Time-coordinated optimal power flow for energy service networks - Modelling Distributed Energy Resources in Energy Service Networks - page 103

Equation (5.17) refers to the nodal balance of natural gas flow conservation that
must be met in each node; although for simplicity purposes the demand injections
from CHP technologies are not specified. Meanwhile, (5.18) represents pressure lim-
its at nodes, while (5.19) gives the load flow constraints in the pipes, thus meeting
conditions of primary concern for proper natural gas delivery. Similarly, (5.20) spec-
ifies the allowed range of operation for the compressors in the networks. Statement
(5.21) details the CHP natural gas consumption at each node, while (5.22) and (5.23)
limit the amount of thermal power that can be charged and discharged for each nodal
storage system. Finally, (5.24) ensures that nodal thermal storage systems must have
at all times a SOC equal to or greater than zero.
The above snapshot constraints are the basic equations that limit the operation
of the energy systems present in the TCOPF framework.
The global constraints focus on the conditions that must be met after a complete
period.

5.3.2.3 Concerning PHEV devices embedded in electrical networks

EV store
Bα

= 0 ∀ α ∈ P n (5.25)

EVSOC store
α , β

EVSOC store
α , max

= ∀ α ∈ P n (5.26)

P phev
Dα , β

hr total
nβ

G 2 V store
α , β

− · = ∀ ∈ ∀ ∈

0 α P n , β nβ (5.27)

P phev
Gα , β

hr total
nβ

V 2 G store
α , β

− · = 0 ∀ α ∈ P n , ∀ β ∈ nβ (5.28)

Equation (5.25) guarantees a net zero storage balance is met for all battery sys-
tems, while not forgetting to fully charge the batteries for a specific time if requested
(5.26). Consequently, (5.27) and (5.28) verify all the energy charged and discharged
by PHEVs matches the sum of their individual power injection counterparts.

5.3.2.4 Concerning CHP devices embedded in natural gas networks

T store
Bα

= 0 ∀ α ∈ G n (5.29)

TSOC store
α , β

TSOC store
α , max

= ∀ α ∈ G n (5.30)

T store
Dα , β

hr total
nβ

EC store
α , β

− · = 0 ∀ α ∈ G n , ∀ β ∈ nβ (5.31)

T store
Gα , β

hr total
nβ

ED store
α , β

− · = ∀ ∈ ∀ ∈

0 α G n , β nβ (5.32)

Equation (5.29) establishes a net zero storage balance is met for all thermal
store systems during the day being analysed, while not forgetting to fully charge the
stores for a specific time interval if requested (5.30). Subsequently, (5.31) and (5.32)
verify all the energy charged and discharged by thermal stores matches the sum of
their individual power injection counterparts.