16 9 2012 9 ELECTRI C MACHINES AND CONTROL Vol. 16 No. 9 Sep. 2012 1 2 3 1 2 1 2 1. 100190 2. 100190 3. 100049 TM 614 A 1007-449X 2012 09-0033- 06 Speed control of large scale wind turbines based on active disturbance rejection control XIA An-jun 1 2 3 HU Shu-ju 1 2 XU Hong-hua 1 2 1. Institute of Electrical Engineering Chinese Academy of Sciences Beijing 100190 China 2. Key Laboratory of Wind Energy Utilization Chinese Academy of Sciences Beijing 100190 China 3. Graduate University Chinese Academy of Sciences Beijing 100049 China Abstract A large-scale wind turbine typically has a greater moment of inertia which prevents the machine from changing speed fast enough to follow the maximum power point when wind speed changes. In order to improve the wind energy utilization of wind turbines in low winds the speed control strategy based on active disturbance rejection control ADRC was proposed. Internal and external disturbance of the system was observed by the extended state observer ESO based on the feedback of rotor speed. The wind turbine was equivalent to a first-order linear system by compensating the disturbance. The speed controller of the system was designed based on the active disturbance rejection control theory. The speed setpoint was calculated on the basis of the mechanic power captured by the wind turbine which was estimated realtimely and the rotor speed was controlled directly by the speed controller. Simulation results show that compared to traditional power control strategy the speed control strategy based on ADRC has distinct advantages of tacking the maximum power point more quickly and improving the wind energy utilization of wind turbines when wind speed changes and has less dependence on the parameters of wind turbine. Key words wind turbine maximum power point tracking moment of inertia active disturbance rejection control extended state observer tracking differentiator 2012-03 - 21 1981 1978 1967
34 16 0 1 1 11 P mech = 1 2 C P λ β Aρv 3 1 P mech λ β A ρ v C P λ β β λ β C P λ β λ 1 maximum power point tracking MPPT 1 0.6 C pmax 0.5 2 3-5 6 0.1 7 姿 opt 0 8 0 2 4 6 8 10 12 14 叶尖速比姿 1 C p Fig. 1 Power coefficient C p C Ρ λ β λ λ = ΩR ν Ω rad /s R m 1 P mech = 1 2 C P λ β Aρ R3 Ω 3 = kω 3 2 λ 3 k = 1 2 C P λ β Aρ R3 λ 3 9 λ opt Ω opt 2 10 P mech = 1 2 C Pmax λ β Aρ R3 Ω 3 λ 3 opt = k opt Ω 3 opt 3 opt k opt = 1 2 C Pmax λ β Aρ R3 3 λ 3 opt 4 2 风能转换系数 Cp 0.4 0.3 0.2 λ = λ opt C Ρ λ β = C pmax
9 35 机械功率 Fig. 2 P P 3 P 2 P 1 2 v 1 v 2 v 3 赘 1 赘 2 赘 3 赘 转子转速 Turbine s mechanical power-rotor speed 2 Ω * Ω 2. 1 Ω 1 Ω 2 b d Ω * Ω 2 Ω 3 d 4 Ω * Ω 3 2. 2 Ω opt = 槡 3 P mech /kopt 4 12 4 JΩ = Q a - GQ g - Q l 5 J 4 Q a ( Q a = 1 2 C P λ β Aρ R3 2 Ω ) G Q MPPT λ 3 l 5 3 Q a = JΩ + GQ g + Q l 6 v1 Ω 1 6 Ω ΩQ a = JΩ Ω + GQ g Ω + Q l Ω 7 ΩQ a JΩ Ω GQ g Ω Q l Ω v 1 a v 1 v 4 a b P 1 P 2 4 c P mech = JΩ Ω + GQ g Ω + Q l Ω Ω 2 = 槡 3 P 2 /kopt Ω 机械功率 P P 3 P 2 P 1 3 Fig. 3 b a v 1 v 2 c d 赘 1 赘 2 赘 3 机组转速 v 4 The MPPT scheme 赘
36 16 β 1 = 2 槡 2 β2 x 1 t + h = x 1 t + hx 2 t 8 e x 2 t + h = x 2 t + hu u r } 1 = Ω * - z 1 8 u = fst x 1 t - v t x 2 t r h 0 d = rh 0 d 0 = dh 0 u 0 = k T e 1 - z 2 /b 11 10 9 Ω = kt e 1 11 12 y = x 1 - v t + h 0 x 2 a 0 = 槡 d 2 + 8r y k T Ω * a = x 2 + a 0 - d sgn y /2 y > d 0 k { T x 2 + y /h 0 y d 0 ra /d a d 12 fst = - { rsgn a a > d k T h r x 1 t v t x 2 t x 1 t h 0 3 v t r h 0 3 v 1 a v 1 v 4 a b 2. 3 P 1 P 2 3 P 1 Ω = P2 /Ω - P 1 /Ω - Q l /J 13 13 12 - J J 5 2. 4 MPPT G Ω = - J Q g - Q a - Q l /G 9 Q a - Q l /J 4 赘 d 赘 /dt 最大功率曲线微分跟踪器赘 e = z 1 - Ω } * u z 1 = z 1 + h z 2 - β 1 e + bu 0 10 0 自抗扰转速控制器赘 z 2 = z 2 + h - β 2 e 4 z 1 z 2 Fig. 4 MPPT control system u 0 b = - G /J β 1 β 2 Wind 风电机组 P e P loss P mech
9 37 13 12 P e 11 10 P loss P mech Ω * 9 u 0 8 3 6 m /s 风速 /(m s -1 ) 8.5 8 7.5 7 6.5 6 5.5 100 150 200 250 300 350 400 Fig. 5 5 Wind speed 6 320 7 300 280 转子转速 /(rad s -1 ) 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 100 150 200 250 300 350 400 6 Fig. 6 Rotor speed 叶尖速比 7 6 100 150 200 250 300 350 400 bladed 7 Fig. 7 The tip speed ratio 80 m 2 MW 18 r /min 13 403 N m 6 029 000 kg m 2 83. 33 4 m /s8 a 8 b 6 m /s 8 25 m /s k * opt 1 000 N m / s 8 m /s 6 m /s m / rad /s 2 k * opt k opt = k * optg 5 143 s 6 m /s 8 m /s293 s 8 m /s 机械功率 /kw 机械功率 /kw Fig. 8 700 690 680 670 660 650 640 630 620 610 600 130 150 360 340 140 160 170 180 190 200 (a) 风速从 6m/s 变化为 8m/s 时的情况 260 240 220 290 294 298 302 306 310 (b) 风速从 8m/s 变化为 6m/s 时的情况 8 The mechanical power of wind turbine
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