Induction Machine Current Controller

Discrete-time induction machine current PI controller

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Libraries:
Simscape / Electrical / Control / Induction Machine Control

Description

The Induction Machine Current Controller implements discrete-time proportional-integral (PI) based induction machine current control in the rotor d-q reference frame. You typically use the Induction Machine Current Controller in a series of blocks that make up a control structure. For example, to convert the dq0 reference frame output voltage to voltage in an abc reference frame, connect the Induction Machine Current Controller to an Inverse Clarke Transform in the control structure.

Equations

The block uses the backward Euler discretization method.

Two PI current controllers that are implemented in the rotor reference frame produce the reference voltage vector:

$v_d^{ref}=\left(K_{p\_id}+K_{i\_id}\frac{T_{s}z}{z-1}\right)\left(i_d^{ref}-i_d\right)+v_{d\_FF},$

and

$v_q^{ref}=\left(K_{p\_iq}+K_{i\_iq}\frac{T_{s}z}{z-1}\right)\left(i_q^{ref}-i_q\right)+v_{q\_FF},$

where

• $$v_d^{ref}$$, and $$v_q^{ref}$$ are the d-axis and q-axis reference voltages, respectively.

• $$i_d^{ref}$$, and $$i_q^{ref}$$ are the d-axis and q-axis reference currents, respectively.

• $$i_d$$ and $$i_q$$ are the d-axis and q-axis currents, respectively.

• K_{p_id}, and K_{p_iq} are the proportional gains for the d-axis and q-axis controllers, respectively.

• K_{i_id} and K_{i_iq} are the integral gains for the d-axis and q-axis controllers, respectively.

• v_{d_FF}, and v_{q_FF} are the feedforward voltages for the d-axis and q-axis, respectively. The feedforward voltages are obtained from the machine mathematical equations and provided as inputs.

• T_s, is the sample time of the discrete controller.

Voltage Saturation

Saturation is imposed when the stator voltage vector exceeds the voltage phase limit V_{ph_max}:

$\sqrt{v_d^2+v_q^2}\le V_{ph\_max},$

where v_d, and v_q are the d-axis and q-axis voltages, respectively.

In the case of axis prioritization, the voltages v₁ and v₂ are introduced, where:

• For d-axis prioritization — v₁ = v_d and v₂ = v_q.

• For q-axis prioritization —v₁ = v_q and v₂ = v_d.

The constrained (saturated) voltages $$v_1^{sat}$$ and $$v_2^{sat}$$ are obtained as:

$v_1^{sat}=\text{min}\left(\max \left(v_1^{unsat},-V_{ph\_max}\right),V_{ph\_max}\right)$

and

$v_2^{sat}=\text{min}\left(\max \left(v_2^{unsat},-V_{2\_max}\right),V_{2\_max}\right),$

where:

• $$v_1^{unsat}$$ and $$v_2^{unsat}$$ are the unconstrained (unsaturated) voltages.

• v_{2_max} is the maximum value of v₂ that does not exceed the voltage phase limit. The equation that define v_{2_max} is $v_{2\_max}=\sqrt{{\left(V_{ph\_max}\right)}^2-{\left(v_1^{sat}\right)}^2}.$

In the case of d-q equivalence, the direct and quadrature axes have the same priority, and the constrained voltages are:

$v_d^{sat}=\text{min}\left(\max \left(v_d^{unsat},-V_{d\_max}\right),V_{d\_max}\right)$

and

$v_q^{sat}=\text{min}\left(\max \left(v_q^{unsat},-V_{q\_max}\right),V_{q\_max}\right),$

where:

$V_{d\_max}=\frac{V_{ph\_max}\left|v_d^{unsat}\right|}{\sqrt{{(v_d^{unsat})}^2+{(v_q^{unsat})}^2}}$

and

$V_{q\_max}=\frac{V_{ph\_max}\left|v_q^{unsat}\right|}{\sqrt{{(v_d^{unsat})}^2+{(v_q^{unsat})}^2}}.$

Integral Anti-Windup

An anti-windup mechanism is employed to avoid the saturation of the integrator output. In such a situation, the integrator gains become:

$K_{i\_id}+K_{aw\_id}\left(v_d^{sat}-v_d^{unsat}\right)$

and

$K_{i\_iq}+K_{aw\_iq}\left(v_q^{sat}-v_q^{unsat}\right),$

where K_{aw_id}, K_{aw_iq}, and K_{aw_if} are the anti-windup gains for the d-axis, q-axis, and field controllers, respectively.

Assumptions and Limitations

• The plant model for the direct and quadrature axes can be approximated with a first-order system.

Examples

Torque Control in Three-Level Converter-Fed Asynchronous Machine Drive

Control the torque in an asynchronous machine (ASM) based electrical-traction drive. A high-voltage battery feeds the ASM through a three-phase three-level neutral-point clamped controlled converter. The ASM operates in both motoring and generating modes. An ideal angular velocity source provides the load. The Control subsystem uses the field-oriented control strategy to control the flux and torque. The current control is PI-based. A proportional controller regulates the neutral point voltage. The simulation uses several torque steps in both motor and generator modes. The Scopes subsystem contains scopes that allow you to see the simulation results.

• Open Model

Ports

Input

idqRef — Reference currents

vector

Desired d- and q-axis currents for control of the induction machine, in A.

Data Types: single | double

idq — Measured currents

vector

Actual d- and q-axis currents of the controlled induction machine, in A.

Data Types: single | double

vdqFF — Feedforward voltages

vector

Feedforward pre-control voltages, in V.

Data Types: single | double

VphMax — Maximum phase voltage

scalar

Maximum allowable voltage in each phase, in V.

Data Types: single | double

Reset — External reset

scalar

External reset signal (rising edge) for integrators.

Data Types: Boolean

Output

vdqRef — Reference voltages

vector

Desired d- and q-axis voltages for control of the induction machine, in V.

Data Types: single | double

Parameters

Control Parameters

D-axis current proportional gain — d-axis proportional gain

1 (default)

Proportional gain for direct-axis current control.

D-axis current integral gain — d-axis integral gain

100 (default)

Integral gain for direct-axis current control.

D-axis current anti-windup gain — d-axis anti-windup gain

1 (default)

Anti-windup gain for direct-axis current control.

Q-axis current proportional gain — q-axis proportional gain

1 (default)

Proportional gain for quadrature-axis current control.

Q-axis current integral gain — q-axis integral gain

100 (default)

Integral gain for quadrature-axis current control.

Q-axis current anti-windup gain — q-axis anti-windup gain

1 (default)

Anti-windup gain for quadrature-axis current control.

Sample time (-1 for inherited) — Block sample time

-1 (default) | positive scalar

Time, in s, between consecutive block executions. During execution, the block produces outputs and, if appropriate, updates its internal state. For more information, see What Is Sample Time? and Specify Sample Time.

If this block is inside a triggered subsystem, inherit the sample time by setting this parameter to -1. If this block is in a continuous variable-step model, specify the sample time explicitly using a positive scalar.

Axis prioritization — Axis prioritization for voltage limiter

Q-axis (default) | D-axis | D-Q equivalence

Prioritize or maintain the ratio between the d- and q-axes when the block limits voltage.

Enable pre-control voltage — Pre-control voltage

on (default) | off

Enable or disable pre-control voltage.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2017b