This paper presents a sensorless control for a variable speed wind turbine (WT) operating at partial load in order to eliminate the direct measurement of the wind speed. In this proposal, the estimated aerodynamic torque is used to determine the optimal reference of the speed control for maximum energy conversion. The maximization of the efficiency on energy conversion and the minimization of detrimental dynamical loads are control trade-offs considered in the design of an optimal discrete-time feedback LQG/LTR controller for the Wind Energy Conversion System (WECS), which is based on the optimization of a quadratic cost function. The performance of the proposed control when the WT is submitted to a gust or step variation on wind speed is evaluated from computational simulations. It is also presented some proposals for sensorless control of the electrical generator. (c) 2010 Elsevier Ltd. All rights reserved.