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Enhanced maximum power point tracking using hippopotamus optimization algorithm for grid-connected photovoltaic system
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  • Published: 20 February 2026

Enhanced maximum power point tracking using hippopotamus optimization algorithm for grid-connected photovoltaic system

  • Salah A. Taha1,
  • Mohammed Abdulla Abdulsada1,
  • Mohamed Ahmed Ebrahim Mohamed2,
  • Mohammed Alruwaili3 &
  • …
  • Ahmed Emara4 

Scientific Reports , Article number:  (2026) Cite this article

We are providing an unedited version of this manuscript to give early access to its findings. Before final publication, the manuscript will undergo further editing. Please note there may be errors present which affect the content, and all legal disclaimers apply.

Subjects

  • Energy science and technology
  • Engineering
  • Mathematics and computing

Abstract

In this study, an advanced maximum power point tracking (MPPT) control strategy is proposed for a grid-connected photovoltaic (PV) system using the Hippopotamus Optimization Algorithm (HOA). The Incremental Conductance (IC) MPPT technique is integrated with three control approaches: Integral (I), Proportional-Integral (PI), and Fractional-Order Proportional-Integral (FOPI) controllers. The HOA is employed to optimally tune the controller parameters, and its performance is benchmarked against two other nature-inspired algorithms: the Arithmetic Optimization Algorithm (AOA) and the Grey Wolf Optimizer (GWO). A 100 kW grid-tied PV system connected to a medium-voltage distribution network is modeled and simulated in MATLAB/Simulink 2025a. The optimization process aims to minimize four classical performance indices: IAE, ISE, ITAE, and ITSE. Simulation results demonstrate that the HOA-based FOPI-IC-MPPT configuration achieves superior dynamic performance, exhibiting a minimum rise time of 0.0073 s and a maximum extracted power of 100.72 kW. Under the IAE criterion, compared to AOA and GWO, the proposed method reduces the rise time by 9.88% and the settling time by 19.73%. Although the GWO-based controller outperformed in certain metrics (e.g., ISE), the HOA-based approach achieved a better trade-off between dynamic response and maximum power tracking accuracy, making it a promising solution for real-time grid-connected PV applications under variable environmental conditions.

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Abbreviations

A:

Addition arithmetic operator

a:

Ideality factor for diode

best (xj ):

Position of best-attained solution till now C_Iter

D:

Division arithmetic operator

dI/Dv:

Incremental conductance term

e:

Error

Eg :

Bandgap energy of polycrystalline silicon

G:

Solar irradiance

I/V:

Instantaneous incremental conductance

Id :

Diode current

Io :

Reverse saturation current of the diode

Iph :

Photogenerated current

ISCn :

Short circuit current at STC

Ish :

Current through parallel resistance

K:

Boltzmann constant (1.38 × 10–23 J/K)

KI :

Integral gain

KP :

Proportional gain

λ:

Lambda

KT :

Temperature coefficient

LBj :

Lower boundary of the jth position

M:

Multiplication arithmetic operator

M_Iter:

Maximum number of iterations

F:

Dimension

Min:

Function

MOA:

Math Optimizer Accelerated

MOP:

Math Optimizer probability

Ns :

The number of series cells

q:

Electron charge (1.6 × 10–19 C)

r1-r3:

Random numbers

Rs :

Series resistance of PV cell

Rsh :

Shunt resistance

S:

Subtraction arithmetic operator

Tc :

Temperature of PV cell in Kelvin

tss :

Steady-state time response

UBj :

Upper boundary of the jth position

V:

Terminal voltage

VOCn :

Open circuit voltage at STC

Vt :

Thermal voltage

AI:

Artificial intelligence

AOA:

Arithmetic optimization algorithm

HOA:

Hippopotamus Optimization Algorithm

I-V:

Current-Voltage relationship

DDM:

Double diode model of PV cell

FOSV:

Fractional open-circuit voltage

FSCC:

Fractional short circuit current

GWO:

Grey wolf optimization

IAE:

Integral absolute error

IC:

Incremental conductance

IRENA:

International renewable energy agency ITAE Integral time absolute error

ITSE:

Integral time square error

ITAE:

Integral time absolute error

MPPT:

Maximum PowerPoint tracking

FOPI:

Fractional-Order Proportional-Integral controller

PI:

Proportional-Integral controller

I:

Integral controller

PV:

Photovoltaic

P-V:

Power-Voltage relationship

SDM:

Single diode model of PV cell

STC:

Standard test condition

TDM:

Triple diode model

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Acknowledgements

The authors extend their appreciation to the Deanship of Scientific Research at Northern Border University, Arar, KSA, for funding this research (through the project number NBU-FFR-2026-2124-01).

Funding

This research was funded by the Deanship of Scientific Research at Northern Border University, Arar, KSA, for funding this research (through the project number NBU-FFR-2026-2124-01).

Author information

Authors and Affiliations

  1. Electrical Engineering Technical College, Middle Technical University, Baghdad, Iraq

    Salah A. Taha & Mohammed Abdulla Abdulsada

  2. Department of Electrical Engineering, Faculty of Engineering at Shoubra, Benha University, Cairo, Egypt

    Mohamed Ahmed Ebrahim Mohamed

  3. Department of Electrical Engineering, College of Engineering, Northern Border University, Arar, 91431, Saudi Arabia

    Mohammed Alruwaili

  4. Electrical Engineering Department, University of Business and Technology, Jeddah, 23435, Saudi Arabia

    Ahmed Emara

Authors
  1. Salah A. Taha
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  2. Mohammed Abdulla Abdulsada
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  3. Mohamed Ahmed Ebrahim Mohamed
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  4. Mohammed Alruwaili
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Contributions

Salah A. Taha: Conceptualization, methodology, supervision, and overall project administration.Mohammed Abdulla Abdulsada: Software implementation, simulation, and data analysis.Mohamed Ahmed Ebrahim Mohamed: Validation, result interpretation, and manuscript drafting.Mohammed Alruwaili: Resources, visualization, and technical review of the manuscript.Ahmed Emara: Formal analysis, manuscript revision, and correspondence with the journal.All authors contributed to manuscript revision, approved the final version, and agreed to be accountable for all aspects of the work.

Corresponding authors

Correspondence to Salah A. Taha or Ahmed Emara.

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Taha, S.A., Abdulsada, M.A., Mohamed, M.A.E. et al. Enhanced maximum power point tracking using hippopotamus optimization algorithm for grid-connected photovoltaic system. Sci Rep (2026). https://doi.org/10.1038/s41598-026-40918-4

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  • Received: 10 November 2025

  • Accepted: 17 February 2026

  • Published: 20 February 2026

  • DOI: https://doi.org/10.1038/s41598-026-40918-4

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Keywords

  • Photovoltaic (PV)
  • grid-tied inverter
  • MPPT
  • Hippopotamus Optimization Algorithm (HOA)
  • Grey Wolf Optimizer (GWO)
  • active power
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