Generators - Wind Energy Systems for Electric Power Generation - page 31

a)

b)

Fig. 3.4 T-model variants containing loss resistors ( a ) conventional iron loss resistor R Fe ;
( b ) resistor R p representing constant losses

3.2.2.2 Operation at Given Stator Voltage

The voltage equation (3.2) can be solved for the currents, when the machine is fed
from the grid or a voltage-source inverter of fundamental frequency 1 .Asim-

plification may be introduced by neglecting stator winding resistance R 1 , which is
permissible for R 1 / (

ω

1 L 1 ) << 1. The following equations describe the complex
stator and rotor currents as well as the torque. They come in two equivalent repre-
sentations:

ω

a) with slip s as variable, using short-circuit reactance X k and breakdown-slip s k as
parameters.

I 2
I 1

I 1 = −

j U 1
X k

σ + js / s k

1 + js / s k

js / s k X m

X 2

2 s / s k
1 +( s / s k ) 2

; = − , T = T k

σ + js / s k

R 2
σ

where X k = σ X 1 ; s k =

X 2
b) with the rotor frequency as variable, using rotor time constants

τ k2 (short-circuit)

and τ 02 (no-load) as parameters.

I 2
I 1

U 1 σ + j ω τ k 2 j ω τ L m

L 2

2 ω τ k 2 2 2 02 2

I 1 = ; = − ; T = T k

j ω 1 σ L 1 1 + j ω 2 τ k 2 1 + j ω 2 τ 02 1 + ω 2 2 τ k 2 2

k 2 = σ

L 2
R 2

02 = L 2
R 2

where τ ; τ

U 1 2
ω

U 1 2
ω

T k = z p 3
2

1 − σ

X k

= z p 3
2

1 − σ

σ

The breakdown-torque is (3.3)

1 2

L 1 1

When the stator frequency is considered variable, as by converter supply, a sim-
plified control law requires adjusting the voltage according to:

U 1
ω 1 = const .

(3.4)

ω 1 is approximately kept constant.
Then current and torque depend only on rotor frequency, as shown in Fig. 3.5. The

Under this condition the flux linkage Ψ 1 = U 1 /