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Smooth air-gap synchronous machine with main flux saturation.
Electrical / Machines
This synchronous machine has one damper winding on the direct axis and two damper windings on the quadrature axis of the rotor. Main flux saturation is modeled by means of a continuous function.
The machine operates as a motor or generator; if the mechanical torque has the same sign as the rotational speed the machine is operating in motor mode, otherwise in generator mode. All electrical variables and parameters are viewed from the stator side. In the component icon, phase a of the stator winding and the positive pole of the field winding are marked with a dot.
In order to inspect the implementation, please select the component in your circuit and choose Look under mask from the Edit menu. If you want to make changes, you must first choose Break library link and then Unprotect, both from the Edit menu.
Stator flux linkages:
The machine model offers two different implementations of the electrical system: a traditional rotor reference frame and a voltage-behind-reactance formulation.
Rotor Reference Frame Using Park's transformation, the 3-phase circuit equations in physical variables are transformed to the dq rotor reference frame. This results in constant coefficients in the stator and rotor equations making the model numerically efficient. However, interfacing the dq model with the external 3-phase network may be difficult. Since the coordinate transformations are based on voltage-controlled current sources, inductors and naturally commutated devices such as diode rectifiers may not be directly connected to the stator terminals. In these cases, fictitious RC snubbers are required to create the necessary voltages across the terminals.
Voltage behind Reactance This formulation allows direct interfacing of arbitrary external networks with the 3-phase stator terminals. The rotor dynamics are expressed using explicit state-variable equations while the stator branch equations are described in circuit form. However, due to the resulting time-varying inductance matrices, this implementation is numerically less efficient than the traditional rotor reference frame. Currently, it can only be used with the continuous state-space method.
In both implementations, the value of the main flux inductance is not constant but depends on the main flux linkage
as illustrated
in the
diagram. For flux linkages
far below the transition
flux
, the relationship between flux and current is almost linear and
determined by the unsaturated magnetizing inductance
. For large flux
linkages the relationship is governed by the saturated magnetizing inductance
.
defines the knee of the transition between unsaturated and
saturated main flux inductance. The tightness of the transition is defined
with the form factor
. If you do not have detailed information about the
saturation characteristic of your machine,
is a good starting value. The
function
plsaturation(Lm0, Lmsat, PsiT, fT)
plots the main flux vs. current curve and the magnetizing inductance vs. current curve for the parameters specified.
The model accounts for steady-state cross-saturation, i.e. the steady-state magnetizing inductances along the d-axis and q-axis are functions of the currents in both axes. For rotating reference frame formulation, the stator currents, the field current and the main flux linkage are chosen as state variables. With this choice of state variables, the representation of dynamic cross-saturation could be neglected without affecting the performance of the machine. The computation of the time derivative of the main flux inductance was not required.
Electromagnetic torque:
Mechanical rotor speed :
Most parameters for the Salient Pole Synchronous Machine are also applicable to this round rotor machine. The following parameters are different:
Same as for the Salient Pole Synchronous Machine.
Most probe signals for the Salient Pole Synchronous Machine are also available with this machine. Only the following probe signal is different: