Aggregate Volatility in Complex Power Grid Networks Under Uncertain Market Conditions

The power grid is of crucial importance to the modern economy and in recent years it has drawn also the attention of researchers in the nascent field of complex network science. Most previous works in this field have been descriptive and mainly concerned with highlighting the structure that power grids share with other types of networked (e.g., small world). We propose and develop the first steps of a prescriptive study that investigates the situation in which a continuous shock (either in demand or supply) propagates on a power grid. We are interested obtaining a tractable, analytic expression of the aggregate volatility resulted from the shock, yet preserving the characteristcs of an engineering network that obeys certain physical laws (i.e., Kirchhoff’s theorems). This framework can be then used to set-up problems of economic interest in this context, such as an optimum investment in network elements to achieve minimum disruptions due to a shock. Here we report on identifying the physics-motivated interaction mechanisms between elements in the network. Preliminary results indicate that under certain assumptions and simplifications certain quantities (power flow into a node and likely an “investment“ cost associated with that node) may be expressed via a typical network centrality measure the Bonacich centrality (related to Google’s PageRank). Moreover, we plan to use our framework to study empirically shocks on a power grid. For this we implemented algorithms from the complex power networks literature to generate random test networks with realistic characteristics that may be tuned to highlight certain properties or results. As instructed by Prof. Leskovec, I mention that the week during which the project was due, I had an accident in which I have broken my right arm (which I use to write). This resulted in me not being able to go through a part of the derivations and implementations that I proposed in the milestone.