Sets and Parameters - iea-etsap

2.2.4 Overview of all user input sets
All the input sets which are under user control in TIMES are listed in Table 4. For a few sets
default settings exist that are applied if no user input information is given. Set names starting
with the prefix ‘com_’ are associated with commodities, the prefix ‘prc_’ denotes process
information and the prefix ‘uc_’ is reserved for sets related to user constraints. Column 3 of
Table 3 is a description of each set. In some cases (especially for complex sets), two
(equivalent) descriptions may be given, the first in general terms, followed by a more precise
description within square brackets, given in terms of n-tuples of indices.
Remark
Set are used in basically two ways:
- as the domain over which summations must be effected in some mathematical
expression, or
- as the domain over which a particular expression or constraint must be
enumerated (replicated)
In the case of n-dimensional sets, some indexes may be used for enumeration and others for
summation. In each such situation, the distinction between the two uses of the indexes is
made clear by the way each index is used in the expression.
An example will illustrate this important point: consider the 4-dimensional set top, having
indexes r,p,c,io (see table 3 for its precise description). If some quantity A(r,p,c,io) must be
enumerated for all values of the third index (c=commodity) and of the last index
(io=orientation), but summed over all processes (p) and regions (r), this will be
mathematically denoted:
EXPRESSION1
∑
c, io
= A(
r,
p,
c,
io)
r,
p,
c,
io∈top
It is thus understood from the indexes listed in the name of the expression (c,io), that these
two indexes are being enumerated, and thus, by deduction, only r and p are being summed
upon. Thus the expression calculates the total of A for each commodity c, in each direction io
(‘IN’ and ‘OUT’), summed over all processes and regions.
Another example illustrates the case of nested summations, where index r is enumerated in
the inner summation, but is summed upon in the outer summation. Again here, the expression
is made unambiguous by observing the positions of the different indexes (for instance, the
outer summation is done on the r index)
EXPRESSION2
=
∑
B
∑
A r
c, io
( ) ( , )
r,
p,
c,
io∈top
p
r
p
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