Nonlinear Optimal Control for the Synchronization of Distributed Marine-turbine Power Generation Units

Abstract

Power generation from marine-turbines offers a vast potential for raising the contribution of renewable energy sources to the electricity grid. Typically, marine-turbine power units comprise marine-turbines that receive mechanical excitation from sea currents or tidal streams and synchronous or asynchronous generators that are finally connected to the electricity grid. Due to connection to the same transmission lines, interactions between the excitations of the individual generators appear. To achieve stabilization of the generators’ functioning, as well as synchronization to the grid’s frequency the generators’ control has to compensate for such interactions. The article proposes a nonlinear optimal control approach for distributed marine-turbine power units that use synchronous generators. First, the dynamic model of the distributed power system undergoes approximate linearization around a temporary operating point which is re-computed at each time-step of the control algorithm. The linearization relies on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. For the approximately linearized model of the distributed power system a stabilizing H-infinity (optimal) feedback controller is designed. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each time-step of the control method. The global stability properties of the control scheme are proven through Lyapunov analysis. The proposed control method retains the advantages of optimal control, that is fast and accurate tracking of the reference setpoints, under moderate variations of the control inputs. Among the advantages of the proposed control method one can note: (i) the presented nonlinear optimal control method has improved performance when compared against other nonlinear control schemes that one can consider for the dynamic model of the distributed marine power system (actually other control methods are neither of proven optimality, nor of proven global stability), (ii) avoids complicated state-space transformations and the related appearance of singularities in the computation of the control inputs which are applied to the nonlinear model (iii) minimizes the consumption of energy by the control system of the distributed marine-turbine generators, thus also reducing the functioning cost of such power units.