A controller and method is disclosed for operating a variable speed turbine to track wind speed fluctuations for high efficiency in conversion of wind energy to electrical energy. The controller of the invention controls the rotor speed in accordance with a wind speed supplied by a wind observer in order to approximately follow the varying wind speeds. A yaw angle error sensor senses the degree to which the turbine is misaligned with the wind. The wind observer predicts the average wind speed at a subsequent point in time. The average wind speed is applied to a parameter schedule to determine desired values for rotor speed and torque which are used by a rotor speed stabilizer to command a reference load torque. The load torque of the generator is controlled in accordance with the commanded load torque, and therefore the desired rotor speed is approximated. During operation, the wind speed prediction process is repeated at each subsequent time interval, and the load torque, and therefore rotor speed, is controlled accordingly. The wind observer calculates the aerodynamic torque and then calculates net torque. The wind speed is predicted as a function of the present (previously predicted) wind speed and correction terms including net torque, the yaw angle error, and the difference between the predicted and actual rotor speed. The wind observer is useful whenever the wind turbine rotor is turning, whether or not it is producing power.