Online computation of polytopic flexibility models for demand shifting applications

In this paper, we propose two methods for computing a polytopic approximation of the demand shifting flexibility of a load unit over a future horizon, using a mathematical optimization framework. The computed polytopic approximation, as an abstraction of load unit's flexibility, can be used in a receding horizon control framework for the grid operator to simultaneously coordinate multiple loads. One method is to use a parallelotope to represent the flexibility, which shows in the experiments a performance advantage over related approaches using zonotopes or hyper-ellipsoids. Another method that uses a resource polytope model shows a better performance but at a cost of extended runtime due to its nonlinear formulation.