THERMAL ENERGY STORAGE
THERMAL ENERGY STORAGE  Title
Thermal Energy Storage Component Model
THERMAL ENERGY STORAGE  model overview
Model Overview
Author / organization: Benedikt Leitner / AIT
Domain: Thermal storage
Intended application: Returnsupply connections in, e.g., district heating networks and possibly in combination with a heater unit
Modelling of spatial aspects: Discretized (single device)
Model dynamics: Dynamic
Model of computation: Timecontinuous
Functional representation: Explicit
THERMAL ENERGY STORAGE  input and output
Input and Output
Input variables : Modelica.Fluid.Interfaces.FluidPort port_a (acausal): fluid port at return side
Output variables :
 Real T_i: temperature of layer I [K]
 Modelica.Fluid.Interfaces.FluidPort port_b (acausal): fluid port at supply side
THERMAL ENERGY STORAGE related documents
THERMAL ENERGY STORAGE description
Short Description
A model of a stratified storage tank for thermal energy storage. Intended to be used for returnsupply connections in, e.g., district heating networks and possibly in combination with a heater unit. The temporal resolution is minutes to hours. The model represents a stratified storage tank. The tank uses several volumes to model the stratification. The tank has a fixed volume. Thus, the same mass flow injected at the top of the tank leaves the tank at the bottom and vice versa. Heat conduction is modelled between the volumes through the fluid, and between the volumes and the ambient. Effects modelled include buoyancy, heat transfer between layers as a result of heat conduction and mass flow as well as heat transfer of each layer to the ambient. The model is able to capture flow reversals and zero flow.
Present use / development status
The model is part of AIT’s internal Modelica library for district heating and is usable for cosimulation with electric network models. The Modelica library uses the Modelica standard library and the IBPSA library as a core.
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THERMAL ENERGY STORAGE
Model Details
Domain 
 
Intended application (including scale and resolution) 
Intended to be used for returnsupply connections in, e.g., district heating networks and possibly in combination with a heater unit. The temporal resolution is minutes to hours.  
Modelling of spatial aspects 
The model represents a stratified storage tank. The tank uses several volumes to model the stratification. The tank has a fixed volume. Thus, the same mass flow injected at the top of the tank leaves the tank at the bottom and vice versa.  
Model dynamics 
Heat conduction is modelled between the volumes through the fluid, and between the volumes and the ambient. Effects modelled include buoyancy, heat transfer between layers as a result of heat conduction and mass flow as well as heat transfer of each layer to the ambient. The model is able to capture flow reversals and zero flow.  
Model of computation 
 
Functional representation 

Input variables (name, type, unit, description) 
 
Output variables (name, type, unit, description) 
 
Parameters (name, type, unit, description) 
 
Internal variables (name, type, unit, description) 
See Modelica models:
 
Internal constants (name, type, unit, description) 
See Modelica models:
 
Model equations  Governing equations  
See Modelica models:
 
Constitutive equations  
See Modelica models:
 
Initial conditions 
 
Boundary conditions  Connections to fluid ports at top and bottom layer.
 
Optional: graphical representation (schematic diagram, state transition diagram, etc.) 

Model Validation  
Narrative  The electric heater is connected to a cold source (30°C) and receives mass flow setpoints. These setpoints start at zero and rise above the nominal mass flow of the component to show its behaviour at both design and offdesign situations.  
Test system configuration  The simulation runs for 4 hours. The Modelica standard library and the IBPSA library are needed, including IBPSA.Media.Water used as medium. The mass flow through the component is controlled using a step function.  
Inputs and parameters 
Model parameters:
 
Control function (optional)  A step function is used to control the mass flow m_flow through the component. The function starts at zero. After one hour it is increased to 1 and stays at this value till the end of the simulation.
 
Initial system state  The system starts without any mass flow. Temperature of the medium of each layer i is set to its initial value T_init_i.
 
Temporal resolution  CVode is used as an integrator. It uses a variable integrator step size based on tolerance settings. Here a relative tolerance of 0.0001 is used. Simulation result outputs are generated every 60 seconds or on events (if any).
 
Evolution of system state 
The system starts in thermal equilibrium. The tank and the ambient are at the same temperature and, thus, do not exchange heat (no losses). No mass flow is running through the tank. Once a mass flow with hot water enters the tank at the top, the temperature of the tank starts to increase from top to bottom. Cold water from the bottom of the tank is leaving the tank. As the water at the bottom of the tank is becoming warmer, also the water leaving the tank is becoming warmer. This temperature reaches nearly (losses) the supply temperature once the tank is full.  
Results  At the beginning the tank is in a thermal equilibrium with the ambient, both have a temperature of 20 °C. Thus, heat losses are zero. After 1 h a mass flow of 1 kg/s with a temperature of 70 °C is injected into the top of the tank. This causes a mixing of the fluid of the different layers in the tank. As a result, the temperature of each layer is increased. The increase starts at the top layer while also affecting lower layers with some delay. Consequently, heat losses of the tank rise. After around 3 hours the tank is “full”. Thus, water with approximately 70 °C, i.e., the supply temperature, is exiting the tank at the bottom. The heat losses of the “full” tank reach a value of 174 W.  
Sensitivity analysis (optional)  
Narrative  The storage volume is varied. The sensitivity of the state of charge and the heat losses on tank volume is assessed.  
Test system configuration  Simulation runs for 6 hours. Rest is same as in model validation.  
Source of uncertainty  The tank volume VTan is varied in the range of 1 m3 to 10 m3 with a step size of 1 m3.  
Inputs and parameters  Same as in model validation. Only difference is the tank volume as described above.  
Control function (optional)  Same as in model validation.  
Initial system state  Same as in model validation.  
Temporal resolution  Same as in model validation.  
Evolution of system state  With higher tank volumes the tank will need more time to get fully charged. Also heat losses are expected to rise due to the higher surface area of the tank.  
Results  Results for the SOC show that the higher the tank volume, the later it is fully charged. This is not surprising as the mass flow into the tank is the same for all cases. A tank that is 1 m3 bigger takes around 22 minutes longer to fully charge. The heat losses of the storage tank increase with larger tank volumes. This is mainly due to the higher surface area.  
Model harmonization  
Narrative  Same as in model validation.  
Test system configuration  Same as in model validation.  
Source of uncertainty  Same as in model validation.  
Inputs and parameters  Same as in model validation.  
Control function (optional)  Same as in model validation.  
Initial system state  Same as in model validation.  
Temporal resolution  Same as in model validation.  
Evolution of system state  With higher tank volumes the tank will need more time to get fully charged. Also heat losses are expected to rise due to the higher surface area of the tank.  
Results  State of charge of the tank: ???= number of layers with temperature>???? Where ???? is the minimum temperature at which a layer is counted to be fully charged. Total heat losses during simulation: Where ????? is the heat loss. 