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Salient Pole Synchronous Machine

Purpose

Detailed model of a synchronous machine with salient poles.

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Description

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There are two different models for the Salient Pole Synchronous Machine, which are mathematically equivalent. The standard model can only be used with the continuous state-space method. The discretizable model can be used with both the continuous and the discrete state-space method.

The machine is modeled in the rotor reference frame. It 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 referred to the stator side. 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

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Stator flux linkages:

'd = Llsid + Lm;d id + i0f + i0k;d


'q = Llsiq + Lm;q iq + i0k;q

Electromagnetic torque:

Te = 3p ('d iq   'qid)
     2

Mechanical System

Mechanical rotor speed !m:

       1
!m  = J- (Te    F!m    Tm)

m  = !m

Parameters and Dialog Box

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Stator resistance
Armature or stator winding resistance Rs in ohms (_O_).
Stator leakage inductance
Armature or stator leakage inductance Lls in henries (H).
Magnetizing inductance
A two-element vector containing the stator magnetizing inductance Lm;d and Lm;q of the d-axis and the q-axis. The values in henries (H) are referred to the stator side.
Field resistance
d-axis field winding resistance Rf0 in ohms (_O_), referred to the stator side.
Field leakage inductance
d-axis field winding leakage inductance Llf0 in henries (H), referred to the stator side.
Damper resistance
A two-element vector containing the damper winding resistance Rk;d0 and Rk;q0 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 Llk;d0 and Llk;q0 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 !m;0 in radians per second (s1).
Initial rotor position
Initial mechanical rotor angle m;0 in radians. If m;0 is an integer multiple of 2=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 is;a;0 and is;b;0 of phase a and b in amperes (A).
Initial field current
Initial current if;00 in the field winding in amperes (A), referred to the stator side.

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 5 signals:

(1) Rotor speed
The rotational speed !m of the rotor in radians per second (s1).
(2) Rotor position
The mechanical rotor angle m in radians.
(3) Electrical torque
The electrical torque Te of the machine in Nm.
(4-5) Mutual flux
The magnetizing mutual flux linkages 'm;d and 'm;q in Vs:


'm;d = Lm;d id + i0f + i0k;d


'm;q = Lm;q iq + i0k;q