2.1. Converter Topology

The Three-Phase Three-Level NPC converter is shown in Figure 3 below.

Figure 3: Three-Phase Three-Level NPC Converter

The bridge is composed of three arms.
Each arm comprises (i) four IGBT associated to their antiparallel diodes and (ii) two additional diodes with their midpoint  clamped to the ground together with the midpoint of the capacitors.
The IGBT/diode switches are numbered  to  and the remaining six diodes go from  to .

The converter has three inputs: (i) positive and (ii) negative terminals of the DC voltage source and (iii) the ground connected to the capacitors’ midpoint .
It also has three outputs , and, which feed the three-phase load.

The role of the two identical capacitors and  is to create the midpoint together with the two voltage levels and .
In the sequel, an exercise will be dedicated to the dimensioning of these two identical capacitors.

It is noteworthy that the neutral of the load might be unreachable, which corresponds to practical cases, for example a delta-connected load.
Consequently, the ground  of the NPC will not be connected to the neutral  of the load at any time. Therefore, the voltage  will not be identically zero.

Hence, for a symmetric load, we have:

which leads to:

Besides the practical aspect, removing the connection between the electrical points and  has its benefit harmonic-wise for symmetrical load.
Indeed, the absence of connection eliminates all the odd harmonics that are multiple of three, which is explained thoroughly in Reference 1.
The interested reader is redirected there for more details.

2.2. Control of the Switches & PWM Generation

The control of the switches of the first arm, that is displayed in Figure 4 below, is explained below.
The same control is to be applied for arms two and three with a phase shift of -120^o and +120^o, respectively.

The PWM train is generated using the method of intersection between the reference signal that is a sine-wave signal oscillating at either 60 Hz or 50 Hz, and two triangular carriers, one positive and one negative, oscillating at the switching frequency.
The positive and negative carriers operate on the positive and negative parts of the reference, respectively, as illustrated in Figure 5 below.

The switching frequency is a user-controlled parameter, varying between 900 Hz and 3000 Hz.
It is up to the user to select switching frequency values that are multiples of 60 (or 50) if 60 Hz (or 50 Hz) is chosen as a reference frequency.

The reason behind having two carriers (instead of one) is the fact that each arm contains four IGBTs (instead of two IGBTs, as is the case in a two-level inverter).
This technique is classified under the category of multi-carriers PWM generation for multi-levels inverters.
Exhaustive literature can be found covering this topic.

From the waveforms shown below one can notice that during the positive part of the reference:

• is always ON and  is always OFF.
• and  are complementary offering, thus the two levels  or .

Following the same reasoning, during the negative part of the reference:

• is always ON and  is always OFF.
• and  are complementary offering, thus the two levels  or .

Figure 4: First Arm of the NPC Converter

Figure 5: PWM Generation for the First Arm of the NPC Converter

2.3. Output Voltages and Waveforms

The voltages at the output of the inverter can take a specific number of values (levels), depending on the switch combinations.
Table 1 below summarizes these values, while Figure 6 below shows the voltages waveforms.
It is noteworthy that, in this section, we will consider all the possible voltage levels regardless of the control of the switches generating them, as exercise 4.1.3 in the sequel will be dedicated to that matter.

For instance, when the DC voltage source is:

the corresponding levels for  are:

while for the line-to-neutral voltage  they become:

And finally, for the line-to-line voltage  we have:

Table 1: Voltage Levels at the Inverter Output

Figure 6: Voltages V_AO, V_AN, and V_AB

2.4. Load and Filter in Inverter Mode

In inverter mode, the load and filter are given in figure 7 below:

Figure 7: Load and Filter in Inverter Mode

2.4.1. Load

The load is composed of the combination in series of (i) a constant resistance , (ii) a constant inductance  and (iii) a controllable three-phase AC-source.
Therefore, the student controls the three parameters of the AC-source, namely, the amplitude, frequency, and phase shift.
In Section 4, exercises showing the impact of changing these parameters will be covered thoroughly.

2.4.2. Filter

The filter is composed of inductances in series with the load, while the capacitances  are mounted in delta configuration between phases.
The filter inductance value corresponds to 10% of the load inductance.
The value of the capacitance will be computed in an exercise, later, to ensure a cut-off frequency of 600 Hz, which represents 10x the reference frequency (60 Hz).

Note that the capacitors can be connected or disconnected as shown in Figure 7 above; exercises covering this matter will be given too.

2.5. Load and Filter in Rectifier Mode

When simulating the converter in rectifier mode, the AC-source on the load side becomes the generator.
Additionally, the DC voltage source is disconnected and the PWM generator is disabled, rendering the rectifier passive (i.e., the DC voltage at the output of the rectifier cannot be regulated).
There is a possibility to connect/disconnect a resistive load at the output of the rectifier. Figure 8 below shows the circuit in rectifier mode.

Figure 8: Load and Filter in Rectifier Mode

2.6. Converter Parameters and Nameplate

Table 2: Converter Parameters and Nameplate Ratings

2.7. Measurements

 Three spots were considered for current, voltage and power measurements, as shown in Figure 9 below:

• The DC bus at the input of the converter bridge.
• The AC bus at the output of the converter bridge.
• The input of the load.

Figure 9: Measurements

It is worth noticing that for the three-phase power measurements, i.e., at the second and third spots, a transformation is required first to move from line-to-line voltages to line-to-neutral voltages .
For instance, at the inverter output we have:

Then the instantaneous power is obtained as