Time-coordinated optimal power flow for energy service networks - Modelling Distributed Energy Resources in Energy Service Networks - page 99

Expression (5.1) describes the criteria that reduce the usage of both compressor
stations and on-load tap-changers (refer to subsection 5.2.1 for a greater description).

5.3.1.2 For fuel cost minimisation

⎡ ⎤

nβ nG g nP g

⎣ ⎦

min G Fα , β + P Fα , β (5.2)

β = 1 α = 1 α = 1

⎧
⎨
⎩

α is the unit index being analysed
β is the time interval being analysed
nβ is the number of time intervals into which the full period is divided
nG g is the number of supply points in the natural gas network
nP g is the number of supply points in the electrical network
G Fα , β is the natural gas fuel cost at supply point α in time β
P Fα , β is the electrical fuel cost at node α in time β
Note : The electric fuel costs P F is the sum of the costs from its supply point
and the DERs allocated in each node; this implies the cuadratic costs from offering
micro-CHPs and PHEV V2G services are added to the cuadratic supply point cost
function.
Term (5.2) aims at reducing the total cost of fuel consumption by considering
the natural gas delivery costs and the costs from all the units that contribute with
active power generation measured in monetary units (refer to subsection 5.2.2 for
more information).

where

5.3.1.3 For energy loss minimisation

⎡ ⎤

nG p

nβ nP l

⎣ ⎦

min G Lα , β + P Lα , β (5.3)

β = 1 α = 1 α = 1

⎧
⎨ α is the unit index being analysed

β is the time interval being analysed
nβ is the number of time intervals into which the full period is divided
nG p is the number of pipes in the natural gas network
nP l is the number of lines in the electrical network
G Lα , β is the power loss incurred in the natural gas network at pipe α in
time β
P Lα , β is the power loss incurred in the electrical network at line α in time β
Equation (5.3) states the minimum loss criterion that reduces the energy losses
occurring on all individual pipelines and cable lines present in the energy service
networks measured in watts (refer to subsection 5.2.3 for further details).

where

⎩