Modelling embedded technologies in energy service networks - Modelling Distributed Energy Resources in Energy Service Networks - page 69

flows, the mass capacity of the storage medium, and the specific heat characteristics
of the fluid used to store the energy.
Taking these facts into consideration, the heat flow equation for storing thermal
energy in a material mass is commonly calculated in the literature by:

Q = mc p T (4.30)

⎧
⎨

m is the mass of the material (kg)
c p is the specific heat of the material (J/kgK)
T is the temperature difference (K)

where

⎩

If the mass of the material is divided by its density, then the volume of the fluid
in the hot water tank can be defined. Therefore, the thermal store performance of a
unit will depend on the volumetric storage capacity and the energy required fulfilling
the specified water temperature differences in the system. Usually these temperature
differences range in dwellings from 30 to 40 ◦ C; for example 20 and 60 ◦ C [87].
The thermal storage is charged based on buoyancy forces. This fact ensures that
during the charging period, hot water is supplied to the top of the tank, while the
same amount of cold water is removed from its lower structure. The thermal charging
process begins when heat production surpasses thermal power consumption, while
the opposite process applies during the discharge of the storage tank.
The thermal layers within a storage unit that occur during the stratification pro-
cess should be as thin as possible to minimise losses. Currently, sensible storage
systems typically have a 90% efficiency, this is because its losses are mainly caused
by heat-transfer processes. The main factors that contribute to the degradation of
stored energy are heat conduction between fluids at different temperatures and heat
conduction with the storage wall [193].
In this topic, modelling sensible TES operation logic is approached by apply-
ing a piecewise time optimisation that simulates operation control commands. This
optimisation approach is analogous to the electro-chemical energy storage modelling
applied for PHEV technology (see section 4.4).
For sake of simplicity, the thermal storage units are modelled as if they were a
large single storage tank unit representing the group of micro-CHPs present within
a particular node. Therefore, the nodal thermal storage capacity is an aggregated
quantity which is equal to the sum of all individual stores. Additionally, the charging
and discharging constraints of the storage units need to be satisfied at each time
interval, while the global constraints regarding minimum and maximum SOC values
must be met for the entire period being analysed.
In order to complement the nodal CHP equations presented in the previous sub-
section, it is necessary to define the variables that keep track on the state of charge
(SOC) of the storage resources. For this, it is imperative to introduce a time variable.
Likewise, it is required to define the limits on how much energy the thermal stores
are able to charge and discharge in terms of total capacity and per unit of time.
We begin by addressing the storage balance equation that must be fulfilled for
the whole period being analysed ( e.g. single day). Therefore, there must be a term