*2.2. Extended Structure*

The multistep DC-link circuit can be extended by keeping the proposed MLI's main bridge construction. This enables the proposed inverter to achieve a higher amount of voltage steps using a small quantity of power equipment. To extend the multistep DC-link circuit, the half-bridge power module and (*n*) multiple units of full-bridge power modules are connected following series connection to generate (*N* – 1) sequent voltage steps as depicted in Figure 2. For full-bridge power cells:

$$Vdc\\_fb1 = \mathfrak{Z}^{(0)}Vdc\tag{4}$$

$$Vdc\\_fbm = \mathfrak{Z}^{(n-1)}Vdc.\tag{5}$$

**Figure 2.** Proposed structure of three-phase *N*-level multilevel inverter.

For half-bridge power cells:

$$Vdc\\_hb = \mathfrak{Z}^{(n)}Vdc.\tag{6}$$

For a single DC voltage supply:

$$Vd\mathbf{c\\_s} = Vd\mathbf{c} + \sum\_{i=1}^{i=n} \mathbf{3^{(n-1)}}Vd\mathbf{c} = \left(\frac{\mathbf{1} + \mathbf{3^{(n)}}}{2}\right)Vd\mathbf{c}.\tag{7}$$

Hence, the highest number of voltage steps that can be achieved are:

$$N = \frac{3}{2} \left( 1 + \mathfrak{Z}^{(n)} \right). \tag{8}$$

Here, *N* = [6, 15, 42, 123, ........]. The total required numbers of IGBTs (*M\_sw*) and DC supplies (*M\_DC*) in terms of voltage steps are given as:

$$M\_-sw = 4\log\_3\left(\frac{2}{3}N - 1\right) + 14\tag{9}$$

$$M\_-DC = \mathcal{L}\log\_3\left(\frac{2}{3}N - 1\right) + 2.\tag{10}$$
