## 4 Results and Discussion  
Power converters in SG generate supra-harmonics in the frequency range 2-150 kHz (there is no standard to limit CEs in this range), which is commonly used by NB-PLC for Smart Metering in SG applications. These emissions may affect the communication system even if the NB-PLC technologies, such as PRIME, G3-PLC, or IEEE 1901.2, allow the use of robust modulation and coding techniques [26; 27]. Therefore, among the available EMI mitigation techniques, RPWM is preferable since it is easy to implement and less costly than others, and it is being deployed in many converters, such as inverters (PV systems, wind turbine, electrical vehicle charging, and motor controllers) and DC-DC converters for SG applications. Nevertheless, the influence of RPWM in power grids involving PLC systems still requires investigations. Toward this objective, two test cases will be considered in the following. In the first test case, the switching frequency of the DC-DC converter is set to 25 kHz, and the modulation frequency of the QPSK modulator to 5 kHz. In this case, RPWM led to an increased bit error rate (1016 errors out of 10,000 samples) with respect to PWM (572 errors), as shown in Figure 11. This is because the peaks of the noise exiting the DC-DC converter do not affect the communication signal, i.e., the frequency of the communication signal does not overlap with the significant noise peaks from the DC-DC converter. This is shown in Figure 12, where the CEs of the DC-DC converter with conventional PWM (blue) and RPWM (red) are shown and compared with the QPSK modulated message signal (black). It is shown that resorting to RPWM modulation reduces the noise peaks by more than 10 dB compared to the conventional PWM. However, RPWM spreads the noise spectrum, which exhibits higher amplitude than the conventional PWM in the frequency range around 5 kHz (see the black box in Figure 12), with a consequent increase of the interference with the communication signal. This conclusion is in line with the one drawn in Reference [21], where it was proven that RPWM causes more frame error rate than the conventional PWM. However, the RPWM scheme considered in Reference [21] is based on varying the switching frequency of the pulse signal, i.e., the RPWM strategy adopted in that work is different from the one exploited here. Conversely, the advantages of RPWM modulation can be seen if the switching frequency of the DC-DC converter is reduced to 10 kHz, and the modulation frequency of the QPSK modulator is increased to 15 kHz. Figure 13 shows the frequency spectrum of the noise exiting the DC-DC converter with PWM (blue) and RPWM (red), along with the spectrum of the QPSK modulated signal (black). In this case, the peaks of the noise spectra  
Figure 10: Message signal: (**top**) original signal, (**bottom**) scaled down signal. of the DC-DC converter overlap with the spectral components of the modulated signal. Since the amplitude of the noise peaks is reduced, thanks to RPWM, the bit error rate with RPWM reduces from 1016 to 454, while the bit error rate with PWM reduces from 572 to 464, as shown in Figure 11. It is worth noticing that lower switching frequency, even for PWM, also results in less interference to the communication signal. To assess the effects that symmetrical/asymmetry of the power cables plays on the PLC system, an additional example is simulated. To this end, the communication signal was connected between two phases rather than one phase and ground as in the previous examples. Figure 14 shows the bit error rate obtained when the communication signal is transmitted between the two phases (the switching frequency of DC-DC converter, in this case, is 25 kHz). The bit error rate drops from 572 to 523 for conventional PWM and from 1016 to 525 for RPWM when the communication signal is connected between the two phases of the AC system.