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Table S. 1 presents the statistics of the five test problems. The Linking rows and columns
are those constraints and variables which have nonzero enaies in the matrices L, when the
original problerns are decomposed into four parts. The parenthesis in "Linking Cols (or "Linking
Rows") shows the ratio of the number of linking columns (or rows) to the number of columns
(or rows).
Problems
TEP
NAEP
#of
regions
Iscenarios
4
7
Table 5.1 Statistics of the test problems
~olumns
321
3949
~ows
165
2325
~iakiag
Cols.
120 (37%)
234 (5.9%)
Linking
Rows
Nonzeroes
40 (24%) 841
234 (9.6%) 12033
The linking variables in TEP are 'LFLOWS (R.RR.T)' representing the arnount of
electricity that flows from region R to region RR at time T, and the Iinking consaaints are the
elecuicity demand consuaints in each region R at time T, 'LTRADE(R,T)'. NAEP has 7 regions
of Westem Canada (WC), Eastern Canada (EC), Westem US. 0, Northern U.S. (NU),
Eastern U.S. (EU). Southem U.S. (SU) and the Rest of the World (RW). The 7 regions were
muped into 4 pans: WC, EC and RW. WU and NU, and EU and SU. The linking variables and
C
consmints of NAEP are those representing energy flows arnong the 4 parts. HEPGl is fomiulated
using rime index and scenario index as shown in Figure 5.5, so it cm be divided into the