Investigations of Small Oscillations in Complex Electric Systems
Keywords:
electric system, model, system decomposition, pole loci, modeling
Abstract
The mathematical model of a controlled multimachine electric power system in matrix form is developed. The model is based on space state equations and on using the system nesting technology. By using the obtained mathematical model, it is possible to investigate small-signal stability of a controlled complex electric system through determining the eigenvalues of the system dynamics matrix. The method of decomposing the complex electric system initial model by means of semi-orthogonal matrix zero dividers is applied for shifting the system poles to the desired positions.
References
Anderson P.M., Fouad A.A. Power system control and stability, Second edition, Willey-Interscience A John Wiley & Sons Inc, USA, 2002, 664 p.
Мисриханов М.Ш., Рябченко В.Н. Размещение полюсов при управлении большой энергетической системой. — Автоматика и телемеханика, 2011, вып. 10, с. 129—153.
Буков В.Н. Вложение систем. Аналитический подход к анализу и синтезу матричных систем. Калуга: Изд-во Н.Ф. Бочкаревой, 2006, 720 с.
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Веников В.А. Переходные электромеханические процессы в электрических системах. М.: Высшая школа, 1985, 537 c.
Klos A. Mathematical Models of Electrical Network Systems: Theory and Applications - An Introduction. Springer International Publishing AG, 2017, 108 p.
Мисриханов М.Ш. Инвариантное управление многомерными системами. М.: Наука, 2007, 284 с.
Abdellatif B.M. Stability with respect to part of the variables of nonlinear Caputo fractional differential equations. — Mathematical Communications, 2018, 23, pp. 119—126.
Gotman V.I. Common algorithm of static stability estimation and computation of steady states of power systems. — Power engineering, 2007, vol. 311, No. 4, pp. 127—130.
Holali K.D., Efimov D., Richard J.-P. Interval Observers for Linear Impulsive Systems. — 10th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2016), Monterey, California, United States, 2016, pp. 867—872.
Kovalenko S., Sauhats A., Zicmane I., Utans A. New Methods and Approaches for Monitoring and Control of Complex Electrical Power Systems Stability. — IEEE 16th Intern. Conf. on Environment and Electrical Engineering (EEEIC 2016), 2016, pp. 270-275.
Makhmudov T. Technology of embedding systems as a method for studying the dynamic regimes of complex electric systems. - American Journal of Energy and Power Engineering, 2018, vol. 5, No. 2, pp. 15-19.
Автоматизация управления энергообъединениями/Под ред. С.А. Совалова. М.: Энергия, 1979, 431 с.
Irwanto M. et al. Improvement of Dynamic Electrical Power System Stability Using Riccati Matrix Method. — Applied Mechanics and Materials, 2015, vol. 793, pp. 29—33.
Фазылов Х.Ф., Насыров Т.Х. Установившиеся режимы электроэнергетических систем и их оптимизация. Ташкент: Молия, 1999, 370 с.
Allaev K.R., Makhmudov T.F. Analysis of Small Oscillations in Complex Electric Power Systems. — Engineering (USA), 2018, vol. 10, No. 5, pp. 253—261.
Мисриханов М.Ш. Классические и новые методы анализа многомерных динамических систем. M.: Энергоатомиздат, 2004, 566 с.
Андреюк В.А. Использование абсолютного угла для управления переходными режимами энергосистемы/Под ред. Л.А. Кощеева. — Изв. НИИ постоянного тока, 2011, № 65, с. 27-42.
Андреюк В.А., Асанбаев Ю.А., Сказываева Н.С. Статическая устойчивость энергосистемы, регулируемой по абсолютному углу. — Изв. НИИ постоянного тока, 1997, № 56, с. 146-156.
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Anderson P.M., Fouad A.A. Power system control and stability, Second edition, Willey-Interscience A John Wiley & Sons Inc, USA, 2002, 664 p.
Misrikhanov M.Sh., Ryabchenko V.N. Avtomatika i telemekhanika — in Russ. (Automation and telemekhanics), 2011, iss. 10, pp. 129—153.
Bukov V.N. Vlozheniye sistem. Analiticheskiy podkhod k analizu i sintezu matrichnykh sistem (An analytical approach to analysis and synthesis of matrix systems). Kaluga, Publ. of N.F. Bochkarevoy, 2006, 720 p.
Allayev K.R., Mirzabaev A.M. Matrichnye metody analiza malykh kolebaniy elektricheskikh sistem (Matrix methods of analysis of small vibrations of the electric systems). Tashkent: Fan va texnologiya, 2016, 432 p.
Venikov V.A. Perekhodnye elektromekhanicheskiye protsessy v elektricheskikh sistemakh (Transitional electromechanical processes in electrical systems). Moscow, Vysshaya shkola, 1985, 537 p.
Klos A. Mathematical Models of Electrical Network Systems: Theory and Applications. —.An Introduction. Springer International Publishing AG, 2017, 108 p.
Misrikhanov M.Sh. Invariantnoe upravleniye mnogomernymi sistemami (Invariant management by the multidimensional systems). Moscow, Nauka, 2007, 284 p.
Abdellatif B.M. Stability with respect to part of the variables of nonlinear Caputo fractional differential equations. — Mathematical Communications, 2018, 23, pp. 119—126.
Gotman V.I. Common algorithm of static stability estimation and computation of steady states of power systems. — Power engineering, 2007, vol. 311, No. 4, pp. 127—130.
Holali K.D., Efimov D., Richard J.-P. Interval Observers for Linear Impulsive Systems. — 10th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2016), Monterey, California, United States, 2016, pp. 867—872.
Kovalenko S., Sauhats A., Zicmane I., Utans A. New Methods and Approaches for Monitoring and Control of Complex Electrical Power Systems Stability. — IEEE 16th Intern. Conf. on Environment and Electrical Engineering (EEEIC 2016), 2016, pp. 270—275.
Makhmudov T. Technology of embedding systems as a method for studying the dynamic regimes of complex electric systems. — American Journal of Energy and Power Engineering, 2018, vol. 5, No. 2, pp. 15—19.
Avtomatizatsiya upravleniya energoob’yedineniyami/Pod red. S.A. Sovalova (Automation of management of energyassosiations/Edit. by S.A. Sovalov). Moscow, Nauka, 1979, 431 p.
Irwanto M. et al. Improvement of Dynamic Electrical Power System Stability Using Riccati Matrix Method. — Applied Mechanics and Materials, 2015, vol. 793, pp. 29—33.
Fazylov Kh.F., Nasyrov T.Kh. Ustanovivshiyesya rezhimy elektroenergeticheskikh sistem i ikh optimizatsiya (Set modes of the electroenergy systems and their optimization). Tashkent, Moliya, 1999, 370 p.
Allaev K.R., Makhmudov T.F. Analysis of Small Oscillations in Complex Electric Power Systems. — Engineering (USA), 2018, vol. 10, No. 5, pp. 253—261.
Misrikhanov M.Sh. Klassicheskiye i novye methody analiza mnogomernykh dinamicheskikh sistem (Classic and new methods for analyzing multidimensional dynamic systems). Moscow, Energoatomizdat, 2004, 566 p.
Andreyuk V.A. Izv. NIIpostoyannogo toka — in Russ. (News of the Research Institute of Direct-Current), 2011, No. 65, pp. 27—42.
Andreyuk V.A., Asanbaev Yu.A., Skazyeva N.S. Izv. NII postoyannogo toka — in Russ. (News of the Research Institute of Direct-Current), 1997, No. 56, pp. 146—156.
Мисриханов М.Ш., Рябченко В.Н. Размещение полюсов при управлении большой энергетической системой. — Автоматика и телемеханика, 2011, вып. 10, с. 129—153.
Буков В.Н. Вложение систем. Аналитический подход к анализу и синтезу матричных систем. Калуга: Изд-во Н.Ф. Бочкаревой, 2006, 720 с.
Аллаев К.Р., Мирзабаев А.М. Матричные методы анализа малых колебаний электрических систем. Ташкент: Fan va texnologiya, 2016, 432 с.
Веников В.А. Переходные электромеханические процессы в электрических системах. М.: Высшая школа, 1985, 537 c.
Klos A. Mathematical Models of Electrical Network Systems: Theory and Applications - An Introduction. Springer International Publishing AG, 2017, 108 p.
Мисриханов М.Ш. Инвариантное управление многомерными системами. М.: Наука, 2007, 284 с.
Abdellatif B.M. Stability with respect to part of the variables of nonlinear Caputo fractional differential equations. — Mathematical Communications, 2018, 23, pp. 119—126.
Gotman V.I. Common algorithm of static stability estimation and computation of steady states of power systems. — Power engineering, 2007, vol. 311, No. 4, pp. 127—130.
Holali K.D., Efimov D., Richard J.-P. Interval Observers for Linear Impulsive Systems. — 10th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2016), Monterey, California, United States, 2016, pp. 867—872.
Kovalenko S., Sauhats A., Zicmane I., Utans A. New Methods and Approaches for Monitoring and Control of Complex Electrical Power Systems Stability. — IEEE 16th Intern. Conf. on Environment and Electrical Engineering (EEEIC 2016), 2016, pp. 270-275.
Makhmudov T. Technology of embedding systems as a method for studying the dynamic regimes of complex electric systems. - American Journal of Energy and Power Engineering, 2018, vol. 5, No. 2, pp. 15-19.
Автоматизация управления энергообъединениями/Под ред. С.А. Совалова. М.: Энергия, 1979, 431 с.
Irwanto M. et al. Improvement of Dynamic Electrical Power System Stability Using Riccati Matrix Method. — Applied Mechanics and Materials, 2015, vol. 793, pp. 29—33.
Фазылов Х.Ф., Насыров Т.Х. Установившиеся режимы электроэнергетических систем и их оптимизация. Ташкент: Молия, 1999, 370 с.
Allaev K.R., Makhmudov T.F. Analysis of Small Oscillations in Complex Electric Power Systems. — Engineering (USA), 2018, vol. 10, No. 5, pp. 253—261.
Мисриханов М.Ш. Классические и новые методы анализа многомерных динамических систем. M.: Энергоатомиздат, 2004, 566 с.
Андреюк В.А. Использование абсолютного угла для управления переходными режимами энергосистемы/Под ред. Л.А. Кощеева. — Изв. НИИ постоянного тока, 2011, № 65, с. 27-42.
Андреюк В.А., Асанбаев Ю.А., Сказываева Н.С. Статическая устойчивость энергосистемы, регулируемой по абсолютному углу. — Изв. НИИ постоянного тока, 1997, № 56, с. 146-156.
#
Anderson P.M., Fouad A.A. Power system control and stability, Second edition, Willey-Interscience A John Wiley & Sons Inc, USA, 2002, 664 p.
Misrikhanov M.Sh., Ryabchenko V.N. Avtomatika i telemekhanika — in Russ. (Automation and telemekhanics), 2011, iss. 10, pp. 129—153.
Bukov V.N. Vlozheniye sistem. Analiticheskiy podkhod k analizu i sintezu matrichnykh sistem (An analytical approach to analysis and synthesis of matrix systems). Kaluga, Publ. of N.F. Bochkarevoy, 2006, 720 p.
Allayev K.R., Mirzabaev A.M. Matrichnye metody analiza malykh kolebaniy elektricheskikh sistem (Matrix methods of analysis of small vibrations of the electric systems). Tashkent: Fan va texnologiya, 2016, 432 p.
Venikov V.A. Perekhodnye elektromekhanicheskiye protsessy v elektricheskikh sistemakh (Transitional electromechanical processes in electrical systems). Moscow, Vysshaya shkola, 1985, 537 p.
Klos A. Mathematical Models of Electrical Network Systems: Theory and Applications. —.An Introduction. Springer International Publishing AG, 2017, 108 p.
Misrikhanov M.Sh. Invariantnoe upravleniye mnogomernymi sistemami (Invariant management by the multidimensional systems). Moscow, Nauka, 2007, 284 p.
Abdellatif B.M. Stability with respect to part of the variables of nonlinear Caputo fractional differential equations. — Mathematical Communications, 2018, 23, pp. 119—126.
Gotman V.I. Common algorithm of static stability estimation and computation of steady states of power systems. — Power engineering, 2007, vol. 311, No. 4, pp. 127—130.
Holali K.D., Efimov D., Richard J.-P. Interval Observers for Linear Impulsive Systems. — 10th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2016), Monterey, California, United States, 2016, pp. 867—872.
Kovalenko S., Sauhats A., Zicmane I., Utans A. New Methods and Approaches for Monitoring and Control of Complex Electrical Power Systems Stability. — IEEE 16th Intern. Conf. on Environment and Electrical Engineering (EEEIC 2016), 2016, pp. 270—275.
Makhmudov T. Technology of embedding systems as a method for studying the dynamic regimes of complex electric systems. — American Journal of Energy and Power Engineering, 2018, vol. 5, No. 2, pp. 15—19.
Avtomatizatsiya upravleniya energoob’yedineniyami/Pod red. S.A. Sovalova (Automation of management of energyassosiations/Edit. by S.A. Sovalov). Moscow, Nauka, 1979, 431 p.
Irwanto M. et al. Improvement of Dynamic Electrical Power System Stability Using Riccati Matrix Method. — Applied Mechanics and Materials, 2015, vol. 793, pp. 29—33.
Fazylov Kh.F., Nasyrov T.Kh. Ustanovivshiyesya rezhimy elektroenergeticheskikh sistem i ikh optimizatsiya (Set modes of the electroenergy systems and their optimization). Tashkent, Moliya, 1999, 370 p.
Allaev K.R., Makhmudov T.F. Analysis of Small Oscillations in Complex Electric Power Systems. — Engineering (USA), 2018, vol. 10, No. 5, pp. 253—261.
Misrikhanov M.Sh. Klassicheskiye i novye methody analiza mnogomernykh dinamicheskikh sistem (Classic and new methods for analyzing multidimensional dynamic systems). Moscow, Energoatomizdat, 2004, 566 p.
Andreyuk V.A. Izv. NIIpostoyannogo toka — in Russ. (News of the Research Institute of Direct-Current), 2011, No. 65, pp. 27—42.
Andreyuk V.A., Asanbaev Yu.A., Skazyeva N.S. Izv. NII postoyannogo toka — in Russ. (News of the Research Institute of Direct-Current), 1997, No. 56, pp. 146—156.
