Вирішення оптимізаційної задачі керування роботою газоперекачувальних агрегатів в умовах невизначеності

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. Решена задача оптимального управления группы параллельно работающих газоперекачивающих агрегатов при минимизации общих затрат на эксплуатацию нагнетателей при условии ограничения частоты вращения нагнетателя, температуры газа на выходе из нагнетателя и температуры продуктов сгорания на выходе турбины низкого давления. Учтены нечеткость производительности нагнетателя вызванная большой погрешностью измеренияРозв’язано задачу оптимального керування групи паралельно працюючих газоперекачувальних агрегатів при мінімізації загальних витрат на експлуатацію нагнітачів за умови обмеження частоти обертання нагнітача, температури газу на виході із нагнітача та температури продуктів згорання на виході турбіни низького тиску. Враховано нечіткість продуктивності нагнітача спричинена великою похибкою вимірюванн

Solution of the Optimization Problem on the Control Over Operation of Gas Pumping Units Under Fuzzy Conditions

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