Domain

• thermal storage

Intended application (including scale and resolution)

Intended to be used for optimisation processes. Temporal resolution depends on the component: for daily storage resolution can go up to an hour/minute range; for seasonal storage representative days have to be used. 

Modelling of spatial aspects

• discretized (single device)

For each of the two layers of the storage tank, mass and temperature are considered homogeneous. 

Model dynamics

• quasi-static

Thermal equilibrium is assumed at every time step considered. 

Model of computation

• other, please specify: to be used by an optimization algorithm

Equations describing the state of the battery are time-continuous, while the sensors measuring the real-time status are discrete event-based. 

Functional representation

• implicit

The model is an equivalent circuit model including lookup tables. 

Input variables (name, type, unit, description)

• Real Pdemand: thermal demand (kW)
• Real Tdemand,in: input temperature of the demand (degC)
• Real Tdemand,out: output temperature of the demand (degC)
• Real Psource,max: maximum power of the heat source (kW)
• Real Tsource,in: input temperature of the source (degC)
• Real Tsoure,out: output temperature of the source (degC)

Output variables (name, type, unit, description)

• Real Vtot: total volume (m³)
• Real Vup: Upper layer’s volume at every time step (m³)
• Real Vdown: Lower layer’s volume at every time step (m³)
• Real Vload: Volume of water corresponding in the exchange during the loading phase(m³)
• Real Vunload: Volume of water corresponding in the exchange during the unloading phase (m³)
• Real Tup: Upper layer’s temperature (degC)
• Real Tdown: Lower layer’s temperature (degC)
• Real MC: heat mass of the cold flow (corresponding to the loading phase) (kW/K)
• Real MH: heat mass of the hot flow (corresponding to the unloading phase) (kW/K)

Parameters (name, type, unit, description)

• Real Vmax: maximum total volume (m³)
• Real Vmin: minimum volume (m³)
• Real Tmaxup: maximum temperature for upper layer (degC)
• Real Tminup: minimum temperature for upper layer (degC)
• Real Tmaxdown: maximum temperature for lower layer (degC)
• Real Tmindown: minimum temperature for lower layer (degC)

Internal variables (name, type, unit, description)

• Real C₀= 4186 J/(kg⋅degC): thermal capacity of water
• Real p₀= 1000 kg/m³: density of water

Internal constants (name, type, unit, description)

Model equations

Governing equations

1. Vtot = Vup + Vdown
2. Vup[t0] = Vup[t0+1] (same state of the storage at the beginning and end of its cycle)

3. Vup[t+1] = Vup[t] + Vload[t] - Vunload[t]
4. Vdown[t+1] = Vdown[t] - Vload[t] + Vunload[t]
5. MC* dur = Vload * p₀* C
6. MH* dur = Vunload * p₀ * C
7. Vload*Vunload <= 0 (no simultaneous loading / unloading)
8. Verification of the temperature levels of the storage in order to allow (or not) the loading/unloading (see related link in section “Additional Information” below)
9. Power and energy exchanges can be calculated from the product of mass (calculated via the density and the volume of the water) and the temperature levels.

Constitutive equations

10. C = C₀

Boundary conditions

• Vtot <= Vmax
• Vup >= Vmin
• Vdown >= Vmin
• The system respects a number of constraints regarding its charging/discharging phase and temperature levels (see related link in section “Additional Information” below).

Optional: graphical representation (schematic diagram, state transition diagram, etc.)

Model Validation

Narrative

Given a specific heat demand profile, this test allows the sizing of a storage tank when coupled with a production unit. Temperatures are fixed for both sides in order to allow the simulation models that do not account for the temperature level match to run the optimisation.
The objective function is the minimisation of the total exergy consumed. The production unit and the storage tank can be used to satisfy the demand.

Test system configuration

•  Requires models for the production units, the demand and the network
• Optimisation period: 1 day (1-hour time step, 24 periods)

Inputs and parameters

• Real Pdemand(t) (input data file)
• Real Tdemand,in = 45°C 
• Real Tdemand,out=65°C
• Real Psource,max(t) (input data file)
• Real Tsource,in = 80°C
• Real Tsoure,out = 75°C
• Real Vmax = 1000 m3
• Real Vmin = 0
• Real Tup = 70°C
• Real Tdown = 50°C
• Real Pinc = 5

Pdemand(t) and Psource,max(t) are provided as time series in the attached data file (Storage_input.csv in data file EDF_ 2VolumeThermalStorage_data.zip).

Control function

Initial system state

Temporal resolution

24 periods are investigated, considering a 1-hour step in order to represent a day

Evolution of system state

In this configuration, the production unit and the storage tank are the two elements to be sized in order to satisfy the demand. The total power produced by the production unit is therefore equal to the total energy demand.
The total volume of the storage tank is obtained accordingly, in order to store the energy when available and discharge it when needed. The initial state of the storage must be equal to its final state for the optimisation’s time horizon, in order to ensure that no extra energy is supplied to the system.
The optimal volume implies that the storage tank is emptied and fully charged at least once during the time horizon given.

Results

• Total storage volume: 4.714 m3

The results are provided as time series in the attached data file (Storage_output.csv in data file EDF_2VolumeThermalStorage _data.zip).

Model harmonization

Narrative

Test system configuration

Inputs and parameters

Control function (optional)

Initial system state

Temporal resolution

Evolution of system state

Results

Real EnergyCharg = 135.03 kWh: total energy stored within the 24 hours of optimisation time (integral of Pcharging)