# Power Quality Phenomena, Standards, and Proposed Metrics for DC Grids

## Abstract

**:**

## 1. Introduction

- high-performance control uses information on current not only to improve performance with feed-forward control, but also to control impedance [22];
- distorted current is a cause of induced disturbance through cables, in particular for common-mode components that are often the result of large capacitance to ground (as resulting either by the distributed capacitance of the source or load, such as PV panels or battery banks, or by purposely inserted capacitors to reduce EMI) [20]; common-mode current is not evaluated by the commonly used PQ indexes, being usually ascribed to EMC, and those uncontrolled common-mode currents, aside from interference, may also increase the overall human exposure to magnetic field right where limits are particularly low [37];
- distorted current may also directly cause disturbance for specific signaling systems using the return circuit or ground wire as an active conductor; examples may be found in metros and railways (track circuits using the running rails as part of a coded signal transmission to detect the presence of trains) and in the automotive sector (negotiation of the charging profile of an electric vehicle following SAE J2836-1 [38] and IEC 61851-1 [39] standards, using pulse-width-modulated signals).

## 2. Relevant Power Quality Phenomena

- interference to sources and loads as an EMC (electromagnetic compatibility) problem, affecting e.g., measurement and control quantities;
- interference to sources and loads as an operational problem, resulting in poor voltage quality (fluctuations and variations) disrupting source or load operation, causing flicker, torque variation, etc.; in this respect, DC grids intrinsically perform better thanks to a large amount of local storage;
- issues of network instability and low-frequency oscillations (LFOs), in particular when stressed by major transients, that trigger undamped response of sources and loads; by convention, LFOs in AC networks are confined below the fundamental; here, without loss of generality, LFO may be considered to occur up to a hundred Hz;
- resonances occurring at higher frequency (often named high-frequency oscillations, HFO, or harmonic resonances, HR), above usual control bandwidths, related to network resonances, influenced by the physical extension and interaction with parasitics and reactive elements; and
- impact in terms of overheating and accelerated aging, as for filter capacitors, cables, storage devices, and transformer insulation; ripple current and in general the rms value and the number of charging/discharging cycles are the parameters of the electrical interface considered for quantification of stress and aging of batteries and supercapacitors, in addition to environmental conditions and in particular temperature.

#### 2.1. EMC and Interference

- Residual current devices (RCDs), a class of devices common to AC and DC applications, relying on current measurements for detection of fault conditions with a wide range of fault impedance values. Type B of AC RCDs could be used for DC applications, although they are not fully specified for it; such devices may have an unspecified sensitivity to high-frequency components [43,44]. Conversely, RCDs for DC applications are required to be immune from high-frequency ripple (see section 8.17 in [45]), but the amplitude and frequency of such ripple are not better specified. Coordinated solutions are being proposed complementing the limited immunity of single devices to a wide range of disturbance with an increased information set collected by distance protections and networked devices [46].
- DC leakage monitors: the latest IEC 62020-1 [47] does not yet include DC devices, but they are covered by the EN 61557-8 [48], considering their application to “pure DC IT systems”. Practically speaking, a pure DC IT grid does not exist as some amount of differential- and common-mode ripple is always present. Such devices have been available on the market for a long time (such as Bender [49], Danisense [50] or THIIM [51] brands) with sensitivities that expose them to unwanted tripping, as caused by current ripple, that may also occur on the earth conductors due to unavoidable potential difference between remote locations (in particular when switching power converters are used). In some cases, a selectable filter [50] allows to limit the bandwidth, but the real susceptibility to high-frequency ripple is rarely declared, nor disciplined by any kind of standard. Personal experience with one of these devices indicates susceptibility (and unwanted tripping at the DC threshold of about 10 mA) in the range 50–70 mArms for ripple occurring at some kHz.
- Series arcs detection methods [4,52]. The method in [4] is based on the comparison of current drop estimates in successive short time intervals (50 μs) and with running average values on longer intervals (50 ms), showing a factor of 2 of difference in the indicators with and without arc; the required sampling is 200 kSa/s, thus potentially exposed to high-frequency pollution from static converters, then reduced by successive averaging. Similarly, in [53], min and max current values are run over optimized window lengths (5 to 25 ms), whose difference is an indicator of intermittence; the influence of system noise was not investigated, although the number of consecutive windows used in estimates can be used to filter out grid transients such as load steps, avoiding them being detected as arcs. A much lower sampling of 1440 Sa/s is required in [52], thus less exposed to system noise and high-frequency switching components. Commercially available AFDDs/AFCIs are mainly focused on AC grids (the EN 62606 [54] considers only AC distribution, whereas the UL 1699B [55] specifically addresses arcs in DC grids and PV systems), but the extensive deployment of PV systems has fostered the design of some specific devices [56,57]. The detection method is not detailed, but the monitored frequency range is reported as above 20 kHz [57] and between 20 and 40 kHz [56]. In both cases, this detection range would be exposed to distortion from the AC network (for transformerless PV systems), transient responses to, e.g., step changes [58], and most of all to supraharmonics originating from converters, as it is evident in [56], where the 16 kHz-spaced switching harmonics have almost the same amplitude of the targeted arc noise (and there are cases of noise profiles dominated by such harmonic peaks). Tests of effectiveness and performance indicated by the UL 1699B include a change of distance from the arc to detect (farther by 66 m) to check sensitivity and the verification of correct operation with an inverter connected. A quantitative framework would be welcome, specifying the minimum signal-to-noise ratio with respect to supraharmonics, that should be in any case subject to limitations.
- DC protections for large-power installations are implemented as assisted circuit breakers (called “hybrid”) [11] or fully static semiconductor-based devices [10], driven by detection algorithms. Various techniques have been proposed and applied to DC railways [3,59] and distributed generation DC grids [60,61], exploiting various methods and monitored grid quantities: (i) methods based on autonomous signal injection and impedance estimation [3,59] are rather immune to distortion, as ideally, the applied intensity may increase until a satisfactory operation is achieved; (ii) the criterion proposed for the DC side of a wind power system in [60] is based on DC ripple, that in normal conditions must be low (0.2%) for the method to work; (iii) the robust technique correlating internal current waveforms to separate faults of internal and external origin [61] was tested against uncorrelated Gaussian noise, but not with signal distortion, which is highly correlated as well.

#### 2.2. Voltage Fluctuations and Variations

#### 2.3. Network Instability, Oscillations, and Resonances

#### 2.3.1. High-Frequency Oscillations (HFOs)

_{s}and parallel admittance Y

_{p}of their equivalent circuits, respectively, including the impedance of connecting cables. As demonstrated in [75] and applied to DC grids in [29], where the two curves Z

_{s}and 1/Y

_{p}cross each other and the phase difference approaches 180°, the Nyquist condition is met for sustained oscillations and instability. This usually occurs in the interval of hundreds of Hz to some kHz, distinguishing a first resonance f

_{r}

_{1}where Z

_{s}is inductive and 1/Y

_{p}is capacitive, followed by a second one (f

_{r}

_{2}) with the opposite behavior about a decade above. The first resonance f

_{r}

_{1}is generally characterized by a large value of Z

_{s}that has only started its decreasing slope to intersect the increasing 1/Y

_{p}curve, and is thus of the oscillating voltage type. Conversely, the second resonance f

_{r}

_{2}will see much lower impedance values with amplification of the current. Resonance frequencies may be excited by a wide range of phenomena of both transient and steady nature: load step within the dc grid, step reduction in the generators also within the grid, harmonics of the connected generators and loads, or voltage sags/swells from outside the DC grid through the interface converters. The second intersection is located at some kHz or a ten of kHz in the supraharmonic range.

#### 2.3.2. Low-Frequency Oscillations (LFOs)

#### 2.4. Stress, Heating, and Aging of Components

#### 2.4.1. Capacitors

_{p}, K

_{rms}, and K

_{s}.

- the peak value of the electric field (or voltage) indicates the stress on dielectric;
- the total rms value compared to the fundamental weights the overall distortion of the waveform and this is applicable in general to voltage and current;
- components at higher frequency cause additional heating not only for more pronounced skin effect in conductors (and possibly proximity effect), but also increased dielectric losses, and this is indicated by K
_{s}; this index was derived focusing on the impact of signals with a large derivative, weighting thus each component by its harmonic order; the harmonic order h is in general recognized as related to increased power losses, although they do not go necessarily linearly with h.

_{0}are the lifetime under actual the use conditions and as tested, respectively;

_{0}are the voltage at use condition and as tested, respectively;

_{0}are the temperature in Kelvin at use condition and as tested;

_{a}is the activation energy;

_{B}is the Boltzmann’s constant (8.62 × 10

^{–5}eV/°K); and

_{a}and n are in the range of 1.2–1.5 and 1.5–7, respectively [80]; the highest values of n are for new technologies using thinner dielectric layers. A similar relationship is shown for Al-caps in [84] with n ranging from 1 to 6.

_{r}

_{,f0}indicates a reference ripple current at a given frequency f

_{0}, usually selected at the two ends of the band, namely 100/120 Hz or 100 kHz.

_{f}that weights the relevance of a component to ESR value with respect to a reference frequency, in the present case, 100 kHz (in other cases, also 100 Hz or 120 Hz, the typical ripple of a single-phase diode rectifier, may be taken as reference). Values are shown in Figure 1. The most relevant variation occurs in the first decade of frequency, with K

_{f}almost doubling for the lowest capacitance values and increasing by 10–20% for the largest values. Aluminum capacitors of higher voltage rating (i.e., 100 to 400 V) have higher values of ESR and their increase with frequency is less relevant: K

_{f}increases by 30% in the first decade of frequency at 1 kHz and another 10–15% going up to 10 kHz.

_{rms}that will be discussed in Section 3.4.3, the various R

_{rms,i}terms calculated over frequency intervals FI

_{i}are rms summed after weighting by w

_{i}is applied:

#### 2.4.2. Supercapacitors

- the effect of 100 Hz and 100 kHz in [34] is the same;
- aging due to the amount of current ripple is evident when above about 20% [33];
- the aging figures with respect to ESR and capacitance obtained by [89] are similar/lower than those appearing in [34] for the same time interval; observing that the difference is in the ripple frequency, we may conclude that high frequency would contribute to the aging factors moderately, but up to a factor of 2 for capacitance reduction (although in contrast to [34], this is in agreement with what was observed for aluminum capacitors and commented on in Section 2.4.1).

#### 2.4.3. Batteries

_{chem}of several Farads and kFarads (related to the slower chemical process), a smaller geometrical capacitance C

_{geo}, determined by electrode geometry and deviating high-frequency components away from the charge process (represented by C

_{chem}). At high frequency, the penetration of ions in the porous structure of the electrodes decreases and the high-frequency capacitance is that of a simple planar electrodes capacitor.

_{rms}(or distortion D), as FF = 1 + R

_{rms}, a band-limited approach is thus confirmed as suitable, separating pulsed waveforms (0.1–10 Hz), low-order harmonics (10–1000 Hz), and switching components (>1 kHz), the latter relevant for over-heating only. Ripple during charging reduces the battery efficiency: a 5% R

_{rms}causes a loss of 5% of capacity, stabilized to −10% when the ripple amounts to 20%, at a rate of 5 C. Discharging is less sensitive, with 1% reduction when R

_{rms}= 20%.

#### 2.4.4. Photovoltaic Panels

^{2}insolation and 25 °C; I

_{PV,sc}indicates the short circuit current available at that insolation level). Loss of efficiency is almost proportional to the frequency at the same ripple amplitude; at low ripple, the accuracy of measurements is such that no meaningful figures can be derived.

#### 2.4.5. Fuel Cells

_{pp}) of 45% and 33%, respectively. A second effect is the appearance of ripple in the FC output voltage due to its limited short-circuit power (i.e., its internal resistance). This indicates that moderate ripple current levels are tolerable as for loss of efficiency, and that the current ripple may be set to about 10–20% peak-to-peak by design of the downstream converter.

_{avg}(that corresponds to some utilization % of the FC, with about 45 A corresponding to a 100% level of utilization). Ripple amplitude is measured as peak–peak ripple over the DC steady value. Ripple frequency varied between 30 and 1250 Hz. Hydrogen concentration is less influenced, with a reduction of 2% only above 70% cell utilization and at the lowest tested ripple of 30 Hz, becoming negligible above 120 Hz. Conversely, oxygen concentration is more affected. Data were extracted from [105] and are shown in Table 4.

## 3. Standard Classification of Power Quality Phenomena

#### 3.1. Voltage Swells, Sags, and Interruptions

_{dc}value replaces the rms and in principle it can be calculated over an arbitrary time interval, although there is general convergence on 1 s for its definition [107].

#### 3.2. Fast Transients (Spikes and Surges)

#### 3.3. Inrush Current and Short-Circuit Current

_{max}test in the IEC 61000-3-3 [124] is carried out by repetitive inrush with a feeding inductance of 796 μH corresponding to a more extended network (in the order of 1 km). A fully developed DC grid of similar extension, but with larger deployed capacitance, will exhibit both resonances and significant voltage drops if not locally compensated (at the expense of increasing somewhat local inrush phenomena and rapid overshoot, as initially commented).

_{3}and capacitance C

_{p}) superposed to the exponential decay to the nominal situation.

#### 3.4. Harmonics, Ripple, and Periodic Variations

#### 3.4.1. Harmonics

_{dc}, obtaining the distortion factor DF = D/V

_{dc}. Attention is drawn on two points: the extension of the frequency interval and the definition of V

_{dc}.

_{dc}is conventionally taken as the average over a time interval usually in the order of 1 s; other time intervals may be used, or the steady value replaced by the nominal value.

#### 3.4.2. Supraharmonics

- primary emissions, whose sources are recognized in the switching components of various kinds of converters, interfacing, and regulating sources and loads; primary emissions are caused by the identified sources in relation to the network impedance, often substituted by the LISN during laboratory tests;
- secondary emissions are caused instead by the loading of nearby sources and loads, including in particular EMI filters, modifying as a matter of fact the overall network impedance seen at the measurement terminals; this phenomenon has been recently considered as a significant source of variability and deviation of measurement results from those referred to the network alone [20,127];
- a quite general third type of emission can be identified in the interaction of low-frequency network distortion with mechanisms of emission for non-linear loads, for which the behavior in real use conditions would be different from ideal lab testing in controlled supply condition.

- Combined disturbance of N equipment of the same type connected to the same distribution area would increase by √N, assuming a random distribution of the phase for emission components at the same frequency; already at N = 4 the margin is reached, and compatibility would not be ensured.
- Different types of equipment are likely to position their emissions at different frequencies, thus not summing for the determination of the overall spectrum of emissions, but all concurring for the determination of the overall distortion D. In this case, the margin with respect to D values discussed in Section 3.4.3 is much wider, as by summing all components of Figure 8, we would get a contribution of about 0.2 Vrms.
- Network resonances amplify network distortion and as discussed for the inrush case, resonance occurred in the kHz range for cables in the order of 50 m of length, including the effect of the significant amount of deployed capacitance. The factor of merit taking into consideration resistance and inductance of cables in [124] would be in the order of 1.5–1.7. The shallow profile between 500 Hz and 3 kHz in Figure 8, compared to the profile in Figure 9, seems to indicate that a margin of 5 dB was taken, possibly right for resonance phenomena.

#### 3.4.3. Ripple and Voltage Fluctuations

_{dc}”: this is an instantaneous definition, with V

_{max}, V

_{min}, and V

_{dc}taken over a predetermined interval.

_{pp}is considered and then divided by 2, and compared to the mean value of the network voltage V

_{dc}.

_{p}

_{,3}value, as shown in the example of Figure 10: V

_{max}= 20, V

_{min}= 5, therefore R

_{p}

_{,3}= 0.6 for both, but the two waveforms are centered around 7.5 and 12.5, resulting in an asymmetric and symmetric ripple, respectively. That is not captured by R

_{p,3}; R

_{p}

_{,1}would result in 12.67 and 0.6. The result of 0.6 when the steady value is centered between min and max is not surprising, as (8) is self-centering by definition.

_{p}can be made equivalent: R

_{p}= √2 D. In general, an instantaneous definition of ripple is clearly preferable for further processing but must be accompanied by the quantification of the selected time interval for its calculation, which is equivalent to the bandwidth, as shown later in Section 4.2. For rectification harmonics, as commonly considered in standards, the bandwidth should capture at least the 2nd up to the 6th harmonic of the AC system upstream [68].

_{rms}and 5% for “voltage cyclic variation deviation”, that is not defined and appears only once in that Table 2 (it is surely in relation with rectification harmonics). A similar expression may be found in IACS E5 [108], Table 2, and Lloyd’s rules [109], Part 6, Chap 2, sec. 1.8.4.

#### 3.5. Common-Mode Disturbance

^{2}, that translated into capacitance per installed kW may range between 50 and 150 nF/kW [135]; additional minor effects may be expected by the presence of water, depending on the extent of coverage of the panel and the degree of sealing of the structure [136].

## 4. PQ Indexes for Quantification of Phenomena

#### 4.1. Spectrum Components, Harmonic/Supraharmonic Analysis, and Aggregation

- the IEC 61000-4-30 indicates a rms approach, so that ${X}_{10\mathrm{min}}=\sqrt{\frac{1}{N}{\displaystyle \sum _{1}^{N}{X}_{3\mathrm{sec}}^{2}}}$, where N = 10 min/3 s = 200;
- the statistical distribution of index results may be more informative, provided that a compact representation is provided, such as mean and dispersion, median, percentile, or similar (as applied to ripple in Section 4.2.2).

- The IEC 61000-4-7 for AC systems requires grouping of inter-harmonic components, in principle not applicable to DC systems and also does not transfer well to higher frequency intervals above 9 kHz.
- The IEC 61000-4-30 hints at the use of CISPR 16-1-2 frequency scan method, which has a major drawback: the resolution bandwidth (RBW) is 200 Hz for frequencies up to 150 kHz and this is inadequate to capture highly localized emissions caused by switching by-products, as shown in [142]; a larger RBW should be used, losing, however, the major strength pointed out in the IEC 61000-4-30, that is the direct comparison with limits or reference levels of IEC/CENELEC standards.
- A band limited method using 2 kHz spacing is also proposed by the IEC 61000-4-30, using a time-domain acquisition followed by Fourier analysis, but alternative methods may be implemented, such as a bank of filters or multiresolution signal decomposition (MSD) algorithms (e.g., wavelet packet decomposition and variational or empirical mode decomposition [142,143,144]). The 2 kHz resolution matches the observations in [142], where 0.5–1 ms time localization was identified as optimal for the accurate estimate of non-stationary components related to switching pulses. A broader frequency resolution is also in line with the broadband characteristics of the mechanisms of interference and the minimum channel width of PLC systems.

#### 4.2. Ripple

_{min}and maximum V

_{max}of the network voltage, without clarifying which time interval is considered, or in other words the shortest and longest distance in time between the samples corresponding to V

_{min}and V

_{max}. This was formalized in [106] writing down a time-domain definition, q

_{pp}

_{,T}:

_{1}and k

_{2}indicating the extremes of an interval that is defined as the minimum time difference T

_{min}and the observation window length T, namely k

_{1}= T

_{min}/t

_{s}, k

_{2}= T/t

_{s}.

_{k}, a recursive formula may be used that compares new samples with the previously stored x

_{min,k-1}and x

_{max,k-1}, reducing the operations to 2 M comparisons, for the M new samples.

_{LFSD}and in [41] with RDF. When applied to the current, it quantifies more directly phenomena such as load steps and inrush.

_{dc}without considering two other signal characteristics, the spectrum occupation (or, alternatively, the time-domain dynamics) and the rate of occurrence, which are discussed in the following.

_{SA}and q

_{SAP}, respectively,

_{thr}), to avoid the inclusion of noise in the determination of the q quantities on the left side. The results shown in [106] indicate that using absolute values only leads to an overestimation of ripple and that including phase of DFT components give results in line with the time-domain calculation.

#### 4.2.1. Band-Limited Ripple Index

_{bl}is used (the notation used in [106] was ${\tilde{q}}_{pp,T}$).

_{band}for frequency selection, equivalent to the K

_{thr}set for the selection of significant components).

_{bl}can be immediately implemented as a filters bank for a set of frequency bands, selecting the intervals to match the outcome of the discussion of physical phenomena (see Section 2) and normative requirements (Section 3). Different weights may be then assigned to the various frequency intervals, as anticipated by Equation (5). The accurate distinction of components in terms of amplitude and frequency is unnecessary, as long as the examined phenomena of interference and impact on devices are not frequency-selective and use generic indications such as low-order harmonics, high-order harmonics, and supraharmonics.

#### 4.2.2. Statistics and Time-Series Analysis

^{+}

_{y}

_{%}is the y-th percentile of samples of vector x with value exceeding the median of the vector itself, and x

^{−}

_{y}

_{%}is the complementary percentile, that corresponds to the (100-y-th) percentile. This difference measures the number of samples lying in the central part of the signal, within the boundary set by the y% value.

_{y}

_{%}is then defined as the ratio of the two complementary y-th percentiles just considered:

#### 4.3. Transients and Pulsed Loads: Area, Energy, Duration, and Power Trajectory

_{eq}and half-amplitude time duration T

_{50}, as it is commonplace for surges and lightning induced phenomena [155]. The combination of the two elements leads to two straightforward measures of the intensity: the area S and the energy E, both calculated over a convenient interval [t

_{1}, t

_{2}] by taking the ac portion $\tilde{x}(t)$ of the network quantity x(t) (voltage or current), having subtracted the steady value X.

_{eq}, as duration of the rectangular signal of amplitude A (the peak value of the original signal) and same area:

^{2}s.

_{P}(t) is defined, for which an incremental additional energy ΔE

_{P}is calculated as its integral over a given time interval T

_{P}.

_{P}(t) by exploiting the Fourier series of the absorbed power, an equivalent expression in the frequency domain was obtained in [154], as follows:

_{P}(t) is analyzed for its spectral properties, individual and total harmonic distortion may be calculated in analogy to what has been recently done for AC grids onboard US Navy electric ships in Appendix A of [156], where power distortion (PD) is calculated over the frequency interval 1 Hz–2 kHz for the harmonic active power components P

_{n}with respect to the total active power P

_{av}named “real power”:

_{P}

_{,d}, d

_{P}

_{,g}, S

_{0}, and E

_{0}(shown in brown) calculated for the power trajectory, which exhibit a much wider variation distinguishing well the three considered intervals.

## 5. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Nomenclature

AFCI | arc-fault circuit interrupter |

AFFD | arc fault detection device |

BPL | broadband over power line |

C_{chem} | electrochemical capacitance |

C_{geo} | geometrical capacitance |

D | distortion |

DF | distortion factor |

EMC | electromagnetic compatibility |

ESR | equivalent series resistance |

FC | fuel cell |

FCC | federal communication commission |

FF | form factor |

HFO | high-frequency oscillation |

I_{avg} | average (DC steady) current |

I_{pp} | peak-peak ripple current |

I_{rms} | current rms value |

I_{PV,sc} | short-circuit current PV panel |

LFO | low-frequency oscillation |

LV | low voltage |

MPPT | maximum power point tracking |

MV | medium voltage |

PEM | proton exchange membrane |

PLC | power line communication |

PQ | power quality |

PV | photovoltaic |

RCD | residual current devices |

R_{p} | peak ripple |

R_{pp} | peak–peak ripple |

R_{rms} | rms ripple |

SPD | surge protecting device |

THD | total harmonic distortion |

VLRA | valve regulated lead acid |

XLPE | cross-link poly ethylene |

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**Figure 2.**Aluminum electrolytic capacitors: aging of (

**a**) capacitance, (

**b**) ESR, and (

**c**) weight loss (expressed in grams) vs. ripple frequency and elapsed time (peak–peak ripple amplitude 10%) [89].

**Figure 3.**Profile of allowed transient overvoltage/undervoltage: (

**a**) avionics (in blue the normal range and in brown the exceptional range, dark for 270 Vdc and light for 28 Vdc systems; the triangles indicate the permanent network voltage excursion around nominal values; MIL-STD-704F [107]); (

**b**) railways (overlapped curves of immunity tests as per Figure 6 through 11 of EN 50155 [116]; colors just distinguish the profiles with no particular meaning).

**Figure 4.**Inrush limits for telecommunications and data centers (EN 300 132-2 [111] © ETSI 2019. All rights reserved), having indicated with I

_{m}the maximum steady state input current of the ICT equipment.

**Figure 5.**Overlapped inrush events as caused by EMI filter Cy capacitors and leveling capacitors of the first input stage of DC equipment (EN 300 132-2 [111] © ETSI 2019. All rights reserved).

**Figure 6.**Voltage transient caused by short-circuit at one connected load of a power distribution cabinet with short power cables (EN 300 132-3-1 [125] © ETSI 2011. All rights reserved).

**Figure 7.**Profile of harmonic and supraharmonic network limits for avionics, as per MIL-STD-704F [107], DC bus 28 Vdc (for the 270 Vdc bus limits are 10 dB higher).

**Figure 8.**Profile of harmonic and supraharmonic limits of emission for equipment in telecommunications and data centers, 48 Vdc, as per EN 300 132-2 [111] © ETSI 2019, all rights reserved. Measurement is carried out with 10 Hz resolution bandwidth up to 10 kHz and 200 or 300 Hz between 10 and 20 kHz.

**Figure 9.**Profile of harmonic and supraharmonic levels of immunity for telecommunications and data centers, –48 Vdc (EN 300 132-2 [111] © ETSI 2019. All rights reserved).

**Figure 10.**Two sketched voltage profiles for which the R

_{p}

_{,3}value is the same, but different steady state values and evidently different R

_{p}

_{,1}ripple value: (

**a**) symmetric and (

**b**) symmetric ripple.

**Figure 11.**Exemplified harmonic/supraharmonic conducted disturbance: (

**a**) resonant converter to interface a fuel cell with an electric vehicle [138]: V

_{FC}(light blue), I

_{FC}(blue), AC coupled V

_{FC}(red) where voltage transients are visible; (

**b**) resonant DC/DC 400/12 V converter for data center [139]: AC coupled V

_{out}; (

**c**) random modulation DC/DC converter for Li-ion batteries [140]: deterministic modulation (red), random modulation (black).

**Figure 12.**PPL profile with periodic pulsation and superposed ripple (elaborated from [154]): voltage (black) and current (grey) use the left axis, power (red) uses the right axis. Calculation of metrics for three consecutive periods: top black are for the voltage profile V(t) (S, E, and τ with the prime indicating subtraction of the steady state value V

_{dc}), middle brown for the power trajectory P

_{P}(t) (metric d

_{P}calculated using “difference” of adjacent samples, d

_{P,d}, and “gradient”, d

_{P,g}, a central difference where samples are separated by an empty place; metrics S and E applied to P

_{P}(t) as a network quantity, having subtracted the steady value for each period).

**Table 1.**Summary of effect of sources and loads (and their number) on DC microgrid main resonance [29].

Sources and Loads ^{(1)}(Increase Number or Rated Power) | Grid Parameters | ||||
---|---|---|---|---|---|

Stability ^{(2)} | Impedance | Main Res. Freq. | Main Res. Damping | ||

Sources | Voltage controlled (VCS) | ↑ | ↓ | ↑↑ | ↑↑ |

Current controlled (CCS) | ↓ | ↑ | ↓ | ↓↓ | |

Loads | Constant current (CCL) | ↑ | — | ↑↑ | ↑↑ |

Constant impedance (CIL) | ↑ | — | ↑↑ | ↑↑ | |

Constant power (CPL) ^{(3)} | ↓ | — | ↓ | ↓↓ |

^{(1)}Effect of sources and loads is evaluated assuming that their number or their rated power increase;

^{(2)}Contribution to stability is neutrally evaluated, as a consequence of damping;

^{(3)}CPLs in their operating bandwidth behave like negative CILs.

**Table 2.**Supercapacitors: dependency of ESR and capacitance on frequency, ripple, and number of cycles.

Ripple | ESR | Capacitance | Ref. |
---|---|---|---|

20% rms, 0.1 Hz (±5 Apk sin. on 30 Adc) | linear +50% at 0–60% ripple | −5% at ≥20% ripple | Sarr * et al. [33] |

10% rms, 100 and 10 kHz (12 Arms sin. on 120 Adc) | +2/+20% at 1000 h, +25/+70% at 5000 h | −10/−16% at 1000 h, −25/−30% at 5000 h | German et al. [34] |

16.7% p-p (9.6% rms), 0.1–0.5 Hz (±5 Apk triang. on 30 Adc) | 0% at 0.2 Hz, +15% at 0.5 Hz +8% at 1000 cy (110 h), +8% at 8000 cy (900 h), +12% at 14,000 cy (1550 h) | −2% at 0.2 Hz, −3% at 0.5 Hz −2% at 1000 cy (110 h), −5% at 8000 cy (900 h), −6% at 14,000 cy (1550 h) | Bellache et al. [89] |

**Table 3.**PV panel efficiency as a function of ripple (frequency and peak-peak amplitude) [102].

Efficiency % | Ripple Amplitude (mA) | Ripple Frequency (kHz) | ||
---|---|---|---|---|

5 | 10 | 25 | ||

Low insolation 0.07 kW/m ^{2}I _{PV,sc} = 175 mA | 50 | >99 | >99 | 98 |

100 | 98.5 | 96 | 91.5 | |

150 | 97 | 87 | 74 | |

High insolation 0.193 kW/m ^{2}I _{PV,sc} = 483 mA | 100 | >99 | 99 | 98 |

200 | 99 | 94 | 92 | |

400 | — | 81 | 75 |

**Table 4.**Fuel cell efficiency * as a function of ripple (frequency and peak–peak amplitude, expressed by ripple factor I

_{pp}/I

_{avg}) [105].

Test Type | Operating Point % | Ripple Factor % | Ripple Frequency (kHz) | |||
---|---|---|---|---|---|---|

30 | 60 | 120 | 1250 | |||

Hydrogen concentration | ≤80 | >99 | >99 | >99 | >99 | |

98 | 91 | 96 | — | — | ||

Oxygen concentration | 25 | 3 | >99 | >99 | >99 | >99 |

9 | >99 | >99 | >99 | >99 | ||

30 | 97 | 98.5 | 99 | >99 | ||

62 | 3 | >99 | >99 | >99 | >99 | |

9 | 98 | 99 | 99 | >99 | ||

30 | 93 | 95 | 96.5 | 99 | ||

98 | 3 | 99 | >99 | >99 | >99 | |

9 | 95 | 97.5 | 98 | >99 | ||

30 | 85 | 87 | 91 | 97.5 |

**Table 5.**Limits and test values for transient phenomena (voltage swells, sags, and interruptions) (E = emission, I = immunity, G = generator, A = ambient specification).

Standard | Phenomenon | Type | Nom. Volt. U_{n} [V] | Ref. Values | |
---|---|---|---|---|---|

MIL-STD-704F | Voltage var. | A | 28, 270 | see Figure 3a | |

EN 61000-4-29 | Voltage var. | I | 24–110 | 85–120%, 0.1–10 s | |

EN 61000-4-29 | Voltage dip | I | 24–110 | 40, 70%, 0.01–1 s | |

EN 61000-4-29 | Voltage interr. HiZ and LoZ | I | 24–110 | 0%, 0.001–1 s | |

IACS | Voltage var. | I | ≤1kV | 95–105% | |

Lloyd Reg. | Voltage var. | I | LV & MV | 90–110% | |

EN 50155 | Voltage var. | I | 24–110 | see Figure 3b | |

EN 50155 | Voltage interr. | I | 24–110 | 0%, 0.01–0.03 s | |

L.1200 | Voltage var. | A | 300, 380 | U_{n}→400→U_{n}, 1 minU _{n}→260→U_{n}, 1 minU _{n}→410→U_{n}, 1 sU _{n}→420→U_{n}, 10 ms | |

L.1200 | Voltage dip | I | 300, 380 | 40%, 0.01 s | |

L.1200 | Voltage interr. HiZ & LoZ | I | 300, 380 | 0%: 0.01 s (LoZ), 1 s (HiZ) |

**Table 6.**Limits and reference values for ripple (voltage ripple, if not otherwise specified) (E = emission, I = immunity, G = generator, A = ambient specification).

Standard | Type | Nom. Volt. U_{n} (V) | Ref. Values | |
---|---|---|---|---|

MIL-STD-704F | A | 28 | DF < 3.5%; R_{p}_{,1} < 1.5/28 V | |

MIL-STD-704F | A | 270 | DF < 1.5%; R_{p}_{,1} < 6/270 V | |

EN 61000-4-17 | G | ≤360 V | V_{rip-gen} = R_{pp} = 2, 5, 10, 15% | |

IACS | I | ≤1 kV | R_{rms} < 10% ^{(1)} | |

EN 50155 | I | 24–110 | R_{p}_{,2}, R_{p}_{,3} < 5% | |

IEEE Std. 1662 | I | LV & MV ^{(2)} | R_{rms} < 10% ^{(1)} | |

IEC 61851-23 ^{(3)} | A,E | LV | R_{p}_{,1} < 5 V | |

Lloyd Reg. | I | LV & MV | R_{rms} < 10% ^{(1)} |

^{(1)}accompanied by specification of “voltage cyclic variation” of 5%;

^{(2)}for MV reference to IEEE Std. 1709, that covers 1 to 35 kV DC;

^{(3)}ripple specified for the charger–vehicle interface during pre-charge and charging.

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**MDPI and ACS Style**

Mariscotti, A.
Power Quality Phenomena, Standards, and Proposed Metrics for DC Grids. *Energies* **2021**, *14*, 6453.
https://doi.org/10.3390/en14206453

**AMA Style**

Mariscotti A.
Power Quality Phenomena, Standards, and Proposed Metrics for DC Grids. *Energies*. 2021; 14(20):6453.
https://doi.org/10.3390/en14206453

**Chicago/Turabian Style**

Mariscotti, Andrea.
2021. "Power Quality Phenomena, Standards, and Proposed Metrics for DC Grids" *Energies* 14, no. 20: 6453.
https://doi.org/10.3390/en14206453