The 10 th international Enery Conference (IEC 2014) Wind Turbine Interated Control durin Full Load Operation 1. Hamed Habibi and 2. Ahil Yousefi-Koma 1. MSc, Centre of Advanced Systems and Technoloies (CAST), Collee of Enineerin, University of Tehran 2. Professor, Centre of Advanced Systems and Technoloies (CAST), Collee of Enineerin, University of Tehran Abstract All Wind turbine technoloies and researches, have always focused on power cost reduction. This oal can be achieved by power increase without any sinificant increase in structural load. In this research an adaptive fuzzy controller is employed in full load operation. This has been done by two adaptive fuzzy controller units, includin power and velocity controllers those use enerated power and anular velocity of enerator as feedbacks. These feedbacks are employed to reulate load torque on enerator and blade pitch anle, respectively. Adaptive rules those have been used in fuzzy controller, are defined based on the differences between state variables of the enerated power and anular velocity of the enerator and their nominal values. Results are compared with verified PI controllers. Hiher efficiency of the adaptive fuzzy controller rather than classical controllers in full load operation is then concluded. Additionally, by employin this controller, the controller robustness with respect to uncertainties, such as wind speed, is uaranteed. Keywords: wind turbine, adaptive fuzzy controller, full load reion. 1. Introduction Today, wind enery is the most competitive form of renewable enery. In the past decade, the size and capacity of wind turbines have been increased dramatically. Meanwhile, the structural components have been made relatively lihter to keep down costs. This has put hiher demands on wind turbine control schemes, and implementation of advanced control systems should be considered as a promisin way of decreasin fatiue loads [1]. There are two operational reions in the typical ideal power curve for a wind turbine, as it is shown in Fiure 1. Cut in wind speed is lowest and cut out wind speed is the hihest wind speed for wind turbine operation, respectively [2]. In terms of control, the wind turbine works in two distinct reions, the reion between nominal 1
The 10 th international Enery Conference (IEC 2014) wind speed (the wind speed that turbine produces at its nominal power) and cut in wind speed is partial load operation and from nominal wind speed to cut out speed is full load operation. In full load operation, the available enery in wind is reater than nominal turbine power and turbine should be avoided from danerous vibrations those damae the turbine structure and cause fatiue. In fact durin full load operation keepin safe the turbine structure is more profitable than extractin maximum enery available in wind. This idea shapes the control objective in full load reion [3]. Fiure 1: The ideal power curve Nowadays, utilizin of fuzzy inference system and adaptive schemes in controller efficiency, have been increased. F.Gao et al [4] with prorammin of a PI fuzzy controller tried to control the pitch anle. Also in a similar research, X.J. Jun et al [5] studied the variable pitch wind turbine with fuzzy loic. R. Ata and Y. Kocyiit [6] used an adaptive neuro-fuzzy inference system model to predict the tip speed ratio and the power factor of a wind turbine. Also S. Bououden et al [7] dealed with fuzzy model based multivariable predictive control (FMMPC) for wind turbine enerator. Y. Qi et al [8] applied the theory of fuzzy control and PID control for control of enerator speed and blade pitch anle. Adaptive fuzzy controller can be mentioned as a newest controller scheme that has attracted researchers' attention [9, 10]. X. Yan and X. Liu [9] developed a fuzzy adaptive with variable structure to increased turbine efficiency. H. Goulian et al [11] implemented same controller in partial load reion to maximize extracted enery in low wind conditions. The ability of adaptive controller to adapt with variable wind condition as a disturbance has been proven [12, 13]. In previous works, the control variable is limited to either velocity or power. In fact there has been a combination controllers those work separately [14]. But in this research, a new approach includin velocity and power control is introduced, simultaneously. In next two section the wind turbine model and control stratey will be introduced. After that, the suested controller structure with two independent feedbacks for two fuzzy adaptive controllers is desined and simulated in MATLAB software. Finally comparison and conclusion will be stated. 2
The 10 th international Enery Conference (IEC 2014) 2. Wind turbine modellin A non-linear model of a 4.8MW wind turbine is used for the proposed control alorithms [3]. 2.1 Aerodynamic model The rotor of the wind turbine transfers enery from the wind to the rotor shaft, rotatin at the speed () t. The power from the wind depends on the wind speed, the r air density, and the swept area, A power coefficient, C P ( ( t ), ( t )) which depends on the pitch anle of the blades, () t and the ratio between the speed of the blade tip and the wind speed, denoted tip-speed ratio, () t [3]. 1 T t AV C t t Nm 3 a ( ) r P ( ( ), ( )) [ ] 2 r ( t ) r. R V r T () a t is aerodynamic torque. The coefficient C p describes the aerodynamic efficiency of the rotor by a nonlinear mappin and a real one provided by kkelectronics A/S [15]. An empirical formula for C instead of look up table is usually used. Because this look up table is not available enerally and usin an empirical formula will decrease computation time. Such this formula for power coefficient is shown as follows [16]. C 5 C 2 i 1 3 4 6 i C (, ) C ( C C ) e C P 1 1 0.035 i 3 0.08 1 p (1) (2) In Eq. 2 the constant coefficients are C1 0.5176, C 2 116, C 3 0.4, C 4 5, C 5 21 andc 6 0.0068. The surface of Eq. 2 is shown in Fiure 2. The maximum of C is 0.48 and occurs at 0 and 8.1. p 2.2 Drive train model The drive train model consists of a low-speed shaft and a hih-speed shaft havin inertias J and J respectively. The shafts are interconnected by a ear r ratio, N, combined with torsion stiffness, K dt and torsion dampin, Bdt which result in a torsion anle. 3
The 10 th international Enery Conference (IEC 2014) The drive train has efficiency T t at a speed () enerator, () J ( t ) T ( t ) K ( t ) r r a dt Bdt ( B r Bdt ) r ( t ) ( t ) N dt Kdt dt Bdt J ( t ) ( t ) r ( t ) N N B ( B ) ( t ) T ( t ) dt dt 2 N dt and drives the loadin torque from the t. The linear model is iven as [3]: 1 ( t ) r( t ) ( t ) (5) N (3) (4) Fiure 2: The surface of empirical equation for power coefficient 2.3 Pitch system model The pitch system should track a reference value, ref and is modeled as a first order system. Its time constant is and includes also a communication delay, t d [3]. 1 1 ( t ) ( t ) ref ( t td ) (6) 2.4 Generator and converter models Electric power is enerated by the enerator, while a power converter interfaces the wind turbine enerator output with the utility rid and controls the currents in the enerator. The enerator torque in Eq. 7 is adjusted by the reference T, ref. The dynamics of the converter is approximated by a first order system with time constant and communication delay t d,. 4
The 10 th international Enery Conference (IEC 2014) 1 1 T ( t ) T ( t ) T ( t t ) (7), ref, d The power produced by the enerator can be approximated by Eq. 8, where denotes the efficiency of the enerator. P ( t ) ( t ) T ( t ) (8) 2.5 Assembled model The flow diaram of the wind turbine sub-models is illustrated in Fiure 3. Fiure 3: Block diaram of the wind turbine model It should be noticed that available measurements, are enerator torque, pitch anle, enerator speed, and rotor speed and the output power is evaluated as the product of the measurements of the enerator speed and enerator torque. Generator torque and pitch anle actuators have some limitations such as maximum values T,max and max minimum values T,min and min. 3. Control stratey The main objective, as deified in previous section, is trackin the ideal power curve as close as possible. This curve shows that optimize operation in full load reion should be denoted as eneratin constant power. The preliminary control stratey is fixin enerator torque on optimal value and controllin anular velocity on maximum allowable value [17]. In this case, pitch anle will be controlled to lead desirable output while enerator torque is fixed on nominal value. Steady state error in enerated power should be eliminated and for this, power is controlled by reulatin enerator torque as well as velocity control due to pitch anle reulatin [2]. This error is reduced by independence of power control form velocity control. In this research, pitch anle (velocity control unit) and enerator torque (power control unit) are adjusted based on anular velocity of enerator and enerated power, respectively. 5
The 10 th international Enery Conference (IEC 2014) 4. Adaptive Fuzzy Controller The total schematic plan for adaptive fuzzy controller is shown Fiure 4. In this research to increase controller robustness with respect to wind speed as a perturbation and uncertainty, the direct fuzzy adaptive controller is used [12]. As it is mentioned earlier, both torque and pitch anle control sinals are active and there have been two separated fuzzy adaptive control units. Fiure 4: Fuzzy adaptive controller structure Adaptive rules those are applied on centers of output membership functions [10, 13], will be defined as below: d s( x) dt (9) Where is centers of output membership functions vector, is learnin rate and s is slide surface. 1 T [ c,..., c ] (10) T s k e (11) Where k is hyper slide surface coefficients vector and e is errors between state variables and reference ones vector. x and and are state variables vector and fuzzy principal function, respectively. Fuzzy control sinal will be defined as below: T u ( x ) ( x ) (12) c n m l 1 ( ) 1 fil x l i : fuzzy basis function ( FBF ) n ( ( x )) l 1 fil i 6 (13)
The 10 th international Enery Conference (IEC 2014) m, n and fil, are rules number, state variables number and Gaussian membership function. Fuzzy Inference enine is product; includin, alebraic t-norm, sinleton fuzzifier and centers mean defuzzifier. Initial values are supposed as ( t 0) 0. State variables those act as turbine outputs and adaptive fuzzy controller inputs, are considered as enerated power and its derivation for power controller and enerator anular velocity and its derivation for velocity controller. It should be noted that to avoid computational error durin simulation all of them have been normalized. In fiure 5 membership functions for both controllers are shown. Fiure 5: Membership functions of (a) normalized power and its derivation (b) normalized anular velocity and its derivation Slide surfaces for power and velocity controller are defined as: s 0.399e 0.001e T P P s 8e 2e (14) Where e P and e P are power error state variable and its derivation with respect to its nominal value and e and e are enerator anular velocity error state variable and its derivation with respect to its nominal value. With respect to number of membership functions, 77 49 rules are defined. Learnin rate for velocity and power adaptive controllers rules are 1 and P 6, respectively. As issued, controller stratey is fixin power and anular velocity at their nominal values; therefore references for their derivations are zero. 7
The 10 th international Enery Conference (IEC 2014) 5. Simulation All simulations have been done in MATLAB software. The wind turbine parameters are shown in appendix [2]. A turbulent model is used wind modelin as it is shown in fiure 6. All these parameters are for a wind turbine model with nominal power P, 4.8MW. The nominal wind speed is V, 12 m / s and maximum allowable N enerator speed is supposed 162.45 rad / s [3]. The evaluation has been done by comparison between adaptive fuzzy controller responses and classical PI controller [8, 18]. w N Fiure 6: (a) Wind speed (b) Generated power comparison between adaptive controller and PI (c) Generated anular velocity comparison between adaptive controller and PI In Fiure 6 the simulation results for anular velocity of enerator and enerated power are shown. The modified operation of adaptive fuzzy controller rather than classical accepted PI [8, 18] is obvious. The overshoot at beinnin has been reduced and error with respect to nominal values is decreased.the main aspect of adaptive fuzzy controller is in lower wind 8
The 10 th international Enery Conference (IEC 2014) speed where this controller has reduced error enormously by adoptin its centers of membership functions. 6. Conclusion In the present research, performance improvement of a wind turbine as a clean enery supply, by employin adaptive fuzzy controller in the full load reion, has been modified. The control stratey in the full load operation is keepin enerated power on the nominal value to avoid danerous vibration. The adaptive fuzzy controller has been employed to increase controller robustness with respect to uncertainty. In addition to the enerator anular velocity control for keepin pitch anle on its nominal value, the power control also has been performed by torque controller to eliminate steady state error. Therefore, the controller consists of two velocity and power controller units. The controller is evaluated by comparin its responses with classical and verified PI controller ones. This comparison showed that the overshoot and steady state error are reduced sinificantly. This improvement is due to the adaption of adaptive fuzzy controller durin varyin wind condition. Consequently, this is shown that adaptive fuzzy controller is more robust and efficient than the classical PI controller. References [1] C. Sloth, T. Esbensen, M. O.K. Niss, J. Stoustrup, and P. F. Odaard, Robust LMI-Based Control of Wind Turbines with Parametric Uncertainties, 18th IEEE International Conference on Control Applications Part of IEEE Multi-conference on Systems and Control, (2009), Russia, pp. 776-781. [2] T. Esbensen, B. T. Jensen, M. O. Niss, and C. Sloth, Joint Power and Speed Control of Wind Turbines, Technical report, (2008), Aabor University. [3] F.D. Bianchi, H. De Battista, and R. J. Mantz, Wind turbine control systems: principles, modellin and ain schedulin desin, Spriner, (2007). [4] F. Gao, D. Xu, and Y. Lu, Pitch-control for lare-scale wind turbines based on feed forward fuzzy-pi, 7th World Conress on Intellient Control and Automation, IEEE, (2008), China, pp. 2277-2282. [5] X. J. Jun, Y. L. Mei, Q. X. Nin, J. C. Lei, and J. R. Wan, Study of variablepitch wind turbine based on fuzzy control, 2nd International Conference on Future Computer and Communication, IEEE, (2010), China, pp. 235-239. [6] R. Ata, and Y. Kocyiit, An adaptive neuro-fuzzy inference system approach for prediction of tip speed ratio in wind turbines, Expert Systems with Applications, (2010), vol. 53, pp. 5454 5460. [7] S. Bououden, M. Chadli, S. Filali, and A. El Hajjaji, Fuzzy model based multivariable predictive control of a variable speed wind turbine: LMI approach, Renewable Enery, (2012), vol. 37, pp. 434-439. 9
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