Modelling electric vehicle mobility in energy service networks - Modelling Distributed Energy Resources in Energy Service Networks - page 150

owner or utility companies. The proposed objective function for PHEV charging via
cost minimisation can be stated as follows:

7.2.2.1 For PHEV charging cost minimisation scenario

min C phev + C dno minPHEV costs = (7.1)

⎡ ⎤

nP g nP g

nβ

⎣ ⎦

minC phev = min P Eα , β + P Pα , β (7.2)

= = =

β 1 α 1 α 1

⎡ ⎤

nP g

nβ

⎣ ⎦

minC dno = min P Fα , β (7.3)

β = 1 α = 1

Equation (7.1) is composed from calculating electricity costs from both spot
and carbon markets (7.2) and the electricity costs from energy delivery (7.3), there-
fore making sure the management of the whole energy system is optimised from an
economic perspective. This formulation establishes the priority of charging PHEVs
when it is most beneficial to vehicle owners, the grid and the environment.
The equality and inequality constraints of the formulation are responsible for
defining the region of feasible solution for the energy system being analysed. Con-
straints employed are similar to the ones described in Chapter 5 for electrical net-
works and for embedded devices, minus the relevant terms that can be omitted
since gas networks, CHPs and V2G flows are not considered in this formulation.
Consequently, snapshot and global constraints are included in this formulation.
The snapshot constraints are stated for each time period β :

P Gα − P Dα − P T α = 0 ∀ α ∈ P n (7.4)

Q Gα − Q Dα − Q T α = 0 ∀ α ∈ P n (7.5)

V α , min ≤ V α ≤ V α , max ∀ α ∈ P n (7.6)

| | α , min ≤ | | α ≤ | | α , max ∀ ∈

t t t α P t (7.7)

P phev
Dα , min

P phev
Dα

P phev
Dα , max

≤ ≤ ∀ α ∈ P n (7.8)

EVSOC store
α

≥ 0 ∀ α ∈ P n (7.9)

The global constraints are subject to the complete period being analysed:

P phev
Dα , β

hr total
nβ

G 2 V store
α , β

− · = 0 ∀ α ∈ P n , ∀ β ∈ nβ (7.10)

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 network node for
each time interval. Expression (7.6) represents voltage limit at nodes, while (7.7)
specifies the allowed range of operation for on-load tap-changers (OLTCs). Equation
(7.8) details the flexible PHEV demand permitted at each node-akeyconstraint