Synchronverters: Grid-friendly Inverters that Mimic Synchronous Generators - Control of Power Inverters in Renewable Energy and Smart Grid Integration - page 265

be automatically shared by using the well-known frequency and voltage droop mechanism.
Synchronverters can also easily be operated in the stand-alone mode and hence they provide an
ideal solution for microgrids and smart grids. Extensive simulation and experimental results
are presented.

18.1 Mathematical Model of Synchronous Generators
The model of a synchronous generator can be found in many sources, e.g., (Fitzgerald et al .
2003; Grainger and Stevenson 1994; Kundur 1994; Walker 1981). Most of the references
make various assumptions, e.g. steady state and/or balanced sinusoidal voltages/currents, to
simplify the analysis. Here, a model that is a passive dynamic system without any assumptions
on the signals is established, from the perspective of system analysis and controller design,
for a round rotor machine (without damper windings), with p pairs of poles per phase (and p
pairs of poles on the rotor) and with no saturation effects in the iron core.
Since a synchronous generator is an electrical machine, it has an electrical part and a
mechanical part.

18.1.1 Electrical Part
The details of the geometry of the windings can be found in (Fitzgerald et al . 2003; Walker
1981). The field and the three identical stator windings are distributed in slots around the
periphery of the uniform air gap. The stator windings can be regarded as concentrated coils
having self-inductance L and mutual inductance

1

− M ( M > 0 with a typical value

2 L ,the

3 rad), as shown in Figure 18.1. The field (or
rotor) windings can be regarded as a concentrated coil having self-inductance L f . The mutual
inductance between the field coil and each of the three stator coils varies with the (electrical)
rotor angle

2

negative sign is due to the phase angle of

θ as follows:

M af = M f cos ( θ ) ,

M f cos

2 3

M bf = θ − ,

M f cos

4 3

= θ − .

M cf

The flux linkages of the windings are

a = Li a − Mi b − Mi c + M af i f ,

b =− Mi a + Li b − Mi c + M bf i f ,

c =− Mi a − Mi b + Li c + M cf i f ,

f = M af i a + M bf i b + M cf i c + L f i f ,