Synchronous Reluctance Machine (SynRM)

Symbol

Description

Synchronous Reluctance Machine (SynRM)

Model of a three-phase Synchronous Reluctance Machine (SynRM). In motor operation torque and speed have the same sign. Rotor Angle is defined as an angle between the a-phase magnetic axis and the d-axis.In this model, the saturation can be modeled using a piecewise linear approximation of direct and quadratic axis inductances. Stator winding is star connected in this model. To access the neutral point pin, check the "Neutral Point" checkbox in the properties menu.

Electrical model and equations

vd_vq_circuits

$v_a = R_s i_a + \frac{d}{dt} (L_{aa} i_a + L_{ab} i_b + L_{ac} i_c)$

$v_b = R_s i_b + \frac{d}{dt} (L_{ba} i_a + L_{bb} i_b + L_{bc} i_c)$

$v_c = R_s i_c + \frac{d}{dt} (L_{ca} i_a + L_{cb} i_b + L_{cc} i_c)$

where $\omega_r = N_{pp} \Omega$ is the electrical speed of the rotor field.
Phase inductances ( $L_{aa}$ , $L_{ab}$ , $L_{ac}$ ,..., $L_{cc}$ ) are calculated from the rotor reference frame inductance ( $L_{d}$ , $L_{q}$ ) defined in the property panel as the incremental inductance.
This component will use the lineary interpolated inductance when the current is between the two segmented points.

Electromechanical equations

Electro-magnetic torque:

$T_e = 1.5 * N_{ pp}*(i_q * \phi_d - i_d * \phi_q)$

where $\phi_d = L_d i_d$ and $\phi_q = L_q i_q$

Mechanical rotational speed $\Omega$ :

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

Information

The inductance table columns represent q-axis current and its rows represent d-axis current. Both axes must be sorted in ascending order and match the table dimensions. A constant table is supported only when both axes contain exactly one point. Inductance values must be finite and strictly positive.

Library

Electrical > Motors

Parameters

Property	Display Name	Parameter Type	Description
Rs	Rs - Stator Resistance [Ohm]	DoubleParameter	Stator Winding Resistance [Ohm]
Ld	Ld - Direct Axis Inductance [H]	DoubleMatrixParameter	Direct Axis Inductance [H]
Lq	Lq - Quadratic Axis Inductance [H]	DoubleMatrixParameter	Quadratic Axis Inductance [H]
Ld_2D	Ld - d-axis Inductance Look-up Table	DoubleMatrixParameter	Matrix of output values for d-axis inductance LUT(d,q)
Lq_2D	Lq - q-axis Inductance Look-up Table	DoubleMatrixParameter	Matrix of output values for d-axis inductance LUT(d,q)
J	J - Rotor Inertia [kg.m²]	DoubleParameter	Rotor Inertia [kg.m²]
B	B - Rotor Friction Coefficient [N.m/(rad/s)]	DoubleParameter	Rotor Friction Coefficient [N.m/(rad/s)]
InitialSpeed	Rotor Initial Speed [rad/s]	DoubleParameter	Rotor initial speed [ rad/s]
InitialCurrent	Initial Current [A]	DoubleArrayParameter	Initial Current Vector [IA IB IC]
NPP	NPP - Poles pairs	IntParameter	Number of pole pairs
ExposeNeutralPoint	Neutral Point	BoolParameter	Expose Neutral Point (Boolean)
Use2DTable	use 2D inductance table	BoolParameter	Use 2D inductance table (Boolean)
Id	Id - d-axis Input Current Values	DoubleArrayParameter	Vector of input current (d-axis)
Iq	Iq - q-axis Input Current Values	DoubleArrayParameter	Vector of input current (q-axis)

Pins

Property	Pin Name	Type	Description
Pin_A	A	Electrical	Phase A (Electrical)
Pin_B	B	Electrical	Phase B (Electrical)
Pin_C	C	Electrical	Phase C (Electrical)
Pin_R	R	RotationalMechanical	Rotor (Rotational Mechanical)
Pin_Angle	Angle	ControlOut	Rotor Angle in radians, electrical angle (Control)

Default Size

Width	Height
8	8