By using a rotating dq reference frame oriented to the rotor magnetic field axis, each stator current component has a physical meaning. The imaginary component isq is proportional to the electrical torque while the real component isd is proportional to the reactive power. In this way, the machine control is implemented as a current control scheme, where the current references are generated by the external speed control loop.
The model of the machine is used for predicting the behavior of the stator currents, and the cost function must consider the error between the reference currents and predicted currents.
By using the Euler approximation for the stator current derivatives for a sampling time Ts, that is,
These equations allow predictions of the stator currents to be calculated for each one of the seven voltage vectors generated by the inverter. The voltage vectors generated by the inverter are fixed in the stationary reference frame, but they are rotating vectors in ...