Formulating

A number of useful notations and concepts are common in most of the developed models dealing with network optimization in the natural gas industry and can be useful to researchers who want to start modeling. As mentioned previously, the nat­ural gas network is composed of pipelines and compressor stations as arcs and nodes. Several general indices and parameters will be presented here and are depicted in Figure 19.3. For more details, see Rios-Mercado [3]. Indices:

ij: index of nodes, i.jeN = {\,...,\N\] к: index of compressor stations, keC = {1,..., |C|}

m: index of units (turbocompressor) of compressor station, me U = {1.......... |£/|}

/: pipelines, leL = {I,..., |L|} n: nodes

с: compressor stations

^>0 o₍ = 0 Qj = 0

P,

Supply node

Figure 19.3 Basic notations for planning models in natural gas networks.

Figure 19.4 The behavior of compressor station units.

Parameters:

P,j. associate capacity between /th and jlh nodes

С if. transshipment cost for each unit of natural gas between i th and y'th nodes Variables:

Pj\ the gas pressure at node /

Xif. the mass flow rate between nodes i and j

a,-: the net flow through the node i

{1, if unit m of compressor station к must be opened 0, if unit m of compressor station к must be closed

Considering the above notations, S_a = LuС in a manner that LnС = 0. In some problem areas, the nonlinear behaviors of compressor stations units (tur- bocompressors) are considered. Figure 19.4 presents the positions of turbocompres- sors in a compressor station. Turning these turbocompressors on and off is one of the main decisions that have to be taken in the natural gas network [3|.