Synchronverters: Grid-friendly Inverters that Mimic Synchronous Generators - Control of Power Inverters in Renewable Energy and Smart Grid Integration - page 266

( )

θ = 0

a- axis

i a
a

Rotor field axis

θ

+

υ a

R s , L

Rotation

-

M

M

R f , L f

i f

+

N

f

Field voltage

u f

R s , L R s , L

-

f ′

-

υ b

υ c

+

+

c- axis

b- axis

i b

M

i c

c

b

Figure 18.1 Structure of an idealised three-phase round-rotor synchronous generator with p = 1,

modified from Grainger and Stevenson 1994, Figure 3.4

where i a , i b and i c are the stator phase currents and i f is the rotor excitation current. Denote

⎡ ⎤ ⎡ ⎤

a
b
c

i a
i b
i c

⎣ ⎦ , ⎣ ⎦

= i =

and

⎡
⎣

⎤
⎦ , sin

⎡
⎣

⎤
⎦ .

θ
cos θ −

θ
sin θ −

cos sin

2 3 2 3

cos θ = θ =

cos θ −

4 3

sin θ −

4 3

Assume for the moment that the neutral line is not connected, then

i a + i b + i c = 0 .

It follows that the stator flux linkages can be rewritten as

= L s i + M f i f cos θ, (18.1)