鲁棒近似反馈线性化方法及其在HVDC系统中的应用
|
摘要
研究非线性系统的控制问题具有重要的理论意义和实用价值。高压直流输电系统(简称HvDC系统)是典型非线性系统,HVDC系统是高度可控的,其中控制系统是直流输电技术的核心。HVDC系统能否正常运行与其基本控制器的性能息息相关。本论文对鲁棒近似反馈线性化控制方法进行了研究,研究结果解决了一类非线性系统的控制问题,并应用到HVDC系统中,并设计了相应的控制器。
本论文的主要内容和研究结果包括:
1)研究了单变量非线性系统的鲁棒近似反馈线性化控制方法,通过对单变量非线性系统的拓展研究,进行了多变量非线性系统的鲁棒近似反馈线性化方法的理论研究,核心思想是对包含非线性动态、外部扰动等系统不确定总体的扩张状态进行自动的估计和补偿,在避免复杂数学运算、抵消系统的非线性动态的同时,增强了对未知强非线性和不确定强扰动作用的鲁棒性和适应性。同时完善了相应的鲁棒近似反馈线性化控制器的设计方法。
2)研究了HvDC系统及其控制特性,首先建立了HVDC系统的状念方程,并将鲁棒近似反馈线性化方法应用到HVDC直流输电系统中,在整流侧采用定直流电流,逆变侧定无功功率的控制方式,设计了高压直流输电系统鲁棒近似反馈线性化控制器。最后通过PSCAD和MATLAB分别对此控制器进行仿真,仿真结果证明了所设计控制器的有效性与优越性。
It is valuable in both theoretical and practical area to study the control of nonlinear systems. High Voltage Direct Current Transmission (HVDC) is a typical nonlinear system. HVDC is high controllable. The control system is the core of DC transmission system. The performance of its basic controller decides the operation condition of HVDC system. This dissertation researches and improves a novel nonlinear robust approximate feedback linearization method based on model observers to solve the control problems for a class of nonlinear systems. Also the application problems of HVDC control system are discussed in detail. And a nonlinear controller for HVDC system is designed.
The main results and contributions of this dissertation are as follows:
Firstly, robust approximate feedback linearization method is analyzed for single-variable nonlinear system. The multivariable nonlinear system is researched based on the analysis of the single-variable nonlinear system. The core ideas of the presented method are to estimate and compensate the extended state which includes the nonlinear dynamics, parameter uncertainties and disturbances. This method can avoid complex mathematic operations, counteract the nonlinear dynamics and enhance the robustness and adaptability of the control system against uncertainties. The corresponding design scheme of robust approximate feedback linearization is discussed and perfected.
Secondly, HVDC system and its control characteristics are researched. First the state equations are established. Then the robust approximate feedback linearization method is applied to the HVDC system. This dissertation adopts the constant current control at the rectifier and the constant reactive power control at the inverter, and designs the robust approximate feedback linearization controller for HVDC system. At last, the simulation is done by PASCAD and MATLAB in this paper. The effectiveness and superiorities of new controller have been testified through simulation.
本论文的主要内容和研究结果包括:
1)研究了单变量非线性系统的鲁棒近似反馈线性化控制方法,通过对单变量非线性系统的拓展研究,进行了多变量非线性系统的鲁棒近似反馈线性化方法的理论研究,核心思想是对包含非线性动态、外部扰动等系统不确定总体的扩张状态进行自动的估计和补偿,在避免复杂数学运算、抵消系统的非线性动态的同时,增强了对未知强非线性和不确定强扰动作用的鲁棒性和适应性。同时完善了相应的鲁棒近似反馈线性化控制器的设计方法。
2)研究了HvDC系统及其控制特性,首先建立了HVDC系统的状念方程,并将鲁棒近似反馈线性化方法应用到HVDC直流输电系统中,在整流侧采用定直流电流,逆变侧定无功功率的控制方式,设计了高压直流输电系统鲁棒近似反馈线性化控制器。最后通过PSCAD和MATLAB分别对此控制器进行仿真,仿真结果证明了所设计控制器的有效性与优越性。
It is valuable in both theoretical and practical area to study the control of nonlinear systems. High Voltage Direct Current Transmission (HVDC) is a typical nonlinear system. HVDC is high controllable. The control system is the core of DC transmission system. The performance of its basic controller decides the operation condition of HVDC system. This dissertation researches and improves a novel nonlinear robust approximate feedback linearization method based on model observers to solve the control problems for a class of nonlinear systems. Also the application problems of HVDC control system are discussed in detail. And a nonlinear controller for HVDC system is designed.
The main results and contributions of this dissertation are as follows:
Firstly, robust approximate feedback linearization method is analyzed for single-variable nonlinear system. The multivariable nonlinear system is researched based on the analysis of the single-variable nonlinear system. The core ideas of the presented method are to estimate and compensate the extended state which includes the nonlinear dynamics, parameter uncertainties and disturbances. This method can avoid complex mathematic operations, counteract the nonlinear dynamics and enhance the robustness and adaptability of the control system against uncertainties. The corresponding design scheme of robust approximate feedback linearization is discussed and perfected.
Secondly, HVDC system and its control characteristics are researched. First the state equations are established. Then the robust approximate feedback linearization method is applied to the HVDC system. This dissertation adopts the constant current control at the rectifier and the constant reactive power control at the inverter, and designs the robust approximate feedback linearization controller for HVDC system. At last, the simulation is done by PASCAD and MATLAB in this paper. The effectiveness and superiorities of new controller have been testified through simulation.
引文
[1]吕伟业.中国电力工业发展及产业结构调整[M].中国电力出版社, 2002, 35(1),1-7.
[2]浙江大学发电教研组直流输电科研组.直流输电[M].北京:水利电力出版社,1985,1-12.
[3]韩京清.一类不确定对象的扩张状态观测器[J].控制与决策, 1995, 10(1):85-88.
[4]韩京清.自抗扰控制器及其应用[J].控制与决策, 1998, 13(1):19-23.
[5]黄一,张文革.自抗扰控制器的发展[J].控制理论与应用, 2002, 19(4):485-492.
[6]韩京清.从PID技术到“自抗扰控制”技术[J].控制工程, 2002, 9(3):13-18.
[7]韩京清,张荣.二阶扩张状态观测器的误差分析[J].系统科学与数学, 1999, 19(4):465-471.
[8]黄一,韩京清.非线性连续二阶扩张状态观测器的分析与设计[J].科学通报, 2000, 45(13):1373-1378.
[9]张荣,韩京清.串联型扩张状态观测器构成的自抗扰控制器[J].控制与决策, 2000, 15(1): 121-124.
[10] Hou Y., Gao Z., Jiang F., Boulter B.T. Active disturbance rejection control for web tension regulation [C]. Proceedings of the 40th IEEE Conference on Decision and Control, 2001, 4974-4979.
[11] Xia Y., Shi P., Liu G.P., Han J. Active disturbance rejection control for uncertain multivariable systems with time-delay [J]. Control Theory and Applications, 2007, 1(1):75-81.
[12] Zhang M., Wu J., Hou C. The control system of renewable energy connected grid based on the ADRC technology [C]. Proc. of the 5th World Congress on Intelligence Control and Automation, 2004, 64-67.
[13] Gao Z.Q. Scaling and parameterization based controller tuning [C]. Proceedings of the 2003 American Control Conference, 2003, 6:4989-4996.
[14] Gao Z.Q. Active disturbance rejection control: A paradigm shift in feedback control system design [C]. Proceedings of the 2006 American Control Conference, 2399-2406.
[15] Gao Z.Q. A DSP-based active disturbance rejection control design for a 1-kw H-bridge DC-DC power converter [J]. IEEE Trans. on industrial electronics, 2005, 52(5):1271-1277.
[16] Miklosovic R., Gao Zhiqiang. A robust two-degree-of-freedom control design technique and its practical application [C]. Industry Applications Conference, 2004, 3:1495-1502.
[17] Miklosovic R., Radka A., Gao Zhiqiang. Discrete implementation and generalization of the extended state observer [C]. Proceedings of the 2006 American Control Conference, 2209-2214.
[18] Zheng Q., Gao Z.Q. Motion control design optimization: problem and solutions [J]. International Journal of Intelligence Control and Systems, 2005, 10 (4):269-276.
[19] Zheng Q., Chen Z. Z., Gao Z.Q. A disturbance rejection based dynamic decoupling control approach [C]. Proceedings of the 2007 American Control Conference, Accepted.
[20] Tornambe A., Valigi P.A. Decentralized controller for the robust stabilization of a class of MIMO dynamical systems [J].Journal of Dynamic Systems, Measurement, and Control,1994,116:293-304.
[21]顾晓荣,方勇杰,薛禹胜.柔性交流系统稳定控制综述[J].电力系统自动化,1999,23(12),50~56.
[22]李海峰,李乃湖. FACTS装置用于电力系统稳定控制的综述[J].电力系统自动化,1998,22(9),31-37.
[23] Isidori A. Nonlinear Control Systems. 3rd ed. Berlin(Germany): Springer-Verlag, 1995,112-120.
[24] Brockett R. W. Nonlinear systems and differential geometry [C]. Proceedings of the IEEE, 1976, 64 (1):61-71.
[25] Krener A. J., Isidori A. Linearization by output injection and nonlinear observers [J]. Systems and Control Letters, 1989, No.3:47-52.
[26] Meyer G., Su R., Hunt L. R. Application of nonlinear transformation to automatic flight control [J]. Automatica, 1984, 20(1):103-107.
[27] Liao Z.L., Jia H.P., Liu G.H. Comparative study on vector control and defferential geometry decoupling control method of induction motor [C]. Proceedings of 8th International Conference on Electrical Machines and Systems, 2005, 2: 1539-1543.
[28] Tarn, T.J., Bejczy, A.K., Isidori A, et al. Nonlinear feedback in robot arm control [C]. In: Proceedings 23rd IEEE Conference on Decision and Control, 1984:736-751.
[29] Lu Q., Sun Y., Xu Z. et al. Decentralized nonlinear optimal excitation control. IEEE Trans. on Power system, 1996, 11(4):1957-1962.
[30]张怡哲,邓建华.逆系统方法在飞行控制律设计中的工程应用[J].西北工业大学学报, 2006, 24(1):35-39.
[31]李春文,张平,冯元琨.一种基于逆系统方法的化学反应器改进控制方案[J].控制与决策, 1998, 13(5): 577-580.
[32]李东海,姜学智,李立勤,等.逆系统方法在电力系统控制中的应用[J].电网技术, 1997, 21(7):10-12.
[33] Reboulet C., Champetier C. A new method for linearizing nonlinear system: the pseudolinearization [J]. International Journal of Control, 1984, 40(4):631-638.
[34] Champetier C., Mouyon P., Reboulet C. Pseudolinearization of multi-input nonlinear systems [C]. In: Proceedings of the 23rd IEEE Conference on Decision and Control, 1984. 96-97.
[35] Champetier C., Mouyon, P., Magni, J. F. Pseudolinearization of nonlinear systems by dynamic pre-compensation [C]. In: Proceedings of the 24th IEEE Conference on Decision & Control. 1985, 1371-1372.
[36]郭朝晖,郑加成,吴铁军.近似线性化方法综述[J].控制与决策, 1999, 14(9):385-391.
[37] Guardabassi G. O., Savaresi S. M. Approximate linearization via feedback-an overview [J]. Automatica, 2001, 37:1-15.
[38]申铁龙. H∞控制理论及应用[M].北京:清华大学出版社, 1996,26-35.
[39] Bartolini G., Ferrara A., Giaocomin L. A robust control design for a class of uncertain nonlinear systems featuring a second-order sliding mode [J]. International Journal of Control, 1999, 72(4):321-331.
[40]葛友,李春文. H∞滑模鲁棒励磁控制器设计[J].中国电机工程学报, 2002, 22(5):1-4.
[41]韩京清,王伟.非线性跟踪-微分器[J].系统科学与数学, 1994, 14(2):177-183.
[42]余涛.电力系统非线性鲁棒协调控制方法的研究[D].北京:清华大学, 2003.
[43]吕为龙,吴丹,王先逵,等.自抗扰精密跟踪运动控制器的设计[J].清华大学学报(自然科学版), 2007, 47(2):190-193.
[44]赵汪洋,庄良杰,杨功流.自抗扰控制器在平台惯导系统动基座下初始对准应用[J] .控制与决策, 2007, 22(2):179-183.
[45]夏长亮,俞卫,李志强.永磁无刷直流电机转矩波动的自抗扰控制[J].中国电机工程学报, 2006, 26(24):137-142.
[46]朱承元,杨涤,李顺利.用户卫星天线跟踪指向自抗扰控制方法[J].北京理工大学学报, 2006, 26(1):82-86.
[47]陈新龙,杨涤,耿斌斌.自抗扰控制技术在某型导弹上的应用[J].飞行力学, 2006, 24(1):81-84.
[48]宋金来,杨雨,许可康,等.惯性平台稳定回路的自抗扰控制[J].系统仿真学报, 2002, 14(3):391-393.
[49] Indri M., Tornambe A. Robust trajectory tracking for flexible piezoelectric structures [J], IEE Proceedings on Control Theory and Applications, 1994, 141(5):289-294.
[50]曾河华.发电机组的自抗扰PID控制[D].北京:清华大学, 2005.
[51]宁喜荣.水轮机调节系统的非线性鲁棒控制优化研究[D].北京:清华大学, 2006.
[52]黄炳红.自抗扰控制器在飞控及火控系统中的应用研究[D].北京:北京理工大学, 2006.
[53]周双喜,昌仕丽,张元鹏.直流输电对电压稳定性的影响[J].清华大学学报, 1999, 39(3): 4-7.
[54] Slotine J J E, Li W P. Applied Nonlinear Control [J]. Englewood Cliffs(New Jersey): Prentice Hall, 1991,12-15.
[55]吴青华,蒋林.非线性控制理论在电力系统中应用综述[J].电力系统自动化, 2001, 5(3), 1~10.
[56]卢强,孙元章.电力系统非线性控制[M].北京:科学出版社,1993,219-240.
[57] Qiang Lu, Yuanzhang Sun and Gordon K.F.Lee. Nonlinear Optimal Excitation Control for Multimachine Systems [J]. IFAC Symposium on Power System Modeling and Control Application, Brussels, Sept., 1998, 22:29-33.
[58] Qiang Lu and Yuanzhang Sun. Nonlinear Stabilizing Control of Multimachine System [J]. IEEE. PES, 4(1), Feb, 1989, 8: 120-122.
[59]卢强,孙元章,高景德.非线性系统几何结构理论的发展及其在电力系统中的应用[J].中国电机工程学报电工数学特刊, No.1, 1990.
[60] Huang J., Lin C.F., Cloutier J.R., et al. Robust feedback linearization approach to autopilot design [C]. In: Proceedings of the 1st IEEE Conference on Control Application, 1992, 1:220-225.
[61] Hassan K.Khalil. Adaptive output feedback control of nonlinear systems represented by input-output models [J]. IEEE Trans. on Automatic Control, 1996, 41(2):177-188.
[62]陈金莉.鲁棒近似反馈线性化方法及其在航天器姿态控制中的应用[D].北京航空航天大学,2007.
[63] John H., Shankar S., Petar K. Nonlinear control via approximate input-output linearization: the ball and beam example [J]. IEEE Trans. on Automatic Control, 1992, 37(3):392-398.
[64] Denis Lee Hau Ai K, Gōram Andersson. Voltage Stability Analysis of Multi-Infeed HVDC System [J]. IEEE Trans. on Power Delivery, 1997, 12(3):1309-1316.
[65] Franken B. Analysis of HVDC Converters Connected to Weak AC Systems [J]. IEEE Trans. on Power Systems, 1990, 5(1), 235-242.
[66]徐政.联于弱交流系统的直流输电特性研究之二:控制方式与电压稳定性[J].电网技术, 1997,21(3): 1-4.
[67] Hammad AE, Kuhn W. A Computation Algorithm for Assessing Voltage Stability at AC/DC Interconnection [J]. IEEE Trans. on Power System, 1986, PWRS-1(1): 209-216.
[68] M. Szechtman, W. W. Ping, E. Salgado, and J.P. Bowles. Unconventional HVDC Control Technique for Stabilization of a Weak Power System [J]. IEEE Trans. on Power Apparatus and System, 1984, PAS-103(8): 2244-2248.
[69]陈凌云.高压直流输电系统中非线性控制策略的研究[D].四川大学, 2004.
[70]段富海,韩崇昭.动态逆方法和微分几何反馈线性化方法的对比[J].自动化与仪器仪表, 2002, 3: 4-5.
[71] CIGRE Working Group 14.02, The CIGRE HVDC Benchmark Model- A New Proposal with Revised Parameters[J], Electra, 1994, (157): 61-64
[2]浙江大学发电教研组直流输电科研组.直流输电[M].北京:水利电力出版社,1985,1-12.
[3]韩京清.一类不确定对象的扩张状态观测器[J].控制与决策, 1995, 10(1):85-88.
[4]韩京清.自抗扰控制器及其应用[J].控制与决策, 1998, 13(1):19-23.
[5]黄一,张文革.自抗扰控制器的发展[J].控制理论与应用, 2002, 19(4):485-492.
[6]韩京清.从PID技术到“自抗扰控制”技术[J].控制工程, 2002, 9(3):13-18.
[7]韩京清,张荣.二阶扩张状态观测器的误差分析[J].系统科学与数学, 1999, 19(4):465-471.
[8]黄一,韩京清.非线性连续二阶扩张状态观测器的分析与设计[J].科学通报, 2000, 45(13):1373-1378.
[9]张荣,韩京清.串联型扩张状态观测器构成的自抗扰控制器[J].控制与决策, 2000, 15(1): 121-124.
[10] Hou Y., Gao Z., Jiang F., Boulter B.T. Active disturbance rejection control for web tension regulation [C]. Proceedings of the 40th IEEE Conference on Decision and Control, 2001, 4974-4979.
[11] Xia Y., Shi P., Liu G.P., Han J. Active disturbance rejection control for uncertain multivariable systems with time-delay [J]. Control Theory and Applications, 2007, 1(1):75-81.
[12] Zhang M., Wu J., Hou C. The control system of renewable energy connected grid based on the ADRC technology [C]. Proc. of the 5th World Congress on Intelligence Control and Automation, 2004, 64-67.
[13] Gao Z.Q. Scaling and parameterization based controller tuning [C]. Proceedings of the 2003 American Control Conference, 2003, 6:4989-4996.
[14] Gao Z.Q. Active disturbance rejection control: A paradigm shift in feedback control system design [C]. Proceedings of the 2006 American Control Conference, 2399-2406.
[15] Gao Z.Q. A DSP-based active disturbance rejection control design for a 1-kw H-bridge DC-DC power converter [J]. IEEE Trans. on industrial electronics, 2005, 52(5):1271-1277.
[16] Miklosovic R., Gao Zhiqiang. A robust two-degree-of-freedom control design technique and its practical application [C]. Industry Applications Conference, 2004, 3:1495-1502.
[17] Miklosovic R., Radka A., Gao Zhiqiang. Discrete implementation and generalization of the extended state observer [C]. Proceedings of the 2006 American Control Conference, 2209-2214.
[18] Zheng Q., Gao Z.Q. Motion control design optimization: problem and solutions [J]. International Journal of Intelligence Control and Systems, 2005, 10 (4):269-276.
[19] Zheng Q., Chen Z. Z., Gao Z.Q. A disturbance rejection based dynamic decoupling control approach [C]. Proceedings of the 2007 American Control Conference, Accepted.
[20] Tornambe A., Valigi P.A. Decentralized controller for the robust stabilization of a class of MIMO dynamical systems [J].Journal of Dynamic Systems, Measurement, and Control,1994,116:293-304.
[21]顾晓荣,方勇杰,薛禹胜.柔性交流系统稳定控制综述[J].电力系统自动化,1999,23(12),50~56.
[22]李海峰,李乃湖. FACTS装置用于电力系统稳定控制的综述[J].电力系统自动化,1998,22(9),31-37.
[23] Isidori A. Nonlinear Control Systems. 3rd ed. Berlin(Germany): Springer-Verlag, 1995,112-120.
[24] Brockett R. W. Nonlinear systems and differential geometry [C]. Proceedings of the IEEE, 1976, 64 (1):61-71.
[25] Krener A. J., Isidori A. Linearization by output injection and nonlinear observers [J]. Systems and Control Letters, 1989, No.3:47-52.
[26] Meyer G., Su R., Hunt L. R. Application of nonlinear transformation to automatic flight control [J]. Automatica, 1984, 20(1):103-107.
[27] Liao Z.L., Jia H.P., Liu G.H. Comparative study on vector control and defferential geometry decoupling control method of induction motor [C]. Proceedings of 8th International Conference on Electrical Machines and Systems, 2005, 2: 1539-1543.
[28] Tarn, T.J., Bejczy, A.K., Isidori A, et al. Nonlinear feedback in robot arm control [C]. In: Proceedings 23rd IEEE Conference on Decision and Control, 1984:736-751.
[29] Lu Q., Sun Y., Xu Z. et al. Decentralized nonlinear optimal excitation control. IEEE Trans. on Power system, 1996, 11(4):1957-1962.
[30]张怡哲,邓建华.逆系统方法在飞行控制律设计中的工程应用[J].西北工业大学学报, 2006, 24(1):35-39.
[31]李春文,张平,冯元琨.一种基于逆系统方法的化学反应器改进控制方案[J].控制与决策, 1998, 13(5): 577-580.
[32]李东海,姜学智,李立勤,等.逆系统方法在电力系统控制中的应用[J].电网技术, 1997, 21(7):10-12.
[33] Reboulet C., Champetier C. A new method for linearizing nonlinear system: the pseudolinearization [J]. International Journal of Control, 1984, 40(4):631-638.
[34] Champetier C., Mouyon P., Reboulet C. Pseudolinearization of multi-input nonlinear systems [C]. In: Proceedings of the 23rd IEEE Conference on Decision and Control, 1984. 96-97.
[35] Champetier C., Mouyon, P., Magni, J. F. Pseudolinearization of nonlinear systems by dynamic pre-compensation [C]. In: Proceedings of the 24th IEEE Conference on Decision & Control. 1985, 1371-1372.
[36]郭朝晖,郑加成,吴铁军.近似线性化方法综述[J].控制与决策, 1999, 14(9):385-391.
[37] Guardabassi G. O., Savaresi S. M. Approximate linearization via feedback-an overview [J]. Automatica, 2001, 37:1-15.
[38]申铁龙. H∞控制理论及应用[M].北京:清华大学出版社, 1996,26-35.
[39] Bartolini G., Ferrara A., Giaocomin L. A robust control design for a class of uncertain nonlinear systems featuring a second-order sliding mode [J]. International Journal of Control, 1999, 72(4):321-331.
[40]葛友,李春文. H∞滑模鲁棒励磁控制器设计[J].中国电机工程学报, 2002, 22(5):1-4.
[41]韩京清,王伟.非线性跟踪-微分器[J].系统科学与数学, 1994, 14(2):177-183.
[42]余涛.电力系统非线性鲁棒协调控制方法的研究[D].北京:清华大学, 2003.
[43]吕为龙,吴丹,王先逵,等.自抗扰精密跟踪运动控制器的设计[J].清华大学学报(自然科学版), 2007, 47(2):190-193.
[44]赵汪洋,庄良杰,杨功流.自抗扰控制器在平台惯导系统动基座下初始对准应用[J] .控制与决策, 2007, 22(2):179-183.
[45]夏长亮,俞卫,李志强.永磁无刷直流电机转矩波动的自抗扰控制[J].中国电机工程学报, 2006, 26(24):137-142.
[46]朱承元,杨涤,李顺利.用户卫星天线跟踪指向自抗扰控制方法[J].北京理工大学学报, 2006, 26(1):82-86.
[47]陈新龙,杨涤,耿斌斌.自抗扰控制技术在某型导弹上的应用[J].飞行力学, 2006, 24(1):81-84.
[48]宋金来,杨雨,许可康,等.惯性平台稳定回路的自抗扰控制[J].系统仿真学报, 2002, 14(3):391-393.
[49] Indri M., Tornambe A. Robust trajectory tracking for flexible piezoelectric structures [J], IEE Proceedings on Control Theory and Applications, 1994, 141(5):289-294.
[50]曾河华.发电机组的自抗扰PID控制[D].北京:清华大学, 2005.
[51]宁喜荣.水轮机调节系统的非线性鲁棒控制优化研究[D].北京:清华大学, 2006.
[52]黄炳红.自抗扰控制器在飞控及火控系统中的应用研究[D].北京:北京理工大学, 2006.
[53]周双喜,昌仕丽,张元鹏.直流输电对电压稳定性的影响[J].清华大学学报, 1999, 39(3): 4-7.
[54] Slotine J J E, Li W P. Applied Nonlinear Control [J]. Englewood Cliffs(New Jersey): Prentice Hall, 1991,12-15.
[55]吴青华,蒋林.非线性控制理论在电力系统中应用综述[J].电力系统自动化, 2001, 5(3), 1~10.
[56]卢强,孙元章.电力系统非线性控制[M].北京:科学出版社,1993,219-240.
[57] Qiang Lu, Yuanzhang Sun and Gordon K.F.Lee. Nonlinear Optimal Excitation Control for Multimachine Systems [J]. IFAC Symposium on Power System Modeling and Control Application, Brussels, Sept., 1998, 22:29-33.
[58] Qiang Lu and Yuanzhang Sun. Nonlinear Stabilizing Control of Multimachine System [J]. IEEE. PES, 4(1), Feb, 1989, 8: 120-122.
[59]卢强,孙元章,高景德.非线性系统几何结构理论的发展及其在电力系统中的应用[J].中国电机工程学报电工数学特刊, No.1, 1990.
[60] Huang J., Lin C.F., Cloutier J.R., et al. Robust feedback linearization approach to autopilot design [C]. In: Proceedings of the 1st IEEE Conference on Control Application, 1992, 1:220-225.
[61] Hassan K.Khalil. Adaptive output feedback control of nonlinear systems represented by input-output models [J]. IEEE Trans. on Automatic Control, 1996, 41(2):177-188.
[62]陈金莉.鲁棒近似反馈线性化方法及其在航天器姿态控制中的应用[D].北京航空航天大学,2007.
[63] John H., Shankar S., Petar K. Nonlinear control via approximate input-output linearization: the ball and beam example [J]. IEEE Trans. on Automatic Control, 1992, 37(3):392-398.
[64] Denis Lee Hau Ai K, Gōram Andersson. Voltage Stability Analysis of Multi-Infeed HVDC System [J]. IEEE Trans. on Power Delivery, 1997, 12(3):1309-1316.
[65] Franken B. Analysis of HVDC Converters Connected to Weak AC Systems [J]. IEEE Trans. on Power Systems, 1990, 5(1), 235-242.
[66]徐政.联于弱交流系统的直流输电特性研究之二:控制方式与电压稳定性[J].电网技术, 1997,21(3): 1-4.
[67] Hammad AE, Kuhn W. A Computation Algorithm for Assessing Voltage Stability at AC/DC Interconnection [J]. IEEE Trans. on Power System, 1986, PWRS-1(1): 209-216.
[68] M. Szechtman, W. W. Ping, E. Salgado, and J.P. Bowles. Unconventional HVDC Control Technique for Stabilization of a Weak Power System [J]. IEEE Trans. on Power Apparatus and System, 1984, PAS-103(8): 2244-2248.
[69]陈凌云.高压直流输电系统中非线性控制策略的研究[D].四川大学, 2004.
[70]段富海,韩崇昭.动态逆方法和微分几何反馈线性化方法的对比[J].自动化与仪器仪表, 2002, 3: 4-5.
[71] CIGRE Working Group 14.02, The CIGRE HVDC Benchmark Model- A New Proposal with Revised Parameters[J], Electra, 1994, (157): 61-64