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

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 to

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 and the remaining six diodes go from

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 to

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.

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

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,

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.

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

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