*4.1. NPC Converter Control*

Figure 4 shows a simplified machine-side 3L-NPC converter control strategy. Voltage equation considering the input inductive filter in stationary 'abc' frame can be written as:

$$L\_{\rm gx} \frac{d\dot{l}\_{\rm x}}{dt} = \mathcal{U}\_{\rm x} - \mathcal{U}\_{\rm gx} \tag{8}$$

Whereas, *x* = *a*, *b*, *c*

> *ux* = converter input voltage *ugx* = grid supply voltage *Lgx* = *Input inductor*

A commonly used voltage oriented control (VOC) has been applied for the 3L-NPC converter control. The classical type proportional-integral controllers (PI) method has been adopted to obtain good performance on dc values with small steady-state error [37]. Therefore, the stationary frame requires conversion into a synchronous d–q reference frame. Moreover, active power control is achived by setting the d-axis along with the grid voltage amplitude, whereas the q-axis has been set to zero. Active and reactive power can be controlled by the d and q-axis of the current, as illustrated in Equations (9) and (10).

$$P\_{\mathcal{S}} = \frac{3}{2} v\_{\mathcal{S}^d} i\_{\mathcal{S}^d} \tag{9}$$

$$Q\_{\mathcal{S}} = -\frac{3}{2} v\_{\mathcal{S}^d} i\_{\mathcal{S}^d} \tag{10}$$

Park and Clark's transformation is required to transform a stationary frame to a synchronous frame, and vice versa, to implement the VOC method. For the balanced amplitude of the sinusoidal waveform, the transformation from 'dq0' frame to 'abc' frame have done while using Equation (11).

$$
\begin{pmatrix} u\_{\mathcal{S}^{\text{R}}} \\ u\_{\mathcal{S}^{\text{B}}} \\ u\_{\mathcal{S}^{\text{C}}} \end{pmatrix} = \begin{pmatrix} \text{Cov}(\boldsymbol{\theta}\_{\varepsilon}) & -\text{Sim}(\boldsymbol{\theta}\_{\varepsilon}) & \frac{1}{\sqrt{2}} \\ \text{Cov}(\boldsymbol{\theta}\_{\varepsilon} - \frac{2\pi}{3}) & -\text{Sim}\left(\boldsymbol{\theta}\_{\varepsilon} - \frac{2\pi}{3}\right) & \frac{1}{\sqrt{2}} \\ \text{Cov}(\boldsymbol{\theta}\_{\varepsilon} + \frac{2\pi}{3}) & -\text{Sim}\left(\boldsymbol{\theta}\_{\varepsilon} + \frac{2\pi}{3}\right) & \frac{1}{\sqrt{2}} \end{pmatrix} \begin{pmatrix} u\_{\mathcal{S}^{\text{B}}} \\ u\_{\mathcal{S}^{\text{B}}} \\ 0 \end{pmatrix} \tag{11}
$$

Similarly, voltage vectors in the 'abc' frame can also be directly transformed into the 'dq0' frame, according to the multiplication of the matric, as given by Equation (12).

$$
\begin{pmatrix} u\_{\mathcal{S}^d} \\ u\_{\mathcal{S}^q} \\ 0 \end{pmatrix} = \frac{2}{3} \begin{pmatrix} \cos(\theta\_\varepsilon) & \cos\left(\theta\_\varepsilon - \frac{2\pi}{3}\right) & \cos\left(\theta\_\varepsilon + \frac{2\pi}{3}\right) \\ -\sin(\theta\_\varepsilon) & -\sin\left(\theta\_\varepsilon - \frac{2\pi}{3}\right) & -\sin\left(\theta\_\varepsilon + \frac{2\pi}{3}\right) \\ \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \end{pmatrix} \begin{pmatrix} u\_{\mathcal{S}^d} \\ u\_{\mathcal{S}^b} \\ u\_{\mathcal{S}^c} \end{pmatrix} \tag{12}
$$

The VOC approach consists of two closed-loop controllers, one for dc-link (outer loop) and the second one for current control (inner loop). In the outer loop control, two dc voltage controller have been taken to ensure the voltage balancing across each capacitors, among two voltage controllers one controller take the input error signal after comparing the reference dc voltage and the sum of measured individual capacitor voltages, while the other controller takes the error signal that was generated by the voltage di fference across each capacitor to suppress the zero leakage current. The error that was generated by both controller was sent to two separate PI controllers for tuning. Finally, the sum of two PI controller results in a reference current *igd*1\_*re f* . Meanwhile, *igq*1 is set zero to deal with active power only. In Figure 4, both *isd*1 and *isq*1 are the feedback currents that were obtained by transforming the grid current into a rotating reference frame for inner loop control. The voltage controller sets the reference current *isd*1\_*re f* . Subsequently, the di fferences between the reference and actual currents are sent to the inner loop of the PI controller. The output of these current controller was provided to the PWM generator to obtain the appropriate signal. The outputs of the PWM generator were applied to the NPC switches for proper operation.

**Figure 4.** Control strategy of a proposed hybrid converter.
