矩阵变换器—永磁同步电机调速系统稳定性研究
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摘要
矩阵变换器无需大的储能元件即可实现交-交直接功率变换,具有对电网谐波污染小、能量双向流动、结构紧凑、功率密度高等特点,是一类极具发展潜力的功率变换器。矩阵变换器在输出功率超过一定限值时运行会变得不稳定,输入侧电压、电流出现高频振荡,导致向电网注入谐波并危害功率器件,因此开展对矩阵变换器稳定性问题的研究具有实际意义。
本文结合非线性动力学理论研究了矩阵变换器的稳定性问题。针对矩阵变换器-阻感负载系统在不稳定运行时的高频振荡现象,从非线性动力学角度研究了其本质原因,分析了系统在功率限值附近的特性。建立了矩阵变换器-阻感负载系统在dq旋转坐标系下的基波模型,对其在平衡点处做线性化处理,并通过数值方法获得近似线性化矩阵的特征值变化轨迹。根据特征值轨迹的变化规律验证了Hopf分岔定理的条件,据此判定矩阵变换器不稳定振荡的本质是非线性系统在临界点处的Hopf分岔现象。对系统在功率限值附近的特性做了仿真和实验研究,结果验证了矩阵变换器基波模型在低频范围内的有效性。
针对矩阵变换器-阻感负载系统数学模型体现出的强非线性,研究了其混沌动力学特性。建立了系统的无量纲数学模型,比较模型相轨线和典型混沌系统相轨线之间的异同,指出无量纲系统具有混沌系统的典型特征——轨线对初值的极端敏感性及自相似性。对仿真结果做频谱分析并计算非线性系统的Lyapunov指数,分别从定性和定量角度证明:系统基波模型在输出功率大于稳定功率限值时具有混沌特性。对矩阵变换器不稳定振荡时的非线性特性做了实验分析,根据实验数据获得电压、电流变量的相轨迹并做频谱分析,结果在一定程度上与仿真结果相近,说明矩阵变换器在不稳定振荡时可能存在混沌特性。
将稳定性问题研究扩展至矩阵变换器-永磁同步电机系统,分析了其稳定运行边界随系统参数的变化规律。用“占空比矢量法”描述矩阵变换器的输入输出关系,建立了包括电源、变换器、永磁同步电机和矢量控制器在内的系统微分方程模型,推导了系统在平衡点附近的小信号模型。根据Lyapunov稳定判据,通过数值方法得到系统的稳定运行边界。分析了稳定边界的功率特性及系统参数对稳定运行区域的影响。理论分析及数值计算表明,矩阵变换器输出功率限值与电机稳态工作点的选取有关;参数对系统稳定性的影响表现出一定的规律性。仿真结果验证了文中的建模和分析正确、有效,相关结论和实验研究对矩阵变换器-永磁同步电机系统参数设计和性能分析具有指导意义。
Matrix Converter has received a lot of attention from researchers due to some advantages over traditional rectifer-inverter type power converters, such as small reactive components, reduced harmonic injection to the power grid, reversible energy transforming, compact structure and high power density. As a result, the promising prospect on development of matrix converter has been widely noticed. An unstable oscillation emerges when output power of matrix converter exceeds some upper limit. The oscillation increases harmonics and results a breaking hazard to the power devices of matrix converter, which makes research on the stability issues of matrix converter very important to its practical application.
The stability issues on matrix converter are studied by considering its nonlinear dynamic characteristics. The essential cause of the unstable oscillation is analyzed for an electrical drive fed by three phase to three phase matrix converter in a view of nonlinear dynamic theory, and behavior of the system close to the upper limit of output power is investigated. A fundamental-harmonic model is derived in rotating dq coordinate system. The model is linearized at the equilibrium point, and the characteristic root loci are acquired by solving the Jacobian matrix numerically. The Hopf bifurcation nature of unstable oscillation of matrix converter is concluded by checking Poincaré-Andronov-Hopf theorem, with output power as its bifurcation parameter. Behavior of the system near the critical power is examined by simulation and experiment. Simulation results coincide with experimental results very well in the low frequency region, which proves the validity of the fundamental-harmonic model.
Chaotic dynamic characteristics of the fundamental-harmonic model of matrix converter are studied. Dimensionless equations of the system are derived and analyzed by simulation. The trajectories from simulation show some typical chaotic characteristics such as the extreme sensitivity to initial values and self-similarity. Fast Fourier transform (FFT) of the simulation results is done to analyze its characteristic in frequency domain, and the Lyapunov Exponents of the system are calculated. The analysis and calculation results verify chaotic behavior of the studied matrix converter drive system qualitatively and quantitatively respectively. Experimental research is also developed. The trajectories drawn by using experimental data express similar behavior with simulation results. It expresses a possible, but not definite, chaos in the electrical drive system fed by matrix converter.
An extended stability research on permanent magnet synchronous motor(PMSM) drive system fed by matrix converter(MC-PMSM) is launched, and the stable operation region variation against system parameters are analyzed. The input-output relationship of matrix converter is expressed simply using the“duty-cycle space-vector”. The differential equations of the system, including both power stage and control stage, are derived with the variables in rotating coordinates, and a small-signal equation is obtained. Then stable region and its boundary can be determined according to a Lyapunov-type stability analysis. Power characteristics of the stable boundary is presented and analyzed, and the influence of the parameters of input and digital filters on stable region is discussed. Numerical calculation results show that the output power limit of matrix converter varies with operating points of the PMSM, and is not constant. In addition, the influence of the parameters on stability appears to follow some rules. The modeling and analyzing is verified by computer simulations. Experimental research is carried out to give qualitative verification. The research of this paper can be used as a guide for stability design and parameters selection for MC-PMSM systems.
本文结合非线性动力学理论研究了矩阵变换器的稳定性问题。针对矩阵变换器-阻感负载系统在不稳定运行时的高频振荡现象,从非线性动力学角度研究了其本质原因,分析了系统在功率限值附近的特性。建立了矩阵变换器-阻感负载系统在dq旋转坐标系下的基波模型,对其在平衡点处做线性化处理,并通过数值方法获得近似线性化矩阵的特征值变化轨迹。根据特征值轨迹的变化规律验证了Hopf分岔定理的条件,据此判定矩阵变换器不稳定振荡的本质是非线性系统在临界点处的Hopf分岔现象。对系统在功率限值附近的特性做了仿真和实验研究,结果验证了矩阵变换器基波模型在低频范围内的有效性。
针对矩阵变换器-阻感负载系统数学模型体现出的强非线性,研究了其混沌动力学特性。建立了系统的无量纲数学模型,比较模型相轨线和典型混沌系统相轨线之间的异同,指出无量纲系统具有混沌系统的典型特征——轨线对初值的极端敏感性及自相似性。对仿真结果做频谱分析并计算非线性系统的Lyapunov指数,分别从定性和定量角度证明:系统基波模型在输出功率大于稳定功率限值时具有混沌特性。对矩阵变换器不稳定振荡时的非线性特性做了实验分析,根据实验数据获得电压、电流变量的相轨迹并做频谱分析,结果在一定程度上与仿真结果相近,说明矩阵变换器在不稳定振荡时可能存在混沌特性。
将稳定性问题研究扩展至矩阵变换器-永磁同步电机系统,分析了其稳定运行边界随系统参数的变化规律。用“占空比矢量法”描述矩阵变换器的输入输出关系,建立了包括电源、变换器、永磁同步电机和矢量控制器在内的系统微分方程模型,推导了系统在平衡点附近的小信号模型。根据Lyapunov稳定判据,通过数值方法得到系统的稳定运行边界。分析了稳定边界的功率特性及系统参数对稳定运行区域的影响。理论分析及数值计算表明,矩阵变换器输出功率限值与电机稳态工作点的选取有关;参数对系统稳定性的影响表现出一定的规律性。仿真结果验证了文中的建模和分析正确、有效,相关结论和实验研究对矩阵变换器-永磁同步电机系统参数设计和性能分析具有指导意义。
Matrix Converter has received a lot of attention from researchers due to some advantages over traditional rectifer-inverter type power converters, such as small reactive components, reduced harmonic injection to the power grid, reversible energy transforming, compact structure and high power density. As a result, the promising prospect on development of matrix converter has been widely noticed. An unstable oscillation emerges when output power of matrix converter exceeds some upper limit. The oscillation increases harmonics and results a breaking hazard to the power devices of matrix converter, which makes research on the stability issues of matrix converter very important to its practical application.
The stability issues on matrix converter are studied by considering its nonlinear dynamic characteristics. The essential cause of the unstable oscillation is analyzed for an electrical drive fed by three phase to three phase matrix converter in a view of nonlinear dynamic theory, and behavior of the system close to the upper limit of output power is investigated. A fundamental-harmonic model is derived in rotating dq coordinate system. The model is linearized at the equilibrium point, and the characteristic root loci are acquired by solving the Jacobian matrix numerically. The Hopf bifurcation nature of unstable oscillation of matrix converter is concluded by checking Poincaré-Andronov-Hopf theorem, with output power as its bifurcation parameter. Behavior of the system near the critical power is examined by simulation and experiment. Simulation results coincide with experimental results very well in the low frequency region, which proves the validity of the fundamental-harmonic model.
Chaotic dynamic characteristics of the fundamental-harmonic model of matrix converter are studied. Dimensionless equations of the system are derived and analyzed by simulation. The trajectories from simulation show some typical chaotic characteristics such as the extreme sensitivity to initial values and self-similarity. Fast Fourier transform (FFT) of the simulation results is done to analyze its characteristic in frequency domain, and the Lyapunov Exponents of the system are calculated. The analysis and calculation results verify chaotic behavior of the studied matrix converter drive system qualitatively and quantitatively respectively. Experimental research is also developed. The trajectories drawn by using experimental data express similar behavior with simulation results. It expresses a possible, but not definite, chaos in the electrical drive system fed by matrix converter.
An extended stability research on permanent magnet synchronous motor(PMSM) drive system fed by matrix converter(MC-PMSM) is launched, and the stable operation region variation against system parameters are analyzed. The input-output relationship of matrix converter is expressed simply using the“duty-cycle space-vector”. The differential equations of the system, including both power stage and control stage, are derived with the variables in rotating coordinates, and a small-signal equation is obtained. Then stable region and its boundary can be determined according to a Lyapunov-type stability analysis. Power characteristics of the stable boundary is presented and analyzed, and the influence of the parameters of input and digital filters on stable region is discussed. Numerical calculation results show that the output power limit of matrix converter varies with operating points of the PMSM, and is not constant. In addition, the influence of the parameters on stability appears to follow some rules. The modeling and analyzing is verified by computer simulations. Experimental research is carried out to give qualitative verification. The research of this paper can be used as a guide for stability design and parameters selection for MC-PMSM systems.
引文
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