# Energy Efficiency Evaluation and Revenue Distribution of DC Power Distribution Systems in Nearly Zero Energy Buildings

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## Abstract

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## 1. Introduction

- In this paper, a time sequential simulation is proposed based on energy efficiency model with accurate load flow calculation for LVAC and LVDC networks, where the piecewise linear fitting is applied to model the function between converter efficiency and its power flow.
- According to the current load type, the benchmark comparison models of LVAC and LVDC distribution power systems are established. Then a comprehensive and fair system energy efficiency evaluation indicator is defined considering temporal characteristics.
- The phasor diagram method is employed to obtain the power flow results for LVAC and LVDC systems, based on which the accurate power loss calculation equations are derived for each branch including converters and power lines.
- An income distribution method is proposed to adjust the interests of multi-stakeholders, which paves a way for the liberation and promotion of DC distribution.
- The efficiency data of converters under different conditions are all from actual experiment results or provided by manufacturers of household appliances applied in numerical case studies.

## 2. Methods

#### 2.1. Typical Structure of LVAC (LVDC) System and Energy Efficiency Definition

_{D}is the total power energy consumption of the load during the calculation period, while E

_{loss,L}and E

_{loss,C}represent total power energy loss of power lines and converters in the calculation period, respectively.

#### 2.2. System Level Energy Efficiency Indicators

_{p}branches connected to buses in the system, including distributed PV branch, distributed energy storage branch, load branch and grid-connected branch. According to the time sequential simulation results, assuming that the power losses of converters and lines in time and branch are calculated as P

_{loss,C,k}(t) and P

_{loss,L,k}(t), while the various types of load demand are denoted by P

_{D,i}(t), $i\in \left\{\mathrm{I},\mathrm{II},\mathrm{III},\mathrm{IV}\right\}$. According to Formula (1), the energy efficiency evaluation model at system level can be derived as shown in Formula (2):

#### 2.3. Energy Efficiency Model of Converters

_{0}, P

_{1}, …, P

_{n}, and the corresponding efficiencies are η

_{0}, η

_{1}, …, η

_{n}, the efficiency of working point p can be calculated according to Formula (3):

_{in}and P

_{out}represent the input and output power of the converter, η denotes efficiency.

#### 2.4. Loss Comparison of AC and DC System of NZEB

#### 2.4.1. AC and DC Line Loss Comparison

_{line,dc}(t) is the loss of the DC line, P(t) is the power transmitted in the line, U

_{DC}is the rated voltage between the poles of the DC line, R

_{dc}is the unit resistance of the DC line, and L is the line length. In the formula, since the high-power devices in the AC system are powered by 3 phases, P

_{line,ac1}represents the AC line loss corresponding to the outdoor or high-power devices such as photovoltaics, energy storage, air conditioners, etc., and U

_{AC}represents the three-phase inter-pole voltage, which is 1.732 times of the indoor AC power supply voltage U

_{AC0}; P

_{line,ac2}is the line loss of electrical equipment such as adapters in the AC system indoors, and also needs to consider the resistance of the zero line loop, so the impedance needs to be multiplied by 2. φ means the phase difference among the three phases in AC system, R

_{ac}represents the unit resistance of the AC line.

_{high}and λ

_{low}, in the high-power branch and the low-power branch of NZEB is shown in (8).

_{high}, the AC voltage U

_{AC}is 380 V, and the DC voltage U

_{DC,high}is 750 V. Since the inductive reactance cannot be neglected in the AC power grid with long distance transmission, the power factor $\mathrm{cos}\phi $ is assumed to be 0.9. At the same time, due to the existence of the skin effect, the equivalent resistance of AC distribution network is larger, which is assumed to be 1.5 times of the equivalent resistance of the DC distribution network. Therefore, the DC distribution network line loss of NZEB with a high-power load is 0.277 times of the AC distribution network.

_{low}, the AC voltage U

_{AC0}is 220 V, and the DC voltage U

_{DC,low}is 375 V. The resistance difference between AC and DC system is small enough to be neglected. The other conditions are assumed to be the same as the high-power branch. Therefore, the NEZB DC distribution network line loss of the high-power load is 0.279 times of the AC distribution networks. Therefore, the line loss of DC system is obviously lower than AC system in all conditions.

#### 2.4.2. AC and DC System Loss Comparison

_{loss,AC}and DC distribution system P

_{loss,DC}can be obtained, respectively, as shown in (9) and (10).

_{k}is the power of each branch, k is the number of branches; η

_{DC-DC,k}, η

_{DC-AC,k}, η

_{AC-DC,k}, and η

_{m}represent the transmission efficiency of DC/DC, DC/AC, AC/DC converters and transformer, which ignore the difference between AC and DC system and in different operating conditions; P

_{D,i}is the load power of each branch, ${P}_{\mathrm{ES}}^{+}$ is the charging power of the energy storage system, P

_{pv}is the power of the solar panel, and ${P}_{\mathrm{ES}}^{-}$ is the discharging power of the energy storage system. The loss difference between the DC system and AC system can be calculated by (9) and (10), as shown in (11):

#### 2.5. Economic Assessment and Multi-Stakeholder Income Adjustment Method

_{new}is the new electricity price, unit is yuan/kWh. EP

_{sell}is the current electricity sales revenue, the unit is ten thousand yuan. EP

_{change_DC}is the income from the DC transformation of the power grid, the unit is ten thousand yuan. E

_{sell}is total electricity sold, unit is kWh.

## 3. Results and Discussion

#### 3.1. Introduction of the Test System

#### 3.2. Efficiency Comparison of AC and DC Networks in Benchmark Scenario

#### 3.3. Efficiency Comparison of AC and DC Networks with DG and DES

^{+}and the decreasing grid tie branch energy loss as ΔE

^{−}. When the PV capacity is low, ΔE

^{+}is bigger than ΔE

^{−}so that the total efficiency increases. However, when the capacity exceeds some threshold value, ΔE

^{+}would be lower than ΔE

^{−}and the efficiency decreases.

#### 3.4. Energy Efficiency Analysis in Typical Scenarios in Tests

**P**and

_{loss,l}**P**mean the total loss of lines and converters, respectively, η

_{loss,C}_{PV}means the proportion of PV output, η

_{a}means the average energy efficiency, Δη

_{a,max}means the maximum energy efficiency difference in the relative building and region. From the results in Appendix A Table A1, Table A2, Table A3, Table A4 and Table A5, it can be seen that in office buildings, the line losses varied from 62.2 MWh~97.4 MWh, while the transformer losses varied from 193.3 MWh~361 MWh, which is about three times the line losses. The DC advantages were relatively obvious in Beijing—1.15%, which showed a positive correlation with photovoltaic percentage. The DC advantage increased in the hotel buildings by as high as 3.22% in Beijing, which also showed a positive correlation with the photovoltaic. In business buildings, there was more space to arrange the photovoltaics, which accounts for about half of the energy demand in Beijing, where DC’s separate topology saved 3.27% energy. However, since the use of renewable energy needs to pass through more converters and longer transmission lines, the average energy efficiency was about 81%. Through the average efficiency was not as high as in the lower photovoltaic scene which ignored the synchronization and transportation waste of power generation, the utilization of renewable energy had increased. In educational buildings, there are no obvious differences in DC advantages among different regions, whose power consumption is similar to the office buildings. The main difference is that there are no central air conditioners in educational buildings and residential buildings so that there is no need to build a DC separate supply topology. With an average 27% photovoltaic generation, the advantages of DC over AC system were as high as 3.34% in 375 V. Lastly, in the residential buildings, since the air conditioners were arranged in 375 V/240 V, there was no need to set a separate bus with high voltage. The DC advantage was about 5% higher than the AC system in all three tested regions, which verified DC topology had a higher efficiency no matter in which building or in any region.

_{D}means the total load, η

_{hp}means the proportion of high-power devices, S

_{ES}means the energy storage capacity. Through the advantage of the DC system over the AC system had been verified by the 15 scenarios, the influence factors of efficiency improvement are not clear, and need to be studied further.

#### 3.5. Comparison of AC and DC Energy Efficiency in Typical Scenarios and Analysis of Impact Indicators

#### 3.6. Sensitivity Analysis of Influencing Factors in Typical Scenarios

#### 3.7. Impact Assessment of DC Retrofit on Multi-Stakeholder Benefits

- (1)
- Beijing: Beijing area at a rate of 0.443 yuan per kilowatt-hour. In order to achieve an equitable distribution of the interests of the three stakeholders-customers, power grids and equipment manufacturers-the interest per stakeholder should be 0.087 yuan/W. Electricity prices are estimated to rise to 0.501 yuan/kWh, an increase of 13.1%. At the same time, equipment manufacturers should reduce the price of equipment by 0.113 yuan/W.
- (2)
- Shenzhen: Shenzhen’s electricity price is calculated at 0.663 yuan/kWh. In order to achieve an equitable distribution of the interests of the three stakeholders-customers, power grids and equipment manufacturers-the interest per stakeholder should be 0.082 yuan/W. Measured at [21], the definitive electricity price was raised to 0.718 yuan/kWh, up 8.2%. At the same time, equipment manufacturers should reduce the price of equipment by 0.108 yuan/W.
- (3)
- Shanghai: The electricity price in Shanghai is calculated as 0.617 yuan/kWh. In order to achieve an equitable distribution of the benefits of the three stakeholders of users, power grids and device makers, the benefits of each stakeholder should be set at 0.083 yuan/W. After the calculation in [21], it is concluded that the electricity price should be raised to 0.672 yuan/kWh, with an increase of 8.9%. At the same time, device makers should reduce the price of equipment by 0.097 yuan/W, as shown in Figure 18.

## 4. Conclusions

- (1)
- There were about 6% annual energy savings in LVDC compared with LVAC. With the increase of the DG or DES integration, the efficiency savings by LVDC increased, which indicated that the DC system had more advantage in energy efficiency, especially with high penetration of DG.
- (2)
- The 375 V separate topology DC distribution network has the highest energy efficiency with less transformation process and line transmission loss, followed by the 375 V centralized DC distribution network.
- (3)
- Through SPSS correlation analysis, the preliminary judgment result was confirmed, which indicated that there was a certain correlation between the improvement of AC and DC energy efficiency and photovoltaic, energy storage and high-power loads. Specifically, the advantage of DC distribution showed a high correlation with the high-power load’s ratio.
- (4)
- According to the multi-stakeholder income adjustment, the electricity price should be raised, while the device makers should reduce the device price to balance the revenue of device makers, power grids and users.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

_{loss,l}, transformer loss P

_{loss,C}, percentage of photovoltaic generation η

_{PV}, and the system efficiency η

_{a}in different regions and different power supply plans, as listed in Table A1, Table A2, Table A3, Table A4 and Table A5, and corresponding to the analysis reported in Section 3.4.

**Table A1.**Comparison of energy efficiency of office buildings with different topologies in three regions.

Region | Plan | P_{loss,l} (MWh) | P_{loss,C} (MWh) | η_{PV}/% | η_{a}/% | Δη_{a,max} |
---|---|---|---|---|---|---|

Beijing | AC220 | 76.131 | 192.851 | 13.27% | 83.02% | 1.15% |

DC375 concentration | 62.366 | 206.807 | 13.26% | 83.02% | ||

DC240 concentration | 92.519 | 263.898 | 13.26% | 78.69% | ||

DC375 separate | 65.472 | 182.080 | 13.26% | 84.17% | ||

DC240 separate | 97.399 | 239.767 | 13.26% | 79.61% | ||

Shenzhen | AC220 | 76.668 | 221.862 | 9.41% | 83.57% | 0.60% |

DC375 concentration | 62.642 | 247.206 | 9.41% | 83.06% | ||

DC240 concentration | 92.670 | 315.977 | 9.41% | 78.80% | ||

DC375 separate | 64.929 | 220.796 | 9.41% | 84.17% | ||

DC240 separate | 96.269 | 289.246 | 9.41% | 79.75% | ||

Shanghai | AC220 | 75.752 | 200.511 | 12.71% | 83.18% | 0.96% |

DC375 concentration | 62.151 | 218.017 | 12.71% | 83.00% | ||

DC240 concentration | 92.201 | 278.071 | 12.71% | 78.69% | ||

DC375 separate | 64.452 | 193.260 | 12.71% | 84.14% | ||

DC240 separate | 95.825 | 253.480 | 12.71% | 79.65% |

**Table A2.**Comparison of energy efficiency of hotel buildings with different topologies in three regions.

Region | Plan | P_{loss,l} (MWh) | P_{loss,C} (MWh) | η_{PV}/% | η_{a}/% | Δη_{a,max} |
---|---|---|---|---|---|---|

Beijing | AC220 | 58.613 | 443.384 | 7.84% | 85.44% | 3.22% |

DC375 concentration | 39.598 | 358.045 | 7.84% | 88.11% | ||

DC240 concentration | 61.562 | 465.406 | 7.84% | 84.83% | ||

DC375 separate | 41.417 | 335.840 | 7.84% | 88.65% | ||

DC240 separate | 65.051 | 442.342 | 7.84% | 85.31% | ||

Shenzhen | AC220 | 59.724 | 541.159 | 5.15% | 85.92% | 1.88% |

DC375 concentration | 43.332 | 485.136 | 5.15% | 87.41% | ||

DC240 concentration | 63.731 | 631.520 | 5.15% | 84.07% | ||

DC375 separate | 42.869 | 458.782 | 5.15% | 87.81% | ||

DC240 separate | 63.335 | 602.462 | 5.15% | 84.42% | ||

Shanghai | AC220 | 60.142 | 475.989 | 5.95% | 85.63% | 2.66% |

DC375 concentration | 40.215 | 402.573 | 5.95% | 87.84% | ||

DC240 concentration | 62.408 | 523.547 | 5.95% | 84.51% | ||

DC375 separate | 39.053 | 373.688 | 6.11% | 88.29% | ||

DC240 separate | 60.896 | 491.346 | 6.11% | 84.93% |

**Table A3.**Comparison of energy efficiency of business buildings with different topologies in three regions.

Region | Plan | P_{loss,l} (MWh) | P_{loss,C} (MWh) | η_{PV}/% | η_{a}/% | Δη_{a,max} |
---|---|---|---|---|---|---|

Beijing | AC220 | 274.348 | 473.035 | 56.41% | 77.40% | 3.27% |

DC375 concentration | 185.154 | 438.486 | 56.25% | 80.45% | ||

DC240 concentration | 312.040 | 553.503 | 56.36% | 74.74% | ||

DC375 separate | 180.332 | 427.844 | 56.88% | 80.67% | ||

DC240 separate | 303.729 | 552.319 | 56.88% | 74.83% | ||

Shenzhen | AC220 | 265.325 | 574.008 | 35.25% | 79.97% | 2.42% |

DC375 concentration | 180.519 | 574.589 | 35.19% | 81.63% | ||

DC240 concentration | 305.628 | 737.376 | 35.23% | 76.27% | ||

DC375 separate | 177.028 | 539.851 | 35.23% | 82.38% | ||

DC240 separate | 299.660 | 701.856 | 35.23% | 77.06% | ||

Shanghai | AC220 | 261.607 | 488.961 | 43.26% | 78.54% | 2.95% |

DC375 concentration | 133.523 | 465.762 | 43.13% | 82.14% | ||

DC240 concentration | 303.702 | 599.120 | 43.22% | 75.28% | ||

DC375 separate | 174.877 | 447.645 | 43.35% | 81.49% | ||

DC240 separate | 297.547 | 579.936 | 43.35% | 75.82% |

**Table A4.**Comparison of energy efficiency of educational buildings with different topologies in three regions.

Region | Plan | P_{loss,l} (MWh) | P_{loss,C} (MWh) | η_{PV}/% | η_{a}/% | Δη_{a,max} |
---|---|---|---|---|---|---|

Beijing | AC220 | 47.108 | 134.105 | 26.94% | 82.55% | 3.34% |

DC375 concentration | 44.798 | 95.724 | 27.00% | 85.89% | ||

DC240 concentration | 64.569 | 127.620 | 27.00% | 81.66% | ||

Shenzhen | AC220 | 59.436 | 151.428 | 19.07% | 82.45% | 3.26% |

DC375 concentration | 51.773 | 112.997 | 19.11% | 85.71% | ||

DC240 concentration | 76.837 | 150.639 | 19.11% | 81.29% | ||

Shanghai | AC220 | 51.175 | 131.501 | 20.62% | 83.47% | 3.24% |

DC375 concentration | 46.356 | 94.656 | 20.66% | 86.71% | ||

DC240 concentration | 67.543 | 128.988 | 20.66% | 82.40% |

**Table A5.**Comparison of energy efficiency of residential buildings with different topologies in three regions.

Region | Plan | P_{loss,l} (MWh) | P_{loss,C} (MWh) | η_{PV}/% | η_{a}/% | Δη_{a,max} |
---|---|---|---|---|---|---|

Beijing | AC220 | 2.665 | 40.872 | 33.21% | 85.70% | 4.41% |

DC375 concentration | 3.696 | 24.963 | 33.19% | 90.10% | ||

DC240 concentration | 4.854 | 33.222 | 33.20% | 87.27% | ||

Shenzhen | AC220 | 3.191 | 50.612 | 21.10% | 86.19% | 4.96% |

DC375 concentration | 3.978 | 28.933 | 20.91% | 91.15% | ||

DC240 concentration | 5.282 | 38.926 | 20.92% | 88.45% | ||

Shanghai | AC220 | 3.253 | 51.605 | 20.84% | 86.18% | 4.89% |

DC375 concentration | 3.977 | 29.605 | 20.82% | 91.07% | ||

DC240 concentration | 7.613 | 39.767 | 20.83% | 87.84% |

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**Figure 12.**Correlation comparison between the proportion of photovoltaic output and energy efficiency improvement in 15 scenarios.

**Figure 13.**Correlation comparison between the proportion of high-power devices and energy efficiency improvement in 15 scenarios.

**Figure 14.**Comparison of the correlation between the ratio of energy storage capacity to total load and energy efficiency improvement in 15 scenarios.

**Figure 15.**The relationship between the proportion of high-power load and the improvement of DC–AC energy efficiency.

**Figure 16.**The relationship between the proportion of photovoltaic power generation and the improvement of DC–AC energy efficiency.

**Figure 17.**The relationship between the proportion of energy storage capacity and the improvement of DC–AC energy efficiency.

Type | Power Supply Form | Examples |
---|---|---|

I | LVAC (380 V) or LVDC (±375 V) | VSD air conditioner |

II | Extra LVDC (48 V) | Mobile phone, computer |

III | LVDC (±375 V) | DC charging piles |

IV | LVAC (380 V) | Squirrel-cage motor |

Output Power | 10% P_{n} | 20% P_{n} | 40% P_{n} | 60% P_{n} | 80% P_{n} | 100% P_{n} |
---|---|---|---|---|---|---|

Correction coefficient | 0.970 | 0.990 | 1.00 | 1.00 | 0.995 | 0.990 |

End Use Load | Load Type | Rated Power/kW |
---|---|---|

Air conditioner | I | 95 |

Illumination | II | 36 |

Extra LVDC appliances | II | 40 |

LVDC appliances | III | 92 |

Data Center | III | 80 |

Total | 343 |

Period | The Time-of-Use Electricity Price/RMB | Operation Status of DES |
---|---|---|

9:00–11:30, 14:00–16:30, 19:00–21:00 | 1.025 | Discharging |

7:00–9:00, 11:30–14:00, 16:30–19:00, 21:00–23:00 | 0.6724 | OFF |

23:00–7:00 (next day) | 0.2284 | Charging |

Wiring End Use | Detail Appliance | Unit Spacing (m) | DC Resistance (Ω/km) | AC Resistance (Ω/km) |
---|---|---|---|---|

Illumination | LED lighting | 475 | 8.83 | 8.21 |

Emergency lighting | 450 | 5.39 | 5.09 | |

Public lighting | 450 | 5.39 | 5.09 | |

LVDC appliances | 48 V socket | 475 | 5.39 | 5.09 |

Security system | 450 | 1.85 | 1.95 | |

HVDC appliances | 375 V socket | 385 | 0.794 | 0.798 |

Air ventilation recycle systems | 200 | 1.25 | 1.24 | |

External air conditioner | 195 | 5.39 | 5.09 | |

Data center | 50 | 1.25 | 1.24 | |

Energy storage | 160 | 1.25 | 1.24 | |

PV | 160 | 1.25 | 1.24 |

Annual Electricity Consumption/MWh | Annual Power Loss Consumption/MWh | Energy Efficiency/% | |
---|---|---|---|

AC | 1353.47 | 269.05 | 83.42 |

DC | 1353.47 | 160.97 | 89.37 |

Building | Area | Δη_{a,max} | P_{D}/(MWh) | η_{PV}/% | η_{hp}/% | S_{ES}/(MWh) |
---|---|---|---|---|---|---|

Office | Beijing | 1.15% | 1305.80 | 13.27% | 39.68% | 85 |

Shenzhen | 0.60% | 1506.22 | 9.41% | 34.40% | 130 | |

Shanghai | 0.96% | 1354.23 | 10.53% | 38.26% | 130 | |

Hotel | Beijing | 3.22% | 2947.73 | 7.84% | 56.33% | 250 |

Shenzhen | 1.88% | 3367.49 | 5.15% | 36.94% | 250 | |

Shanghai | 2.66% | 3197.15 | 5.95% | 51.94% | 300 | |

Commerce | Beijing | 3.27% | 2520.68 | 57.27% | 35.96% | 200 |

Shenzhen | 2.42% | 3325.53 | 35.51% | 27.26% | 400 | |

Shanghai | 2.95% | 2720.68 | 43.68% | 33.32% | 250 | |

Education | Beijing | 3.34% | 856.66 | 26.96% | 54.85% | 60 |

Shenzhen | 3.26% | 988.11 | 19.12% | 60.80% | 40 | |

Shanghai | 3.24% | 920.00 | 20.67% | 58.19% | 50 | |

Residential | Beijing | 4.41% | 247.19 | 35.04% | 65.81% | 40 |

Shenzhen | 4.96% | 326.73 | 21.68% | 74.13% | 30 | |

Shanghai | 4.89% | 329.85 | 21.62% | 74.38% | 40 |

Analytical Method | PV Ration | High-Power Load Ratio | Storage Capacity Total Load | |
---|---|---|---|---|

Energy Efficiency Increasing | Pearson correlation | 0.391 | 0.794 | 0.394 |

Significance (two-tailed) | 0.149 | 0 | 0.146 | |

Number of cases | 15 | 15 | 15 |

**Table 9.**Income of various stakeholders in different regions in the office building scenario (unit: Yuan/W).

Area | User | Grid | Device Makers | Total Revenue | Equal Distribution of Income |
---|---|---|---|---|---|

Beijing | 0.06 | 0 | 0.2 | 0.26 | 0.087 |

Shenzhen | 0.055 | 0 | 0.19 | 0.245 | 0.082 |

Shanghai | 0.068 | 0 | 0.18 | 0.248 | 0.083 |

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## Share and Cite

**MDPI and ACS Style**

Jiang, K.; Li, H.; Ye, X.; Lei, Y.; Lao, K.-W.; Zhang, S.; Hu, X. Energy Efficiency Evaluation and Revenue Distribution of DC Power Distribution Systems in Nearly Zero Energy Buildings. *Energies* **2022**, *15*, 5726.
https://doi.org/10.3390/en15155726

**AMA Style**

Jiang K, Li H, Ye X, Lei Y, Lao K-W, Zhang S, Hu X. Energy Efficiency Evaluation and Revenue Distribution of DC Power Distribution Systems in Nearly Zero Energy Buildings. *Energies*. 2022; 15(15):5726.
https://doi.org/10.3390/en15155726

**Chicago/Turabian Style**

Jiang, Keteng, Haibo Li, Xi Ye, Yi Lei, Keng-Weng Lao, Shuqing Zhang, and Xianfa Hu. 2022. "Energy Efficiency Evaluation and Revenue Distribution of DC Power Distribution Systems in Nearly Zero Energy Buildings" *Energies* 15, no. 15: 5726.
https://doi.org/10.3390/en15155726