A simplified three phase matrix converter model is shown in Figure below and
consists of 9 ideal bidirectional switches which allows each of the three output lines to be connected to any of the three input lines. The three converter inputs are connected to a 3 phase system, vR , vS , vT , which represent the voltages after the input filter. The output lines are connected to a three phase current source, iA , iB and iC , which acts as the load. Input voltages and output currents are given by equations given below.
where vR , vS and vT are three-phase input sinusoidal voltages and Vin is the peak
value of the input voltages. Assuming that the output voltage waveforms are sinusoidal and assuming a linear load, the output currents iA , iB and iC are also sinusoidal. Iout is the peak value of the output currents and φo is the phase between output voltages and currents. ωi and ωo are the input and output angular frequencies respectively. The column matrices viP h and ioP h provide a compact mathematical form of expressing the input voltages and output currents, respectively.
The nature of these voltage and current sources leads to restrictions on the possible states of the matrix converter switches. Firstly, lines which are connected to a low impedance source must never be short-circuited. If these lines are short-circuited, the current rises to a value that will destroy the semiconductor switches. Also, lines connected to a high impedance source must not be left open-circuited. The converter must always provide a path for the output current. In order to fulfil these restrictions, only one of the three switches associated with each output line must be closed at any given time. Using the existence function of each switch, the constraints can be expressed as
sj1 + sj2 + sj3 = 1J ∈ 1, 2, 3
These constraints lead to only 27 possible combinations of switches or states
of a three phase matrix converter.
consists of 9 ideal bidirectional switches which allows each of the three output lines to be connected to any of the three input lines. The three converter inputs are connected to a 3 phase system, vR , vS , vT , which represent the voltages after the input filter. The output lines are connected to a three phase current source, iA , iB and iC , which acts as the load. Input voltages and output currents are given by equations given below.
where vR , vS and vT are three-phase input sinusoidal voltages and Vin is the peak
value of the input voltages. Assuming that the output voltage waveforms are sinusoidal and assuming a linear load, the output currents iA , iB and iC are also sinusoidal. Iout is the peak value of the output currents and φo is the phase between output voltages and currents. ωi and ωo are the input and output angular frequencies respectively. The column matrices viP h and ioP h provide a compact mathematical form of expressing the input voltages and output currents, respectively.
The nature of these voltage and current sources leads to restrictions on the possible states of the matrix converter switches. Firstly, lines which are connected to a low impedance source must never be short-circuited. If these lines are short-circuited, the current rises to a value that will destroy the semiconductor switches. Also, lines connected to a high impedance source must not be left open-circuited. The converter must always provide a path for the output current. In order to fulfil these restrictions, only one of the three switches associated with each output line must be closed at any given time. Using the existence function of each switch, the constraints can be expressed as
sj1 + sj2 + sj3 = 1J ∈ 1, 2, 3
These constraints lead to only 27 possible combinations of switches or states
of a three phase matrix converter.
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