Power Grids as Complex Networks: Formulating Problems for Useful Science and Science Based Engineering

This exploratory workshop will attempt to bridge the gap between network science and power systems engineering. We will start with one very basic question: what are the various abstractions of the power grid in the literature, and what problems can be appropriately analyzed with each abstraction? Most abstractions have a range of problems for which they are useful, and others for which the abstraction makes assumptions that do not hold within the problem domain. This workshop aims to identify the problem domains, particularly in the general areas of robustness and sustainability, for which the various abstractions can yield real and useful insights.

The social and ecological importance of the power grid cannot be overstated. How can we create a power grid that can take advantage of renewable power sources, whose output fluctuates with the weather? How can we deal with increased demand from electric cars? How can we make it robust to intentional attack? How can we reduce the probability of large cascading failures?

The power grid is nothing if not a complex system. It is also a network, and SFI is a leading institution in the study of networks. But the power grid poses an extreme challenge to network science as it exists today. Most work on networks uses a “thin” graph-theoretic approach that pays attention just to network topology: there are nodes with edges between them, period.

In contrast, both the edges and the nodes of the power grid are highly inhomogeneous. Edges have flows and capacities, and nodes are highly dynamic. Even thinking of edges as transmission lines can be misleading, since influences in the power grid can travel very quickly over large dis­tances. In addition, different types of generators have dynamics at very different time scales. Solar panels can be taken on-or off-line almost instantaneously, but coal-fired power plants have huge turbines that take hours to spin up. Internal pricing markets, obeying different rules in different regions, add yet another level of complexity. Finally, the power grid interacts with other utilities, the Internet, and transportation networks. Modeling these “networks of networks,” with failures that can spread from one type of network to another, is even more challenging.

As a result, much of the existing work on the power grid in the network theory community is naive or unrealistic. Theorists assume that topological measures like betweenness or centrality play important roles in network vulnerability, but this is not necessarily the case. Simple models of cascading failure assume that failures spread from one node to its neighbors, as in epidemi­ological models or Granovetter-like models of social influence. However, electric current, and subsequently power and energy, travel through a network according to Kirchhoff’s and Ohm’s laws, which mean that power travels over all paths between sources and sinks. When failures in nodes or edges occur, power re-routes at nearly the speed of light to all parallel paths, in inverse proportion to impedances. Because simple contagion models do not capture this behavior, many of the contributions from network theory are viewed with some disdain by power engineers.

At the other extreme, power engineers have an enormous amount of domain-specific knowl­edge, and access to large (but balkanized, and in some cases proprietary) data sets. They have built highly detailed “flight simulators” of pieces of the power grid, and these can be very helpful to understand the grid at an engineering level. But our goal as scientists is not to build life-size maps of the world. We want to abstract away irrelevant details, leaving us with models that are amenable to analysis, while being realistic enough to give insight into the real system.