Abstract
Since the gas transportation system of Ukraine has excessive capacity, it becomes a relevant task to choose such rotation frequencies of centrifugal compressors of the gas compressor units that would minimize the overall consumption of fuel gas on pumping. Calculation of the volumetric productivity of a centrifugal compressor by the pressure differential on confuser produces an error of tens of percent due to the inaccuracy of measurement. Thus, it is advisable to consider volumetric productivity as a fuzzy magnitude with a triangular shape of the membership that makes it possible to build an adequate mathematical model of the process of natural gas compression. A triangular shape of the membership function is inconvenient when used in order to solve the problem on the optimal control over the process of natural gas compression. That is why, in the present work, it is proposed to approximate it by a Gaussian membership function. This allowed us to state the optimization problem in terms of fuzzy magnitudes and, on this basis, to develop effective methods for solving it with consideration of constraints for the controlling actions. In order to obtain empirical models, based on the results of observing the work of GPU, we applied a method of synthesis of empirical models on the basis of genetic algorithms. We developed algorithmic provision and software in the MATLAB environment and solved the problem of optimal control, which made it possible to determine rotation frequencies of the rotors of centrifugal compressors of natural gas, at which the total costs of the fuel gas for the natural gas compression are minimal. Since technological parameters of the gas pumping unit change over time, there appears a need to recalculate the model's parameters in order to solve the optimization problem on the process of natural gas compression. Determination of frequency of recalculation of the model's parameters is an unsolved scientific problem at present and it is a promising task for further research.
Highlights
A network of gas pipelines that run through the territory of Ukraine ensures continuous supply of gas both to enterprises of the country and for export to the countries of Central and Eastern Europe
The author rightly indicates that the problem on stabilizing the performance of compressors is rather controversial, while achieving the lowest consumption of fuel gas requires a certain technique to distribute the load on working units, the model presented does not account for the fuzziness of technological parameters
Performance efficiency of centrifugal compressors are considered as fuzzy magnitudes with triangular membership functions, approximated by exponential functions, with their parameters calculated, which allowed us to formalize the problem on the optimal control over the process of natural gas compression taking into account the fuzziness in the productivity of compressors and constraints for controlling actions
Summary
A network of gas pipelines that run through the territory of Ukraine ensures continuous supply of gas both to enterprises of the country and for export to the countries of Central and Eastern Europe. As present [1], the total length of gas pipelines reaches 34.8 thousand km. The estimated through-put capacity of gas transportation system when entering Ukraine is 288 billion m3 per year (800 million m3 per day). Design capacity of the gas transportation system (GTS) of Ukraine in the direction of countries of Western Europe and Turkey is 142 billion cubic meters per year while the actual volume of transit in 2014 was 60 billion cubic meters [2]. The Ukrainian GTS has excessive capacity, which makes it a relevant task to choose the number of parallel working units at each compressor station and their rotation frequency, based on the selected criteria for performance efficiency of the groups of parallel units
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