A network calculus foundation for smart-grids where demand and supply vary in space and time

We study the exciting potential of a smart-grid where large adoption of Electric Vehicles (EVs) intersects with wide deployment of Distributed Energy Resources (DERs). In such a grid, both demand and supply of energy are expected to vary in time, but crucially also in space. This exposes a continuum of policies between displacing demand in space and displacing demand in time, for matching demand and supply. To formally model and analyse such policies, we propose Multi-dimensional Network Calculus (MNC), which extends the classical Network Calculus from a single dimension of time to multiple dimensions. As foundational aspects of MNC, we introduce abstractions of arrival and ser- vice surfaces, their properties, and analyses under different policies. As a concrete example, we analyse a smart-grid- enabled highway that is plied by EVs with swappable batteries which are exclusively charged by a set of solar farms stationed along the highway. With real-world traffic and solar output data, we analyse such a setting and demonstrate the application of MNC to design policies and provide bounds on Quality-of-Service (QoS) metrics.