Waveform distortion is one of the most common electromagnetic disturbances in electrical systems. It is the deviation of voltages and currents from the ideal sine waveform. Periodic distorted voltages and currents are usually studied using the Fourier transform, which decomposes the original distorted signals into a linear combination of pure sinusoids at different frequencies. Using the Fourier transform, the total waveform distortion can be separated into:

Harmonics: spectral components with frequencies that are integer multiples of the fundamental frequency (50 Hz or 60 Hz in most electrical systems).

In order to assess those disturbances, indexes such as total harmonic distortion (THD) for voltage and current, and the individual magnitude for each harmonic are used. The THD is calculated as:

where U _h is the magnitude of the harmonic component of order h, and U ₁ is the magnitude of the fundamental component (component with the fundamental frequency). The THD can be also applied to current signals (THD¡).

Tenti, Paredes, and Mattavelli (2011); Padayattil, Thobias, Thomas, Sebastian, and Pathirikkat (2016); Agundis-Tinajero etal. (2018); and Garde, Casado, Santamaria, and Aguado (2015) report the THD _u from simulations of different islanded microgrids with different load compositions (only non-linear loads, only linear loads, and a mix between linear and non-linear loads). These references show that microgrids with non-linear loads present higher THD _u values than microgrids composed of only linear loads (see Table 1). According to Padayattil et al. (2016) the variation of the THD _u values depends on the type of electronic-based generation and the amount of non-linear load connected.

Table 1

Generation	Load	THDu [%]
Electronic-based	Non-linear	29,9
	Linear	3,48 to 15,76
	Mix	3,57 to 41,67

Source: Authors based on references (Tenti et al., 2011; Padayattil et al., 2016; Agundis-Tinajero et al., 2018; Garde et al., 2015).

Some studies implement control strategies in order to reduce the THDu in those kinds of microgrids. Some of the proposed strategies include adding virtual impedance (Savaghebi, Shafiee, Vasquez, and Guerrero, 2015; Golsorkhi, Lu, Savaghebi, Vasquez, and Guerrero, 2016; Yang, Chen, Dong, and Han, 2015; Micallef, Apap, Spiteri-Staines, Guerrero, 2012; Blanco, Tardelli, Reigosa, Zanchetta, and Briz, 2019), harmonic controller (Zeng, Yi, Zhai, Zhuo, and Wang, 2017; Thai, Raisz, Monti, Ponci, and Ahmadifar 2018; Dehghani, Vahedi, Savaghebi, and Guerrero, 2012), compensations (Phan and Lee, 2019) Fuzzy-PI (Lhachimi, Sayouti, and Kouari, 2020) and artificial neural network (ANN) controllers (Kaushal and Basak, 2020). Table 2 shows the THDu variation of five islanded microgrids when different control strategies are implemented. In most of the cases, the THDu is reduced.

Table 2

Source: Authors based on references (Golsorkhi et al., 2016; Yang et al., 2015; Micallefet al., 2012; Blanco et al., 2019; Zeng et al., 2017; Thai et al., 2018; Dehghani et al., 2012; Phan and Lee, 2019; Kaushal and Basak, 2020).

Additionally, some approaches, such as the one in Lhachimi et al. (2020), apply control strategies integrating IEEE standards in order to reduce the THDu levels in microgrids and accomplish regulation limits in both islanded and connected modes.

Studies by Laaksonen and Kauhaniemi (2008); Nomm, Ronnberg, and Bollen (2018a); Kulia, Molinas, Lundheim, and Fosso (2017); Zhou, Yuan, and Wang (2012); and Algaddafi, Brown, Gammon, Altuwayjiri, and Alghamdi (2016) discuss harmonic distortion in a microgrid when it operates in islanded and interconnected modes. A summary of the results is presented in Table 3 for the THDu index, Table 4 for the THD¡ index, and Table 5 for the first odd harmonic voltage magnitudes. For all the studied microgrid systems, generation sources are electronic-based and could include DGs and ESS. Additionally, four types of load are considered: non-linear load, linear load, motor, and mixed loads (linear and non-linear loads).

Table 3

Source: Authors based on references (Laaksonen and Kauhaniemi, 2008; Nomm et al., 2018a; Kulia et al., 2017; Zhou et al., 2012; Algaddafi et al., 2016).

Table 4

Source: Authors based on references (Laaksonen and Kauhaniemi, 2008; Nomm et al., 2018a; Kulia et al., 2017; Zhou et al., 2012; Algaddafi etal., 2016).

Table 5

Source: Authors based on references (Nomm et al., 2019).

As shown in Table 3, THDu in islanded mode increases by up to 14,6% compared to the values in interconnected mode. Microgrids with only non-linear loads show the highest THDu values in both operation modes. According to Laaksonen and Kauhaniemi (2008), microgrid components such as filters and the switching frequency of converters directly affect harmonic distortion, especially if the load of the microgrids is completely non-linear.

Voltage distortion levels in islanded microgrids depend not only on the type of loads, but also on their size. In Hicks, Baghzouz, and Haddad (2018), THD y is 2,3% in a no-load condition islanded microgrid. When a non-linear load (980W) is connected, the THDu increases to 3,6%. However, when a larger linear load (1,9 kW) is connected to the microgrid, it reaches up to 6,9%.

In Table 4, the THD¡ values for interconnected and islanded modes are presented. Interestingly, THD¡ values not always increase during islanded mode. This is caused by the change in network impedance, which results in a different behavior between loads and generators. According to Laaksonen and Kauhaniemi (2008), Nomm et al. (2018a), and Zhou et al. (2012), when the microgrid has a mixed load, THD _I values increase up to 0,87%, but if the load were completely linear, the THD _I would have similar behavior or could even be reduced, as in the results obtained by Algaddafi, et al. (2016), in interconnected and islanded modes.

Another way to assess waveform distortions is through the harmonic voltage for each harmonic component. Table 5 presents the assessed harmonic voltage for the 3rd to the 15th harmonic. As a general result all harmonic components increase when the microgrid operates in islanded mode, up to 1,44 V (Nomm et al., 2019).

In Nomm et al. (2018a), THDu values are compared against regulatory limits. PQ standards as IEEE Std 519 (IEEE, 2014) and SS-EN 50160 (SEK, 2011) are applied. The study shows that, while in islanded mode, THDu exceeds the established limit, not only in magnitude but also in duration. This means that, within a 48-hour period, THDu values exceed the 8% limit for 10 hours. A comparison against compatibility levels provided in IEC 61000-2-2 as basis for EMC coordination was not performed.

Table 6 summarizes the maximum voltage magnitude in the supraharmonic frequency range interconnected and islanded operation mode in a microgrid with non-linear loads. Laaksonen and Kauhaniemi (2008) and Ronnberg et al. (2017) identified supraharmonics while in interconnected and islanded modes. Both studies show frequency components near the switching frequency (10-12 kHz) of the converters, thus jeopardizing microgrid operations due to possible resonances. Also, it is noted that during islanded operation, more components are present, and the magnitudes become higher by up to 3,5% compared to the interconnected mode.

Table 6

Source: Authors based on references (Laaksonen and Kauhaniemi, 2008; Ronnberg et al., 2017).

The most common indexes to assess fast voltage variations include short-term flicker severity (P _ST ), long-term flicker severity (P _LT ), and the 3-second very short variations index (Ronnberg et al., 2017; Nomm et al., 2019), while slow voltage variations are usually quantified by the variation of 10 min values. Tables 7, 8, and 9 show the maximum value for each index when the microgrid operates in interconnected and islanded modes.

Table 7

Source: Authors based on references (Ronnberg et al., 2017; Nomm et al., 2019).

Table 8

Source: Authors based on references (Ronnberg et al., 2017; Nomm et al., 2019).

Table 9

Source: Authors based on references (Ronnberg et al., 2017; Nomm et al., 2019).

According to Tables 7 and 8, higher values for short-term and long-term flicker were observed while in islanded mode. The P _ST can increase up to 4,66 and, once again, the increase depends on the type of loads.

The results for 10-min variations and 3-second very short variations (VSV) obtained by Nomm et al. (2019) show that the 10-minute VSV values are less severe during islanded operation (see Table 9). However, the 3-second VSV values reach higher maximums during islanded operation. The possible cause of the 3s very short variations in islanded mode is the switching behavior of inverter operation due to solar irradiance variation.

In Ronnberg et al. (2017) and Nomm et al. (2019), microgrid measurements in interconnected and islanded operation modes are compared against regulatory limits, namely the values proposed in IEEE Std 519 (IEEE, 2014) or EN 50160 (SEK, 2011). For Ronnberg et al. (2017), voltage variation indexes are below regulatory limits, but Nomm et al. (2019) states that P _LT values exceed the EN 50160 limit for a maximum of three weeks during a complete year. Both studies measured the same type of loads but received different results. For that reason, it is important to develop further and systematic measurement studies.

The studies presented in Ronnberg et al. (2017) and Nomm et al. (2019) show that voltage unbalance in islanded microgrids is higher than in the interconnected mode. The results of both studies are summarized in Table 10.

Table 10

Source: Authors based on references (Ronnberg et al., 2017; Nomm et al., 2019).

Two operational modes, A and B, in islanded operation are studied in Nomm et al. (2019), depending on their short circuit impedance: mode A fluctuates between 0,1 and 1,0 Ω; and mode B between 0,1 and 2,0 Ω. Voltage unbalance is higher in operational mode B than in mode A with an increase of up to 2 times the values while in mode A. The same analysis for the other PQ parameters, namely voltage variation and harmonic distortion, showed similar results.

Due to the interactions between loads and DGs, frequency variations in an islanded microgrid can be more pronounced, more frequent, and longer (Bollen et al., 2017b). For example, in Nomm et al. (2018b) measurements were performed in a microgrid for 48 weeks. As a result, 89% of the frequency variations were outside the 42,5-57,5 Hz band defined in EN 50160 (SEK, 2011) for islanded grids. Consequently, short interruptions occurred commonly, which might have some adverse effects on certain equipment.

In a network with high DG penetration, some of the DGs may be disconnected from it after a fault. During periods of high DG generation, this might result in local variations in system frequency. This is an evolving issue, and current distribution systems are not necessarily equipped to properly support system frequency, but depend on the interconnected system for load-generation balance (Bollen et al., 2017b). Studies such as Rodrigues et al. (2020) propose a novel frequency control, that allows the frequency setpoint to change adaptively throughout the evolution of the microgrid's islanded operation.