Table of Contents

Open Access

ISSN 2690-1692

© 2024 by the authors; CC BY 4.0 licence

Journal of Energy and Power Technology , Volume 6 , Issue 1 (2024)

Pages: 193

Published: March 2024

(This book is a printed edition that was published in Journal of Energy and Power Technology)

Download PDF

Cover Story: In this article, a novel nonlinear optimal control method is developed for the dynamic model a wave energy conversion unit that includes a Permanent Magnet Linear Synchronous Generator (PMLSG) serially connected to a three-phase AC/DC Voltage Source Converter (VSC). The dynamic model of the integrated PMLSG-VSC-based power unit is presented in state-space form, and differential flatness properties are proven about it. Differential flatness is also an implicit proof of the system’s controllability and its input-output linearizability. Indeed, through successive differentiations of the power unit’s flat outputs, this system is transformed into the input-output linearized form, and a stabilizing feedback controller is developed about it using the eigenvalues assignment technique. Applying the nonlinear optimal control schemes mentioned above can help avoid the complicated and elongated state-space model transformations characteristic of this control method.
In the article’s nonlinear optimal control approach, the dynamic model of the PMSLG-VSC-based wave energy conversion system undergoes first approximate linearization through Taylor series expansion. This approximate linearization process occurs at each sampling instance around a time-varying operating point defined by the present value of the system’s state vector and the last sampled value of the control inputs vector. The linearization primarily relies on computing the system’s Jacobian matrices and updating them at each sampling interval. The modeling error arising from the truncation of higher-order terms in the Taylor series is regarded as a perturbation that is asymptotically compensated for by the robustness of the control algorithm.
A stabilizing H-infinity feedback controller is designed for the approximately linearized PMSLG-VSC-based wave energy conversion unit model. This controller solves the optimal control problem for the wave energy conversion system under model uncertainty and external perturbations. It represents a min-max differential game between (i) the control inputs, which try to minimize a quadratic function of the state vector’s tracking error, and (ii) the model uncertainty or perturbation terms, which try to maximize this cost function. To compute the controller’s gains, an algebraic Riccati equation is solved repetitively at each time step of the control method. The global stability properties of this control scheme are demonstrated through Lyapunov analysis. Initially, it is established that the control loop satisfies the H-infinity tracking performance criterion, indicating significant robustness to model uncertainties and external perturbations.View this paper.