Grid Integration and Power Quality - Wind Energy Systems for Electric Power Generation - page 142

Fig. 7.1 Model of
short-circuit impedance
between generator and grid
and voltage variation

a) b)

The WES is modeled by the generator symbol which includes line and trans-
former impedance components between terminals and connection point, referred to
the relevant nominal voltage. In an example of a WES connected to medium volt-
age 20 kV, with a transformer 110/20 kV feeding into the distribution system, where
S k = 120 MVA referred to the 20 kV-side, the short-circuit impedance is given by:

ψ k = 51 ◦ Z k =(2 , 1 + j2 , 6) Ω ; | Z k | = 3 , 342 Ω ;

Current regulations require WES to declare a factor k ψ , of influence for switching
actions, which depends on the phase angle ψ k of the short-circuit impedance Z k .

Consider a generator operating at an apparent power S = P + j Q , the voltage
variation at CP is approximately:

U aV = R k I P

S + X k I Q

I
S ( R

Δ = · P + X · Q )

S

When the generator is operating at rated values, with current I N and power factor
cos

ϕ N , the relative voltage increase becomes:

u aV = Δ

U aV
U N

= Z k I N
U N

Δ cos( ψ kV − ϕ N )

Note that the angles are in consumer system notation, where the sign of a lag-
ging current (with respect to voltage) is positive, and the sign of the ohmic-inductive
impedance Z k is positive. In Fig. 7.1b an example vector diagram is shown which re-
flects the above equation under the condition that

1. Note that in this
case U B > U V due to the case of a directly coupled asynchronous generator draw-
ing its magnetizing current component from the grid. Theoretically, in the above
example the voltage deviation would become zero when operating the generator at
ϕ

| U B / U V − 1 |

= 141 ◦ .