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Scientific Reports , Article number: (2026)
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.
Two area multi-unit thermal hydro (TAMTH) system integrated with solar and dish-Stirling solar thermal system (DSTS) is investigated to regulate the frequency disturbance. An adaptive controller with a combination of Fuzzy Logic Control (FLC), Fractional Order proportional integral derivative (FOPID) and 2 Degree of Freedom PID (2 DOFPID) is designed to achieve frequency stability. The decisive parameters of the proposed Fuzzy based FOPID-2DOFPID (FFOPID-2DOFPID) controller are optimized by Crow Search Algorithm (CSA) and craziness factor of crow in CSA (CCSA). The proposed FFOPID-2DOFPID controller is enforced in each area for both thermal and hydro units to contribute a fine-tuned stable power system. The conformation of superiority of projected controller is presented by a comparative analysis with different kind of controllers along with some newly published research works. The comparative simulation performance analysis is performed by considering undershoot, overshoot and settling time of deviations to show the supremacy of the FFOPID-2DOFPID controller.
The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.
Two area multi-unit thermal hydro
Dish-stirling solar thermal system
Fuzzy logic control
Fractional order proportional integral derivative
2 Degree of freedom PID
Fuzzy based FOPID-2DOFPID
Crow search algorithm
Craziness crow search algorithm
Load frequency control
Renewable energy system
Photovoltaic
Model predictive controller
Proportional-integral-derivative
Cascade fractional order tilt integral derivative
Fuzzy PID
Multi-area power system
Interval type-2 fuzzy inference systems
Governor dead band
Generation rate constraint
High voltage direct current
Fractional order integral double derivative controller with derivative filter
Teaching learning-based algorithm
Local unimodal sampling TLBO
Two area multi-unit thermal hydro system
Integrated time absolute error
Squirrel-cage induction generator
TAMTH integrated with PV
TAMTH-PV integrated with DSTS
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The authors extend their appreciation to the Northern Border University, Saudi Arabia for supporting this work through project number “NBU-CRP-2026-2448”.
The authors extend their appreciation to the Northern Border University, Saudi Arabia for supporting this work through project number “NBU-CRP-2026-2448”.
Department of Electrical Engineering, ITER, Siksha ‘O’ Anusandhan (Deemed to be University), Bhubaneswar, 751030, Odisha, India
Priyambada Satapathy, Pradeep Kumar Mohanty, Jyoti Ranjan Nayak, Manoj Kumar Debnath & Binod Kumar Sahu
Department of Electrical Engineering, Graphic Era (Deemed to be University), Dehradun, 248002, India
Mohit Bajaj
Department of Theoretical Electrical Engineering and Diagnostics of Electrical Equipment, Institute of Electrodynamics, National Academy of Sciences of Ukraine, Beresteyskiy, 56, Kyiv, 03680, Ukraine
Viktoriia Bereznychenko
Center for Scientific Research and Entrepreneurship, Northern Border University, Arar, 73213, Saudi Arabia
Ezzeddine Touti
Hourani Center for Applied Scientific Research, Al-Ahliyya Amman University, Amman, Jordan
Mohit Bajaj
College of Engineering, University of Business and Technology, Jeddah, 21448, Saudi Arabia
Mohit Bajaj
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Priyambada Satapathy, Pradeep Kumar Mohanty, Jyoti Ranjan Nayak, Manoj Kumar Debnath: Conceptualization, Methodology, Software, Visualization, Investigation, Writing- Original draft preparation. Binod Kumar Sahu, Ezzeddine Touti: Data curation, Validation, Supervision, Resources, Writing – Review & Editing. Mohit Bajaj, Viktoriia Bereznychenko: Project administration, Supervision, Resources, Writing – Review & Editing.
Correspondence to Viktoriia Bereznychenko or Ezzeddine Touti.
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Parameter description
Notation
Value
Nominal System Frequency
(:f)
60 Hz
Frequency Bias Factor (area 1 and area 2)
(:{B}_{1}) and (:{B}_{2})
(:0.425:p.u) MW/Hz
Speed Regulation (Governor Droop for Area 1 and Area 2 )
(:{R}_{1}:and:{R}_{2})
(:2.4) Hz/p.u
Speed Governor Time Constant
(:{T}_{g1})
(:0.08:s)
Steam Turbine Time Constant
(:{T}_{t1})
(:0.3:s)
Power System Gain
(:{K}_{p})
120 Hz/p.u
Power System Time Constant
(:{T}_{p})
20 s
Gain for the PV Model
(:{K}_{pv})
1
Time Constant for the PV Model
(:{T}_{pv})
1.8 s
Synchronizing Coefficient
(:{T}_{12})
0.0433 p.u
Area Capacity Ratio
(:{a}_{12})
-1
Hydro Turbine Gain
K1
1
Water Column Time Constant
T1
48.7s
Hydro Governor Reset Time
Tw
1s
Hydro Governor Derivative Time
T2
0.513s
Reheat Time Constant
Tr
5s
Output power of the photovoltaic (PV) system
(:{P}_{PV})
Efficiency of solar panel
(:eta:)
10%
Ambient temperature
(:{T}_{a})
250c
Surface area of the solar panel
S
4084m2
Solar irradiance
(:phi:)
1000 W/m2
Heaviside step function
(:Hleft(tright))
(:Hleft(tright)=0:for:t<0),
(:Hleft(tright)=1:for:t:ge:0)
Solar irradiance as a function of time
(:phi:left(tright))
Random fluctuations in solar irradiance (noise term)
(:{phi:}_{n}left(tright))
Transfer function of PV system
(:{G}_{pv})
Change in PV output power
(:varDelta:{P}_{PV})
Change in solar irradiance
(:varDelta:{varnothing})
Gain of DSTS
(:{K}_{DSTS})
1
Time constant of DSTS
(:{T}_{DSTS})
0.1s
Proportional gain
(:{K}_{PP})
Integral gain
(:{K}_{I})
Derivative gain
(:{K}_{D})
Controller output
(:y)
Integral order
(:gamma:)
Derivative order
(:mu:)
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Satapathy, P., Mohanty, P.K., Nayak, J.R. et al. Load frequency control of a PV–DSTS integrated thermal–hydro power system using a CCSA-optimized fuzzy fractional-order parallel controller. Sci Rep (2026). https://doi.org/10.1038/s41598-026-49421-2
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DOI: https://doi.org/10.1038/s41598-026-49421-2
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