Subnetworks

Transmission

Some of the problems of natural gas, which have been formulated mathematically, obey the general frame of mathematical models. This means each mathematical model includes an objective function, some constraints, and a number of variables in such a manner that the differences among these components separate developed models.

Chung et al. [17] developed a fuzzy mathematical model that considered more than one objective to solve the planning problem of transmission networks, which tries to optimize investment cost, reliability, and environmental impacts. The developed model was solved through a GA, and efficient results were achieved. To minimize the operational cost of natural gas networks, one of the most critical operations studied by some researchers is the compressor selection. This problem is important because it is associated with the cost of turning compressors on and off, which is a considerable part of total operation cost. Uraikul et al. [5] P^re" sented the compressor selection problem in the form of a mixed-integer linear programming (MILP) and by considering three types of the cost including operat­ing cost, start, and stop penalties. The mentioned penalties refer to the cost of turning the compressors on and off in such a way that the energy used for start­ing a compressor is more than the required energy for stopping it. To escap^e from being trapped in this model into nonlinearity, some types of cost, which are based on time or have uncertainties such as maintenance cost, have not been con­sidered in the developed model. Among researchers who have focused on the nat­ural gas network optimization, only a few have adopted the difficulties of cyclic topologies and have not simplified the problem to the linear or tree structure. The research work of Borraz-Sanchez and Rios-Mercado [4] is in this group. They presented the problem of optimal operation of a natural gas pipeline system in cyclic topologies through combining a nonsequential DP approach within a Tabu search (TS) technique through four main phases: preprocessing, finding an initial feasible flow, finding an optimal set of pressure values, and flow modifications. What makes this work different from noncyclic research is flow modification, which was done in noncyclic approaches by determining a unique set of optimal flow values in the preprocessing phase. What makes this work a little far from reality are its steady-state assumptions.

Kabirian and Hemmati [16] developed a nonlinear optimization mathematical model for formulating a strategic planning model to find the best feasible develop­ment plan for natural gas transmission networks. The objective of the developed model was determining the type, location, and installation schedule of pipelines and compressor stations over a long planning horizon with the goal of least cost and with a consideration of network constraints. To achieve optimal or near opti­mal plans, an algorithm based on random searches was applied. Mahlke et al. [20] formulated the problem of transient technical optimization in the form of a mixed- integer nonlinear problem with the aim of minimizing the fuel gas consumption. Because of difficulties with the time-dependent natural gas transmission network, they limited their work to achieve a good feasible solution in a suitable run time through a simulated annealing (SA).

Distribution

In spite of the simplicity of distribution networks and the relatively low importance the transmission network from the perspective of design cost, it is very critical to satisfy costumers. A considerable number of optimization methods in the form mathematical models have been developed for distribution networking to find the best design and optimal operation along the pipelines. Among reviewed papers, Carvalho and Ferreira [15] tried to develop a mathematical model for large-scale distribution networks to make robust expansion on variable conditions and ^under deregulation. Wu et al. [8] considered a nonlinear network and proposed the Problem of minimizing the investment cost through the distribution network under steady-state assumptions. They developed a model by introducing new variable and converting the primal problem to a nonconvex constrained problem. Therefore, by escaping from the available difficulties in solving the primal nonsmooth and non- convex problem of designing a distributed layout, a global optimization approach ^was achieved. Moreover, Davidson et al. [10] also focused on investment planning ¹¹¹ the natural gas distribution networks.