Reference Generation

For Induction Machines

For induction machines, the motulator.drive.control.im.ReferenceGenerator class implements a simple reference generation that can be used with flux-vector control. Figure 1 illustrates this method that consists of field weakening, current limitation (CL), and breakdown torque limitation.

For current limitation, the priority is given to the flux. The stator flux limit and the torque limit, respectively, are

(1)\[\begin{split} \psi_\mathrm{s}^\mathrm{cl} &= \hatLsgm \ismax + \hatabspsiR \\ \tau_\mathrm{M}^\mathrm{cl} &= \frac{3\np}{2} \hatabspsiR \sqrt{(\ismax)^2 - \left(\frac{\hatabspsiR}{\hatLM}\right)^2}\end{split}\]

where \(\hatabspsiR\) is the rotor flux magnitude estimate and \(\ismax\) is the maximum current. The breakdown torque limit is

(2)\[ \tau_\mathrm{M}^\mathrm{b} = \frac{3\np}{2} \frac{(\abspsisref)^2}{2\hat{L}_\ell}\]

where the leakage inductance estimate can be expressed by means of the inverse-Γ parameters as \(\hat L_\ell = [(\hatLM + \hatLsgm)/\hatLM]\hatLsgm\).

This reference generation is used in the motulator.drive.control.im.FluxVectorController class, which implements flux-vector control for induction machines. See also the 2.2-kW saturated IM, FVC example.

Figure 1: Reference generation for induction machines, including field weakening, current limitation (CL), and breakdown torque limitation. The limited torque reference is denoted by \(\overline{\tau}_\mathrm{M}^\mathrm{ref}\) and the rated stator flux by \(\psi_\mathrm{s}^\mathrm{nom}\). The parameter \(k_\mathrm{u}\) is the voltage utilization factor.

Figure 1: Reference generation for induction machines, including field weakening, current limitation (CL), and breakdown torque limitation. The limited torque reference is denoted by \(\overline{\tau}_\mathrm{M}^\mathrm{ref}\) and the rated stator flux by \(\psi_\mathrm{s}^\mathrm{nom}\). The parameter \(k_\mathrm{u}\) is the voltage utilization factor.

For Synchronous Machines

For synchronous machines, the motulator.drive.control.sm.ReferenceGenerator class implements the optimal reference generation that can be used both with current-vector control and flux-vector control. Figure 2 illustrates this method, including field weakening, maximum-torque-per-ampere (MTPA), maximum-power-per-voltage (MTPV), and current limitation (CL) [Awan et al., 2018, Meyer and Böcker, 2006]. Figure 3 shows an example of the optimal reference characteristics for a 5.6-kW permanent-magnet synchronous reluctance machine (PM-SyRM). See also the MTPV and MTPA Conditions document and the 5.6-kW saturated PM-SyRM, FVC example for more details.

Note that the reference generation of flux-vector control is simpler than that of current-vector control, since the two-dimensional transformation to the current reference is avoided. For simplicity, we compute this transformation to the current vector using the root-finding method, while other approaches such as a two-dimensional lookup table could be used.

Figure 2: Optimal reference generation for synchronous machines, including field weakening, maximum-torque-per-ampere (MTPA), maximum-power-per-voltage (MTPV), and current limitation (CL). These are single-dimensional lookup tables, see the example in Figure 2. Two-dimensional transformation to the current reference is needed only in the case of current-vector control.

Figure 2: Optimal reference generation for synchronous machines, including field weakening, maximum-torque-per-ampere (MTPA), maximum-power-per-voltage (MTPV), and current limitation (CL). These are single-dimensional lookup tables, see the example in Figure 3. Two-dimensional transformation to the current reference is needed only in the case of current-vector control.

Figure 3: Example of optimal reference characteristics for a 5.6-kW PM-SyRM.

Figure 3: Example of optimal reference characteristics for a 5.6-kW PM-SyRM.