Materials
and processes for energy: communicating current research and technological developments (A. Méndez-Vilas, Ed.)
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Simulation Study of Squirrel Cage Induction Generator Fed by a Back-toBack Converter and by using a LCL filter
Vital P. Batista Júnior1, R. V. Jacomini1, A. J. Sguarezi Filho1
1
Universidade Federal do ABC – UFABC, Rua Santa Adélia, Santo André- SP, Brasil
Nowadays the wind energy systems are widely used for power generation. In this book chapter are developed the rotorflux-oriented for torque and flux control of the squirrel cage induction generator (SCIG), and the grid-voltage-oriented for
DC bus voltage and reactive power control of the grid using a LCL filter. Both the currents controllers for the generator
and for the grid are implemented using proportional-integral (PI) current controllers in the d-q frame. In order to determine
the stator currents references, the errors signal of torque and rotor flux are regulated by PI controllers with respect to the
generator. On grid side converter the errors signal of DC bus voltage and reactive power are also regulated by means of PI
controllers. The design of LCL filter is also presented. The control strategies employed in the grid and generator side
converters and the LCL filter are evaluated by simulation for several speed operation of wind energy conversion system
Keywords: wind generator, LCL filter, squirrel-cage induction generator, power control
1. Introduction
Nowadays the wind energy systems are widely used for power generation. Wind farms can be composed of fixed-speed
or variable speed generators; they are doubly-fed induction generator (DFIG) and squirrel cage induction generator
(SCIG) or permanent magnets synchronous generator (PMSG) and wound rotor synchronous generator (WRSG). When
compared to the synchronous generators, the induction generators have the advantages, such as low cost, good
reliability and robustness [1]. SCIG can be implemented as variable-speed generators by using full rate power converter
between grid and generator; back-to-back pulse-width modulated (PWM) converter generally is most suitable for this
implementation [2], its configuration is shown in Fig. 1. This converter consists of a generator-side converter (rectifier)
and a grid-side converter (inverter) connected to a common dc-link. The generation systems connected to the network
must meet the grid codes with regard to total harmonic distortion of current injected. Therefore, some types of filters as
L, LC and LCL are used on the grid side converter.
The purpose of the filter is to reduce current harmonics due to the switching of the IGBT´s of the converter. One
solution widely used is based on L filter. However a high value of inductance would be necessary, which means that for
high power application, the design becomes expensive and moreover, the dynamic system deterioration due to excessive
voltage drop across the reactance and the dynamic response of the system becomes slow. An attractive solution for this
problem is the use of LCL filter (as shown in Fig. 1). Thus, the values of inductors and capacitors must be properly
designed, considering the allowable ripple current and the filter must be adequately damped to avoid resonance. So, the
result is a low inductance value and consequently reducing the cost of the inductor.
Fig. 1 Configuration of a SCIG using back-to-back pulse converter with LCL filter.
To control both the grid side converters and the generator side converters, solutions have been developed for several
vector control techniques. The most widely used techniques way be classified within the Field-Oriented Control (FOC),
Voltage-Oriented Control (VOC) and the Direct Control [2,3]. The principles of these techniques are the independent
control of flux and torque through the control of independent stator current d-q components for the generator and, active
and reactive power control through the control of independent grid current d-q components for the grid side converters.
One way to obtain this independent control, are using set of PI-type controller, which has a wide application range and
consolidated for ac machines drive [3], e.g., induction motor, permanent magnet machine and double fed induction
generator [4].
This book chapter makes a simulation study of squirrel cage induction generator fed by a back-to-back converter and
by using a LCL filter for wind energy systems. The controllers are PI controllers, current control, rotor-flux- oriented
for converter connected to the SCIG and grid–voltage-oriented for the converter connected to the grid. Simulations
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results are carried out to validate the systems operation. This book chapter is organized as follows: Section 2, model and
SCIG control using the rotor flux orientation for the torque and flux controls, that are regulated by means of PI
controllers; Section 3, model and control of grid side converter using grid voltage orientation for the dc-link voltage and
reactive power controls, that are also regulated by means of PI controllers; Section 4, it is performed the step-by-step
procedure for designing of the LCL filter that is connected between the grid-side converter and a grid; In Section 5, the
control strategies employed in the generator - and grid side converters taking into account the good choice of the LCL
filter parameters are evaluated by simulation study for operation speed operation of wind energy conversion system.
2. Generator-side converter control
2.1 Squirrel-cage induction machine model
The induction machine can be represented by the model dq synchronous reference frame is given by [3]:
=
+
+
0=
+
+ (
(1)
−
)
(2)
The relationship between current and flux are expressed by
=
+
(3)
=
+
(4)
The quantities , and are the space vectors of voltage, current and magnetic flux respectively. is the electrical
resistance per phase winding, is the inductance per phase winding, the subscripts 1,2 and M denote the stator, rotor
is the angular speed of the mechanical
and magnetization, respectively,
is the number of pairs of poles and
rotor.
The mechanical dynamics is done by:
=
where Te is the electromagnetic torque and
−
(5)
is the mechanical torque.
2.2 Rotor-flux-orientated control
The concept of the rotor-flux–orientated control consists in fixing the direct axis of the synchronous coordinate system
with the rotor flux vector expressed in the stationary coordinates, given by [3]
=
(6)
where
is the magnitude and is the instantaneous spatial position of the rotor flux vector.
If the coordinate reference system
is chosen such that its direct axis coincides with the rotor flux vector, have that
= 0) and, therefore the direct-axis component is in the actual rotor flux:
the quadrature axis component is zero (
|
|=
=
(7)
The fact that the direct axis of the coordinate system is fixed to the rotor flux vector makes the electromagnetic
torque become proportional to the product of the rotor flux by the quadrature axis component of the stator current, such
and the current
are equivalent to the primary field flux and
as occurs in machines DC: where the rotor flux
armature current respectively. In mathematical terms, the electromagnetic torque when it is adopted the rotor flux
orientation is given by:
3p L
λ i
(8)
T =
4 L
The relationship between rotor flux and the stator current is obtained using Equations (3) and (4), given by:
=
(9)
It can be observed that in Equations (8) and (9), the electromagnetic torque and the rotor flux can be controlled by the
d-q components of stator current. Therefore, by adjusting the rotor flux or q-component of stator current allows the
control of electromagnetic torque of SCIG.
2.3 SCIG control
The SCIG control is performed using the rotor-flux-oriented control as presented in Section 2.1. Due to the use of
voltage source inverter, it is necessary to control the current of the SCIG using PI controllers that generates the d-q
components of controlled stator voltage. The references of d-q components of stator current are achieved by PI
controllers that process the errors signal of torque and rotor flux. Thereby, the stator currents references calculations are
decoupled, allowing both current control loops to work independently. The SCIG control block diagram is presented in
Fig. 2.
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Fig. 2 Control diagram of generator-side converter.
As seen in Fig. 2, the torque and rotor flux are performed in closed-loop. The outputs of the PIs controllers of rotor
∗
, as shown below
flux and torque are the reference d-q components of the stator current ∗
∗
=(
∗
−
). (
∗
=(
∗
−
)(
+
+
)
(10)
)
(11)
The reference d-q components of the stator voltage ∗ and ∗ are calculated using PI controllers (proportional +
integral), processing error currents. The expressions that enable the calculation of voltages are given by:
∗
=(
∗
−
). (
+
)
(12)
∗
=
∗
−
.(
+
)
(13)
and
are the proportional gains and,
and
are the gains of the integrator. The reference d-q
where:
components of the stator voltages ( ∗ and ∗ ) presented are transformed to the stationary reference frame (αβ) with
the use of the spatial position of the rotor flux and, then are applied to the algorithm of sinusoidal PWM which enable
the activation of the IGBTs.
2.4 Rotor flux estimation
The rotor flux operation needs to calculate its position and its magnitude. They are calculated by using the equations
estimators based on machine model. In this work, the rotor flux is estimated using the following equation:
−
=
(
−
) +
(14)
From the Equation (15), the position and magnitude of rotor flux are determined by:
=
=
(15)
=
=
+
(16)
3. Grid-side converter control
The grid side converter control is achieved by using grid voltage orientation due to it allows an independent control of
grid active and reactive power. This orientation consists in fixing the q axis of the synchronous coordinate system with
the grid stator vector expressed in the stationary coordinates. Thus, the active power which is responsible for evolution
of the DC bus voltage ( ), is controlled by the and, the reactive power is controlled by the .
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3.1 Grid-side converter model
For modeling of the grid side converter, the grid voltage orientation is adopted and this implies to align the quadrature
= 0 and
=
. Thus, the equations expressed in
axis of the reference system with the vector of voltage, i.e.,
terms of space vector are given by [5,6]
=
+
−
+
(17)
is the control voltage provided by the converter
where is the resistance of the inductor and and its inductance,
and
is the grid-side filter current. It is observed in these equations, which the dq components of grid current are
controlled by correct choice of voltage generated by converter. Thus, as an alternative are using PIs controllers to
command a sinusoidal PWM to generate the voltages should control these currents.
The DC link voltage dynamics is given by
( )
1
= −
(18)
2
where C is the capacitance, is the generator power and P is output power of the grid-side converter.
In synchronous dq reference system the active and reactive power for a symmetrical three-phase system when doing
= . Thus, the equations of active and reactive power, are done by:
orientation rotated 90°; it has = 0 and
3
= (
)
(19)
2
3
= (
)
(20)
2
3.2 Control of the grid active and reactive power
Equations (19) and (20) allows the control of the grid active and reactive power are performed through the currents
and , respectively. The control of DC bus voltage is achieved by the control of
and it is done by:
∗
(
=
∗
−
(
)+
∗
−
)
(21)
The control of reactive power is achieved by the control of
and they are done by:
2 ∗
∗
=
Q
(22)
3. e
where, Q∗ = (P ∗ √1 − PF ∗ )/PF ∗ and, PF is reference power factor.
The DC bus voltage control ( ) is done by a PI controller which determines the reference value ∗ , while the ∗
value is kept at zero to ensure that the power factor is unitary. The current references ( ∗ and ∗ ) values are compared
with values obtained from the power grid ( and ) and the errors are processed by two PI controllers to generate the
voltage
. The expressions that permit to calculate the voltages are given by:
∗
=
∗
−
.
+
−
∗
=
∗
−
.
+
+ Lωi + e
Lωi
(23)
(24)
where the
and
are the proportional gains,
and
are the gains of the integrator of the PIs
controllers, respectively. The feed forward terms are added in order to improve the coupling between d and q
components and, consequently, to reduce the steady-state errors in and .
The d-q components of control voltage are transformed to
using the grid voltage vector position which it is
computed by a phase-locked loop (PLL). The − components of control voltage will be used to generate the signals
to drive the IGBTs of the converter with the use of any technique of sinusoidal PWM. The control scheme of the
converter is shown in Fig. 3.
4. LCL filter design
In this section is presented the design parameters for the LCL filter, which is based on paper [5]. For this purpose, it is
necessary to know the values of the rated inverter power (Pn) - given by power-generator, the rated frequency network
(ωn) and the switching frequency of the converter (ωsw). In subsequent development, filter values are reported as a
percentage of base line values, given by
(25)
=
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=
1
(26)
where Em is the rms line voltage, ωn is the frequency of the network and Pn is the nominal active power of the generator,
absorbed by the converter. The resonant frequency is referred to the switching frequency value by
=
(27)
where, k is the factor that expresses how much the switching frequency is higher than the resonance frequency.
Thus, the LCL filter design is performed according to some criteria, given below:
a)
For the reactive power of the capacitor not interfere with the operation of the converter current control, the
value of the capacitor is limited so that the reactive power absorbed at nominal conditions is less than 5% of
the nominal power GIGE.
b) To limit the voltage drop across the inductor, the value of the total inductance (LT = Lg + L) should be less than
10% of the base impedance.
c) To avoid resonance problems at low and high frequencies of the harmonic spectrum, the resonance frequency
must be in a range between 10 times of the line frequency and half of the switching frequency.
d) The Rd value must be sufficient to prevent oscillations, but cannot be so high such that it reduces efficiency.
Fig. 3 Control diagram of grid-side converter.
Based on the criteria adopted above, the filter design will be performed for the system that uses value of line voltage
of 230 Vrms (line to line), 60 Hz and rated power of 75kW (SCIG nominal power). The switching frequency of 5 kHz
was adopted. Thus, according to the equations (25) and (26), are determined the base impedance Zb and base
capacitance Cb, given by 0.71 Ω and 3.76mF, respectively. Therefore, it follows the steps shown below to the design of
the filter parameters:
1) Initially, it is defined an impedance of the inductor L of 2.7%, i.e., L = 50.85 μ H.
The maximum value of the filter capacitor is given by Cf = 0.05 x 3.76 m = 188 μ F, which satisfies the limit of the
condition (a). If adopted a value of Cf much smaller than the calculated maximum, you may need a very high value of
inductance.
2) To determine the value of the inductor Lg, one uses the criterion (b) and also as objective to obtain a tolerable
ripple attenuation of the grid current. Thus, the inductor Lg is calculated as a function of L using index r, given
by
= .
(28)
where, index r is the relation between the two inductances. The ripple attenuation is defined by [5], as
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( )
1
=
(29)
( )
[ . ( + 1). . . ]
1+
Therefore the calculation of L is determined according to this equation. Considering an attenuation of approximately
20%, a value of about r = 1.2 is calculated, corresponding to Lg = 61 μ H, i.e., impedance of 3.24%. Thus, the sums of
the two inductances respect condition (b).
3) From the information of L, Lg and Cf obtained above, one can calculate the resonance frequency using the
following equation [5]
=
.
(30)
.
Thus ωres = 3770 Hz, it is verified that this value satisfies the criterion (c).
4) The Rd value is chosen on the first estimate to be equal to the impedance of the capacitor Cf in the resonance
frequency, thus Rd =1.8 Ω.
5. Simulation results
Tests of computer simulation of the vector control for the stator side converter and the grid side converter in order to
control the flow of active and reactive power to the grid was carried out with the use of MATLAB/Simulink. System
parameters, including control loop parameters are shown in Table 1.
Table 1 SCIG parameters and PIs controllers.
SCIG parameters
Parameters of the PIs controller
of SCIG
Rated power
75 kW
Kp = 50 (current controller)
Stator voltage
460 V
Ki = 500 (current controller)
nominal frequency 60 Hz
Kp = 4000 (flux controller)
Rs
0.03957 Ω
Ki = 5500 (flux controller)
Rr
0.02215 Ω
Kp = 1 (torque controller)
Lm
0.01664 H
Ki = 100 (torque controller)
Ls
0.017 H
Lr
0.017 H
Parameters of the PIs controller of
GSC
Kp = 0.67 (current controller)
Ki = 12 (current controller)
Kp = 3000 (dc-voltage controller)
Ki = 6500 (dc-voltage controller)
VDC = 650 V
In order to examine the dynamic behavior of the torque and flux rotor control for stator side converter, and the
control of the DC link voltage and reactive power for the converter side of the grid, simulation studies with operation in
variable rotor mechanical speed with sinusoidal profile and references variations of active power and power factor with
step profile are presented in Fig. 4.
The initial active power and the power factor references were, respectively, -40 kW and +0.7 (inductive), thus the
reference reactive power is 41 kvar. The active power reference was changed from -40 kW to -70 kW at 1.2 s and the
power factor reference is maintained constant in +0.7, which leads to a change in reactive power of 41 kvar to
61.2 kvar. At 1.25 s, the power factor was changes from +0.7 to +1 and active power reference is maintained constant in
-60 kW, consequently this leads to a change of the reactive power from 61.2 kvar to 0 var. At time of 1.45, the active
power reference was changed from -60 kW to -70 kW, with constant power factor reference in +1, thus the reactive
power is maintained constant in 0 var. Finally, at 1.5 s, the power factor reference was changed from
+1 to -0.7 (capacitive) and, the active power reference maintained constant in -70 kW, consequently this leads to a
change of the reactive power from 0 to –71.4 kVAR.
It can be observed that the active and reactive power references are attended by control carried in the stator converter
side and the grid converter side, also the Fig. 4 illustrates that the responses of Ps and Qg are decoupled when either of
them is changes. Fig. 5 shows the transitory of stator power in detail the power factor was changes from +0.7 to +1 and
active power reference is maintained constant in -60 kW, which demonstrates the good performance of the controller.
The result presented in Figure 6 shows that the high-frequency current ripple has been reduced by using of LCL filter,
thus meeting its goal as defined in Section 4. It is verified that the converter current THD is 25.2% and the measured
grid current has a THD, with about 3.79%.
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(a)
(b)
(c)
Fig. 4 Control of active power and power factor of the GIGE in speed variation.
Fig. 5 Stator voltage and current during power factor references changed from +0.7 to +1 and active power reference maintained
constant in -60 kW.
a)
Converter current.
(b) Grid current.
Fig. 6 Frequency spectra of steady-state converter and grid currents.
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5.1 SCIG control
In Fig. 7(a), the electromagnetic torque value evolution is represented, which presents a behavior identical to rotor
speed because of its dependence on this speed. In the Fig. 7(b) shows that the rotor flux remains constant over its
reference value, independent of variations of torque and speed. The d-q components of the stator current can be seen in
Fig. 7(c) and (d). The d- component remains constant because it is determined by means of flux open loop by using PI
controller, where the flux reference is set constant. Unlike, the q- component constantly changes because of its
dependence on the torque variation.
(a)
(b)
(c)
(d)
Fig. 7 Rotor flux oriented vector control for the generator-side converter.
5.2 Grid-side converter control
In Figs. 8 (a) and (c), it can be observed how the d-q component varies like the reactive and active power, respectively
(Figs. 8 (b) and (d)). The grid voltage orientation allows independent control of grid active and reactive power through
the grid current components: P is controllable by iq and Q by id. As can be observed in Fig. 8, the DC-voltage remains
constant over its reference values from the power control regulation, such that the net power exchanged with the
DC-bus capacitor is kept at zero.
(a)
(b)
(c)
(d)
(e)
Fig. 8 Grid voltage oriented vector control for the grid-side converter.
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6. Conclusion
This book chapter presented a SCIG connected to the grid using a back to back converter and using LCL filter. The
SCIG control was made by the converter connected to the its stator, by using rotor flux orientation and PI controllers
that control the torque and the rotor flux of the generator. The active and reactive power were controlled by the
converter connected to the grid, grid voltage orientation and PI controllers allow to control the DC-voltage and reactive
power. The controllers have a satisfactory performance due to the fact that the references are followed. The LCL filter
was designed using the parameters of the generator and allows to reduce or mitigates the harmonics components
amplitude. This filter has a better performance, minor volume and costs than L filter.
Thus, the PI controllers and LCL filter can be used in wind power applications using SCIG connected to the grid by
back to back converter and LCL filter.
Acknowledgements The authors acknowledgement to the FAPESP by the financial support.
References
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squirrel Cage induction generator wind turbine, Computers and Mathematics with Applications 64 (2012) 102-114.
[3] W. Leonhard. Control of Electrical Drives. Springer-Verlag Berlin Heidelberg New York Tokyo, 1985.
[4] Jiahu Guo, Xu Cai, and Youming Gong. Decoupled control of active and reactive power for a grid-connected
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and Power Technologies. DRPT 2008., pages 2620 – 2625, April 2008.
[5] M. Liserre, F. Blaabjerg, and S. Hansen. Design and control of an lcl-filter based three-phase active rectifier. 1:299–307 vol.1,
30 2001-Oct. 4.
[6] J. R. Rodríguez, J. W. Dixon, R. Espinoza, J. Pontt, and P. Lezana. Pwm regenerative rectifiers: State of the art.
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