Short-memory discrete fractional difference equation wind turbine model and its inferential control of a chaotic permanent magnet synchronous transformer in time-scale analysis

Abdulaziz Khalid Alsharidi; Saima Rashid; S. K. Elagan; Abdulaziz Khalid Alsharidi; Saima Rashid; S. K. Elagan

doi:10.3934/math.2023975

AIMS Mathematics

2023, Volume 8, Issue 8: 19097-19120. doi: 10.3934/math.2023975

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Short-memory discrete fractional difference equation wind turbine model and its inferential control of a chaotic permanent magnet synchronous transformer in time-scale analysis

1.
Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Hasa 31982, Saudi Arabia
2.
Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
3.
Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
4.
Department of Mathematics and Computer Sciences, Faculty of Science Menoufia University, Shebin Elkom, Egypt

Received: 16 January 2023 Revised: 24 May 2023 Accepted: 25 May 2023 Published: 07 June 2023
MSC : 46S40, 47H10, 54H25

The aerodynamics analysis has grown in relevance for wind energy projects; this mechanism is focused on elucidating aerodynamic characteristics to maximize accuracy and practicability via the modelling of chaos in a wind turbine system's permanent magnet synchronous generator using short-memory methodologies. Fractional derivatives have memory impacts and are widely used in numerous practical contexts. Even so, they also require a significant amount of storage capacity and have inefficient operations. We suggested a novel approach to investigating the fractional-order operator's Lyapunov candidate that would do away with the challenging task of determining the indication of the Lyapunov first derivative. Next, a short-memory fractional modelling strategy is presented, followed by short-memory fractional derivatives. Meanwhile, we demonstrate the dynamics of chaotic systems using the Lyapunov function. Predictor-corrector methods are used to provide analytical results. It is suggested to use system dynamics to reduce chaotic behaviour and stabilize operation; the benefit of such a framework is that it can only be used for one state of the hybrid power system. The key variables and characteristics, i.e., the modulation index, pitch angle, drag coefficients, power coefficient, air density, rotor angular speed and short-memory fractional differential equations are also evaluated via numerical simulations to enhance signal strength.
- permanent magnet synchronous generator,
- chaotic system,
- Lyapunov function,
- equilibrium points,
- short-memory,
- time-scale analysis
Citation: Abdulaziz Khalid Alsharidi, Saima Rashid, S. K. Elagan. Short-memory discrete fractional difference equation wind turbine model and its inferential control of a chaotic permanent magnet synchronous transformer in time-scale analysis[J]. AIMS Mathematics, 2023, 8(8): 19097-19120. doi: 10.3934/math.2023975

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Abstract

The aerodynamics analysis has grown in relevance for wind energy projects; this mechanism is focused on elucidating aerodynamic characteristics to maximize accuracy and practicability via the modelling of chaos in a wind turbine system's permanent magnet synchronous generator using short-memory methodologies. Fractional derivatives have memory impacts and are widely used in numerous practical contexts. Even so, they also require a significant amount of storage capacity and have inefficient operations. We suggested a novel approach to investigating the fractional-order operator's Lyapunov candidate that would do away with the challenging task of determining the indication of the Lyapunov first derivative. Next, a short-memory fractional modelling strategy is presented, followed by short-memory fractional derivatives. Meanwhile, we demonstrate the dynamics of chaotic systems using the Lyapunov function. Predictor-corrector methods are used to provide analytical results. It is suggested to use system dynamics to reduce chaotic behaviour and stabilize operation; the benefit of such a framework is that it can only be used for one state of the hybrid power system. The key variables and characteristics, i.e., the modulation index, pitch angle, drag coefficients, power coefficient, air density, rotor angular speed and short-memory fractional differential equations are also evaluated via numerical simulations to enhance signal strength.

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