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Salient pole synchronous machine with main flux saturation.
Machines
The Salient Pole Synchronous Machine models main flux saturation by means of a continuous function. The model is implemented with machine equations in the rotor reference frame (Park transformation). Since the machine terminals have current-source characteristic, no external inductors may be connected. They must be included in the leakage inductances. The machine can be used with both the continuous and the discrete state-space method.
The machine operates as a motor or generator; the sign of the mechanical torque determines the mode of operation (positive for motoring, negative for generating). 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.
The electrical system of the machine model is implemented with state-variable
equations that are derived from the equivalent circuit in the rotor reference frame.
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. In the implementation, the stator currents, the field current and the main flux linkage are chosen as state variables. With this type of model, the representation of dynamic cross-saturation can be neglected without affecting the machine's performance. The computation of the time derivative of the main flux inductance is not required.
Electromagnetic torque:
Mechanical rotor speed :
The output vector "m" contains the following 3 signals: