Abstract
The solution of the problem of reliable functioning of an electric power system (EPS) in steady-state and transient regimes, prevention of EPS transition into asynchronous regime, maintenance and restoration of stability of post-emergency processes is based on formation and realization of mathematical models of an EPS processes. During the functioning of electric power system in asynchronous regime, besides the main frequencies, the currents and voltages include harmonic components, the frequencies of which are multiple of the difference of main frequencies. At the two-frequency asynchronous regime the electric power system is being made equivalent in a form of a two-machine system, functioning for a generalized load. In the article mathematical models of transient process of a two-machine system in natural form and in d–q coordinate system are presented. The mathematical model of two-machine system is considered in case of two windings of excitement at the rotors. Also, in the article varieties of mathematical models of EPS transient regimes (trivial, simple, complete) are presented. Transient process of a synchronous two-machine system is described by the complete model. The quality of transient processes of a synchronous machine depends on the number of rotor excitation windings. When there are two excitation windings on the rotor (dual system of excitation), the mathematical model of electromagnetic transient processes of a synchronous machine is represented in a complex form, i.e. in coordinate system d, q, the current of rotor being represented by a generalized vector. In asynchronous operation of a synchronous two-machine system with two excitation windings on the rotor the current and voltage systems include only harmonics of two frequencies. The mathematical model of synchronous steady-state process of a two-machine system is also provided, and the steady-state regimes with different structures of initial information are considered.
Highlights
The solution of the problem of reliable functioning of an electric power system (EPS) in steady-state and transient regimes, prevention of EPS transition into asynchronous regime, maintenance and restoration of stability of post-emergency processes is based on formation and realization of mathematical models of an EPS processes
At the two-frequency asynchronous regime the electric power system is being made equivalent in a form of a two-machine system, functioning for a generalized load
The mathematical model of two-machine system is considered in case of two windings of excitement at the rotors
Summary
Математические модели переходных процессов можно разделить на три категории: а) тривиальная модель – учитываются только электромеханические переходные процессы синхронных и асинхронных машин [1, 2], электромагнитные переходные процессы в контурах ротора и статора машин, а также в электрической сети не учитываются; б) упрощенная модель – учитываются электромеханические и электромагнитные переходные процессы в электрических машинах, а электрическая сеть представляется моделью установившегося (стационарного) режима [1, 3,4,5,6,7,8,9,10]; в) полная модель – электрические машины представляются электромеханической и электромагнитной моделями, а электрическая сеть, в отличие от упрощенной модели, также представляется моделью переходного процесса. In the article mathematical models of transient process of a two-machine system in natural form and in d–q coordinate system are presented. Transient process of a synchronous two-machine system is described by the complete model. The quality of transient processes of a synchronous machine depends on the number of rotor excitation windings.
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