# Energy Loss Savings Using Direct Current Distribution in a Residential Building with Solar Photovoltaic and Battery Storage

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

- Experimentally obtained efficiency characteristics of power electronic converters (PECs) and battery cells;
- Quantification of the loss discrepancy when using fixed and load-dependent converter and battery efficiencies;
- Quantification of the effect on the system technical performance of the inclusion of a PV and battery system;
- The magnitude of the loss origins in the AC and DC topologies;
- Statistical identification of most significant correlating factor for DC savings.

## 2. Theory

#### 2.1. AC Building Topology with PV and Battery System

#### 2.2. Electrical Losses in Buildings

#### 2.2.1. Cable Conduction Losses

#### 2.2.2. Voltage Conversion Losses

## 3. Case Setup

#### 3.1. Electrical Load and Photovoltaic Profiles

#### 3.2. Proposed DC System Topology with PV and Battery System

#### 3.3. Investigated System Topologies

**AC**—230 VAC with load-dependent efficiency.Conventional system. See Figure 1 for the system layout including PV and battery system. Here, cable conduction losses occurred with the 230 VAC distribution.**DC${}_{1}$**—380 VDC with load-dependent efficiency.**DC${}_{2}$**—380 VDC with fixed converter efficiency.**DC${}_{3}$**—380 and 20 VDC with load-dependent efficiency.A 20 VDC sub-voltage level was added to DC${}_{1}$ and DC${}_{2}$ to supply the smaller loads and lighting through a central DC/DC converter (see Figure 1 in [37] for an example of such a system topology). Since this "Class A" voltage level is considered not to be dangerous for humans, safety designs are substantially cheaper [38]. Additionally, this sub-voltage level aligns with the supply voltage of the USB Type–C standard.

## 4. Power Electronic Converter Measurements

#### 4.1. Experimental Setup

#### 4.2. Results—Converter Measurements

## 5. System Modelling

#### 5.1. Loss Modelling

#### 5.1.1. Cable Conduction Losses

#### 5.1.2. Converter Losses

#### 5.2. Building Performance Metrics

## 6. Results and Discussion

- The bidirectional converter losses significantly differed when modelled with fixed and load-dependent efficiency characteristics; see cases DC${}_{1}$ and DC${}_{2}$. Assuming constant efficiency as in many previous studies, e.g., [39,44,45], was thus not eligible. As this study was for a residential building with varying net grid interaction, the converter covered the entire load range during operation. Considering the efficiency characteristics of the converter (see Figure 5), the constant efficiency approach was relatively accurate under loading >20% but underestimated the losses below that loading. The results also suggest that with assumed constant efficiency, the DC topology could achieve energy savings even without the inclusion of PV or battery storage, contradicting the findings in [8,9,17]. In relative numbers, the losses of the grid-tied converter using a constant efficiency approach (DC${}_{2}$) were 34% lower (or in absolute terms, an underestimation of 63 kWh) than those in the case implementing load-dependent efficiency (DC${}_{1}$). Using (14), the system efficiency values of the respective systems (AC and DC${}_{1-3}$) were 95.3, 94.3, 95.8, and 93.7%, respectively.
- Adding a DC sub-voltage level (DC${}_{3}$) added 7.3% (29.0 kWh/a) to the total losses when operated at 20 VDC. These added losses also transferred to the load-side conversion (DC/DC) losses, which were 3% higher with DC${}_{3}$ than in the other cases. The cable conduction losses, identified in [23] as an essential factor to consider, amounted to 2.4 and 1.5% of the total losses in the AC and DC${}_{1}$ cases, respectively, which is in line with findings in previous works [46,47].

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

A | Cable cross-section area |

AC | Alternating current |

DC | Direct current |

${E}_{load}$ | Annual load demand |

${E}_{loss}^{j}$ | Annual losses for topology j |

$grid$ | Energy imported from the grid |

j | Topology denotation (AC ∨ DC) |

${k}_{n}$ | Rational polynomial curve-fitted constant ($n\in 1-3$) |

L | Cable length |

${m}_{n}$ | Rational polynomial curve-fitted constant ($n\in 1-2$) |

NPC | Neutral-point-clamped |

${p}_{load}$ | Power demand from load |

${p}_{x}^{loss}$ | Power losses of component “x” |

${p}_{x}$ | Power to/from source “x” |

${p}_{pv}^{gross}$ | Gross energy yield from PV modules |

${P}_{max}$ | Maximum battery (converter) power |

PEC | Power Electronic Converter |

pp | Percentage points |

PV | Photovoltaic |

$p{v}_{exp}$ | PV energy exported to the grid |

${Q}_{batt}^{rated}$ | Rated battery capacity (Ah) |

R | Resistance (in the cable) |

${r}_{batt}\left({i}_{batt}\right)$ | Internal battery cell resistance |

SOC | Battery state of charge |

SOC${}_{min}$ | Minimum battery state of charge |

SOC${}_{max}$ | Maximum battery state of charge |

${U}_{dist}$ | Distribution voltage level |

${u}_{ocv}$ | Battery open-circuit voltage |

${\eta}_{batt}^{j}$ | Combined battery efficiency, including converter and battery cell losses |

${\eta}_{conv}^{grid}$ | Efficiency of bidirectional grid-tied converter |

${\eta}_{x}$ | Efficiency of component “x” |

${\kappa}_{x}^{j}$ | PV utilisation (subscript “PV”) or system efficiency (subscript “system”) |

$\rho $ | Resistivity in cable material |

## Appendix A

**Table A1.**Taxonomy table of journal publications on AC vs. DC in buildings; methods, data profiles, DC sources included, data period analysed, and presented energy savings.

PEC Efficiency | Data Profile | Battery Loss | DC Source | Data Period | Savings * | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Ref. | Building Type | Load-Dependent | Fixed | Synthetic | Measured | Load-Dependent | Fixed | PV | Battery | Single Day(s) | Full Year | % |

[8] | Residential | (✓) ^{a} | ✓ | ✓ | ✓ | ✓ | ✓ | 9–20 ^{b} | ||||

[9] | Residential | ✓^{c} | ✓ | ✓ | ✓ | ✓ | ✓ | 5 ^{d} | ||||

[11] | Residential | ✓ | ✓ | – | – | ✓ | ✓^{e} | 4–10% ^{f} | ||||

[12] | Residential | ✓ | ✓ | – | – | ✓^{e} | −6–−2% | |||||

[15] | Residential | (✓) ^{g} | ✓ | ✓^{g} | ✓ | ✓ | ✓ | – ^{h} | ||||

[17] | Commercial | (✓) ^{g} | ✓ | ✓ | ✓ | ✓ | ✓ | 1–18% ^{i} | ||||

[18] | Residential | ✓ | ✓ | – | – | ✓ | ✓ | – ^{h} | ||||

[19] | Commercial | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | 5% | ||||

[20] | Commercial | (✓) ^{j} | ✓ | ✓ | ✓ | ✓ | ✓ | 2–5% | ||||

[21] | Residential | (✓) ^{k} | ✓ | – | – | ✓ | ✓ | – ^{h} | ||||

[27] | Residential | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | 1–9% ^{l} | ||||

This work | Residential | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | Section 6 |

^{a}Presents max and min values for the converters and claims that the same efficiency degradation is used for AC/DC and DC/DC PECs, but it is not clear whether the full efficiency range is considered in the loss analysis.

^{b}The savings increase to 14–25% when including battery storage.

^{c}Acknowledges the efficiency degradation at part load but only considers a single efficiency point below 20% of full-load operation. The work also includes a sensitivity analysis on PEC efficiency and concludes that improvements favouring either AC or DC will most likely concur; thus, the relative gains remain unchanged.

^{d}The savings increase to 14% when including battery storage.

^{e}Not explicitly mentioned, but to the best of our knowledge, it seems that the analysis is performed for an entire year’s operation.

^{f}The savings vary depending on the chosen DC distribution voltage (48–380 VDC) and wire gauge.

^{g}Presents efficiency curves for the PECs but only down to 10% part load. It is thus unclear how efficiency is treated in loading cases below 10%.

^{h}Only compares on the basis of a single day’s operation and thus not relevant to present savings in relation to the other studies.

^{i}The span represents the result from parametric simulations with varying PV and battery sizes for small and medium zero net energy office buildings.

^{j}Presents PEC efficiency curves down to 20% part load operation, but it is unclear how the efficiency is treated below that loading.

^{k}It remains unclear how the converter losses are treated.

^{l}Energy savings vary with the size of the PV/battery system and the geographical location studied.

**Table A2.**Numerical values for the modelled converters to be used in (8).

DC/DC${}_{\mathit{charge}}$ | DC/DC${}_{\mathit{dis}.}$ | PV${}_{\mathit{inv}.}$ | AC/DC | DC/AC | |
---|---|---|---|---|---|

${k}_{1}$ | 0.9887 | 0.9876 | 0.9843 | 0.9617 | 0.9621 |

${k}_{2}$ | $4.8\times {10}^{-7}$ | $4.2\times {10}^{-6}$ | $7.3\times {10}^{-6}$ | 0.607 | 0.662 |

${k}_{3}$ | $-3.1\times {10}^{-9}$ | $-4.6\times {10}^{-10}$ | $-9.9\times {10}^{-11}$ | $-4.7\times {10}^{-7}$ | $-4.3\times {10}^{-8}$ |

${m}_{1}$ | 0.0021 | 0.0028 | 0.0015 | 0.615 | 0.667 |

${m}_{2}$ | $1.78\times {10}^{-5}$ | $2.07\times {10}^{-5}$ | $4.60\times {10}^{-6}$ | 0.003 | 0.002 |

R${}^{2}$ | 1.000 | 1.000 | 0.999 | 0.999 | 1.000 |

RMSE | 0.0019 | 0.0014 | 0.0024 | 0.0019 | 0.0008 |

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**Figure 3.**Modelled DC distribution topology with individual converters for the PV and battery system. Loads are distinguished as ”BIG” and ”SMALL” depending on their rated powers, where the m smaller loads are supplied by 20 VDC via galvanically isolated DC/DC converters.

**Figure 8.**Annual system losses for a system configuration with 3.7 kWp PV array and 7.5 kWh battery storage. Low-voltage cable conduction was zero for both topologies but is included in the legend for consistency with the other figures.

**Figure 9.**Power flow distribution in annual operation for (

**a**) grid import and export, and (

**b**) battery charge and discharge, and PV generation.

**Figure 10.**Heat map per daily hour and month in 2016 showing (

**a**) loss differences in AC and DC operations (positive values indicate savings with DC), (

**b**) accumulated PV generation, and (

**c**,

**d**) accumulated battery charge and discharge, respectively.

**Figure 11.**Relative changes in annual losses during DC operation with various PV and battery system configurations. The $\Delta $-comparison is with reference to AC performance; thus, positive values indicate higher losses during DC operation.

**Figure 12.**Loss split in AC and DC operations and the modelled PV and battery system configurations. Low-voltage cable conduction is zero for all topologies but is included in the legend for consistency with the other figures.

**Table 1.**Standardised cable cross-section area per maximum current according to IEC 60228 and the corresponding resistance per meter from (4), using the resistivity of copper (0.0171 $\mathrm{\Omega}$mm${}^{2}$/m).

Current (A) | Cross-Section (mm${}^{2}$) | Resistance ($\mathbf{\Omega}$/m) |
---|---|---|

6 | 0.75 | 0.023 |

10 | 1.5 | 0.011 |

16 | 2.5 | 0.007 |

20 | 4 | 0.004 |

Efficiency/Case | AC | DC${}_{1}$ | DC${}_{2}$ | DC${}_{3}$ |
---|---|---|---|---|

${\eta}_{conv}^{grid}$ (%) | 100 | $f\left(s\right)$ | 97.6 ^{1} | $f\left(s\right)$ |

${\eta}_{conv}^{batt,\phantom{\rule{4pt}{0ex}}j}$ (%) | $f\left(s\right)$ | $f\left(s\right)$ | 98.5 ^{1} | $f\left(s\right)$ |

${\eta}_{pv}^{j}$ (%) | $f\left(s\right)$ | $f\left(s\right)$ | 98.3 ^{1} | $f\left(s\right)$ |

${\eta}_{AC/DC}$ (%) [10] | 97 | 100 | 100 | 100 |

${\eta}_{DC/DC}$ (%) [10] | 87 | 87 | 87 | 87 |

^{1}Peak efficiency from measurements of the converter.

**Table 3.**Comparison of system performance with AC and DC${}_{1}$ with 3.7 kWp PV and 7.5 kWh battery storage.

AC | DC${}_{1}$ | Difference (%) | |
---|---|---|---|

System losses (kWh) | 583 | 490 | −15.8 |

PV energy (kWh) | 3113 | 3161 | 1.5 |

${\kappa}_{PV}$ (%) | 91.3 | 93.7 | 2.6 |

${\kappa}_{system}$ (%) | 90.8 | 92.3 | 1.7 |

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## Share and Cite

**MDPI and ACS Style**

Ollas, P.; Thiringer, T.; Persson, M.; Markusson, C. Energy Loss Savings Using Direct Current Distribution in a Residential Building with Solar Photovoltaic and Battery Storage. *Energies* **2023**, *16*, 1131.
https://doi.org/10.3390/en16031131

**AMA Style**

Ollas P, Thiringer T, Persson M, Markusson C. Energy Loss Savings Using Direct Current Distribution in a Residential Building with Solar Photovoltaic and Battery Storage. *Energies*. 2023; 16(3):1131.
https://doi.org/10.3390/en16031131

**Chicago/Turabian Style**

Ollas, Patrik, Torbjörn Thiringer, Mattias Persson, and Caroline Markusson. 2023. "Energy Loss Savings Using Direct Current Distribution in a Residential Building with Solar Photovoltaic and Battery Storage" *Energies* 16, no. 3: 1131.
https://doi.org/10.3390/en16031131