Control of a Doubly Fed Induction Machine Wind Power Generator with Rotor Side Matrix Converter

Transcription

1 Control of a Doubly Fed Induction Machine Wind Power Generator with Rotor Side Matrix Converter Ricardo Jorge Pires dos Santos Abstract A method for control of a doubly fed induction machine (DFIM) in a variable speed constant frequency (VSCF) wind generation system is presented in this paper. It combines the advantages of a recently developed direct power control (DPC) algorithm, with a model reference adaptive system (MRAS) method for sensorless rotor positioning and a matrix converter. Simulation results demonstrate that the controller proposed has an excellent power control, at constant frequency, as well as a perfect rotor sector recognition using the MRAS observer. Nomenclature, Stator active and reactive reference powers., Stator active and reactive Power., Error in the active and reactive power, respectively., Stator and rotor voltage, respectively., Stator and rotor current, respectively. Angle between the stator flux and rotor flux., Stator and rotor frequency, respectively. Stator flux, rotor flux and air-gap flux, respectively. Component of the rotor current along the flux., Fluxes in αβ domain., Fluxes in dq domain. M Magnetizing inductance. Stator resistance. Ls Lr Stator inductance. Rotor inductance. PI proportional and integral parameters respectively. I Introduction The progressive depletion of fossil fuels, and concerns regarding environmental changes, are acting as major motivation for research and development of new sources for electric power generation. Wind power generation is becoming a viable and very attractive source of clean and renewable energy. In a conventional wind power generator, a constant speed mode of operation is used to keep the output frequency identical to the grid. In this paper, a VSCF system is proposed, since it has been widely demonstrated that variable speed generation systems have a higher energy capturing and converting efficiency than the fixed speed generation. In such system, the stator is directly connected to the grid, while an electronic converter is connected to the rotor, to control the active and reactive power, while maintaining unity power factor and constant output frequency. The conventional method used for independent control of active and reactive powers is stator flux oriented vector control, dependent on rotor position sensors. However, the use of these sensors is undesirable, as it causes the system to be highly dependent on the accuracy of computation of the stator flux and the accuracy of the rotor position, as well as drawbacks in terms of maintenance, cost, cabling and robustness []. Several research groups have proposed alternative methods that do not require rotor position information, such as direct torque control (DTC), but this method has been mostly used for cage rotor induction machines. In this work, a method for direct and independent control of active and reactive power, DPC, is presented, in which the measurements are carried in one winding, the stator, while the switching action is carried at another winding, the rotor [2]. However, rotor positioning information is needed, in order for the DPC technique to work properly. The MRAS is a well known method for the sensorless control of the squirrel cage induction machine, and its application to the DFIM is recently being analyzed. This system is used to estimate the rotational speed of the rotor, and the position is derived from that variable []. In this control system, a matrix converter is used to regulate the exciting voltage applied to the rotor, according to the principles of the integrated DPC/MRAS system and a power factor control algorithm. This method has the advantage of controlling the active and reactive power as well as providing unity power factor at constant output frequency, while processing only a fraction of the total power being transferred by the machine. The matrix converter control relies on the space vector modulation and sliding mode control methods [3], [4]. In figure, a basic model of the system under study is presented, and the interaction between each individual system mentioned above can be seen. This paper starts with the introduction of some relevant concepts, such as the DPC algorithm, the MRAS observer and the matrix converter technology. Then, simulation results are presented to validate the performance of the system, and some major conclusions are expressed in a last chapter.

2 DFIG Grid Filter MRAS DPC Power Control. P.Factor Control Figure. Control system basic model. II - DPC Algorithm It can be demonstrated, that active power handled by the stator can be increased with an increase in the angular separation between the rotor flux vector, and the reactive power drawn by the stator can be increased by reducing the magnitude of the rotor flux and vice versa [2]. It is important, then, to understand the effect of application of a voltage vector control to the amplitude and magnitude of the rotor flux vector, which is the key idea behind direct power control. With the three phase rotor winding orientation presented in figure 2, and in order to make an appropriate voltage vector selection, the phasor plane can be subdivided in six different 6º sectors,,2,.,6, with a voltage vector U, U2,,U6 corresponding to each one of them, as can be seen in figure 3. Phase b Phase c Phase a Figure 2. Three phase rotor winding spacial disposition. In a generating mode of operation, and considering anti clockwise direction of rotation of the flux vectors in the rotor reference frame to be positive, the flux is ahead of, as can be seen in figure 3. The application of voltage vectors U2 and U3 accelerates in the positive direction, resulting in an increase in angular separation between the two fluxes, consequently leading to an increase in the active power generated by the stator. U4 U3 Sector 3 Sector 4 U5 Figure 3. Phasor diagram of DPC Voltage Vectors. On the other hand, application of vector U5 and U6 would result in a decrease in angular separation between the rotor and stator fluxes, leading to a decrease in the active power generated by the stator. The reactive powers are controlled through the manipulation of the magnitude of the rotor flux. Application of voltage vectors U, U2, and U6, results in an increase in the magnitude of, indicating that an increased amount of reactive power is being fed from the rotor side and consequently less power is being drawn from the stator side. In an opposite direction, application of vectors U3, U4, and U5, reduces the magnitude of, increasing the amount of reactive power being drawn from the stator side, lowering the power factor. Assuming the power drawn by the stator as being positive and the power generated as being negative, and if the rotor flux is in the sector k, where k=,2, 6, it can be concluded, from the above discussion, that [2]: U2 Sector 2 Sector 5 Sector 6 U6 U The application of vectors U(k) and U(k2) would result in a decrease in the stator active power and vectors U(k-), U(k-2) would result in an increase in the stator active power. 2

3 Table. DPC algorithm voltage vectors. Perr<= Perr> Sector Sector 2 Sector 3 Sector 4 Sector 5 Sector 6 Qerr > U3 U4 U5 U6 U U2 Qerr <= U2 U3 U4 U5 U6 U Qerr> U5 U6 U U2 U3 U4 Qerr <= U6 U U2 U3 U4 U5 The application of vectors U(k), U(k) and U(k-), decreases the reactive power drawn from the stator side and U(k2), U(k-2), U(k3) increases the reactive power drawn from the stator side. The central idea of the DPC algorithm is to use the rotor side converter to select an appropriate voltage vector, forcing the stator active and reactive powers to follow the reference signal within the narrow band permitted by the hysteresis controllers. To estimate the active and reactive powers on the stator, and assuming a balanced three phase three wire system, only two stator currents and voltages need to be measured. The two stator voltages can be expressed as: And for the currents: Finally, the powers can be calculated as: () (2) (3) (4) (5) (6) This process is similar for both active and reactive powers. The control strategy that has been described can be summarized, as is presented in the table. In this table, the voltage vectors are organized according to their effect in the active and reactive powers. If for example it is convenient to decrease the active power while simultaneously increasing the reactive power, and assuming the rotor flux vector to be in sector 3, then vector 5 should be applied. III - MRAS Observer The key idea behind MRAS theory is to create a closed loop controller, where the output of the system is compared to a desired response from a reference model. The model parameters are continuously updated based on this error. Applied to the sensorless identification of the rotor flux vector sector, this system has a voltage model and a current model []. The voltage model provides the reference flux, and can be estimated through: (8) The stator flux can also be calculated from the stator current model, using the machine inductances, the estimated rotor position and the rotor and stator currents. These powers can be made to track any given reference, staying in a narrow band defined by the error that is assumed to be tolerable. This error is defined by the difference between the estimated powers (5), (6) and the reference. This concept is illustrated in the figure 4. The error between the reference flux estimated flux, in α-β components is: (9) and the () Figure 4. Controlled active power variation. The error in the active power is positive as long as the estimated power keeps rising, until the limit allowed by the hysteresis controllers is reached. At that point, a change in the instantaneous switching state is required, and afterwards the estimated power begins to decrease, until the minimum value allowed by the controllers, leading to the application of another voltage vector. Defined in this way, the error can be reduced by adjusting the estimated rotor position. With the above discussion in mind, a model of the MRAS observer is presented in figure 5. The PI controller drives the error defined in () to zero, and it s output is the estimated rotational speed, which by integration provides the estimated rotor angle. The band-pass filter in the voltage model is used to block the dc components of the measured voltages and currents. IV-MRAS: PI Controller Parameters Estimation 3

4 - \ Voltage Model Current Model r Figure 5. MRAS implementation model. The error, in d-q components, is: = - () The small signal model for the error is obtained as: = - - = - ( = ) (2) Assuming an orientation along the stator flux ( = ), and referring to a synchronous rotating frame: = (3) The d-q flux, derived from the current model, is not a DC signal unless the estimated speed is equal to the real speed, so replacing in (3) yields: = = (4) Finally, assuming =, and are obtained as: => M Δ (5) Using expressions (2), (4) and (5), a smallsignal model, used for designing the PI controller can be derived, as can be seen in figure 6. - Figure 6. MRAS small signal model. The open loop transfer function, derived from figure 6, is: G (s) = = (6) The closed loop transfer function has to be defined, to estimate the PI proportional parameter,, and integer parameter, : Assuming =, in order to isolate in (7): (7) (8) This transfer function has one simple pole, defined as: Finally, for the PI parameters: For T V-MRAS: Stability Analysis. (9) = (2) (2) In this section, the MRAS system stability is analysed, through the inspection of the closed loop transfer function: = (22) In this expression, M, and are constant. Consequently, the system s stability is only dependent on the product, which represents 4

5 the component of the rotor current along the flux, as can be understood through the observation of figure 7 [5]. restrictions can be summarized in the following expression: Figure 7. Component of the rotor current along the flux. This component of the rotor current along the flux can be computed as: = (23) The condition that guaranties system stability is: VI-Matrix Converter (24) The matrix converter is an AC-AC converter, assembled from individual semiconductor switches which act directly on the connections between the generator and the load. For that reason it is commonly called a direct converter. This converter consists of nine bi-directional switches, arranged as a 3x3 matrix, as shown in figure 8, so that any input phase can be connected to any output phase at any time [4]. This means that, at any instant, one and only one switch can be ON in each of the matrix lines. With these restrictions, only 27 states are allowed for the control of the matrix converter. Applying the space vector modulation method, these states can be represented in vector form, as can be seen in table 2 [4], [6]: Table 2. Space vector modulation of possible commutation states State Vector Figure 8: -Matrix converter topology. The matrix converter topology being described can be made to control the input currents and the output voltages through an appropriate control strategy. A space vector modulation (SVM) strategy is combined with sliding mode control in this paper to control the converter [3], [4]. Each individual switch has two possible states (ON/OFF), and there are 9 switches, which configures possible combinations. However, since the converter is supplied by a voltage source, the input phases must never be shorted, and due to the inductive nature of the load, the DFIG, none of the output phases can be left open. These To avoid further complexity, the vectors numbered from to 6 and the zero vectors are not used. The voltage and current vectors can be represented in the α-β plane, as shown in figures 9 and. 7, 8, 4, 5,, 2, Figure 9: - Generic voltage vectors representation. 5

6 2, 5, 3, 6, a) When =>, to decrease the error. b) When =>, to decrease the error., 4, To implement this control system, hysteresis controllers are used to maintain the error within tolerable limits (typically 2 Δ), using the command law (28): Figure : - Generic current vectors representation. (28) The vectors represented in these two figures, are fixed in space, but their magnitudes can change, reflecting the variations in the input voltages, in the case of voltage vectors or the output currents in the case of current vectors. At any given time and in each one of the directions shown, there are three vectors, all with different magnitudes, and three in the opposite direction in the α-β plane. For control purposes, and because a fast response of the system is highly desirable, only the two with bigger magnitudes are used [6], []. Along with SVM, sliding mode control is used in this work. This is a non-linear control technique, particularly fit to be used in power converters, in which the application of a high-frequency switching control between two discontinuity surfaces allows for the state space trajectory of the system to slide through the discontinuity surface [3]. Hysteresis Band Figure. Space state trajectory. In sliding mode control, the application of an infinite frequency switching control would allow the state space trajectory to exactly follow the reference signal. But as conventional semiconductors are frequency limited, it is impossible to exactly follow the reference signal, so there is an error defined as: (25) VII - DFIG Control with Rotor Side Matrix Converter With the previous chapter s theoretic considerations in mind, it is now possible to focus in the key idea behind this work, the control of a DFIG, whose stator is directly connected to the power grid, while acexcited by a matrix converter in the rotor side (Fig. ). To achieve this objective, the converter output (rotor side) voltages and input currents (grid side) must be controlled. The output voltages are imposed by the DPC algorithm, which generates voltage vectors depending on the estimated stator powers and according to the rotor flux position information, provided by the MRAS observer. Following this method, active and reactive power control can be achieved. On the other side, input currents must be controlled to guaranty grid side unity power factor. The active and relative power control can be achieved by establishing a relation between the 6 DPC method voltage vectors, with the 8 voltage vectors resulting from the space vector modulation technique. It must be kept in mind, though, that these 8 voltage vectors have fluctuating magnitudes, depending on the input voltages relative position [6]. Considering that at a certain instant in time they have the following α-β plane representation (Fig. 2): A control law is presented (26), in which Δ is a dynamic error: Δ (26) Using this control law, the system will be immune to perturbations and independent of circuit parameters, or operation point. The high frequency control applied, has to be alternately positive and negative, to guaranty a near zero dynamic error Δ, and so, condition (27) has to be followed [7], [8]. Consequently, it can be understood that: (27) Figure 2. Output Voltage Vectors. The selection of the U3 voltage vector (Fig. 3), according to the DPC method, implies that, to properly control the active and reactive powers, a decrease in the α component and an increase in the β component of the voltages is mandatory. Then, assuming the matrix converter voltage vectors 6

7 Reactive Power Active Power Park Transformation d,q αβ, Concordia Transformation,, αβ a,b,c Grid - - Current commutation Function DPC algorithm Vector Selection Vector Vector Matrix Converter,, DFIG MRAS Observer Stator Power Estimation Figure 3. Control System Implementation Model. representation of figure 2, it is clear that vector -6, 5, 4 should be applied to the rotor to obtain the same effect in the αβ components described above. On the other hand, it can be demonstrated that the unity power factor can be controlled, if the following condition is respected [6]: (29) This means that the q component of the input current must be null, in order to achieve unity power factor. Using sliding mode control, the error between this current and the defined reference ( =) is defined by: (3) The input current can then be made to track the given reference, using hysteresis controllers, with the following commutation function [8], [9]: (3) The function can only assume two logic levels, and -. When (3) is at level, meaning that reference signal is superior to the current, the system is expected to apply a vector with positive q component, decreasing the error, and otherwise, when is at level -, a vector with negative q component should be applied. These two strategies, the DPC voltage control and the unity power factor control have to be combined, when selecting an appropriate vector to control the machine. The DPC voltage control imposes the matrix converter output voltages, while the input currents are defined by a power factor control method. This means, that both the machine side and the power grid side, have to be taken under consideration at any instant in time. bidirectional power flow, unity power factor control and input/output characteristics are evaluated in this chapter. Fig.4, 5 shows the system s transient response due to a step change in active and reactive power command, from the initial = p.u., to =.9 p.u. at t=.4s, while is maintained at.2 p.u Figure 4. Active power transient response t[s] Figure 5. Reactive power transient response. VIII - Simulation Results A simulations study is carried out to verify the above control strategy. The power control, 7

8 Input voltage and current Input voltage and current [pu] Active and Reactive power Active and Reactive power [pu] [pu] Output voltage Input Current Figure 6. Output voltage Figure 9. Input currents Figure 7. Active and reactive powers Figure 2. Active and reactive powers Figure 8. Converter input voltage and current. As can be seen, the system exhibits excellent active and reactive power control, with a fast response to the active power reference step. The responses in the active and reactive power are perfectly decoupled. In the same simulation, Fig. 6 shows the output voltage, with a characteristic waveform, due to the high-frequency semiconductors commutation. The input currents presented in Fig. 9, exhibit some distortion, due to the fact that in this work, the use of null vectors was discarded. This leads to an excessive commutation frequency which causes current oscillation and noise. Another simulation was performed, in which the bidirectional power flow in the matrix converter was evaluated. Fig 7 and 8, show the active and reactive powers, and the input (grid-side) voltage and current respectively, when the DFIG is operating in sub synchronous mode. The input voltage and current are approximately in phase with each other Figure 2. Converter input voltage and current., and the reactive power is nearly zero, indicating that unity power factor can be achieved. In this situation, the rotor is being supplied with active power from the grid side, through the matrix converter. On the other hand, Fig. 2 and 2 show the active and reactive power as well as the input voltages and currents, with the machine operating in super synchronous mode. In this case, the opposite phase relation between the input voltage and current indicates that the rotor is supplying active power to the grid. The reversing of the input current between sub synchronous and super synchronous mode of operation, demonstrates the matrix converter bidirectional power flow capacity. Another simulation was performed on the MRAS observer, and the results are presented in Fig. 22 and 23. The first simulations done using this method encountered some stability problems, and so a robust system was tested, validating the condition expressed 8

9 Error Sector r Figure 22. MRAS sector identification Figure 23. MRAS error in (24). Perfect rotor flux sector identification was achieved (Fig. 22), and a rapid error convergence to zero is observed (Fig. 23). IX Conclusion The simulation study on the proposed method, has clearly demonstrated that sensorless power control, through the application of an appropriate alternated excitation to the rotor, using a matrix converter is a viable solution to a DFIG based wind power generator control. The DPC algorithm allows independent active and reactive power control, and is insensitive to the parameters of the machine, since it depends only on the currents and voltages measured in the stator. The MRAS observer exhibits an excellent tracking performance under simulation, allowing sensorless power control. The matrix converter has bidirectional power flow capacity, implementing the DPC algorithm while simultaneously controlling the power factor and maintaining a constant output frequency. Input and output waveforms show an acceptable distortion level, which could be significantly decreased if null vectors were used. [8] Aparício, L.; Esteves, P.; Conversor Matricial: Aplicação em Aproveitamentos Eólicos com Máquina de Indução Duplamente Alimentada, Trabalho Final de Curso da Licenciatura em Engenharia Electrotécnica e de Computadores, Instituto Superior Técnico, Setembro de 27. [9] Huber, L.; Borojevic, D., Burany, N.; Analysis, design and implementation of the space-vector modulator for forced-commutated cycloconvertors, IEE Proceedings- B, Vol. 39, No. 2, March 992. [] Holmes, D.; Lipo, T.; "Implementation of a Controlled Rectifier Using AC-AC Matrix Converter Theory"; IEEE Transactions on Power Electronics, Vol. 7, No, January 992, pp X References [] Cárdenas,R.; Peña, R., Asher,G., Clare, J., Cartes, J., MRAS Observer for Doubly Fed Induction Machines, IEEE Transactions on Energy Conversion, Vol. 9, No. 2, June 24. [2] Datta, R. ;Ranganathan, V.; Direct Power Control of Grid-Connected Wound Rotor Induction Machine Without Rotor Position Sensors, IEEE Transactions on Power Electronics, Vol. 6, No. 3, May 2. [3] Huber, L.; Borojevic, D.;, Space Vector Modulated Three-phase to Three-phase Matrix Converter with Input Power Factor Correction, IEEE Transactions on Industry Applications, Vol. 3, No 6, Novemver/December 995. [4] Silva, J.Fernando; Electrónica Industrial; Fundação Calouste Gulbenkian, Lisboa, Portugal, 998, Pag [5] Marques, Gil; Controlo de Máquinas Eléctricas ; A.E.I.S.T., Lisboa, Fevereiro 26. [6] Menino, A.; Antunes, J.; Processamento Electricamente não Poluente de Energia Eléctrica, Trabalho Final de Curso da Licenciatura em Engenharia Electrotécnica e de Computadores, Instituto Superior Técnico, Julho de 22. [7] Pinto, S.; Aparício, L.; Esteves, P.; Direct Controlled Matrix Converters in Variable Speed Wind Energy Generation Systems, IEEE PowerEng Conference 27, Setúbal, Portugal, April 27. 9