This first set of exercises deals with the design aspects.
The first two exercises cover the sizing of the two capacitors at the input of the inverter, and the three delta-connected capacitors at the output of the inverter.
The third one is dedicated to the control of the switches and the PWM generation.

This exercise refers to the two capacitors

 and

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located at the input of the inverter bridge. For more details, see Figure 3.

The voltage across the two capacitors is fixed to

, in other words:

which leads to:

That means that the charging current of

equals the discharging current of

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, and vice versa.

Starting from this reasoning, consider the combination where 

and

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, and do the following:

• Express 

  and 
  as functions of the source current

• Compute the instantaneous values of 

  and
  as functions of
  and the instantaneous load currents given as: 
  , 
  and 

• Show that there should be a minimal value of

  and
  in order to ensure a minimum of fluctuation in the voltages 
  and

• Compute that value.

This exercise refers to the three capacitors mounted in delta configuration and composing the C-Filter.
See Figure 7 for more details.

The values of the load resistances and inductances as well as the filter inductances are summarized in Table 2.
The point of this exercise is to compute the value of the filter capacitance, for that do the following:

• Compute the transfer function of the LC filter

• Compute the cut-off frequency of the filter

• Compute the value of the filter capacitance that ensures a cut-off frequency of 600 Hz.

This exercise refers to the material introduced in Sections 2.2, namely, the control of the switches and the PWM generation.

See Figure 3 for the topology of the whole inverter, Figure 4 for the topology of one arm and Figure 5 for the control of the four switches, which is based on the intersection between the reference signal and the two carriers.

Since this exercise is intended to help the student understand and design the PWM generator, he is asked to do the following:

• Determine the control status (On/Off) of the twelve switches and fill out Table 8 below.

• Design the circuit, based on (i) relational operator and (ii) logical operators that produces the switches control of Figure 5.

Table 8: Voltage Outputs and Associated Control Switches

This exercise refers to Section 2.3 and is intended to change the value of the DC Voltage source and observe its impact on the levels and waveforms, essentially, the inverter voltages.

• For that, keep all the parameters unchanged except for the slider: Vdc (V)

• Apply the changes, as shown in the first column of Table 9 below, observe the waveforms and fill out the rest:

• Verify that the voltage value of Display₄ follows Vdc/2*Reference Amplitude*sqrt (3/2) for each Vdc value in Table 9 above.

This exercise is intended to highlight the pulsations phenomenon obtained during the loss of synchronization between the AC-source and the inverter output, a phenomenon like the loss of synchronization between a power grid and a synchronous generator.

• Change the slider Frequency (Hz) and observe the pulsations in the inverter currents as shown in Figure 14 below.

• Click the SYNCHRONIZE button that forces the PWM reference frequency to stick to the BEMF frequency and observe the waveforms of Figure 15 below:

This exercise is intended to show the impact of changing the phase shift of the AC Source with respect to the reference signal.
Using the slider PhaseShift (Deg) do the following:

• Choose positive values, thus rendering the load more inductive, and observe the waveforms of the voltages and currents as shown in Figure 16 below.

• Repeat the exercise with negative values (capacitive load) as shown in Figure 17 below.

This exercise is intended to change the PWM frequency and observe its impact on the waveforms and the power flow.
For that, keep all the parameters unchanged except for the slider: PWM Frequency (Hz).

• Apply the PWM frequency values of the first column of Table 10 below, observe the waveforms, read the displays, and fill out below:

• Disable the LC Filter button and repeat the same exercise.