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.
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.
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.
Machine Configuration
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.
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.
Machine Configuration
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.
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.
Channel Name
Symbol
Type
Units
Default Value
Description
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.
Channel Name
Symbol
Type
Units
Default Value
Description
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.
(1)
(2)
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:
(3)
where n is the timestep index and the coefficient matrices Ad, Bd, and C are defined as:
(4)
(5)
(6)
where Ts is the Applied Solver Timestep and Id is the identity matrix. The state variable matrices and output matrices referenced in equations (3) through 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.