# Stability Analysis and Design of Variable Step-Size P&O Algorithm Based on Fuzzy Robust Tracking of MPPT for Standalone/Grid Connected Power System

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## Abstract

**:**

## 1. Introduction

- Modified P&O algorithm established along with fuzzy controller to control the inverter, while variable step size P&O is utilized to control the dc-dc converter;
- Limitations associated with fixed step size P&O are encountered by using an approach of variable step size through the ant colony optimization technique;
- The stability analysis of the system is tested and ensures the effectiveness of the proposed work.

## 2. Proposed Methodology

#### 2.1. ACO-Based Variable Step P&O

#### 2.2. Ant Colony Optimization

#### 2.3. PID Controller Tuning via ACO

## 3. Results and Discussion

## 4. Under Decreasing–Increasing Irradiance Conditions

^{2}is analyzed and the results clarify the greater tracking of the proposed controller in term of settling time and lost energy.

## 5. Extended Analysis of Algorithm for PV Connected Grid

## 6. Stability Analysis of the System

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Javed, M.Y.; Mirza, A.F.; Hasan, A.; Rizvi, S.T.H.; Ling, Q.; Gulzar, M.M.; Safder, M.U.; Mansoor, M. A Comprehensive Review on a PV Based System to Harvest Maximum Power. Electronics
**2019**, 8, 1480. [Google Scholar] [CrossRef] [Green Version] - Khan, A.; Chenggang, Y.; Hussain, J.; Kui, Z. Impact of technological innovation, financial development and foreign direct investment on renewable energy, non-renewable energy and the environment in belt & Road Initiative countries. Renew. Energy
**2021**, 171, 479–491. [Google Scholar] [CrossRef] - Ahmad, U.S.; Usman, M.; Hussain, S.; Jahanger, A.; Abrar, M. Determinants of renewable energy sources in Pakistan: An overview. Environ. Sci. Pollut. Res.
**2022**, 29, 29183–29201. [Google Scholar] [CrossRef] [PubMed] - Jately, V.; Azzopardi, B.; Joshi, J.; Sharma, A.; Arora, S. Experimental Analysis of hill-climbing MPPT algorithms under low irradiance levels. Renew. Sustain. Energy Rev.
**2021**, 150, 111467. [Google Scholar] [CrossRef] - Alik, R.; Jusoh, A. An enhanced P&O checking algorithm MPPT for high tracking efficiency of partially shaded PV module. Sol. Energy
**2018**, 163, 570–580. [Google Scholar] [CrossRef] - Singh Chawda, G.; Prakash Mahela, O.; Gupta, N.; Khosravy, M.; Senjyu, T. Incremental con-ductance based particle swarm optimization algorithm for global maximum power tracking of solar-pv under nonuniform operating conditions. Appl. Sci.
**2020**, 10, 4575. [Google Scholar] [CrossRef] - Hanan, M.; Ai, X.; Javed, M.Y.; Gulzar, M.M.; Ahmad, S. A two-stage algorithm to harvest maximum power from photovoltaic system. In Proceedings of the 2018 2nd IEEE Conference on Energy Internet and Energy System Integration (EI2), Beijing, China, 20–22 October 2018; pp. 1–6. [Google Scholar]
- Javed, M.Y.; Murtaza, A.F.; Ling, Q.; Qamar, S.; Gulzar, M.M. A novel MPPT design using generalized pattern search for partial shading. Energy Build.
**2016**, 133, 59–69. [Google Scholar] [CrossRef] - Touil, S.-A.; Boudjerda, N.; Boubakir, A.; Drissi, K.E.K. A sliding mode control and artificial neural network based MPPT for a direct grid-connected photovoltaic source. Asian J. Control
**2019**, 21, 1892–1905. [Google Scholar] [CrossRef] - Al-Majidi, S.D.; Abbod, M.F.; Al-Raweshidy, H.S. A novel maximum power point tracking technique based on fuzzy logic for photovoltaic systems. Int. J. Hydrog. Energy
**2018**, 43, 14158–14171. [Google Scholar] [CrossRef] - Harrag, A.E.; 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] [CrossRef] - Titri, S.; Larbes, C.; Toumi, K.Y.; Benatchba, K. A new MPPT controller based on the Ant colony optimization algorithm for Photovoltaic systems under partial shading conditions. Appl. Soft Comput.
**2017**, 58, 465–479. [Google Scholar] [CrossRef] - Khan, F.U.; Gulzar, M.M.; Sibtain, D.; Usman, H.M.; Hayat, A. Variable step size fractional incremental conductance for MPPT under changing atmospheric conditions. Int. J. Numer. Model. Electron. Netw. Devices Fields
**2020**, 33, e2765. [Google Scholar] [CrossRef] - Wasim, M.S.; Amjad, M.; Habib, S.; Abbasi, M.A.; Bhatti, A.R.; Muyeen, S. A critical review and performance comparisons of swarm-based optimization algorithms in maximum power point tracking of photovoltaic systems under partial shading conditions. Energy Rep.
**2022**, 8, 4871–4898. [Google Scholar] [CrossRef] - Nadjemi, O.; Nacer, T.; Hamidat, A.; Salhi, H. Optimal hybrid PV/wind energy system sizing: Application of cuckoo search algorithm for Algerian dairy farms. Renew. Sustain. Energy Rev.
**2017**, 70, 1352–1365. [Google Scholar] [CrossRef] - Fathy, A. Recent meta-heuristic grasshopper optimization algorithm for optimal reconfiguration of partially shaded PV array. Sol. Energy
**2018**, 171, 638–651. [Google Scholar] [CrossRef] - Sundareswaran, K.; Vigneshkumar, V.; Sankar, P.; Simon, S.P.; Nayak, P.S.R.; Palani, S. Development of an Improved P&O Algorithm Assisted Through a Colony of Foraging Ants for MPPT in PV System. IEEE Trans. Ind. Inform.
**2015**, 12, 187–200. [Google Scholar] [CrossRef] - Abdolrasol, M.G.M.; Hussain, S.M.S.; Ustun, T.S.; Sarker, M.R.; Hannan, M.A.; Mohamed, R.; Ali, J.A.; Mekhilef, S.; Milad, A. Artificial Neural Networks Based Optimization Techniques: A Review. Electronics
**2021**, 10, 2689. [Google Scholar] [CrossRef] - Kermadi, M.; Berkouk, E.M. Artificial intelligence-based maximum power point tracking controllers for Photovoltaic systems: Comparative study. Renew. Sustain. Energy Rev.
**2017**, 69, 369–386. [Google Scholar] [CrossRef] - Ahmed, J.; Salam, Z.; Kermadi, M.; Afrouzi, H.N.; Ashique, R.H. A skipping adaptive P&O MPPT for fast and efficient tracking under partial shading in PV arrays. Int. Trans. Electr. Energy Syst.
**2021**, 31, e13017. [Google Scholar] [CrossRef] - Xu, L.; Cheng, R.; Yang, J. A Modified INC Method for PV String Under Uniform Irradiance and Partially Shaded Conditions. IEEE Access
**2020**, 8, 131340–131351. [Google Scholar] [CrossRef] - Nahas, N.; Nourelfath, M.; Ait-Kadi, D. Coupling ant colony and the degraded ceiling algorithm for the redundancy allocation problem of series–parallel systems. Reliab. Eng. Syst. Saf.
**2007**, 92, 211–222. [Google Scholar] [CrossRef] - Kozak, J.; Boryczka, U. Collective data mining in the ant colony decision tree approach. Inf. Sci.
**2016**, 372, 126–147. [Google Scholar] [CrossRef] - Hu, X.; Luo, P.; Zhang, X.; Wang, J. Improved Ant Colony Optimization for Weapon-Target Assignment. Math. Probl. Eng.
**2018**, 2018, 6481635. [Google Scholar] [CrossRef] [Green Version]

**Figure 8.**Close-up section of the proposed technique with response time and loss in energy is highlighted.

**Figure 9.**Close-up section of the proposed technique with response time and the loss in energy is highlighted.

**Figure 10.**ACO-P&O controller response at random temperature with fixed irradiance ($1000\mathrm{W}/{\mathrm{m}}^{2}$).

**Figure 18.**Stability of the system at (

**a**) $1000\mathrm{W}/{\mathrm{m}}^{2}$ (

**b**) $800\mathrm{W}/{\mathrm{m}}^{2}$ (

**c**) $600\mathrm{W}/{\mathrm{m}}^{2}$ (

**d**) $400\mathrm{W}/{\mathrm{m}}^{2}$.

Criteria | ACO |
---|---|

PV array dependent | No |

Periodic tuning | No |

Voltage and current sensing | Yes |

Convergence Speed | Fast |

Initial parameter requirement | Yes |

Complexity | Simple |

Ability to track true maxima | Yes |

Description | Parameters |
---|---|

Number of iterations | 50 |

Number of Ants | 25 |

Pheromones | 0.06 |

Positive Pheromones | 0.2 |

Negative Pheromones | 0.3 |

Irradiance $(\frac{\mathbf{W}}{{\mathbf{m}}^{2}})$ | Time (s) |
---|---|

1000 | 0–2 |

800 | 2–4 |

600 | 4–6 |

400 | 6–8 |

Gain Value | Error% | ${\mathit{K}}_{\mathit{P}}$ | ${\mathit{K}}_{\mathit{I}}$ | ${\mathit{K}}_{\mathit{D}}$ | |
---|---|---|---|---|---|

Irradiation | |||||

$1000$ | 7.351–7.578 | $0.21245$ | $3.14871$ | $1.00189$ | |

$800$ | 6.010–6.524 | $0.012540$ | $2.98454$ | $0.32545$ | |

$600$ | 4.583–4.891 | $0.112101$ | $1.42541$ | $0.852410$ | |

$400$ | 3.241–3.245 | $0.101045$ | $1.15401$ | $1.154217$ |

Controller | Response Time $\left(\mathbf{ms}\right)$ | Energy Lost $\left(\mathbf{W}\right)$ | Overshoot $\left(\%\right)$ |
---|---|---|---|

ACO-P&O | 11 | 0.10 | 0.067 |

GA-P&O | 16 | 7 | 4.63 |

P&O | 22 | 8.1 | 5.74 |

Irradiance $\left(\frac{\mathbf{W}}{{\mathbf{m}}^{2}}\right)$ | Time $\left(\mathbf{s}\right)$ |
---|---|

1000 | 0–1 |

800 | 1–2 |

600 | 2–3 |

400 | 3–4 |

600 | 4–5 |

400 | 5–6 |

Controller | Response Time $\left(\mathbf{ms}\right)$ | Energy Lost $\left(\mathbf{W}\right)$ | Overshoot $\left(\%\right)$ |
---|---|---|---|

ACO-P&O | $98$ | $0.002$ | $0.0025$ |

GA-P&O | $200$ | $10$ | $12.5$ |

P&O | $320$ | $19$ | $23.75$ |

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**MDPI and ACS Style**

Sibtain, D.; Gulzar, M.M.; Shahid, K.; Javed, I.; Murawwat, S.; Hussain, M.M.
Stability Analysis and Design of Variable Step-Size P&O Algorithm Based on Fuzzy Robust Tracking of MPPT for Standalone/Grid Connected Power System. *Sustainability* **2022**, *14*, 8986.
https://doi.org/10.3390/su14158986

**AMA Style**

Sibtain D, Gulzar MM, Shahid K, Javed I, Murawwat S, Hussain MM.
Stability Analysis and Design of Variable Step-Size P&O Algorithm Based on Fuzzy Robust Tracking of MPPT for Standalone/Grid Connected Power System. *Sustainability*. 2022; 14(15):8986.
https://doi.org/10.3390/su14158986

**Chicago/Turabian Style**

Sibtain, Daud, Muhammad Majid Gulzar, Kamal Shahid, Imran Javed, Sadia Murawwat, and Muhammad Majid Hussain.
2022. "Stability Analysis and Design of Variable Step-Size P&O Algorithm Based on Fuzzy Robust Tracking of MPPT for Standalone/Grid Connected Power System" *Sustainability* 14, no. 15: 8986.
https://doi.org/10.3390/su14158986