# Electric Grid

The push toward renewable energy considers electric power sources that have higher variation in output compared to fossil fueled plants.  While hydroelectricity is relatively constant over a day’s time, wind turbines and solar panels see variations on every time scale from hourly to monthly.  Control of the electric grid is challenged to optimize profit under varying sources and dynamic pricing conditions while meeting demands that also vary hourly and seasonally.  To do this effectively, the electric grid control is a combination of frequent measurements and calculations to inform operators and support rapid decisions.  Power sources, power storage, delivery hardware and demand-load are important components of the theoretical model of a transient electric grid.  There are also busses or microgrids that can operate on their own controls in concert with other grids.  Some isolation is good to mediate events and prevent problems from propagating.  As peak demand increases, the challenge is greater and new solutions are sought.  The US DOE has interest in this topic through the ‘Advanced Modeling Grid Research Program.’

The Electric Grid project was initiated to replace Monte-Carlo or extreme-case uncertainty calculations with duals arithmetic that calculates uncertainty simultaneously.  The first model represents every component according to its AC current and voltage behavior.  This includes the lines, transformers, loads, generators and decomposition of power into active and reactive portions.  These components are then built into a grid to form a multi-dimensional system that can be cast as a matrix.  The geometric nature of this is ‘nodes and lines’ and an adjacency matrix can be used underneath.  This provides a way to connect and disconnect components if the controller calls for it.  Based on the power behavior, the system is non-linear and the solution requires iteration until stable convergence is demonstrated.

Once a complete model is verified, it can be converted to duals arithmetic by representing each number with error and change all arithmetic, including matrix and iterative steps, to use duals arithmetic.  The resulting power flows, currents and voltages each have uncertainty reported and this information is multi-dimensional, allowing an examination of the dominant components of uncertainty and devising control schemes based on uncertainty and not just the immediate status of the grid.  The duals arithmetic has been demonstrated on simple grid problems such as two-bus, two-generators and one load.  Small problems allow the evaluation of the duals arithmetic’s advantages prior to tackling larger problems.