TY - JOUR
T1 - A 1-dimensional continuous and smooth model for thermally stratified storage tanks including mixing and buoyancy
AU - Lago, Jesus
AU - De Ridder, Fjo
AU - Mazairac, Wiet
AU - De Schutter, Bart
PY - 2019
Y1 - 2019
N2 - To mitigate the effects of the intermittent generation of renewable energy sources, reliable and efficient energy storage is critical. Since nearly 80% of households energy consumption is destined to water and space heating, thermal energy storage is particularly important. In this context, we propose and validate a new model for one of the most efficient heat storage systems: stratified thermal storage tanks. The novelty of the model is twofold: first, unlike the non-smooth models from the literature, it identifies the mixing and buoyancy dynamics using a smooth and continuous function. This smoothness property is critical to efficiently integrate thermal storage vessels in optimization and control problems. Second, unlike models from literature, it considers two types of buoyancy: slow, linked to naturally occurring buoyancy, and fast, associated with charging/discharging effects. As we show, this distinction is paramount to identify accurate models. To show the relevance of the model, we consider a real tank that can satisfy heat demands up to 100 kW. Using real data from this vessel, we validate the proposed model and show that the estimated parameters correctly identify the physical properties of the vessel. Then, we employ the model in a control problem where the vessel is operated to minimize the cost of providing a given heat demand and we compare the model performance against that of a non-smooth model from literature. We show that: (1)the smooth model obtains the best optimal solutions; (2)its computation costs are 100 times cheaper; (3)it is the best alternative for use in real-time model- based control strategies, e.g. model predictive control.
AB - To mitigate the effects of the intermittent generation of renewable energy sources, reliable and efficient energy storage is critical. Since nearly 80% of households energy consumption is destined to water and space heating, thermal energy storage is particularly important. In this context, we propose and validate a new model for one of the most efficient heat storage systems: stratified thermal storage tanks. The novelty of the model is twofold: first, unlike the non-smooth models from the literature, it identifies the mixing and buoyancy dynamics using a smooth and continuous function. This smoothness property is critical to efficiently integrate thermal storage vessels in optimization and control problems. Second, unlike models from literature, it considers two types of buoyancy: slow, linked to naturally occurring buoyancy, and fast, associated with charging/discharging effects. As we show, this distinction is paramount to identify accurate models. To show the relevance of the model, we consider a real tank that can satisfy heat demands up to 100 kW. Using real data from this vessel, we validate the proposed model and show that the estimated parameters correctly identify the physical properties of the vessel. Then, we employ the model in a control problem where the vessel is operated to minimize the cost of providing a given heat demand and we compare the model performance against that of a non-smooth model from literature. We show that: (1)the smooth model obtains the best optimal solutions; (2)its computation costs are 100 times cheaper; (3)it is the best alternative for use in real-time model- based control strategies, e.g. model predictive control.
KW - Modeling
KW - Numerical Optimization
KW - Optimal Control
KW - Parameter Estimation
KW - Stratified Tank
KW - Thermal Storage
UR - http://www.scopus.com/inward/record.url?scp=85064743368&partnerID=8YFLogxK
U2 - 10.1016/j.apenergy.2019.04.139
DO - 10.1016/j.apenergy.2019.04.139
M3 - Article
SN - 0306-2619
VL - 248
SP - 640
EP - 655
JO - Applied Energy
JF - Applied Energy
ER -