【作者】 辛焕海；

【导师】 邱家驹； 甘德强；

【作者基本信息】 浙江大学 ， 电力系统及其自动化， 2007， 博士

【摘要】 以超高压、长距离输电、大容量机组、大范围互联和大容量的区域间交换为显著特征的现代电力系统，其稳定性一旦遭受破坏，必将造成巨大的经济损失和灾难性的后果，致使电力系统安全稳定问题一直是研究的热点，其中功角稳定分析作为电力系统安全稳定分析中最基本的问题尤为引人注目。虽然国内外对此作了大量的研究，有些方法在实际中已经得到了应用，但仍然有一些重要的问题没有得到很好的解决，如考虑不确定参数时的暂态稳定问题、考虑控制器饱和非线性时的小干扰稳定问题等。本文针对这几个问题，从稳定域的角度对电力系统的功角稳定进行深入地研究，扩展和补充了一些非线性系统的理论和分析方法。在电力系统暂态稳定方面，论文研究了自治系统稳定域的估计方法、参数可行域的拓扑性质、参数不确定性对暂态稳定的影响、基于暂态稳定约束的优化最优解的存在性问题以及暂态稳定约束的等价变换问题。在此方面，论文具体的研究成果为，1．基于泰勒展开式和拉萨尔不变性原理，针对普通的自治系统提出了一组稳定域的估计方法，并将此方法应用于电力系统暂态稳定分析。不同于传统的基于能量函数法的估计方法，此方法具有假设条件少，避免计算不稳定平衡点、稳定域可以用简明的数学公式表示，无需复杂的计算等优点。2．提出了基于微分代数方程的参数可行域的概念，得到了参数可行域的一些拓扑性质和结论。在此基础上，讨论了一类含暂态稳定约束的优化问题并得到一些理论上的结论，如最优解的存在性，利用经验判据代替暂态稳定约束的充分条件等，为深入分析和快速计算含暂态稳定约束的优化问题提供了一些理论基础。3．提出了一种分析参数不确定性对暂态稳定影响的解析方法。该方法基于“一致最终有界”思想，通过比较某一运行方式下的计算指标与极限指标，为断言该系统的参数偏差不会引起暂态稳定性变化提供了充分条件。方法本质是解析的，虽然结果保守，但方法严格可靠，而且计算量小。在电力系统小干扰稳定方面，论文研究了饱和线性系统稳定域的估计方法，以及奇异的饱和线性系统稳定域估计的降阶方法，并将这些方法应用于电力系统。以饱和PSS控制系统为例，论文分析了控制器的饱和非线性环节对电力系统小干扰稳定的影响。在此方面，论文具体的研究成果为，1．在忽略外界干扰的情况下，讨论了饱和线性系统稳定域的估计方法，并利用单目标LMI凸优化减少稳定域估计的保守性。论文证明了此优化问题的最优解位于可行域的边界、最优解与饱和约束的上界成线性关系等结论，这些结论为求解此LMI优化问题和奇异系统的降阶方法提供了理论基础。论文将此方法应用于电力系统，以饱和PSS控制系统为例，提出一种定量分析电力系统饱和控制器控制性能的解析方法。2．当外界扰动和饱和非线性并存时，论文通过构建一个多目标的LMI优化问题估计系统的实用稳定域和最大可承受扰动量，并利用交叉迭代算法求解此优化问题的Pareto最优解，从理论上证明了此迭代算法的收敛性。在此基础上，论文也以饱和PSS系统为例，基于Pareto最优解，定量地分析了饱和控制器的控制性能，并利用电力系统算例验证了分析方法的有效性。3．由于在含饱和PSS控制器的电力系统中，变量的振荡模式差别很大，出现奇异性的问题。论文基于奇异摄动理论，提出一种奇异饱和系统稳定域估计的降阶方法。该方法利用低维系统来估计高维饱和系统的稳定域，不仅可以克服原来系统的奇异性，还减少了稳定域估计的计算量。此外，论文从理论上证明了此降阶方法的严格性，数值仿真也验证法了方法的有效性。更多还原

【Abstract】 The insecurity and instability problems will certainly cause enormous losses and catastrophic results for modern power systems featured with extra high voltage and long-distance transmission lines, large capacity generators, cross-regional inter-connections and huge inter-area power exchanges. Therefore, studies on the power system security and stability have been paid much attention for a long time. Since the angle stability of power systems is the basic problem in the analysis of the power system security and stability, studies on angle stability have become more and more essential and important. Although much research work on angle stability has been done, there are still many important issues to be solved, such as the impact of parameter uncertainties on the transient stability, and the impact of the saturation nonlinearities on the small-signal stability. This dissertation focuses these problems concerning the angle stability, and some theoretical contributions to nonlinear systems are provided.In the first part of this dissertation, some research work is done, including the stability region estimation of a large class of general autonomous systems, the topological properties of the parameter feasible regions, the impact of parameter uncertainties on the transient stability, the existence of an optimal solution and the equivalent condition about the transient stability constraint. Details are as follows,1. Based on the Taylor Series Expansion and the LaSalle Invariance Principle, a class of methods for estimating the stability region of nonlinear autonomous systems is suggested, and they are used to analyze the transient stability of a power system. Compared to other methods based on the energy function, the methods provided in this dissertation need fewer assumptions and can avoid calculating the unstable equilibrium points. The estimated stability region can be expressed analytically, and the complex calculation is avoided as well.2. The concept of the parameter feasible regions is provided based on the differential-Algeria equations, and some topological properties about the region are obtained as well. Further more, a class of optimization problems consisting of the constraint of transient stability are analyzed with emphasis on the feasible region. Some theoretical conclusions are derived, i.e., the optimal solution may not exist; under certain conditions, the constraints of transient stability can be replaced by an engineering criterion. These results are useful for analyzing and solving the optimized problem.3. An analytical method is suggested to deal with the impact of parameter uncertainties on the transient stability. This method is based on the idea of"Uniformly Ultimately Bound", and a sufficient condition that judges whether the stability characteristics will be changed or not is derived by comparing the limit index and the calculated index in some operating point. The methods suggested are analytically sound, thus the advantage lies in the few calculation and reliability, although they are conservative to some extent.In the second part of this dissertation, some research work is done, including a method for estimating the stability region of a linear system with saturation nonlinearities, a reduced-order method for estimating the stability region of singular linear system with saturation nonlinearities. Further more, these methods are applied to analyze the impact of saturation nonlinearities on power system small-signal stability with the saturated PSS controller. Details are as follows,1. When the disturbance rejection is not considered, a method is suggested to estimate the stability region of linear system with saturation nonlinearities. To reduce the conservativeness in the estimation, a simple convex optimization with linear matrix inequality(LMI) constraints is presented, and it is proved that the optimal solution lies on the boundary of the feasible region, and the optimal solution is in proportion to the upper-bound of the saturation function. Furthermore, an analytical method is suggested to evaluate the performance of saturated PSS controller.2. When both the disturbance rejection and saturation nonlinearities are considered, a multi-objective optimization model is presented to estimate the practical stability region and maximum tolerable disturbance rejection. This optimization problem is solved by an iterative method, which converges to the Pareto Optimal Solution(POS) of the optimization problem in theory. Moreover, as an application of this approach to power systems, an analytical method, based on the POS, to analyze the performance of a controller with saturation nonlinearities and disturbance rejection is introduced to deal with the saturated PSS. Numerical results of a test power system are described, indicating the reliability and simplicity of the approach.3. In the PSS control system mentioned above, there is large difference in the decay speeds of the transient, so the dynamical system is fundamentally singular. To overcome the singularity, a reduced-order method is suggested to estimate the stability region of the singular system with saturation nonlinearities based on the singular perturbation theory. In the reduced-order method, a low system model is constructed to estimate the stability region of the primary high order system, so that the singularity is eliminated, and the estimation process is simplified. In addition, the analytical foundation of the reduction method is proved in theory, and it is validated by some numerical examples.更多还原