https://doi.org/10.1140/epjs/s11734-023-00927-0
Regular Article
Multistability, coexisting behaviours and control of fractional order dissipative small scale grid with disturbances and noise
1
Department of Electrical Engineering, NIT Meghalaya, Laitumkhrah, 793003, Shillong, Meghalaya, India
2
Electrical Engineering Department, National Institute of Technology Meghalaya, Laitumkhrah, 793003, Shillong, Meghalaya, India
Received:
30
March
2023
Accepted:
2
July
2023
Published online:
26
July
2023
This paper introduces nonlinear analysis and control of a fraction order small-scale grid (SSG) under the influence of disturbances and noise. Random wind power supply and uncertain load demand are considered as disturbances while the additive white Gaussian noise is considered as external noise. The nonlinear dynamic behaviours such as multistability and coexisting bifurcation behaviours are investigated along with period-2, period doubling bifurcation route to chaos and instability (chaos breaking) of the rotor angle which is not expected under normal operating condition and reveal stability issue in the proposed SSG. Also, the presence of nontrivial behaviours, multistability and coexistence of attractors, may be of capital importance in understanding dynamic remedy of the fractional order SSG behaviour since serious impediments may occur even after the present required safeguard. An adaptive fractional second order PID sliding mode control (AFSO-PIDSMC) is proposed to control the chaos and multistability behaviours in the fractional order SSG. The proposed control technique includes the design adaptive control based on the designed fractional and second-order PID sliding mode control. Required asymptotic stability condition is derived by using Lyapunov stability theory. Furthermore, the proposed control technique is compared and has fast convergence, parameter estimation and chatter-free response. Numerical simulations are performed in MATLAB environment and validate the theoretical aspects.
Prakash Chandra Gupta and Piyush Pratap Singh have contributed equally to this work.
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