Page 181 - Renewable Energy Devices and System with Simulations in MATLAB and ANSYS

168 Renewable Energy Devices and Systems with Simulations in MATLAB and ANSYS ®
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and a possible energy capture of wind power. Three machines have been discussed, one based on
ferrite magnet and two on NdFeB magnets to extract the wind energy. Although the NdFeB magnet
has a mass–energy index greater, the market evolution associated with the difficulties in obtaining
rare-earth magnet, the ferrite configuration is still a serious alternative in the future. A direct-drive
electrical generator could be designed and implemented, eliminating the gearbox and making a
small-scale turbine very competitive and possibly the best solution for rural systems, small farms,
and villages. Section 7.6 discusses small wind energy systems connected to the utility grid plus
principles of Magnus turbines–based wind systems.

7.6 GRID-TIED SMALL WIND TURBINE SYSTEMS
A back-to-back converter (shown in Figure 7.11) can control a small wind turbine with either an IG
or a PMSG. Figure 7.13 shows the block diagram of a full-fledged PMSG back-to-back converter
solution. Such a converter topology provides speed control for the machine-side converter to track the
optimum power point, and the grid-side converter aims to control the power and keep DC-link volt-
age constant. The equivalent circuit of a PMSG is used in the rotating reference frame. The equations
of the d-axis and q-axis in the rotating reference frame (not taken into account the core losses) are

d
r
v ds =− R i sd − L d i d − ω L i q (7.11)
dt eq
d
r
v qs =− R i sq − L q i q + ω L i d + ω ψ (7.12)
dt ed e m
where the instantaneous power is given by

3
P i =  v i d + v i q  (7.13)
r
r
2  ds qs 
and the electromagnetic torque is given by
3 p
T e =  ψ m +( L d − )  (7.14)
L ii q
4  q d 
The rotational angular speed is expressed as

1
d r ω = ( T w − T e − Bω ) (7.15)
dt J r

where
T w is the torque produced by the wind turbine
J is the turbine moment of inertia
B is the friction coefficient
The angular electrical speed is related to the rotor speed by

p
ω e = ω r (7.16)
2
where p is the number of poles of the machine.