Subject : Power system Analysis
Introduction to development of Modern power system
- As shown in Figure, the Synchronous Machine Model Contain three stator windings which is separately distributed.
- The winding currents are denoted by i_{a} , i_{b} and i_{c}.
- The rotor contains the field winding the current through which is denoted by i_{f} .
- The field winding is aligned with the so-called direct ( d ) axis.
- We also define a quadrature ( q ) axis that leads the d -axis by 90°.
- The angle between the d-axis and the a-phase of the stator winding is denoted by θ_{d}.
Schematic diagram of a synchronous generator
Let the self-inductance of the stator windings be denoted by L_{aa}, L_{bb}, L_{cc} such that
[Eq. (1.80)]
And the mutual inductance between the windings be denoted as
[Eq. (1.81)]
The mutual inductances between the field coil and the stator windings vary as a function of θ_{d} and are given by
[Eq. (1.82)]
[Eq. (1.83)]
[Eq. (1.84)]
The self-inductance of the field coil is denoted by L_{ff}.
The flux linkage equations are then given by
[Eq. (1.85)]
[Eq. (1.86)]
[Eq. (1.87)]
[Eq. (1.88)]
For balanced operation we have
Hence the flux linkage equations for the stator windings (1.85) to (1.87) can be modified as
[Eq. (1.89)]
[Eq. (1.90)]
[Eq. (1.91)]