# A Fuzzy Logical-Based Variable Step Size P&O MPPT Algorithm for Photovoltaic System

^{*}

## Abstract

**:**

## 1. Introduction

^{®}and Simulink

^{®}2016a. The PV emulator mathematical model and electrical characteristics, as well as circuit connection, were also shown. Simulation and experimental results of the proposed MP&O MPPT algorithm show the method is efficient in tracking the maximum power point with changes in solar irradiance.

## 2. Maximum Power Point Tracking Techniques

_{oc}) and short circuit current (I

_{sc}) as shown in Figure 1.

_{pv}/ΔV

_{pv}and compares it with the instantaneous conductance I

_{pv}/V

_{pv}to decide the operation for tracking maximum power point MPP. This algorithm has an advantage over P&O as it can calculate the direction in which to perturb the array operating point to reach MPP and stop perturbing when MPPT has reached its maximum operating point. Also, under rapidly changing atmospheric conditions it does not track in the wrong direction away from MPP [27,28]. However, the main drawback of incremental conductance MPPT algorithm is the complexity of its hardware implementation as its need to not only measure the current and voltage but as well calculates the instantaneous and incremental conductance value.

## 3. Proposed Fuzzy Logical Based Variable Step Size P&O MPPT Algorithm

_{actual}represents the power produced by the PV array under the control of the MPPT and P

_{max}is the real maximum power the PV array can produce under the given irradiance and temperature.

_{pv}and V

_{pv}are the terminal current and voltage of the PV array. With the proposed variable step size P&O MPPT algorithm, the variable step size was determined by a fuzzy logic algorithm to allow the PV array operating point to be automatically tuned by providing a variable step size reference voltage ∆V

_{pv}to the connected power converter. Mamdani ‘s fuzzy logic rule-based method with a structure of Max-Min operation was used to determine the variable step size control action. The fuzzy logic controller consists of four parts as shown in Figure 3. The controller was designed with ”if” and ”then” format and has 25 rules. Furthermore, the labels of the fuzzy were set as: positive very small (PVS), positive small (PS), positive medium (PM), positive high (PH) and positive very high (PVH) respectively as shown in Table 1.

_{pv}(k)·V

_{pv}(k), ΔP(k) = ∆P

_{pv}(k) − ∆P

_{pv}(k − 1) and ∆V

_{pv}(k) = V

_{pv}(k) − V

_{pv}(k − 1).

_{c}resulting from the inference is mapped to a crisp output using the membership functions Figure 4, in the defuzzification phase to form the variable step size of the controller control signal.

_{pv}(k) is the prescribed conclusion of each of the 25 rules implemented in the fuzzy logic controller. With two inputs and one output in the design of the fuzzy logic controller, the input-output mapping is a surface which is called the control viewer surface. Figure 5 shows a mesh plot of the control viewer surface input and output mapping relationship between fixed perturbation voltage step size and the instantaneous measured PV curve slope S(k) on the premise side, and the control action output variable step size ∆V

_{pv}(k) on the vertical side, resulting from the 25 rules in Table 1.

#### 3.1. Simulation Results of the Proposed Variable Step Size P&O MPPT Algorithm

^{2}to 600 W/m

^{2}. The result indicates that the FLC-based variable step size P&O MPPT have a faster dynamic response. The convergence of rising time towards maximum power point gives a settling time of 0.11 s compared with the fixed step size P&O MPPT with a step size of ΔV = 0.04 (scale down value) with a settling time of 0.16 s. It also shows that the proposed MPPT with a variable FLC step size has a lower oscillation of PV output voltage around the maximum power point under steady-state conditions when compared with the fixed step size P&O MPPT which have more oscillations of PV output voltage around the maximum power point under steady-state conditions.

^{2}to 600 W/m

^{2}. The proposed MPPT has a faster transient response in contrast with the fixed step size P&O MPPT.

## 4. Experiment System Setup for Testing the MPPT Algorithm

#### 4.1. Boost DC-DC Converter

_{pv}is controlled by the boost DC-DC converter. The theoritical relationship of the PV voltage and the output voltage is expressed as V

_{pv}= V

_{o}(1 − D), where D is the duty cycle of the switching device. By regulating the duty cycle, the required PV terminal voltage can be achieved. The switching frequency of the boost DC-DC converter hardware is set to 20 kHz; this was implemented using hardware-in-the-loop simulations and rapid control prototyping dSPACE MATLAB

^{®}/Simulink

^{®}PC-based simulation platform Modular Hardware/DS4002 Timing and Digital I/O Board to generate the PWM pulse digital signal for the emulating system shown in Figure 11. The boost converter captures energy generated from the connected PV source and transfers it to the resistive load. The boost DC-DC design parameter is given in Table 2. The same parameters were also implemented in the emulated PV system using MATLAB/Simulink system tool box to obtain the simulation results in Section 3.1.

#### 4.2. dSPACE-Based MPPT Controller Implementation

^{®}and Simulink

^{®}. An RTI (real-time interface) block of Modular Hardware/DS2004 High-Speed A/D Board was used in measuring the output current (I

_{pv}) and voltage(V

_{pv}) of the emulated PV source as shown in Figure 10. The measured I

_{pv_emul}and V

_{pv_emul}was then used in implementing the MPPT algorithm. The instantaneous measured I

_{pv}and V

_{pv}were scaled down using a current and voltage measurement circuit on the DC-DC boost converter because the signal applied to the dSPACE Analogue to Digital (ADC) channel must be in the range of −10 V to +10 V. To get the actual sensed measured value rather than the scaled down value, the gains for the current and voltage are 2.6 and 28 respectively.

#### 4.3. The Emulated PV Source

_{cs}represent the external excitement current. For a conventional commercial PV panel, the external excitement current will be injected into the solar panel through the internal series resistor.

_{ph}≈ 0, therefore the I-V characteristics of the emulated PV panel are expressed by Equations (3)–(5) respectively:

_{CS}represents the external excitement current to emulate the photo-generated current at direct sunlight, I

_{0}represents the dark saturation current, R

_{s}represents the panel series resistance, R

_{sh}represents the panel parallel resistance, N

_{s}is the number of cells connected in series, V

_{t}represents the junction thermal voltage given by equation V

_{T}= KT

_{c}/q, k is Boltzmann’s constant 1.381 × 10

^{−23}J/K and q represents the elementary charge 1.602 × 10

^{−19}C. The parameters of the solar panel under standard testing condition (STC) are presented in Table 3. STC is an industry-wide standard under which solar panels are tested i.e., by applying the following test coditions (irradiance 1000 W/m

^{2}, module temperature 25 °C and an air mass of 1.5 (AM1.5)) [29]. The electrical characteristics of the proposed emulated PV source using different excitement currents is shown in Figure 13.

#### 4.4. Experimental Results

_{o}was charged through the inductor and diode by the emulated PV source. The charging current was naturally limited by the connected current source, so no extra power resistor is required in the charging circuit.

_{mppt}= 5 ms).

_{cs}of 1 Amp (equivalent to 200 W/m

^{2}) the PV output voltage is continuously oscillating around the voltage (35.48 V) at the maximum power point.

_{cs}of 1 Amp which is equivalent to 200 W/m

^{2}the PV output voltage is continuously oscillating around the voltage (34.40 V) at MPP. It is also observed that the proposed FLC variable step size MPPT shows a better dynamic transient response with a sudden change in excitement current I

_{cs}of 1 Amp (equivalent 200 W/m

^{2}) to I

_{cs}of 3 Amp (equivalent 600 W/m

^{2}) as shown on the marked oval shape in Figure 14 and Figure 15.

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

## References

- Owusu, P.A.; Asumadu-Sarkodie, S. A review of renewable energy sources, sustainability issues and climate change mitigation. Cogent Eng.
**2016**, 3, 1167990. [Google Scholar] [CrossRef] - Panwar, N.L.; Kaushik, S.C.; Kothari, S. Role of renewable energy sources in environmental protection: A review. Renew. Sustain. Energy Rev.
**2011**, 15, 1513–1524. [Google Scholar] [CrossRef] - Munawwar, S.; Ghedira, H. A review of renewable energy and solar industry growth in the GCC region. Energy Procedia
**2014**, 57, 3191–3202. [Google Scholar] [CrossRef] - Saridakis, S.; Koutroulis, E.; Blaabjerg, F. Optimal design of modern transformerless PV inverter topologiesd. IEEE Trans. Energy Convers.
**2013**, 28, 394–404. [Google Scholar] [CrossRef] - Serban, E.; Paz, F.; Ordonez, M. Improved PV Inverter Operating Range Using a Miniboost. IEEE Trans. Power Electron.
**2017**, 32, 8470–8485. [Google Scholar] [CrossRef] - Chakraborty, S.; Razzak, M.A.; Chowdhury, M.S.U.; Dey, S. Design of a transformer-less grid connected hybrid photovoltaic and wind energy system. In Proceedings of the 2014 9th International Forum on Strategic Technology (IFOST 2014), Cox’s Bazar, Bangladesh, 21–24 October 2014; pp. 400–403. [Google Scholar]
- Femia, N.; Petrone, G.; Spagnuolo, G.; Vitelli, M. Optimization of perturb and observe maximum power point tracking method. IEEE Trans. Power Electron.
**2005**, 20, 963–973. [Google Scholar] [CrossRef] - Ahmed, J.; Ahmed, J.; Member, S.; Salam, Z. A Modified P&O Maximum Power Point Tracking Method with Reduced Steady State Oscillation and Improved Tracking Efficiency. IEEE Trans. Sustain. Energy
**2016**, 3029, 1–10. [Google Scholar] - Kumar, N.; Hussain, I.; Singh, B.; Panigrahi, B.K. Framework of Maximum Power Extraction From Solar PV Panel Using Self Predictive Perturb and Observe Algorithm. IEEE Trans. Sustain. Energy
**2018**, 9, 895–903. [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] - Menniti, D.; Pinnarelli, A.; Brusco, G. Implementation of a novel fuzzy-logic based MPPT for grid-connected photovoltaic generation system. In Proceedings of the 2011 IEEE PES Trondheim PowerTech: The Power of Technology for a Sustainable Society (POWERTECH 2011), Trondheim, Norway, 9–23 June 2011. [Google Scholar]
- Tey, K.S.; Mekhilef, S. Modified incremental conductance MPPT algorithm to mitigate inaccurate responses under fast-changing solar irradiation level. Sol. Energy
**2014**, 101, 333–342. [Google Scholar] [CrossRef] - Schofield, D.M.K.; Foster, M.P.; Stone, D.A. Low-cost solar emulator for evaluation of maximum power point tracking methods. Electron. Lett.
**2011**, 47, 208. [Google Scholar] [CrossRef] - Punitha, K.; Devaraj, D.; Sakthivel, S. Artificial neural network based modified incremental conductance algorithm for maximum power point tracking in photovoltaic system under partial shading conditions. Energy
**2013**, 62, 330–340. [Google Scholar] [CrossRef] - Daraban, S.; Petreus, D.; Morel, C. A novel MPPT (maximum power point tracking) algorithm based on a modified genetic algorithm specialized on tracking the global maximum power point in photovoltaic systems affected by partial shading. Energy
**2014**, 74, 374–388. [Google Scholar] [CrossRef] - Manickam, C.; Raman, G.P.; Raman, G.R.; Ganesan, S.I.; Chilakapati, N. Fireworks enriched P&O algorithm for GMPPT and detection of partial shading in PV systems. IEEE Trans. Power Electron.
**2017**, 32, 4432–4443. [Google Scholar] - Zhao, J.; Zhou, X.; Gao, Z.; Ma, Y.; Qin, Z. A novel global maximum power point tracking strategy (GMPPT) based on optimal current control for photovoltaic systems adaptive to variable environmental and partial shading conditions. Sol. Energy
**2017**, 144, 767–779. [Google Scholar] [CrossRef] - Esram, T.; Chapman, P.L. Comparison of Photovoltaic Array Maximum Power Point Tracking Techniques. IEEE Trans. Energy Convers.
**2007**, 22, 439–449. [Google Scholar] [CrossRef] - Sahu, T.P.; Dixit, T.V. Modelling and analysis of perturb and observe and incremental conductance MPPT algorithm for PV array using Ċuk converter. In Proceedings of the 2014 IEEE Students’ Conference on Electrical, Electronics and Computer Science (SCEECS 2014), Bhopal, India, 1–2 March 2014. [Google Scholar]
- Ahmed, J.; Salam, Z. An improved perturb and observe (P&O) maximum power point tracking (MPPT) algorithm for higher efficiency. Appl. Energy
**2015**, 150, 97–108. [Google Scholar] - Femia, N.; Petrone, G.; Spagnuolo, G. Optimizing Sampling Rate of P & O MPPT Technique. In Proceedings of the 35th Annual IEEE Power Electronics Specialists Conference, Aachen, Germany, 20–25 June 2004; pp. 1945–1949. [Google Scholar]
- Baraskar, S.; Jain, S.K.; Padhy, P.K. Fuzzy logic assisted P and O based improved MPPT for photovoltaic systems. In Proceedings of the International Conference on Emerging Trends in Electrical, Electronics and Sustainable Energy Systems (ICETEESES 2016), Majhitar, India, 17–18 December 2016; pp. 250–255. [Google Scholar]
- Yüksek, G.; Mete, A.N. A hybrid variable step size MPPT method based on P&O and INC methods. In Proceedings of the 2017 10th International Conference on Electrical and Electronics Engineering (ELECO), Bursa, Turkey, 30 November–2 December 2017; pp. 949–953. [Google Scholar]
- Harrag, A.; Messalti, S. Variable step size modified P&O MPPT algorithm using GA-based hybrid offline/online PID controller. Renew. Sustain. Energy Rev.
**2015**, 49, 1247–1260. [Google Scholar] - Kollimalla, S.K.; Member, S.; Mishra, M.K.; Member, S. Variable Perturbation Size Adaptive P&O MPPT Algorithm for Sudden Changes in Irradiance. IEEE Trans. Sustain. Energy
**2014**, 5, 718–728. [Google Scholar] - Jusoh, A.; Alik, R.; Guan, T.K.; Sutikno, T. MPPT for PV System Based on Variable Step Size P&O Algorithm. Telkomnika
**2017**, 15, 79–92. [Google Scholar] - Hohm, D.P.; Ropp, M.E. Comparative study of maximum power point tracking algorithms. Prog. Photovolt. Res. Appl.
**2003**, 11, 47–62. [Google Scholar] [CrossRef] - Hohm, D.P.; Ropp, M.E. Comparative study of maximum power point tracking algorithms using an experimental, programmable, maximum power point tracking test bed. In Proceedings of the 28th IEEE Photovoltaic Specialists Conference, Anchorage, AK, USA, 15–22 September 2000; pp. 1699–1702. [Google Scholar]
- Elibol, E.; Özmen, Ö.T.; Tutkun, N.; Köysal, O. Outdoor performance analysis of different PV panel types. Renew. Sustain. Energy Rev.
**2017**, 67, 651–661. [Google Scholar] [CrossRef]

**Figure 4.**The membership function of the proposed fuzzy logic controller for the variable step size MPPT algorithm (

**a**) fixed step size perturbation; (

**b**) PV curve slope S(k); (

**c**) variable step ∆V

_{pv}(k).

**Figure 5.**Mesh plot of the input and output mapping of the relationship between the fixed perturbation voltage step size and the measured PV curve slope S(k) and the output variable step ∆V

_{pv}(k).

**Figure 6.**Comparison of conventionally fixed step size P&O MPPT and the proposed FLC-based variable step size P&O MPPT with a startup.

**Figure 7.**Comparison of PV voltage with fixed step size P&O MPPT and the proposed FLC-based variable step size P&O MPPT with a step change in solar irradiance.

**Figure 8.**Comparison of PV current with fixed step size P&O MPPT and the proposed FLC-based variable step size P&O MPPT with a step change in solar irradiance.

**Figure 9.**Comparison of PV power with fixed step size P&O MPPT and the proposed FLC-based variable step size P&O MPPT with a step change in solar irradiance.

**Figure 13.**Measured electrical characteristics of the emulated PV source with excitement different currents.

**Figure 14.**MP&O fuzzy logic controller Variable step size MPPT Test results with variable current source currents (emulating the variable photo-generated current).

**Figure 15.**Conventional P&O (fixed step size) MPPT Test results with variable current source currents (emulating the variable photo-generated current).

Δe = S(k) | PVS | PS | PM | PH | PVH | |
---|---|---|---|---|---|---|

E = Voltage Step | ||||||

PVS | PVH | PVS | PVS | PS | PS | |

PS | PVH | PVS | PVS | PS | PS | |

MP | PS | PS | PS | PVH | PVH | |

HP | PS | PVH | PS | PVS | PVH | |

PVH | PVS | PVS | PVH | PH | PVH |

Boost DC-DC Converter Parameter | |
---|---|

Switching frequency | 20 kHz |

Input capacitor | 220 µF |

Output capacitor | 440 µF |

Inductor | 100 µH |

Rated Maximum power | 175 Watts |

Voltage at the maximum power point (V_{mpp}) | 35.2 Volts |

Current at the maximum power point (I_{mpp}) | 4.95 Amp |

Short circuit current (I_{sc}) | 5.2 Amp |

Open circuit voltage (V_{oc}) | 44.2 Volts |

Normal operating cell temperature | 50 °C |

© 2018 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**

Macaulay, J.; Zhou, Z.
A Fuzzy Logical-Based Variable Step Size P&O MPPT Algorithm for Photovoltaic System. *Energies* **2018**, *11*, 1340.
https://doi.org/10.3390/en11061340

**AMA Style**

Macaulay J, Zhou Z.
A Fuzzy Logical-Based Variable Step Size P&O MPPT Algorithm for Photovoltaic System. *Energies*. 2018; 11(6):1340.
https://doi.org/10.3390/en11061340

**Chicago/Turabian Style**

Macaulay, John, and Zhongfu Zhou.
2018. "A Fuzzy Logical-Based Variable Step Size P&O MPPT Algorithm for Photovoltaic System" *Energies* 11, no. 6: 1340.
https://doi.org/10.3390/en11061340