Abstract
The Immersion and Invariance (I&I) wind speed estimator is a powerful and widely-used technique to estimate the rotor effective wind speed on horizontal axis wind turbines. Anyway, its global convergence proof is rather cumbersome, which hinders the extension of the method and proof to time-delayed and/or uncertain systems. In this letter, we illustrate that the circle criterion can be used as an alternative method to prove the global convergence of the I&I estimator. This also opens up the inclusion of time-delays and uncertainties. First, we demonstrate that the I&I wind speed estimator is equivalent to a torque balance estimator with a proportional correction term. As the nonlinearity in the estimator is sector bounded, the well-known circle criterion is applied to the estimator to guarantee its global convergence for time-delayed systems. By looking at the theoretical framework from this new perspective, this letter further proposes the addition of an integrator to the correction term to improve the estimator performance. Case studies show that the proposed estimator with an additional integral correction term is effective at wind speed estimation. Furthermore, its global convergence can be guaranteed by the circle criterion for time-delayed systems.
Highlights
W IND energy has received increasingly considerable attention in the international energy markets in recent years
We illustrate that the circle criterion can be used as an alternative global convergence proof to the Immersion and Invariance (I&I) estimator which opens up the inclusion of time-delays and uncertainties
We show that the I&I estimator can be rewritten as an estimator with a proportional correction term
Summary
W IND energy has received increasingly considerable attention in the international energy markets in recent years. The torque balance estimator can be seen as a type of Lur’e system [8] formed by a negative feedback interconnection of a linear estimator and a bounded nonlinearity on the turbine power coefficient In this context, a common restriction for such Lur’e type estimators is the lack of sufficient asymptotic stability conditions on the linear stable estimator such that the feedback interconnection is stable. The derivation of such a proof is rather cumbersome and, the presence of time-delays did not receive enough attention This cannot be neglected as the wind speed estimator is usually implemented as a digital system, where the lack of available asymptotic stability conditions will limit its application to real wind turbines.
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