# A Low-Voltage DC Backbone with Aggregated RES and BESS: Benefits Compared to a Traditional Low-Voltage AC System

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## Abstract

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## 1. Introduction

- Conversion and cable losses: As has already been discussed, in an LVDC backbone grid architecture the number of converters is highly reduced. However, the number of conversion stages is the same compared to a traditional AC grid. The multiple small DC/AC inverters are replaced by one common inverter. The comparison of both will be performed based on converter loss models. Secondly, the cable losses will be analysed for both architectures. In a traditional AC grid, the produced and stored energy can be directly consumed by the grid user, while for an architecture with an LVDC backbone additional cable losses occur on the DC side. Nevertheless, the losses can be reduced due to the higher operating DC voltage and the reduced unbalance.
- SCI and SSI: It has been shown in various other works that the aggregation of demand and sharing of PV and BESS increases the SCI and SSI. In this work, this will be analysed taking into account the cable and converter losses that occur. This will be carried out for three situations: a traditional AC architecture with individual PV and BESS (i) without energy sharing and (ii) with energy sharing, as well as (iii) an LVDC backbone architecture with energy sharing.
- Savings in assets: The savings in PV and BESS are here analysed for an LVDC backbone compared to a traditional AC grid with individual PV and BESS and the possibility to share energy. The savings will be calculated assuming, as a starting point, that the same benefits in terms of SSI should be achieved as with a traditional AC architecture with energy sharing. The savings in assets could be translated into a saving of materials and therefore an environmental benefit.

## 2. Studied Systems

#### 2.1. Grid Architectures

- ‒
- Individual PV and BESS on AC grid without the possibility to share energy (Figure 1a): Every household has its own energy meter so that the energy provider can invoice the household pro rata their electric consumption. The produced PV energy of each household that has not been directly consumed or stored is injected into the grid. As the feed-in tariff is declining every year or even phased out in some countries, it is assumed in this study that the grid user could only benefit from the self-consumed energy [26].
- ‒
- Shared PV and BESS on AC grid with the possibility to share energy (Figure 1a): The grid is considered as a closed distribution grid and its users forms a community. Hence, the community is considered as a single entity connected to the grid, with one single meter measuring the net consumed energy. The community will be invoiced pro rata their net consumed energy, and this cost will be divided among the participants according to their real consumption.
- ‒
- Shared PV and BESS on LVDC backbone (Figure 1b): The same for this architecture, however, the PV and BESS are now connected to a unipolar LVDC backbone. Instead of having small individual PV installations and BESS, a larger community PV installation as well as a community BESS is foreseen.

#### 2.2. Case Description

## 3. Materials and Methods

#### 3.1. Flowchart

#### 3.2. Conversion Loss Model

- ‒
- Effects of temperature on device phenomena. In this article, a constant temperature of 25 ${}^{\xb0}$C has been assumed.
- ‒
- The dynamics that occur at higher frequencies due to parasitics as they have a time scale that is typically much shorter than the switching period.
- ‒
- Other dynamics related to the switching phenomena, such as the diode reverse recovery and the tail current of the switch.

- ‒
- Switching losses ${P}_{sw}$: These losses occur during the transition phase of the switching state and depend on the voltage ${V}_{S}$ across the switch and the current ${I}_{S}$ flowing through the switch. The faster the switching element switches on or off, the lower the switching losses. The higher the switching frequency or parasitic capacitance, the higher these losses [33].$${P}_{sw}=\frac{1}{2}{I}_{S}{V}_{S}({t}_{on}+{t}_{off}){f}_{s}+\frac{1}{2}{C}_{OSS}{V}_{s}^{2}{f}_{s}$$
- ‒
- Conduction losses ${P}_{j}$ in the switching elements: In the model, MOSFETs are considered as switching elements. These elements have a certain on-state resistance which causes conduction losses when the switch current with waveform ${i}_{S}\left(t\right)$ is flowing. The time period of the switching cycle is represented by ${T}_{s}$.$${P}_{j}={R}_{DS,on}\frac{1}{{T}_{s}}{\int}_{0}^{{T}_{s}}\phantom{\rule{-0.166667em}{0ex}}{i}_{S}{\left(t\right)}^{2}\phantom{\rule{0.166667em}{0ex}}\mathrm{d}t$$
- ‒
- Conduction losses ${P}_{D}$ in the diodes: The same applies for the diodes. However, the losses occuring in the diodes are often smaller than those occuring in the switching elements [34].$${P}_{D}=\frac{1}{{T}_{s}}{\int}_{0}^{{T}_{s}}\phantom{\rule{-0.166667em}{0ex}}{i}_{S}\left(t\right){V}_{F}+{i}_{S}{\left(t\right)}^{2}{r}_{T}\phantom{\rule{0.166667em}{0ex}}\mathrm{d}t$$
- ‒
- Core losses ${P}_{Lc}$ in the inductor: As no materials exhibit a perfect magnetic response, losses occur in the core when the magnetic flux B changes. Thus, there is no direct proportionality with the magnitude of the current. The calculation of these losses is based on the approach of the generalised Steinmetz equation and is calculated per volume unit [35]. The improved Steinmetz parameter is obtained by Equation (5), with $\omega t$ representing the angular frequency.$${P}_{Lc,V}=\frac{1}{{T}_{s}}{\int}_{0}^{{T}_{s}}\phantom{\rule{-0.166667em}{0ex}}{k}_{i}{\left(\right)}^{\frac{\mathrm{d}B}{\mathrm{d}t}}\alpha $$$${k}_{i}=\frac{k}{{\left(2\pi \right)}^{\alpha -1}{\int}_{0}^{2\pi}\phantom{\rule{4pt}{0ex}}{\left(\right)}^{cos\omega t}\alpha}$$
- ‒
- DC conduction losses ${P}_{L,dc}$ in the inductor: Due to the DC resistance of the windings, conduction losses occur. ${I}_{L}$ is the current flowing through the inductor.$${P}_{L,dc}={R}_{L,dc}{I}_{L}^{2}$$
- ‒
- AC conduction losses ${P}_{L,ac}$ in the inductor: Skin effects occur due to the high switching frequency, causing the resistance ${R}_{L,dc}$ to increase. It should be noted that here only the AC component of the current ${I}_{L,ac}$ is taken into account. Secondly, a constant current density is assumed in the current flowing part of the conductor.$${P}_{L,ac}={R}_{L,ac}{I}_{L,ac}^{2}$$$${R}_{L,ac}=\frac{\rho {l}_{c}}{\pi {r}_{c}^{2}-\pi {({r}_{c}-\frac{1}{\sqrt{\pi \sigma {\mu}_{0}{f}_{s}}})}^{2}}$$
- ‒
- Conduction losses ${P}_{C}$ in the capacitor: Capacitors have a certain equivalent seriea resistance which represents conduction losses. The current flowing through the capacitor is represented by ${i}_{c}$. The capacitor design parameters can be found in Table A5.$${P}_{C}={R}_{C}\frac{1}{{T}_{s}}{\int}_{0}^{{T}_{s}}\phantom{\rule{-0.166667em}{0ex}}{i}_{C}{\left(t\right)}^{2}\phantom{\rule{0.166667em}{0ex}}\mathrm{d}t.$$

#### 3.3. Consumption Profiles

#### 3.4. PV-BESS System

#### 3.5. System Voltage

- ‒
- Battery voltage:
- ‒
- Single- and three-phase system: When looking at the market nowadays, two general centres of gravity are observed: low-voltage systems of 48 V and high-voltage systems in the range of 400 V. While 48 V batteries are widely available and accepted as standard for the telecommunication market, high-voltage systems can have different voltages. This makes 48 V more adequate, as it can be parallelised with existing systems, combined with other battery technologies, or easily be replaced [41,42,43]. Moreover, this voltage is within the range of the extra-low-voltage class defined by the IEC 60038. Consequently, those systems have a lower risk of electric shock than high-voltage systems. It should be noted that this voltage is the nominal voltage.
- ‒

- ‒
- PV voltage:
- ‒
- Single- and three-phase system: The Flemish regulation, the Synergrid C10/11 states that for peak powers of DER larger than or equal to 5 kVA a three phase connection is committed [46]. Small systems (<5 kVA) are here configured with five panels per string while larger systems (≥5 kVA) have ten panels per string. Knowing that the voltage for maximal power of the considered module type is 29.5 V, this leads to the voltages shown in Table 3.
- ‒
- LVDC backbone: For larger PV systems, the number of panels in series is further increased to 24 to obtain higher voltages in order to limit the cable losses.

- ‒
- DC voltage:
- ‒
- Single- and three-phase system: A unity amplitude modulation index (${m}_{a}=1$) is considered in this work to calculate the DC-bus voltage of the inverter. This is based on research [31] done in that field, were it has been found that overmodulation (${m}_{a}>1$) leads to a considerable increase in third harmonics in the current, which increases the current in the neutral conductor as well as the harmonic distortion of the voltage at grid side. At the other hand ${m}_{a}<1$ leads to a higher current and voltage harmonic distortion [47,48].
- ‒
- LVDC backbone: As already discussed before, the operation voltage level of LVDC systems is today a matter of debate. A trade off has to be made between reliability, safety, cost, and efficiency. For the presented LVDC architecture, the efficiency aspect is related to the cable losses but also to the conversion losses. The latter is very dependent on the nominal voltage the battery and the PV system is operating on. The optimal voltage level for maximal efficiency will be determined and used in the further analysis.

#### 3.6. Power Flow Analysis

#### 3.7. Loss Calculation

#### 3.8. SCI and SSI

## 4. Optimal Voltage Level

## 5. Results and Discussion

#### 5.1. Conversion and Cable Losses

#### 5.2. SCI and SSI

#### 5.3. Saving in BESS and PV

## 6. Further Investigation

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Parameters and Specifications

#### Appendix A.1. General Parameters

Symbol | Parameter | Value |
---|---|---|

${V}_{F}$ | Diode forward voltage | 1.45 V |

${r}_{T}$ | Dynamic resistance | 0.5 m$\mathsf{\Omega}$ |

${f}_{s,dcdc}$ | Switching frequency DC/DC-converters | 50 kHz |

${f}_{s,dcac}$ | Switching frequency DC/AC-converters | 4 kHz |

$\Delta u$ | Maximal allowable voltage ripple | 5% |

$\Delta i$ | Maximal alowable current ripple | 5% |

${\mu}_{0}$ | Permeability of free-space | $4\pi {10}^{-7}$ H/m |

${\mu}_{r}$ | Relative permeability of the core material | 256 |

$\rho $ | Specific resistance of the inductor winding | 1.68 × ${10}^{-8}$ $\mathsf{\Omega}$m |

${B}_{max}$ | Saturated magnetic flux density of core material | 0.5 T |

$\alpha $ | Steinmetz material constant 1 | 1.43 |

$\beta $ | Steinmetz core material constant 2 | 1.585 |

k | Steinmetz core material constant 3 | 15.144 |

$\sigma $ | Conductivity of the inductor winding | 5.96 × ${10}^{7}$ S/m |

${A}_{e,type}$ | Effective area of the typical core | 279 mm^{2} |

${l}_{e,type}$ | Effective length of the typical core | 144 mm |

${l}_{e,type}$ | Effective turn length of the typical conductor | 97 mm |

${l}_{air}$ | Air gap length | 10 mm |

J | Allowed current density in the inductor winding | 2 × ${10}^{6}$ A/m |

K | Window utilization factor of the inductor | 0.5 |

#### Appendix A.2. Switch Parameters

I_{D} (A) | V_{ce} (V) | R_{DS,ON} ($\mathbf{\Omega}$) | t_{on} (ns) | t_{off} (ns) | C_{oss} (nF) | Type |
---|---|---|---|---|---|---|

5 | 1700 | 1 | 6 | 11 | 0.012 | C2M1000170D |

10 | 1200 | 0.28 | 5.2 | 10.8 | 0.023 | C2M0280120D |

15 | 900 | 0.17 | 27 | 25 | 0.04 | E3M0120090D |

35 | 1000 | 0.065 | 20 | 19 | 0.06 | C3M0065100K |

72 | 1700 | 0.045 | 48 | 65 | 0.171 | C2M0045170D |

118 | 900 | 0.02 | 40 | 63 | 0.296 | NTHL020N090SC1 |

219 | 1200 | 0.012 | 35 | 150 | 0.66 | APTMC60TLM14CAG |

423 | 1200 | 0.0042 | 76 | 168 | 2.57 | CAS300M12BM2 |

800 | 1700 | 0.01 | 485 | 790 | 0.3 | 5SND 0800M170100 |

1000 | 1700 | 0.0084 | 270 | 570 | 1.285 | 5SNG 1000X170300 |

#### Appendix A.3. Converter Design Equations

DC/DC Buck | DC/DC Boost | DC/AC Inverter | |
---|---|---|---|

Inductance (mH) | $L=\frac{({V}_{i}-{V}_{o}){t}_{on}}{\Delta {I}_{max}}$ | $L=\frac{({V}_{o}-{V}_{i}){t}_{off}}{\Delta {I}_{max}}$ | $L=\frac{{V}_{dc}}{\Delta {I}_{max}m{f}_{s}}$ |

Area product | ${A}_{p}=\frac{L{I}_{max}}{JK{B}_{max}}$ | ||

Scale factor | ${S}_{f}=\frac{{A}_{p}}{{A}_{p,type}}$ | ||

Effective core length (m) | ${l}_{e}={l}_{e,type}{S}_{f}$ | ||

Effective core area (m^{3}) | ${A}_{e}={A}_{e,type}{S}_{f}$ | ||

Total reluctance (Ampère-Turns/Wb) | ${\Re}_{t}={\Re}_{fe}+{\Re}_{air}=\frac{{l}_{e}}{{\mu}_{0}{\mu}_{r}{A}_{e}}+\frac{{l}_{air}}{{\mu}_{0}{A}_{e}}$ | ||

Turns | $N=\sqrt{\Re L}$ | ||

Total conductor length (m) | ${l}_{c}={l}_{c,type}{S}_{f}N$ | ||

Winding conductor radius (m) | ${r}_{c}=\sqrt{\frac{I}{J\pi}}$ | ||

Total conductor DC resistance ($\mathsf{\Omega}$) | ${R}_{L,DC}=\frac{\rho N{L}_{w,type}{S}_{f}}{{A}_{c}}$ | ||

Core volume (m^{3}) | ${V}_{c}={V}_{c,type}{S}_{f}^{3}$ |

DC/DC Buck | DC/DC Boost | |
---|---|---|

Capacitor (F) | $C=\frac{\Delta {I}_{max}}{8{f}_{s}\Delta {V}_{max}}$ | |

Equivalent serie resistance ($\mathsf{\Omega}$) | ${R}_{C}=\frac{\Delta {V}_{max}}{\Delta {I}_{max}}$ |

#### Appendix A.4. Cable Parameters

A (mm${}^{2}$) | ${\mathit{I}}_{\mathit{z}}$ (A) | ${\mathit{r}}_{\mathit{t}}$ ($\mathbf{\Omega}$/km) |
---|---|---|

35 | 140 | 0.868 |

50 | 165 | 0.641 |

70 | 205 | 0.443 |

95 | 245 | 0.32 |

120 | 280 | 0.253 |

150 | 315 | 0.206 |

#### Appendix A.5. Test Setup Bidirectional BESS DC/DC Converter

## Appendix B. Power Flows and Losses Visualisation

#### Appendix B.1. Traditional AC Grid Architecture

**Figure A2.**Visualisation of the total power flows and losses for the AC grid architecture with (

**a**) the power flows and (

**b**) the conversion and cable losses for a cloudy day in the winter and (

**c**) the power flows and (

**d**) the conversion and cable losses for a sunny day in the summer.

#### Appendix B.2. LVDC Backbone Architecture

**Figure A3.**Visualisation of the total power flows and losses for the LVDC backbone architecture with (

**a**) the power flows and (

**b**) the conversion and cable losses for a cloudy day in the winter and, (

**c**) the power flows and (

**d**) the conversion and cable losses for a sunny day in the summer.

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**Figure 1.**Illustration of the considered architectures with (

**a**) a traditional AC grid with individual BESS and PV with an individual meter or shared meter (

**b**) and an LVDC backbone with shared PV and BESS.

**Figure 3.**Iterative process for assessment of (

**a**) a traditional AC grid architecture and (

**b**) an LVDC backbone architecture.

**Figure 5.**Converter circuits: (

**a**) is a DC/DC buck converter, (

**b**) is a DC/DC bidirectional boost converter, and (

**c**,

**d**) are single- and three-phase DC/AC inverters.

**Figure 6.**Distribution of the annual consumption for (

**a**) the residential individual consumption, (

**b**) the consumption of SMEs, and (

**c**) the aggregated consumption.

**Figure 9.**Optimal voltage: (

**a**) sensitivity analysis on voltage in function of total losses and (

**b**) optimal voltage in function of the cable length.

**Figure 11.**Distribution of the (

**a**) self-consumption and (

**b**) self-sufficiency for the three grid architectures.

**Figure 12.**Sensitivity analysis of SSI in function of (

**a**) the PV penetration level, (

**b**) the BESS size and the savings in (

**c**) PV and (

**d**) BESS for aggregated PV and BESS on an LVDC backbone compared to a traditional AC grid with shared PV and BESS.

**Figure 13.**Prices and weight information of DC/AC-inverters with (

**a**) the weight per nominal power unit and (

**b**) the price per nominal power unit.

Building Cluster j | Rooftop Area Suitable for PV (m${}^{2}$) ${\mathit{A}}_{\mathit{j}}$ | PV Potential (kWp) ${\mathit{P}}_{\mathbf{pot},\mathit{j}}$ | Cable Length to Next DC-Connection (m) |
---|---|---|---|

1 | 350 | 50.8 | 145 |

2 | 490 | 71.1 | 55 |

3 | 360 | 52.3 | 145 |

4 | 510 | 74.1 | 55 |

Total | 1710 | 248.3 | 400 |

Asset | LVAC | LVDC |
---|---|---|

PV | ${P}_{pv,l}=\frac{{\sum}_{t=1}^{35,040}{P}_{cons,l}\left(t\right)\xb70.25\xb7\zeta}{1000}$ | ${P}_{pv,j}={\sum}_{j=1}^{n}\frac{{\sum}_{t=1}^{35,040}{P}_{cons,l}\left(t\right)\xb70.25\xb7\zeta}{1000}\xb7\frac{{A}_{j}}{{A}_{tot}}$ |

BESS | ${E}_{BESS,l}={P}_{pv,l}$ | ${E}_{BESS}={\sum}_{j=1}^{n}{P}_{pv,j}$ |

Single Phase System | Three Phase System | LVDC Backbone | |
---|---|---|---|

BESS ${v}_{i,bess}$ | 48 V | 48 V | 720 V |

PV ${v}_{i,pv}$ | 147.5 V | 295 V | 708 V |

DC-voltage ${v}_{i,dc};\phantom{\rule{0.222222em}{0ex}}{v}_{o,dc}$ | 325 V | 650 V | - |

AC-voltage ${v}_{o,ac}$ | 230 V | 400 V | 400 V |

Peak Power (kW) | 1–2 | 2–3 | 3–4 | 4–5 | 5–6 | 6–7 | 7–8 |
---|---|---|---|---|---|---|---|

Single-phase connections | 100.0% | 87.9% | 81.2% | 65.8% | 54.5% | 37.7% | 29.6% |

Peak Power (kW) | 8–9 | 9–10 | 10–11 | 11–12 | 12–13 | 13–14 | 14–15 |

Single-phase connections | 9.0% | 33.3% | 0.5% | 0.7% | 0.0% | 0.0% | 0.0% |

Parameter | Value |
---|---|

Cable type | EAXVB |

Conductors | 4 |

Core material | Alu |

l (m) | 400 |

AC-connections n | 25 |

DC-connections m | 4 |

${A}_{t}$ (mm${}^{2}$) | |

${r}_{t}$ ($\mathsf{\Omega}$/km) | See Appendix A.4 |

${I}_{z}$ (A) |

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## Share and Cite

**MDPI and ACS Style**

Azaioud, H.; Claeys, R.; Knockaert, J.; Vandevelde, L.; Desmet, J.
A Low-Voltage DC Backbone with Aggregated RES and BESS: Benefits Compared to a Traditional Low-Voltage AC System. *Energies* **2021**, *14*, 1420.
https://doi.org/10.3390/en14051420

**AMA Style**

Azaioud H, Claeys R, Knockaert J, Vandevelde L, Desmet J.
A Low-Voltage DC Backbone with Aggregated RES and BESS: Benefits Compared to a Traditional Low-Voltage AC System. *Energies*. 2021; 14(5):1420.
https://doi.org/10.3390/en14051420

**Chicago/Turabian Style**

Azaioud, Hakim, Robbert Claeys, Jos Knockaert, Lieven Vandevelde, and Jan Desmet.
2021. "A Low-Voltage DC Backbone with Aggregated RES and BESS: Benefits Compared to a Traditional Low-Voltage AC System" *Energies* 14, no. 5: 1420.
https://doi.org/10.3390/en14051420