PLECS 2.2 Online Help

Salient Pole Synchronous Machine

Purpose

Salient pole synchronous machine with main flux saturation.

Library

Machines

Description

pict

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.

Electrical System

pict

pict

Stator flux linkages:

Yd = Llsid + Lm,d (id +i′f + i′k,d)

                (       )
Yq = Llsiq + Lm,q iq + i′k,q

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 Lm,d   and Lm,q   are not constant but depend on the main flux linkage Ym   as illustrated in the Ym∕im   diagram.

pict

In this machine model, the anisotropic factor

    ∘ ------------  ∘---------
m =   L    ∕L     ≡  L   ∕L    = const.
       m,q,0  m,d,0      m,q   m,d

is assumed to be constant at all saturation levels. The equivalent magnetizing flux Y
  m   in an isotropic machine is defined as

      ∘ -2------2----2-
Ym  =   Ym,d + Y m,q∕m .

For flux linkages Ym   far below the transition flux YT  , the relationship between flux and current is almost linear and determined by the unsaturated magnetizing inductance Lm,0  . For large flux linkages the relationship is governed by the saturated magnetizing inductance Lm,sat  . YT   defines the knee of the transition between unsaturated and saturated main flux inductance. The tightness of the transition is defined with the form factor fT  . If you do not have detailed information about the saturation characteristic of your machine, fT = 1   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.

Electro-Mechanical System

Electromagnetic torque:

Te =  3p (iqYd - idYq)
      2

Mechanical System

Mechanical rotor speed ω
 m  :

       1-
ωm  =  J (Te - Fωm - Tm)

θm  = ωm

Parameters and Dialog Box

[Picture]

Stator resistance
Armature or stator winding resistance Rs   in ohms (_O_  ).
Stator leakage inductance
Armature or stator leakage inductance Lls   in henries (H).
Unsaturated magnetizing inductance
A two-element vector containing the unsaturated stator magnetizing inductance Lm,d,0   and Lm,q,0   of the d-axis and the q-axis. The values in henries (H) are referred to the stator side.
Saturated magnetizing inductance
The saturated stator magnetizing inductance Lm,d,sat   along the d-axis, in H. If no saturation is to be modeled, set Lm,d,sat = Lm,d,0  .
Magnetizing flux at saturation transition
Transition flux linkage YT  , in Vs, defining the knee between unsaturated and saturated main flux inductance.
Tightness of saturation transition
Form factor fT   defining the tightness of the transition between unsaturated and saturated main flux inductance. The default is 1.
Field resistance
d-axis field winding resistance   ′
R f   in ohms (_O_  ), referred to the stator side.
Field leakage inductance
d-axis field winding leakage inductance  ′
Llf   in henries (H), referred to the stator side.
Damper resistance
A two-element vector containing the damper winding resistance R ′k,d    and R′k,q    of the d-axis and the q-axis. The values in ohms (_O_  ) are referred to the stator side.
Damper leakage inductance
A two-element vector containing the damper winding leakage inductance L′
 lk,d   and L′
 lk,q   of the d-axis and the q-axis. The values in henries (H) are referred to the stator side.
Inertia
Combined rotor and load inertia J   in Nms2  .
Friction coefficient
Viscous friction F   in Nms.
Number of pole pairs
Number of pole pairs p  .
Initial rotor speed
Initial mechanical speed ωm,0   in radians per second (s- 1  ).
Initial rotor position
Initial mechanical rotor angle θm,0   in radians. If θm,0   is an integer multiple of 2π ∕p   the d-axis is aligned with phase a of the stator windings at simulation start.
Initial stator currents
A two-element vector containing the initial stator currents ia,0   and ib,0   of phase a and b in amperes (A).
Initial field current
Initial current i′f,0    in the field winding in amperes (A), referred to the stator side.
Initial stator flux
A two-element vector containing the initial stator flux   ′
Y d,0   and  ′
Yq,0   in the rotor reference frame in Vs.

Inputs and Outputs

Mechanical torque
The input signal Tm   represents the mechanical torque at the rotor shaft, in Nm.

The output vector "m" contains the following 3 signals:

(1) Rotational speed
The rotational speed ωm   of the rotor in radians per second (s-1  ).
(2) Rotor position
The mechanical rotor angle θm   in radians.
(3) Electrical torque
The electrical torque Te   of the machine in Nm.

Probe Signals

Stator phase currents
The three-phase stator winding currents ia  , ib   and ic  , in A. Currents flowing into the machine are considered positive.
Field currents
The excitation current i′f   in A, referred to the stator side.
Damper currents
The damper currents  ′
ik,d   and  ′
ik,q   in the stationary reference frame, in A.
Stator flux (dq)
The stator flux linkages Yd   and Yq   in the stationary reference frame in Vs.
Magnetizing flux (dq)
The magnetizing flux linkages Ym,d    and Ym,q    in the stationary reference frame in Vs.
Rotational speed
The rotational speed ωm   of the rotor in radians per second (s-1  ).
Rotor position
The mechanical rotor angle θm   in radians.
Electrical torque
The electrical torque Te   of the machine in Nm.

References

K. A. Corzine, B. T. Kuhn, S. D. Sudhoff, H. J. Hegner, "An improved method for incorporating magnetic saturation in the Q-D synchronous machine model", IEEE Transactions on Energy Conversion, Vol. 13, No. 3, Sept. 1998.
E. Levi, "Saturation modelling in D-Q axis models of salient pole synchronous machines", IEEE Transactions on Energy Conversion, Vol. 14, No. 1, March 1999.
E. Levi, "Impact of cross-saturation on accuracy of saturated synchronous machine models", IEEE Transactions on Energy Conversion, Vol. 15, No. 2, June 2000.