Simultaneous estimation of mass and aerodynamic rotor imbalances for wind turbines

Jenny Niebsch,Ronny Ramlau

doi:10.1186/2190-5983-4-12

Abstract

The safe operation of wind turbines requires a well-balanced rotor. The balancing of the rotor requires a method to determine its imbalances. We propose an algorithm for the reconstruction of two types of imbalances, i.e., mass and aerodynamic imbalances from pitch angle deviation. The algorithm is based on the inversion of the (nonlinear) operator equation that links the imbalance distribution of the rotor to its vibrations during operation of the wind turbine. The algorithm requires a simple finite element model of the wind turbine as well as the minimization of a Tikhonov functional with a nonlinear operator. We propose the use of a gradient-based minimization routine. The approach is validated for artificial vibration data from a model of a Nordwind NTK 500 wind turbine.

Highlights

In the growing field of wind energy extraction, the topic of rotor imbalances of wind turbines (WT) is of vital importance for the operation, safety, and durability of the turbines
This paper focuses on a stable reconstruction method of mass imbalance and pitch angle deviation based on the minimization of the Tikhonov functional
The resulting operator equation is Ax = y where the operator A maps the imbalance x of the rotor in terms of mass imbalance and pitch angle deviation to the displacement y in the nodes that can be observed by measurements

Summary

Introduction

In the growing field of wind energy extraction, the topic of rotor imbalances of wind turbines (WT) is of vital importance for the operation, safety, and durability of the turbines. This paper focuses on a stable reconstruction method of mass imbalance and pitch angle deviation based on the minimization of the Tikhonov functional To this end, the nonlinear forward operator A is derived in detail and its Frechet derivative is computed which is new compared to [ ]. The resulting operator equation is Ax = y where the operator A maps the imbalance x of the rotor in terms of mass imbalance and pitch angle deviation to the displacement y in the nodes that can be observed by measurements This operator equation represents the forward problem. Whereas the mass imbalance force can be directly computed, the aerodynamic imbalance forces need to be determined via, e.g., the Blade-Element-Momentum (BEM) method, a nonlinear procedure.

The total tangential force

In detail we have

It follows that A is given by

Hence the Tikhonov functional now reads

It follows that