Stability of Large Scale Systems With Order Model Reduction

ECS-9803055模型降阶大系统的PAI稳定性在新的电力系统结构中具有重要意义。将需要更快、更可靠的工具来计算动态可用传输能力(DATC)。这项提案涉及将影响这一领域的三个方面。首先，对于仅基于故障后系统的动态安全评估(DSA)，轨迹灵敏度已经得到了可靠的结果，现在将扩展到包括故障动态和故障后动态。这将意味着建立在代数部分具有间断的微分代数方程组的动态灵敏度函数。这将使得能够直接计算对关键清除时间以及对负载、分接设置等变化的敏感度。第二个目标是找到更好和健壮的预条件，用于通过迭代方法求解类型为Ax=b的大型稀疏系统。然后，这将被用作使用同时隐式方法的快速动态模拟算法的一部分。最后，将采用两种新的模型简化方法。首先，我们将使用非线性动态响应的轨迹灵敏度来识别相干发电机。到目前为止，只有工作点附近的线性化模型被用于一致性分组或一些其他启发式标准。其次，我们将使用Krylov投影仪技术来开发降阶动力学模型。这是最近开发的用于DAE系统的数值线性代数工具。

ECS-9803055 Pai Stability of large scale systems with model reduction is going to be important in the emerging new structure of power systems. Faster and reliable tools for computing dynamic available transfer capabilities (DATC) will be needed. This proposal addresses three aspects which will impact this area. Firstly, trajectory sensitivities which have yielded reliable results for dynamic security assessment (DSA) based on post-fault systems only, will now be extended to cover both faulted and post-fault dynamics. This will imply formulating dynamic sensitivity functions for systems of differential algebraic equations with discontinuities in the algebraic portion. This will enable the direct computation of sensitivities to critical clearing time as well to changes in load, tap settings, etc. A second objective is to find better and robust preconditioners for solving large sparse systems of the type Ax = b by iterative methods. This will then be used as part of the fast dynamic simulation algorithm using the simultaneous implicit method. Finally two new approaches to model reduction will be taken. First, we will use trajectory sensitivities of the nonlinear dynamic response to identify coherent generators. To date only linearized models around an operating point have been used for coherency grouping or some other heuristic criteria. Secondly, we will use the Krylov projector technique to develop reduced order dynamic models. This is a recently developed tool in numerical linear algebra for DAE systems.