Main Problems
Fuel Cost Minimization
Because of the long distances among the supply and consumption nodes in the natural gas network, many compressor stations are used along the route to set the natural gas pressure throughout the pipeline systems. By considering the tremendous amount of transported gas in pipelines per day, minimizing the gas consumed by compressors is critically important. Global optimization can be lead to a 20% saving in fuels consumed by compressor stations [21]. To date, a great deal of research has been performed to develop new techniques to decrease the consumed fuel of consumption in compressor stations.
In the problem of fuel cost minimization, the decision variables are pressure dropped at each node of the network, flow rate at each pipeline, and the number of units operating within each compressor station 122]. In general, defined problems for the fuel cost minimization differ from each other because of some assumptions and methodologies applied by researchers to determine the value of variables in the optimal case. In a number of previous works, to avoid or decrease the nonlinearity of the model, the number of compressor units in each compressor station has been considered as fixed. In addition, some of the developed models have been simplified by considering only one unit for each compressor station, whereas compressor stations usually have multiple units. Balancing or not balancing the network is another matter. If the network is assumed balanced, then in each node of the network the sum of all net flows will equal zero. This means there are no differences between the total output flows of supply nodes and input flows to demand nodes [23]. Other assumptions may be related to a steady state or a transient state of the model or topology of the networks, which are referred to the problem statement. In addition, regarding the methodology, in some research if there is more than one variable, the values of variables are achieved simultaneously. In contrast, some of the researchers have proposed methodologies based on multistage iterative procedures. Rios-Mercado et al. [6] developed a two-stage procedure to optimize the fuel cost minimization in such a way that gas flow variables were fixed at the first stage and optimal pressure variables were found via DP. Then the pressure variables were considered fixed at the second stage, and a set of flow variables was achieved, taking the network topology into consideration to improve the objective function. Some authors relax the nonconvex and nonlinear models by relaxation techniques because generally such problems are very difficult to solve. For example, for fuel cost minimization, Wu et al. [8] developed a mathematical model with steady-state assumptions and a nonconvex feasible domain; a nonlinear, nonconvex, and discontinuous fuel function; and a nonconvex set of pipeline flow equations. To solve the developed model, it was relaxed in two ways. First, the fue cost objective function is relaxed; second, nonconvex and nonlinear compressor domains are relaxed. In their procedure solution, the optimal solution of the origi" nal problems involves upper bound, and the optimum solution of the relaxed pr0' blems is lower bound. The general formation of fuel cost minimization in
natural gas network, considered to be the most applied variables including flow rate and pressure, has been presented by Rios-Mercado [3]. Another research that investigated the fuel cost minimization of compressor stations belongs to Mora and Ulieru [24]. It focused on developing a new method to achieve a near optimal feasible solution in a shorter reasonable time for minimizing the amount of natural gas consumed by the compressor station units.
Some of the latest papers on minimizing the fuel costs of compressor stations and variables that have been used to achieve optimal values are cited in Table 19.3.
Investment Cost Optimization
| (19.4) |
Carvalho and Ferreira [15] presented the general form of optimizing investment policies, which have been adapted to the information structure of scenarios, based on the minimum cost as follows: Minimize fX£/)subject to
UeY
U(s)efis
ScS
where F is a function of operational and investment costs, U presents a policy, and Y is universe of not opposing decision policies; the universe of admissible policies for the 5th scenario has been presented in f?v; and, finally, S illustrates a set of available scenarios.
To make an investment strategy for minimizing the risk and increasing profits, Davidson et al. [10] developed a dynamic model integrated with a geographical
Table 19.3 Common Decision Variables in Fuel Cost Minimization Problems Author Mass Flow Rates Suction Pressure and Number of