Dear Alec,
Thanks for the suggested improvement to TrimCase = 2 option in the FAST linearization process. We don’t have any immediate plans to improve the trim solution of FAST, but we’ll look at your suggestion when we get the chance.
For those that are following this post, here is some background information on the basic problem:
The “Linearization” chapter of the “FAST User’s Guide” warns of a possible instability while trimming with generator torque (i.e., TrimCase = 2). Specifically, I wrote “the solution may become unstable if your desired rotor speed is below the rotor speed that results in the maximum power coefficient at a given wind speed and rotor-collective blade-pitch angle. In this case, the only way to obtain a successful trim solution is to increase your desired rotor speed condition.” The instability can be understood by examining the curve of aerodynamic torque coefficient (Cq) versus tip-speed ratio (TSR) for a given blade-pitch angle. Cq usually reaches a maximum at a TSR slightly below the TSR for optimal power coefficient (Cp) for a given blade-pitch angle. If a given TSR is below the TSR for maximum Cq, then increased TSR leads to increased aerodynamic torque, which further accelerates the rotor, hence local instability. If a given TSR is above the TSR for maximum Cq, the reverse is true and the system is stable. The trim solver in FAST uses simple control logic in TrimCase = 2 to trim generator torque to reach the desired rotor speed. The generator torque is computed as a positive gain times the integral of the speed error. This trim solution is only stable if the target TSR is above the TSR for maximum Cq. Plotting Cp and Cq = Cp/TSR versus TSR for a given blade-pitch angle should help determine the TSRs that bring about maximum Cq and maximum Cp, and hence, where TrimCase = 2 is stable.
Best regards,