Time-coordinated optimal power flow for energy service networks - Modelling Distributed Energy Resources in Energy Service Networks - page 102

The TCOPF constraints can be classified into:

Snapshot constraints ( i.e. for each time interval);

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Global constraints ( i.e. for the entire problem horizon).

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The snapshot constraints are formulated for each time period β .

5.3.2.1 Concerning electrical networks

P Gα − P Dα − P T α = 0 ∀ α ∈ P n (5.8)

Q Gα − Q Dα − Q T α = 0 ∀ α ∈ P n (5.9)

V α , min ≤ V α ≤ V α , max ∀ α ∈ P n (5.10)

P T α , min ≤ P T α ≤ P T α , max ∀ α ∈ P l (5.11)

| t | α , min ≤ | t | α ≤ | t | α , max ∀ α ∈ P t (5.12)

P chp
Gα , min

P chp
Gα

P chp
Gα , max

≤ ≤ ∀ α ∈ P n (5.13)

P phev
Dα , min

P phev
Dα

P phev
Dα , max

≤ ≤ ∀ α ∈ P n (5.14)

P phev
Gα , min

P phev
Gα

P phev
Gα , max

≤ ≤ ∀ α ∈ P n (5.15)

EVSOC store
α

≥ ∀ ∈

0 α P n (5.16)

Equations (7.4) and (7.5) refer, respectively, to the nodal balance for active and
reactive power flow conservation that must be met in each node, although for simplic-
ity purposes the demand and generation injections from DER technologies are not
specified. Now, (7.6) represents voltage limits at nodes, while (7.7) gives the thermal
constraints in the lines, thus meeting conditions of primary concern for proper power
delivery; while (7.8) specifies the allowed range of operation for the tap-changers.
Term (7.9) details the CHP generation permitted at each node, likewise (7.10) and
(5.15) limit the amount of power PHEVs can charge and discharge in each node.
Lastly, (5.16) ensures that nodal PHEV storage systems must have at all times a SOC
equal to or greater than 0.

5.3.2.2 Concerning natural gas networks

G Gα − G Dα − G T α = 0 ∀ α ∈ G n (5.17)

p α , min ≤ p α ≤ p α , max ∀ α ∈ G n (5.18)

G T α , min ≤ G T α ≤ G T α , max ∀ α ∈ G p (5.19)

R com
α , min

R com
α

R com
α , max

≤ ≤ ∀ ∈

α G c (5.20)

G chp
Dα , min

G chp
Dα

G chp
Dα , max

≤ ≤ ∀ α ∈ G n (5.21)

T store
Dα , min

T store
Dα

T store
Dα , max

≤ ≤ ∀ α ∈ G n (5.22)

T store
Gα , min

T store
Gα

T store
Gα , max

≤ ≤ ∀ α ∈ G n (5.23)

TSOC store
α

≥ 0 ∀ α ∈ G n (5.24)