Distributed Model Predictive Control of Aquifer Thermal Energy Storage Smart Grids

Aquifer Thermal Energy Storage (ATES) systems are used to store large quantities of thermal energy in underground aquifers enabling the reduction of energy usage and CO2 emissions of the heating and cooling systems in buildings. In dense urban environments, the proximity of hot and cold wells in nearby ATES systems installations may lead to undesired interactions between such energy storage systems leading to suboptimal operation or conservative design choices [1, 5]. The interactions between ATES systems are dynamically time-varying and plagued by uncertainty due to the absence of detailed underground models and cooperation between operators regarding the influence of nearby systems. ATES systems interact via the aquifer in a way comparable to how distributed sources and sinks of electricity are interacting via the electricity smart grid [3]. In a smart grid setting, every agent represents an ATES system and has the potential to contribute to the local thermal balance of the grid. A single ATES system is linked to the neighboring agents via the aquifer that is defined as a complicating constraint. Therefore, coordination is expected to provide improvements in the local and system-wide thermal energy cost and efficiency, while fulfilling all coupling constraints. Thus the motivation for ATES smart grids can be both economical and environmental. When designing controllers for the underlying interconnected dynamical system, distributed solutions are sought in order to reduce the computational complexity, and allow individual operators to operate their installations locally without the need for a central entity to determine the systemwide optimal pumping schedules. The proposed distributed approach should provide performance close to that of a centralized one, while being robust to uncertainties in the subsystem models and their interactions, and relying only on a limited amount of information exchange. Distributed MPC (DMPC) is a promising methodology in this context since it is able to fulfill local and complicating constraints between subsystems while striving for economically and environmentally optimal operation (see [2, 4] and the references therein). 1Research supported by the Netherlands Organization for Scientific Research (NWO) under the project Aquifer Thermal Energy Storage Smart Grids (ATES-SG) with grant number 408-13-030. In this work, we propose a price-based (Lagrangian) coordination scheme that is based on solving a local agent problem subject to the local constraints in parallel. Each ATES system optimizes its own objective function that is modified according to a set of prices assigned for the thermal energy resource. The goal of this price-based method is to coordinate agents by finding equilibrium resource prices which lead to a globally optimal ATES smart grid state. Due to the fact that ATES system operates in various modes in each season, the optimization problem becomes a mixed integer program. We first introduce a mathematical model for a single ATES system, based on the physical description and limitations, that is suitable for an optimal control problem formulation. Subsequently, we extend the single system model to an interconnected grid by introducing the complicating constraints. As part of our future work, we will develop a methodology that ensures tractability while providing convergence and performance guarantees with respect to the centralized optimum of the whole networked system. The efficiency and practical feasibility of the theoretical results will be investigated by applying them to a real case study.