# JMAG-RT PMSM ## Description

Three-phase Permanent Magnet Synchronous Machine(PMSM) 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 3-phase base motor differential equation is used to represent the motor dynamics.

v_a = R_s i_a + \frac{d}{dt} (L_{aa} i_a + L_{ab} i_b + L_{ac} i_c) + \frac{d }{dt} \phi_m \sin{(\omega_r t)}
v_b = R_s i_b + \frac{d}{dt} (L_{ba} i_a + L_{bb} i_b + L_{bc} i_c) + \frac{d }{dt}\phi_m \sin{(\omega_r t - \frac{2 \pi }{3})}
v_c = R_s i_c + \frac{d}{dt} (L_{ca} i_a + L_{cb} i_b + L_{cc} i_c) + \frac{d }{dt} \phi_m \sin{(\omega_r t + \frac{2 \pi }{3})}

where ($L_{aa}$, $L_{ab}$, $L_{ac}$,..., $L_{cc}$) are the phase inductances depending on the 3-phase current, $\phi_m$ is the permanent magnet flux linkage depending on the 3-phase current, and$\omega_r$ is the electrical speed of the rotor field.

Information

In the JMAG-RT PMSM block, the 3-phase base 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:
When either "SpatialHarmonicDifferential" or "SpatialHarmonicIntegral" is selected as an accuracy type, a torque lookup table in the input RTT file will be used for the output torque. When "LdLqTable" is selected as an accuracy type, a torque equation based on LdLq will be used for the output torque.

Mechanical rotational speed $\Omega$:
The following equation is solved to get mechanical rotational speed.

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

### Model fidelity

In JMAG-RT, multiple fidelity levels are available to represent the motor characteristics. They are displayed as accuracy types in the JMAG-RT block property panel.

• [LdLqTable]: Use JMAG-RT LdLq model. The magnetic saturation can be considered in this model. The slot harmonics are not captured in this model. This model is solved using the motor differential equation using the implicit method.
• [SpatialHarmonicDifferential]: Use the JMAG-RT spatial harmonic (differential) model. The magnetic saturation and the slot harmonics can be considered in this model. This model is solved using the motor differential equation using the implicit method.
• [SpatialHarmonicIntegral]: Use the JMAG-RT spatial harmonic (integral) model. The magnetic saturation and the slot harmonics can be considered in this model. This model is solved using the motor differential equation using the explicit method.

According to JSOL Corp., “Spatial Harmonic Differential” is generally the most recommended to use.

### 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_4 * 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, $K_4$ is a correction factor for magnets, $K_5$ 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

In order to represent the temperature dependency of the motor characteristics, JMAG-RT models the phase resistance and the magnet flux in the following manner.

R'_s = R_s (1+\alpha (T_{cnow} - T_{cbase}))
\phi'_m = \phi_m (1+\frac{\kappa}{100} (T_{mnow} - T_{mbase}))

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

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 and the magnet thermal port are used as 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. JMAG-RT does not calculate the magnet loss.

## 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, mechanical angle (Control)
Pin_Pcore Core (Thermal)
Pin_Pwinding Winding (Thermal)
Pin_Pmagnet Magnet (Thermal)

## Parameters

Name Description
RttFilePath RTT File Path
AccuracyType Accuracy type. (Available options : "LdLqTable", "SpatialHarmonicDifferential","SpatialHarmonicIntegral")
J Rotor Inertia [kg.m²]
ConnectionType Connection Type (Star or Delta)
Rs Phase resistance [Ohm]
Offset Angle to align the rotor magnet to A-phase [Mech.deg]
AverageLossCalcFreq Average Loss Calcualtion Frequency [Hz]
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
CoefMag Correction factor for magnets
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