IM SM Section

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.

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 Configuration
Machine Model Settings
Name		Specifies the name of the machine model.
Description		Specifies a description for the machine model.
	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	R_s	Ω	0.6	Stator winding resistance of phases A, B, and C.
Stator Leakage Inductance	L_ls	H	0.00035	Stator winding leakage inductance of phases A, B, and C.
Mutual Inductance	L_m	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	T_s	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	T_sm	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.

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	R_s	Ω	0.6	Stator winding resistance of phases A, B, and C.
Stator Leakage Inductance	L_ls	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	L_md	H	0.00097153	Direct-axis magnetizing inductance.
Stator Q Magnetizing Inductance	L_mq	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	T_s	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	T_sm	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 Reserved are not used.

Channel Name	Symbol	Type	Units	Default Value	Description

Channel Name	Symbol	Type	Units	Description
Stator Current Phase A	I_sa	Output	A	Phase A stator current.
Stator Current Phase B	I_sb	Output	A	Phase B stator current.
Stator Current Phase C	I_sc	Output	A	Phase C stator current.
Stator Direct Axis Current	I_sd	Output	A	Direct-axis stator current, as defined by the rotor reference frame.
Stator Quadrature Axis Current	I_sq	Output	A	Quadrature-axis stator current, as defined by the rotor reference frame.
Stator Direct Axis Voltage	V_sd	Output	V	Direct-axis stator voltage, as defined by the rotor reference frame.
Stator Quadrature Axis Voltage	V_sq	Output	V	Quadrature-axis stator voltage, as defined by the rotor reference frame.
Stator Direct Axis Flux	Φ_sd	Output	Wb	Direct-axis stator flux, as defined by the rotor reference frame.
Stator Quadrature Axis Flux	Φ_sq	Output	Wb	Quadrature-axis stator flux, as defined by the rotor reference frame.
Rotor Current Phase A	I'_ra	Output	A	Phase A rotor current referred to the stator.
Rotor Current Phase B	I'_rb	Output	A	Phase B rotor current referred to the stator.
Rotor Current Phase C	I'_rc	Output	A	Phase C rotor current referred to the stator.
Rotor Direct Axis Current	I'_rd	Output	A	Direct-axis rotor current referred to the stator, as defined by the rotor reference frame.
Rotor Quadrature Axis Current	I'_rq	Output	A	Quadrature-axis rotor current referred to the stator, as defined by the rotor reference frame.
Rotor Direct Axis Voltage	V'_rd	Output	V	Direct-axis rotor voltage referred to the stator, as defined by the rotor reference frame.
Rotor Quadrature Axis Voltage	V'_rq	Output	V	Quadrature-axis rotor voltage referred to the stator, as defined by the rotor reference frame.
Rotor Direct Axis Flux	Φ'_rd	Output	Wb	Direct-axis rotor flux referred to the stator, as defined by the rotor reference frame.
Rotor Quadrature Axis Flux	Φ'_rq	Output	Wb	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	Description
Stator Current Phase A	I_sa	Output	A	Phase A stator current.
Stator Current Phase B	I_sb	Output	A	Phase B stator current.
Stator Current Phase C	I_sc	Output	A	Phase C stator current.
Stator Direct Axis Current	I_sd	Output	A	Direct-axis stator current, as defined by the rotor reference frame.
Stator Quadrature Axis Current	I_sq	Output	A	Quadrature-axis stator current, as defined by the rotor reference frame.
Stator Direct Axis Voltage	V_sd	Output	V	Direct-axis stator voltage, as defined by the rotor reference frame.
Stator Quadrature Axis Voltage	V_sq	Output	V	Quadrature-axis stator voltage, as defined by the rotor reference frame.
Stator Direct Axis Flux	Φ_sd	Output	Wb	Direct-axis stator flux, as defined by the rotor reference frame.
Stator Quadrature Axis Flux	Φ_sq	Output	Wb	Quadrature-axis stator flux, as defined by the rotor reference frame.
Damper Kd Current	I'_kd	Output	A	Direct-axis damper winding current, referred to the stator.
Field Current	I'_f	Output	A	Field winding current, referred to the stator.
Rotor Field Voltage	V_rf	Output	V	Field voltage, referred to the rotor.
Damper Kd Flux	ψ'_kd	Output	H	Direct-axis damper winding flux, referred to the stator.
Field Flux	ψ'_f	Output	H	Field winding magnetic flux, referred to the stator.
Rotor Field Current	I_rf	Output	A	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, θ_r. 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 A_d, B_d, and C are defined as:

(4)

(5)

(6)

where T_s is the Applied Solver Timestep and I_d 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.

where ω is the rotational speed of the reference frame and ω_r is the rotational speed of the electrical rotor frame. The Squirrel-Cage Induction Machine is modeled in the rotor reference frame, meaning that ω = ω_r. 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.

Torque Equation

For both machine types, the electromagnetic torque is described by equation , where Ψ is the flux linkage.

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.