Аналіз несиметричних трифазних кіл за допомогою методу контурних струмів

Abstract

UA: У роботі розглянуто несиметричні режими роботи трифазних кіл. Проаналізовано методи розрахунку струмів в разі несиметрії навантаження і в разі несиметрії джерела. Виявлено, що для визначення струмів кола за несиметрії навантаження застосовується метод двох вузлів, а за несиметрії джерела – метод симетричних складових. Недоліком вказаних методів є значна кількість розрахункових дій. Для спрощення розрахунку сил струмів у фазах кола запропоновано застосовувати метод контурних струмів. На базі цього методу складено рівняння для визначення сил струмів трипровідних і чотирипровідних трифазних кіл у несиметричних режимах роботи. /// EN: The article discusses three-phase electrical circuits operating in asymmetrical modes. It is noted that the causes of asymmetry in such circuits in practice may be the uneven distribution of single-phase loads between the phases of a three-phase system, the connection of powerful single-phase consumers, the influence of photovoltaic modules and charging stations, damage to electrical equipment, etc. The occurrence of asymmetry causes disruption to the normal functioning of three-phase loads, in particular a reduction in efficiency, increased electricity consumption and additional heating. An analysis of publications on this topic has revealed that, at present, the calculation of currents in asymmetrical three-phase circuits is based on the two-node method or the symmetrical component method. The first method is mainly used in the analysis of three-phase circuits in cases of load or power line asymmetry. Its essence lies in determining the neutral displacement voltage and then the current forces in the circuit phases. The second method is mainly used in the analysis of three-phase circuits in the case of source asymmetry. Its essence lies in determining the symmetrical components of voltages and currents, and then the current forces in the circuit phases. One of the disadvantages of these methods is that their use involves a significant amount of calculations. Therefore, the aim of this article was to justify the possibility of using the contour current method to determine the current forces in the phases of a three-phase circuit under asymmetrical operating conditions. To achieve this goal, the application of this method was considered for three-wire and four-wire three-phase circuits in the case of load or source asymmetry. Based on the results, a comparative analysis was made with the two-node method and the symmetrical component method. In the course of the study, the calculation diagrams of the circuits with marked contour currents and the compiled systems of equations using the contour current method were presented. The solutions to these systems of equations were expressions of the complexes of the effective values of the circuit currents. A numerical comparison of the obtained equations with the current equations using the two-node and symmetrical component methods was performed. As a result, it was established that the obtained equations have fewer calculation steps, but do not allow obtaining the value of the neutral displacement voltage complex during the calculation process. Further research should be aimed at clarifying the feasibility of using other methods of calculating branched circuits for the analysis of asymmetrical three-phase circuits.