STRUCTURAL SYNTHESIS OF A ROTOR SPEED OBSERVER FOR A DOUBLY FED MACHINE

Abstract

The prerequisite for the studies presented in this paper is the fact that observers of the rotor angular speed of induction machines are, as a rule, constructed on the basis of open loop flux linkage observers. For doubly fed machines (DFM) the equations of electromagnetic processes of the induction machine, written in orthogonal axes attached to the rotor, are taken as the basis for synthesis. The state variables of the observer are the d–q projections of the rotor current vectors and the stator flux linkage vectors. From these variables and their comparison with the actual rotor currents an adaptation function is formed, the integral of which represents an estimate of the rotor speed of the DFM. During the derivation of the observer adaptation algorithm, a quadratic form arises whose matrix consists of the sum of the state matrix and its transpose. However the resulting matrix is not negative definite. Therefore in order to impart the property of global stability to the flux linkage and speed observer, corrective feedbacks based on current mismatch signals are introduced into the equations of electromagnetic processes in such a way that the off-diagonal coefficients of the quadratic form matrix are eliminated, and the matrix itself becomes negative definite. This ensures global stability of the flux linkage observer. Subsequently an adaptation function is added to it in the form of the vector product of the stator flux linkage vector and the rotor current estimation error vector, with an internal controller, at the output of which a signal estimating the angular speed of the DFM is obtained. Thus the observer structure consists of an electromagnetic process subsystem, a corrective feedback subsystem and structural elements that form the speed estimate. The resulting observer is closed-loop since all its state variables are obtained as a result of solving its own dynamic equations. The input variables are only the stator and rotor voltages as well as the rotor currents. The observer forms a dynamic feedback loop for the vector control system of the DFM. The stability of such a system is verified by numerical experiments under operating conditions with the stator connected to the grid and with the stator short-circuited, in the regenerative braking mode at speeds below synchronous.