(SMDVC), DFIG., SMDVC,,. 2 (Model analysis) 1 DFIG. DFIG, PWM, DFIG,. 1 DFIG Fig. 1 Wind Turbine Based on the DFIG DFIG,, DFIG d-q : u dqs d λ

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1 : (2012) Control Theory & Applications Vol. 29 No. 2 Feb , 1, 1, 2 (1., ; 2., ) : PI,, (SMDVC), (DFIG)., SMDVC PI,, DFIG. : ; ; : TM315 : A Sliding-mode-direct-voltage-control of wind turbines based on double-fed induction generators ZHANG Miao 1, LI Yun-de 1, CHEN Si-zhe 1, WU Jie 2 (1. Faculty of Automation, Guangdong University of Technology, Guangzhou Guangdong , China; 2. College of Electric Power, South China University of Technology, Guangzhou Guangdong , China) Abstract: To handle the slow dynamic response and the dependency on accurate machine parameters in PI vector control, we propose a sliding-mode direct-voltage-control (SMDVC) with constant switching frequency to realize the gridsynchronized control for the double-fed induction generators (DFIG). Experimental results show that the proposed SMDVC method is with better dynamic performance than the PI vector control; it can effectively control the stator voltages of DFIG to accurately track the grid voltages under imbalance conditions. Key words: wind power generation; doubly-fed induction generator; sliding-mode-direct-voltage-control 1 (Introduction),, 1. (double-fed induction generators, DFIG),,,,.,.,,. 2, d-q,,,. 3,,. PI DFIG,., 4 DFIG,,. 5 DFIG,,.,,, 6 7. PI,, : ; : : (2009A ); ( ); 211 ( 431).

2 (SMDVC), DFIG., SMDVC,,. 2 (Model analysis) 1 DFIG. DFIG, PWM, DFIG,. 1 DFIG Fig. 1 Wind Turbine Based on the DFIG DFIG,, DFIG d-q : u dqs d λ dqs dt + jω e λdqs, (1) u dqr R r i dqr + d λ dqr + j(ω e p n ω r ) dt λ dqr, (2) λdqs L m i dqr, (3) λdqr L r i dqr, (4) : R r, L m, L r, u dqs, λ dqs, u dqr, i dqr, λ dqr, ω e, ω r, p n. (1) (4), DFIG, dq., (RGA), d-q d-q d-q,. RGA. RGA, 8., d-q d-q. (3) (1),, : u ds u qs L m s ω e L m ω e L m L m s i dr i qr, (5) : u, i, s, d q d, q, s r. (5) RGA T 1 L m s ω e L m. L m s ω e L m ω e L m L m s ω e L m L m s 1 s 2 ωe 2, (6) s 2 + ωe 2 ωe 2 s 2.. RGA,, RGA, RGA 8., (6) : 1 s 2 ωe (7) s 2 + ωe 2 ωe 2 s (7) RGA, (5) : d q ; q d., d-q d-q. (4) (2),, : u dr u qr R r + L r s ω s L r ω s L r R r + L r s ω s (ω e p n ω r ). (8) RGA R r + L r s ω s L r ω s L r R r + L r s. T 1 R r + L r s ω s L r ω s L r R r + L r s 1 (R r + L r s) 2 + (ω s L r ) 2 i dr i qr, (8) (R r +L r s) 2 (ω s L r ) 2. (ω s L r ) 2 (R r +L r s) 2 (9) DFIG, ω s, (9) 1 (R r + L r s) 2 + (ω s L r ) 2 (R r + L r s) 2 (ω s L r ) 2 (ω s L r ) 2 (R r + L r s) (10) (10) RGA, (8) : d d ;

3 2 : 247 q q. DFIG ±30%, RGA., DFIG d-q d-q : d q, q d.,. (5) s, su ds L m s 2 sω e L m i dr. (11) su qs sω e L m L m s 2 i qr RGA, (11),. (8) (11), su ds su qs ω e L m u qr + L r u dr R r ω s ω e L m L r R i dr + L m s 2 i dr. (12) r ω i s qr i qr L r 3 (Design of SMDVC),,,, 9. DFIG, DFIG, q, d. DFIG d-q d-q,. d-q d-q : x d x q u ds u dg u qg u qs. (13) : s d x t d x d (z) 0 + c dz, s q x q x q (z) 0 : c, z. (14) (14) 0 x d (z) dz 1 x d0, (15) x q (z) c x q0 x d0 x q0 x d x q., t 0 0 (14) : s d (t 0 ) x d (t 0 ) x d0 0. (16) s q (t 0 ) x q (t 0 ) x q0 0 (16), (15),,. u qr u eq qr u u dr u eq + qr. (17) dr u dr DFIG,. (16),, ṡ d ṡ q 0. (18) u eq qr L r0 ω s R r0 i u eq dr + dr R r0 L r0 ω s i qr ( ) L r0 x d c + d u ds ω e L m0 x q dt u qs, (19) R r0, L r0, L m0..,,. u qr u dr K d1 x d sgn(s d x d ) + K d2 sgn s d K q1 x q sgn(s q x q ) + K q2 sgn s q, (20) K,, : s d ṡ d 0 <. (21) s q ṡ q 0 SMDVC 2. (19), u ds, u qs,,., 2 u ds, u qs,. (20)., 2,,., 9.

控制理论与应用 248 第 29 卷图 2 SMDVC算法框图 Fig. 2 Block diagram of the proposed SMDVC 4 实验结果 (Experimental results) 在实验室中搭建了图3所示的基于DFIG的风力发电实验平台. 采用直流电动机代替风力机与DFIG同轴连接.

4 控制理论与应用 248 第 29 卷图 2 SMDVC算法框图 Fig. 2 Block diagram of the proposed SMDVC 4 实验结果 (Experimental results) 在实验室中搭建了图3所示的基于DFIG的风力发电实验平台. 采用直流电动机代替风力机与DFIG同轴连接. DFIG的定转子绕组均采用星型联接方式, 定子绕组通过并网开关和三相自耦调压器与电网连接, 转子绕组由基于智能功率模块的PWM变换器进行励磁控制. 实验平台中的控制器采用型号dSpace DS1103. dspace以5 khz的频率采样电网电压定子电压转子电流和电机转速, 按设计的控制算法进行处理, 并产生开关频率为10 khz的svpwm信号以驱动转子变换器. 实验过程中的数据和波形可在安装dSpace的计算机上显示和保存. 变化速度分别限定为±5000 V/s和±500 V/s, 滑动面系数c的值设定为80. 为确定开关控制常数, 假定DFIG参数误差范围为额定值±50%, 为满足式 (21)的滑模存在条件, 式(20)中开关常数应设定为 Kd1 0.04, Kd , Kq1 0.04, Kq 在相同的实验条件下对传统PI矢量控制方法与提出的SMDVC方法进行比较. PI矢量控制采用双闭环结构, 内环为转子电流控制环, 外环为定子电压控制环, 通过设定PI控制器参数, 使内外环的闭环时间常数分别为2 ms和20 ms. 首先, 在正常情况下进行实验研究. 图4为PI矢量控制下的电网q轴电压定子q轴电压和定子d轴电压波形(电网d轴电压为零, 图中未画出). PI矢量控制有效地控制定子d-q轴电压分别跟踪电网d-q轴电压, 且具有良好的控制性能. 由于定子d-q轴电压很好地实现了对电网d-q轴电压的跟踪, 图5中的定子线电压在4个周期后即获得与电网电压相同的幅值频率和相位, 满足了并网条件. 图 3 基于DFIG的实验平台在相同的条件下, SMDVC方法的实验结果如图6 7所示. 图6为电网q轴电压定子q轴电压和定子d轴电压波形. 图7为电网定子线电压波形. 可见, SMDVC同样在4个周期内使定子电压与电网电压具有相同的幅值频率和相位. Fig. 3 Experimental platform based on DFIG 实验平台中DFIG的额定功率为1.8 kw, 额定频率为50 Hz, 同步转速为1500 RPM, 定转子匝数比为3.1667, 定转子额定电压分别为380 V, 120 V, 定转子额定电流分别为4.5 A, 10 A, 定转子间互感为 H(折算到定子侧), 定转子漏感均为 H(折算到定子侧), 转子电阻为 Ω(折算到定子侧), 定子电阻为 Ω. 在SMDVC算法中, 定子q轴和d轴电压参考值图 4 PI矢量控制的电网定子d-q 轴电压 Fig. 4 Grid, stator d-q axis voltages with PI vector control

5 第2期张淼等: 双馈感应风力发电机组的滑模直接电压控制 249 由图4 7可见, 在正常情况下, PI矢量控制与提出的SMDVC都能很好地实现DFIG的电网同步控制, 且都具有良好的控制性能. 大型风电场常处于长输电线末端, 即使在电网正常运行的情况下, 也可能由于不平衡输电线阻抗三相不平衡负载或单相大功率负载等原因, 造成风力发电机组接入点处的电网电压不平衡10. 不平衡电压矢量由正负序分量组成. 在同步旋转坐标系中, 正序分量为直流量, 负序分量为二倍电网频率的交流量, 因此不平衡电网电压将体现为直流分量与100 Hz交流分量的叠加. 在电网电压不平衡工况下, 同步旋转坐标系中的电网d-q轴电压是周期性变化的, 这对DFIG电网同步控制方法的动态性能提出了较高的要求. 图 5 PI矢量控制的电网定子线电压 Fig. 5 Grid, stator line voltages with PI vector control 在实验平台中, 增加一台调压器单独降低C相电压, 以模拟不平衡程度为10%的电网电压, 对PI 矢量控制方法和SMDVC方法进行实验对比. 图8 9为PI矢量控制的实验结果. 由于矢量控制的动态响应速度慢, DFIG定子q轴电压无法实现对周期变化的电网q轴电压的准确跟踪, 因此定子线电压与电网线电压间存在较大的偏差, 将会引起并网时刻的电流冲击. 图 6 SMDVC的电网定子d-q 轴电压图10 11为采用SMDVC方法的实验结果. 采用 SMDVC后, DFIG定子q轴电压迅速跟踪周期变化的电网q轴电压, 两者基本不存在偏差, 因此定子线电压很好地实现了对不平衡电网电压的跟踪. Fig. 6 Grid, stator d-q axis voltages with SMDVC 图 8 电网电压不平衡时PI矢量控制电网定子d-q 轴电压 Fig. 8 Grid, stator d-q axis voltages with PI vector control under unbalanced grid voltage 图 7 SMDVC的电网定子线电压 Fig. 7 Grid, stator line voltages with SMDVC

6 PI Fig. 9 Grid, stator line voltages with PI vector control under unbalanced grid voltage,., SMDVC, DFIG, PI., SMDVC PI,, DFIG. (References): 1,. J., 2004, 21(6): (WU Jie, YANG Junhua. Control on green energy source and ecologic environmentj. Control Theory & Applications, 2004, 21(6): ) 2 MOREL L, GODFROID H, A MIRZAIAN, et al. Double-fed induction machine: converter optimisation and field oriented control without position sensorj. IEE Proceedings on Electric Power Applications, 1998, 145(4): SMDVC d-q Fig. 10 Grid, stator d-q axis voltages with SMDVC under unbalanced grid voltage 3 WONG K C, HO S L, CHENG K W E. Direct voltage control for grid synchronization of doubly-fed induction generatorsj. Electric Power Components and Systems, 2008, 36(9): G MEZ S A, AMENEDO J L R. Grid synchronisation of doubly fed induction generators using direct torque controlc //Proceedings of the 28th IEEE Industrial Electronics Annual Conference. Piscatway: IEEE, 2002: ARBI J, GHORBAL M J B, SLAMA-BELKHODJA I, et al. Direct virtual torque control for doubly fed induction generator grid connectionj. IEEE Transactions on Industrial Electronics, 2009, 56(10): BUJA G S, KAZMIERKOWSKI M P. Direct torque control of PWM inverter-fed AC motors-a surveyj. IEEE Transactions on Industrial Electronics, 2004, 51(4): HOLTZ J. Pulsewidth modulation for electronic power conversionj. Proceedings of the IEEE, 1994, 82(8): ALBERTOS P, SALA A. Multivariable Control SystemsM. London: Springer-Verlag, 2004: UTKIN V I, GÜLDNER J, SHI J X. Sliding Mode Control in Electromechanical SystemsM. Florida: CRC, 1999: XU L, WANG Y. Dynamic modeling and control of DFIG-based wind turbines under unbalanced network conditionsj. IEEE Transactions on Power Systems, 2007, 22(1): SMDVC Fig. 11 Grid, stator line voltages with SMDVC under unbalanced grid voltage 8 11, SMDVC PI,, DFIG. 5 (Conclusion) RGA DFIG, : (1968 ),,,,, bezhangm@gdut.edu.cn; (1982 ),,,, liyund456@163.com; (1981 ),,,,, cszscut@126.com; (1937 ),,,, epjiewu@scut.edu.cn.

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