4.1. Design Aspects

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.

4.1.1. Computation of the Bridge Capacitors

This exercise refers to the two capacitors  and 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 , and vice versa.

Starting from this reasoning, consider the combination where  and , 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.

4.1.2. Computation of the Filter Capacitors

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.

4.1.3. Voltage Levels and Associated Switches Control

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

4.2. Inverter Mode

4.2.1. Changing DC Voltage Source

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)

Figure 13: Changing DC Voltage Source

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

Table 9: Output Voltage Levels

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

4.2.2. Changing AC-Source Frequency - Synchronization On/Off

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.

Figure 14: Changing AC-source Frequency

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

Figure 15: Synchronize Button Activated

4.2.3.  Changing AC-Source Phase Shift

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.

Figure 16: Changing AC-source Phase Shift; Load More Inductive

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

Figure 17: Changing AC-source Phase Shift; Load More Capacitive

4.3. LC Filter Activated

4.3.1. Changing PWM Frequency

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).

Figure 18: Changing PWM Frequency

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

Table 10: Changing PWM Frequency with LC Filter ON

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

Table 11: Changing PWM Frequency with LC Filter OFF

• How does the change of PWM Frequency impact the THD of load and inverter currents?
  Hint: Please observe the values of Display₆ and Display₇.

4.3.2. Changing AC-Source Amplitude

This exercise is intended to show the impact of changing the amplitude of the AC Source and to observe the source current and the power flow.
Using the slider Amplitude (V), do the following:

• Increase the value of the amplitude to 75 V and observe the waveforms and the power flow.

Figure 19: Changing AC-source Amplitude to 75 V

• Increase the value to 82 V and redo the same observations.

Figure 20: Changing AC-source Amplitude to 82 V

• Determine the amplitude at which the power flow vanishes.

4.3.3. Changing AC-Source Phase Shift

This exercise is a repetition of 4.2.3 except that the LC filter is ON. Repeat the same steps as before.

Figure 21: Changing AC-source Phase Shift; Load More Inductive

Figure 22: Changing AC-source Phase Shift; Load More Capacitive

4.4. Rectifier Mode

As previously mentioned, in Rectifier Mode, when the PWM_Disable button is activated (i) the DC source is disconnected, (ii) the PWM generation is disabled and (iii) the first set of control parameters is disabled.

• Click the Connect Filter button, observe the waveforms and read the displays

Figure 23: Rectifier Mode; LC Filter ON

• Click the APPLY_RECT_LOAD button, observe the waveforms and read the displays

Figure 24: Rectifier Mode; LC Filter ON & DC Load Connected

• Check that the current and voltage at the DC side are coherent with the value of the DC resistance.