JMAG-RT WFSM

Symbol

Description

Three-phase Wound Field Synchronous Machine(WFSM) 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.

$v_a = R_s i_a + \frac{d}{dt} (L_{aa} i_a + L_{ab} i_b + L_{ac} i_c + L_{af} i_f) + \frac{d }{dt} \phi_f \sin{(\omega_r t)}$

$v_b = R_s i_b + \frac{d}{dt} (L_{ba} i_a + L_{bb} i_b + L_{bc} i_c + L_{bf} i_f) + \frac{d }{dt}\phi_f \sin{(\omega_r t - \frac{2 \pi }{3})}$

$v_c = R_s i_c + \frac{d}{dt} (L_{ca} i_a + L_{cb} i_b + L_{cc} i_c + L_{cf} i_f) + \frac{d }{dt} \phi_f \sin{(\omega_r t + \frac{2 \pi }{3})}$

$v_f = R_f i_f + \frac{d}{dt} (L_{fa} i_a + L_{fb} i_b + L_{fc} i_c + L_{ff} i_f)$

where ( $L_{aa}$ , $L_{ab}$ , $L_{ac}$ ,..., $L_{ff}$ ) are the inductances depending on the 3-phase current and the rotor DC field current, $\phi_f$ is the field magnetic flux linkage supplied from the DC field winding, and $\omega_r$ is the electrical speed of the rotor field.

Information

In the JMAG-RT WFSM 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:
A torque lookup table in the input RTT file will be used for the output torque.

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

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

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.

AC copper loss modeling

AC copper loss is a dissipation of electrical energy generated in copper winding due to the skin effect and the proximity effect 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

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

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.

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

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_F	Rotor DC Field (Electrical)
Pin_R	Rotor (Rotational Mechanical)
Pin_Angle	Rotor Angle in radians, electrical angle (Control)
Pin_Pcore	Core (Thermal)
Pin_Pwinding	Winding (Thermal)

Parameters

Name	Description
IronLossType	Iron loss type
ACCopperLossType	ACCopper Loss type (Available options : "GeometryBaseACCopperLoss", "UserDefinedACCopperLoss")
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
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]
ConnectionType	Connection Type (Star or Delta)
Rs	Phase resistance [Ohm]
Rf	Field resistance [Ohm]
Offset	Angle to align the rotor magnet to A-phase [Mech.deg]
AverageLossCalcFreq	Average Loss Calcualtion Frequency [Hz]