# Preventing wind turbine tower natural frequency excitation with a quasi-LPV model predictive control scheme

## TL;DR

This paper presents a quasi-LPV model predictive control scheme to prevent wind turbine tower excitation at natural frequencies, balancing energy output and structural fatigue in flexible, tall towers.

## Contribution

Introduction of a quasi-LPV-MPC method that enables effective trade-offs between energy maximization and fatigue load reduction for wind turbines.

## Key findings

- Prevents rotor speed from operating at tower natural frequency.
- Enables rapid passage over natural frequency for higher energy production.
- Effective in both synthetic and realistic high-fidelity simulations.

## Abstract

With the ever increasing power rates of wind turbines, more advanced control techniques are needed to facilitate tall towers that are low-weight and cost effective, but in effect more flexible. Such soft-soft tower configurations generally have their fundamental side-side frequency in the below-rated operational domain. Because the turbine rotor practically has or develops a mass imbalance over time, a periodic and rotor-speed dependent side-side excitation is present during below-rated operation. Persistent operation at the coinciding tower and rotational frequency degrades the expected structural life span. To reduce this effect, earlier work has shown the effectiveness of active tower damping control strategies using collective pitch control. A more passive approach is frequency skipping by inclusion of speed exclusion zones, which avoids prolonged operation near the critical frequency. However, neither of the methods incorporate a convenient way of performing a trade-off between energy maximization and fatigue load minimization. Therefore, this paper introduces a quasi-linear parameter varying model predictive control (qLPV-MPC) scheme, exploiting the beneficial (convex) properties of a qLPV system description. The qLPV model is obtained by a demodulation transformation, and is subsequently augmented with a simple wind turbine model. Results show the effectiveness of the algorithm in synthetic and realistic simulations using the NREL 5-MW reference wind turbine in high-fidelity simulation code. Prolonged rotor speed operation at the tower side-side natural frequency is prevented, whereas when the trade-off is in favor of energy production, the algorithm decides to rapidly pass over the natural frequency to attain higher rotor speeds and power productions.