29 0 202 0 : 000 852(202)0 365 06 Control Theory & Applications Vol. 29 No. 0 Oct. 202,, 2, 3 (., 50006; 2., 464000; 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 464000, 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, 237669MW, 430TWh, 2.5%, 6. 20 763 MW, 46%, 62364 MW, 200, [].,,,,.,,. : 20 06 09; : 202 06 2. : (60534040); (IDSYS20070); (2009B00900052); (S202040007895); (202003).
366 29 :, 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 + 0.08β 0.035 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
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
368 29 4.3 (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, 0 22.3 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 = 0.0068. 5 0 m/s 4 m/s. 4 Fig. 4 Structure of the nonlinear controller
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