602*10-19 C), Vo/p is the output voltage of a PV cell, Ns is the 132 number of series cell, A is the ideal factor of the cell dependent on PV technology, K is the 133 Boltzmann constant (1.38*10-23 J), Tac is the actual operating temperature. 134 In the present work, Sun Power Solar panel X22-360 PV module is used. Table 1 shows the sun 135 power solar panel specifications used for simulation and modeling of PV module. An array of (3x1) 136 PV modules viz. M1, M2, M3, each of 360W, connected in series is considered, as shown in figure 1, 137 and is simulated using MATLAB/Simulink. The maximum power obtained by the array is (360x3) 138 1.08kW. 139 140 Figure 3 shows the influence of irradiation and temperature on the I-V and P-V characteristics of PV 141 array. I-V and P-V curve shows that, with the change in temperature, voltage changes appreciably 142 and change in irradiation causes appreciable change in current. Also, it can be seen from figure 3 143 when modules are uniformly irradiated there is only one maxima. 144

145

3. DC-DC Converter 146

In the proposed PV system, the boost converter is used as a dc-dc converter (figure 1). The main 147 components of boost converter along with IGBT switch are the series inductor and shunt capacitor, 148 which are passive components. The values of an inductor, capacitor, duty ratio and resistive load 149 are calculated below as given by equation 2-5. 150

𝐿 =𝑉𝑜/𝑝 𝛼

(∆𝐼1𝑓𝑠𝑤) (2) 151

𝛼 = 1 − (𝑉𝑎

𝑉𝑜/𝑝) (3) 152

𝐶 = 𝐼𝑎 𝛼

(∆𝑉𝑓𝑠𝑤) (4) 153

𝑅𝑜 =𝑅𝑖𝑛

(1−𝛼)2 (5) 154

155 where, ∆I1 is output ripple current, and it is considered as the 10% of the input current, 𝑉𝑜/𝑝 is the 156

output voltage, fsw is switching frequency and α is the duty ratio, Va is the input voltage, Ia is the 157 average output current. ∆V is the peak ripple voltage, and the value of ∆V is taken as 3% of the 158 output voltage, Rin is the input resistance, Ro is the load resistance which comes out to be 122 Ω. The 159 values of inductance, capacitance and duty ratio are 1.1mH, 500μF and 0.5-0.7 respectively. 160

4. Maximum Power Point Tracking Techniques 161

4.1 Conventional algorithm (Perturb and Observe algorithm) 162

The perturb and observe(P&O) maximum power point algorithm works on the criterion that on the 163 right of the MPP, if voltage increases, power decreases and perturbation is made on the opposite 164 direction whereas towards the left of MPP, if voltage increases, power also increases then 165 perturbation is made in the same direction. Implementation of a P&O algorithm in the proposed PV 166 system is shown figure 4. 167 168 The main drawback of the P&O algorithm is its lack of ability to track maximum power point due to 169 the oscillations near MPP region under varying environmental conditions. To overcome these 170 disadvantages, FLC based algorithm is implemented which can minimize oscillations near operating 171

5

point, and hence energy wastage in a PV system is also minimized. Further, in the proposed AFLC 172 based algorithm, the output power is further enhanced by asymmetrical distribution of fuzzy 173

membership functions. 174

4.2 Intelligent algorithm (Asymmetrical FLC) 175

Fuzzy logic is a logical system that does not require an accurate mathematical model. FLC uses 176 “If…Then…” command to frame rule base. The fuzzy inference system can be Mamdani or Sugeno, 177 and both can have symmetrical or asymmetrical membership functions [28,29]. The main 178 drawback of conventional fuzzy logic algorithms is that it may not track GMPP. In the proposed 179 work, asymmetrical FLC based control algorithm has been designed, the input/output membership 180 functions of symmetrical FLC is further fine-tuned by the heuristic approach and carefully designed 181 rule base to track MPP under PSCs. 182

183 In proposed AFLC algorithm, the asymmetric distribution of input and output membership 184 functions includes both convergent (+β) and divergent (-β) type asymmetry for the fuzzy variables. 185 The values of [+β, -β] have been tuned to achieve the MPP without oscillations. Figure 5 shows the 186 block diagram of asymmetrical FLC based control algorithm for MPPT. It primarily has: 187 fuzzification, inference method and defuzzification as explained below. 188 189 4.2.1 Fuzzification 190

In proposed asymmetrical FLC based MPPT algorithm, the two inputs, are error and change in 191 error. The power is calculated from the sensed voltage and current. An error is then calculated 192 using equation 6. Change in error is derived from the derivative of error and can be calculated using 193 equation 7. 194

𝐸𝑟(𝑛) =𝑃𝑜/𝑝(𝑛)−𝑃𝑜/𝑝(𝑛−1)

𝐼𝑜/𝑝(𝑛)−𝐼𝑜/𝑝(𝑛−1) (6) 195

∆𝐸𝑟(𝑛) = 𝐸𝑟(𝑛) − 𝐸𝑟(𝑛 − 1) (7) 196

where, Er is the error calculated, Po/p and Io/p are the power and current output of the proposed PV 197 system and ∆Er is the change in error. 198

The universe of discourse (UOD) or membership function is a curve that denotes how each point in 199 the input space is mapped between 0 and 1. Input and output universe of discourse of fuzzy sets 200 consist of seven triangular membership functions respectively. Figure 6 shows the asymmetrical 201 distribution of fuzzy input and output membership function used in the proposed system for 202 tracking maximum power under steady-state as well as dynamic condition. The universe of 203 discourse for input variable is divided into seven fuzzy sets: S1 (Small 1), S2 (Small 2), S3 (Small 3), 204 ZO (Zero), B1 (Big 1), B2 (Big 2) and B3 (Big 3) [24]. In the proposed AFLC, the membership 205 functions are denser at the centre to provide greater sensitivity in the region near the MPP. Input 206 membership functions are normalized, and suitable tuning gains are used to match the inputs to the 207

respective universe of discourse. 208

209 4.2.2 Inference Method 210

6

The inference method implements the rules to the fuzzy input to determine the fuzzy output. Rules 211 are made based on membership function in error and change in error. In the proposed system, the 212 rules have been made using “If…Then…” logic. Example If an error is S1, change in error is S3 then 213 duty ration is ZO. 214

215 216

The idea behind making rule base in the form of a matrix is to bring operating point near maximum 217 power point with less fluctuations by increasing or decreasing the duty ratio as per the direction in 218 which maximum peak is occurring [30,31]. In figure 7, rule base for the proposed system is shown 219 which consists of 49 fuzzy control rules. These rules can also be represented in a 3-D graph known 220 as a surface viewer as shown in figure 8. In the present work, Mamdani’s MAX-MIN method is used 221 for inference of fuzzy controller. The output membership function of each rule is given by the 222 minimum operator whereas collective fuzzy output (x) is provided by maximum operator [32]. 223

224 4.2.3 Defuzzification 225

Defuzzification is used to convert the fuzzy inference output into crisp output which can be given by 226 equation 8: 227 𝑧𝑜 = 𝑑𝑒𝑓𝑢𝑧𝑧𝑖𝑓𝑖𝑒𝑟(𝑥) (8) 228

where, x is the aggregate output and defuzzifier is defuzzification operator. 229

Defuzzification can be done by using the center of area, the max criterion method, etc. In the 230 present work, the center of area defuzzifier operator is used and is represented by equation 9: 231

𝑥 = ∑ 𝜇(𝑥𝑖)𝑥𝑖

𝑛𝑖=1

∑ 𝜇𝑥𝑖𝑛𝑖=1

(9) 232

where, μxi is the activation degree on rule ‘i’, xi is the center of the Max-Min composition of the 233

output membership functions and x is the required output i.e. duty ratio. 234

235

5. Simulation Results and Performance Evaluation 236

The MATLAB/Simulink environment is used to develop the stand-alone PV system and the 237 proposed asymmetrical FLC based MPPT algorithm has been implemented to track maximum 238 available power under varying environmental conditions. The result of AFLC has been compared 239 with P&O and FLC under three conditions viz. (i) STC (ii) PSC (iii) Dynamic condition. 240

Also, the performance of the proposed algorithm has been evaluated and compared w.r.t other 241 algorithms on the basis of performance criteria’s viz. GMPP tracking and shading losses. 242

i) Maximum Power: The maximum power point is the point having maximum voltage and 243 current. It can be given by equation 10. 244

PMP = VMP * IMP (10) 245

246 ii) Shading Losses: In spite of the advancement in technology, the adverse effect of partial 247

shading on the PV system leads to power loss. The power loss due to shading is called 248 shading loss. Shading loss is the difference in power between the maximum power 249

7

obtained from an array under STC (PMP, withoutshading) and the total maximum available 250 power under PSCs (PMP, shading) [33]. It can be represented by equation 11: 251

PMP,shadinglosses = PMP, withoutshading - PMP,shading (11) 252 253

In the present, all the three PV modules of the proposed system are connected in series and the 254 maximum power obtained from this series arrangement is 1.08 kW. The modules are excited with 255 different irradiation level to give various shading patterns work as shown in figure 9. 256 257 Case1: All the three PV modules (M1, M2, M3) are at STC, i.e., solar insolation at 1000 W/m2 and 258 temperature at 25°C. Case 1 is shown in figure 9(a). 259 Case 2: PV module M1 is at 1000 W/m2, M2 at 900 W/m2 and M3 at 500 W/m2. Case 2 is shown in 260 figure 9(b). 261 Case 3: PV module M1 is at 500 W/m2, M2 at 400 W/m2 and M3 at 700 W/m2. Case 3 is shown in 262 figure 9(c). 263 Case 4: PV module M1 is at 450 W/m2, M2 at 250 W/m2 and M3 at 500 W/m2. Case 4 is shown in 264 figure 9(d). 265 Case 5: PV module M1 is at 100 W/m2, M2 at 100 W/m2 and M3 at 200 W/m2. Case 5 is shown in 266 figure 9(e). 267 268 Figure 10 shows the I-V and P-V characteristics of the proposed stand-alone PV system under 269 various shading patterns considered. Table 2 gives the global and local maximum power under 270 various shading pattern. 271 272 5.1 Steady-state response: 273 274 Figure 11 compares the steady-state response of the proposed AFLC based MPPT with P&O and FLC 275 algorithm under various shading patterns. The results are tabulated in table 3. Table 4 gives the 276 corresponding shading losses. 277

278 Case1: Under this case, the highest maximum power is tracked by AFLC algorithm which is 970.5 W, 279 with no fluctuation around GMPP. The shading losses are lowest viz. 109.5 W. FLC tracks 965.4 W 280 while conventional P&O MPPT algorithm tracks only 930W power, i.e. the lowest power and 281 shading losses are highest at 150W. 282

283 Case2: In this case, proposed AFLC based MPPT algorithm tracks maximum power 583.5W and the 284 shading losses 496.5W are least as compared to other MPPT approaches. Also, in this case the AFLC 285 MPPT algorithm tracks power more accurately as compared to other approaches. 286

287 Case3: Under this case, the highest maximum power is tracked by AFLC algorithm which is 419 W, 288 with no fluctuation around GMPP. The shading losses are also lowest viz. 661W. FLC tracks 417.5 W 289 and Conventional P&O MPPT algorithm tracks 402 W power i.e. the lowest power tracked and 290 shading losses are also highest at 678W. 291 292 Case4: In this case, the highest maximum power is tracked by AFLC algorithm which is 223W, with 293 no fluctuation around GMPP. The shading losses are also lowest viz. 857W. FLC tracks 220.5 W and 294 Conventional P&O MPPT algorithm tracks 201W power i.e. the lowest power tracked in this case 295 and shading losses are also more which is 879W. 296

297

8

Case5: In this case, the highest maximum power is tracked by AFLC algorithm which is 50.5 W, with 298 no fluctuation around GMPP. The shading losses are also lowest viz. 1029.5 W. FLC tracks 49.5 W 299 and Conventional P&O MPPT algorithm tracks 46W power i.e. the lowest power tracked with large 300 perturbations. Shading losses are highest at 1034W. 301

302 As seen from table 3 and 4 power tracked is maximum and shading losses are minimum in 303 proposed Asymmetrical FLC. Also, from figure 11 it can be seen that P&O algorithm has large 304 perturbations in the output. Figure 12 and 13 shows the comparative analysis of tracked power and 305 shading loss on bar chart respectively. 306 307 5.2 Transient response: 308 309 In this case, the proposed asymmetrical FLC based MPPT has been evaluated under transient 310 conditions. The change in insolation level for each PV module for the given time duration is shown 311 in table 5. Figure 14 shows the comparative analysis of asymmetrical FLC based MPPT algorithm 312 with other approaches under transient condition. The results are tabulated in table 6 and table 7 313 gives the corresponding shading losses. 314 315 As seen from table 6 and 7 power tracked is maximum and shading losses are minimum in 316 proposed Asymmetrical FLC based algorithm. Also, the settling time of proposed asymmetrical FLC 317 is least under all the conditions while P&O has the highest settling time. 318 319 6. Conclusion 320

In this paper, an intelligent asymmetrical FLC based MPPT algorithm for stand-alone PV system 321 under partial shading conditions has been presented. To establish the superiority of the proposed 322 algorithm, it has been compared with other conventional and intelligent techniques viz. P&O and 323 FLC. The proposed asymmetrical FLC algorithm has been designed, developed and validated to 324 track the global maximum power under various shading scenarios of steady-state as well as under 325 dynamic condition. Simulation results demonstrated that asymmetrical FLC can effectively track 326 global maximum power point under various test conditions. Additionally, the proposed 327 asymmetrical FLC based MPPT algorithm has lower shading losses and least settling time as 328 compared to other algorithms. The implementation of the asymmetrical FLC based MPPT algorithm 329 improves the overall steady state and dynamic behavior of the PV system under consideration. 330 Therefore, there is less wastage of environment friendly solar power. Furthermore, these studies 331 shall be useful for system designers. 332

333 334

References 335

[1] Ellabban O., Abu-Rub H. and Blaabjerg F. “Renewable energy resources: current status, future 336 prospects and their enabling technology”, Renew. Sustain. Energy Rev.,39(C), pp.748-764(2014). 337

[2] Abdourraziq M.A., Maaroufi M. and Ouassaid M. “A new variable step size INC MPPT method for PV 338 systems” Int. Conf. Multimed. Comput. Syst. Proc.,55(7), pp.1563-1568 (2014). 339

[3] Koutroulis E. and Blaabjerg F. “A new technique for tracking the global maximum power point of PV 340 arrays operating under partial-shading conditions” IEEE J. Photovoltaics, 2(2), pp. 184–190(2012). 341

9

[4] Patel H. and Agarwal V. “Maximum power point tracking scheme for PV systems operating under 342 partially shaded conditions” IEEE Trans. Ind. Electron,55(4), pp. 1689–1698(2008). 343

[5] Ji Y.H., Jung D.Y., Kim J.G. et al. “A real maximum power point tracking method for mismatching 344 compensation in PV array under partially shaded conditions” IEEE Trans. Power Electron.,26(4), pp. 345 1001–1009(2011). 346

[6] Al-Majidi S. D., Abbod M. F. and Al-Raweshidy H. S. “A novel maximum power point tracking 347 technique based on fuzzy logic for photovoltaic systems” Int. J. of hydrogen Energy,43(31), pp.14158-348 14171(2018). 349

[7] Liu C., Wu B. and Cheung R. “Advanced algorithm for MPPT control of photovoltaic systems” In: 350 Proceedings of the Canadian solar buildings conference. Montreal; August pp.20–24(2004). 351

[8] Azab M.A. “New maximum power point tracking for photovoltaic systems” International Journal 352 Electrical Electron. Engineering,2(8), pp.1600-1603 (2009). 353

[9] Chaouachi A., Kamel R.M. and Nagasaka K.A. “Novel multi-model neuro-fuzzy-based MPPT for novel 354 multi- model neuro-fuzzy-based MPPT for three-phase grid- connected photovoltaic system 355 photovoltaic system” Sol. Energy, 84(12), pp. 2219-2229 (2010). 356

[10] Reisi A.R., Moradi M.H. and Jamasb S. “Classification and comparison of maximum power point 357 tracking techniques for photovoltaic system” Renew. Sustain. Energy Rev.,19, pp.433–443(2013). 358

[11] Tsai H.F. and Tsai H.L. “Implementation and verification of integrated thermal and electrical models 359 for commercial PV modules” Sol. Energy,86(1), pp.654–665 (2012). 360

[12] Ali O. A. M., Ali A. Y. and Sumait B.S.“Comparison between the Effects of Different Types of 361 Membership Functions on Fuzzy Logic Controller Performance” Int. Journal of Emerging Engg. 362 Research and Tech.,3(3), pp.76–83(2015). 363

[13] Asim N., Sopian K., Ahmadi S. et al. “A review on the role of materials science in solar cells” 364 Renewable Sustainable Energy Rev., 16(8), pp. 5834–5847 (2012). 365

[14] Esram T., et al. Dynamic maximum power point tracking of photovoltaic arrays using ripple 366 correlation control. IEEE Trans. Power Electron., 21(5), pp.1281–1291 (2006). 367

[15] Balasankar R., Arasu G. T., and Christy Mano Raj J. S., “A global MPPT technique invoking 368 partitioned estimation and strategic deployment of P&O to tackle partial shading conditions,” Sol. 369 Energy,143, pp.73–85(2017). 370

[16] Kharb R. K., Shimi S. L.,Chatterji S.et al. “Modeling of solar PV module and maximum power point 371 tracking using ANFIS,” Renew. Sustain. Energy Rev.,33, pp.602–612(2014). 372

[17] Sahoo S.K. “Solar photovoltaic energy progress in India: a review.” Renew. Sustain. Energy Rev.,59, 373 pp.927–939(2016). 374

[18] Ishaque K., Salam Z.and Syafaruddin “A comprehensive MATLAB Simulink PV system simulator with 375 partial shading capability based on two-diode model” Sol. Energy, 85(9), pp.2217–2227(2011). 376

[19] Karami N., Moubayed N.and Outbi R. “General review and classification of different MPPT 377 Techniques” Renew. Sustain. Energy Rev.,68(1), pp.1-18(2017). 378

[20] Li G., Jin Y., Akram M.W., et al. “Application of bio-insopired algorithms in maximum power point 379 tracking for PV system under partial shading conditions” A review. Renewable and Sustainable 380 Energy,81(1), pp.840–873 (2018). 381

[21] Singh N. “A Modified Variant of Grey Wolf Optimizer” Int. Journal of Science & Tech., 382 DOI: 10.24200/SCI.2018.50122.1523 (2018). 383

[22] Vaez S. R. H. and Minaei Z. “Pulse extraction of pulse like ground motions based on particle swarm 384 optimization algorithm” Int. Journal of Science & Tech., DOI:10.24200/SCI.2018.5607.1374 (2018). 385

[23] Ram J.P., Babu T.S. and Rajasekar N. “A comprehensive review on solar PV maximum power point 386 tracking techniques” Renew. Sustain. Energy Rev.,67, pp.826–847 (2017). 387

[24] Kumar P. and Mahajan A. “Soft computing techniques for the control of an active power filter” IEEE 388 Trans. Power Deliv.,24(1), pp.452-461(2009). 389

[25] Sundareswarm K., Sankar P., Nayak P. S. R. et al. Enhanced energy output from a PV system under 390 partial shaded conditions through artificial bee colony. IEEE Trans. Sustain. Energy,6(1), pp.198–391 209(2015). 392

10

[26] Verma P., Mahajan P. and Garg R. “Comparison of Intelligent and Conventional MPPT Algorithms for 393 PhotoVoltaic system under Partially Shaded Conditions” IEEE International Conference. RDCAPE-394 2017.India, pp.505-510(2017). 395

[27] Gow J.A. “Development of a model for photovoltaic arrays suitable for use in simulation studies of 396 solar energy conversion systems” 6th Int. Conf. Power Electron. Variable Speed Drives, Nottingham, 397 UK, pp.69–74(1996). 398

[28] Al-Gizi A., Al-Chlaihawi S., Louzazni M. et al. “Genetically Optimization of an Asymmetrical Fuzzy 399 Logic Based Photovoltaic Maximum Power Point Tracking Controller” Advances in Elec. and 400 Computer Engg.,17(4), pp.69-76(2017). 401

[29] Liu C. L., Chen J. H, Liu Y. H. et al. “An Asymmetrical Fuzzy-Logic-Control-Based MPPT Algorithm for 402 Photovoltaic Systems” Energies,7, pp. 2177-2193(2014). 403

[30] Kuo T.J. and Chen J. F. “Novel maximum-power-point tracking controller for photovoltaic energy 404 conversion system” IEEE Trans. Ind. Electron.,48(3), pp.594–601(2001). 405

[31] Casadei D. “Single-phase single-stage photovoltaic generation system based on a ripple correlation 406 control maximum power point tracking” IEEE Trans. Energy Convers.,21(2), pp.562–568(2006). 407

[32] Gupta N. and Garg R. “Tuning of asymmetrical fuzzy logic control algorithm for SPV system 408 connected to grid” International Journal of Hydrogen Energy,42(26), pp.16375-16385(2017). 409

[33] El-Dein, M.S., Kazerani M. and Salama M.M.A “Optimal photovoltaic array reconfiguration to reduce 410 partial shading losses” IEEE Trans. Sustain. Energy, 4(1), pp.145–153(2013). 411

412 List of Captions 413 414 Figure 1. Block Diagram of a Stand-alone PV System 415 Figure 2. Equivalent circuit of a single diode model of a PV cell416 Figure 3. Current Vs Voltage and Power Vs Voltage curve of proposed SPV system at a) Variable 417 irradiation b) Variable temperature 418 Figure 4. Block diagram of the P&O algorithm 419 Figure 5. Block diagram of asymmetrical FLC based control algorithm for MPPT 420 Figure 6. Membership functions for input variable ‘Error’, ‘Error Change’ and Output variable ‘Duty 421 Ratio’ for Asymmetrical FLC 422 Figure 7. Fuzzy rule base for computing output variable ‘Duty ratio ‘in Matrix form 423 Figure 8. 3-D surface view representation between two inputs (error and change in error) and 424 output (duty ratio) generated by AFLC of a proposed PV system 425 Figure 9. Shading patterns of PV Modules for the proposed system 426 Figure 10. Simulated Current Vs. Voltage and Power Vs. Voltage curve for the various shading 427 patterns of the proposed system 428 Figure 11. Simulated Power Vs. Time plot of the three algorithms under the steady-state condition 429 with different shading patterns 430 Figure 12. Comparative analysis of tracked power on bar chart 431 Figure 13. Comparative analysis of shading loss on bar chart 432 Figure 14. Simulated Power Vs. Time plot of the three algorithms under transient condition 433 434 TABLE 1. Specification of Sun Power PV Module 435 TABLE 2. Power at GMPP and LMPP under various shading pattern 436 TABLE 3. Steady state response of various MPPT techniques under study 437 TABLE 4. Shading loss (W) in various MPPT techniques under study 438 TABLE 5. Shading pattern of PV modules for transient response 439 TABLE 6. Transient response of various MPPT techniques under study 440 TABLE 7. Shading loss (W) in various MPPT techniques under study 441 442

11

443

MPPT

Algorithms

L

Cout

D

IGBTVo

Boost Converter

Duty

Ratio (D)

M1

PV Array

M1

M2

M3

CoutCin

444 Figure 1 445

446 447

Rsh

IshRs

Vo/p(PVcell)Ics

Io/p(PVcell)

Ideal PV Cell

Practical PV Cell 448

Figure 2 449 450

12

(a) (b)451

452 Figure 3 453

454

455

456 Figure 4. 457

13

Vo/p

Unit

Delay

Unit

Delay

Unit

Delay

Fuzzification(Asymmetrical

membership

functions)

Inference

EngineDefuzzification

Fuzzy Set

Fuzzy RulesChange in error

Error

Knowledge Base

Duty

Ratio

Asymmetrical Fuzzy Logic Controller

Io/p

Po/p

Io/p(n-1)

Io/p(n)Io/p(n) - Io/p(n-1)

Po/p(n)- Po/p(n-1)

Po/p(n-1)

458 459

Figure 5 460 461 462

463 Figure 6 464

465 466 467 468 469 470 471 472 473 474 475 476

14

E

ΔE S1 S2 S3 ZO B3 B2 B1

S1 ZO ZO ZO S1 S1 S1 S1

S2 ZO ZO ZO S2 S2 S2 S2

S3 S3 S3 ZO ZO ZO B3 B3

ZO S3 ZO ZO ZO ZO ZO B3

B3 B3 B3 ZO ZO ZO S3 S3

B2 B2 B2 B2 B2 ZO ZO ZO

B1 B1 B1 B1 B1 ZO ZO ZO

Figure 7 477

478 479

Figure 8 480

15

M1=1000W/m2

M2= 1000W/m2

M3= 1000W/m2

M1= 1000W/m2

M2= 900W/m2

M3= 500W/m2

M1=500 W/m2

M2=400 W/m2

M3=700 W/m2

(a) Case 1

M1=450 W/m2

M2=250 W/m2

M3=500 W/m2

M1=100 W/m2

M2=100 W/m2

M3=200 W/m2

(b) Case 2 (c) Case 3

(d) Case 4 (e) Case5 481

482 Figure 9 483

Case 1Case 2

Case 3

Case 4

Case 5

484 Figure 10 485

486

16

487 (a) Case 1 488

489

490 (b) Case 2 491

492 (c) Case 3 493

494 (d) Case 4 495

17

496

497 (e) Case 5 498

499 Figure 11 500

501 Figure 12 502

503 Figure 13 504

930

540

402

201

46

965.4

578.5

417.5

220.5

49.5

970.5

583.5

419

223

50.5

CASE 1 CASE 2 CASE 3 CASE 4 CASE 5

P&O FLC AFLC

150

540 678 879 1034

114.6

501.5

662.5

859.5

1030.5

109.5

496.5

661 857 1029.5

C ASE 1 CASE 2 CASE 3 CASE 4 CASE 5

P&O FLC AFLC

18

505 506

Figure 14 507 508

Table 1. Specification of Sun Power PV Module

SPR-X22-360 Power Nominal (Max), Pnom 360W Rated Voltage, Vm 60.6V Rated Current, Im 5.94A Open-Circuit Voltage, Voc 69.5V Short-Circuit Current, Iscc 6.48A Total No. of Cell in Series, Ns 96

509 Table 2. Power at GMPP(W) and LMPP(W) under various

shading pattern Case1 Case 2 Case 3 Case 4 Case 5

PGMPP (W) 1080 630 425 250 78

PLMPP (W) - 332; 555

227; 347

141; 198 55

510 511

Table 3. Steady state response of various MPPT techniques under study MPPT

techniques

Case 1 Case 2 Case 3 Case 4 Case 5

P&O PMP

(W) 930 540 402 201 46

V (V) 360 276 236.5 167 82.8

19

I (A) 2.583 1.956 1.699 1.203 0.55

FLC

PMP

(W) 965.4 578.5 417.5 220.5 49.5

V (V) 360 279.4 205 161.5 81.06 I (A) 2.681 2.070 2.036 1.362 0.61

AFLC

PMP

(W) 970.5 583.5 419 223 50.5

V (V) 360 280.8 204 172.5 80.25 I (A) 2.695 2.080 2.053 1.380 0.62

512 513

Table 4. Shading loss (W) in various MPPT techniques under study MPPT

techniques Case 1 Case 2 Case 3 Case 4 Case 5

P&O 150 540 678 879 1034 FLC 114.6 501.5 662.5 859.5 1030.5

AFLC 109.5 496.5 661 857 1029.5 514

Table 5. Shading pattern of PV Modules for transient response Shading Pattern

Irradiation Level (kW/m2) Time (Sec)

SP1 [M1:0.9, M2:0.7, M3:0.6] 0-2.5 SP2 [M1:0.5, M2:0.8, M3:0.3] 2.5-5 SP3 [M1:0.6, M2:0.3, M3:0.1] 5-7

515 Table 6. Transient response of various MPPT techniques under study

MPPT techniq

ues

0-2.5 (Sec) 2.5-5 (Sec) 5-7 (Sec) Power

(W) Settling

Time (sec) Power

(W) Settling

Time (sec) Power

(W) Settling

Time (sec) P&O 486 0.26 249 0.6 190 0.2 FLC 517.5 0.19 250.1 0.3 196.5 0.1

AFLC 521.5 0.19 250.6 0.3 198.1 0.1 516

517 Table 7. Shading loss (W) in various MPPT techniques under study

MPPT techniques 0-2.5 (sec) 2.5-5 (sec) 5-7 (sec)

Shading loss (W)

Shading loss (W)

Shading loss (W)

P&O 594 831 890 FLC 562.5 829.9 883.5

AFLC 558.5 829.4 881.9 518

Biographies 519

Pallavi Verma has received B. Tech degree in 2009 from K.I.E.T., Ghaziabad, India in Electrical and 520 Electronics Engineering and M.E. degree in Instrumentation & Control in 2015 from NITTTR, 521 Chandigarh, India. Presently, she is pursuing her Ph.D. in Electrical Engineering Department from 522

20

Delhi Technological University, Delhi. Her research interest is on renewable energy, power 523 electronics and control system. 524

Rachana Garg (IEEE SM’10) received the B.E. and M.E. degree in 1986 and 1989 respectively from 525 National Institute of Technology, Bhopal, India. She has obtained her Ph.D. in Electrical Engineering 526 from Delhi University, India in 2009. Presently, she is working as Professor in Delhi Technological 527 University, Delhi, India. Her area of interest is modeling of transmission lines, power system 528 operation and control, smart grid and renewable energy. 529 530

Priya Mahajan received B.E. from Thapar Institute of Engineering and Technology in 1996 and 531 M.E. from Punjab Engineering College in 1998, Punjab, India. She has obtained her Ph.D. in 532 Electrical Engineering from Delhi University, India in 2015. Presently, she is working as Professor 533 in Delhi Technological University, Delhi, India. Her area of interest is railway electric traction 534 system and power system. 535