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Ensuring Fault Ride Through for Wind Turbines with Doubly Fed Induction Generator: a Model Predictive Control Approach
Proceedings of the 18th World Congress The International Federation of Automatic Control Milano (Italy) August 28 - September 2, 2011
Ensuring Fault Ride Through for Wind Turbines with Doubly Fed Induction Generator: a Model Predictive Control Approach M. Soliman, O.P. Malik and D.T. Westwick
Electrical Engineering Department, University of Calgary, Calgary, AB T2N 1N4 Canada ( e-mail: {msoliman,maliko,dwestwic}@ucalgary.ca )
Abstract: This paper proposes a novel control strategy, based on Model Predictive Control (MPC), which ensures Fault Ride Through (FRT) for wind turbines with Doubly Fed Induction Generators (DFIGs). During large voltage dips, large currents are induced in the rotor that can destroy the rotor converter. The common approach used to protect the rotor converter is to disable the converter and to dissipate the rotor power via a crowbar circuit. This approach is currently not accepted by most grid codes which dictate that grid connected wind turbines should remain connected to the grid during severe faults with full control over their active and reactive power. The proposed strategy ensures FRT for DFIG grid connected wind turbines without using a crowbar and therefore meets recent grid codes requirements. This is achieved by using a Dynamic Series Resistance and an MPC controller incorporating most of the DFIG’s constraints. Keywords: Model Predictive Control, Wind Power Generation, Doubly Fed Induction Generators.
1. INTRODUCTION Wind turbines equipped with DFIGs are currently the most used configuration for wind power generation (Lopez et al., 2009). With its partially rated power converters (typically 2030% of the system rated power), variable speed operation of the wind turbine is provided at relatively low cost.
to the grid during faults, but also control over its active and reactive power should be maintained (FERC, June 2005). Generally, FRT capability is specified by a region like in Fig. 2, in which the wind turbine must not trip under symmetrical faults at the point of interconnection. Different countries have adopted different FRT curves like the one shown in Fig. 2 (Zavadil et al., 2007).
A DFIG based wind turbine, shown in Fig. 1, consists of a turbine rotor coupled to a Wound Rotor Induction Generator (WRIG) through a gear box. The rotor of the WRIG is connected to the grid through the rotor side converter (RSC), the DC link and the grid side converter (GSC).
β*
Initially, DFIGs with active crowbars were viewed as meeting the FRT requirement dictated by grid codes. However, the use of a crowbar results in a loss of control over the DFIG. Furthermore, when the crowbar is active, the DFIG behaves like a conventional WRIG, consuming more reactive power, possibly resulting in voltage stability deterioration. Quite recently, grid codes were modified such that for a wind turbine to be FRT capable, it must not only remain connected 978-3-902661-93-7/11/$20.00 © 2011 IFAC
* Qs* QGC Vdc*
Tg*
RSC Controller
vr*
The main drawback of DFIGs is that they are very sensitive to changes in their terminal voltage (Lopez, et al., 2009; Morren & de Haan, 2005). For example, when an external fault occurs, large voltage dip is produced resulting in Large rotor currents that can lead to the destruction of the RSC. Typically, an active crowbar circuit, shown in Fig. 1, is installed in DFIGs to protect the RSC during grid faults (Morren & de Haan, 2005). The main idea is to divert high rotor currents from the RSC to a resistor bank, called a crowbar, to protect the RSC.
Turbine Controller
vC*
RSC DC link GSC
Gear box
Wind turbine
GSC Generator Controller Controller
Crowbar
Filter
Grid
WRIG
Fig. 1. DFIG based wind turbine.
A huge research effort has recently been undertaken in order to come up with a new control/protection strategy to ensure FRT capability for DFIGs (Dawei et al., 2006; de Almeida et al., 2004; Jin et al., 2010; Lopez, et al., 2009). One approach followed by many authors is to modify the conventional RSC control algorithm (Pena et al., 1996) such that FRT is achieved without using additional protection hardware. De Almeida, et al. (2004) suggested using fuzzy logic controllers to control the rotor currents. Stator flux demagnetization using RSC control was proposed by Dawei, et al. (2006). Lopez, et al. (2009) showed that FRT cannot be met solely by
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10.3182/20110828-6-IT-1002.03060
18th IFAC World Congress (IFAC'11) Milano (Italy) August 28 - September 2, 2011
the DFIG control when the voltage dip is severe and suggested using a combination of flux demagnetization and crowbar protection. A combined converter protection scheme based on using a Dynamic Series Resistance (DSR) and conventional crowbar is proposed by Jin, et al. (2010).
quantities, respectively. The superscripts denote quantities referred to arbitrary, stationary, synchronously rotating and rotor reference frames, respectively.
This paper proposes a novel control strategy that ensures FRT for wind turbines with DFIGs. The proposed strategy uses a multivariable MPC controller to control the RSC and a DSR to protect the RSC during severe grid faults. The proposed strategy does not require the disconnection of the RSC and meets recent grid codes’ requirements.
(3) (4) (5) (6) Remark 1: Dynamic equations of the WRIG written in the stationary, synchronously rotating and rotor reference frames can be obtained from (1) by replacing by , and , respectively, where denotes the synchronous speed. Using (5)-(6), the rotor flux linkage and the rotor voltage can be written in the rotor reference frame as in (7)-(8),
Beginning of voltage dip
0.8
0.9 pu
Wind Plant Must Not Trip
Vdip
Voltage at the point of interconnection, pu
1.0
0.6 Test Fault
0.4 0.2
0.15 pu 0
Using the space vector notation, in (1) can be written as:
where
Wind Plant May Trip
, equations
and the rotor internal voltage,
, is
defined in (9) (Lopez et al., 2007).
0.625 s 0.5
1
1.5 2 Time, s
2.5
3
(7)
3.5
Fig. 2. Fault Ride Through standard according to US grid codes (Zavadil, et al., 2007).
2. OVERVIEW OF THE DFIG CONTROL SYSTEM The DFIG based wind turbine has two control levels as shown in Fig. 1 (Soliman et al., 2010). The turbine control level supervises the pitch control system and the RSC controller such that the aerodynamic efficiency is maximized. This is achieved by manipulating the pitch angle set point, , and the generator torque set point, . The second control level contains the generator controller which controls the RSC and the GSC. The RSC controller adjusts the rotor voltage, , such that the generator torque, , and the stator reactive power, , track certain desired set points, and , respectively. The GSC controller regulates the DC link voltage and the reactive power exchange with the grid to certain desired values, and , respectively. 3. DFIG BEHAVIOUR UNDER VOLTAGE DIPS
(8) (9) Based on (8), an equivalent circuit of the rotor dynamics can be drawn as in Fig. 3. rr
err
Lr
ir r vrr
Rotor Side Converter
Fig. 3. DFIG rotor equivalent circuit (Lopez, et al., 2007).
3.2 DFIG behaviour under full voltage dip During normal operation, the stator voltage space vector is rotating steadily with constant speed, , and magnitude, . If the resistance is neglected, expression (11) for can be obtained from (3) and (10). (10) (11)
3.1 Induction Generator model The dynamics of a WRIG described in a d-q reference frame rotating at an arbitrary speed, , are written in (1)- (2).
Using (11) and (9), it is easy to show that the magnitude of the rotor internal voltage can be approximated by (12) (Lopez, et al., 2007). (12) Typically, the slip,
, varies from
to
; and
therefore, the RSC is rated slightly higher than of the rated stator voltage, in the case of unity windings turn ratio. (1)
The analysis of the DFIG’s behavior under voltage dips is studied in (Lopez, et al., 2007). It was shown that during a full voltage dip, the maximum magnitude of the rotor internal voltage can be approximated by (13).
(2) In (1), , , and denote voltages, currents, flux linkages, rotor speed and the pair poles, respectively. The subscripts and denote the direct and quadrature axes, respectively. The subscripts and denote stator and rotor
(13) It can be concluded from (12) and (13) that the amplitude of the voltage induced in the rotor at the first moment of the dip
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18th IFAC World Congress (IFAC'11) Milano (Italy) August 28 - September 2, 2011
is similar to the stator rated voltage instead of the small percentage induced in normal operation. The overvoltage caused by the dip notably exceeds the maximum voltage of the rotor converter. Typically, and have very small values; and therefore high rotor currents are likely to appear.
Tg*
Qs*
' vqr
* idr
PI
' vdr
vqr cc vqr
vdr
Induction machine model
cc vdr
idr
Tg&Qs Controller Current Controller Decoupler
Currently, active crowbar protection (Morren & de Haan, 2005), is the most employed protection scheme for DFIGs. An active crowbar consists of a resistor bank that can be connected and disconnected from the rotor windings. Once a fault is detected, the RSC is blocked and the crowbar circuit is activated short circuiting the rotor winding though the resistor bank and protecting the RSC. Once safe operation of the RSC is detected, the crowbar is deactivated and normal operation of the RSC is resumed. Dynamic Series Resistance (DSR) protection Jin, et al. (2010) proposed a new protection configuration based on using a DSR, shown in Fig. 4. During normal operation, the DSR switch is closed and the series resistance is bypassed. Once a fault occurs and rotor currents increase above the maximum allowable limit of the RSC, the DSR switch is opened and the resistance is inserted in series with the rotor and the RSC, limiting the rotor current. Turbine Controller
Tg*
* Qs* QGC Vdc*
RSC Controller
vr*
Wind turbine
PI iqr
PI
ucrow
Decision Maker
* iqr
Qs
Crowbar protection
Gear box
PI Tg
3.3 RSC protection schemes
β*
feedback
RSC Controller idr iqr
DSR
Generator GSC Controller Controller
Filter
Fig. 5. Baseline control strategy.
5. PROPOSED CONTROL STRATEGY BASED ON MPC AND DSR PROTECTION SCHEME 5.1 Motivation for using MPC The use of MPC techniques (Maciejowski, 2000) for RSC control offers many advantages. MPC techniques can handle constraints and can therefore explicitly incorporate rotor current and voltage constraints. Furthermore, feed-forward compensation of measurable disturbances, such as the stator voltage, can be achieved effectively. This can ensure fast rejection of stator voltage dips without waiting for the rotor currents to reach high values. In addition, the MPC controller can be easily reconfigured by changing the prediction model used. This feature is useful since the dynamics of the controlled system (WRIG) change when the DSR is switched on and off. 5.2 Overview of the proposed control strategy
vC*
RSC DC link GSC
vds vqs
The proposed control strategy for RSC control is shown in Fig. 6. The proposed strategy differs from the conventional one, shown in Fig. 5, in that the PI current controllers and the cross-coupling compensation block are replaced with an MPC current controller. Furthermore, the MPC uses the stator voltage measurements, and as measurable disturbances. The binary signal, , defined in (14), is used to switch the DSR on and off, and is fed to the MPC controller to determine the suitable prediction model for the WRIG.
Grid
WRIG
Fig. 4. DFIG based wind turbine with DSR for RSC protection.
4. Baseline control strategy Vector control is currently the standard approach to control DFIGs (Pena, et al., 1996). A typical RSC controller based on vector control (Pena, et al., 1996) is shown in Fig. 5, where all signals are referred to a stator flux-oriented reference frame. With such orientation, it can be shown that and can be controlled independently by controlling and , respectively (Pena, et al., 1996). To decouple the direct and quadrature axis rotor currents’ dynamics, cross-coupling compensation terms and , are added as shown in Fig. 5. Two SISO PI controllers are used to ensure fast control over and . The rotor current controllers are governed by torque and reactive power controllers, which are tuned to have relatively slow responses, as compared to the current controllers. The binary signal, , is used to switch the crowbar on and off, depending on the operating conditions of the DFIG (Lopez, et al., 2009; Morren & de Haan, 2005).
(14) feedback
RSC Controller idr,iqr Decision irn Maker Tg*
PI Tg
Qs*
PI Qs Tg&Qs Controller
uDSR
* idr
* iqr
vdr MPC vqr idr iqr ids iqs vds vqs
Fig. 6. Proposed control strategy.
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Induction machine model
18th IFAC World Congress (IFAC'11) Milano (Italy) August 28 - September 2, 2011
The main idea of the proposed strategy is based on using an MPC controller that switches between two internal models to control the RSC. The first model represents the WRIG without the DSR while the second one represents the WRIG with the DSR in series with the rotor. The first model is used during normal operation. During severe voltage dips, the DSR switch is opened and the second model is used by the MPC controller, controlling the RSC. Once safe operation is detected, the DSR switch is closed and the first model becomes active again. The design of the MPC and decision blocks shown in Fig. 6 is detailed in Sections 5.3 and 5.4. 5.3 MPC design The main components of the MPC controller are the prediction model and the optimization problem that is solved at each sampling time.
within safe limits is achieved by solving the Quadratically Constrained Quadratic Program (QCQP) in (20)-(24).
(20) Subject to: Prediction model equations in (19)
(21) (22)
(23) (24) Here, is the prediction horizon, is the control horizon, , and . The weights and are defined in (25). The definitions and are used in (20), (22) and (23). .
(25)
Prediction model The WRIG model in a stator voltage oriented reference frame rotating at synchronous speed is given in (15)-(18), where is the control input, is the state vector, is the measurable disturbance and is the controlled output. This model is obtained by eliminating the stator and rotor flux linkages in (1). The term is introduced in (16) to reflect the fact that the value of the effective rotor resistance is either equal to if the DSR switch is closed, or if the DSR switch is opened. (15)
The rotor current magnitude constraint in (23) is soft. Soft output constraints are used to avoid infeasibility of the QCQP during real time control. Possible MPC implementation approaches Many approaches can be used to implement the MPC controller discussed above. The first approach is to use a Semi-Definite Program solver, such as SeDumi (Sturm, 1999), to solve the QCQP in (20)-(24). This approach will be referred by . Another alternative is to approximate the quadratic constraints in (28) and (29) by two polytopes such as the one shown in Fig. 7. In that case the QPQC in (20)-(24) can be approximated by the QP in (26)-(30), where is a vector entirely composed of and , , , and can be easily derived from the polytope vertices.
(26)
(16)
Subject to: Prediction model equations in (19) , ,
(27) (28) (29) (30)
vqr u3
,
u2
(17) V r,m
u4
ax
u1 vdr
(18) Two discrete time models in (19) can be obtained by discretizing (15) when and . (19) MPC optimization problem Good tracking performance of the rotor currents while keeping the magnitude of the rotor voltages and currents
u5
u6
Fig. 7. Polytopic approximation of a quadratic constraint.
For the QP in (26)-(30), two possible MPC implementations can be used. The first approach relies on using a QP solver, such as QPC (Wills, 2010), to solve the optimization problem in (26)-(30) online at each sampling time. This approach will be referred by . The other one, known as explicit MPC, relies on solving the QP offline for all possible initial
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18th IFAC World Congress (IFAC'11) Milano (Italy) August 28 - September 2, 2011
states within certain set of interest. (Bemporad et al., 2002) showed that the explicit solution of the QP can be calculated. The resulting control law is a piecewise affine function of the states and therefore can be implemented as a lookup table. Explicit MPC controllers can be calculated using the MultiParametric Toolbox (MPT) (Kvasnica et al., 2006). This approach will be referred by . 5.4 Decision maker design The main function of the decision maker block in Fig. 6 is to generate the DSR signal . The decision maker used in this paper is shown in Fig. 8. Once rotor currents exceed the maximum allowable limit, the DSR should be inserted in series with the rotor and the RSC. To determine when to disconnect the DSR and resume normal operation, the approach proposed in (Lopez, et al., 2009) is used. idr iqr
2 2 idr iqr
RS Flip Flop S Q
> Ir,max
irn
uDSR
R
irn
< Ir,max
and
R 0 0 1 1
Q S 0 Last state 1 1 0 0 1 Last state
6.2 Evaluation of the proposed control strategy In this section, the proposed control strategy, implemented using , is compared with the conventional strategy in Fig. 5 with an active crowbar protection scheme. Both controllers are tuned to achieve the same tracking performance of the rotor currents under normal operation. The 1.5 MW DFIG based wind turbine model described by (Soliman, et al., 2010) was used. Within simulations, the DFIG is operating at full load with a rotor speed of 1.2 p.u. The rotor converter current limit, , and voltage limit, , are assumed to be 1.5 p.u. and 0.4 p.u. respectively. The test fault, shown in Fig. 2, with duration of 300 ms is applied at at the DFIG terminals. Two cases with different voltage dip magnitudes, , are considered. Case 1 (small voltage dip, p.u.): In this case, neither the crowbar nor the DSR were activated. Simulation results are shown in Fig.9-10. It can be seen that the proposed strategy offers much faster rejection of the grid disturbances. Furthermore, it can be noticed that the oscillations in the torque are effectively reduced. Consequently, the proposed strategy can be expected to reduce transient loads occurring in the drive train of the wind turbine during grid faults. 2
Fig. 8. Decision maker block.
MPC PI
1.5
Tg, pu
6. SIMULATION RESULTS 6.1 Comparison of different MPC implementations
1 0.5
The objective is to compare the computational speed of , and , described in Section 5.3. Eight vertices are used to approximate the norm constraint shown in Fig. 7. The MPC controllers’ data are given in Table 1.
0
0
0.5
1 time, s
Fig. 9. Generator torque,
(
1.5
2
p.u.).
0.6
Table 1. Different MPC implementation approaches.
MPC PI
0.4
Table 2. CPU time statistics for different MPCs. CPU time C1 (1.66 GHz, 2 MB) C2 (3.16 GHz, 6 MB) statistics Max time 510 0.55 376.9 176.8 0.16 138.1 (ms) AVG time 218.4 0.17 49.8 70.6 0.067 16.2 (ms) % (time 0 100 60 0 100 70 < 1 ms)
0.2 Qs , pu
8, 4 8, 4 3, 2 Compl- 12 quadratic 96 linear 22000 polytopic exity constraints constraints regions in solver SeDumi QPC MPT The closed loop system is simulated for 10 seconds with a sampling period of 1 ms and random changes in the rotor current set points and the stator voltages. Simulations are carried using Matlab® on two dual core PCs. The first PC, C1, is 1.66 GHz with 2 MB cache while the second one, C2 is 3.16 GHz with 6 MB cache.
0 -0.2 -0.4 0
0.5
1 time, s
Fig. 10. Stator reactive power,
(
1.5
2
p.u.).
Case 2 (large voltage dip, p.u.): In this case, both the crowbar and the DSR were triggered during simulations. Simulation results are shown in Fig. 11-14. It can be seen that fast rejection of the grid voltage disturbances is achieved using the proposed approach. Furthermore, it can be seen from Fig. 13-14, that the MPC controller kept the rotor currents and voltages within allowable limits of the RSC. 7. CONCLUSIONS
Table 2 provides an idea about the computational time required by each MPC algorithm. It can be seen that the use of is suitable for RSC control at fast sampling rates.
This paper proposes a novel control strategy that ensures FRT requirement for wind turbines with DFIGs according to recent grid codes. The proposed strategy uses a multivariable MPC controller for controlling the RSC. Limits on the RSC currents and voltages are explicitly incorporated in the
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18th IFAC World Congress (IFAC'11) Milano (Italy) August 28 - September 2, 2011
controller. To limit the RSC current during severe grid faults a DSR is inserted in series with the rotor. The proposed approach provides fast rejection of the stator voltage variations and better damping for generator torque and reactive power oscillations when compared with the conventional PI based control with crowbar protection scheme. Alternative implementations of the MPC algorithm are compared in terms of computational speed in order to evaluate the feasibility of the proposed strategy for DFIG control at fast sampling rates. Experimental validation of the proposed strategy is currently under investigation. 3 MPC PI
Tg, pu
2
0
0
0.5
1 time, s
Fig. 11. Generator torque,
(
1.5
p.u.).
Lopez, J., Gubia, E., Olea, E., Ruiz, J., and Marroyo, L. (2009). Ride through of wind turbines with doubly fed induction generator under symmetrical voltage dips. IEEE Transactions on Industrial Electronics, 56, 4246-4254.
2 MPC PI
Qs , pu
1 0.5
Lopez, J., Sanchis, P., Roboam, X., and Marroyo, L. (2007). Dynamic behavior of the doubly fed induction generator during three-phase voltage dips. IEEE Transactions on Energy Conversion, 22, 709-717.
0 -0.5 -1 0
0.5
1 time, s
Fig. 12. Stator reactive power,
(
1.5
Maciejowski, J. (2000). Predictive Control with Constraints (Vol. 1st): Prentice Hall.
p.u.).
1
ir,abc ,pu
2
Morren, J., and de Haan, S. W. H. (2005). Ridethrough of wind turbines with doubly-fed induction generator during a voltage dip. IEEE Transactions on Energy Conversion, 20, 435-441.
Ir,max
0 -1 0
0.5
1 time,s
1.5
2
Fig. 13. Three phase rotor currents (p.u.) using the MPC controller ( p.u.).
vr,abc ,pu
0.5
0
-0.5
Federal Energy Regulatory Commission (FERC). (June 2005). Interconnection for wind energy. Docket No. RM05-4-000, Order No. 661.
Kvasnica, M., Grieder, P., and Baotic, M. (2006). Multi Parametric Toolbox (MPT). Available: http://control.ee.ethz.ch/~mpt/.
2
1.5
de Almeida, R. G., Lopes, J. A. P., and Barreiros, J. A. L. (2004). Improving power system dynamic behavior through doubly fed induction machines controlled by static converter using fuzzy control. IEEE Transactions on Power Systems, 19, 1942-1950.
Jin, Y., Fletcher, J. E., and O'Reilly, J. (2010). A SeriesDynamic-Resistor-Based Converter Protection Scheme for Doubly-Fed Induction Generator During Various Fault Conditions. IEEE Transactions on Energy Conversion, 25, 422-432.
1
-1
Dawei, X., Li, R., Tavner, P. J., and Yang, S. (2006). Control of a doubly fed induction generator in a wind turbine during grid fault ride-through. IEEE Transactions on Energy Conversion, 21, 652-662.
0.5
1 time,s
1.5
Soliman, M., Malik, O. P., and Westwick, D. (2010). Multiple Model MIMO Predictive Control for Variable Speed Variable Pitch Wind Turbines. In 2010 American Control Conference. Baltimore, MD, USA. Sturm, J. F. (1999). Using SeDuMi 1.02, a Matlab toolbox for optimization over symmetric cones. Optimization Methods and Software, 11-12, 625–653.
Vr,max 0
Pena, R., Clare, J. C., and Asher, G. M. (1996). Doubly fed induction generator using back-to-back PWM converters and its application to variable-speed wind-energy generation. IEE Proceedings-Electric Power Applications, 143, 231-241.
2
Fig. 14. Three phase rotor voltages (p.u.), using the MPC controller ( p.u.).
REFERENCES Bemporad, A., Morari, M., Dua, V., and Pistikopoulos, E. N. (2002). The explicit linear quadratic regulator for constrained systems. Automatica, 38, 3–20.
Wills, A. G. (2010). Quadratic Programming in C (QPC). Available:http://www.sigpromu.org/quadprog/index.html. Zavadil, R., Miller, N., Ellis, A., Muljadi, E., Camm, E., and Kirby, B. (2007). Queuing up [power system interconnection]. IEEE Power & Energy Magazine, 5, 47-58.
1715
Ensuring Fault Ride Through for Wind Turbines with Doubly Fed Induction Generator: a Model Predictive Control Approach M. Soliman, O.P. Malik and D.T. Westwick
Electrical Engineering Department, University of Calgary, Calgary, AB T2N 1N4 Canada ( e-mail: {msoliman,maliko,dwestwic}@ucalgary.ca )
Abstract: This paper proposes a novel control strategy, based on Model Predictive Control (MPC), which ensures Fault Ride Through (FRT) for wind turbines with Doubly Fed Induction Generators (DFIGs). During large voltage dips, large currents are induced in the rotor that can destroy the rotor converter. The common approach used to protect the rotor converter is to disable the converter and to dissipate the rotor power via a crowbar circuit. This approach is currently not accepted by most grid codes which dictate that grid connected wind turbines should remain connected to the grid during severe faults with full control over their active and reactive power. The proposed strategy ensures FRT for DFIG grid connected wind turbines without using a crowbar and therefore meets recent grid codes requirements. This is achieved by using a Dynamic Series Resistance and an MPC controller incorporating most of the DFIG’s constraints. Keywords: Model Predictive Control, Wind Power Generation, Doubly Fed Induction Generators.
1. INTRODUCTION Wind turbines equipped with DFIGs are currently the most used configuration for wind power generation (Lopez et al., 2009). With its partially rated power converters (typically 2030% of the system rated power), variable speed operation of the wind turbine is provided at relatively low cost.
to the grid during faults, but also control over its active and reactive power should be maintained (FERC, June 2005). Generally, FRT capability is specified by a region like in Fig. 2, in which the wind turbine must not trip under symmetrical faults at the point of interconnection. Different countries have adopted different FRT curves like the one shown in Fig. 2 (Zavadil et al., 2007).
A DFIG based wind turbine, shown in Fig. 1, consists of a turbine rotor coupled to a Wound Rotor Induction Generator (WRIG) through a gear box. The rotor of the WRIG is connected to the grid through the rotor side converter (RSC), the DC link and the grid side converter (GSC).
β*
Initially, DFIGs with active crowbars were viewed as meeting the FRT requirement dictated by grid codes. However, the use of a crowbar results in a loss of control over the DFIG. Furthermore, when the crowbar is active, the DFIG behaves like a conventional WRIG, consuming more reactive power, possibly resulting in voltage stability deterioration. Quite recently, grid codes were modified such that for a wind turbine to be FRT capable, it must not only remain connected 978-3-902661-93-7/11/$20.00 © 2011 IFAC
* Qs* QGC Vdc*
Tg*
RSC Controller
vr*
The main drawback of DFIGs is that they are very sensitive to changes in their terminal voltage (Lopez, et al., 2009; Morren & de Haan, 2005). For example, when an external fault occurs, large voltage dip is produced resulting in Large rotor currents that can lead to the destruction of the RSC. Typically, an active crowbar circuit, shown in Fig. 1, is installed in DFIGs to protect the RSC during grid faults (Morren & de Haan, 2005). The main idea is to divert high rotor currents from the RSC to a resistor bank, called a crowbar, to protect the RSC.
Turbine Controller
vC*
RSC DC link GSC
Gear box
Wind turbine
GSC Generator Controller Controller
Crowbar
Filter
Grid
WRIG
Fig. 1. DFIG based wind turbine.
A huge research effort has recently been undertaken in order to come up with a new control/protection strategy to ensure FRT capability for DFIGs (Dawei et al., 2006; de Almeida et al., 2004; Jin et al., 2010; Lopez, et al., 2009). One approach followed by many authors is to modify the conventional RSC control algorithm (Pena et al., 1996) such that FRT is achieved without using additional protection hardware. De Almeida, et al. (2004) suggested using fuzzy logic controllers to control the rotor currents. Stator flux demagnetization using RSC control was proposed by Dawei, et al. (2006). Lopez, et al. (2009) showed that FRT cannot be met solely by
1710
10.3182/20110828-6-IT-1002.03060
18th IFAC World Congress (IFAC'11) Milano (Italy) August 28 - September 2, 2011
the DFIG control when the voltage dip is severe and suggested using a combination of flux demagnetization and crowbar protection. A combined converter protection scheme based on using a Dynamic Series Resistance (DSR) and conventional crowbar is proposed by Jin, et al. (2010).
quantities, respectively. The superscripts denote quantities referred to arbitrary, stationary, synchronously rotating and rotor reference frames, respectively.
This paper proposes a novel control strategy that ensures FRT for wind turbines with DFIGs. The proposed strategy uses a multivariable MPC controller to control the RSC and a DSR to protect the RSC during severe grid faults. The proposed strategy does not require the disconnection of the RSC and meets recent grid codes’ requirements.
(3) (4) (5) (6) Remark 1: Dynamic equations of the WRIG written in the stationary, synchronously rotating and rotor reference frames can be obtained from (1) by replacing by , and , respectively, where denotes the synchronous speed. Using (5)-(6), the rotor flux linkage and the rotor voltage can be written in the rotor reference frame as in (7)-(8),
Beginning of voltage dip
0.8
0.9 pu
Wind Plant Must Not Trip
Vdip
Voltage at the point of interconnection, pu
1.0
0.6 Test Fault
0.4 0.2
0.15 pu 0
Using the space vector notation, in (1) can be written as:
where
Wind Plant May Trip
, equations
and the rotor internal voltage,
, is
defined in (9) (Lopez et al., 2007).
0.625 s 0.5
1
1.5 2 Time, s
2.5
3
(7)
3.5
Fig. 2. Fault Ride Through standard according to US grid codes (Zavadil, et al., 2007).
2. OVERVIEW OF THE DFIG CONTROL SYSTEM The DFIG based wind turbine has two control levels as shown in Fig. 1 (Soliman et al., 2010). The turbine control level supervises the pitch control system and the RSC controller such that the aerodynamic efficiency is maximized. This is achieved by manipulating the pitch angle set point, , and the generator torque set point, . The second control level contains the generator controller which controls the RSC and the GSC. The RSC controller adjusts the rotor voltage, , such that the generator torque, , and the stator reactive power, , track certain desired set points, and , respectively. The GSC controller regulates the DC link voltage and the reactive power exchange with the grid to certain desired values, and , respectively. 3. DFIG BEHAVIOUR UNDER VOLTAGE DIPS
(8) (9) Based on (8), an equivalent circuit of the rotor dynamics can be drawn as in Fig. 3. rr
err
Lr
ir r vrr
Rotor Side Converter
Fig. 3. DFIG rotor equivalent circuit (Lopez, et al., 2007).
3.2 DFIG behaviour under full voltage dip During normal operation, the stator voltage space vector is rotating steadily with constant speed, , and magnitude, . If the resistance is neglected, expression (11) for can be obtained from (3) and (10). (10) (11)
3.1 Induction Generator model The dynamics of a WRIG described in a d-q reference frame rotating at an arbitrary speed, , are written in (1)- (2).
Using (11) and (9), it is easy to show that the magnitude of the rotor internal voltage can be approximated by (12) (Lopez, et al., 2007). (12) Typically, the slip,
, varies from
to
; and
therefore, the RSC is rated slightly higher than of the rated stator voltage, in the case of unity windings turn ratio. (1)
The analysis of the DFIG’s behavior under voltage dips is studied in (Lopez, et al., 2007). It was shown that during a full voltage dip, the maximum magnitude of the rotor internal voltage can be approximated by (13).
(2) In (1), , , and denote voltages, currents, flux linkages, rotor speed and the pair poles, respectively. The subscripts and denote the direct and quadrature axes, respectively. The subscripts and denote stator and rotor
(13) It can be concluded from (12) and (13) that the amplitude of the voltage induced in the rotor at the first moment of the dip
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18th IFAC World Congress (IFAC'11) Milano (Italy) August 28 - September 2, 2011
is similar to the stator rated voltage instead of the small percentage induced in normal operation. The overvoltage caused by the dip notably exceeds the maximum voltage of the rotor converter. Typically, and have very small values; and therefore high rotor currents are likely to appear.
Tg*
Qs*
' vqr
* idr
PI
' vdr
vqr cc vqr
vdr
Induction machine model
cc vdr
idr
Tg&Qs Controller Current Controller Decoupler
Currently, active crowbar protection (Morren & de Haan, 2005), is the most employed protection scheme for DFIGs. An active crowbar consists of a resistor bank that can be connected and disconnected from the rotor windings. Once a fault is detected, the RSC is blocked and the crowbar circuit is activated short circuiting the rotor winding though the resistor bank and protecting the RSC. Once safe operation of the RSC is detected, the crowbar is deactivated and normal operation of the RSC is resumed. Dynamic Series Resistance (DSR) protection Jin, et al. (2010) proposed a new protection configuration based on using a DSR, shown in Fig. 4. During normal operation, the DSR switch is closed and the series resistance is bypassed. Once a fault occurs and rotor currents increase above the maximum allowable limit of the RSC, the DSR switch is opened and the resistance is inserted in series with the rotor and the RSC, limiting the rotor current. Turbine Controller
Tg*
* Qs* QGC Vdc*
RSC Controller
vr*
Wind turbine
PI iqr
PI
ucrow
Decision Maker
* iqr
Qs
Crowbar protection
Gear box
PI Tg
3.3 RSC protection schemes
β*
feedback
RSC Controller idr iqr
DSR
Generator GSC Controller Controller
Filter
Fig. 5. Baseline control strategy.
5. PROPOSED CONTROL STRATEGY BASED ON MPC AND DSR PROTECTION SCHEME 5.1 Motivation for using MPC The use of MPC techniques (Maciejowski, 2000) for RSC control offers many advantages. MPC techniques can handle constraints and can therefore explicitly incorporate rotor current and voltage constraints. Furthermore, feed-forward compensation of measurable disturbances, such as the stator voltage, can be achieved effectively. This can ensure fast rejection of stator voltage dips without waiting for the rotor currents to reach high values. In addition, the MPC controller can be easily reconfigured by changing the prediction model used. This feature is useful since the dynamics of the controlled system (WRIG) change when the DSR is switched on and off. 5.2 Overview of the proposed control strategy
vC*
RSC DC link GSC
vds vqs
The proposed control strategy for RSC control is shown in Fig. 6. The proposed strategy differs from the conventional one, shown in Fig. 5, in that the PI current controllers and the cross-coupling compensation block are replaced with an MPC current controller. Furthermore, the MPC uses the stator voltage measurements, and as measurable disturbances. The binary signal, , defined in (14), is used to switch the DSR on and off, and is fed to the MPC controller to determine the suitable prediction model for the WRIG.
Grid
WRIG
Fig. 4. DFIG based wind turbine with DSR for RSC protection.
4. Baseline control strategy Vector control is currently the standard approach to control DFIGs (Pena, et al., 1996). A typical RSC controller based on vector control (Pena, et al., 1996) is shown in Fig. 5, where all signals are referred to a stator flux-oriented reference frame. With such orientation, it can be shown that and can be controlled independently by controlling and , respectively (Pena, et al., 1996). To decouple the direct and quadrature axis rotor currents’ dynamics, cross-coupling compensation terms and , are added as shown in Fig. 5. Two SISO PI controllers are used to ensure fast control over and . The rotor current controllers are governed by torque and reactive power controllers, which are tuned to have relatively slow responses, as compared to the current controllers. The binary signal, , is used to switch the crowbar on and off, depending on the operating conditions of the DFIG (Lopez, et al., 2009; Morren & de Haan, 2005).
(14) feedback
RSC Controller idr,iqr Decision irn Maker Tg*
PI Tg
Qs*
PI Qs Tg&Qs Controller
uDSR
* idr
* iqr
vdr MPC vqr idr iqr ids iqs vds vqs
Fig. 6. Proposed control strategy.
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Induction machine model
18th IFAC World Congress (IFAC'11) Milano (Italy) August 28 - September 2, 2011
The main idea of the proposed strategy is based on using an MPC controller that switches between two internal models to control the RSC. The first model represents the WRIG without the DSR while the second one represents the WRIG with the DSR in series with the rotor. The first model is used during normal operation. During severe voltage dips, the DSR switch is opened and the second model is used by the MPC controller, controlling the RSC. Once safe operation is detected, the DSR switch is closed and the first model becomes active again. The design of the MPC and decision blocks shown in Fig. 6 is detailed in Sections 5.3 and 5.4. 5.3 MPC design The main components of the MPC controller are the prediction model and the optimization problem that is solved at each sampling time.
within safe limits is achieved by solving the Quadratically Constrained Quadratic Program (QCQP) in (20)-(24).
(20) Subject to: Prediction model equations in (19)
(21) (22)
(23) (24) Here, is the prediction horizon, is the control horizon, , and . The weights and are defined in (25). The definitions and are used in (20), (22) and (23). .
(25)
Prediction model The WRIG model in a stator voltage oriented reference frame rotating at synchronous speed is given in (15)-(18), where is the control input, is the state vector, is the measurable disturbance and is the controlled output. This model is obtained by eliminating the stator and rotor flux linkages in (1). The term is introduced in (16) to reflect the fact that the value of the effective rotor resistance is either equal to if the DSR switch is closed, or if the DSR switch is opened. (15)
The rotor current magnitude constraint in (23) is soft. Soft output constraints are used to avoid infeasibility of the QCQP during real time control. Possible MPC implementation approaches Many approaches can be used to implement the MPC controller discussed above. The first approach is to use a Semi-Definite Program solver, such as SeDumi (Sturm, 1999), to solve the QCQP in (20)-(24). This approach will be referred by . Another alternative is to approximate the quadratic constraints in (28) and (29) by two polytopes such as the one shown in Fig. 7. In that case the QPQC in (20)-(24) can be approximated by the QP in (26)-(30), where is a vector entirely composed of and , , , and can be easily derived from the polytope vertices.
(26)
(16)
Subject to: Prediction model equations in (19) , ,
(27) (28) (29) (30)
vqr u3
,
u2
(17) V r,m
u4
ax
u1 vdr
(18) Two discrete time models in (19) can be obtained by discretizing (15) when and . (19) MPC optimization problem Good tracking performance of the rotor currents while keeping the magnitude of the rotor voltages and currents
u5
u6
Fig. 7. Polytopic approximation of a quadratic constraint.
For the QP in (26)-(30), two possible MPC implementations can be used. The first approach relies on using a QP solver, such as QPC (Wills, 2010), to solve the optimization problem in (26)-(30) online at each sampling time. This approach will be referred by . The other one, known as explicit MPC, relies on solving the QP offline for all possible initial
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18th IFAC World Congress (IFAC'11) Milano (Italy) August 28 - September 2, 2011
states within certain set of interest. (Bemporad et al., 2002) showed that the explicit solution of the QP can be calculated. The resulting control law is a piecewise affine function of the states and therefore can be implemented as a lookup table. Explicit MPC controllers can be calculated using the MultiParametric Toolbox (MPT) (Kvasnica et al., 2006). This approach will be referred by . 5.4 Decision maker design The main function of the decision maker block in Fig. 6 is to generate the DSR signal . The decision maker used in this paper is shown in Fig. 8. Once rotor currents exceed the maximum allowable limit, the DSR should be inserted in series with the rotor and the RSC. To determine when to disconnect the DSR and resume normal operation, the approach proposed in (Lopez, et al., 2009) is used. idr iqr
2 2 idr iqr
RS Flip Flop S Q
> Ir,max
irn
uDSR
R
irn
< Ir,max
and
R 0 0 1 1
Q S 0 Last state 1 1 0 0 1 Last state
6.2 Evaluation of the proposed control strategy In this section, the proposed control strategy, implemented using , is compared with the conventional strategy in Fig. 5 with an active crowbar protection scheme. Both controllers are tuned to achieve the same tracking performance of the rotor currents under normal operation. The 1.5 MW DFIG based wind turbine model described by (Soliman, et al., 2010) was used. Within simulations, the DFIG is operating at full load with a rotor speed of 1.2 p.u. The rotor converter current limit, , and voltage limit, , are assumed to be 1.5 p.u. and 0.4 p.u. respectively. The test fault, shown in Fig. 2, with duration of 300 ms is applied at at the DFIG terminals. Two cases with different voltage dip magnitudes, , are considered. Case 1 (small voltage dip, p.u.): In this case, neither the crowbar nor the DSR were activated. Simulation results are shown in Fig.9-10. It can be seen that the proposed strategy offers much faster rejection of the grid disturbances. Furthermore, it can be noticed that the oscillations in the torque are effectively reduced. Consequently, the proposed strategy can be expected to reduce transient loads occurring in the drive train of the wind turbine during grid faults. 2
Fig. 8. Decision maker block.
MPC PI
1.5
Tg, pu
6. SIMULATION RESULTS 6.1 Comparison of different MPC implementations
1 0.5
The objective is to compare the computational speed of , and , described in Section 5.3. Eight vertices are used to approximate the norm constraint shown in Fig. 7. The MPC controllers’ data are given in Table 1.
0
0
0.5
1 time, s
Fig. 9. Generator torque,
(
1.5
2
p.u.).
0.6
Table 1. Different MPC implementation approaches.
MPC PI
0.4
Table 2. CPU time statistics for different MPCs. CPU time C1 (1.66 GHz, 2 MB) C2 (3.16 GHz, 6 MB) statistics Max time 510 0.55 376.9 176.8 0.16 138.1 (ms) AVG time 218.4 0.17 49.8 70.6 0.067 16.2 (ms) % (time 0 100 60 0 100 70 < 1 ms)
0.2 Qs , pu
8, 4 8, 4 3, 2 Compl- 12 quadratic 96 linear 22000 polytopic exity constraints constraints regions in solver SeDumi QPC MPT The closed loop system is simulated for 10 seconds with a sampling period of 1 ms and random changes in the rotor current set points and the stator voltages. Simulations are carried using Matlab® on two dual core PCs. The first PC, C1, is 1.66 GHz with 2 MB cache while the second one, C2 is 3.16 GHz with 6 MB cache.
0 -0.2 -0.4 0
0.5
1 time, s
Fig. 10. Stator reactive power,
(
1.5
2
p.u.).
Case 2 (large voltage dip, p.u.): In this case, both the crowbar and the DSR were triggered during simulations. Simulation results are shown in Fig. 11-14. It can be seen that fast rejection of the grid voltage disturbances is achieved using the proposed approach. Furthermore, it can be seen from Fig. 13-14, that the MPC controller kept the rotor currents and voltages within allowable limits of the RSC. 7. CONCLUSIONS
Table 2 provides an idea about the computational time required by each MPC algorithm. It can be seen that the use of is suitable for RSC control at fast sampling rates.
This paper proposes a novel control strategy that ensures FRT requirement for wind turbines with DFIGs according to recent grid codes. The proposed strategy uses a multivariable MPC controller for controlling the RSC. Limits on the RSC currents and voltages are explicitly incorporated in the
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18th IFAC World Congress (IFAC'11) Milano (Italy) August 28 - September 2, 2011
controller. To limit the RSC current during severe grid faults a DSR is inserted in series with the rotor. The proposed approach provides fast rejection of the stator voltage variations and better damping for generator torque and reactive power oscillations when compared with the conventional PI based control with crowbar protection scheme. Alternative implementations of the MPC algorithm are compared in terms of computational speed in order to evaluate the feasibility of the proposed strategy for DFIG control at fast sampling rates. Experimental validation of the proposed strategy is currently under investigation. 3 MPC PI
Tg, pu
2
0
0
0.5
1 time, s
Fig. 11. Generator torque,
(
1.5
p.u.).
Lopez, J., Gubia, E., Olea, E., Ruiz, J., and Marroyo, L. (2009). Ride through of wind turbines with doubly fed induction generator under symmetrical voltage dips. IEEE Transactions on Industrial Electronics, 56, 4246-4254.
2 MPC PI
Qs , pu
1 0.5
Lopez, J., Sanchis, P., Roboam, X., and Marroyo, L. (2007). Dynamic behavior of the doubly fed induction generator during three-phase voltage dips. IEEE Transactions on Energy Conversion, 22, 709-717.
0 -0.5 -1 0
0.5
1 time, s
Fig. 12. Stator reactive power,
(
1.5
Maciejowski, J. (2000). Predictive Control with Constraints (Vol. 1st): Prentice Hall.
p.u.).
1
ir,abc ,pu
2
Morren, J., and de Haan, S. W. H. (2005). Ridethrough of wind turbines with doubly-fed induction generator during a voltage dip. IEEE Transactions on Energy Conversion, 20, 435-441.
Ir,max
0 -1 0
0.5
1 time,s
1.5
2
Fig. 13. Three phase rotor currents (p.u.) using the MPC controller ( p.u.).
vr,abc ,pu
0.5
0
-0.5
Federal Energy Regulatory Commission (FERC). (June 2005). Interconnection for wind energy. Docket No. RM05-4-000, Order No. 661.
Kvasnica, M., Grieder, P., and Baotic, M. (2006). Multi Parametric Toolbox (MPT). Available: http://control.ee.ethz.ch/~mpt/.
2
1.5
de Almeida, R. G., Lopes, J. A. P., and Barreiros, J. A. L. (2004). Improving power system dynamic behavior through doubly fed induction machines controlled by static converter using fuzzy control. IEEE Transactions on Power Systems, 19, 1942-1950.
Jin, Y., Fletcher, J. E., and O'Reilly, J. (2010). A SeriesDynamic-Resistor-Based Converter Protection Scheme for Doubly-Fed Induction Generator During Various Fault Conditions. IEEE Transactions on Energy Conversion, 25, 422-432.
1
-1
Dawei, X., Li, R., Tavner, P. J., and Yang, S. (2006). Control of a doubly fed induction generator in a wind turbine during grid fault ride-through. IEEE Transactions on Energy Conversion, 21, 652-662.
0.5
1 time,s
1.5
Soliman, M., Malik, O. P., and Westwick, D. (2010). Multiple Model MIMO Predictive Control for Variable Speed Variable Pitch Wind Turbines. In 2010 American Control Conference. Baltimore, MD, USA. Sturm, J. F. (1999). Using SeDuMi 1.02, a Matlab toolbox for optimization over symmetric cones. Optimization Methods and Software, 11-12, 625–653.
Vr,max 0
Pena, R., Clare, J. C., and Asher, G. M. (1996). Doubly fed induction generator using back-to-back PWM converters and its application to variable-speed wind-energy generation. IEE Proceedings-Electric Power Applications, 143, 231-241.
2
Fig. 14. Three phase rotor voltages (p.u.), using the MPC controller ( p.u.).
REFERENCES Bemporad, A., Morari, M., Dua, V., and Pistikopoulos, E. N. (2002). The explicit linear quadratic regulator for constrained systems. Automatica, 38, 3–20.
Wills, A. G. (2010). Quadratic Programming in C (QPC). Available:http://www.sigpromu.org/quadprog/index.html. Zavadil, R., Miller, N., Ellis, A., Muljadi, E., Camm, E., and Kirby, B. (2007). Queuing up [power system interconnection]. IEEE Power & Energy Magazine, 5, 47-58.
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