Dynamics Modeling and Periodic Control of Horizontal-Axis Wind Turbines

Abstract

The development of large multi-megawatt wind turbines has increased the need for active feedback control to meet multiple performance objectives. Power regulation is still of prime concern but there is an increasing interest in mitigating loads for these very large, dynamically soft and highly integrated power systems. This work explores the opportunities for utilizing state-space modeling, modal analysis, and multi-objective controllers in advanced horizontal-axis wind turbines. A linear state-space representation of a generic, multiple degree-of-freedom wind turbine is developed to test various control methods and paradigms. The structural model, SymDyn, provides for limited flexibility in the tower, drive train and blades assuming a rigid component architecture with joint springs and dampers. Equations of motion are derived symbolically, verified by numerical simulation, and implemented in the Matlab with Simulink computational environment. AeroDyn, an industry-standard aerodynamics package for wind turbines, provides the aerodynamic load data through interfaced subroutines. Linearization of the structural model produces state equations with periodic coefficients due to the interaction of rotating and non-rotating components. Floquet theory is used to extract the necessary modal properties and several parametric studies identify the damping levels and dominant dynamic coupling influences. Two separate issues of control design are investigated: full-state feedback and state estimation. Periodic gains are developed using time-varying LQR techniques and many different time-invariant control designs are constructed, including a classical PID controller. Disturbance accommodating control (DAC) allows the estimation of wind speed for minimization of the disturbance effects on the system. Controllers are tested in simulation for multiple objectives using measurement of rotor position and rotor speed only and actuation of independent blade pitch. It is found that periodic control is capable of reducing cyclic blade bending moments while regulating speed but that optimal performance requires additional sensor information. Periodic control is also the only design found that could successfully control the yaw alignment although blade loads are increased as a consequence. When speed regulation is the only performance objective then a time-invariant state-space design or PID is appropriate.