**6. Results**

The test system (see Figure 2) was implemented in MATLAB/Simulink and was executed on a desk-computer INTEL(R) Core(TM) i7–7700 CPU, 3.60 GHz, 8 GB RAM with 64-bits Windows 10 Professional by using MATLAB2019b. The switching frequency for the VSCs was fixed at 5 kHz. The parameters for the PI-PBC approach were tuned using the diagonal method developed in [20], which is suitable when the connection between the internal control of the model and the PI controller is lost, as presented with the proposed controller in this paper. The PI controller is computed, as follows:

$$k\_{p\_{12}} = \frac{\ln(\theta)L}{t\_s}, k\_{i\_{12}} = \frac{\ln(\theta)R}{t\_s}, \tag{21}$$

where *L* and *R* are values of the inductance and resistance of the AC filter and *ts* = 10−<sup>4</sup> is the desired settling time.
