Sets and Parameters - iea-etsap

2 Sets
Sets are used in TIMES to group elements or combinations of elements with the purpose of
specifying qualitative characteristics of the energy system. One can distinguish between onedimensional
and multi-dimensional sets. The former sets contain single elements, e.g. the set
prc contains all processes of the model, while the elements of multi-dimensional sets are a
combination of one-dimensional sets. An example for a multi-dimensional set is the set top,
which specifies for a process the commodities entering and leaving that process.
Two types of sets are employed in the TIMES framework: user input sets and internal sets.
User input sets are created by the user, and used to describe qualitative information and
characteristics of the depicted energy system. One can distinguish the following functions
associated with user input sets:
• definition of the elements or building blocks of the energy system model (i.e. regions,
processes, commodities),
• definition of the time horizon and the sub-annual time resolution,
• definition of special characteristics of the elements of the energy system.
In addition to these user sets, TIMES also generates its own internal sets. Internal sets
serve to both ensure proper exception handling (e.g., from what date is a technology available,
or in which time-slices is a technology permitted to operate), as well as sometimes just to
improve the performance or smooth the complexity of the actual model code.
In the following sections, the user input sets and the internal sets will be presented. A
special type of set is an one-dimensional set, also called index, which is needed to build multidimensional
sets or parameters. At the highest level of the one-dimensional sets are the master
or “domain” sets that define the comprehensive list of elements (e.g., the main building
blocks of the reference energy system such as the processes and commodities in all regions)
permitted at all other levels, with which GAMS performs complete domain checking, helping
to automatically ensure the correctness of set definition (for instance, if the process name used
in a parameter is not spelled correctly, GAMS will issue a warning). Therefore, before
elaborating on the various sets, the indexes used in TIMES are discussed.
2.1 Indexes (One-dimensional sets)
Indexes (also called one-dimensional sets) contain in most cases the different elements of the
energy model. A list of all indexes used in TIMES is given in Table 2. Examples of indexes
are the set prc containing all processes, the set c containing all commodities or the set all_reg
containing all regions of the model. Some of the one-dimensional sets are subsets of another
one-dimensional set, e.g., the set r comprising the so-called internal model regions is a subset
of the set all_reg which in addition also contains the so-called external model regions 2 . To
express that the set r depends on the set all_reg, the master set all_reg is put in brackets after
the set name r: r(all_r).
The set cg comprises all commodity groups 3 . Each commodity c is considered as a
commodity group with only one element the commodity itself. Thus the commodity set c is a
subset of the commodity group set cg.
Apart from indexes that are under user control, some indexes have fixed elements to serve
as indicators within sets and parameters and should not be modified by the user (Table 1). The
only exception to this rule is the set prc_grp: while the process groups IRE, NST, PRV,
2 The meaning and the role of internal and external regions is discussed in Section 2.2.
3 See Section 2.2.1 for a more in-depth treatment of commodity groups.
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