Limit voltage in the rotor direct-quadrature reference frame

**Library:**Simscape / Electrical / Control / Protection

The d-q Voltage Limiter block implements a voltage limiter in the rotor
direct-quadrature (*d*-*q*) reference frame.

The figure shows the circle that limits the
*d*-*q* voltage vector.

That is,

$$\sqrt{{v}_{d}^{2}+{v}_{q}^{2}}\le {V}_{ph\_max}$$

where:

*v*is the_{d}*d*-axis voltage.*v*is the_{q}*q*-axis voltage.*V*is the maximum phase voltage._{ph_max}

Three cases of voltage limiting are possible:

*d*-axis prioritization*q*-axis prioritization*d*-*q*equivalence

If one axis is prioritized over the other axis, the constrained or saturated voltages are defined as

$${v}_{1}^{sat}=\mathrm{min}\left(\mathrm{max}\left({v}_{1}^{unsat},-{V}_{ph\_max}\right),{V}_{ph\_max}\right)$$

and

$${v}_{2}^{sat}=\mathrm{min}\left(\mathrm{max}\left({v}_{2}^{unsat},-{V}_{2\_\mathrm{max}}\right),{V}_{2\_\mathrm{max}}\right),$$

where:

$${v}_{2\_max}=\sqrt{{\left({V}_{ph\_max}\right)}^{2}-{\left({v}_{1}^{sat}\right)}^{2}}$$

*v*is voltage of the prioritized axis._{1}*v*is voltage of the nonprioritized axis._{2}

If neither axis is prioritized, the constrained voltages are defined as

$${v}_{d}^{sat}=\mathrm{min}\left(\mathrm{max}\left({v}_{d}^{unsat},-{V}_{d\_\mathrm{max}}\right),{V}_{d\_\mathrm{max}}\right)$$

and

$${v}_{q}^{sat}=\mathrm{min}\left(\mathrm{max}\left({v}_{q}^{unsat},-{V}_{q\_\mathrm{max}}\right),{V}_{q\_\mathrm{max}}\right),$$

where:

$${V}_{d\_max}=\frac{{V}_{ph\_max}\left|{v}_{d}^{unsat}\right|}{\sqrt{{\left({v}_{d}^{unsat}\right)}^{2}+{\left({v}_{q}^{unsat}\right)}^{2}}}$$

$${V}_{q\_max}=\frac{{V}_{ph\_max}\left|{v}_{q}^{unsat}\right|}{\sqrt{{\left({v}_{d}^{unsat}\right)}^{2}+{\left({v}_{q}^{unsat}\right)}^{2}}}$$