Time-coordinated optimal power flow for energy service networks - Modelling Distributed Energy Resources in Energy Service Networks - page 98

objectives. For instance, it could be a bi-objective - cost of spot energy and cost of
carbon emissions - optimisation that focuses on minimising both functions.

5.3 Mathematical TCOPF formulation

This section details the optimisation formulations and the manner in which to state
the problems concerned with this research. As previously mentioned, the impacts of
embedded technologies on optimal operation of energy service networks can cover
various issues such as power delivery, conversion and storage problems. Thus, based
on the objective function selected, the TCOPF formulation 'determines the outcome
of an optimal operating strategy for interconnected electrical and natural gas systems
with DER technologies, thus giving a complete picture of the daily steady-state con-
ditions of the whole energy system, while meeting all security constraints for proper
operation'.

5.3.1 Objective function formulations
The objective function selected by the TCOPF tool will drive the system variables in
order to fulfil a particular goal while calculating the load flows in the networks and
the operating values of the control mechanisms. As it can be inferred, the optimal
solution is sensitivity, thus depending on many factors such as spot prices and the
ability dispatch DERs in particular time intervals.
Based on the proposed operating strategies suggested in section 5.2, the
mathematical formulations are subject to encapsulate all the time intervals being
analysed during the problem's time horizon, hence the integrated gas and electric
TCOPF can be stated as discussed in the following sections.

5.3.1.1 For plug-and-forget scenario

nG c

nβ

nP t

λ cm ·

Dα , β +

λ cm ) · | 1 G com min ( 1 − t | α , β − (5.1)

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 c is the number of compressors in the natural gas network
nP t is the number of OLTCs in the electrical network
G com
Dα , β

where

⎩

is the natural gas demand of the compressor at node α in time β

| α , β is the tap magnitude of the OLTC at node α in time β
λ cm is the control mechanism weighting factor
Note : The tap values are constrained for this formulation and cannot be less
than 1.

| t