ER_SPG: Synthetic Power Graph generation by Erdos-Renyi Model

ER-SPG is a Matlab code for producing synthetic power graphs using well-known Erdos-Renyi Random Model. It scales power graphs and achieves connectivity in each scale by different approach, and accordingly connected graphs with average degree between 2 to 5 (normally between 2.3 to 3.1) can be produced by ER_SPG with the structures similar to power graphs. It also reorders the graph vertices to obtain consecutive numbering similar to power graphs. This algorithm is also provides locations of zero injection buses (ZIBs) as operational data of power graphs. The produced graph expressed by adjacency matrix A, and ZIB location expressed by vector Z. The produced data can be used in Optimal PMU Placement (OPP) problem, which locates PMUs for system observability in vector X. The previously produced A and Z matrices and vectors and their related X vectors reported in Table II of the paper are also available in this data set. The Matlab code also includes a function, which can represent power graphs by Kirk circle. The location of ZIBs and PMUs are also can be presented in this type of representation.Important note: This algorithm uses some functions and routines of “Octave Networks Toolbox” developed by “MIT Strategic Engineering”: http://strategic.mit.edu/downloads.php?page=matlab_networks

ER-SPG是一款基于Matlab的代码，旨在生成使用著名埃尔多斯-雷尼随机模型的合成功率图。该代码通过不同的方法实现不同尺度的功率图缩放，并确保每个尺度的连通性。据此，ER_SPG能够生成平均度数介于2至5之间（通常为2.3至3.1之间）的连通图，其结构与功率图相似。此外，该算法还对图顶点进行重新排序，以获得类似于功率图的连续编号。该算法还提供了零注入母线（ZIBs）的位置，作为功率图的运行数据。生成的图由邻接矩阵A表示，ZIB的位置由向量Z表示。生成的数据可用于最优PMU放置（OPP）问题，该问题在向量X中定位PMU以实现系统可观测性。论文第II表中所报告的先前生成的A和Z矩阵以及相关X向量也包含在本数据集中。Matlab代码还包括一个函数，该函数可以借助柯克圆表示功率图。ZIBs和PMUs的位置也可以以这种类型的表现形式呈现。重要提示：此算法使用了由“MIT Strategic Engineering”开发的“Octave Networks Toolbox”中的某些函数和例程：http://strategic.mit.edu/downloads.php?page=matlab_networks