The principles of formation of mathematical models for the choice of rational modes of operation of complex gas transmission systems with multi-shop compressor stations equipped with different types of gas pumping units are given. It is proposed to optimize the modes on the basis of the use of energy-economic characteristics of the gas transmission system, which are built on the basis of the parameters of the gas transmission system taking into account the technical condition of its elements and economic performance for a certain period. This approach ensures compliance with the principle of operation of the gas transmission system in the field of permissible modes and maximum energy consumption on the one hand and minimizing the cost of gas transportation on the other. If it is possible to use the actual data on the actual technical condition of the equipment and gas pipelines of the system, this method allows to evaluate and take into account in the further procedure the parameters of gas supply reliability. An important requirement for the optimization procedure is the stability of energy efficiency characteristics, which means that in any practical changes of non-basic regime parameters, the energy efficiency characteristic should not be shifted beyond the allowable error. The problem of optimal load distribution in a complex gas transmission system is considered based on their minimum total energy costs at a given volume of gas supply and other planning and technological constraints. The task of optimizing a multiparameter object is to find the extremum of the goal function by selecting a vector of control effects that would satisfy the constraint. The distribution of loads at the highest hierarchy for the system of main gas pipelines is obtained by finding the minimum total cost of gas compression for each pipeline. The method of construction of such characteristics and the procedure of establishing their stability are shown, which allows the formalization of the construction of the criterion dependence of the regime parameters on energy economic factors. The stated basic decisions allow to formalize the function of the purpose for a choice of a rational mode of operation of gas transmission system in the conditions of its incomplete loading.

The problem of choosing the rational control of non-stationary processes in complex gas transmission systems caused by instability of loading in the conditions of limited volume of gas transit is considered. Control effects in such conditions must ensure the transfer of the object from one point of the functional phase space to another, maintaining its specified state under different perturbing effects while fulfilling the condition of minimum total costs. The results of analytical studies of the nature of the flow and duration of non-stationary processes in complex gas transmission systems caused by the exclusion from the mode of operation of individual compressor stations are presented. A mathematical model of the gas pipeline is constructed taking into account the influence of compressor stations on the basis of classical equations of gas flow energy and continuity using the functions of the Dirac source. The implementation of the created mathematical model by applying the integral Fourier and Laplace transforms allowed to obtain in analytical form the dependence that reflects the law of fluctuations in time of mass flow of gas in the initial and final cross section of the pipeline. The constructed dependences of the gas transmission system productivity trend at its beginning and end showed the influence of compressor station placement in the gas transmission system, in particular its serial number on the route number, on the nature of the nonstationary process caused by its shutdown, in particular on the nonstationarity duration. These tasks are the main tasks of operational optimal management of gas transport through main gas pipelines, which allows to solve the problem of uninterrupted supply of gas consumers. For optimal control problems, an algorithm of the method of step variations is proposed, according to which variations of inlet pressure and flow are localized, ie taken as constants at this step, and change of control function mainly affects only outlet pressure. systems, especially if they are not fully loaded.