Synchronous Machine Models

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This page describes the most common synchronous machine models used in stability studies.

Nomenclature

The standard machine parameters are defined as follows:

  • is the armature resistance (pu)
  • is the armature reactance (pu)
  • is the d-axis synchronous reactance (pu)
  • is the q-axis synchronous reactance (pu)
  • is the d-axis transient reactance (pu)
  • is the q-axis transient reactance (pu)
  • is the d-axis subtransient reactance (pu)
  • is the q-axis subtransient reactance (pu)
  • is the d-axis transient open loop time constant (s)
  • is the q-axis transient open loop time constant (s)
  • is the d-axis subtransient open loop time constant (s)
  • is the q-axis subtransient open loop time constant (s)
  • is the machine inertia constant (MWs/MVA)
  • is an additional damping constant (pu)

Note that per-unit values are usually expressed on the machine's MVA base.

6th Order (Sauer-Pai) Model

6th order synchronous machine model based on the book:

Sauer, P.W., Pai, M. A., "Power System Dynamics and Stability", Stipes Publishing, 2006

Stator magnetic equations:

where

Stator electrical equations (neglecting electromagnetic transients):

Equations of motion:

Initialisation:

6th Order (Anderson-Fouad) Model

6th order synchronous machine model based on the book:

Anderson, P. M., Fouad, A. A., "Power System Control and Stability", Wiley-IEEE Press, New York, 2002

Stator magnetic equations:

Stator electrical equations (neglecting electromagnetic transients):

Equations of motion:

Initialisation:

4th Order (Two-Axis) Model

Stator magnetic equations:

Stator electrical equations (neglecting electromagnetic transients):

Equations of motion:

Initialisation:

2nd Order (Classical) Model

Stator equations:

Equations of motion:

Initialisation: