The main aim of simulation programs is to study the behavior of gas pipe networks in certain conditions. Solving a specified set of differential equations describing transient (unsteady) flow in a gas pipeline for the adopted parameters of load and supply will help us find out the value of pressure or flow rate at selected points or along selected sections of the network. Transient gas flow may be described by a set of simple or partial differential equations classified as hyperbolic or parabolic. Derivation of the mathematical model of transient gas flow involves certain simplifications, of which one-dimensional flow is most important. It is very important to determine the conditions of pipeline/transmission network operation in which the hyperbolic model and the parabolic model, respectively, should be used. Parabolic models can be solved numerically in a much simpler way and can be used to design simulation programs which allow us to calculate the network of any structure and any number of non-pipe elements. In some conditions, however, they describe the changes occurring in the network less accurately than hyperbolic models do. The need for analysis, control, and optimization of gas flows in high-pressure gas pipelines with complex structure increases significantly. Very often, the time allowed for analysis and making operational decisions is limited. Therefore, efficient models of unsteady gas flows and high-speed algorithms are essential.

The main goal of this paper is to prove that bi-objective optimization of high-pressure gas networks ensures grater system efficiency than scalar optimization. The proposed algorithm searches for a trade-off between minimization of the running costs of compressors and maximization of gas networks capacity (security of gas supply to customers). The bi-criteria algorithm was developed using a gradient projection method to solve the nonlinear constrained optimization problem, and a hierarchical vector optimization method. To prove the correctness of the algorithm, three existing networks have been solved. A comparison between the scalar optimization and bi-criteria optimization results confirmed the advantages of the bi-criteria optimization approach.

The major optimization problem of the gas transmission system is to determine how to operate the compressors in a network to deliver a given flow within the pressure bounds while using minimum compressor power (minimum fuel consumption or maximum network efficiency). Minimization of fuel usage is a major objective to control gas transmission costs. This is one of the problems that has received most of the attention from both practitioners and researchers because of its economic impact. The article describes the algorithm of steady-state optimization of a high-pressure gas network of any structure that minimizes the operating cost of compressors. The developed algorithm uses the “sequential quadratic programming (SQP)” method. The tests carried out on the real network segment confirmed the correctness of the developed algorithm and, at the same time, proved its computational efficiency. Computational results obtained with the SQP method demonstrate the viability of this approach.