Analytical Models for Power Networks: The Case of the Western U.S. and ERCOT Grids

The topological structure of the power grid plays a key role in the reliable delivery of electricity and price settlement in the electricity market. Incorporation of new energy sources and loads into the grid over time leads to its structural and geographical expansion. This paper presents an intuitive analytical model for the spatio-temporal evolution of large grids and uses it to understand common structural features observed in grids across America. In particular, key graph parameters like degree distribution, graph diameter, betweenness centralities, eigen-spread, and clustering coefficients are used to quantify the model's benefits through comparison with the Western U.S. and ERCOT power grids. The most significant contribution of the developed model is its analytical tractability that provides a closed form expression for the nodal degree distribution observed in large grids. The discussed model can be used to generate realistic test cases to analyze topological effects on grid functioning and new grid technologies.

I. Introduction

The power grid refers to the complex network of energy generators, consumers and connecting transmission lines that are involved in the delivery of electricity. The advent of the ‘smart grid’ has added further complexity to the system due to the introduction of new renewable generation resources and flexible consumer demand response. These advances have the potential to make the grid green as well as to reduce electricity prices. To understand their impact correctly, such technologies need to be implemented on test cases that reflect the structure and functionality of current as well as future grids. A majority of popular power grid test cases used in literature are much smaller in size than real grids [1], [2] and are static in nature. Data for larger grids, baring a few exceptions like the Polish grid [16], are not publicly available due to security reasons. From a topological perspective, there is thus a need to develop test cases that mirror the common trends in large grids around the world, and more so to provide an explanation for the temporal evolution of such common observations.