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11Статья поступила в редакцию 10.01.10. Ред. рег. № 692 The article has entered in publishing office 10.01.10. Ed. reg. No. 692
УДК 621.313.2
УПРАВЛЕНИЕ ВЕТРОУСТАНОВКОЙ С ПОМОЩЬЮ АСИНХРОННОГО ГЕНЕРАТОРА
М. Безза, Б-Эль-Муссауи
LEE&TS - Электротехническое отделение Научно-технологический факультет Мохаммедия - Марокко e-mail: m_bezza@yahoo.fr
Заключение совета рецензентов: 20.01.10 Заключение совета экспертов: 25.01.10 Принято к публикации: 30.01.10
В данной статье рассмотрено напряжение управления на выходе асинхронного генератора, подключенного к инвертеру /выпрямителю PWM. Это устройство предназначено для преобразования энергии ветра в случае использования автономной ветроустановки. Испытываются и сравниваются два способа управления: векторное управление магнитным потоком ротора и прямое управление крутящим моментом (DTC). В обоих случаях в конструкции установки учитывается эффект насыщения. Представлены результаты расчетов для случая изменения скорости вращения ротора.
Ключевые слова: асинхронный генератор, ветрогенератор, векторное управление, DTC, насыщение.
INDUCTION MACHINE BASED WIND-TURBINE CONTROL M. Bezza, B-El-Moussaoui
LEE&TS - Electrical Engineering Department Science and Technology Faculty Mohammadia-Morocco e-mail: m_bezza@yahoo.fr
Referred: 20.01.10 Expertise: 25.01.10 Accepted: 30.01.10
In this paper, we study the control voltage at the output of an asynchronous generator connected to an inverter/rectifier PWM. This device is intended for application of wind energy conversion in the case of an isolated site. Two control techniques are tested and compared: vector control in rotor flux oriented and direct torque control (DTC). In both cases, the effect of saturation is taken into account in the design of the machine. Simulation results are presented in the case of variations in rotor speed.
Keywords: induction generator, wind-generator, vector control, DTC, saturation.
Introduction
Asynchronous machines are widely used in the conversion of wind energy [1], in the case of mass production, using more and more structures wound rotor [2-5]. By connecting the rotor winding to the network through a rectifier and PWM inverter, it is possible to shift control and operate the structure in the variable speed. In the case of autonomous operation, the use of cage induction machines is more common [6-12]. These have advantages such as robustness, reduced maintenance and low cost.
The asynchronous machine with no field winding, it is necessary to provide magnetizing energy. In the case of generator operation, this energy can be generated by a capacitor connected in parallel to the stator windings or
using a converter and capacity connected side of DC-link [1, 6]. However, in operating autonomous mode, the speed and load have not fixed, the stator voltage can vary in large proportions. It then becomes necessary to use a system of regulation appropriate to maintain the output voltage amplitude and constant frequency. Works has been done in this meaning [6-9] by controlling the device consists of an asynchronous generator connected to a rectifier and an inverter controlled PWM.
Using a PWM rectifier can, by controlling the frequency reference signals to maintain a negative shift so that the machine operates in generator. Furthermore the phase shift between signals reference and stator currents can control the flow of reactive power and thereby maintain optimum magnetization of the machine.
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Various control strategies have been proposed [6, 7, 13, 14]. In this paper, we present a comparison of two control strategies. The studied system can be reduced to the machine connected to the rectifier feeding a load equivalent; the purpose of the control system is to maintain a constant voltage DC-bus. We then compare the performance of rotor flux oriented vector control and the command based on direct torque control DTC.
After the introduction of the system studied, we present the model of the machine. This from the classical model in the Park axis, taking into account the effects of saturation magnetic by induction variable. The second part is the presentation of the two control strategies tested. Finally, we present simulation results using both strategies during changes in rotor speed.
The system studied
The overall system studied consists of a wind turbine, an asynchronous generator and inverter-rectifier PWM. In the case of autonomous operation with a load balanced, it is possible to reduce the load of continuous side. Therefore, the study of the command can be restricted to that of the voltage at the output of the PWM rectifier. The system studied is then simplified as shown in Fig. 1.
Fig. 1. System studied schematic Рис. 1. Схема исследуемой системы
R is the load resistance reduced side continuous and C filter output rectifier capacity.
The latter is approximated by a polynomial in function of the magnetizing current im. It's lead to the following matrix system [15]:
Xd' -mJs 0 -maLrn isd
Vsq ® als R.. ® aLm 0 lsq
0 - Rr ЮЛ Rr r (lr + Lm ) lmd
0 _ЮЛ -Rr ®r (lr + Lm ) Rr i mq
l. 0 Lm + L
/ md m ' ~m I . I
0 I
i J
r r md mq
m
L + T ' JOL
i2
-l 0 l + T + T' — T'
h U lr -t- bm + L,m I . I bm ..
i i
m
0 -1
i J
md mq
l + l + L'T=t
r m m
with:
<°r — ■ ma- ;
imd — isd + ird ;
i - i + i ;
mq sq rq >
|m| - 1.2 -2 '4imd + imq
T ' — dLm
Lm — .
im
di.d dt
di.q dt
dimd dt dimq
mq dt
(1)
(2)
(3)
(4)
(5)
(6)
This model of the induction machine can be operated in a marker linked to the rotating field (ma = ros) for the implementation of vector control and a marker linked to the stator (ma = 0) for the direct control of torque.
The evolution of the magnetization inductance of the machine designed according to the current im is shown in the following Fig. 2 [15].
Asynchronous generator model
The model used for simulating the operation of the asynchronous machine takes into account the effect of saturation of materials. Indeed, the gap of asynchronous machines is generally low; the nonlinearity of magnetic materials has a significant effect [1, 15]. This effect is difficult to understand in the case of conventional three-phase models. Therefore, it usually takes two phase models to reflect a comprehensive manner. This obviously implies that the induction is homogeneous in the whole structure. In our approach, we adopt the model of Park dq induction machine. The effect of saturation is taken into account through a magnetizing inductance Lm.
Fig. 2. Magnetization curve Рис. 2. Кривая намагничивания
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+
Asynchronous generator control
The objective is to control the voltage input of the inverter VDC. From the desired value of the voltage, it is possible to express the power of reference by
Vdc-ref^dc Pref '
(7)
where idc is the output of the rectifier.
Neglecting the different losses, we obtain directly the expression of electromagnetic torque:
T — Pref
em — Q
(8)
T — pФ i .
em Г l r sq
(9)
L i d
ф _ m sd
1 + Ts
(10)
maintained at this value, determining other parameters of the model order. The values obtained are not accurate transient but it simplifies the control and not to resort to adaptive correction.
Thus, considering the steady controlled, rotor flux is only carried by the axis d and maintained at the value &rd f By introducing the expression module of the magnetizing current, we can write:
L
ф
md
rd-ref _ I 2 Фг-ref
3 ' '
M„
(12)
The control voltage Vdc can be done through the setting of the electromagnetic torque, which amounts to the same approach as that used in the case of a classical motor control operating.
Driving vector The model of induction machine made for the development of the command is the model linearized in a landmark associated with rotating field and the command is classical in rotor flux oriented vector: orientation of reference is chosen so that = ®r and we order to keep constant.
The implementation of the command needs to estimate the electromagnetic torque, the rotor flux and the stator pulsation The electromagnetic torque is expressed from the current isq by:
The intersection between the characteristic Lm (im) and the curve defined by (12) determines the value of the magnetizing inductance Lm to be considered in the command. Fig. 3 summarizes the algorithm of vector control adopted.
pa ■
isd ■
is,
I/ d t Tem-ref Isq-ref
pi -
Ib-ref
The rotor flux is, in turn, according to the current isd and the rotor time constant Tr = Lr/Rr:
Pf-
Fig. 3. Algorithm of the vector drive Рис. 3. Алгоритм векторного управления
Knowing ensures the validity of equations because the repository "dq" must always follow the rotating field. For this it uses the internal angular relationship = ror + ro with ro = pQ. The speed of the machine is measured and that the rotor field is estimated. Then obtained for ros:
ю s — -
L i
m sq
T„ Ф,
- + pQ.
(11)
The flow is controlled through the current isd and torque by isq.
The implementation of the command requires knowledge of various parameters of the asynchronous machine (Lm, Ls and Tr) these are not constant from the non-linear materials. However, if the flow is controlled at a constant value these parameters can be considered constant for the magnetic state. We can then determine the value taken by the magnetizing inductance Lm for the reference flux and, assuming that the magnetic state is
Note that the reference power is calculated in agreement on the load receptor, we reverse the sign of the current isq-ref to ensure a functioning generator.
Direct torque control (DTC)
Classically DTC is developed from the expressions of the model of induction machine expressed in the stator reference [16]. Thus, the amplitude of stator flux is estimated from its components along the axes a and P [16, 17]:
(t)_ J (Vsa- Rsisa d 0 ,
ф, (t) — J (V,- R,i„ )dt
ф, — ,/ф?„ + ф2Р.
(13)
(14)
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The electromagnetic torque is then obtained by:
Tem = p (^„Ap-^* )• (15)
The correction flow is designed to maintain the vector in a circular band around the reference value. The correction torque performs the same function for the latter. In the case of a generator in operation, the reference torque is negative. Fig. 4 shows the structure of the direct control of the torque adopted for the application.
Fig. 4. Algorithm of DTC Рис. 4. Алгоритм DTC
Таблица переключений Switching table
Таблица 1 Table 1
N 1 2 з 4 6 б
CTOR = 1 V2 Vз V4 V, V6 Vl
Cflw = 1 CTOR = 0 V? Vo V? Vo V? Vo
CTOR=-1 V6 Vl V2 Vз V4 V,
CTOR = 1 Vз V4 V, V6 Vl Vo
Cflw = 0 CTOR = 0 Vo V? Vo V? Vo V?
CTOR=-1 V, V6 Vl V2 Vз V4
With:
V0 _[О О О]; V _[l о О]; V2 _ [l О О]; Vз _[0 1 0]; V4 _[0 1 1]; V, _[0 0 1]; V6 _[1 0 1]; V? _[1 1 1].
The control Table 1 given below is built according to the state variables C^ corrector flow and CTOr, the correction torque and the area N the position of It is a standard table for a functioning 4 quadrants.
It is noteworthy that in the case of the direct control of torque the effect of material nonlinearity is implicitly taken into account since the magnitudes of state are constituted by flows.
Results of simulation
We simulated the system behaviour under the environment MATLAB-SIMULINK. The two strategies introduced above were then tested in the case of variations in rotor speed. In what follows, we detail the aspects of each of the two strategies and we compare simulation results. In both strategies, the reference voltage at the output of the rectifier is taken as Vdcref = 465 V. Moreover, the same variations of speed, given in Fig. 5.
Fig. 5. Speed training Рис. 5. Изменение скорости вращения
Vector control In the case of the vector control, reference value of rotor flow is chosen Фrd-ref = 0.7 Wb, Fig. 6 shows evolution of this flow.
Fig. 6. Rotor flux Рис. 6. Поток ротора
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The voltage at the output of the rectifier is in Fig. 7. One can see that both quantities are well regulated and that the flow is insensitive to variations in speed. In the case of the voltage response to a change in speed is relatively fast and does not exceed 5% of the reference value during the two disturbances.
Fig. 7. Rectified voltage output Рис. 7. Напряжение на выходе выпрямителя
10
-5
-10
-15
-20
/ ? Ца
t(s)
Fig. 8. Direct and quadrature currents of stator Рис. 8. Постоянная и поперечная составляющая тока
In Fig. 8 we represent the variation evolution of currents isd and isq. The pace of current isd is similar to that of rotor flux. The latter is well regulated and insensitive to changes in speed. The current isq, meanwhile, responds to them to adjust the torque to the tension, and therefore the power generated, remains constant equal to the baseline.
In Fig. 9 we see zoom of stator phase current evolution (isa). The amplitude and frequency adjust after the change of speed.
Direct torque control In the case of DTC, the stator's reference flow, is also taken as &sref = 0.7 Wb. Fig. 10 represents the two components of flow. Once the transitional exceeded the value of the module flow remains close to the reference and is not influenced by changes in speed.
Fig. 10. Stator flow Рис. 10. Поток статора
The response of the rectified voltage is approximately as fast as in the case of vector control (Fig. 11). This is also the case of disturbance rejection, made in our case by changes in speed.
Fig. S. Stator current isa Рис. S. Ток статора isa
Fig. 11. Rectified voltage Рис. 11. Выпрямленное напряжение
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On the following Fig. 12, 13, we present along the Concordia axis (a and P), stator flows and currents. In both cases, we see clearly the change in frequency due to the speed. However the flows amplitudes remain constant because the regulation of the latter (Fig. 10).
Fig. 12. Flow in Concordia axis Рис. 12. Течение по оси Concordia
Fig. 13. Concordia components stator courants Рис. 13. Компоненты Concordia тока статора
A temporal extension of a phase current at a speed variation is also shown in Fig. 14. Again, we see the effect of speed variation on the frequency currents. The evolution of the current phase is very close to that obtained by the control vector.
In Table 2 we present a synthetic way, the stator frequency signal obtained by the two control strategies at different speeds.
Table 2
Stator frequency
Таблица 2
Частота статора
Speed of entrainment Stator frequency, Hz
vectorial order direct torque control
?,0 tr/mn 46.0829 45.4545
900 tr/mn ,6.1?98 55.5556
600 tr/mn 3,.2113 34.2466
Through the simulation results obtained, both strategies of control seem give very similar results in dynamics and disturbance rejection However, since the direct control of the torque induced losses by switching and iron which are higher share of the random frequency and relatively high converter, further studies on power quality and performance of the device controlled by the two strategies will be interesting.
Conclusion
In this paper, we presented the study of the control voltage of a system consisting of asynchronous generator to feed a rectifier PWM.
The first is based on vector control in rotor flux oriented and the second the direct torque control.
Using an analytical model taking into account the saturation both strategies have been studied using simulations in the MATLAB/SIMULINK.
We tested their responses when the rotor speed varies. These results should be supplemented by an analysis of the losses generated by each of the two strategies.
Appendices
Table 3 gives the parameters of the machine studied.
Table 3
Machine's parameters
Таблица 3
Параметры генератора
Fig. 14. Stator current ¡sa Рис. 14. Ток статора ¡sa
Parameters Value Parameters Value
Pn kW J 0.23 kg-m2
Un 230/240 V D 0.002, Nm/rads-1
In 23.8/13.? A Rs 1.0?131 а
F ,0 Hz Rt 1.29,11 а
Nn 690 tr/mn p 4
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