07-07-2012, 02:26 PM
SYNCHRONOUS MACHINE MODELS
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SYNCHRONOUS MACHINE MODELS – 1Synchronous Machine Theory and Modelling
• The power system stability problem is largely one of keeping
interconnected synchronous machines in synchronism.
• An understanding of their characteristics and accurate
modeling of their dynamic performance are of fundamental
importance to the study of power system stability.
Direct and Quadrature Axes
• Magnetic circuits and all rotor windings are symmetrical with
respect to both polar axis and the inter-polar axis.
• The direct (d) axis, centred magnetically in the centre of
the north pole;
• The quadrature (q) axis, 90 electrical degrees ahead of the
d-axis.
• The position of the rotor relative to the stator is measured
by the angle θ between the d-axis and the magnetic axis of
phase 'a' winding.
Simplifications essential for large-scale studies
For stability analysis of large systems, it is necessary to
neglect the following for stator voltage:
• The transformer voltage terms, pψd and pψq
• The effect of speed variations.
Neglect of Stator pψ Terms
• The pψd and pψq terms represent the stator transients.
• With these terms neglected, the stator quantities contain
only fundamental frequency components and the stator
voltage equations appear as algebraic equations.
• This allows the use of steady-state relationships for
representing the interconnecting transmission network.
Neglecting the Effect of Speed Variations on Stator Voltages
• The assumption of per unit ωr = 1.0 (i.e., ωr = ω0 rad/s) in the
stator voltage equations does not contribute to computational
simplicity in itself.
• The primary reason for making this assumption is that it
counterbalances the effect of neglecting pψd, pψq terms so far as
the low-frequency rotor oscillations are concerned.