PLECS 3.0 Online Help

Synchronous Machine (Round Rotor)

Purpose

Smooth air-gap synchronous machine with main flux saturation.

Library

Electrical / Machines

Description

pict

The Round Rotor Synchronous Machine models main flux saturation by means of a 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.

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.

Electrical System

pict

pict

Stator flux linkages:

Yd = Llsid + Lm,d (id +i′f + i′k,d)

                 (          )
Yq = Llsiq + Lm,q iq + i′g + 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 inductance Lm   is not constant but depends on the main flux linkage Ym   as illustrated in the Ym ∕im   diagram. 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.

pict

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:

T  =  3p (i Y  - i Y )
 e    2   q  d   d q

Mechanical System

Mechanical rotor speed ωm  :

       1
ωm  =  --(Te - Fωm - Tm)
       J

θm  = ωm

Parameters

Most parameters for the Salient Pole Synchronous Machine are also applicable to this round rotor machine. The following parameters are different:

Unsaturated magnetizing inductance
The unsaturated magnetizing inductance Lm,0  . The value in henries (H) is referred to the stator side.
Saturated magnetizing inductance
The saturated magnetizing inductance Lm,sat  , in H. If no saturation is to be modeled, set Lm,sat = Lm,0  .
Damper resistance
A three-element vector containing the damper winding resistance R′k,d  , R′k,q1   and R′k,q2   of the d-axis and the q-axis. The values in ohms (_O_  ) are referred to the stator side.
Damper leakage inductance
A three-element vector containing the damper winding leakage inductance L′lk,d  , L′lk,q1    and L ′lk,q2    of the d-axis and the q-axis. The values in henries (H) are referred to the stator side.
Initial field/damper current
A two-element vector containing the initial currents i′f,0   in the field winding and i′k,q1,0   in one of the damper windings in amperes (A), referred to the stator side.

Inputs and Outputs

Same as for the Salient Pole Synchronous Machine.

Probe Signals

Most probe signals for the Salient Pole Synchronous Machine are also available with this machine. Only the following probe signal is different:

Damper currents
The damper currents i′k,d  , i′k,q1   and i′k,q2   in the stationary reference frame in A, referred to the stator side.

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, "Modelling of magnetic saturation in smooth air-gap synchronous machines", IEEE Transactions on Energy Conversion, Vol. 12, No. 2, March 1997.
E. Levi, "Impact of cross-saturation on accuracy of saturated synchronous machine models", IEEE Transactions on Energy Conversion, Vol. 15, No. 2, June 2000.