SM Permanent Magnet Damper Cage - MapleSim Help

SM Permanent Magnet

Permanent magnet synchronous induction machine

Description

The SM Permanent Magnet component models a three phase permanent magnet synchronous induction machine. The resistance and stray inductance of the stator is modeled directly in stator phases, then using space phasor transformation and a rotor-fixed Air Gap model. The resistance and stray inductance of the rotor's squirrel cage is modeled in two axis of the rotor-fixed coordinate system. Permanent magnet excitation is modeled by a constant equivalent excitation current feeding the d-axis.

The following losses are modeled:

 • heat losses in the temperature dependent stator winding resistances
 • optional, when enabled: heat losses in the temperature dependent damper cage resistances
 • friction losses
 • core losses (only eddy current losses, no hysteresis losses)
 • permanent magnet losses

Whether a damper cage is present or not, can be selected with Boolean parameter useDamperCage (default = true).

Connections

 Name Description Modelica ID $\mathrm{flange}$ Shaft flange ${i}_{}$ Damper cage currents ir ${\mathrm{idq}}_{\mathrm{dr}}$ Damper space phasor current / rotor fixed frame idq_dr ${\mathrm{plug}}_{\mathrm{sn}}$ Negative stator plug plug_sn ${\mathrm{plug}}_{\mathrm{sp}}$ Positive stator plug plug_sp $\mathrm{support}$ Support at which the reaction torque is acting support $\mathrm{thermalPort}$ thermalPort

Parameters

General Parameters

 Name Default Units Description Modelica ID ${f}_{s,\mathrm{nom}}$ 50 $\mathrm{Hz}$ Nominal frequency fsNominal ${J}_{r}$ 0.29 $\mathrm{kg}{m}^{2}$ Rotor moment of inertia Jr ${J}_{s}$ ${J}_{r}$ $\mathrm{kg}{m}^{2}$ Stator moment of inertia Js $p$ 2 Number of pole pairs (Integer) p ${T}_{r,\mathrm{oper}}$ 293.15 $K$ Operational temperature of (optional) damper cage TrOperational ${T}_{s,\mathrm{oper}}$ 293.15 $K$ Operational temperature of stator resistance TsOperational ${V}_{s,\mathrm{oc}}$ 293.15 $V$ Open circuit RMS voltage per phase at nominal frequency VsOpenCircuit Use Support Flange $\mathrm{false}$ True (checked) means stator support is enabled useSupport Use Thermal Port $\mathrm{false}$ True (checked) means heat port is enabled useThermalPort

Friction Losses

 Name Default Units Description Modelica ID ${P}_{\mathrm{ref}}$ $0$ $W$ Reference friction losses PRef ${\omega }_{\mathrm{ref}}$ ${\omega }_{\mathrm{nom}}$ $\frac{\mathrm{rad}}{s}$ Reference angular velocity wRef ${p}_{\omega }$ $2$ $V$ Exponent of friction power_w

See Friction for details of the friction loss model.

Permanent Magnet Losses

 Name Default Units Description Modelica ID $c$ $0$ Part of permanent magnet losses at zero current, independent of current c ${I}_{\mathrm{ref}}$ $A$ Reference stator RMS current IRef ${P}_{\mathrm{ref}}$ $0$ $W$ Reference permanent magnet losses at ${I}_{\mathrm{ref}}$ and ${\omega }_{\mathrm{ref}}$ PRef ${p}_{I}$ $2$ Exponent of permanent magnet loss torque w.r.t. stator current power_I ${p}_{\omega }$ $1$ Exponent of permanent magnet loss torque w.r.t. angular velocity power_w ${\omega }_{\mathrm{ref}}$ $\frac{\mathrm{rad}}{s}$ Reference angular velocity wRef

See Permanent Magnet Losses for details on the permanent magnet losses.

Stator Core Losses

 Name Default Units Description Modelica ID ${P}_{\mathrm{ref}}$ $0$ $W$ Reference rotor core losses PRef ${V}_{\mathrm{ref}}$ $V$ Reference RMS voltage VRef ${\omega }_{\mathrm{ref}}$ $2\pi {f}_{s,\mathrm{nom}}$ $\frac{\mathrm{rad}}{s}$ Reference angular velocity wRef

See Core for details of the core loss model.

 Name Default Units Description Modelica ID ${I}_{\mathrm{ref}}$ ${I}_{{a}_{\mathrm{nom}}}$ $W$ Reference RMS current IRef ${P}_{\mathrm{ref}}$ $0$ $W$ Reference friction losses PRef ${\omega }_{\mathrm{ref}}$ ${\omega }_{\mathrm{nom}}$ $\frac{\mathrm{rad}}{s}$ Reference angular velocity wRef ${p}_{\omega }$ $1$ $V$ Exponent of stray load loss power_w

 Name Default Units Description Modelica ID ${\mathrm{\alpha }}_{r}$ 0 $\frac{1}{K}$ Temperature coefficient of damper resistances in d- and q-axis alpha20r ${\mathrm{\alpha }}_{s}$ 0 $\frac{1}{K}$ Temperature coefficient of stator resistance at 20 degC alpha20s ${L}_{\mathrm{md}}$ $\frac{0.15\mathrm{\pi }}{{f}_{s,\mathrm{nom}}}$ $H$ Main field inductance in d-axis Lmd ${L}_{\mathrm{mq}}$ $\frac{0.15\mathrm{\pi }}{{f}_{s,\mathrm{nom}}}$ $H$ Main field inductance in q-axis Lmq ${L}_{r\sigma d}$ $\frac{0.025\mathrm{\pi }}{{f}_{s,\mathrm{nom}}}$ $H$ Damper stray inductance in d-axis Lrsigmad ${L}_{r\sigma q}$ ${L}_{r\sigma d}$ $H$ Damper stray inductance in q-axis Lrsigmaq ${L}_{s\sigma }$ $\frac{0.05\mathrm{\pi }}{{f}_{s,\mathrm{nom}}}$ $H$ Stator stray inductance per phase Lssigma ${L}_{\mathrm{s0}}$ ${L}_{s\sigma }$ $H$ Stator zero sequence inductance Lszero ${R}_{\mathrm{rd}}$ 0.04 $\mathrm{\Omega }$ Damper resistance in d-axis at TRef Rrd ${R}_{\mathrm{rq}}$ ${R}_{\mathrm{rd}}$ $\mathrm{\Omega }$ Damper resistance in q-axis at TRef Rrq ${R}_{s}$ 0.03 $\mathrm{\Omega }$ Warm damper resistance in q-axis Rs ${T}_{r,\mathrm{ref}}$ 293.15 $K$ Reference temperature of damper resistances in d- and q-axis TrRef ${T}_{s,\mathrm{ref}}$ 293.15 $K$ Reference temperature of stator resistance TsRef Use Damper Cage $\mathrm{false}$ True (checked) means damper cage is enabled useDamperCage