This manuscript reports the first step towards building a robust and efficient model reduction methodology to capture transient dynamics in a transmission level electric power system. Such dynamics is normally modeled on seconds-to-tens-of-seconds time scales by the so-called swing equations, which are ordinary differential equations defined on a spatially discrete model of the power grid. Following Seymlyen (1974) and Thorpe, Seyler, and Phadke (1999), we suggest to map the swing equations onto a linear, inhomogeneous Partial Differential Equation (PDE) of parabolic type in two space and one time dimensions with time-independent coefficients and properly defined boundary conditions. We illustrate our method on the synchronous transmission grid of continental Europe. We show that, when properly coarse-grained, i.e., with the PDE coefficients and source terms extracted from a spatial convolution procedure of the respective discrete coefficients in the swing equations, the resulting PDE reproduces faithfully and efficiently the original swing dynamics. We finally discuss future extensions of this work, where the presented PDE-based modeling will initialize a physics-informed machine learning approach for real-time modeling, $n-1$ feasibility assessment and transient stability analysis of power systems.
翻译:本手稿报告了建立强大而高效的减少模式方法的第一步,以捕捉传输水平电力系统中的瞬时动态,这种动态通常以所谓的回旋方程式以秒到秒秒的时间尺度建模,这些平方程式是在空间离散的电网模型上定义的普通差异方程式。继Seymlyen(1974年)和Thorpe、Seyler和Phadke(1999年)之后,我们建议将回旋方程式绘制成一个线性、不相容的局部平方程式,在两个空间和一个时空尺度上,以时间独立的系数和适当界定的边界条件建模。我们展示了我们在欧洲大陆同步传输网上采用的方法。我们表明,在适当粗略的分层公式下,即从滚动方程式中各自离散系数的空间变相中提取的PDE系数和源术语,由此产生的PDE将忠实和高效地复制最初的回旋动动态。我们最后讨论了这项工作的未来扩展情况,在这个模型上提出了基于PDE的以美元为根据的动力的模型的模型,将进行真实的模型和可靠的空间稳定分析。