Adaptive passivity-based control for maximum power extraction of stand-alone windmill systems Fernando Mancilla-David a , Romeo Ortega b,n a Department of Electrical Engineering, University of Colorado Denver, 1200 Larime St., Denver, Colorado 80217, USA b Laboratoire de Signaux et Systemes, Supe´lec, Plateau de Moulon, 91192 Gif-sur-Yvette, France article info Article history: Received 13 January 2011 Accepted 21 October 2011 Available online 9 November 2011 Keywords: Adaptive control Nonlinear control Windmills Wind speed Renewable energy systems Power control abstract This paper addresses the high performance regulation of stand-alone windmill systems consisting of a wind turbine coupled to a generator and a battery charging system, which is a challenging problem for at least two reasons. First, the dynamics of the overall system are described by a highly coupled set of nonlinear differential equations. Since the range of operating points of the system is very wide, classical linear controllers yield below par performances. Second, in many applications it is desirable to extract from windmill systems their maximum power. This operating point is a nonlinear function of the wind speed, which is hard to measure. In this paper, a nonlinear passivity-based controller that ensures asymptotic convergence to the maximum power extraction point, which is rendered adaptive combining it with a wind speed estimator previously proposed by the authors, is proposed. Detailed computer simulations are presented to validate the approach. & 2011 Elsevier Ltd. All rights reserved. 1. Introduction Wind power is becoming increasingly popular around the world due to its low footprint on the environment. Countries such as Denmark, Germany, Spain, the US and others have launched aggressive policies in order to drastically increase the wind power penetration in their energy portfolio for electricity generation (Wiser & Bolinger, 2009). Although most of the effort has been focused on the development of utility scale wind power, in recent years small wind turbines (1–100 kW) have been receiving attention as serious contributors for powering homes, farms and small businesses. The American Wind Energy Associa- tion in its ‘‘Small Wind Turbine Roadmap’’ study (Bergey, 2002) identifies the dynamic modeling and analysis of small wind turbines as a key issue to further advance in the understanding of these systems. An important type of small wind turbines are those using surface- mount permanent magnets synchronous generators (PMSG), due to their higher efficiency and simplicity of construction (Binder & Schneider, 2005). The controller design of this kind of small-scale windmill systems is complicated because the generator dynamics cannot be neglected, as usually done for large wind turbines (Cigre, 2007; Johnson, Pao, Balas, & Fingersh, 2006). Hence, the behavior of the overall system is described by a highly coupled set of nonlinear differential equations. Moreover, it is often desirable to operate this kind of systems at the point of maximum power extraction. To achieve this objective it is necessary to know the wind speed, which is usually not available for measurement. Since, the unknown wind speed enters into this dynamics in a nonlinear way, we are confronted with the problem of adaptively controlling a nonlinear, and nonlinearly parameterized, system—for which, besides practi- cally questionable high-gain designs, almost no theoretical results are available in the control literature. Several publications have appeared in the literature concern- ing modeling (Cigre, 2007; Reed et al., 2007), and control (Borowy & Salameh, 1997; Boukhezzar & Siguerdidjane, 2010; Venkataramanan, Milkovska, Gerez, & Nehrir, 1996; Ostergaard, Brath, & Stoustrup, 2007; Valenciaga, Puleston, & Battaiotto, 2003; Valenciaga & Puleston, 2005), PMSG-based small-scale windmill systems without wind velocity measurement but, to the best of the authors’ knowledge, none have conducted a rigorous theoretical stability analysis. In the interesting paper (Valenciaga et al., 2003) the well-known passivity-based and sliding mode control techniques are used to provide some guide- lines for the controller design. Unfortunately, as indicated by the authors, the assumptions required by these techniques—in parti- cular, a relative degree one condition—are not satisfied and the controller is designed invoking some approximations. In Johnson et al. (2006), neglecting the dynamics of the generator and assuming direct control of the generated torque, it is proposed to adapt the ‘‘gain’’ of the standard o 2 m controller (Cigre, 2007), Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/conengprac Control Engineering Practice 0967-0661/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.conengprac.2011.10.008 n Corresponding author. Tel.: þ33 1 6985 1766; fax: þ33 1 6985 1765. E-mail addresses: Fernando.Mancilla-David@ucdenver.edu (F. Mancilla-David), ortega@lss.supelec.fr (R. Ortega). Control Engineering Practice 20 (2012) 173–181