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