QUANTICOL - Multiscale modelling informed by smart grids

Gast N., Bortolussi L., Jane H., Paskauskas R., Trinabastone M.

Stochastic processes  B.2.2 ARITHMETIC AND LOGIC STRUCTURES. Performance Analysis and Design Aids 

Multiple scales are inherent to collaborative adaptive systems (CAS). They can be temporal, for example, adjusting the production of a large power plant takes hours while appliances can switched on or of the instant a signal is received. They can also be organizational and represent a hierarchical structure, for example a smart building that contains rooms. Fluid approximations, and in particular mean-field limits, are a powerful tool to conduct a quantitative analysis of large stochastic systems. Yet existing techniques are not well adapted to study multiple-scale behaviour. This deliverable reports on Task 1.1 and 1.2 of Work Package 1. We mainly focus on two aspects: (1) how to define and construct mean-field limits in the presence of multiple scales and (2) what approximations are needed to build efficient control algorithms for smart grids. This deliverable presents results from published papers by the members of the project as well as the relevant literature. Our approach is to develop the theory in a way informed by examples. The results presented in this deliverable are motivated by their applicability to model smart grids and smart buildings. Hence, each section contains at least one concrete example of how the results apply to our case-studies. We rst present a review of model reduction techniques in the presence of multiple time scales. This occurs when the states of some objects evolve at a much faster time scale than others (for example, small electric appliances and big power plants). We compare existing reduction techniques for deterministic dynamical systems, a mature subject, with on-going work on stochastic systems. This review shows that a number of time-scale reduction techniques can be readily applied to mean-field models. It gives us tools to develop the analog for stochastic systems. We then describe the situation when there are multiple population scales. Our basic example is when one centralized controller interacts with many appliances. We show that in such cases, the limit is naturally described by a stochastic hybrid system. We describe how to construct the limit and the limitations of the approach. This technique reduces greatly the complexity of the simulation while maintaining a good accuracy. We develop a novel formalism to describe systems of systems. This can model systems that have a hierarchical organization. This formalism allows us to automatically reduce the complexity of the mean-field equations, by exploiting symmetries in the model. This method can be applied iteratively, to construct hierarchical abstractions of systems. We illustrate our method to describe the behaviour of a collection of smart buildings. In the last section, we demonstrate the use of optimization tools for building control algorithms in electrical systems that have a large production of renewable energy. We model and treat two challenges: large forecast uncertainties and presence of delay due to multiple time scales. We study two directions based on centralized and distributed control. We develop storage and demand/response management policies, where a central controller sends signals to smart users to adapt the consumption to the production. These policies are more robust to forecast errors than existing strategies. To conclude, this work package reports on progress that has been made on the fundamental aspects of multi-scale modeling as well as on advances in the smart-grid case study. This constitutes a rst attempt to build generic tools that will be applicable to the analysis and the optimization of the other case studies. We will continue the development of these generic methods to incorporate spatial behaviour (Work Package 2) and apply these techniques to uid model checking (Work Package 3).

Source: Project report, QUANTICOL, Deliverable D1.1, 2014