The Multifaceted Mathematics Center for Complex Energy Systems

2012 - presentpresent

The infrastructure planning challenge needs new representations of stability and transient response constraints which are suitable for integrated dynamics analysis – system planning. These may be obtained by using the new stochastic parameterizations coupled with probability densities on initial states based on Hamiltonian structure. These allow a probabilistic description of consequences of initial contingencies, and responses can be created by advanced sampling of high-dimensional and rare events coupled with scalable dynamic simulations. In turn, this creates the data necessary for a multi-scale reduction process where the proper coarse scale variable to parameterize transient response can thus be identified. In addition, new data-driven parameterizations of stability and transient response will be obtained, and novel small-signal stability metrics will be obtained from graph theory tools. At this stage, a new constraint representation of dynamical response will be created which will allow for the first time planning with coupled dynamics analysis in a hierarchical decision framework. Models of residual error of data-driven models for both dynamic transients and demand, stochastic DAE models of physics, reduced with time-oriented multi-scale techniques, and sampling of ambient uncertainty using high-dimensional rare events sampling will be used to completely define the uncertainty space of the planning problem. The resulting nonlinear non-convex stochastic optimization problem with mixed integer and continuous variables will be transcribed in the M2AC2S-I framework and approached by scalable optimization techniques with complexity/accuracy trade-offs exposed by decomposition and relaxation techniques from integrated mathematical analysis and abstraction frameworks and various descriptive levels as induced by the multi-scale thought process. With various complexity/accuracy solution points we now return to predictive modeling and understand what are the most promising facets to explore to further improve the complexity/accuracy balance. Due to the enormous number of choices in the solution several iterations will be necessary. By constant interaction at each iteration of the teams responsible for research in the listed concepts and as their impact is gauged on the sub-challenge problems, integration will be achieved. Each of the sub-challenges will ellicit a similarly comprehensive process, and will increase the success prospects of integration of mathematics as well as its overall impact.