Many problems in nature can be solved by resorting to numbers in a particular sequence. For example, the numbers in the so called Fibonacci sequence have been successfully applied in computer science, mathematics and game theory. Another example is the triangular number sequence, which has two main applications: the handshake problem and the round-robin tournament. These two sequences can be found in the Pascal's triangle. With the aim of enhancing the waveform quality at the output of a multilevel inverter, this paper explores the suitability of the triangular number sequence to compute the commutation angles in Pulse Width Modulation switching pattern. It has been found that this approach provides a harmonic performance comparable to the results obtained with other calculation techniques such as the Newton Raphson method or Genetic Algorithm, but without the difficulty of solving the complex non-linear equation.
This paper presents the mathematical modeling and control design procedure of the compressor motor of an air conditioner using the energy from a photovoltaic system combined with the power grid in a DC microgrid. A comprehensive model considers the interconnection of the photovoltaic cells with their associated DC/DC converter, the DC bus, the three-phase squirrel-cage induction motor with its driver, the bidirectional DC/AC converter, the output filter, and the power grid. The state-of-the-art showed that a complete mathematical model of the proposed system is unavailable. Therefore, the mathematical model of the system is compared and validated in simulation with a block diagram in the Matlab/Simulink environment. In addition, several control approaches are used in the whole system to track the maximum power point of the photovoltaic cells, obtain a soft start on the machine, control the velocity using the variable frequency drive, regulate the DC bus voltage, and manage the power flow between the DC bus and the power grid.
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