计及励磁饱和环节的电力系统动态行为分析与域估计研究

Due to that the modern power systems are operated and controlled close to their capability limits, the risks that they would undergo unstable accidents are increasing unprecedentedly. The saturation element starts to function when the excitation voltage reaches the upper threshold, which consequently causes excitation voltage to become a constant and makes the synchronous generator excitation lose its capability in voltage adjustment. It has already been clearly demonstrated in both literatures and the applicant's previous studies that the lost capability of synchronous generators to regulate voltage has significant adverse impacts on load flow calculation, voltage stability and security operation. The aim of the proposed project is to study the mechanism of how saturation elements effect power systems' dynamic behaviors near their operation limits and therefore to fundamentally improve both the theories and methodologies used for estimating region of attraction and security region accordingly. To be more specific, the proposed research consists of the following closely linked workpackages: i) it will fully consider the dynamic characteristics of all types of excitation systems to build nonlinear mathematic models for power systems with excitation saturation elements; ii) it will investigate the mechanisms behind the phenomena that over excitation limiters affect power systems' dynamic behaviors on different time scales by analyzing the dynamics of state track at switching surfaces; iii) it will design a region of attraction estimation method for nonlinear system stability analysis based on convex optimization theory; iv) the dynamic behavior and the region of attraction for a power system with excitation saturation elements in the contingency sets will be extensively analyzed; and v) the research will also pay special attention to study the dynamic voltage security regions of power systems. This proposed research helps to reveal the internal relations and interactions between external disturbances, regions of attraction and security regions. It will produce important novel theory and methodologies for studying the stability of power systems and contribute to the development and application of nonlinear system theory.

现代电力系统已越来越接近运行和控制极限，发生不稳定事故的风险显著增加。大量文献与前期研究证实，饱和环节产生作用后，励磁电压为常数，将使发电机失去电压调节能力，影响电力系统潮流计算、电压稳定和系统安全运行，然而，其对电力系统动态的具体作用机理目前尚未清楚。因此，本项目旨在从域的角度研究励磁饱和环节对电力系统动态行为的作用机制，完善吸引域和安全域估计的理论体系。项目拟采用非线性理论与方法，在极限运行状态下，充分考虑各类励磁系统的动态特征，构建含饱和环节的系统数学模型，分析状态轨迹在切换面上的动态过程，深入研究过励限制器对系统动态行为的作用机理，从而提出饱和非线性系统吸引域估计的优化算法，以及电压稳定安全域的计算方法，进一步提高域估计的准确性。项目研究成果，将有助于认识扰动、吸引域、安全域三者间的内在规律，为电力系统稳定性研究提供重要理论与方法，同时也为非线性系统理论的发展和应用作出一定贡献。

以超高压、长距离和大容量区域间功率交换为特征的现代电力系统，其稳定性一旦破坏，将会给国民经济造成巨大损失，因此电力系统的稳定问题一直是电力系统研究的热点。同步发电机励磁系统作为电力系统的重要组成部分，其动态特性对系统的稳定性具有重要影响。受到物理结构的限制，其励磁电压只能在一个安全的范围内变化，这使得励磁系统模型中含有输入饱和环节，其具有非线性特征。已有研究表明：励磁系统饱和环节的存在与混沌现象及电压崩溃的发生有密切关系。以往在利用线性化模型对稳定问题的研究中，人们往往忽略这种关键的非线性环节。由于输入饱和环节是客观存在的，任意忽略它的存在将可能使得分析结论偏于乐观。因此，研究励磁系统饱和环节对稳定性的影响对电力系统具有重要的理论和现实意义。本项目对计及励磁饱和环节的电力系统稳定问题进行了深入研究，主要研究内容包括：（1）建立含励磁饱和环节的有理非线性系统的数学模型；（2）计及励磁饱和环节的电力系统吸引域计算；（3）考虑饱和环节影响的电力系统小扰动稳定域；（4）构建基于吸引域和安全域的理论与方法。项目提出了以椭球吸引域体积为指标确定小扰动稳定域边界点的新算法，计算了定义在注入空间的小扰动稳定域。研究表明：当可镇定的扰动较小时，即椭球吸引域体积指标较小时，获得的小扰动稳定域与采用Hopf分岔获得的小扰动稳定域基本相同；当可镇定的扰动较大时，即椭球吸引域体积指标较大时，小扰动稳定域减小；考虑风机爬坡率后，系统出现Fold分岔，失稳点距离临界稳定点更远。由于该方法可以将小扰动稳定域大小与可镇定的扰动大小建立联系，因此扩展了吸引域和小扰动稳定域的研究范畴。