JMAG-RT IM

Description

Squirrel Cage Induction Machine block using JMAG-RT model

JMAG-RT model is a look-up table base motor solution for power electronics/system simulators developed by JSOL Corporation. It solves motor differential equations using parameters from look-up tables created by electromagnetic FEA software JMAG-Designer. JMAG, JMAG-Designer and JMAG-RT are registered trademarks of JSOL Corporation (https://www.jmag-international.com/).

Electrical model and equations

In this block, the below equation is used to represent the motor dynamics.

$$v_{s\alpha} = R_s i_{s\alpha} + \frac{d }{dt} \phi_{s\alpha}$$

$$v_{s\beta} = R_s i_{s\beta} + \frac{d }{dt}\phi_{s\beta}$$

$$0 = R_r i_{r\alpha} + \frac{d }{dt} \phi_{r\alpha} - \omega \phi_{r\beta}$$

$$0 = R_r i_{r\beta} + \frac{d }{dt} \phi_{r\beta} - \omega \phi_{r\alpha}$$

Where v_sα is α-axis stator voltage [V], v_sβ is β-axis stator voltage[V], i_sα is α-axis stator current[A], i_sβ is β-axis stator current[A], i_rα is α-axis rotor current[A], i_rβ is β-axis rotor current[A], R_s is stator phase resistance[Ω], R_r is rotor resistance[Ω], ω is rotor speed in electrical angle[rad / sec], ϕ_sα is α-axis stator flux[Wb], ϕ_sβ is β-axis stator flux[Wb], ϕ_rα is α-axis rotor flux[Wb], ϕ_rβ is β-axis rotor flux[Wb],

The magnetic flux in induction motors can be represented using the inductance as follows.

$$\phi_{s\alpha} = L_s i_{s\alpha} + L_m i_{r\alpha}$$

$$\phi_{s\beta} = L_s i_{s\beta} + L_m i_{r\beta}$$

$$\phi_{r\alpha} = L_r i_{r\alpha} + L_m i_{s\alpha}$$

$$\phi_{r\beta} = L_r i_{r\beta} + L_m i_{s\beta}$$

Where L_s is the stator self-inductance[H], L_r is the rotor self-inductance[H], L_m is the mutual inductance across from the stator to the rotor[H].

Information

In the JMAG-RT IM block, the motor differential equation will be solved using a module developed by JSOL Corporation. For details, contact the JSOL Corporation (https://www.jmag-international.com/contact/) or a distributor in your country.

Electromechanical equations

Electro-magnetic torque:

$$T_e = 1.5 * N_{ pp}*(i_{s\beta} * i_{r\alpha} - i_{s\alpha} * i_{r\beta} )$$

Mechanical rotational speed $\Omega$:

$$J \frac{d\Omega}{ dt} = T_e - B \Omega$$

Iron loss modeling

Following iron loss types are available:

• [FundamentalCurrentBaseIronLoss]: Use iron loss tables created using the sinusoidal current in JMAG-Designer.
• [HarmonicsCurrentBaseIronLoss]: Use equivalent iron loss resistance tables to capture the iron loss components due to the carrier frequency and spatial harmonics.
• [UserDefinedIronLoss]: Uses iron loss tables added to JMAG-RT models from CSV files created by the user.

AC copper loss modeling

AC copper loss is a dissipation of electrical energy generated in copper winding due to the skin effect and proximity effects caused by the high-frequency current. Following AC copper loss types are available:

• [GeometryBaseACCopperLoss]: Use the motor slot geometry information in the JMAG-RT model to calculate the AC Copper loss.
• [UserDefinedACCopperLoss]: Use AC copper loss tables added to JMAG-RT models from CSV files created by the user.

Information

When AC copper loss is not used, the "copper loss" scope outputs only DC copper loss, i.e. a sum of the product of the phase resistance and the squared phase current. When AC copper loss is used, the "copper loss" scope outputs a sum of AC coper loss and DC copper losses

Skew

Skew is a technique used in the machine design process to twist motor geometry and reduce ripples in the current and the torque. The following skew types are available:

• [LinearSkew]
• [VSkew]
• [StepSkew]

Correction factors

Correction factors are applied to the input motor model in the following manner.

$$L_{new} = K_1 * K_5 * (\frac{N_{1}}{N})^2 * L(I_{new})$$

$$\phi_{new} = K_2 * K_5 * \frac{N_{1}}{N} * \phi$$

$$T_{new} = K_3 * K_5 * T(I_{new})$$

$$I_{new} = \frac{N_{2}}{N}$$

Where $\phi$ is total magnetic flux linkage [wb], $K_1$ is a correction factor for inductance, $K_2$ is a correction factor for total magnetic flux linkage, $K_3$ is a correction factor for torque, $K_5$ is a correction factor for steel core, $N$ is the original number of turns, $N_1$ is a new number of turns used to modify the inductance value and total magnetic flux linkage value as a function number of turns, and $N_2$ is a new number of turns used to modify the current used to refer to the look-up tables.

Thermal modeling

The phase resistance temperature dependency in the JMAG-RT IM block is modeled in the following manner.

$$R'_s = R_s (1+\alpha (T_{cnow} - T_{cbase}))$$

Where $\alpha$ is temperature correction factor for winding [ppm / $^\circ C$ ],
$T_{cnow}$ is the coil temperature at the current step [$^\circ C$ ],
$T_{cbase}$ is the base coil temperature for windings[$^\circ C$ ]

Information

Temperature correction factors and base temperatures are defined when the JMAG-RT model is created and stored in the JMAG-RT model. The temperature at the winding thermal port is the current temperature in the above equation. The losses dissipated in the machine at every step are available as the core losses and copper losses from the core thermal port and the winding thermal port respectively.

Library

Electrical > Motors

Pins

Name	Description
Pin_A	Phase A (Electrical)
Pin_B	Phase B (Electrical)
Pin_C	Phase C (Electrical)
Pin_R	Rotor (Rotational Mechanical)
Pin_Angle	Rotor Angle in radians, electrical angle (Control)
Pin_Pcore	Core (Thermal)
Pin_Pwinding	Winding (Thermal)
Pin_Pcage	Cage (Thermal)

Parameters

Name	Description
IronLossType	Iron loss type
UseFilterInductance	Use filter inductance (Active only when "HarmonicsCurrentBaseIronLoss" is selected as the iron loss type.)
FilterInductanceValue	Filter inductance value (Active only when "UseFilterInductance" is selected.)
ACCopperLossType	ACCopper Loss type (Available options : "GeometryBaseACCopperLoss", "UserDefinedACCopperLoss")
RotorSkewType	Rotor skew type (Available options : "LinearSkew", "VSkew","StepSkew")
StatorSkewType	Stator skew type (Available options : "LinearSkew", "VSkew","StepSkew")
RotorSkewAngle	Rotor skew angle [deg]
StatorSkewAngle	Stator skew angle [deg]
RotorSkewSteps	Rotor skew steps (Active only when the step skew is selected for the rotor.)
StatorSkewSteps	Stator skew steps (Active only when the step skew is selected for the stator.)
UseCorrection	Correction factor checkbox
CoefInd	Correction factor for inductance
CoefFlux	Correction factor for total flux linkage
CoefTorque	Correction factor for torque
CoefMat	Correction factor for steel materials
TurnCorr1	Correction factor for number of turns #1
TurnCorr2	Correction factor for number of turns #2
InterpolationType	Interpolation type (Linear or Cubic)
TemperatureCorrection	A flag to activate temperature correction
RttFilePath	Path to the RTT library (String)
J	Rotor Inertia [kg.m²]
B	Rotor Friction Coefficient [N.m/(rad/s)]
InitialSpeed	Rotor initial speed [ rad/s]
Rs	Phase resistance [Ohm]
NPP	Number of pole pairs
AverageLossCalcFreq	Average Loss Calculation Frequency [Hz]