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Salient pole synchronous machine with main-flux saturation
Electrical / Machines
This synchronous machine has one damper winding each on the direct and 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.
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 for 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.
In both implementations, the value of the main flux inductances and
are not constant but depend on the main flux linkage
as illustrated in
the
diagram.
is assumed to be constant at all saturation levels. The equivalent magnetizing flux
in an isotropic machine is defined as
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 :
The output vector “m” contains the following 3 signals: