直流变换器与逆变器级联系统的非线性特性及其控制研究
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摘要
随着分布式供电、新能源发电和电动汽车系统等的不断发展,级联成为电力电子变换器越来越常见的连接方式,级联系统所特有的非线性特性、动态和稳定性问题也随之成为研究的热点。电力电子变换器一般都是闭环调节控制,当作为负载变换器时在输入端便会表现出恒功率负载特性。如果没有合理的控制方案,恒功率负载的时变负阻抗特性将可能引起前级变换器的输出不稳定甚至振荡问题。
电力电子变换器是典型的开关非线性系统,基于传统控制理论的线性化控制方案从本质上讲不是最佳的控制方案,且在平衡点进行线性化处理的系统小信号模型也无法解决大信号扰动带来的一系列问题。故基于非线性控制理论的非线性控制方法成为近年来的研究热点。本文将非线性控制理论应用到级联系统前级直流变换器的建模与控制中,得到非线性控制策略,提高了系统的控制性能。
以Boost变换器与逆变器组成的级联系统为例,首先分析了后级逆变器作为负载对前级Boost变换器的影响：闭环控制的逆变器平均功率恒定,具有时变负阻抗特性,严重影响了Boost变换器的闭环控制的稳定性和输出动态特性。
其次,选取新的状态变量,利用状态空间平均法对级联系统进行建模,得到系统的仿射非线性模型。理论证明该模型符合精确线性化的两个条件,级联系统经过状态反馈精确线性化变换为一个线性可控系统。
最后分别利用经典控制理论中典型二阶系统的特性和最优控制理论的线性二次型最优控制的方法求得被转换后的线性可控系统的最优控制解,从而得到最终的非线性控制策略。两种控制策略均用Matlab仿真工具进行验证。仿真结果表明,两种方法确定的非线性控制策略均可使系统达到理想的目标。故状态反馈精确线性化技术可以实现对Boost变换器带逆变器负载的控制,在电源及负载大范围变化时,能够保证系统的稳定运行,具有大信号稳定特性。
Distributed power architectures comprised of power electronic converters are becoming increasing common in recent years. Tightly regulated closed-loop converters exhibit instantaneous constant-power-load (CPL) characteristics. Without appropriate controls, the negative impedance characteristics of CPL may lead to significant oscillations in the output voltage of feeder converters and impact power quality and system stability. And because of the nonlinearity of converters, classical linear control methods, which are often used to design controllers, have stability limitations. This paper introduced nonlinear control theory into modeling and control design of interconnecting converters to ensure large-signal stability.
Take a Boost converter operating with an inverter as an example, the nonlinear characteristics, dynamics, and stability problems are analyzed firstly. Tightly-regulated inverters, which have negative impedance characteristics at the input terminals, might seriously impact the dynamics and stability of the Boost converter.
Then, this paper presents an exact linearization technique for DC-DC converters feeding inverters. An affine nonlinear model of a Boost converter operating with an inverter has been set up by introducing control aims into system state equations. Exact state feedback linearization is proved to be easily performed on this model. A nonlinear feedback can be found to cancel the nonlinearity of the interconnecting system.
Finally the classical control theory and the optimal control method are respectively used to deduce the control law of the transformed linear system and nonlinear controllers derived can approximately linearize the system. The controllers are exemplified and validated by a Matlab Simulation model. Simulation results illustrate that the output voltage of the boost converter feeding an inverter has a large-signal stability characteristic. It is conclude that state feedback exact linearization ensures cascaded systems operating steadily.
电力电子变换器是典型的开关非线性系统,基于传统控制理论的线性化控制方案从本质上讲不是最佳的控制方案,且在平衡点进行线性化处理的系统小信号模型也无法解决大信号扰动带来的一系列问题。故基于非线性控制理论的非线性控制方法成为近年来的研究热点。本文将非线性控制理论应用到级联系统前级直流变换器的建模与控制中,得到非线性控制策略,提高了系统的控制性能。
以Boost变换器与逆变器组成的级联系统为例,首先分析了后级逆变器作为负载对前级Boost变换器的影响：闭环控制的逆变器平均功率恒定,具有时变负阻抗特性,严重影响了Boost变换器的闭环控制的稳定性和输出动态特性。
其次,选取新的状态变量,利用状态空间平均法对级联系统进行建模,得到系统的仿射非线性模型。理论证明该模型符合精确线性化的两个条件,级联系统经过状态反馈精确线性化变换为一个线性可控系统。
最后分别利用经典控制理论中典型二阶系统的特性和最优控制理论的线性二次型最优控制的方法求得被转换后的线性可控系统的最优控制解,从而得到最终的非线性控制策略。两种控制策略均用Matlab仿真工具进行验证。仿真结果表明,两种方法确定的非线性控制策略均可使系统达到理想的目标。故状态反馈精确线性化技术可以实现对Boost变换器带逆变器负载的控制,在电源及负载大范围变化时,能够保证系统的稳定运行,具有大信号稳定特性。
Distributed power architectures comprised of power electronic converters are becoming increasing common in recent years. Tightly regulated closed-loop converters exhibit instantaneous constant-power-load (CPL) characteristics. Without appropriate controls, the negative impedance characteristics of CPL may lead to significant oscillations in the output voltage of feeder converters and impact power quality and system stability. And because of the nonlinearity of converters, classical linear control methods, which are often used to design controllers, have stability limitations. This paper introduced nonlinear control theory into modeling and control design of interconnecting converters to ensure large-signal stability.
Take a Boost converter operating with an inverter as an example, the nonlinear characteristics, dynamics, and stability problems are analyzed firstly. Tightly-regulated inverters, which have negative impedance characteristics at the input terminals, might seriously impact the dynamics and stability of the Boost converter.
Then, this paper presents an exact linearization technique for DC-DC converters feeding inverters. An affine nonlinear model of a Boost converter operating with an inverter has been set up by introducing control aims into system state equations. Exact state feedback linearization is proved to be easily performed on this model. A nonlinear feedback can be found to cancel the nonlinearity of the interconnecting system.
Finally the classical control theory and the optimal control method are respectively used to deduce the control law of the transformed linear system and nonlinear controllers derived can approximately linearize the system. The controllers are exemplified and validated by a Matlab Simulation model. Simulation results illustrate that the output voltage of the boost converter feeding an inverter has a large-signal stability characteristic. It is conclude that state feedback exact linearization ensures cascaded systems operating steadily.
引文
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[2]Lee F.C., Peng D.. Power electronics building blocks and system integration[C]. in Proc. IEEE PEMC,2000.
[3]Oliver, J.A., Prieto, R., Laguna, L., Cobos, J.A.. Modeling and simulation requirements for the analysis and design of DC distributed power electronic systems[C], in Proc. IEEE Power Electronics Congress (CIEP):204-209.
[4]Boroyevich, D., Burgos, R., Arnedo, L., Wang F.. Synthesis and integration of future electronic power distribution systems[C]. in Proc. Power Conversion Conference (PCC), Nagoya,2007:K-1 -K-8.
[5]吴涛,软新波.分布式供电系统中源变换器输出阻抗的研究[J].中国电机工程学报,2008,28(3)：66-71.
[6]王润新,刘进军,侯丹.用于实现互联系统仿真的电源模块大信号模型[J].西安交通大学学报,2009,43(6)：76-81.
[7]Feng X., Liu J., Lee F. C.. Impedance specifications for stable DC distributed power system[J]. IEEE Trans. Power Electronics,200,17(2):157-162.
[8]Feng F.. Liu J. Lee F.C.. Impedance specification and Impedance improvement for DC distributed power system[C]. In Proc. IEEE PESC,1999.
[9]Rivetta. C., Williamson, G.A. Global behaviour analysis of a DC-DC boost power converter operating with constant power load[C], In Proc. International Symposium on Circuits and Systems (ISCAS).:V-956-V-959 Vol.5.
[10]Rivetta. C.H., Emadi, A., Williamson, G.A., Jayabalan. R., Fahimi, B., Analysis and control of a buck DC-DC converter operating with constant power load in sea and undersea vehicles[J]. IEEE Trans. Industry Applications,2006,42(2):559-572.
[11]Liutanakul, P., Awan, A., Pierfederici, S., Nahid-Mobarakeh, B., Linear stabilization of a DC bus supplying a constant power load:A general design approach[J], IEEE Trans. Power Electronics,2010 25(2),:475-488.
[12]朱成花.石健将,严仰光.有前级DC/DC变换器与逆变器相互作用分析[J].南京航空航天大学学报,37(5)：574-578.
[13]高军,赵向华,杨旭DC/DC变换器与DC/AC逆变器连接问题的研究[J].电源技术应用,2001,30(4)：400-402.
[14]邓卫华,张波,胡宗波等CCM Buck变换器的状态反馈精确线性化的非线性解耦控制研究[J].中国电机工程学报,2004,24(5)：120-125.
[15]Emadi, A., Khaligh, A., Rivetta, C.H., Williamson, G.A., Constant power loads and negative impedance instability in automotive systems:definition, modeling, stability, and control of power electronic converters and motor drives[J], IEEE Trans. Vehicular Technology,2006,55(4):1112-1125.
[16]Rivetta, C. Williamson, G.A. Large-signal analysis of a DC-DC buck power converter operating with constant power load[C], in Proc. IEEE IECON,2003, vol.1: 732-737.
[17]王建华,张方华,龚春英.带恒功率负载DC/DC变换器启动过程分析[J].中国电机工程学报,2009,24(4)：121-125.
[18]王建华,张方华,龚春英等.带恒功率负载DC/DC变换器阶跃响应过程[J].中国电机工程学报,2008,28(30)：7-11.
[19]朱成花,严仰光BOOST变换器恒功率负载时动态性能分析[J].南京航空航天大学学报,2005,,37(1)：20-24.
[20]Rahimi, M., Emadi, A., Discontinuous conduction mode DC/DC converters feeding constant power loads[J], IEEE Trans. Industrial Electronics,1999, Vo: PP(99):1-8.
[21]Wang J., Howe D., A power shaping stabilizing control strategy for DC power systems with constant power loads[J]. IEEE Trans. Power Electronics,2008,23(6): 2982-2989.
[22]Liu X., Forsyth. A.J., Cross. A.M., Negative input-Resistance compensator for a constant power load [J]. IEEE Trans. Industrial Electronics,2007,54(6):3188-3196.
[23]朱成花,石健将,严仰光.带有前级DC/DC变换器与逆变器相互作用分析[J].南京航空航天大学学报,37(5)：574-578.
[24]高军,赵向华,杨旭DC/DC变换器与DC/AC逆变器连接问题的研究[J].电源技术应用.2001,30(4)：400-402.
[25]Middlebrook R.D., Input filter consideration in design and application of switching regulators[C], in Proc. IEEE IAS,1976:336-382.
[26]朱成花,严仰光.一种改进的阻抗比判据[J].南京航空航天大学学报,2006,38(3)：315-310.
[27]杨相生.影响直流分布式电源系统稳定性的主要因素[J].甘肃科学学报,2003,15(2)：61-65.
[28]Altowti A, Suntio T., Zenger K. Input filter interactions in multi-module parallel switching model power supply[C], in Proc. IEEE Industrial Technology, 2005:851-856.
[29]吴涛,阮新波.分布式供电系统中源变换器输出阻抗的研究[J].中国电机工程学报,2008,28(3)：66-71.
[30]吴涛,阮新波.分布式供电系统中负载变换器输入阻抗分析[J].中国电机工程学报,2008,28(12)：20-25.
[31]姚雨迎,张东来,徐殿国.级联DC/DC变换器输出阻抗的优化设计与稳定性[J].电工技术学报,2009,24(3)：147-152.
[32]Kwasinski, A., Krein, P.T.. Stabilization of constant power loads in DC-DC converters using passivity-based control[C]. in Proc. IEEE Telecommunications Energy Conference(INTELEC),2007:867-874.
[33]Yan-Fei Liu, Sen, P.C. A general unified large signal model for current programmed DC-to-DC converters, [J]. IEEE Trans. Power Electronics,1994,9 (4): 414-424.
[34]Wilson E.; Liu Y.F.; Sen P.C.. A Simple large signal model for isolated DC-DC converters[C]. Electrical and Computer Engineering,2006. CCECE'06. Canadian Conference on,2006:883-886.
[35]Chen Y. F.. Qiu S. S., Long M.. Nonlinear large-signal modeling of PWM DC-DC switching power converters[C]. in Proc. Communications Circuits and Systems,2004, vol.2:1507-1510.
[36]Veerachary. M.. Modeling of cascade buck converters. Proceedings of the International Symposium on Circuits and Systems (ISCAS),2003, vol.3:Ⅲ-347-111-350.
[37]Lee D.C., Lee K. D., Lee G. M.. Voltage control of PWM converters using feedback linearization[C]. in IEEE Proc. Industry Applications Conference (IAS), 1998. vol.2:1491-1496.
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