**Nomenclature**



## **Appendix A**

By replacing *K* in expression (21), the following is obtained:

$$i\_p = \begin{cases} -\frac{V\_m}{K} \left[ \frac{V\_m C\_{1\vartheta}}{2} \sin 2\omega t - I\_m \sin^2 2\omega t \right] & \text{for } 0 \le \omega t < \pi \\\ -\frac{V\_m}{K} \left[ \frac{V\_m C\_{1\vartheta}}{2} \sin 2\omega t - I\_m \sin^2 2\omega t \right] & \text{for } \pi \le \omega t < 2\pi \end{cases} \tag{A1}$$

Then, Expression (22) can be rewritten as follows:

$$i\_{D3} = \begin{cases} \ -\frac{V\_m}{K} \left[ \frac{V\_m C\_1 \omega}{2} \sin 2\omega t - I\_m \sin^2 2\omega t \right] & \text{for } 0 \le \omega t < \pi \\\ 0 & \text{for } \pi \le \omega t < 2\pi \end{cases} \tag{A2}$$

By replacing (A2), Expression (24) becomes the following:

$$I\_{dc} = \frac{1}{\pi} \int\_0^{\pi} i\eta z d\omega t = \frac{1}{\pi} \left[ -\frac{V\_n \frac{n}{\omega} \zeta\_{\omega} \omega}{4V\_{dc}} \int\_0^{\pi} \sin 2\omega t d\omega t + \frac{I\_0 V\_n \pi}{2V\_{dc}} - \frac{I\_0 V\_n}{8V\_{dc}} \int\_0^{\pi} \cos 4\omega t d\omega t \right].$$

$$I\_{dc} = \frac{1}{\pi} \left[ \frac{V\_n \frac{n}{\omega} \zeta\_{\omega} \omega}{4V\_{dc}} \cos 2\omega t \bigg| \begin{array}{c} \pi \\ 0 \end{array} + \frac{I\_0 V\_n \pi}{2V\_{dc}} - \frac{I\_0 V\_n}{8V\_{dc}} \sin 4\omega t \bigg| \begin{array}{c} \pi \\ 0 \end{array} \right]. \tag{A3}$$

$$I\_{dc} = \frac{I\_0 V\_n}{2V\_{dc}}.$$
