Torque dynamic behaviour of induction machine DTC in 4 quadrant operation

In the framework of direct torque control (DTC) for induction machines, this paper deals with the dynamic behaviour of the torque in all four quadrants of operation. A formal development of the expression of the dynamical machine torque is given. This theoretical derivation is based on a small variation model valid for a short sampling times. It allows to understand and predict the electromagnetic behaviour of the machine in both motor operation and particularly in generator mode. Hence, the "empirical approach", usually used to choose the inverter voltage states (voltage vector), is replaced by an analytical approach. This allows to develop a look up table accurately specifying the inverter states that lead to a four-quadrant DTC strategy. Simulation results are presented demonstrating the control performance as well as the validity of the expression of the torque derivative. The main objective of this work aims at a better understanding of the torque behaviour, particularly for generator operation. This allows to design a DTC strategy based on a formal analysis of the induction machine electromagnetic state.