The Use of a Geometric Approach for the Analysis of a Single-Phase Inverter

Abstract

—In this paper the elementary cell of the inverter is considered without taking into account losses in the converter circle and internal resistance. The use of a geometric approach for the analysis of a single-phase inverter voltage is considered. The vectors of input and output voltages on the load and current consumed from the source are analyzed. It can be seen that during the transition from the space of inputs to the space of output quantities one degree of freedom is lost. Using the cell states indicated in the table, the formation of a sinusoidal load voltage with the use of a pause is shown. In forming the output voltage in this way, the current consumed will be in the form of pulses and such a current may not satisfy the conditions that are pushed to the inverter from the source side. The given method of forming a sinusoidal load voltage, in which on the positive half-period is formed an interval with a negative voltage, and on the negative one - with a positive one. The expressions for calculating the average values of the load voltage and the supply current during the switching period of the transistor are given. Proposed the method of forming the necessary value of the output voltage with the provision of constant consumed current. In this case, the control with ensuring the flow of direct current requires the construction of a system of vectors with the projection of input values on the plane of the output quantities for both the voltage and the currents. It is shown that using the method of providing the necessary voltage using the change in polarity provides a constant current consumption, however, the use of power source is reduced. Vector diagrams are presented, and a timeline describing the work of the inverter cell. Constructed a table in which are formed the voltages and currents that correspond to the particular condition keys of the inverter. The matrices of the transition from the input values in a two-dimensional space to the initial quantities in a one-dimensional space are constructed. It is shown that, unlike voltage vectors, current vectors coincide, so it is expedient to consider them as one on both half-cycles. Thus the vector is obtained that corresponds to the value of the current in the positive and negative half-cycle of the voltage, provided that the half-waves of the voltage is symmetric. Using the data obtained in the article, based on the analysis of the scheme with the help of a geometric approach, it is possible to develop the rules of control of the cell of the inverter.Ref. 10, fig. 3, tabl. 1.