:, PID.,.,.,,, [2 8], [9 5]. [9],,,. [0],,,. [],,,. [2],,. [3],,,. [4],,. [5],.,,,. 2 (Mechanism model of variable speed constant frequency dou

Size: px

Start display at page:

Download ":, PID.,.,.,,, [2 8], [9 5]. [9],,,. [0],,,. [],,,. [2],,. [3],,,. [4],,. [5],.,,,. 2 (Mechanism model of variable speed constant frequency dou"

禄瑞石
5 years ago
Views:

1 : (202) Control Theory & Applications Vol. 29 No. 0 Oct. 202,, 2, 3 (., 50006; 2., ; 3., 50640) :,,,,,., ;,,, ;,.,,. : ; ; ; ; ; : TM35, TP273 : A Feedback linearization control of constant output power for variable pitch wind turbine YANG Jun-hua, ZHENG Jian-hua, YANG Meng-li 2, WU Jie 3 (. College of Automation Science and Engineering, Guangdong University of Technology, Guangzhou Guangdong 50006, China; 2. Xinyang Grid Company, Xinyang Henan , China; 3. School of Electric Power, South China University of Technology, Guangzhou Guangdong 50640, China) Abstract: When the wind speed exceeds the rated value, the wind power captured by the wind turbine must be reduced to guarantee the wind turbine to operate in the safe and stable status. A control scheme for limiting the power of the variable pitch wind turbine based on the differential geometry feedback linearized theory is proposed to keep the rotational speed and output power at the rated value. An affine nonlinear model of the wind turbine is developed and then globally exactly linearized by a differential geometry transformation. With the new linearized model, we design a novel pitch angle controller in which the output feedback variable is the rotational speed and the input control variable is the blade pitch angle. When the wind speed exceeds the rated value, the pitch angle controller changes the blade pitch angle to reduce the rotational speed back to the rated value for ensuring the constant output power. Simulation results show that, when the wind speed is above the rated value, the proposed control strategy effectively implements the constant output power control for the variable pitch wind turbine with fine flexibility and robustness. Key words: wind turbine; power limitation control; feedback linearization; differential geometry; globally precise linearization; variable pitch (Introduction),. 20, MW, 430TWh, 2.5%, MW, 46%, MW, 200, [].,,,,.,,. : ; : : ( ); (IDSYS20070); (2009B ); (S ); (202003).

2 :, PID.,.,.,,, [2 8], [9 5]. [9],,,. [0],,,. [],,,. [2],,. [3],,,. [4],,. [5],.,,,. 2 (Mechanism model of variable speed constant frequency doubly-fed wind generation system),,. : V, T r, ω r, T e, ω g.,,. Fig. Structure of the wind energy generation system 2. (Aerodynamic model) Betz [6], P r = 2 ρπr2 C p (λ, β)v 3, () λ = ω rr V, (2) J r dω r dt = T r T ls, (3) T r = P r ω r = 2ω r ρπr 2 C p (λ, β)v 3. (4) () (4) : P r, ρ, R, C p (λ, β),,, (5) [7],,,. C p (λ) = c ( c 2 c 3 β c 4 )e c 5 λ i + c 6 λ, (5) λ i λ i = λ β β 3 +. β : dβ dt = T β (β r β), (6) : T β, β r. 2.2 (Gear drive model) 2,,,., [8]. 2 Fig. 2 Structure of the drive chain

3 0 : 367, k = T ls T hs = ω g ω r, (7) : k, ω g ω r, T ls T hs. 2.3 (Doubly-fed induction generator) dω g J g = T hs T e, (8) dt : J g ; T hs, ; T e,,. 2.4 (Whole model of system),,,, [2] J v = J r + k 2 J g, (9) : J r ; J g ; k. J v ω r = T r kt e, (0) dβ dt = (β r β). T β () 3 (Feedback linearization theory) [9 20] : ẋ = f(x) + g(x)u, (2) y = h(x). L g L f h(x) L g L n f h(x) 0 y (n) = n h(x) =L n x n f h(x)+l g L n f h(x)u. (6) y (n) =v u = L g L n f h(x) [ Ln f h(x) + v]. (7) 4 (Design the nonlinear controller),. 4. (Control goal of system),,.,,,.,,,,, 3. 3 Fig. 3 Feedback linearization control of wind energy conversion system y, u y, u. : y ẏ = h(x) x = L fh(x) + L g h(x)u. (3) (3) L g h(x) 0, y u, u = L g h(x) [ L fh(x) + v], (4) y v ẏ = v. (3) L g h(x) = 0, ẏ, ÿ = 2 h(x) x 2 = L 2 f h(x) + L g L f h(x)u. (5) 4.2 (Affine model of wind energy conversion system) ω r, β r,, ẋ =f(x)+g(x)u, (8) y = h(x) = ωr ω r, : [ ω r ] x =, u = β r, g(x) = 0, β T β C p (λ, β)ρπr 2 V 3 kt e f(x) = 2J v x. x 2 T β

4 (Inspection of linearization condition) h(x) = [ 0], (9) x f(x) g(x) L f h(x) = f (x), L g h(x) = 0. L f h(x) [ L f h(x) f (x) = x x ] f (x), (20) x 2 : f (x) = C p(λ,β)ρπr 2 V 3 + ρπr2 V 3 C p (λ,β), x x 2 2J v 2J v x x L 2 f h(x) = L fh(x) x f(x) = [ f (x) x f (x) x 2 ] [ ] f (x), f 2 (x) L g L f h(x) = L fh(x) x g(x) = f (x) 0. T β x 2, 2,,. 4.4 (Design controller) z = h(x), z 2 = L f h(x) = f (x). ż = z 2, ż 2 = v, v = L 2 f h(x) + L g L f h(x)u. (2) (22), : v = k f z(x) = k z k 2 z 2, u = β r = L g L f h(x) (v L 2 f h(x)). (23) 4. 5 (Simulation results and analysis) : 300 kw, 24 m, r/min, J r = 600 kg/m 2, k = 67, 500 r/min, J g = 49 kg/m 2. ρ.2. [7], (5) : c = 0.576, c 2 = 6, c 3 = 0.4, c 4 = 5, c 5 = 2, c 6 = m/s 4 m/s. 4 Fig. 4 Structure of the nonlinear controller

5 0 : m/s 4 m/s Fig. 5 Responses curves when wind speed jumps from 0 m/s to 4 m/s,, ( 5(c)),,,, ( 5(b)),,,,.,, ( 5(d)). 6. ( 6(a)),, ( 6(b)), ( 6(c) 6(d)),. 6 Fig. 6 Responses curves under actual wind speed 6 (Conclusions),,,.,.. (References): [] Global Wind Energy Council. Global wind report - annual market update 20 [R]. Brussels Belgium: Global Wind Energy Council, 202. [2] LEE T S. Input-output linearization and zero-dynamics control of three-phase AC/DC voltage-source converters [J]. IEEE Transactions on Power Electronics, 2003, 8(): 22. [3] LIAO Z L, JIA H P, LIU G H, et al. Comparative study on vector control and differential geometry decoupling control method of induction motor [C] //The 8th International Conference on Electrical Machines and Systems. Piscataway, NJ: IEEE, 2005, (2):

6 [4]. [J]., 2005, 22(2): (HUANG Songqing. Stability for motor driver fed by voltage-type inverter [J]. Control Theory & Applications, 2005, 22(2): ) [5],,. [J]., 990, 0(s): 5 2. (LU Qiang, SUN Yuanzhang, GAO Jingde. Development and application of geometric structure theory of nonlinear control system [J]. Proceedings of the Chinese Society for Electrical Engineering, 990, 0(S): 5 2) [6],,. [M]. :, 2008 (LU Qiang, MEI Shengwei, SUN Yuanzhang. Nonlinear Control of Power System [M]. Beijing: Tsinghua University Press, 2008.) [7],. [J]., (5) (SHI Feng, ZHA Xiaoming. Decoupled control of the shunt three-phase active power filter applying differential geometry theory [J] Proceedings of the Chinese Society for Electrical Engineering, (5): 92 97) [8], [J] (9) 2-26 (ZHANG Liang, SUN Yukun. Variable-structure control of bearingless switched reluctance motors based on differential geometry [J]. Proceedings of the Chinese Society for Electrical Engineering, 2006, 26(9): 2 26.) [9],. [J]., 2004, 25(4): (BAO Nengsheng, YE Zhiquan. Active nonlinear control of the stall horizontal wind turbine system [J]. Acta Energiae Solaris Sinica, 2004, 25(4): ) [0],. [J]., 999, 20(2): (BAO Nengsheng, JIANG Tong. Application of differential geometry in horizontal axis fixed speed wind turbine system [J]. Acta Energiae Solaris Sinica, 999, 20(2): ) [],,,. [J]., 2008, 25(2): (CHEN Sizhe, WU Jie, YAO Guoxing, et al. Power limitation control of wind turbine system based on differential geometry theory [J]. Control Theory & Applications, 2008,25(2): ) [2],,. [J]., 999, 6(5): (BAO Nengsheng, JIANG Tong, CHEN Qingxin. Nonlinear control of a variable speed WT system on ARWS - power limitation problem [J]. Control Theory & Applications, 999, 6(5): ) [3],. [J]., 2009, 35(): 8 85 (WANG Xiaolan, WU Dongji. Decoupling control of doubly-fed induction generator based on the differential geometry method [J]. Journal of Lanzhou University of Technology, 2009, 35(): 8 85.) [4] KANNA O, HANBA S, YAMASHITA K. A method of damping transient rush voltage fluctuation of power systems due to a wind driven generator via nonlinear state feedback control [J]. Electrical Engineering in Japan, 998, 24(): [5] BOUKHEZZAR B, SIGUERDIDJANE H, HAND M M. Nonlinear Control of variable-speed wind turbines for generator torque limiting and power optimization [J]. Transactions of the ASME, 2006, 28(): [6]. [M]. :, 2006: (YE Hangye. Control Techniques for Wind Energy Conversion System [M]. Beijing: Machines Press, 2006: ) [7] SLOOTWEG J G, POLINDER H, KLING W L. Initialization of wind turbine models in power system dynamics simulations [C] //IEEE Porto Power Tech Proceedings. New York: IEEE, 200, 4: 6. [8] BIANCHI F D, BATTISTA H D, MANTZ R J. Wind Turbine Control Systems - Principle, Modelling and Gain Scheduling Design [M]. London: Springer, 2007: [9] JEAN-JACQUES E S. Applied Nonlinear Control [M]. Beijing: Machine Press, 2004: [20]. [M]. :, 200: 88 2 (HU Yueming. Theory and Application of Nonlinear Control System [M]. Beijing: Defense Industry Press, 200: 88 2.) : (965 ),,,,, yly93@63.com; (985 ),,,, zhengjianhuaabc@26.com; (984 ),,,, @qq.com; (937 ),,,,, yly930@26.com.

; 3/2, Buck-Boost, 3 Buck-Boost DC-DC ; Y, Fig. 1 1 BBMC The topology of three phase-three phase BBMC 3 BBMC (Study on the control strategy of

; 3/2, Buck-Boost, 3 Buck-Boost DC-DC ; Y, Fig. 1 1 BBMC The topology of three phase-three phase BBMC 3 BBMC (Study on the control strategy of 26 2 2009 2 Control Theory & Applications Vol. 26 No. 2 Feb. 2009 : 1000 8152(2009)02 0203 06 Buck-Boost 1,2, 3, 2, 4, 1 (1., 411201; 2., 410083; 3., 411105; 4., 410004) :, Buck-Boost,.,,. :,,,, : Buck-Boost