d-q Voltage Limiter

Limit voltage in the rotor direct-quadrature reference frame

expand all in page

Libraries:
Simscape / Electrical / Control / Protection

Description

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

Equations

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

That is,

$\sqrt{v_{d}^{2} + v_{q}^{2}} \leq V_{p h_m a x}$

where:

v_d is the d-axis voltage.
v_q is the q-axis voltage.
V_{ph_max} is the maximum phase voltage.

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

$v_{1}^{s a t} = \min (\max (v_{1}^{u n s a t}, - V_{p h_m a x}), V_{p h_m a x})$

and

$v_{2}^{s a t} = \min (\max (v_{2}^{u n s a t}, - V_{2_\max}), V_{2_\max}),$

where:

$v_{2_m a x} = \sqrt{{(V_{p h_m a x})}^{2} - {(v_{1}^{s a t})}^{2}}$
v₁ is voltage of the prioritized axis.
v₂ is voltage of the nonprioritized axis.

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

$v_{d}^{s a t} = \min (\max (v_{d}^{u n s a t}, - V_{d_\max}), V_{d_\max})$

and

$v_{q}^{s a t} = \min (\max (v_{q}^{u n s a t}, - V_{q_\max}), V_{q_\max}),$

where:

$V_{d_m a x} = \frac{V_{p h_m a x} | v_{d}^{u n s a t} |}{\sqrt{{(v_{d}^{u n s a t})}^{2} + {(v_{q}^{u n s a t})}^{2}}}$
$V_{q_m a x} = \frac{V_{p h_m a x} | v_{q}^{u n s a t} |}{\sqrt{{(v_{d}^{u n s a t})}^{2} + {(v_{q}^{u n s a t})}^{2}}}$

Examples

Load Side Converter Control

Control the RMS voltage in a load-side converter. The load is provided by a three-phase series RL element. The Control subsystem uses a PI-based cascade control structure with two control loops, an outer voltage control loop and an inner current control loop. The simulation uses step references. The Scopes subsystem contains scopes that allow you to see the simulation results.

Open Model

Three-Phase PMSM Traction Drive

Control the rotor speed in a permanent magnet synchronous machine (PMSM) based electrical-traction drive. A high-voltage battery feeds the FEM-Parameterized PMSM block through a controlled three-phase converter. A Rotational Friction block provides the load. The position and speed information are obtained by using a high-fidelity resolver. The PMSM controller subsystem includes a cascade control structure which has an outer speed-control loop and two inner current-control loops. During the 0.25 seconds simulation, the rotor speed demand is ramped-up from 0 to 1000 rpm.

Open Model

Synchronous Machine State-Space Control

Control currents in a synchronous machine (SM) based traction drive using state-space control. A high-voltage battery feeds the SM through a controlled three-phase converter for the stator windings and through a controlled two-quadrant chopper for the rotor winding. An ideal angular velocity source provides the load. The SM operates below the base speed. At each sample instant, the torque request is converted to relevant current references using the zero d-axis control approach. A state-feedback controller controls the currents in the rotor reference frame. A Luenberger observer obtains the velocity-dependent feedforward pre-control terms. The simulation uses several torque steps in both motor and generator modes. The task scheduling is implemented as a Stateflow® state machine. The Scopes subsystem contains scopes that allow you to see the simulation results.

Open Model

Ports

Input

expand all