# Global Maximum Power Point Tracking (MPPT) of a Photovoltaic Module Array Constructed through Improved Teaching-Learning-Based Optimization

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Fault and Shading Characteristics of PV Module Arrays

^{2}, and PV module temperature of 25 °C) [26].

#### 2.1. PV Module Simulator Circuit

_{Isc}and VR

_{Voc}. The variable resistor VR

_{Voc}shown in Figure 1 controls the open-circuit voltage of the PV module. When the circuit is open, a current-limiting transistor Q

_{3}is operated at the cutoff region. The open-circuit voltage is calculated using Equation (1):

_{Isc}to operate the current limiting transistor Q

_{3}at the saturation region when the V

_{BE}

_{3}voltage drop crosses over R

_{D}. The short-circuit current is calculated using Equation (2):

_{PV}power source is not provided, the PV module simulator generates zero power output, which is equivalent to the fault situation of the PV module. Using a bypass diode D

_{Bypass}can ensure that PV module arrays generate a certain amount of power during fault events. Accordingly, the electricity parameters of PV modules can be employed to set the required PV module output characteristics.

#### 2.2. PV Module Array Fault and Shading Characteristics Analysis

#### 2.2.1. PV Module Array Characteristics without Faults or Shading

_{mp}, I

_{mp}, and P

_{mp}, the MPP voltage, MPP current, and MPP power of the M serial and N parallel arrays are expressed as M × V

_{mp}, N × I

_{mp}, and M × N × P

_{mp}, respectively.

#### 2.2.2. PV Module Array Characteristics with Faults or Shading

## 3. Teaching-Learning-Based Optimization (TLBO) Method

#### 3.1. Conventional TLBO Method

- Step 1:
- Set the values for the number of students N
_{p}, subjects m, and iterations E. - Step 2:
- Initialize a class S and define the following parameters:
- (a)
- Random student: ${X}_{k}\subset \{{X}_{1},{X}_{2},{X}_{3},\dots ,{X}_{{N}_{P}}\}$
- (b)
- Random subject: ${X}_{j}\subset \{{X}_{1},{X}_{2},{X}_{3},\dots ,{X}_{m}\}$
- (c)
- Target grade of student k in subject j: ${G}_{j,k}$

- Step 3:
- In the teaching phase, learning step r
_{i}, teaching factor T_{F}, and students with the highest grades X_{j,k_best}are given. The mean of a class is calculated according to Equation (3) and substituted into Equation (4) to determine the student mean difference value. Finally, student grades are updated according to Equation (5) to identify the new target grade for each student in the teaching phase:$$M={\displaystyle \sum _{k=1}^{{N}_{P}}\frac{{X}_{k}}{{N}_{P}}}$$$$\begin{array}{cc}Different\_Mea{n}_{j,k}={r}_{i}({X}_{j,k\_best}-{T}_{F}\times M)& i=1,2,\dots ,E\end{array}$$$${X}_{j,k(new)}={X}_{j,k(old)}+Different\_Mea{n}_{j,k}$$ - Step 4:
- In the learning phase, we assume that two random students X
_{P}and X_{Q}participate in mutual learning, in which the student with the lower grade learns from the one with a higher grade. Adjustments were made using Equation (6):$$\begin{array}{c}{{X}^{\prime}}_{j,k(new)}={X}_{j,k(new)}+\left\{\begin{array}{c}ri({X}_{j,P(=k)}-{X}_{j,Q(\ne k)}\\ ri({X}_{j,Q(=k)}-{X}_{j,P(\ne k)}\end{array}\right\}\begin{array}{c},if{X}_{j,P}{X}_{j,Q}\\ ,if{X}_{j,Q}{X}_{j,P}\end{array}\\ {X}_{P},{X}_{Q}\subset \left\{{X}_{1},{X}_{2},{X}_{3},\dots ,{X}_{{N}_{P}}\right\}\end{array}$$ - Step 5:
- Repeat steps 3 and 4 until the iteration is completed.

- Number of students (N
_{p}): Total number of participating students. - Number of iterations (E): Number of teaching and learning phases that the students experience.
- Subject grade (X
_{j,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 (r
_{i}): Parameter for diversifying the student mean difference with a random value between 0 and 1. - Teaching factor (T
_{F}): Teachers’ ability to teach the students. The parameter randomly generates a value of 1 or 2.

_{F}) 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

- Modification 1: The teaching factors T
_{F}were modified to be automatically adjustable according to the students’ learning capacity. The adjustment method is expressed in Equation (7):$${T}_{F}=\frac{{X}_{j,k}}{{X}_{j,k\_best}}$$ - 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):$$\begin{array}{cc}{{X}^{\u2033}}_{j,k(new)}={{X}^{\prime}}_{j,k(new)}+{r}_{i}({{X}^{\prime}}_{j,k(new)}-{{X}^{\prime}}_{j,k-1(new)})& i=1,2,\dots ,E\end{array}$$

_{j,k_best}and M remain unchanged, then Different_Mean

_{j,k}increases as T

_{F}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 X

_{1}(i.e., power value P

_{1}) and X′

_{1}(i.e., power value P′

_{1}), then the teaching factors T

_{F}of the student with the highest grades among all the students X

_{j,k_best}(i.e., MPP value tracked so far P

_{k_best}) are modified using Equations (9) and (10):

_{F}

_{1}value decreases as the Different_Mean value increases when student grade is distant from the MPP (e.g., X

_{1}position), thereby increasing the number of tracking steps needed to approach the maximum value rapidly. By contrast, when the student grade is close to the MPP (e.g., X′

_{1}position), the T

_{F}

_{2}value increases as the Different_Mean value and number of tracking steps decrease to approach the maximum value slowly. Thus, the students can adjust their tracking steps according to their learning capacity. In improvements 2 and 3, students can spontaneously learn from a student who is helpful to them. The term X′

_{j,k-1(new)}represents the student’s previous learning abilities, which is used as a basis for the other student’s self-study. In summary, the self-learning method not only accelerates the learning progress, but also escapes local solutions and reaches global convergence. A flowchart of the proposed I-TLBO MPPT is shown in Figure 5.

#### 3.3. MPP Tracker

_{F}in Table 3 is replaced with the parameter setting in Table 4 whereas all other parameters remain unchanged. Subsequently, the PV module array was tested under five distinct operating situations, as shown in Table 5.

## 4. Measurement Results

#### 4.1. PV Module Array Characteristics under Different Operating Situations

#### 4.2. MPPT Measurement of PV Module Arrays

_{PV}and current I

_{PV}of the PV module arrays were extracted through sensors and signal conversion circuits and entered into the TMS320F2808 digital signal processor. Subsequently, TLBO was applied to perform MPPT. The resulting optimal duty cycle trigger signal was sent to the boost converter to control the on time of power transistors, thereby controlling the maximum power output of the PV module array.

_{PV}and current I

_{PV}measured on the PV module arrays. The power curves are demonstrated as the product of voltage and current through the internal computation functions of the oscilloscope. In the 40th iteration, the quality of the conventional TLBO and the proposed I-TLBO tracking response speed were observed and compared when the power curve approached a stable value.

#### 4.2.1. Case 1 (One-Serial and One-Parallel: 0% Shading)

_{0}and t

_{1}in Figure 12 showed that the proposed I-TLBO (2.5 s) converged faster than did conventional TLBO (3.5 s).

#### 4.2.2. Case 2 (Two-Serial and One-Parallel: 0% and 40% Shading)

#### 4.2.3. Case 3 (Three-Serial and One-Parallel: 0%, 30%, and 70% Shading)

#### 4.2.4. Case 4 (Four-Serial and One-Parallel: 0%, 30%, 50%, and 70% Shading)

_{0}to t

_{1}) to track the MPP. This validates that the proposed I-TLBO outperformed conventional TLBO in tracking.

#### 4.2.5. Case 5 (Two-Serial and Two-Parallel: (0% and 30% Shading)//(0% and 50% Shading))

_{F}in conventional TLBO slowed the MPPT. By contrast, the proposed I-TLBO identified the real MPP within a short time (3.5 s).

#### 4.2.6. Comparison of the Case Measurements

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- 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. [Google Scholar] [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. [Google Scholar] [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. [Google Scholar] [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. [Google Scholar] [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. [Google Scholar] [CrossRef] - Mohammadmehdi, S.; Saad, M.; Rasoul, R.; Rubiyah, Y.; Ehsan, T.R. Analytical modeling of partially shaded photovoltaic systems. Energies
**2013**, 6, 128–144. [Google Scholar] [CrossRef][Green Version] - 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. [Google Scholar] [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. [Google Scholar] [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. [Google Scholar] [CrossRef] - 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. [Google Scholar] [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. [Google Scholar] [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. [Google Scholar] [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. [Google Scholar] [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. [Google Scholar] [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. [Google Scholar] [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. [Google Scholar] [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. [Google Scholar] [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. [Google Scholar] [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. [Google Scholar]
- TMS320F2808 Data Sheet. Available online: http://www.ti.com/lit/ds/symlink/tms320f2808.pdf (accessed on 12 March 2016).

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

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

**Figure 7.**I–V and P–V characteristic curves of one-serial and one-parallel module array with 0% shading.

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

**Figure 9.**I–V and P–V characteristic curves of the three-serial and one-parallel module array with 0%, 30%, and 70% shading.

**Figure 10.**I–V and P–V characteristic curves of the four-serial and one-parallel module array with 0%, 30%, 50%, and 70% shading.

**Figure 11.**I–V and P–V characteristic curves of the two-serial and two-parallel module array with [(0% and 30% shading)//(0% and 50% shading)].

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

**a**) conventional TLBO (P

_{mp}= 27.4 W) and (

**b**) the proposed I-TLBO (P

_{mp}= 27.8 W).

**Figure 13.**Measurement results of the two-serial and one-parallel module array (0% and 40% shading) by using (

**a**) conventional TLBO (P

_{mp}= 35.1 W) and (

**b**) the proposed I-TLBO (P

_{mp}= 35.8 W).

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

**a**) conventional TLBO (P

_{mp}= 37.7 W) and (

**b**) the proposed I-TLBO (P

_{mp}= 38.5 W).

**Figure 15.**Results of the four-serial and one-parallel module array (0%, 30%, 50%, and 70% shading) measured by using (

**a**) conventional TLBO (P

_{mp}= 43.0 W) and (

**b**) the proposed I-TLBO (P

_{mp}= 43.4 W).

**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 (P

_{mp}= 66.5 W) and (

**b**) the proposed I-TLBO (P

_{mp}= 66.7 W).

Parameter | Value |
---|---|

Rated maximum power output (P_{mp}) | 27.8 W |

MPP current (I_{mp}) | 1.63 A |

MPP voltage (V_{mp}) | 17.1 V |

Short-circuit current (I_{sc}) | 1.82 A |

Open-circuit voltage (V_{oc}) | 21.6 V |

Module dimensions | 496 mm × 524 mm |

Component | Model Number and Specifications |
---|---|

Inductance (L_{m}) | 3.3 mH |

Input capacitance (C_{in}) | 220 μF/160 V |

Output capacitance (C_{out}) | 390 μF/450 V |

Switching frequency (f_{s}) | 20 kHz |

Power MOSFET (S) | IRF460 (500 V/20A) |

Diode (D) | DSEP30-12A (1200 V/30A) |

Parameter | Setting |
---|---|

Number of students (N_{P}) | 4 |

Number of iterations (E) | 40 |

Teaching step (r_{i}) | Random value between 0 and 1 |

Teaching factor (T_{F}) | 1 or 2 |

Parameter | Setting |
---|---|

Teaching factor (T_{F}) | ${T}_{F}=\frac{{X}_{j,k}}{{X}_{j,k\_best}}$ |

Case | Serial and Parallel Configurations and Shading Situations | Number of Peaks in the P–V Characteristic Curves |
---|---|---|

1 | One-serial and one-parallel with 0% shading | Single |

2 | Two-serial and one-parallel with 0% and 40% shading | Double |

3 | Three-serial and one-parallel with 0%, 40%, and 70% shading | Triple |

4 | Four-serial and one-parallel with 0%, 30% shading, 50%, and 70% shading | Quadruple |

5 | Two-serial and two-parallel with (30% and 0% shading)//(0% and 50% shading) | Double |

**Table 6.**Comparison between the measurement results of the five cases obtained using ACO, PSO, conventional TLBO and the proposed I-TLBO.

Case | P–V Curve Peaks | ACO [17] | PSO [21] | Conventional TLBO | Proposed I-TLBO | ||||
---|---|---|---|---|---|---|---|---|---|

Average Tracking Time | Average MPP | Average Tracking Time | Average MPP | Average Tracking Time | Average MPP | Average Tracking Time | Average MPP | ||

1 | 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 |

2 | Double | 4.8 s | 35.3 W | 3.0 s | 35.0 W | 2.8 s | 35.1 W | 2.4 s | 35.8 W |

3 | 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 |

4 | Quadrupe | 5.6 s | 43.2 W | Tracking failed | 35.7 W | 3.6 s | 43.0 W | 2.2 s | 43.4 W |

5 | 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 |

© 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/).

## Share and Cite

**MDPI and ACS Style**

Chao, K.-H.; Wu, M.-C.
Global Maximum Power Point Tracking (MPPT) of a Photovoltaic Module Array Constructed through Improved Teaching-Learning-Based Optimization. *Energies* **2016**, *9*, 986.
https://doi.org/10.3390/en9120986

**AMA Style**

Chao K-H, Wu M-C.
Global Maximum Power Point Tracking (MPPT) of a Photovoltaic Module Array Constructed through Improved Teaching-Learning-Based Optimization. *Energies*. 2016; 9(12):986.
https://doi.org/10.3390/en9120986

**Chicago/Turabian Style**

Chao, Kuei-Hsiang, and Meng-Cheng Wu.
2016. "Global Maximum Power Point Tracking (MPPT) of a Photovoltaic Module Array Constructed through Improved Teaching-Learning-Based Optimization" *Energies* 9, no. 12: 986.
https://doi.org/10.3390/en9120986