Modelling embedded technologies in energy service networks - Modelling Distributed Energy Resources in Energy Service Networks - page 70

that takes into account all the energy charged and discharged from the thermal stores.
This expression is defined as the nodal thermal storage balance and for node k , it can
be stated as:

nβ

η ts ·

k , β =

T store
Bk

EC store
k , β

ED store

= − 0 (4.31)

β = 1

⎧
⎨

β is the time interval being analysed
nβ is the number of time intervals into which the full period is divided
η ts is the thermal storage efficiency of the technology
EC store
k , β

where

⎩

is the energy charged into the thermal store (Wh th )

k , β is the energy discharged from the thermal store (Wh th )
To define the SOC for the thermal storage system in node k at time β

ED store

+

1itis
necessary to have the previous storage value at time β , this can be formulated as:

TSOC store
k , β

TSOC store
k , β

TSOC store
k , β

= + (4.32)

+ 1

Needless to mention, the value for TSOC store

k , β must be equal or greater than 0 for
all time intervals because storage levels cannot have a negative value. However, this
constraint does not apply to the term which calculates the change in the SOC for a
specific time interval β , and is determined by:

TSOC store
k , β

EC store
k , β

ED store
k , β

= − (4.33)

Once the TSOC equations are defined, it is necessary to calculate the energy
injections that indicate the amount of charge and discharge, EC store
k , β

k , β respec-
tively. These energy transfer values, that alter the SOC of the thermal stores, are
analogous to the power terms T store
Dk

and ED store

Gk from Figure 4.14.
Taking place in the thermal storage unit at node k for time interval β , these terms
of energy injections can be expressed as:

and T store

hr total
nβ

EC store
k , β

W store
ECk , β

T store
Dk , β

= · · (4.34)

hr total
nβ

ED store
k , β

W store
EDk , β

T store
Gk , β

= · · (4.35)

Similar to variable W chp
k

ED are dispatch factors that
can take either values of 0 or 1, serving the purpose of enabling the time intervals
in which it is possible to charge or discharge the storage systems. Meanwhile, hr total
is the total period of time the urban energy infrastructure is being assessed and the
ratio serves to convert the power injections into energy ( i.e. if a day is divided into
48 time steps then each power injection needs to be multiplied times 0.5). Equations
(4.34) and (4.35) when combined are related to (4.33), thus allowing us to deter-
mine the variation occurring in the SOC of the nodal storage units for each time
interval.

, weight factors W store
EC

and W store