Proceeding of the IEEE 28th Canadian Conference on Electrical and Computer Engineering Halifax, Canada, May 3-6, 2015
Sliding Mode Speed Control for Wind Energy Conversion Systems Adel Merabet, Member, IEEE, Khandker Tawfique Ahmed, Student Member, IEEE, Hussein Ibrahim, Rachid Beguenane, Karim Belmokhtar the students to implement theories of control systems by analysing the major components of a wind turbine-generator system and extracting mathematical models needed in the control design [6]-[7]. In this paper sliding mode controller is used to control the speed of the permanent magnet synchronous generator (PMSG). In section II, the wind turbine is modelled to describe the motion equation. Section III describes the sliding mode control for speed tracking. Finally OPAL-RT Real-time HIL laboratory used to show the robustness of proposed system which is described in section IV.
Abstract—A sliding mode control strategy for speed tracking problem in variable speed wind turbine system is proposed in this paper. It is developed from the mechanical equation of the turbine-generator rotor. The validation of the proposed control is done using OPAL-RT real-time simulator and electrical modules from Lab-Volt. The proposed control strategy provides robustness to the parametric uncertainties of the wind turbine and generator.
I. INTRODUCTION N recent years, wind power is gaining popularity due to its abundance in nature and its environment friendly aspect. As it is difficult to use large wind turbines in laboratory works, a small turbine that can emulate the turbine can be used in laboratory to demonstrate the control strategies. Wind turbine emulators which operate with the power-speed characteristics of a wind turbine are frequently used for research and teaching purposes as account to its simplicity, low power and low cost design [1]. Wind turbine system is complex, nonlinear and prone to unmodeled dynamics and unknown disturbances. So, it is critical to use a robust control system to get maximum power from the wind energy system. Sliding mode control (SMC) is an effective nonlinear robust control strategy, where the system dynamics are not affected by the uncertainties once they are controlled in sliding surface [2][5]. Nowadays, most of the research on wind energy is based on simulation. Hardware-in-the loop system is very important in learning the practical aspects of wind energy system. Developing an experimental set-up to emulate wind energy conversion systems and control systems would bridge the gap between theory and practice. It would allow
I
II. WIND TURBINE EXPERIMENTAL SYSTEM The aerodynamics torque at the turbine shaft neglecting losses in the drive-train is given by Tt = 0.5 ʌ ȡ Ct(Ȝ) R3 v2
(1)
where ȡ is the air density, R is the radius of the turbine blade, v is the wind speed, Ȝ is the ratio of blade tip speed to wind speed defined as the ratio between the turbine rotor speed Ȧr and the wind speed
λ =
ωr R v Cp
(2)
(3) λ Ct is the torque coefficient and Cp is the power coefficient, which is changing with rotational speed and wind speed. The rotor dynamics together with the generator inertia are characterized by the following differential equations Ct =
° J r ω r = Tt − K r ω r − Brθ r − Tls ® °¯ J g ω g = Ths − K g ω g − B gθ g − Tg
(4)
The gearbox ratio is defined as This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC) under Engage Grant EGP 469636-14. A. Merabet and K. T. Ahmed are with the Division of Engineering, Saint Mary’s University, Halifax, NS B3H 3C3 Canada (corresponding author phone: 902-420-5712; fax: 902-420-5021; e-mail: adel.merabet@ smu.ca). H. Ibrahim and K. Belmokhtar are with Wind Energy TechnoCentre, Gaspe, QC, Canada (e-mail:
[email protected]). R. Beguenane is with the Electrical Engineering Department, Royal Military College, Kingston, ON Canada (e-mail:
[email protected]).
978-1-4799-5829-0/15/$31.00 ©2015 IEEE
ng =
ω g Tls = ωr Ths
(5)
The system (4) can be defined as a single-mass system as follows
J t ω r = Tt − K t ω r − Btθ r − Tg
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(6)
where,
η ( t ) ≤ δ e (t )
Jt = Jr + n J g ° 2 ° K t = K r + ng K g ® 2 ° Bt = B r + n g B g ° ¯Tg = n g Tem 2 g
where, į 0. The proposed sliding model conttroller for speed tracking is given by
(7)
u (t ) = − k1sign ( e ) − x (t ) ® ¯ x (t ) = k 2 e + k 3sign ( e )
Since the external stiffness Bt is very low, it can be neglected. Then, the following simplifiedd model will be used for control purpose
J t ω r = Tt − K t ω r − Tg
(8)
m (11.a) and (13) as The torque command is defined from
Tg = −Ktωr − J t (ω ref + k1sign (e) + x) ® ¯x = −k2e − k3sign (e)
A. Speed Control The sliding mode speed controller is devveloped to reach zero speed tracking error (9)
J [− K t ω r − J t (ω ref + k1sign ( e ) + x ) ] °iq ref ( t ) = p φv ® ° x = − k e − k sign ( e ) 2 3 ¯
The time derivative of the speed tracking errror is given by
(10)
B. Current Control Hysteresis band control is adopteed in this work to control the d-q components of the current. This technique is used to control the current of the stator and supply the switching signals to the inverters. When the current c exceeds the upper band, a control signal is generated d to decrease the current and keep it between the band limits. The model for hysteresis band control is shown in Fig. 1. The DC link voltage at the grid siide has been regulated by the vector control strategy, and deetails are not included as they do not represent the contributio on of this work.
= u ( t ) + η (t ) where, u(t) is the new command inpuut and Ș is the uncertainties, and are defined as follows
u (t ) = −
1 Kt ω r − T g − ω ref Jt Jt
(15)
where, p is the number of pole pairss and ijv is the permanent magnet magnetic flux linkage.
e(t ) = ω r (t ) − ω ref (t ) Kt 1 1 ω r − Tg + Tt − ω ref Jt Jt Jt
(14)
The q-current command iqref is expressed from the MSG and the control law electromagnetic torque of the PM (14) by
where, Ȧref is the speed reference.
=−
(13)
where, k1 k2 and k3 are positive consstant.
III. CONTROL SYSTEM DESSIGN
e (t ) = ω r (t ) − ω ref (t )
(12)
(11.a)
1 (11.b) Tt J The uncertainties term Ș is unknown and includes turbine torque, parameters’ variation, unmodeledd quantities and external disturbances; however, it is assum med that this term is bounded by
η (t ) =
Fig. 1. Hysteresis current Control
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IV. EXPERIMENTAL RESULTS
The experimental system, used to emulate a wind turbinegenerator energy conversion system, consists of the OPAL-RT real-time digital simulator (OPAL-RT OP5600), Signal conditioning module, Dynamometer, permanent magnet synchronous machine acting as a generator and coupled with the dynamometer, Back-to-back converter of two IGBT inverters, Line inductors, Power supply to emulate the grid [8][9]. The components used in the experimental setup are shown in Fig. 2. The configuration to develop the wind energy system and the connection between all the modules are shown in Fig 3. Experiments were carried out in order to validate the speed tracking under the proposed control scheme. The control gains were chosen by trial and error to achieve succesfull speed tracking and voltage regulation. A variable reference speed was applied to the dynamometer to emulate a wind turbine under variable wind speed. Fig. 4-6 show the experimental results. In Fig. 4, it can be observed that the speed tracking is successfully achieved with a zero steady state error and a fast response time under the qcurrent command shown in Fig. 5. The DC link voltage is regulated to follow a constant reference, as shown in Fig. 6, to ensure the proper voltage at the grid side. The robustness of the system is tested with 40 percent increase in the generator parameters in the control algorithm and the results are shown in Fig. 7-9. It can be observed that the speed tracking is still good despite the inaccuracies in the system, which ensures the robustness of the controller.
Real Time simulator
Power supply (Grid)
Back-toback converter
Dynamometer (Wind turbine emulator)
PMS Generator
Signal conditioning module
Line Inductor
Encoder
Fig. 2. Experimental setup to emulate a wind energy conversion system (OPALRT systems and LabVolt module
Fig. 3. Schematic of the connected experimental setup to emulate a wind energy conversion system
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Fig. 7. Rotor speed tracking vs. Speed Error (parameters’ increase by 40%)
Fig. 4. Rotor speed tracking vs. Speed Error
Fig. 8. q-current command (parameters’ increase by 40%)
Fig. 5. q-current command
Fig. 9. DC-link voltage regulation (parameters’ increase by 40%)
Fig. 6. DC-link voltage regulation
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V. CONCLUSION
REFERENCES [1]. D.S.L. Dolan, and P.W. Lehn “Real-time wind turbine emulator suitable for power quality and dynamic control studies,” in International Conference on Power Systems Transients, pp. 1-6, 2005. [2]. G. Bartolini, “Modern Sliding Mode Control Theory: New Perspectives and Applications,” Springer, 2008. [3]. K. D. Young, V. I. Utkin and U. Ozguner, “A control engineer's guide to sliding mode control,” IEEE Transactions on Control Systems Technology, , vol. 7, pp. 328-342, 1999. [4]. T. Kuo, Y. Huang, C. Chen and C. Chang, “Adaptive sliding mode control with PID tuning for uncertain systems,” Engineering Letters, 16(3), pp.1-5, 2008. [5]. A. Bartoszewicz (Ed.), “Sliding Mode Control,” InTech, 2011. [6]. Md. Arifujjaman, M.T. Iqbal and J.E. Quacioe, “Development of an isolated small wind turbine emulator,” The Open Renewable Energy Journal, 4, pp. 3-12, 2011. [7]. S. W. Mohod, M. V. Aware, “Laboratory development of wind turbine simulator using variable speed induction motor,” International Journal of Engineering, Science and Technology, vol. 3, no. 5, pp. 73-82, 2011. [8]. “Real-time HIL/RCP laboratory,” OPAL-RT. 2013. [9]. “0.2kW electrical motor laboratory kit,” OPAL-RT. 2013.
A sliding mode control strategy for speed tracking in variable speed wind turbine system has been investigated by developing a control scheme from the mechanical equation of the turbine-generator. Experimentation conducted on an emulated wind turbine and PMSG has shown the effectiveness and the robustness of the proposed control strategy for speed tracking in wind energy systems. APPENDIX TABLE I PARAMETERS OF THE PMSG
Quantity
Unit
Value
Rated power Rated current Stator resistance Stator d-axis inductance Stator q-axis inductance Flux linkage Number of pole pairs Moment of inertia Coefficient of friction
W A ȍ mH mH Wb
260 3 1.3 1.5 1.5 0.027 3 1.7×10-6 0.3141×10-6
kg·m2 Nm·s/rad
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