Synchronous Reluctance Machine
Purpose
Synchronous reluctance machine configurable with lookup tables
Library
Electrical / Machines
Description
This three-phase synchronous reluctance machine has a solid rotor without permanent magnets. Saliency, saturation and cross-coupling are modeled by means of corresponding inductance lookup tables.
Two sets of one-dimensional inductance tables must be provided, one for each axis (d, q), where the first curve corresponds to the case with no cross-saturation, and the second to the case with maximum cross-saturation.
Fig. 242 Inductance vs current characteristics for synchronous reluctance machine
From this information, complete flux linkage and incremental inductance tables are derived, using an interpolation method that ensures a conservative magnetic circuit.
The machine can operate as either a motor or generator. If the mechanical torque has the same sign as the rotational speed, the machine is operating in motor mode; otherwise it is in generator mode. In the component icon, phase a is marked with a dot.
Electical System
The model utilizes the Non-Excited Synchronous Machine component. Use this component directly to model permanent magnet-assisted synchronous reluctance machines, or if more complete flux/inductance data is available. The electrical system is realized by means of the voltage behind reactance (VBR) formulation and is therefore appropriate to simulate switching dead-time and failure modes.
Electro-Mechanical System
Electromagnetic torque:
Mechanical System
Mechanical rotor speed \(\omega_\mathrm{m}\):
Parameters
General
- Stator resistance
Armature or stator resistance \(R_\mathrm{s}\) in \(\Omega\).
- Stator leakage inductance
Leakage inductance of stator windings in henries \((\mathrm{H})\). Stator leakage must be set to a non-zero value.
- Number of pole pairs
Number of pole pairs \(p\).
- Initial stator currents
A two-element vector containing the initial stator currents \(i_\mathrm{a,0}\) and \(i_\mathrm{b,0}\) of phase a and b in amperes \((\mathrm{A})\). \(i_\mathrm{c,0}\) is calculated assuming a neutral connection.
Magnetizing Inductance
- Current lookup vector
d- and q-axis peak current vector serving as input to inductance lookup vectors. Must be a one dimensional vector with 3 or more elements, and monotonically increasing, i.e. \([0 \dots i_\mathrm{d,max}]\) and \([0 \dots i_\mathrm{q,max}]\). The values are in amperes \((\mathrm{A})\).
- Ld (iq = 0) lookup vector
d-axis inductance when there is no cross saturation \((i_\mathrm{q}=0)\). Must be the same size as the Current lookup vector. The values are in henries \((\mathrm{H})\).
- Ld (iq = max) lookup vector
d-axis inductance when there is maximum cross saturation \((i_\mathrm{q} = i_\mathrm{q,max})\). If no cross-saturated data is available, this can be left empty. Must be the same size as the Current lookup vector. The values are in henries \((\mathrm{H})\).
- Lq (id = 0) lookup vector
q-axis inductance in when there is no cross saturation \((i_\mathrm{d}=0)\). Must be the same size as the Current lookup vector. The values are in henries \((\mathrm{H})\).
- Lq (id = max) lookup vector
q-axis inductance when there is maximum cross saturation \((i_\mathrm{d} = i_\mathrm{d,max})\). If no cross-saturated data is available, this can be left empty. Must be the same size as the Current lookup vector. The values are in henries \((\mathrm{H})\).
- Generated table size
User-specified dimension to derive lookup tables for flux linkages and incremental inductances to be used in the underlying Non-Excited Synchronous Machine component.
If left empty, the specified data is used as-is.
Specifying a scalar value, n, will generate equally spaced, n-element d- and q-axis current vectors. The corresponding 2D lookup tables for flux linkage and incremental inductance are also generated. The dimensions of the generated tables must be 3 or more.
The size of the generated tables affect the model initialization and simulation speeds. A smaller size leads to faster model initialization and simulation speeds, but lower resolution in the generated tables. A larger size increases the resolution but adversely affects the model initialization and simulation speeds. Care must be taken when configuring this parameter.
- Current out of range
Configure to ignore, warn, warn and pause simulation, or generate error and stop simulation if the d- or q-axis currents are outside the specified range.
- Co-energy plausibility check
The change in co-energy \((\Delta W)\) between zero and maximum cross saturation is calculated for both the d-axis \((\Delta W_\mathrm{d})\) and q-axis \((\Delta W_\mathrm{q})\). Configure to check if \(\Delta W_\mathrm{d,q}\) are within 5% or 10% of each other to validate the input data. This check can be disabled.
Mechanical
- Inertia
Combined rotor and load inertia \(J\) in \((\mathrm{Nms}^2)\).
- Friction coefficient
Viscous friction \(F\) in \((\mathrm{Nms})\).
- Initial rotor speed
Initial mechanical rotor speed \(\omega_\mathrm{m,0}\) in radians per second \((\frac{\mathrm{rad}}{\mathrm{s}})\).
- Initial rotor position
Initial mechanical rotor angle \(\theta_\mathrm{m,0}\) in radians.
Probe Signals
All probe signals for the Non-Excited Synchronous Machine are also available with this machine.
References
A. Vagati, M. Pastorelli, F. Scapino, G. Franceschini, “Impact of cross saturation in synchronous reluctance motors of the transverse-laminated type”, IEEE Transactions on Industry Applications, Vol. 36, No. 4, Aug 2000.
A. Vagati, M. Pastorelli, G. Franceschini, “Effect of magnetic cross-coupling in synchronous reluctance motors”, Article in PCIM conference proceedings, June 1997.