计及励磁饱和环节的电力系统小扰动稳定性分析与控制
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摘要
励磁系统作为电力系统的重要组成部分,其饱和环节的存在不仅会影响系统的暂态稳定性,而且还可能产生增幅低频振荡,进而影响系统的静态稳定性。在稳定研究中,“域”方法能够提供传统的时域仿真法和频域法所无法获得的信息,已逐渐被人们所认识和接受。本文将从吸引域的角度,对含励磁系统饱和环节的电力系统稳定问题进行深入研究。
研究了计及励磁饱和环节线性化单机系统的全局稳定性问题。针对AVR、AVR+PSS和线性最优励磁控制(LOEC)这3种典型励磁控制策略,建立了计及励磁系统饱和环节的系统数学模型,运用触发映射和二次曲面Lyapunov函数,对饱和系统的全局稳定性进行了判定。指出即使系统的特征根实部均为负,当计及励磁系统饱和环节后,系统也不能完全满足全局稳定条件,可能出现非全局稳定的情况。因此,研究饱和系统的局部稳定问题更加现实、可行。此外,还对饱和发生的时间(切换时间)进行了估计,并在LOEC控制系统中研究了阻尼系数对切换时间的影响,指出阻尼系数的减小会增加励磁系统保持励磁顶值的时间。
对计及励磁饱和环节系统的吸引域进行了估计。对LOEC控制下的系统,将吸引域估计问题转化为凸优化问题,通过求解线性矩阵不等式计算饱和系统的椭球吸引域；对采用不同LOEC控制律的系统椭球吸引域进行了比较,提出用椭球吸引域的体积指标选取LOEC权矩阵和控制律的新方法；通过分析椭球吸引域体积与励磁顶值大小之间的关系,揭示出单机系统中椭球吸引域体积与励磁顶值的三次方成正比,两者呈非线性变化规律；在多机系统中,应用奇异值分解方法,提出了高维椭球吸引域的三维投影方法,解决了高维椭球吸引域的直观显示问题。
提出了利用椭球吸引域确定小扰动稳定域(SSSR)边界的新方法。分析表明,当椭球吸引域很小时,该方法与利用Hopf分岔获得的SSSR差别不大；而当椭球吸引域较大时,该方法要比利用Hopf分岔获得的SSSR小,该方法可以将SSSR大小与扰动大小建立联系,从而扩展了SSSR的研究范畴。此外,还分析了权矩阵、阻尼系数、吸引域指标和负荷模型等因素对SSSR的影响,得出了一些重要结论。
最后,基于域的方法,设计了多目标饱和励磁控制器。设计中考虑了吸引域与初始状态域的关系,将饱和控制器的双线性矩阵不等式转化为松弛的线性矩阵不等式问题,使得在吸引域内确保系统的二次稳定性,仿真验证了控制器的有效性。
Generator excitation system plays a fundamental role in power system. Saturation element of excitation system not only affects on transient stability but also leads to the low-frequency oscillations which result in static instability problems possibly. In studies of system stability, the so-called "region" approach has been proposed and is gradually being accepted by many scholars because the "region" can provide some important information which can't be got by using time-domain simulation approach and frequency-domain approach. This dissertation thoroughly studies on the stability problem with saturation element of excitation system from the point of view of the region of attraction.
The global stability problem of single-machine infinite-bus is studied in this dissertation by using linearized model. The mathematic models are established with saturation element of excitation system under three typical control strategies:automatic voltage regulator (AVR), automatic voltage regulator plus power system stabilizer (AVR+PSS) and linear optimal excitation control (LOEC). Based on impact maps and quadratic surface Lyapunov functions, the global stability of three linearized systems under different damping factors and line impedance values is recognized. The conclusion shows that conditions of global stability can't be satisfied entirely for the linear system after considering saturation element even if the real components of all eigenvalues are negative. So, it is realistic and feasible to study on the local stability of saturation system. Furthermore, the switching time is estimated in the dissertation. After studying on the effect of damping factor on the switching time of saturation system, it is concluded that smaller damping factor is, longer switching time is.
The region of attraction (RA) of power system is estimated with saturation element of excitation system. The linear matrix inequalities (LMIs) are applied to estimate RA of the system with saturation element of excitation system under linear optimal excitation control after transforming the problem of estimating RA of the system under saturated linear feedback control law into LMIs formulations. The developed method is applied to choice the preferable weighting matrix using the volume of n full-dimensional ellipsoids as the criteria, and the expectable result is shown in the simulation test. Based on the nonlinear relation between the excitation limit and the volume of ellipsoidal RA, it is recognized that the volume of ellipsoidal RA is proportional to the cube of the excitation limit. To visualize the high dimension ellipsoidal RA approximately, a novel projection approach based on singular value decomposition for high dimension ellipsoidal RA is proposed in multi-machine case.
Based on RA of saturation system, a novel algorithm is proposed to calculate the boundary of the small signal stability region (SSSR), and used to study on effect of saturation element on SSSR. The case demonstrates that the gained SSSR based on the proposed algorithm is equal approximately to the one using Hopf bifurcation when the criteria of RA is very small, and the proposed algorithm gets smaller SSSR when the criteria of RA is enlarged. These results show that SSSR may consider of the disturbance, which enlarges the facet of studies on SSSR. Moreover, this dissertation analyzes effect of weighting matrix, damping factor, criteria of RA and load model on SSSR, and derives some important conclusions.
Finally, the multi-objective saturation excitation controller for nonlinear system is designed in this dissertation. In order to guarantee the quadratic stability in the given RA, the relation between RA and initial state region is considered of in the procedure of designing the saturation controller. Numerical simulations are provided to validate the effectiveness of the proposed controller.
研究了计及励磁饱和环节线性化单机系统的全局稳定性问题。针对AVR、AVR+PSS和线性最优励磁控制(LOEC)这3种典型励磁控制策略,建立了计及励磁系统饱和环节的系统数学模型,运用触发映射和二次曲面Lyapunov函数,对饱和系统的全局稳定性进行了判定。指出即使系统的特征根实部均为负,当计及励磁系统饱和环节后,系统也不能完全满足全局稳定条件,可能出现非全局稳定的情况。因此,研究饱和系统的局部稳定问题更加现实、可行。此外,还对饱和发生的时间(切换时间)进行了估计,并在LOEC控制系统中研究了阻尼系数对切换时间的影响,指出阻尼系数的减小会增加励磁系统保持励磁顶值的时间。
对计及励磁饱和环节系统的吸引域进行了估计。对LOEC控制下的系统,将吸引域估计问题转化为凸优化问题,通过求解线性矩阵不等式计算饱和系统的椭球吸引域；对采用不同LOEC控制律的系统椭球吸引域进行了比较,提出用椭球吸引域的体积指标选取LOEC权矩阵和控制律的新方法；通过分析椭球吸引域体积与励磁顶值大小之间的关系,揭示出单机系统中椭球吸引域体积与励磁顶值的三次方成正比,两者呈非线性变化规律；在多机系统中,应用奇异值分解方法,提出了高维椭球吸引域的三维投影方法,解决了高维椭球吸引域的直观显示问题。
提出了利用椭球吸引域确定小扰动稳定域(SSSR)边界的新方法。分析表明,当椭球吸引域很小时,该方法与利用Hopf分岔获得的SSSR差别不大；而当椭球吸引域较大时,该方法要比利用Hopf分岔获得的SSSR小,该方法可以将SSSR大小与扰动大小建立联系,从而扩展了SSSR的研究范畴。此外,还分析了权矩阵、阻尼系数、吸引域指标和负荷模型等因素对SSSR的影响,得出了一些重要结论。
最后,基于域的方法,设计了多目标饱和励磁控制器。设计中考虑了吸引域与初始状态域的关系,将饱和控制器的双线性矩阵不等式转化为松弛的线性矩阵不等式问题,使得在吸引域内确保系统的二次稳定性,仿真验证了控制器的有效性。
Generator excitation system plays a fundamental role in power system. Saturation element of excitation system not only affects on transient stability but also leads to the low-frequency oscillations which result in static instability problems possibly. In studies of system stability, the so-called "region" approach has been proposed and is gradually being accepted by many scholars because the "region" can provide some important information which can't be got by using time-domain simulation approach and frequency-domain approach. This dissertation thoroughly studies on the stability problem with saturation element of excitation system from the point of view of the region of attraction.
The global stability problem of single-machine infinite-bus is studied in this dissertation by using linearized model. The mathematic models are established with saturation element of excitation system under three typical control strategies:automatic voltage regulator (AVR), automatic voltage regulator plus power system stabilizer (AVR+PSS) and linear optimal excitation control (LOEC). Based on impact maps and quadratic surface Lyapunov functions, the global stability of three linearized systems under different damping factors and line impedance values is recognized. The conclusion shows that conditions of global stability can't be satisfied entirely for the linear system after considering saturation element even if the real components of all eigenvalues are negative. So, it is realistic and feasible to study on the local stability of saturation system. Furthermore, the switching time is estimated in the dissertation. After studying on the effect of damping factor on the switching time of saturation system, it is concluded that smaller damping factor is, longer switching time is.
The region of attraction (RA) of power system is estimated with saturation element of excitation system. The linear matrix inequalities (LMIs) are applied to estimate RA of the system with saturation element of excitation system under linear optimal excitation control after transforming the problem of estimating RA of the system under saturated linear feedback control law into LMIs formulations. The developed method is applied to choice the preferable weighting matrix using the volume of n full-dimensional ellipsoids as the criteria, and the expectable result is shown in the simulation test. Based on the nonlinear relation between the excitation limit and the volume of ellipsoidal RA, it is recognized that the volume of ellipsoidal RA is proportional to the cube of the excitation limit. To visualize the high dimension ellipsoidal RA approximately, a novel projection approach based on singular value decomposition for high dimension ellipsoidal RA is proposed in multi-machine case.
Based on RA of saturation system, a novel algorithm is proposed to calculate the boundary of the small signal stability region (SSSR), and used to study on effect of saturation element on SSSR. The case demonstrates that the gained SSSR based on the proposed algorithm is equal approximately to the one using Hopf bifurcation when the criteria of RA is very small, and the proposed algorithm gets smaller SSSR when the criteria of RA is enlarged. These results show that SSSR may consider of the disturbance, which enlarges the facet of studies on SSSR. Moreover, this dissertation analyzes effect of weighting matrix, damping factor, criteria of RA and load model on SSSR, and derives some important conclusions.
Finally, the multi-objective saturation excitation controller for nonlinear system is designed in this dissertation. In order to guarantee the quadratic stability in the given RA, the relation between RA and initial state region is considered of in the procedure of designing the saturation controller. Numerical simulations are provided to validate the effectiveness of the proposed controller.
引文
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