INTRODUCTION
Nowadays, among the renewable energy sources, wind systems are more economic
in compare with the others (Weisser and Garcia, 2005). Variable speed
wind systems deliver 20 to 30% more energy tan the constant power systems.
Also they reduce the power oscillation and optimize the reactive power
presentation (Kim and Kim, 2007). In order to get the maximum power in
different wind seeds, turbine speed should be able to vary in a great
rage. Selecting the type of generator depends on different elements such
as kind of function, machine characteristics, maintenance and price. Achieving
the maximum power under direct connection of induction generator to the
grid in constant frequency and voltage condition is impossible, because
if induction generator is connected to grid directly there won`t be the
possibility of a great speed variation between the synchronous speed and
the speed in proportion with the maximum torque.
Doubly fed induction generator (DFIG) has not the ability to operate
in great range of speed variations despite it is greatly used in wind
systems. Permanent Magnet Synchronous Generators (PMSG) are too expensive
to be used in high rate powers.
Squirrel cage induction machines, are used greatly in industrial purposes
because of their low cost, robustness and easy maintenance. These advantages
introduce this machine as an appropriate choice to be applied in variable
speed wind systems (Senjyu et al., 2006).
The power created by the wind is related to the 3rd power of wind speed.
Applying power electronics converters to transfer induction generator`s
power to grid by the possibility of speed variation in a great range,
is preferred be cause of their great advantages. Wind turbines with power
electronics circuits in the 4 to 5 MW power range will be applied greatly
in near future (Badrul and Chellapilla, 2006). The method applied to control
the speed and power of synchronous and induction generators are now applied
to the Wind Energy Converting Systems (WECS) to obtain the maximum power
of wind turbine (Surgevil and Akpınar, 2005). Back to back converter
is an appropriate choice for squirrel cage induction generator used in
wind system (Pena I>et al., 2001). Figure 1 shows wind
power generation system connected through two back to back converters
to grid.
Vector control methods are used to separately control the torque and
machine flux (AboKhalil et al., 2004).

Fig. 1: 
Connection of wind power generation system to grid through
back to back inverters 
In this study indirect
vector control method is used to control generator where, daxis current
controls the flux and qaxis current controls the machine speed. Also
machine speed is regulated in a way that as maximum energy as possible
will be obtained. In order to connect the system to the grid, two back
to back power electronics converters are used. In order to control the
grid side converter, P and Q, injected to grid are calculated in dq axis
and required control to inject the desired valued is applied by PI controllers.
Simulation results are presented by MATLAB/SIMULINK software. Simulation
results confirm the back to back converter`s appropriate operation and
also confirm the operation of power injection to grid applying induction
generator.
MATERIALS AND METHODS
The proposed system is consisted of five main parts: Wind model, Wind
Turbine, Turbine Maximum Power Control, Induction generator, Generator
side converter control and grid side converter control. Theses parts have
discussed and finally the simulation results have been introduced.
Wind model: The model applied for this simulation is composed
of three components and is described as follow (Kim and Kim, 2007):
V_{WIND} = V_{BASE}
+ V_{GUST} + V_{RAMP} 
(1) 
where, V_{BASE} is the main component, V_{GUST} is the
gust component and V_{RAMP} is the ramp component. The main component
is a constant speed. Ramp component can be expressed by a sinusoidal function
which is considered as a composition of several different sinusoidal functions
and gust component is considered as storm and sudden wind.
Wind turbine: The torque generated by wind blow is described by
the following relations:

Fig. 2: 
Power conversion factor in terms of TSR for different
pitch angle values 
where, V_{WIND} is wind speed, R is the blades radius, P is the
air density, ω_{M} is rotor angular speed and λ is the
Tip Speed Ratio (TSR), C_{P} is the power conversion factor which
can be defined as turbine power in proportion with wind power and is related
to blades aerodynamic characteristics. Resulted mechanical torque is applied
as the input torque to the wind generator and makes generator to operate.
Power conversion factor is expressed as the function of tip speed ratio
λ< as follow:
where, β< is blade`s pitch angle. For a turbine with constant pitch,
β< is considered as a constant value, Fig. 2 is
power conversion factor (C_{P}) variations in terms of TSR for
different pitch angle values. In this study β< is considered zero
where, the C_{P} value would be 0.48 then.
Table 1 shows the wind turbine parameters values applied
in simulation.
Turbine maximum power control: Figure 3 shows
the relation between turbine output power and its speed in terms of different
wind speeds. It is seen that rotor`s optimum speed to obtain maximum power
of it, is different in various wind speeds. Also, Fig. 2
shows that C_{P} is a function of λ< and its maximum value
is obtained for λ_{nom}.
So, in order to obtain the maximum power of wind energy λ< should
always be fixed on the λ_{nom} value which is possible by
blades properly designing. So, relation (2) gives:

Fig. 3: 
Maximum power of turbine in term of wind and rotor speed 
The generator reference speed is calculated as follow:
So, by measuring wind speed, generator reference speed is obtained to
get the maximum wind energy (AboKhalil et al., 2004).
Induction generator: In wind system, integrated and high degree
models should be applied to simulate the induction generator in order
to reach to the desired answer (Karrari et al., 2005). Several
kinds of induction generators are studied in different sources (Ong, 1997).
5th degree model is used for simulation in this study. Equations related
to this model are obtained as follow by applying Park`s conversion on
machine voltage and current (Ong, 1997).
where, v_{ds}, v_{qs}, v_{0s}, i_{ds},
_{IQs}, i_{0s} are stator voltages and currents and v_{dr},
v_{qr}, v_{0r}, i_{dr}, _{IQs}, i_{0s}
are rotor voltages and currents in dq axis and:
ψ_{ds} = x_{s}.i_{ds}
+ x_{m}.i_{dr} 
_{}(13) 
ψ_{qs} = x_{s}.i_{ds}
+ x_{m}.i_{dr} 
(14) 
ψ_{0s} = x_{s}.i_{0s}
+ x_{m}.i_{dr} 
(15) 
ψ_{qr} = x_{r}.i_{dr}
+ x_{m}.i_{ds} 
(16) 
ψ_{dr} = x_{r}.i_{qs}
+ x_{m}.i_{qr} 
(17) 
ψ_{0r} = x_{r}.i_{0r} 
(18) 
where, for balanced load i_{0s} = i_{0r} = 0.
The relation of torques applied to induction generator rotor is as follow:
where, T_{m} is the mechanical torque applied to rotor and T_{e}
is generator electrical torque and D.ω_{r} J is damping torque
and J is the sum of turbine and generator inertia. In reference (Ong,
1997) induction generator`s electrical torque is shown as follow:
where, P is the number of induction generator`s poles. Above relations
express the dynamic of induction generator completely. Characteristics
of generator used in simulation are presented in Table 2.
Control of grid connected system: For a specific wind speed, wind turbine`s
operation point (output mechanical power and rotor speed) is determined by turbine`s
and load`s (induction generator) characteristics junction point. The generator
stator voltage is determined by grid voltage which will be used in induction
generator simulation.
Machine equations are converted in the rotor flux frame. Rotor flux is
turning in synchronous speed but in a different angle than stator flux,
if there is a sinusoidal excitation. Choosing daxis on the rotor flux,
q component will be zero. This fact simplifies the equations very much.
Now the torque and flux equations (Ong, 1997) expressed in earlier part
will be changed as follow:
The above relations are the main relations of vector control (Ong, 1997;
Chinchilla et al., 2006). This method simplifies the induction
machine controlling. This method is very similar to Dc machine`s independent
excitation where, flux is the function of field current and torque is
in proportion with flux and rotor current. The main problem of vector
control method is flux axis angle calculation where is done by measuring
the flux in two points with 90°< displacement and then angles are
calculated using the resulted fluxes or estimating in regard to rotor
speed (Ong, 1997).
Generator side converter control: Figure 4 shows
the generator side converter controlling system and structure. In this
part, generator`s speed is controlled to generate the maximum power. In
order to reach this aim, a PI controller is used to control the speed.
Speed controlling loop generates the current component of generator to
control the torque and speed of generator for different wind speed values.
Proportional and integrated PI controller values used in simulation are
K_{P} = 12 and K_{I} = 25. In respect to the fact that
motor power is directly related to air gap flux, this air gap flux will
be maintained in its nominal value and daxis current value can be calculated
by air gap flux on the basis of relation 25. Flux axis angle is calculated
as:
Grid side converter control: Figure 5 shows
the grid side converter controlling system used to control the injective
active and reactive powers.

Fig. 4: 
Configuration and control system of generator side converter 

Fig. 5: 
Configuration and control system of grid side converter 
Relations of these powers in synchronous reference
are as follow (Chinchilla et al., 2006; Hana et al., 2007):
If synchronous reference is synchronized with grid voltage, qaxis component
of grid voltage would be zero and power relations will be as follow:
According to the above relations active and reactive powers are applied
to control qaxis currents, respectively. Two controlling loops are used to control these currents. Capacitor voltage
controlling loop is used to control the daxis reference power transfer.
qaxis reference current is specified by selecting desired injected to
grid reactive power. If unit power factor is considered qaxis reference
current is regulate at zero value. In this simulation, integrated and
proportional values are K_{P} = 2 and K_{I} = 10 for the
PI controller which is controlling the capacitor voltage. PI controller
which is controlling the currents is considered with K_{P} = 0.1
and K_{I} = 80 values.
RESULTS AND DISCUSSION
In order to study the proposed wind turbine system`s operation, mentioned
system is simulated by MATLAB/SIMULINK software with the parameters of
Table 1 and 2.
Mentioned system is simulated for a wind with variable speed for 4 sec.
Figure 6 shows the wind speed curve.
In Fig. 7 and 8 capacitor voltages
and injective reactive power are presented. These two figures show that
the system has appropriately provided the requirements to be connected
to grid. Because capacitor voltage value is maintained constant and the
reactive power transferred to grid is negligible (unit power factor is
considered).
Table 2: 
Induction generator parameters 

Figure 9 presents the true and estimated speeds of
rotor. It is seen that rotor has tracked the calculated speed correctly
to obtain the maximum power of turbine.

Fig. 7: 
DC link voltage (v) 

Fig. 8: 
Injected reactive power to grid (kVAr) 

Fig. 9: 
Actual and reference rotor speed (m sec^{<1}) 

Fig. 10: 
Actual and reference rotor speed (kW) 
Figure 10 shows the electrical and mechanical powers.
It is seen that, injective power`s curve tracks turbine`s maximum mechanical
power. The difference between these two curves is justified by considering
mechanical and electrical losses.
CONCLUSION
Developing wind turbines, different technologies are presented for them.
Despite of vast application of doubly fed induction generators (DFIG),
speed variation possibility in direct drive squirrel cage induction generator
is more than that in DFIG. In this study squirrel cage induction generator
with two back to back voltage source converters is used to connect wind
turbine to the grid. Generator side converter is controlled by indirect
vector control method and the grid side converter is controlled by active
and reactive powers injection to grid method. Simulation results show
that the maximum power of turbine is obtained correctly for different
wind speeds and also show that expected reactive and active powers are
injected properly.