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The Induction Machine / Synchronous Machine (IM SM) model can simulate either a Squirrel-Cage Induction Machine (SCIM) or a Round Rotor Synchronous Machine (RRSM), each with integrated resolver and encoder models. The machines can operate in both motoring mode, when the mechanical torque is positive, and generating mode when the mechanical torque is negative. An optional zero-sequence model can be included to allow the user to model the system as unbalanced.

The Squirrel-Cage Induction Machine model simulates the stator winding and squirrel-cage rotor of a three-phase induction machine. The Round Rotor Synchronous Machine model simulates the machine stator, the field winding, and up to three damper windings--one along the d-axis and two more along the q-axis.

Page Content

Table of Contents
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Configuration Page

In the System Explorer window configuration tree, expand the Power Electronics Add-On custom device and select Circuit Model >> IM SM to display this page and configure the IM SM machine model.

General Parameters

The following parameters are available for any selected Machine Type. They are configurable at edit-time only.

Machine Model Settings

Name

Specifies the name of the machine model.

Description

Specifies a description for the machine model.

Machine Configuration

Default Value

Description

Machine Type

Squirrel-Cage Induction Machine

Choose from one of the following types:

  • Squirrel-Cage Induction Machine

  • Round Rotor Synchronous Machine

Input Mapping Configuration

Use the Input Mapping Configuration to route signals to the Voltage Phase A, Voltage Phase B, and Voltage Phase C inputs of the machine model. In the case of the RRSM, an input is also provided for the Field Voltage of the rotor. Available routing options may vary depending on the selected Hardware Configuration.

Info

The Field Voltage supplied to the RRSM must be greater than 0V.

Group

Specifies the group that will be routed to the input voltages of the machine. The available routing options are defined by the selected Hardware Configuration, however it is typical to see the following options by default:

  • Measurements - eHS circuit model measurements

Element

Specifies the index of the measurement in the group that has been selected as the input voltage of the machine.

Machine-Specific Parameters

Certain parameters of the IM SM page are populated based on the selected Machine Type. Parameters are configurable at edit-time only.

Expand
titleSquirrel-Cage Induction Machine

Machine Configuration

Symbol

Units

Default Value

Description

Enable

True

Indicates whether the selected machine model is enabled. When a machine is enabled, it computes and generates output data at the specified Applied Solver Timestep.

Because up to four machines can be simulated at once, the number of enabled machines impacts the minimum achievable time step of each machine.

Stator Resistance

Rs

Ω

0.6

Stator winding resistance of phases A, B, and C.

Stator Leakage Inductance

Lls

H

0.00035

Stator winding leakage inductance of phases A, B, and C.

Mutual Inductance

Lm

H

0.62

Stator-rotor mutual (magnetizing) inductance of phases A, B, and C.

Rotor Resistance

R'r

Ω

0.62

Equivalent rotor winding resistance of phases A, B, and C, referred to the stator.

Rotor Leakage Inductance

L'lr

H

0.00547

Equivalent rotor winding leakage inductance of phases A, B, and C, referred to the stator.

Pole Pairs

PP

2

Number of machine pole pairs.

Initial Speed

ω0

RPM

0

Initial speed of the machine.

Applied Solver Timestep

Ts

s

4.81E-7

The timestep at which the machine model executes.

New outputs are computed by the FPGA machine model at each timestep. If Optimize Solver Timestep is enabled in the Circuit Model page, the Applied Solver Timestep is automatically set to an optimal value and cannot be edited.

Minimum Solver Timestep

Tsm

s

4.81E-7

The minimum achievable timestep at which the machine model can execute when all four machines are enabled.  The minimum achievable timestep is a function of the number of enabled machines.

Zero Sequence

Don't Include

When Include is selected, the Zero-Sequence Resistance and Zero-Sequence Inductance parameters are enabled to include a Zero Sequence Model. See Including a Zero Sequence Model for more information.

Zero-Sequence Resistance

R0

Ω

0.0029069

Zero-sequence stator winding resistance

This parameter is enabled when Zero Sequence is set to Included.

Zero-Sequence Inductance

L0

H

0.00030892

Zero-sequence stator winding inductance

This parameter is enabled when Zero Sequence is set to Included.

Expand
titleRound Rotor Synchronous Machine

Machine Configuration

Symbol

Units

Default Value

Description

Enable

True

Indicates whether the selected machine model is enabled. When a machine is enabled, it computes and generates output data at the specified Applied Solver Timestep.

Because up to four machines can be simulated at once, the number of enabled machines impacts the minimum achievable time step of each machine.

Pole Pairs

PP

2

Number of machine pole pairs.

Initial Speed

ω0

RPM

0

Initial speed of the machine.

Stator Resistance

Rs

Ω

0.6

Stator winding resistance of phases A, B, and C.

Stator Leakage Inductance

Lls

H

0.00035

Stator winding leakage inductance of phases A, B, and C.

Damper Kd Resistance

R’kd

Ω

0.0664

Direct-axis damper winding resistance, referred to the stator.

Damper Kq1 Resistance

R’kq1

Ω

0.0292

Quadrature-axis damper winding 1 resistance, referred to the stator.

Damper Kq2 Resistance

R’kq2

Ω

0.007907

Quadrature-axis damper winding 2 resistance, referred to the stator.

Damper Leakage Inductance

L’lkd

H

0.001387

Direct-axis damper winding leakage inductance, referred to the stator.

Damper Kq1 Leakage Inductance

L’lkq1

H

0.0006896

Quadrature-axis damper winding 1 leakage inductance, referred to the stator.

Damper Kq2 Leakage Inductance

L’lkq2

H

0.002477

Quadrature-axis damper winding 2 leakage inductance, referred to the stator.

Stator D Magnetizing Inductance

Lmd

H

0.00097153

Direct-axis magnetizing inductance.

Stator Q Magnetizing Inductance

Lmq

H

0.0032164

Quadrature-axis magnetizing inductance.

Field Resistance

R’f

Ω

0.00059013

Rotor field winding resistance, referred to the stator.

Field Leakage Inductance

L’lf

H

0.00030712

Rotor field winding leakage inductance, referred to the stator.

Applied Solver Timestep

Ts

s

4.81E-7

The timestep at which the machine model executes.

New outputs are computed by the FPGA machine model at each timestep. If Optimize Solver Timestep is enabled in the Circuit Model page, the Applied Solver Timestep is automatically set to an optimal value and cannot be edited.

Minimum Solver Timestep

Tsm

s

4.81E-7

The minimum achievable timestep at which the machine model can execute when all four machines are enabled.  The minimum achievable timestep is a function of the number of enabled machines.

Zero Sequence

Don't Include

When Include is selected, the Zero-Sequence Resistance and Zero-Sequence Inductance parameters are enabled to include a Zero Sequence Model. See Including a Zero Sequence Model for more information.

Zero-Sequence Resistance

R0

Ω

0.0029069

Zero-sequence stator winding resistance.

This parameter is enabled when Zero Sequence is set to Included.

Zero-Sequence Inductance

L0

H

0.00030892

Zero-sequence stator winding inductance.

This parameter is enabled when Zero Sequence is set to Included.

Section Channels

The list of available channels in the IM SM section depends on the selected Machine Type. Channel values can be modified dynamically at execution time, and channels named Reservedare not used.

Expand
titleSquirrel-Cage Induction Machine

Channel Name

Symbol

Type

Units

Default Value

Description

Stator Current Phase A

Isa

Output

A

0

Phase A stator current.

Stator Current Phase B

Isb

Output

A

0

Phase B stator current.

Stator Current Phase C

Isc

Output

A

0

Phase C stator current.

Stator Direct Axis Current

Isd

Output

A

0

Direct-axis stator current, as defined by the rotor reference frame.

Stator Quadrature Axis Current

Isq

Output

A

0

Quadrature-axis stator current, as defined by the rotor reference frame.

Stator Direct Axis Voltage

Vsd

Output

V

0

Direct-axis stator voltage, as defined by the rotor reference frame.

Stator Quadrature Axis Voltage

Vsq

Output

V

0

Quadrature-axis stator voltage, as defined by the rotor reference frame.

Stator Direct Axis Flux

Φsd

Output

Wb

0

Direct-axis stator flux, as defined by the rotor reference frame.

Stator Quadrature Axis Flux

Φsq

Output

Wb

0

Quadrature-axis stator flux, as defined by the rotor reference frame.

Rotor Current Phase A

I'ra

Output

A

0

Phase A rotor current referred to the stator.

Rotor Current Phase B

I'rb

Output

A

0

Phase B rotor current referred to the stator.

Rotor Current Phase C

I'rc

Output

A

0

Phase C rotor current referred to the stator.

Rotor Direct Axis Current

I'rd

Output

A

0

Direct-axis rotor current referred to the stator, as defined by the rotor reference frame.

Rotor Quadrature Axis Current

I'rq

Output

A

0

Quadrature-axis rotor current referred to the stator, as defined by the rotor reference frame.

Rotor Direct Axis Voltage

V'rd

Output

V

0

Direct-axis rotor voltage referred to the stator, as defined by the rotor reference frame.

Rotor Quadrature Axis Voltage

V'rq

Output

V

0

Quadrature-axis rotor voltage referred to the stator, as defined by the rotor reference frame.

Rotor Direct Axis Flux

Φ'rd

Output

Wb

0

Direct-axis rotor flux referred to the stator, as defined by the rotor reference frame.

Rotor Quadrature Axis Flux

Φ'rq

Output

Wb

0

Quadrature-axis rotor flux referred to the stator, as defined by the rotor reference frame.

Expand
titleRound Rotor Synchronous Machine

Channel Name

Symbol

Type

Units

Default Value

Description

Stator Current Phase A

Isa

Output

A

0

Phase A stator current.

Stator Current Phase B

Isb

Output

A

0

Phase B stator current.

Stator Current Phase C

Isc

Output

A

0

Phase C stator current.

Stator Direct Axis Current

Isd

Output

A

0

Direct-axis stator current, as defined by the rotor reference frame.

Stator Quadrature Axis Current

Isq

Output

A

0

Quadrature-axis stator current, as defined by the rotor reference frame.

Stator Direct Axis Voltage

Vsd

Output

V

0

Direct-axis stator voltage, as defined by the rotor reference frame.

Stator Quadrature Axis Voltage

Vsq

Output

V

0

Quadrature-axis stator voltage, as defined by the rotor reference frame.

Stator Direct Axis Flux

Φsd

Output

Wb

0

Direct-axis stator flux, as defined by the rotor reference frame.

Stator Quadrature Axis Flux

Φsq

Output

Wb

0

Quadrature-axis stator flux, as defined by the rotor reference frame.

Damper Kd Current

I'kd

Output

A

0

Direct-axis damper winding current, referred to the stator.

Field Current

I'f

Output

A

0

Field winding current, referred to the stator.

Rotor Field Voltage

Vrf

Output

V

0

Field voltage, referred to the rotor.

Damper Kd Flux

ψ'kd

Output

H

0

Direct-axis damper winding flux, referred to the stator.

Field Flux

ψ'f

Output

H

0

Field winding magnetic flux, referred to the stator.

Rotor Field Current

Irf

Output

A

0

Field winding current, referred to the rotor.

Model Description

Reference Frame Transformation

A sine-based Park transformation, described below, is applied to the three-phase (abc) signals to obtain a dq0 rotating reference frame. The rotating frame is positioned 90 degrees behind the phase A axis, such that the q axis is aligned with phase A at t = 0. Because both machine types are modeled in the rotor reference frame, the value of the angle θ is equivalent to the rotor electrical angle, θr. If the Zero Sequence parameter is set to Don’t Include, the V0 term is not used.

Mathblock
anchorDQTransform
alignmentcenter
--uriencoded--\left[\begin%7Barray%7D%7Bl%7D
%7BV_%7Bq%7D%7D \\
%7BV_%7Bd%7D%7D \\
%7BV_%7B0%7D%7D
\end%7Barray%7D\right]=\frac%7B2%7D%7B3%7D\left[\begin%7Barray%7D%7Bccc%7D
%7B\cos (\theta)%7D & %7B\cos \left(\theta-\frac%7B2 \pi%7D%7B3%7D\right)%7D & %7B\cos \left(\theta+\frac%7B2 \pi%7D%7B3%7D\right)%7D \\
%7B\sin (\theta)%7D & %7B\sin \left(\theta-\frac%7B2 \pi%7D%7B3%7D\right)%7D & %7B\sin \left(\theta+\frac%7B2 \pi%7D%7B3%7D\right)%7D \\
%7B\frac%7B1%7D%7B2%7D%7D & %7B\frac%7B1%7D%7B2%7D%7D & %7B\frac%7B1%7D%7B2%7D%7D
\end%7Barray%7D\right]\left[\begin%7Barray%7D%7Bl%7D
%7BV_%7Ba%7D%7D \\
%7BV_%7Bb%7D%7D \\
%7BV_%7Bc%7D%7D
\end%7Barray%7D\right]
Mathblock
anchorInverseDQTransform
alignmentcenter
--uriencoded--\left[\begin%7Barray%7D%7Bc%7D
%7BV_%7Ba%7D%7D \\
%7BV_%7Bb%7D%7D \\
%7BV_%7Bc%7D%7D
\end%7Barray%7D\right]=\left[\begin%7Barray%7D%7Bccc%7D
%7B\cos (\theta)%7D & %7B\sin (\theta)%7D & %7B1%7D \\
%7B\cos \left(\theta-\frac%7B2 \pi%7D%7B3%7D\right)%7D & %7B\sin \left(\theta-\frac%7B2 \pi%7D%7B3%7D\right)%7D & %7B1%7D \\
%7B\cos \left(\theta+\frac%7B2 \pi%7D%7B3%7D\right)%7D & %7B\sin \left(\theta+\frac%7B2 \pi%7D%7B3%7D\right)%7D & %7B1%7D
\end%7Barray%7D\right]\left[\begin%7Barray%7D%7Bl%7D
%7BV_%7Bq%7D%7D \\
%7BV_%7Bd%7D%7D \\
%7BV_%7B0%7D%7D
\end%7Barray%7D\right]

General Equations

The output currents of the machine windings, I, are calculated using the state-space representation of the machine with the magnetic flux linkages Ψ serving as the state variables. The forward Euler discretization of the state space model can be written as follows:

Mathblock
anchorStateSpace
alignmentcenter
--uriencoded--\begin%7Baligned%7D
\boldsymbol%7B\psi%7D[n+1] &=\boldsymbol%7BA_%7Bd%7D%7D[n] \psi(n)+\boldsymbol%7BB_%7Bd%7D%7D[n] \boldsymbol%7Bu%7D[n] \\
\boldsymbol%7BI%7D[n+1] &=\boldsymbol%7BC%7D[n+1]\boldsymbol%7B\psi%7D[n+1]
\end%7Baligned%7D

where n is the timestep index and the coefficient matrices Ad, Bd, and C are defined as:

Mathblock
anchorCoefficientMatrices_A
alignmentcenter
--uriencoded--\boldsymbol%7BA_%7Bd%7D%7D=T_%7Bs%7D\left(\text%7B-%7D\boldsymbol%7BR L%7D%5e%7B-1%7D-\boldsymbol%7B\Omega%7D\right)+\boldsymbol%7BI_d%7D
Mathblock
anchorCoefficientMatrices_B
alignmentcenter
--uriencoded--\boldsymbol%7BB_%7Bd%7D%7D=T_s \times \boldsymbol%7BI_d%7D
Mathblock
anchorCoefficientMatrices_c
alignmentcenter
\boldsymbol{C}=\boldsymbol{L}^{-1}

where Ts is the Applied Solver Timestep and Id is the identity matrix. The state variable matrices and output matrices referenced in equations

Mathblock ref
anchorStateSpace
through
Mathblock ref
anchorCoefficientMatrices_c
differ depending on the selected machine type. Their respective definitions can be found by expanding the sections below. Note that all rotor variables are referred to the stator, as distinguished by a prime sign. Variables containing the subscript 0 pertain to the zero sequence model, and are not used if Zero Sequence is set to Don’t Include.

Expand
titleSquirrel-Cage Induction Machine
Mathblock
anchor
alignmentcenter
--uriencoded--\boldsymbol%7Bu%7D=\left[\begin%7Barray%7D%7Blllll%7D
%7BV_%7Bsq%7D%7D & %7BV_%7Bsd%7D%7D & %7BV_%7Bs0%7D%7D & %7BV'_%7Brq%7D%7D & %7BV'_%7Brd%7D%7D
\end%7Barray%7D\right]%5e%7Bt%7D
Mathblock
anchor
alignmentcenter
--uriencoded--\boldsymbol%7BI%7D=\left[\begin%7Barray%7D%7Blllll%7D%7BI_%7Bsq%7D%5e%7B%7D%7D & %7BI_%7Bsd%7D%5e%7B%7D%7D & %7BI_%7Bs0%7D%7D & %7BI'_%7Brq%7D%5e%7B%7D%7D & %7BI'_%7Brd%7D%5e%7B%7D%7D\end%7Barray%7D\right]%5e%7Bt%7D
Mathblock
anchor
alignmentcenter
--uriencoded--\boldsymbol%7B\psi%7D=\left[\begin%7Barray%7D%7Blllll%7D%7B\psi_%7Bsq%7D%5e%7B%7D%7D & %7B\psi_%7Bsd%7D%5e%7B%7D%7D & %7B\psi_%7Bs0%7D%7D & %7B\psi'_%7Brq%7D%5e%7B%7D%7D & %7B\psi'_%7Brd%7D%5e%7B%7D%7D\end%7Barray%7D\right]%5e%7Bt%7D
Mathblock
anchor
alignmentcenter
--uriencoded--\boldsymbol%7BR%7D=\left[\begin%7Barray%7D%7Blllll%7D
%7BR_%7Bs%7D%7D & %7BR_%7Bs%7D%7D & %7BR_%7B0%7D%7D & %7BR_%7Br%7D%5e%7B\prime%7D%7D & %7BR_%7Br%7D%5e%7B\prime%7D%7D
\end%7Barray%7D\right]%5e%7Bt%7D
Mathblock
anchor
alignmentcenter
--uriencoded--\boldsymbol%7BL%7D=\left[\begin%7Barray%7D%7Bccccc%7D
%7BL_%7Bls%7D%7D & %7B0%7D & %7B0%7D & %7BL_%7Bm%7D%7D & %7B0%7D \\
%7B0%7D & %7BL_%7Bls%7D%7D & %7B0%7D & %7B0%7D & %7BL_%7Bm%7D%7D \\
 %7B0%7D & %7B0%7D & %7BL_%7B0%7D%7D & %7B0%7D & %7B0%7D\\
%7BL_%7Bm%7D%7D & %7B0%7D & %7B0%7D & %7BL_%7Blr%7D%5e%7B\prime%7D%7D & %7B0%7D \\
%7B0%7D & %7BL_%7Bm%7D%7D & %7B0%7D & %7B0%7D & %7BL_%7Blr%7D%5e%7B\prime%7D%7D
\end%7Barray%7D\right]
Mathblock
anchor
alignmentcenter
--uriencoded--\boldsymbol\Omega=\left[\begin%7Barray%7D%7Bccccc%7D
%7B0%7D & %7B\omega%7D & %7B0%7D & %7B0%7D & %7B0%7D \\
%7B-\omega%7D & %7B0%7D & %7B0%7D & %7B0%7D & %7B0%7D \\
 %7B0%7D & %7B0%7D & %7B0%7D & %7B0%7D & %7B0%7D\\
%7B0%7D & %7B0%7D & %7B0%7D & %7B0%7D & %7B\omega-\omega_%7Br%7D%7D \\
%7B0%7D & %7B0%7D & %7B0%7D & %7B-\left(\omega-\omega_%7Br%7D\right)%7D & %7B0%7D
\end%7Barray%7D\right]

where ω is the rotational speed of the reference frame and ωr is the rotational speed of the electrical rotor frame. The Squirrel-Cage Induction Machine is modeled in the rotor reference frame, meaning that ω = ωr. Furthermore, because the machine rotor is not supplied by an external source, it is always the case that V’rq = V’rd = 0.

The following figure illustrates the equivalent circuits of the Squirrel-Cage Induction Machine model in the dq reference frame.

Expand
titleRound Rotor Synchronous Machine
Mathblock
anchor
alignmentcenter
--uriencoded--\boldsymbol%7Bu%7D=\left[\begin%7Barray%7D%7Blllllll%7D%7BV_%7Bsq%7D%7D & %7BV_%7Bsd%7D%7D & %7BV_%7Bs0%7D%7D & %7BV_%7Bf%7D%5e%7B\prime%7D%7D & %7BV_%7Bkd%7D%5e%7B\prime%7D%7D & %7BV_%7Bkq1%7D%5e%7B\prime%7D%7D & %7BV_%7Bkq2%7D%5e%7B\prime%7D%7D\end%7Barray%7D\right]%5e%7Bt%7D
Mathblock
anchor
alignmentcenter
--uriencoded--\boldsymbol%7BI%7D=\left[\begin%7Barray%7D%7Blllllll%7D%7BI_%7Bsq%7D%7D & %7BI_%7Bsd%7D%7D & %7BI_%7Bs0%7D%7D & %7BI_%7Bf%7D%5e%7B\prime%7D%7D & %7BI_%7Bkd%7D%5e%7B\prime%7D%7D & %7BI_%7Bkq1%7D%5e%7B\prime%7D%7D & %7BI_%7Bkq2%7D%5e%7B\prime%7D%7D\end%7Barray%7D\right]%5e%7Bt%7D
Mathblock
anchor
alignmentcenter
--uriencoded--\boldsymbol%7B\psi%7D=\left[\begin%7Barray%7D%7Blllllll%7D%7B\psi_%7Bsq%7D%7D & %7B\psi_%7Bsd%7D%7D & %7B\psi_%7Bs0%7D%7D & %7B\psi_%7Bf%7D%5e%7B\prime%7D%7D & %7B\psi_%7Bkd%7D%5e%7B\prime%7D%7D & %7B\psi_%7Bkq1%7D%5e%7B\prime%7D%7D & %7B\psi_%7Bkq2%7D%5e%7B\prime%7D%7D\end%7Barray%7D\right]%5e%7Bt%7D
Mathblock
anchor
alignmentcenter
--uriencoded--\boldsymbol%7BR%7D=\left[\begin%7Barray%7D%7Blllllll%7D%7BR_%7Bs%7D%7D & %7BR_%7Bs%7D%7D & %7BR_%7Bs%7D%7D & %7BR_%7Bf%7D%5e%7B\prime%7D%7D & %7BR_%7Bkd%7D%5e%7B\prime%7D%7D & %7BR_%7Bkq1%7D%5e%7B\prime%7D%7D & %7BR_%7Bkq2%7D%5e%7B\prime%7D%7D\end%7Barray%7D\right]%5e%7Bt%7D
Mathblock
anchor
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--uriencoded--\boldsymbol%7BL%7D=\left[\begin%7Barray%7D%7Bccccccc%7D%7BL_%7Bq%7D%7D & %7B0%7D & %7B0%7D & %7B0%7D & %7B0%7D & %7BL_%7Bmq%7D%7D & %7BL_%7Bmq%7D%7D\\
 %7B0%7D & %7BL_%7Bd%7D%7D & %7B0%7D & %7BL_%7Bmd%7D%7D & %7BL_%7Bmd%7D%7D & %7B0%7D & %7B0%7D\\
 %7B0%7D & %7B0%7D & %7BL_%7B0%7D%7D & %7B0%7D & %7B0%7D & %7B0%7D & %7B0%7D\\
 %7B0%7D & %7BL_%7Bmd%7D%7D & %7B0%7D & %7BL_%7Bf%7D%5e%7B\prime%7D%7D & %7BL_%7Bmd%7D%7D & %7B0%7D & %7B0%7D\\
 %7B0%7D & %7BL_%7Bmd%7D%7D & %7B0%7D & %7BL_%7Bmd%7D%7D & %7BL_%7Bkd%7D%5e%7B\prime%7D%7D & 0 & 0\\
 %7BL_%7Bmq%7D%7D & %7B0%7D & %7B0%7D & %7B0%7D & %7B0%7D & %7BL_%7Bkq1%7D%5e%7B\prime%7D%7D & %7BL_%7Bmq%7D%7D\\
 %7BL_%7Bmq%7D%7D & %7B0%7D & %7B0%7D & %7B0%7D & %7B0%7D & %7BL_%7Bmq%7D%7D & %7BL_%7Bkq1%7D%5e%7B\prime%7D%7D\end%7Barray%7D\right]
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--uriencoded--\boldsymbol\Omega=\left[\begin%7Barray%7D%7Bccccccc%7D%7B0%7D & %7B\omega%7D & %7B0%7D & %7B0%7D & %7B0%7D & %7B0%7D & %7B0%7D\\ %7B-\omega%7D & %7B0%7D & %7B0%7D & %7B0%7D & %7B0%7D & 0 & 0\\ %7B0%7D & %7B0%7D & %7B0%7D & %7B0%7D & %7B0%7D & 0 & 0\\ %7B0%7D & %7B0%7D & %7B0%7D & %7B0%7D & %7B0%7D & 0 & 0\\ %7B0%7D & %7B0%7D & %7B0%7D & %7B0%7D & 0 & %7B\omega-\omega_%7Br%7D%7D & 0\\ %7B 0%7D & %7B0%7D & %7B0%7D & 0 & %7B-\left(\omega-\omega_%7Br%7D\right)%7D & 0 & %7B\omega-\omega_%7Br%7D%7D\\ %7B0%7D & %7B0%7D & %7B0%7D & %7B0%7D & 0 & %7B-\left(\omega-\omega_%7Br%7D\right)%7D & 0\end%7Barray%7D\right]

where Vf is the Field Voltage supplied to the machine, ω is the rotational speed of the reference frame and ωr is the rotational speed of the electrical rotor frame. Note that the Field Voltage must be greater than 0V to ensure proper operation of the model. Additionally, the Round Rotor Synchronous Machine is modeled in the rotor reference frame, meaning that ω = ωr.

Torque Equation

For both machine types, the electromagnetic torque is described by equation

Mathblock ref
anchorTorque
, where Ψ is the flux linkage.

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--uriencoded--T_%7Be%7D=\frac%7B3%7D%7B2%7D PP * \left(\psi_%7Bd%7D I_%7Bq%7D-\psi_%7Bq%7D I_%7Bd%7D\right)

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Including a Zero Sequence Model

The Zero Sequence option provides configurable Zero-Sequence Resistance and Zero-Sequence Inductance parameters, allowing the user to model an unbalanced system with an open winding, and resulting in better fidelity. When the zero sequence model is included, all three machine stator currents should be mapped back to the circuit model, rather than two currents as is typically done without the zero sequence model.

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titleSquirrel-Cage Induction Machine

For the Squirrel-Cage Induction Machine, the machine currents can be fed back to the circuit model in either a delta configuration or in a wye with neutral configuration.

Wye with Neutral Connection

The Stator Current Phase A, Stator Current Phase B, and Stator Current Phase C output channels of the machine model are mapped to circuit model sources Ia_scim, Ib_scim, and Ic_scim.

Delta Connection

The Stator Current Phase A, Stator Current Phase B, and Stator Current Phase C output channels of the machine model are mapped to circuit model sources Ia_scim, Ib_scim, and Ic_scim.

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titleRound Rotor Synchronous Machine

For the Round Rotor Synchronous Machine, the machine currents are fed back to the circuit model in a wye with neutral configuration.

Wye with Neutral Connection

The Stator Current Phase A, Stator Current Phase B, and Stator Current Phase C output channels of the machine model are mapped back to circuit model sources Ia_rrsm, Ib_rrsm, and Ic_rrsm. The Field Current channel is mapped to model source If_rrsm.