Global Maximum Power Point Tracking (MPPT)

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the differential evolution (DE) [10], the ant colony optimization (ACO) [11], and the ... The pheromones that ants lay down when they find food are .... learning, in which the student with the lower grade learns from the one with a higher grade. ... According to the actual MPPT process of PV module arrays, the tracking increment.
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Global Maximum Power Point Tracking (MPPT) of a Photovoltaic Module Array Constructed through Improved Teaching-Learning-Based Optimization Kuei-Hsiang Chao * and Meng-Cheng Wu Department of Electrical Engineering, National Chin-Yi University of Technology, Taichung 41170, Taiwan; [email protected] * Correspondence: [email protected]; Tel.: +886-4-2392-4505 (ext. 7272); Fax: +886-4-2392-2156 Academic Editors: Senthilarasu Sundaram and Tapas Mallick Received: 10 September 2016; Accepted: 15 November 2016; Published: 25 November 2016

Abstract: The present study proposes a maximum power point tracking (MPPT) method in which improved teaching-learning-based optimization (I-TLBO) is applied to perform global MPPT of photovoltaic (PV) module arrays under dissimilar shading situations to ensure the maximum power output of the module arrays. The proposed I-TLBO enables the automatic adjustment of teaching factors according to the self-learning ability of students. Incorporating smart-tracking and self-study strategies can effectively improve the tracking response speed and steady-state tracking performance. To evaluate the feasibility of the proposed I-TLBO, a HIP-2717 PV module array from Sanyo Electric was employed to compose various arrays with different serial and parallel configurations. The arrays were operated under different shading conditions to test the MPPT with double, triple, or quadruple peaks of power-voltage characteristic curves. Boost converters were employed with TMS320F2808 digital signal processors to test the proposed MPPT method. Empirical results confirm that the proposed method exhibits more favorable dynamic and static-state response tracking performance compared with that of conventional TLBO. Keywords: maximum power point tracking; teaching-learning-based optimization; photovoltaic module array; partial module shading

1. Introduction A photovoltaic (PV) power generation system is composed of a PV module array, a power conditioner, and a power transmission and distribution system. Because the output power of a PV module array changes substantially under the effect of insolation and environmental temperature changes [1], power conditioners not only function as inverters, but also require a maximum power point (MPP) tracker to control the PV module array. Consequently, power loss in the PV module array can be reduced while maintaining MPP output under different environmental conditions. Different sets of power–voltage (P–V) characteristic curves can be generated for different insolation and environmental temperature. To ensure the maximum power output, the duty cycles of a power converter are commonly adopted. Concerning conventional maximum power point tracking (MPPT) techniques, they include the most frequently adopted perturb and observe (P&O) [2–4] and incremental conductance (INC) [5,6] methods. Although the P&O method is simple and involves only a few parameters, a drawback of this method is that users must choose between tracking speed and number of oscillations, in which favorable performance of one comes at the expense of the other. By contrast, the INC method improves tracking speed but features unfavorable tracking stability because precision sensors are required to measure the conductance. Moreover, when PV array modules are faulty or subjected to partial shading, the corresponding P–V characteristic curves exhibit multiple

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peaks [7]. Thus, applying these two conventional MPPT methods generates local MPPs rather than global MPPs. Shaded modules in a PV array are known to incur mismatching problems. In this context, the global MPP cannot be successfully tracked using a typical Field MPPT, that is to say, deteriorated power generation efficiency, due to the multiple peaks on a P–V characteristic curve. A distributed maximum power point tracker (DMPPT) was proposed as a way to resolve this mismatching problem and hence to elevate the overall power generation efficiency [8,9]. However, a clear disadvantage of a DMPP tracker is a rise in the cost and more room occupied. For this sake, to develop a low cost, but high performance, global MPP tracker to deal with the multi-peak problems on a P–V characteristic curve for the optimal performance of a PV array is an important research effort. In recent years, numerous scholars have investigated MPPT methods for PV module arrays exhibiting multiple peaks under partial shading. Commonly adopted intelligent algorithms include the differential evolution (DE) [10], the ant colony optimization (ACO) [11], and the artificial bee colony (ABC) algorithms [12]. The DE algorithm, similar to a genetic algorithm [13,14], performs real number coding on selected groups to search for a global optimal solution through the differential calculation of variance and one-to-one competitive survival strategies. However, as demonstrated in [15], only simulation results were presented. In addition, individual mutation strategies were based on a total of five equations proposed by Storn [16], which not only increases tracking-time calculations, but also requires a more accurate comparison between population codes during crossover coding with microcontrollers. The ACO algorithm is a probabilistic path optimization algorithm based on the foraging behaviors of ants. The pheromones that ants lay down when they find food are used as a food-source indicator, with which other ants can determine the optimal food-finding path; this conserves time otherwise spent on random searching. In [17], pheromone update equations were expressed as exponential functions that yielded random values for transitioning between controlling the pheromone density and path length. Although this approach eliminates the possibility of identifying local optimal solutions, calculating the path length by using exponential functions requires considerably longer tracking time. The ABC algorithm transmits information regarding the quality and position of a food source through the “dance” performed by employed bees, which are responsible for finding larger food sources to increase profitability during the colony food-finding optimization process [18]. However, the employed bee phase relies on random values, resulting in an unstable searching capacity. In addition, in the scout phase, the number of bees selected affects the tracking speed and steady-state performance. As mentioned in [18], obtaining the statistical results of ABC and particle swarm optimization (PSO) algorithms requires 5–6 s, indicating that the tracking response speed can be improved. Moreover, scholars have proposed incorporating intelligent algorithms with conventional MPPT algorithms [19–22], such as incorporating PSO or genetic algorithms with P&O. Although the incorporated methods can successfully identify global optimal solutions, the dynamic response speed is too slow. To address these problems, the present study incorporated a novel teaching-learning-based optimization (TLBO) method [23,24] to track the MPPs of a PV module array subjected to partial shading. The proposed method is advantageous because of its independence from population optimization, high adaptability, few design parameters, simple algorithm, and ease of understanding. In the present study, a conventional TLBO algorithm [25] was modified to improve the convergence and reduce the tracking time to obtain a more efficient algorithm than extant MPPT algorithms. The proposed algorithm improves MPPT tracking effectiveness for PV module arrays exhibiting multiple peaks in their P–V characteristic curves. 2. Fault and Shading Characteristics of PV Module Arrays To increase the power output of a PV power generation system, PV modules are generally combined in serial and parallel configurations. However, external environments can cause shading because of dust, stains, and tall buildings, which generates nonlinear changes and multiple peaks in P–V characteristic curves. To examine the P–V and I–V output characteristics of serial and parallel

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3 of 18 were tested. Table 1 lists the electricity parameter specifications of a single module under standard test conditions (i.e., air mass of 1.5, irradiance of 1000 W/m2, and PV module temperature of 25 °C) [26].module arrays subjected to partial shading, the SANYO HIP 2717 module [26] was adopted and PV

various shading ratios were used. In addition, various arrays of serial and parallel configurations were Table 1. Electricity parameter specifications of the SANYO HIP 2717 PV module. tested. Table 1 lists the electricity parameter specifications of a single module under standard test conditions (i.e., air mass of 1.5, irradiance of 1000 W/m2 , and PV Value module temperature of 25 ◦ C) [26]. Parameter Rated maximum power output (Pmp) 27.8 W Table 1. Electricity parameter specifications of the SANYO HIP MPP current (Imp) 1.63 A 2717 PV module. MPP voltage (Vmp) 17.1 V Short-circuit 1.82 A Parameter current (Isc) Value Open-circuit voltage (V oc) 21.6 Rated maximum power output (Pmp ) 27.8VW Module 496 mm1.63 × 524 MPP currentdimensions (Imp ) A mm MPP voltage (Vmp )

17.1 V 1.82 A Open-circuit voltage (Voc ) 21.6 V The present study adopted thedimensions circuit of a PV module simulator adjustable shading ratios Module 496 mm × with 524 mm

Short-circuit current (Isc ) 2.1. PV Module Simulator Circuit

[27], as shown in Figure 1. The circuit structure primarily comprises a Darlington amplifier, a current limiting circuit,Simulator and a voltage regulator for attaining PV module output characteristics under varying 2.1. PV Module Circuit shading ratios, which were created by adjusting variable resistors VRIsc and VRVoc. The variable TheVR present study adopted the circuit of a PV module simulator with adjustable shading ratios [27], resistor Voc shown in Figure 1 controls the open-circuit voltage of the PV module. When the circuit as showna in Figure 1. Thetransistor circuit structure primarily comprises a Darlington amplifier, voltage a current is open, current-limiting Q3 is operated at the cutoff region. The open-circuit is limiting circuit, and a voltage regulator for attaining PV module output characteristics under varying calculated using Equation (1): shading ratios, which were created by adjusting variable resistors VRIsc and VRVoc . The variable Voc  VPV VCE 2  VDBlocking (1) resistor VRVoc shown in Figure 1 controls theopen-circuit voltage of the PV module. When the circuit is open, a current-limiting transistor Q3 is operated at the cutoff region. The open-circuit voltage is Short-circuit currents(1): can be calculated by adjusting VRIsc to operate the current limiting calculated using Equation transistor Q3 at the saturation region the−VVBE3 voltage drop crosses over RD. The short-circuit Vocwhen = VPV (1) CE2 − VDBlocking current is calculated using Equation (2): Short-circuit currents can be calculated by adjusting VRIsc to operate the current limiting transistor RDdrop  VR ISC Q3 at the saturation region whenItheVIBE3 crosses over RD . The short-circuit current is  Vvoltage (2) sc BE 3  RD  RC calculated using Equation (2): R D + VR ISC Isc = I = V × module (2) BE3PV If the VPV power source is not provided, the generates zero power output, R D × Rsimulator C which is equivalent to the fault situation of the PV module. Using a bypass diode DBypass can ensure If the VPV power source is not provided, the PV module simulator generates zero power output, that PV module arrays generate a certain amount of power during fault events. Accordingly, the which is equivalent to the fault situation of the PV module. Using a bypass diode DBypass can ensure that electricity parameters of PV modules can be employed to set the required PV module output PV module arrays generate a certain amount of power during fault events. Accordingly, the electricity characteristics. parameters of PV modules can be employed to set the required PV module output characteristics.  VCE 2

 VR 

Q2

RC

RA

VRI

Q1  VPV 

 VD 

Blocking

C

I

DBlocking

SC

 VR 

Q3 Q4

RB  VBE 4 

D



VBE 3

Load

RD

VRVoc

Figure Figure 1. 1. PV PV module module simulator simulator circuit. circuit.

DBypass

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2.2. PV Module Array Fault and Shading Characteristics Analysis 2.2. PV Module Array Fault and Shading Characteristics Analysis 2.2.1. PV Module Array Characteristics without Faults or Shading 2.2.1. PV Module Array Characteristics without Faults or Shading When a PV module array has M serial and N parallel arrays without shading or faults and the a PV module array M serial parallel arrays without or faults and the MPPWhen voltage, MPP current, andhas MPP powerand areNrespectively denoted as Vshading mp, Imp, and Pmp, the MPP MPP voltage, MPP current, and MPP power are respectively denoted as V , I , and Pmpas, the mp mp voltage, MPP current, and MPP power of the M serial and N parallel arrays are expressed M ×MPP Vmp, voltage, MPP current, and MPP power of the M serial and N parallel arrays are expressed as M × V mp , N × Imp, and M × N × Pmp, respectively. N × Imp , and M × N × Pmp , respectively. 2.2.2. PV Module Array Characteristics with Faults or Shading 2.2.2. PV Module Array Characteristics with Faults or Shading In a PV module array, fault or shading incidences in a module can decrease the power output of In a PV module array, fault or shading incidences in a module can decrease the power output of the array. Similar to an actual module, a PV module simulator enables a fault module to form a loop the array. Similar to an actual module, a PV module simulator enables a fault module to form a loop through a bypass diode. Using a bypass diode not only ensures that the PV module array maintains through a bypass diode. Using a bypass diode not only ensures that the PV module array maintains a certain level of power generation, but that it also has little effect on the MPPT. However, when the a certain level of power generation, but that it also has little effect on the MPPT. However, when the module is under partial shading, the output voltage and current decrease, causing multiple peaks in module is under partial shading, the output voltage and current decrease, causing multiple peaks in the P–V characteristic curves of the PV module array, which prevents conventional MPP trackers the P–V characteristic curves of the PV module array, which prevents conventional MPP trackers from from controlling the module array to operate at the actual MPPs. controlling the module array to operate at the actual MPPs. Given the aforementioned features of PV module arrays, the SANYO HIP 2717 module Given the aforementioned features of PV module arrays, the SANYO HIP 2717 module simulator simulator was used to compose PV module arrays with different serial and parallel configurations was used to compose PV module arrays with different serial and parallel configurations under distinct under distinct shading ratios to perform a MPPT test. As shown in Figures 2 and 3, SANYO HIP 2717 shading ratios to perform a MPPT test. As shown in Figures 2 and 3, SANYO HIP 2717 PV modules, PV modules, built using the Solar Pro software [28], were adopted to compose a four-serial and onebuilt using the Solar Pro software [28], were adopted to compose a four-serial and one-parallel array. parallel array. The P–V characteristic curves of an array with different numbers of muddles under a The P–V characteristic curves of an array with different numbers of muddles under a shading ratio of shading ratio of 30% were simulated. According to Figures 2 and 3, partial shading of the modules in 30% were simulated. According to Figures 2 and 3, partial shading of the modules in the array resulted the array resulted in multiple peaks on the P–V characteristic curves, and the maximum power point in multiple peaks on the P–V characteristic curves, and the maximum power point (MPP) decreased (MPP) decreased with an increase in the number of modules under shading. with an increase in the number of modules under shading.

Figure 2. Simulated P–V characteristic curves of the four-serial and one-parallel array with different Figure 2. Simulated P–V characteristic curves of the four-serial and one-parallel array with different numbers of modules under 30% shading. numbers of modules under 30% shading.

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Figure 3. characteristic curves curves of of the the four-serial four-serial and and one-parallel array with with different Figure 3. Simulated Simulated I–V I–V characteristic one-parallel array different numbers of modules under 30% shading. numbers of modules under 30% shading.

3. Teaching-Learning-Based Teaching-Learning-BasedOptimization Optimization (TLBO) (TLBO) Method Method 3. concept of TLBO is to TLBO was proposed by Rao, Savsani, and Vakharia [29] in in 2011. 2011. The concept simulate the learning process between a teacher and students, the aim of which is to improve the grades the learning process between a teacher and students, the aim of which is to improve the of the entire through teacher instruction and mutual between between students.students. The students grades of theclass entire class through teacher instruction andlearning mutual learning The are comparable to individuals in an evolutionary algorithm and the teacher the optimal students are comparable to individuals in an evolutionary algorithm and therepresents teacher represents the individual according to the fitness values. optimal individual according to the fitness values. 3.1. Conventional Conventional TLBO TLBO Method Method 3.1. The steps steps of The of the the traditional traditional TLBO TLBO algorithm algorithm are are as as follows: follows: Step 1: 1: Set Setthe thevalues valuesfor forthe thenumber numberof ofstudents studentsN Npp, ,subjects subjectsm, m,and anditerations iterationsE. E. Step Step 2: Initialize a class S and define the following parameters: Step 2: Initialize a class S and define the following parameters: (a) Random student: X k  {X1 , X 2 , X 3 ,..., X NP } (a)(b) Random ⊂{XX,1X, X,2X, X,..., . . ,}X NP 3, . X Random student: subject: XXjk  1 2 3 m (b) Random subject: X j ⊂ { X1 , X2 , X3 , . . . , Xm } (c) Target grade of student k in subject j: G j , k (c) Target grade of student k in subject j: Gj,k Step 3: In the teaching phase, learning step ri, teaching factor TF, and students with the highest grades j,k_best given.phase, The mean of astep classri ,isteaching calculated according to Equation substituted Step 3: XIn theare teaching learning factor TF , and students with(3) theand highest grades into Equation (4) toThe determine student mean difference value. Finally, (3) student grades are Xj,k_best are given. mean ofthe a class is calculated according to Equation and substituted updated according Equationthe (5)student to identify the new target grade for each student in the into Equation (4) toto determine mean difference value. Finally, student grades are teaching updatedphase: according to Equation (5) to identify the new target grade for each student in the teaching phase: NP X M M = NPk Xk (3) (3) ∑ k 1 N P NP k =1



Different _ Mean j ,k j,k  r=i (rXi (jX,kj,k_best TFTF × MM ) ) i i 1, Di f f erent_Mean = 2,..., 1, 2, . E ..,E _ best −

(4) (4)

j,k (new) = X j,k (old) + Di f f erent_Mean j,k X j , k (X new)  X j , k ( old )  Different _ Mean j , k

(5) (5)

Step 4: 4: In Inthe thelearning learning phase, phase, we we assume assume that that two two random and X participate in mutual Step random students students X XPP and XQ Q participate in mutual learning, in which the student with the lower grade learns from the one with aa higher higher grade. grade. learning, in which the student with the lower grade learns from the one with Adjustmentswere weremade madeusing usingEquation Equation(6): (6): Adjustments

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(

X0

j,k (new)

) ri ( X j,P(=k) − X j,Q(6=k) , i f X j,P > X j,Q = X j,k(new) + ri ( X j,Q(=k) − X j,P(6=k) , i f X j,Q > X j,P  XP , XQ ⊂ X1 , X2 , X3 , . . . , X NP

(6)

Step 5: Repeat steps 3 and 4 until the iteration is completed. Parameters used in conventional TLBO are explained as follows: Number of students (Np ): Total number of participating students. Number of iterations (E): Number of teaching and learning phases that the students experience. Subject grade (Xj,k ): Grade of student k in subject j. Five subjects were used in the present study. Class mean (M): Mean grade of the class. Teaching step (ri ): Parameter for diversifying the student mean difference with a random value between 0 and 1. Teaching factor (TF ): Teachers’ ability to teach the students. The parameter randomly generates a value of 1 or 2. In conventional TLBO, the teaching factors (TF ) used in the teaching phase generally comprise two fixed teaching capabilities (1 or 2). However, in real teaching situations, students’ levels differ and their learning capacity varies. Using fixed teaching factors may reduce learning effectiveness. In addition, learning from others (chosen at random) without conforming to students’ individual learning levels might not optimize their learning effectiveness. Thus, this study proposes an improved TLBO (I-TLBO) to solve the problems with conventional TLBO. 3.2. The Proposed I-TLBO Method In the proposed I-TLBO, Steps 3 and 4 in conventional TLBO are modified through the following three improvements: Modification 1: The teaching factors TF were modified to be automatically adjustable according to the students’ learning capacity. The adjustment method is expressed in Equation (7): TF =

X j,k X j,k_best

(7)

Modification 2: In the learning phase, a student selects another student who could benefit their learning the most in order to boost their learning effectiveness. Modification 3: A self-study process was incorporated into the learning phase to enable each student to adjust their self-learning according to their previous experience, as expressed in Equation (8): X 00 j,k(new) = X 0 j,k(new) + ri ( X 0 j,k(new) − X 0 j,k−1(new) )

i = 1, 2, . . . , E

(8)

In Equation (4), if Xj,k_best and M remain unchanged, then Different_Meanj,k increases as TF decreases. According to the actual MPPT process of PV module arrays, the tracking increment is directly proportional to the distance between the individual student grades and the MPP. Therefore, if the student grades in Improvement 1 are X1 (i.e., power value P1 ) and X0 1 (i.e., power value P0 1 ), then the teaching factors TF of the student with the highest grades among all the students Xj,k_best (i.e., MPP value tracked so far Pk_best ) are modified using Equations (9) and (10): TF1 =

TF2 =

P1 Pk_best P0 1 Pk_best

(9)

(10)

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TF 2 

P '1 Pk _ best

7(10) of 18

As depicted in in Figure Figure 4, 4, the the TTF1 F1 value Different_Mean value value increases increases when when As depicted value decreases decreases as as the the Different_Mean student distant from from the the MPP MPP (e.g., (e.g., X X11 position), tracking student grade grade is is distant position), thereby thereby increasing increasing the the number number of of tracking steps needed to approach the maximum value rapidly. By contrast, when the student grade is close steps needed to approach the maximum value rapidly. By contrast, when the student grade is close to 0 to the MPP (e.g., X′ 1 position), the T F2 value increases as the Different_Mean value and number of the MPP (e.g., X 1 position), the TF2 value increases as the Different_Mean value and number of tracking tracking steps decrease to approach the maximum valueThus, slowly. the students can adjust their steps decrease to approach the maximum value slowly. theThus, students can adjust their tracking tracking steps according to their learning capacity. In improvements 2 and 3, students can steps according to their learning capacity. In improvements 2 and 3, students can spontaneously learn 0 spontaneously learn from a student who is helpful to them. The term X′ j,k-1(new) represents the student’s from a student who is helpful to them. The term X j,k-1(new) represents the student’s previous learning previous learning as a basis for theself-study. other student’s self-study. summary, abilities, which is abilities, used as awhich basis is forused the other student’s In summary, the In self-learning the self-learning method not only accelerates the learning progress, but also escapes local solutions method not only accelerates the learning progress, but also escapes local solutions and reaches global and reaches global convergence. A flowchart of theMPPT proposed I-TLBO MPPT 5. is shown in Figure 5. convergence. A flowchart of the proposed I-TLBO is shown in Figure

Figure 4. Adjustment of teaching factors of the proposed I-TLBO.

3.3. MPP Tracker Figure 6 depicts onon the proposed Idepicts the the MPP MPPtracker trackerarchitecture architectureofofthe thePV PVmodule modulearray arraybased based the proposed TLBO. architecture mainly comprises two two subsystems: a DC/DC boost converter and I-TLBOI-TLBO.The The architecture mainly comprises subsystems: a DC/DC boost converter and based MPPT controller. When employed a DC/DCinboost converter, a synchronous is I-TLBO-based MPPT controller. When in employed a DC/DC boost converter, arectification synchronous known to outperform diode rectification in terms of the conversion as well asefficiency the thermal rectification is knownato outperform a diode rectification in terms efficiency of the conversion as performance [30], while a diode[30], rectification is adopted instead in this work due the reliability well as the thermal performance while a diode rectification is adopted instead in to this work due to concern. As stated previously, I-TLBO-based MPPT controller controls the duty cycle the boost the reliability concern. As statedthe previously, the I-TLBO-based MPPT controller controls theofduty cycle converter, theenabling PV module array to generate the maximum power output of the boostenabling converter, the PV module array to generate the maximum power under outputpartial under shading. partial shading. Table DC/DC boost Table 2 lists the DC/DC boostconverter converter parameter parameter settings settings [31] [31] and and Table Table 3 lists lists the the conventional conventional component choices are are made according to [31]. extra effort, TLBO parameter parameter settings. settings.The The component choices made according to Without [31]. Without extra components available in ourinlaboratories but but withwith over specified ratings, effort, components available our laboratories over specified ratings,are aredirectly directlytaken taken to implement the DC/DC DC/DC boost boostconverter. converter. In In I-TLBO, I-TLBO, the the TTFFin inTable Table 33 is replaced with the parameter setting in in Table Table4 4whereas whereas other parameters remain unchanged. Subsequently, themodule PV module allall other parameters remain unchanged. Subsequently, the PV array array was tested under five distinct operating situations, as shown in Table 5. was tested under five distinct operating situations, as shown in Table 5.

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Start

Initialize relevant data

Student k=1

,

Output all students corresponding duty cycle of the converter Extract the PV module array output voltage and current and calculate the power output Setect the student with the optimal grade as Xk_best

Calculate Different_Meanj,k=ri(Xj,k_best-TF×M) Update X j , k ( new)  X j , k ( old )  Different _ Mean j , k

No

Have all students Completed their learning ?

k  k 1

Yes

Choose two students X P and X Q with maximum grade difference participate in mutual learning

Yes

X ' j ,k ( new)



No

X P > XQ ?

X j ,k ( new)  ri ( X j , P (  k )  X j ,Q (  k ) ) X ' j ,k ( new)



X j ,k ( new)  ri ( X j ,Q (  k )  X j , P (  k ) )

Update the grades through the self-study formula X '' j , k ( new)  X ' j , k ( new)  ri ( X ' j , k ( new)  X ' j , k 1( new) ) Is the number

No

of iterations achieved? Yes

Calculate corresponding converter duty cycle and output the value End

Figure 5. MPPT flow chart of the proposed I-TLBO. Figure 5. MPPT flow chart of the proposed I-TLBO.

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PV module array

Load

Boost converter Lm

D

S

Cin

RLoad

Cout

Gate drive circuit

PWM signal Vpv Ipv

TLBO-based MPPT controller

TMS320F2808 Digital signal processor

Figure 6. Architecture of the I-TLBO-based MPPT controller.

Figure 6. Architecture of the I-TLBO-based MPPT controller. Table 2. DC/DC boost converter component parameters. Table 2. DC/DC boost converter component parameters. Component Model Number and Specifications

Component

Inductance (Lm ) Inductance m) Input capacitance (C(L in ) Input capacitance Output capacitance (Cout )(Cin) Switching (fs ) (Cout) Outputfrequency capacitance Power MOSFET (S) Switching frequency (fs) Diode (D)

Power MOSFET (S) Diode (D)

Model Number and Specifications 3.3 mH 3.3 µF/160 mH V 220 220390 μF/160 VV µF/450 20 kHzV 390 μF/450 IRF460 (500 V/20A) 20 kHz DSEP30-12A (1200 V/30A) IRF460 (500 V/20A) DSEP30-12A (1200 V/30A)

Table 3. Conventional TLBO parameter settings.

Table 3. Conventional TLBO parameter settings. Parameter Setting NumberParameter of students (NP ) Number of Number ofiterations students(E) (NP) Teaching step (r ) i Number of iterations (E) Teaching factor (TF )

Teaching step (ri) Teaching factor (TF)

Setting 4 4 40 Random value 40 between 0 and 1 1 or 2 Random value between 0 and 1 1 or 2

Table 4. I-TLBO Parameter Settings.

Table 4. I-TLBO Parameter Settings. Parameter Setting

Parameter

Teaching factor (TF )

Teaching factor (TF)

Setting X j,k

TF =

TF 

X j,k_best j ,k

X

X j ,k _ best Table 5. Cases of the five selected serial and parallel configurations and the shading situations. Number of Peaks in the P–V 5. Cases the fiveConfigurations selected serialand andShading parallel Situations configurations and the shading situations. Case TableSerial andofParallel Characteristic Curves 1 Case 2

1 32 43 4 5

5

One-serial one-parallel with 0% shading Serial andand Parallel Configurations and Shading Situations Two-serial and one-parallel with 0% and 40% shading

One-serial and one-parallel with 0% shading Three-serial andone-parallel one-parallelwith with0% 0%,and 40%,40% andshading 70% shading Two-serial and Four-serial and 30% shading, 50%, and Three-serial andone-parallel one-parallelwith with0%, 0%, 40%, and 70% shading 70% shading Four-serial and one-parallel with 0%, 30% shading, 50%, and Two-serial and two-parallel with (30% and 0% shading)//(0% 70% shading and 50% shading) Two-serial and two-parallel with (30% and 0% shading)//(0% Note: “//” parallel connection. and 50% shading) Note: “//” parallel connection.

Number ofSingle Peaks in the P–V Characteristic Curves Double Single Triple Double Triple Quadruple Quadruple Double

Double

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4. Measurement 4. MeasurementResults Results The PV PV module module simulator simulator circuit circuit in in Figure Figure 11 was was employed employed to to compose compose the the module module array array The configurations under five operating situations as listed in Table 5. The P–V and I–V characteristic configurations under five operating situations as listed in Table 5. The P–V and I–V characteristic curves of of PV PV module module arrays arrays under under different different shading shading ratios ratios were were measured measured using using an an MP MP 170 170 I–V I–V curves checker by EKO Instruments CO. Ltd (Tokyo, Japan). The aim is to tell whether the global MPPs in checker by EKO Instruments CO. Ltd (Tokyo, Japan). The aim is to tell whether the global MPPs in the the 5 testing cases listed in Table 5 can be tracked as expected using I-TBLO MPPT. Subsequently, 5 testing cases listed in Table 5 can be tracked as expected using I-TBLO MPPT. Subsequently, a digitala digitalprocessor signal processor TMS320F2808 was to perform MPPT using conventional TLBO signal TMS320F2808 [32] was[32] used to used perform MPPT by usingby conventional TLBO and the and the proposed I-TLBO. The tracking performance of the two methods was also compared. proposed I-TLBO. The tracking performance of the two methods was also compared. 4.1. PV Module Array Characteristics under Different Operating Situations Figures 7–11 7–11 depict depict the the I–V I–V and P–V characteristic curves of the PV module arrays under the five Figures operating situations situations listed listed in Table Table 5. 5. Figure 7 shows the output characteristics of a single PV operating PV module. module. The output characteristic curve reveals that the parameters related to the output characteristics The output characteristic the parameters to the output characteristics of modules not affected by shading or faults are identical to the electricity parameter specifications listed not affected by shading or faults are identical to the electricity parameter specifications in Table 1. The1.module in Figure 7 was 7used a basis testing the serial (i.e., Cases listed in Table The module in Figure wasas used as afor basis for testing the configurations serial configurations (i.e., 1–4) as well as the serial and parallel configurations (Case 5), as listed in Table 5. Different shading Cases 1–4) as well as the serial and parallel configurations (Case 5), as listed in Table 5. Different ratio conditions conditions were were set set to to produce produce multiple multiple peaks peaks in in the the characteristic characteristic curves curves to to exemplify exemplify the the ratio exceptional performance performance of Figures 8–10 8–10 reveal reveal that that double, double, triple, exceptional of the the proposed proposed I-TLBO I-TLBO on on MPPT. MPPT. Figures triple, and quadruple quadruple peaks peaks occur occur in in Cases Cases 22 to to 4. 4. Thus, Thus, we we inferred inferred that that N N peaks peaks would would appear appear in in P–V P–V and characteristic curves curves when when N N modules modules in in aa serial serial array array were were under under different different shading shading ratios. ratios. Figure Figure 11 11 characteristic shows the I–V and P–V characteristic curves measured on the two-serial and two-parallel shows the I–V and P–V characteristic curves measured on the two-serial and two-parallel configuration configuration of Casetwo 5. Although modules each serial were module array module of Case array 5. Although modulestwo in each serialinmodule weremodule subjected to subjected different to different shading ratios,connection the parallelbetween connection between the two-serial modules generated double shading ratios, the parallel the two-serial modules generated double peaks only in peaks only in the P–V characteristic curve. the P–V characteristic curve.

30

2

Pmax=27.8W

1.8 25

1.6 1.4

I-V curve

20

1.2 PPV 15 (W)

1

0.8

P-V curve

10

IPV (A)

0.6 0.4

5

0.2 0

0 0

5

10

15

20

25

VPV(V)

Figure 7. I–V curves of of one-serial andand one-parallel module array withwith 0% Figure I–Vand andP–V P–Vcharacteristic characteristic curves one-serial one-parallel module array shading. 0% shading.

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Figure 8. 8. I–V and two-serialand andone-parallel one-parallelmodule module array with Figure I–V andP–V P–Vcharacteristic characteristic curves curves of the two-serial array with 0%0% and 40% shading. and 40% shading.

Figure 9. 9. I–V the three-serial three-serialand andone-parallel one-parallelmodule module array with Figure I–Vand andP–V P–Vcharacteristic characteristic curves curves of the array with 0%,0%, 30%, and 70% shading. 30%, and 70% shading.

Figure 10.10. I–V the four-serial four-serialand andone-parallel one-parallelmodule module array with Figure I–Vand andP–V P–Vcharacteristic characteristic curves of the array with 0%,0%, 30%, 50%, and 70% shading. 30%, 50%, and 70% shading.

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Figure 11. I–V P–V characteristiccurves curves of of the two-parallel module arrayarray with with Figure 11. I–V andand P–V characteristic the two-serial two-serialand and two-parallel module [(0% and 30% shading)//(0% and 50% shading)]. [(0% and 30% shading)//(0% and 50% shading)]. Figure Measurement 11. I–V and P–V characteristic curves of the two-serial and two-parallel module array with 4.2. MPPT of PV Module Arrays

4.2. MPPT Measurement of PV Module Arrays [(0% and 30% shading)//(0% and 50% shading)].

The measurement architecture is shown in Figure 6. First, the output voltage VPV and current IPV

The measurement architecture is shown in Figure 6. First, the output voltage VPVand andentered current IPV of the PV module arrays extracted through sensors and signal conversion circuits 4.2. MPPT Measurement ofwere PV Module Arrays of theinto PVthe module arrays were throughSubsequently, sensors andTLBO signalwas conversion entered TMS320F2808 digitalextracted signal processor. applied tocircuits performand MPPT. The measurement architecture is shown inwas Figure First, the output voltage VPV and current IPV The TMS320F2808 resulting optimal duty cycle trigger signal sent6.to the boost converter to control the on time into the digital signal processor. Subsequently, TLBO was applied to perform MPPT. of the PV module arrays were extracted through sensors and signal conversion circuits and entered of power optimal transistors, thereby the maximum power outputconverter of the PV to module array. The resulting duty cyclecontrolling trigger signal was sent to the boost control the on time of into the TMS320F2808 digital signal processor. Subsequently, TLBO was applied to perform MPPT. Figures 12–16 show the waveforms of output voltage PV and current IPV measured on the PV power transistors, thereby controlling the maximum powerVoutput of the PV module array. The resulting optimal duty cycle trigger signal was sent to the boost converter control the through on time module arrays. The power curves are demonstrated as the product of voltagetoand current Figures 12–16 show the waveforms of output voltage V and current Imodule on the PV PV PV measured of power transistors, thereby controlling the maximum power output of the PV array. the internal computation functions of the oscilloscope. In the 40th iteration, the quality of the module arrays. power curves are demonstrated as the product of voltage and current through FiguresThe 12–16 theproposed waveforms of output voltage VPV and current IPV measured the PV the conventional TLBOshow and the I-TLBO tracking response speed were observed and on compared internal computation functions of the oscilloscope. In the 40th iteration, the quality of the conventional module arrays. The power curves are demonstrated as the product of voltage and current through when the power curve approached a stable value. theand internal computation functions of the oscilloscope. Inwere the 40th iteration, quality ofwhen the the TLBO the proposed I-TLBO tracking response speed observed andthe compared conventional TLBO and the proposed I-TLBO tracking response speed were observed and compared power curve approached a and stable value. 4.2.1. Case 1 (One-Serial One-Parallel: 0% Shading) when the power curve approached a stable value. Figure 12a,b depict the MPPT waveforms of Case 1 (0% shading) measured by using the 4.2.1. Case 1 (One-Serial and One-Parallel: 0% Shading) conventional TLBO and the I-TLBO, respectively. The results revealed that under standard 4.2.1. Case 1 (One-Serial andproposed One-Parallel: 0% Shading) test conditions, the output of the PVof module were identical to the electricity Figure 12a,b depict thecharacteristics MPPT waveforms Case simulator 1 (0% shading) measured by using the Figurespecifications 12a,b depict in theTable MPPT waveforms of Case 1 (0% shading) measured by t0using parameter 1. In addition, the tracking time between time points and standard t1the in conventional TLBO and the proposed I-TLBO, respectively. The results revealed that under conventional TLBO and the proposed I-TLBO, respectively. The results revealed that under standard Figure 12 showed that the proposed I-TLBO (2.5 s) converged faster than did conventional TLBO (3.5 s). test conditions, the output characteristics of the PV module simulator were identical to the electricity test conditions, the output characteristics of the PV module simulator were identical to the electricity parameter specifications in in Table the tracking trackingtime timebetween between time points t0 tand t in parameter specifications Table1.1.InInaddition, addition, the time points t0 and 1 in 1 Figure 12 showed that the proposed I-TLBO (2.5 s) converged faster than did conventional TLBO (3.5 s). Figure 12 showed that the proposed I-TLBO (2.5 s) converged faster than did conventional TLBO (3.5 s).

(a)

(a) Figure 12. Cont.

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(b)

(b)

Figure 12. Measurement results of the one-serial and one-parallel module array with 0% shading by

Figure12. 12. Measurementresults resultsof ofthe theone-serial one-serialand andone-parallel one-parallelmodule modulearray arraywith with0% 0%shading shadingby by Figure usingMeasurement (a) conventional TLBO (P mp = 27.4 W) and (b) the proposed I-TLBO (Pmp = 27.8 W). using (a) conventional TLBO (P = 27.4 W) and (b) the proposed I-TLBO (P = 27.8 W). mp mp using (a) conventional TLBO (Pmp = 27.4 W) and (b) the proposed I-TLBO (Pmp = 27.8 W). 4.2.2. Case 2 (Two-Serial and One-Parallel: 0% and 40% Shading)

4.2.2.Case Case22(Two-Serial (Two-Serial and and One-Parallel: One-Parallel: 0% 0% and and 40% 40% Shading) Shading) 4.2.2. Figure 13a,b depict the MPPT waveforms of Case 2 measured by using conventional TLBO and the proposed I-TLBO,the respectively. The two-serial and22one-parallel was composed on and Figure 13a,bdepict depict the MPPTwaveforms waveforms ofCase Case measuredconfiguration byusing usingconventional conventional TLBO and Figure 13a,b MPPT of measured by TLBO the basis of the single module of Case 1. One module in Case 2 was under 40% shading. The empirical the proposed I-TLBO, respectively. The two-serial and one-parallel configuration was composed on the proposed I-TLBO, respectively. The two-serial and one-parallel configuration was composed on results revealed that under partial shading, the PV module array generated a double-peaked P–V thebasis basisof ofthe thesingle singlemodule moduleof ofCase Case1. 1.One Onemodule modulein inCase Case22was wasunder under40% 40%shading. shading.The Theempirical empirical the characteristic curve (Figure 8). Although both the conventional and proposed methods tracked the results revealed revealed that that under under partial partial shading, shading, the the PV PV module module array array generated generated aa double-peaked double-peaked P–V P–V results actual MPP, the proposed I-TLBO (2.4 s) was faster than conventional TLBO (2.7 s) in MPPT response characteristic curve (Figure 8). Although both the conventional and proposed methods tracked characteristic speed. curve (Figure 8). Although both the conventional and proposed methods tracked the the actual the proposed I-TLBO wasthan faster than conventional TLBO (2.7 s) response in MPPT actual MPP,MPP, the proposed I-TLBO (2.4 s) (2.4 was s) faster conventional TLBO (2.7 s) in MPPT response speed. speed.

(a)

(a) Figure 13. Cont.

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(b) (b) one-parallel module Figure 13. Figure 13. Measurement Measurement results results of of the the two-serial two-serial and and one-parallel module array array (0% (0% and and 40% 40% shading) shading) by using (a) conventional TLBO (P mp = 35.1 W) and (b) the proposed I-TLBO (Pmp = 35.8 W). by using (a)13. conventional TLBO = two-serial 35.1 W) and the proposed I-TLBO (Pmp = 40% 35.8shading) W). Figure Measurement results(Pof and(b) one-parallel module array (0% and mpthe by using (a) conventional TLBO (Pmp = 35.1 W) and (b) the proposed I-TLBO (Pmp = 35.8 W).

4.2.3. Case 3 (Three-Serial and One-Parallel: 0%, 30%, and 70% Shading) 4.2.3. Case 3 (Three-Serial and One-Parallel: 0%, 30%, and 70% Shading) 4.2.3. Case 3 (Three-Serial and One-Parallel: 0%, 30%, and 70% Shading) Figure 14a,b depict the MPPT waveforms Case 3 measured by using conventional TLBO and the Figure 14a,b depict the MPPT waveforms Case 3 measured by using conventional TLBO and 14a,b depict the MPPT 3 measured using conventional anddifferent the proposedFigure I-TLBO, respectively. Thewaveforms empirical Case results revealedbythat three modulesTLBO under the proposed I-TLBO, respectively. Theempirical empiricalresults results revealed that three modules under different proposed I-TLBO, respectively. The revealed that three modules under different shading ratios generated triple peaks in the P–V characteristic curve and a long tracking time under shading ratios generated triple peaks curve and a long tracking under shading ratios generated triple peaksininthe theP–V P–V characteristic characteristic curve and a long tracking timetime under conventional TLBO (3.4 s). By contrast, the proposed I-TLBO (2.7 s) tracked the real MPPT in less time. conventional TLBO (3.4 s). By contrast, the proposed I-TLBO (2.7 s) tracked the real MPPT in less conventional TLBO (3.4 s). By contrast, the proposed I-TLBO (2.7 s) tracked the real MPPT in less time. time.

(a)

(a)

(b) Figure 14. Measurement results of the three-serial and one-parallel module array (0%, 30%, and 70%

Figure 14. Measurement results of the three-serial and one-parallel module array (0%, 30%, and 70% shading) by using (a) conventional TLBO (Pmp = 37.7 (b) W) and (b) the proposed I-TLBO (Pmp = 38.5 W). shading) by using (a) conventional TLBO (Pmp = 37.7 W) and (b) the proposed I-TLBO (Pmp = 38.5 W). Figure 14. Measurement results of the three-serial and one-parallel module array (0%, 30%, and 70% shading) by using (a) conventional TLBO (Pmp = 37.7 W) and (b) the proposed I-TLBO (Pmp = 38.5 W).

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4.2.4. Case Case 44 (Four-Serial (Four-Serial and One-Parallel: 0%, 0%, 30%, 30%, 50%, and 70% Shading) Figure 15a,b show the MPPT waveforms waveforms of Case 4 measured by using conventional conventional TLBO TLBO and the proposed proposed I-TLBO, I-TLBO, respectively. respectively. The empirical results revealed that the proposed proposed I-TLBO I-TLBO required required only 2.2 s, whereas conventional TLBO required 3.4 s of tracking time (t 0 to t 1 ) to track the MPP. This only 2.2 s, whereas conventional TLBO required 3.4 s of tracking time (t0 to t1 ) to track the MPP. validates that the I-TLBO outperformed conventional TLBO in tracking. This validates thatproposed the proposed I-TLBO outperformed conventional TLBO in tracking.

(a)

(b) Figure Figure 15. 15. Results Results of of the the four-serial four-serial and and one-parallel one-parallel module module array array (0%, (0%, 30%, 30%, 50%, 50%, and and 70% 70% shading) shading) measured by using (a) conventional TLBO (P mp = 43.0 W) and (b) the proposed I-TLBO (Pmp = 43.4 W). measured by using (a) conventional TLBO (P = 43.0 W) and (b) the proposed I-TLBO (P = 43.4 W). mp

mp

4.2.5. Case 5 (Two-Serial and Two-Parallel: (0% and 30% Shading)//(0% and 50% Shading)) 4.2.5. Case 5 (Two-Serial and Two-Parallel: (0% and 30% Shading)//(0% and 50% Shading)) Figure 16a,b show the MPPT waveforms of Case 5 measured by using conventional TLBO and Figure 16a,b show the MPPT waveforms of Case 5 measured by using conventional TLBO and the proposed I-TLBO, respectively. The empirical results revealed that adopting the random teaching the proposed I-TLBO, respectively. The empirical results revealed that adopting the random teaching factor TF in conventional TLBO slowed the MPPT. By contrast, the proposed I-TLBO identified the factor TF in conventional TLBO slowed the MPPT. By contrast, the proposed I-TLBO identified the real real MPP within a short time (3.5 s). MPP within a short time (3.5 s).

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(a)

(b) Figure 16. Results of the two-serial and two-parallel module array [(0% and 30% shading)//(0% and Figure 16. Results of the two-serial and two-parallel module array [(0% and 30% shading)//(0% and 50% shading)] measured by using (a) conventional TLBO (Pmp = 66.5 W) and (b) the proposed I-TLBO 50% shading)] measured by using (a) conventional TLBO (Pmp = 66.5 W) and (b) the proposed I-TLBO (Pmp = 66.7 W). (Pmp = 66.7 W).

4.2.6. Comparison of the Case Measurements 4.2.6. Comparison of the Case Measurements Table 6 gives the performance comparison in terms of the average tracking time and the average Table the performance comparison in terms of the TLBO, averageACO tracking timePSO and [21], the average MPP for 640gives iterations among the proposed I-TBLO, a typical [17] and both MPP for 40toiterations among the proposed I-TBLO, a typical TLBO, ACO [17]toand PSO [21],the both referred in the Introduction section. This proposal is obviously found outperform referred to in the Introduction section. This proposal is obviously found to outperform the counterparts counterparts in terms of dynamic tracking response and static performance for the five cases in investigated terms of dynamic tracking response and static performance for the five cases investigated in the in the present study underwent MPPT. present study underwent MPPT. Table 6. Comparison between the measurement results of the five cases obtained using ACO, PSO, Table 6. Comparison between the measurement results of the five cases obtained using ACO, PSO, conventional TLBO and the proposed I-TLBO. conventional TLBO and the proposed I-TLBO. Case

Case 1 2 3

1 24 3 5

ACO [17] PSO [21] Conventional TLBO Proposed I-TLBO Average Average Average Average Average Average Average Conventional TLBO Tracking ProposedAverage I-TLBO TrackingACO [17] TrackingPSO [21] Tracking MPP MPP MPP MPP Time Time Time P–V Curve Time Average Average Average Average Average Average Average Average Peaks Single 4.3 s 27.5 W 3.4 s 27.3 W 3.3 s 27.0 W 2.5 s 27.8 W Tracking Tracking Tracking Tracking MPP MPP MPP MPP Double 4.8Time s 35.3 W 3.0Time s 35.0 W 2.8Time s 35.1 W 2.4Time s 35.8 W Triple 5.1 s 37.5 W 3.8 s 37.0 W 3.4 s 37.2 W 2.7 s 38.5 W Single 4.3 s 27.5 W 3.4 s 27.3 W 3.3 s 27.0 W 2.5 s 27.8 W Tracking Double 3.0 s 35.1 Quadrupe 5.64.8 s s 43.235.3 W W 35.735.0 W W 3.62.8 s s 43.0 WW 2.22.4 s s 43.435.8 W W failed Triple 5.1 s 37.5 W 3.8 s 37.0 W 3.4 s 37.2 W 2.7 s 38.5 W Double 5.8 s 66.3 W 5.2 s 64.7 W 4.8 s 66.1 W 3.7 s 66.7 W

P–V Curve Peaks

4

Quadrupe

5.6 s

43.2 W

5

Double

5.8 s

66.3 W

Tracking failed 5.2 s

35.7 W

3.6 s

43.0 W

2.2 s

43.4 W

64.7 W

4.8 s

66.1 W

3.7 s

66.7 W

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5. Conclusions In this study, an I-TLBO was proposed to perform MPPT of PV module arrays. To enhance the TLBO tracking efficiency and performance, an intellectual teaching factor adjustment method was adopted to facilitate automatic adjustments of TLBO teaching factors. In addition, in the learning phase, the students automatically tracked the targets benefiting their learning. Eventually, each student expedited their tracking speed through self-study according to their individual experience. The empirical results verified that the proposed I-TLBO can more rapidly identify the real MPP compared with conventional TLBO, ACO and PSO when certain modules in a PV module array are under partial shading. The results of the measurements of the designed five cases of shading confirmed that the proposed I-TLBO tracked the global MPP within a shorter period than conventional TLBO, ACO and PSO can. These results confirm the feasibility of applying the proposed I-TLBO in PV module array MPPT, particularly in situations where multiple peaks occur on the P–V characteristic curves because of partial shading. This proposed high performance tracking algorithm can be also directly applied to track the MPP for each single PV module using a DC/DC converter, and to track the MPP on a one-peak P–V curve using a central inverter. Acknowledgments: The authors gratefully acknowledge the support of the Ministry of Science and Technology, Taiwan, Republic of China, under the Grant Number MOST 105-ET-E-167-001-ET. Author Contributions: The improved teaching-learning-based optimization (I-TLBO) algorithm was proposed by Kuei-Hsiang Chao, who was responsible for writing the paper. Meng-Cheng Wu carried out the simulations and experiments concerning the typical and improved I-TLBO algorithm for photovoltaic power generation systems, meanwhile, comparing the dynamic tracking and steady-state performance of these two algorithms. Conflicts of Interest: The authors declare no conflict of interest.

References 1.

2. 3. 4. 5. 6. 7. 8.

9. 10.

11. 12.

Wang, X.; Liang, H. Output characteristics of PV array under different insolation and temperature. In Proceedings of the IEEE 2012 Conference on Asia Pacific Power and Energy Engineering (APPEE), Shanghai, China, 27–29 March 2012; pp. 1–4. Femia, N.; Granozio, D.; Petrone, G.; Spagnuolo, G.; Vitelli, M. Predictive and adaptive MPPT perturb and observe method. IEEE Trans. Aerosp. Electron. Syst. 2007, 43, 934–950. [CrossRef] Luigi, P.; Renato, R.; Ivan, S.; Pietro, T. Optimized adaptive perturb and observe maximum power point tracking control for photovoltaic generation. Energies 2015, 8, 3418–3436. [CrossRef] D’Souza, N.S.; Lopes, L.A.C.; Liu, X. Comparative study of variable size perturbation and observation maximum power point trackers for PV systems. Electr. Power Syst. Res. 2010, 80, 296–305. [CrossRef] Lin, C.H.; Huang, C.H.; Du, Y.C.; Chen, J.L. Maximum photovoltaic power tracking for the PV array using the fractional-order incremental conductance method. Appl. Energy 2011, 88, 4840–4847. [CrossRef] Li, C.; Chen, Y.; Zhou, D.; Liu, J.; Zeng, J. A high-performance adaptive incremental conductance MPPT algorithm for photovoltaic systems. Energies 2016, 9, 288–305. [CrossRef] Mohammadmehdi, S.; Saad, M.; Rasoul, R.; Rubiyah, Y.; Ehsan, T.R. Analytical modeling of partially shaded photovoltaic systems. Energies 2013, 6, 128–144. [CrossRef] Balato, M.; Vitelli, M.; Femia, N.; Petrone, G.; Spagnuolo, G. Factors limiting the efficiency of DMPPT in PV applications. In Proceedings of the International Conference on Clean Electrical Power, Ischia, Italy, 14–16 June 2011; pp. 604–608. Vitelli, M. On the necessity of joint adoption of both distributed maximum power point tracking and central maximum power point tracking in PV systems. Prog. Photovolt. Res. Appl. 2014, 22, 283–299. [CrossRef] Iacca, G.; Mallipeddi, R.; Mininno, E.; Neri, F.; Suganthan, P.N. Global supervision for compact differential evolution. In Proceedings of the 2011 IEEE Symposium on Differential Evolution (SDE), Paris, France, 11–15 April 2011; pp. 1–8. Dorigo, M.; Birattari, M.; Stutzle, T. Ant colony optimization. IEEE Comput. Intell. Mag. 2006, 1, 28–39. [CrossRef] Gao, W.; Liu, S.; Huang, L. A global best artificial bee colony algorithm for global optimization. J. Comput. Appl. Math. 2012, 236, 2741–2753. [CrossRef]

Energies 2016, 9, 986

13.

14.

15.

16.

17.

18.

19. 20.

21.

22. 23. 24. 25. 26. 27. 28. 29. 30.

31. 32.

18 of 18

Hadji, S.; Gaubert, J.P.; Krim, F. Genetic algorithms for maximum power point tracking in photovoltaic systems. In Proceedings of the IEEE 2011—14th European Conference on Power Electronics and Applications (EPE), Birmingham, UK, 30 August–1 September 2011; pp. 1–9. Hadji, S.; Gaubert, J.P.; Krim, F. Experimental analysis of genetic algorithms based MPPT for PV systems. In Proceedings of the IEEE Conference on International Renewable and Sustainable Energy (IRSEC), Ouarzazate, Morocco, 17–19 October 2014; pp. 7–12. Tajuddin, M.F.N.; Ayob, S.M.; Salam, Z. Tracking of maximum power point in partial shading condition using differential evolution (DE). In Proceedings of the IEEE 2012 International Conference on Power and Energy (PECon), Kota Kinabalu, Malaysia, 2–5 December 2012; pp. 384–389. Storn, R. On the usage of differential evolution for function optimization. In Proceedings of the Biennial Conference of the North American in Fuzzy Information Processing Society (NAFIPS), Berkeley, CA, USA, 19–22 June1996; pp. 519–523. Lian, J.; Maskell, D.L. A uniform implementation scheme for evolutionary optimization algorithms and the experimental implementation of an ACO based MPPT for PV systems under partial shading. In Proceedings of the IEEE Symposium on Computational Intelligence Applications in Smart Grid (CIASG), Orlando, FL, USA, 9–12 December 2014; pp. 1–8. Sundareswaran, K.; Sankar, P.; Nayak, P.S.R.; Simon, S.P.; Palani, S. Enhanced energy output from a PV system under partial shaded conditions through artificial bee colony. IEEE Trans. Energy Convers. 2015, 6, 198–209. [CrossRef] Lian, K.L.; Jhang, J.H.; Tian, I.S. A maximum power point tracking method based on perturb-and-observe combined with particle swarm optimization. IEEE J. Photovolt. 2014, 4, 626–633. [CrossRef] Daraban, S.; Petreus, D.; Morel, C. A novel global MPPT based on genetic algorithms for photovoltaic systems under the influence of partial shading. In Proceedings of the IEEE 2013—39th Annual Conference on Industrial Electronics Society (IECON), Vienna, Austria, 10–13 November 2013; pp. 1490–1495. Kashif, I.; Zainal, S.; Amir, S.; Muhammad, A. A direct control based maximum power point tracking method for photovoltaic system under partial shading conditions using particle swarm optimization algorithm. Appl. Energy 2012, 99, 414–422. [CrossRef] Chao, K.H.; Lin, Y.S.; Lai, U.D. Improved particle swarm optimization for maximum power point tracking in photovoltaic module arrays. Appl. Energy 2015, 158, 609–618. [CrossRef] Rao, R.V.; Savsani, V.J.; Vakharia, D.P. Teaching-learning-based optimization: A novel method for constrained mechanical design optimization problems. J. Comput. Aided Des. 2011, 43, 303–315. [CrossRef] Satapathy, S.C.; Naik, A.; Parvathi, K. Weighted teaching-learning-based optimization for global function optimization. Appl. Math. Sci. Res. Publ. 2013, 4, 429–439. [CrossRef] Rao, R.V.; Patel, V. An improved teaching-learning-based optimization Algorithm for solving unconstrained optimization problems. Comput. Sci. Eng. Electr. Eng. 2013, 20, 710–720. [CrossRef] SANYO HIP 2717 Datasheet. Available online: http://iris.nyit.edu/~mbertome/solardecathlon/SDClerical/ SD_DESIGN+DEVELOPMENT/091804_Sanyo190HITBrochure.pdf (accessed on 15 January 2016). Chao, K.H.; Chao, Y.W.; Chen, J.P. A circuit-based photovoltaic module simulator with shadow and fault setting. Int. J. Electron. 2016, 103, 424–438. [CrossRef] Solar Pro Official Website. Available online: http://lapsys.co.jp/english (accessed on 10 May 2016). Rao, R.V.; Patel, V.; Chen, J.P. An elitist teaching-learning-based optimization algorithm for solving complex constrained optimization problems. Int. J. Ind. Eng. Comput. 2012, 3, 535–560. [CrossRef] Graditi, G.; Adinolfi, G.; Femia, N.; Vitelli, M. Comparative analysis of synchronous rectification boost and diode rectification boost converter for DMPPT applications. In Proceedings of the 2011 IEEE International Symposium on Industrial Electronics (ISIE), Gdansk, Poland, 27–30 June 2011; pp. 1000–1005. Hart, D.W. Introduction to Power Electronics; Prentice Hall: New York, NY, USA, 2003. TMS320F2808 Data Sheet. Available online: http://www.ti.com/lit/ds/symlink/tms320f2808.pdf (accessed on 12 March 2016). © 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).