Time-coordinated optimal power flow for energy service networks - Modelling Distributed Energy Resources in Energy Service Networks - page 104

As it can be seen, the above global constraints focus on energy storage bal-
ance of thermal stores and electric vehicles. Editing the limits of snapshots or
global terms allows us the flexibility to model various scenarios, thus increasing
greatly the applications of the tool. Furthermore, if required more constraints can
be added to enhance the modelling framework, for example if photo-voltaic gener-
ation is considered. Likewise, the single-day analysis shown in Chapter 6 could be
expanded to consider longer time periods ( e.g. weekly).

5.3.3 TCOPF problem and solution characteristics
As mentioned previously, the TCOPF problem is programmed, executed and solved
by performing a multi-period non-linear optimisation in the gPROMS TM software
[209]. In order for the optimisation problem to be executed in this particular soft-
ware, various files in the gPROMS TM project folder must be specified; these files are:

Model entity : Allows the user to state all the variables and parameters required
in solving the integrated load flow problem, in other words the core mathemati-
cal expressions are developed in this space. Additionally, the set of equations
that compose the energy service networks, control mechanisms, conversion
technologies and storage systems are coded here;

●

Process entity : Includes all the input data ( e.g. node classification, connectiv-
ity matrices, load data, weight factors, cost function coefficients, etc.), thus
allowing the user to assign values to parameters and control variables;

●

Optimisation entity : Permits the user to define the objective function while
also allowing to establish the initial control variable values, as well as defin-
ing lower bound and upper bound of the inequality control variables. Similarly,
the values for equality constrained variables are determined in this file.

●

Once gPROMS TM solves the TCOPF problem at hand, a summary report is
provided, describing the following results:

The time consumed during the optimisation solution process;

●

The final value of the objective function;

●

Details in which time intervals constraint limits are reached;

●

The values of the variables for each time interval for which constraints were
specified;

●

The values of the selected control variables for each time interval.

●

Aside from the 'hard output data' provided by the TCOPF tool which needs to
be analysed in depth, it is important to mention that due to the non-linear characteris-
tics of the problem the Karush, Kuhn, Tucker (KKT) optimality conditions apply for
this peculiar optimisation (see Appendix G). This circumstance has been exploited
in this work just as it is applicable when a typical OPF problem is resolved using
Newton's method (see Appendix H).
Although not initially self-evident, the economic functions concerning fuel cost
provide important data by obtaining the resulting marginal objective values of its