**Hermes Loschi 1,\*, Robert Smolenski 1, Piotr Lezynski 1, Douglas Nascimento <sup>1</sup> and Galina Demidova <sup>2</sup>**


Received: 9 June 2020; Accepted: 13 July 2020; Published: 21 July 2020

**Abstract:** The assessment of electromagnetic compatibility (EMC) is important for both technical and legal reasons. This manuscript addresses specific issues that should be taken into account for proper EMC assessment of energy systems that use power electronic interfaces. The standardized EMC measuring techniques have been used in a laboratory setup consisting in two identical DC/DC converters with deterministic and random modulations. Measuring difficulties caused by the low frequency envelopes, resulting from frequency beating accompanying aggregation of harmonic components of similar frequencies, were indicated as a phenomenon that might lead to significant problems during the EMC assessment using currently binding standards. The experimental results describing deterministic and random modulated converters might be useful for practitioners implementing power interfaces in microgrids and power systems as well as for researchers involved in EMC assurance of power systems consisting in multiple power electronic interfaces.

**Keywords:** conducted electromagnetic interference; electromagnetic compatibility; aggregated electromagnetic interference; power electronic interfaces; frequency beat

### **1. Introduction**

Electromagnetic compatibility (EMC) assessment is demanded for technical as well as legal reasons. EMC evaluation is usually based on the use of the dedicated standards, which determine the permissible limit values for electromagnetic interference (EMI), measurement methods, test equipment and provide classification of products according to their characteristics and electromagnetic environment where they are intended to be used [1]. The shape of conducted EMI depends on the source of the interference as well as complex phenomena accompanying the flow of interference in circuits, including parasitic couplings. In the subject matter literature, some papers emphasize the necessity for assurance of reliable operation of complex energy systems and the need for EMC assurance [2–8]. Furthermore, some papers highlight how approaches concerning deterministic modulation (DetM) and random modulation (RanM), based on the parameters' control of fundamental switching frequency (*fsw*) and duty cycle (*d*), may contribute to achieving EMC requirements [9–20]. Indeed, the RanM has been widely used since the 1980s [21]. From the practical viewpoint, beyond the reduction in the maximum level of voltage or current harmonics, the choice for RanM has been considered in order to provide, for instance, reduced of burdensome acoustic noise related to switching frequency [10]. However, some manuscripts have shown that the aggregation of interference in the case

of deterministic modulation might be accompanied by low frequency envelopes. This phenomenon may lead to misinterpretations during the EMC assessment [22–25].

According to requirements of the EMC Directive [26] "where apparatus is capable of taking different configurations, the electromagnetic compatibility assessment should confirm whether the apparatus meets the essential requirements in the configurations foreseeable by the manufacturer as representative of normal use in the intended applications". Moreover, the EMC Directive defines responsibility of standard organizations in this context: "The European standardisation organisations should take due account of that objective (including the cumulative effects of the relevant types of electromagnetic phenomena) when developing harmonised standards". Taking into account a global approach to standardization, the issues presented in this paper, concerning aggregation of the conducted electromagnetic interference introduced by power electronic converters with deterministic [27] and random modulation, might constitute a contribution to the elaboration of relevant standards as well as practical information for engineers dealing with assurance of EMC in systems consisting power electronic converters.

As mentioned above, random modulation might contribute to a reduction of maximum levels of EMI spectrum due to more even dispersion of interference over frequency range in comparison with deterministic modulation. Figure 1 shows the EMI measurement of one buck converter topology, with the *fsw* = 60 kHz, *d* = 0.5 and with both switch control strategies, DetM and RanM. The EMI measurement presented by Figure 1 was carried out based on the FPGA-based system proposed in [20].

The detailed standard requirements concerning conducted EMI can be found in CISPR 16. Standardized conducted EMI measurements consider the frequency range from 9 kHz to 30 MHz, where the Intermediate Frequency Band Width (IFBW) equal to 200 Hz is applied for the range from 9 kHz to 150 kHz (CISPR A) and IFBW = 9 kHz is applied for the range from 150 kHz to 30 MHz (CISPR B). Since the core concept of the DetM is to provide a *fsw* constant under the time. The power spectral density is concentrated for frequencies equal to the harmonics of the switching frequency. On the other hand, RanM provides the spreading of interference over frequency range, thus the reduction of maximum observed values is obtained.

**Figure 1.** Electromagnetic interference (EMI) measurement of DC/DC converter with the *f sw* = 60 kHz and *d* = 0.5: (**A**) for deterministic modulation (DetM) and (**B**) for random modulation (RanM). Results obtained through the FPGA-based system proposed in [20].

The novelty of this paper lies in the presentation of the comparative analysis concerning aggregated interference generated by converters with DetM and RanM. This approach allows us to comprehend the behavior of low-frequency envelopes phenomena beyond the traditional knowledge related with DetM and RanM, i.e., the absence of *fsw* variation means high disturbance values for the *fsw* and its harmonics. On the other hand, through the introduction of *fsw* variation means reduced of disturbances levels. The analyses presented in this paper consider simulations and experimental results based on a standardized testing setup.

#### **2. Simulation Results of Aggregated EMI Generated by DC/DC Converters with Deterministic and Random Modulation**

The simulations of DC/DC buck converters with deterministic and random modulation have been run on MatLab software. The function spectrogram was used, and it returns the Short-Time Fourier Transform (STFT) of the aggregated signal with a Hamming window.

Figure 2 shows the results of the simulation in the form of 3D spectrograms. Simulations have been performed for the *fsw* = 80 kHz and *d* = 0.5. The spectrogram (A) shows results for one interference signal generated by a single converter with DetM, while spectrogram (B) shows the aggregated interference introduced by two converters operating in parallel. Since the superimpositions of the switching frequency harmonics can be related to the summation of sinusoidal signals of similar frequency. This process of aggregating sinusoidal components with similar frequencies causes modulation of their amplitudes with low frequency envelopes. This phenomenon is well-known in acoustics as frequency beat. The theory of frequency beats [24] highlights that the sum of the harmonic vibrations with the frequencies *f*<sup>1</sup> and *f*<sup>2</sup> of amplitudes equal to 1 can be expressed by:

$$\mathcal{S}\_2\left(t; \{f\_1, f\_2\}\right) = \sin\left(2\pi f\_1 t\right) + \sin\left(2\pi f\_2 t\right) \ = \mathcal{L} \cos\left(2\pi \frac{f\_1 - f\_2}{2} t\right) \sin\left(2\pi \frac{f\_1 + f\_2}{2} t\right) . \tag{1}$$

The frequency beat effect appears when | *f*<sup>1</sup> − *f*2| *f*<sup>1</sup> + *f*2. In such conditions, the absolute value

$$\text{Env}\_2\left(t; \{f\_1, f\_2\} \right) = \left| 2 \cos \left( 2 \pi \frac{f\_1 - f\_2}{2} t \right) \right| \tag{2}$$

is the envelope of the aggregated signal. It is also possible to observe that the period of the envelope does not depend on the frequencies of the components, but on the difference between the frequencies of the aggregated signals [24].

The appearance of low frequency envelopes in the case of aggregated interference might cause significant measuring problems.

Additionally, the comparison between spectrograms (A) and (B) in Figure 2 reveals that the maximum observed amplitude is lower in the case of the aggregated interference. However, it should be noted that the power spectral density in a sufficiently wide frequency range and measuring time is higher in the case of aggregated interferences.

**Figure 2.** Simulation 3D spectrograms of interference caused by one DC/DC converter with DetM (**A**), and two DC/DC converters with DetM (**B**).

Figure 3 shows the spectrograms corresponding to those presented in Figure 2 with the same parameters, but for random modulation. In both cases of Figure 3, item (A) and (B), the interference power has been spread over the frequency range, and is more even in comparison with DetM, Figure 2. As a result of a more even distribution of interference power, the maximum measured levels have been significantly decreased.

**Figure 3.** Simulation 3D spectrograms of interference caused by one DC/DC converter with RanM (**A**), and two DC/DC converters with RanM (**B**).
