During abnormal operation, for example when the load converters are blocked, the speed might increase to a level considerably higher than base speed. This means that the induced back-emf eq (4.23)
might reach levels so high that the controlled transistor converter starts to act as a non-controlled diode rectifier, formed by the freewheeling diodes. To circumvent this potential risk, resulting in lost control of the DC bus voltage, field weakening is introduced. In field weakening, reactive power is consumed so that the machine terminal voltage is kept at the average level
where Ld is the stator inductance in the d-direction. A control law could be formed directly from this expression. However, this implies a high gain and since the speed is estimated this could result in an oscillatory behaviour. To reduce this kind of problem, the d-component of the current is filtered with a first order filter with
Then the difference between the back-emf at rated speed and the actual back-emf minus the actual field weakening component is fed to a Pi-controller, see Figure 4.2.
The gain and integrator time constant of this Pi-controller is selected in such a way that the closed loop poles of the field weakening sub-system, with the assumption that the estimated speed is correct, are given by
where CCid is a weighting factor to reduce the gain of the field weakening subsystem. A suitable value for this factor is aid - 0.55
The gain and integrator time constant used to generate the d-current reference required for field weakening are given by
m lp,id aid for a continuous time controller. For the simulation, a sampled controller is used and, therefore, backward Euler transformation  is applied.
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