Page 242 - Fluid Power Engineering

Basics of Electricity and Generators 209

2
3 3 E 2 g 3 2 3i Z
g
P g = V g E g sin δ = sin 2δ = (K pm ω r p) sin 2δ =
Z 2 Z 8Z tan δ
(10-33)
3 2 3 2
τ g = (K pm p) ω r sin 2δ = K pm p sin 2δ = T max sin 2δ
8Z 4L
2
2
3i Z 3i Lp
g g
= = (10-34)
ω r tan δ 2 tan δ
where Z = ωL is the inductance of the stator. The angular frequency
of generator current is ω = pω r /2, where ω r is the angular speed of
the rotor.
Variable-speed generators will generate voltage and current that
vary in magnitude and frequency, unlike the constant voltage and
frequency of the grid. Therefore, the voltage and frequency from these
generators is conditioned to be compatible with the grid by converting
from variable AC to DC and then back to constant frequency and
voltageAC(seeFigs.10-7and10-8).Thefirstpartofconversionisdone
using rectifier and the second half is done using an inverter. In sequel,
a pulse width modulated (PWM) type of inverter is discussed. The
DC voltage and current after the AC output of PMSG is rectified are:
√
V g 3 6 i g π
V DC = , i DC = √ (10-35)
π 6
As expected, the DC power is P DC = V DC i DC = 3V g i g .
Turning attention to the wind side of rotor, in a variable-speed
turbine, the turbine rotor is directly connected to the generator rotor.
One of the advantages of the variable-speed turbine is the ability to
stay on optimal performance by changing the rotor speed as the wind
speed changes (see Fig. 10-9). Next, a simplistic control mechanism is
described that achieves this objective of keeping the rotation speed to
an optimal value. This involves controlling how much current (i DC )
the PWM inverter draws (see Fig. 10-7). That is, imagine a controller

Synchronous
Generator Rectifier Inverter Transformer
~ = Grid
= ~
V g , i g V DC , i DC V I , i I

Turbine
FIGURE 10-7 Schematic of a variable-speed synchronous generator with
permanent magnet rotor.