The Control of the Frequency Converter Using a Geometric Approach
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Abstract
In this paper, the control of a matrix frequency converter (MFC) is considered using a geometric approach. In the previous work, methods of forming the output voltages according to the law of change of input voltages were considered, but the issue of simultaneous formation of both the output voltage and the input current was not considered. To solve this problem, it is advisable to consider the simplest transforming system using a matrix frequency converter. The purpose of this work is to obtain, along with matrices for the transition from shoulder voltages, as independent variables, to the output values of a two-dimensional space when providing a sinusoidal input current and a voltage of a given frequency.
The construction of controlling output parameters on a two-dimensional plane from a three-dimensional space of input quantities is considered. Shows the three-dimensional appearance of the independent variables in the coordinates of the indicated vectors Ual1, Ual2, Ual3 and the projection of the vectors of the independent variables on the two-dimensional planes V and W. To obtain the vectors of currents on the two-dimensional plane V, it is necessary to make a projection of the input vectors of voltages with a gain on the coefficient of translation voltages in currents. For the input values the shoulder voltages Ual1, Ual2 and Ual3 are selected. For the output values, the voltage on the loading phases Ua, Ub, Uc and the currents of the iA, iB, iC phases. Accordingly, this will enable the MFR to calculate the valve control law to generate phase voltages and sinusoidal current consumption.
The work of the MFC will be considered at an elevated frequency (150 Hz) and at a lower frequency (25 Hz). The base vectors have chosen those shoulder voltages that are formed by only one input vector (one of the three shoulder voltages was equal to one, and the other two to zero). The tables describing the currents and voltages in the MFC at the appropriate valve states at each frequency are constructed. The following tables show matrices that describe the transition from the three-dimensional space of input quantities to two-dimensional spaces of the output quantities. At 25 Hz, there are two switches when the input shoulder voltage is formed by one vector (line 5 and 6 of Table 2), so we have two matrices for currents. Also, at these frequencies, the output voltages are constructed on each of the phases and the input voltages with separated intervals under each switching of valve states.
The resulting matrices for the voltages and the resulting matrix for currents at different frequencies were compared with each other. With the help of elementary transformations of the matrices, their equivalence with each other is proved. Thus, the received matrices allow to calculate independent vectors of three-dimensional space, source vectors in two-dimensional space that will be dependent on each other. That extends the ability to operate with shoulder voltages and key states in the MFC.
Ref. 10, fig. 4.
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