Vahab Rostampour

V. Rostampour, T. Keviczky

This paper presents an energy management framework for building climate comfort (BCC) systems interconnected in a grid via aquifer thermal energy storage (ATES) systems in the presence of two types of uncertainty (private and common). ATES can be used either as a heat source (hot well) or sink (cold well) depending on the season. We consider the uncertain thermal energy demand of individual buildings as a private uncertainty source and the uncertain common resource pool (ATES) between neighbors as a common uncertainty source. We develop a large-scale stochastic hybrid dynamical model to predict the thermal energy imbalance in a network of interconnected BCC systems together with mutual interactions between their local ATES. We formulate a finite-horizon mixed-integer quadratic optimization problem with multiple chance constraints at each sampling time, which is in general a non-convex problem and difficult to solve. We then provide a computationally tractable framework by extending the so-called robust randomized approach and offering a less conservative solution for a problem with multiple chance constraints. A simulation study is provided to compare completely decoupled, centralized and move-blocking centralized solutions. We also present a numerical study using a geohydrological simulation environment (MODFLOW) to illustrate the advantages of our proposed framework.

V. Rostampour, T. Keviczky

This paper presents a distributed stochastic model predictive control (SMPC) approach for large-scale linear systems with private and common uncertainties in a plug-and-play framework. Using the so-called scenario approach, the centralized SMPC involves formulating a large-scale finite-horizon scenario optimization problem at each sampling time, which is in general computationally demanding, due to the large number of required scenarios. We present two novel ideas in this paper to address this issue. We first develop a technique to decompose the large-scale scenario program into distributed scenario programs that exchange a certain number of scenarios with each other in order to compute local decisions using the alternating direction method of multipliers (ADMM). We show the exactness of the decomposition with a-priori probabilistic guarantees for the desired level of constraint fulfillment for both uncertainty sources. As our second contribution, we develop an inter-agent soft communication scheme based on a set parametrization technique together with the notion of probabilistically reliable sets to reduce the required communication between the subproblems. We show how to incorporate the probabilistic reliability notion into existing results and provide new guarantees for the desired level of constraint violations. Two different simulation studies of two types of systems interactions, dynamically coupled and coupling constraints, are presented to illustrate the advantages of the proposed framework.