1. Introduction
The solar photovoltaic (PV) and battery markets have seen rapid price reduction and exponential growth in recent years [
1,
2]. The interest in direct current (DC) systems has also gained more momentum following the latest technological development in power electronics [
3] and the increased penetration of PV and battery storage [
4]. As PV modules generate DC and batteries operate with DC, a DC topology enables efficient interaction between the two, with fewer power semiconductors in the current path for voltage conversion. Furthermore, almost all electronic loads in buildings are DC-operated [
5]. Lastly, the expected growth in electric vehicles, which are also DC-operated, is an additional motivator for DC in and adjacent to buildings [
6]. Today’s conventional alternating current (AC) topologies require conversions between AC and DC before the final user stage, generating losses. Adopting DC distribution reduces or even avoids some conversion losses, thereby increasing the system performance. In an expert survey among market stakeholders [
7], the top priority identified for further DC market penetration was the need for more research on this topic.
Many attempts have been made to estimate the energy savings when switching from AC to DC distribution in buildings. The reported findings differ substantially, with reported savings of up to 25%, depending on the chosen reference case, types of appliances (i.e., loads included), and systems studied (with or without PV and battery) [
8,
9,
10,
11,
12,
13], including studies where no energy savings are observed [
12]. In [
8], the study’s novelty includes the use of real household profiles from 120 residential buildings, unlike previous studies where synthetic profiles are used [
9,
12,
14,
15]. Here, savings vary between 9 and 20% and increase to 14–25% with the inclusion of battery storage. Vossos et al. used synthetic load and PV profiles in 14 cities in the US to determine the energy savings derived from DC distribution [
9]. The cities were chosen to examine the effect of varying solar radiation, and the findings report savings in the range of 5–14%. Siraj et al. compared the performance of a DC home at three DC voltage levels (48, 220, and 380 VDC) and a 220 VAC case and reported savings of 4–10% at the highest DC voltage levels [
11]. Dastgeer et al. performed a comparative study of AC and DC distribution in a residential building and concluded that no energy savings were achieved with DC [
12]. However, previous works [
3,
10,
16,
17,
18] acknowledge that including PV and battery as native DC generator and storage, respectively, is a prerequisite for achieving energy savings with DC. These components were not included in [
12]. A comprehensive simulation comparison for zero net energy (ZNE) office buildings by [
17] shows a significant variation in savings, ranging between 1 and 18%. The variation comes from parametric simulations varying PV, battery, and power electronic converter (PEC) sizes and demonstrates the effect of the system design on energy savings. Ahmad et al. performed a day-by-day comparative analysis of AC and DC distribution performance in a residential building and analysed the output through parametric simulations of PEC efficiency, solar power, and seasonal variation [
18]. The work by Alshammari et al. reports a 5% reduction in annual grid energy with DC distribution in a commercial building (school) [
19]. This study also compares the seasonal variations in energy savings by studying days of the four seasons. Spiliotis et al. studied the energy savings in an office building in five geographical locations; they concluded that 380 VDC outperformed the conventional 230 VAC in terms of energy efficiency and presented a loss split for the included components [
20]. To minimise the conversion losses for AC and DC operation, [
21] demonstrated a system control scheme for the internal power flows and source origin (grid, PV, or battery). Chinnathambi et al. performed measurements at the sources in this real-life demonstration, but it remains unclear how the control scheme treats the converter losses.
As pointed out in previous works, e.g., [
16,
17,
22], this research topic requires more comprehensive efforts, deepening the detail level of modelling to enable an accurate comparison of the two topologies. A comprehensive review article by Gelani et al. [
23] concludes that the findings from previous works are conflicting, and the combined efforts fail to give a final verdict on the feasibility of DC operation and under what circumstances DC is favourable.
Table A1 gives an overview of related journal publications on DC energy savings in buildings concerning methods, data profiles, and inclusion of DC sources, i.e., solar photovoltaic (PV) and battery. The last row in the table relates this work to previous efforts.
Typical in previous works, e.g., [
9,
11,
14,
24], is the use of constant efficiency for power electronic converters (PECs) and battery when assessing the energy savings derived from DC distribution. This approach neglects the load-dependent efficiency characteristics, which represent a deciding factor for an accurate comparison [
10,
17,
18,
20,
23,
25]. Despite acknowledging the importance of load-dependent efficiency, [
12] only includes a variety of fixed efficiency values when quantifying the effect of the converter characteristic. Studies acknowledging the efficiency load dependency are, e.g., [
15,
17,
20]. However, the presented PEC efficiency curves only include part of the loading range and thus make it unclear how the low loading range is treated in modelling. Using constant efficiency or neglecting the entire operating range—without considering PEC power operating constraints in the latter case—leads to inaccurate results. Examples of varying efficiency characteristics and their effect on system performance are examined in [
12,
18,
26]. However, these studies only present the effect on a single day’s performance [
18,
26] or the effect of various constant efficiency values [
12]. While the referred studies leave room for improvement, they demonstrate the need for the proper modelling of converters for a fair and accurate comparison.
In addition to constant efficiency, another gap is the access and usage of data profiles (PV and load) in modelling [
23]. Several of the previous studies use synthetic profiles for the full-year comparison, and these are either based on average profiles [
9,
12,
17,
18] or modelled using building and occupant-specific factors [
20,
27]. Averaging data leaves out peaks and variations while modelling synthetic data using performance indexes, e.g., internal heat dissipation (W/person or appliance) and ventilation flow rates (l/s), often resulting in repetitive profiles that may not reflect the building actual behaviour. Another vital aspect for an accurate comparison is the data period analysed, where comparisons based on a single day’s operation [
15,
18,
21] neglect the seasonal variations in load and PV profiles. Ref. [
15] presents daily variation in energy savings with DC operation, but as proven in other studies, seasonal variations also affect the performance [
18,
19,
27,
28]. With these arguments, an accurate comparison requires full-year, measured operation data of both PV and load profiles.
Furthermore, other studies identify the need for more detailed modelling of the battery losses and dynamic load behaviour [
17,
23], which previous important works [
8,
9,
17] lack.
Given the identified gaps, the topic needs more detailed analyses to address whether a DC topology results in lower losses, and if so, to what extent, and the decisive factors. The latter is also identified as a top priority in an expert assessment on the future of direct current in buildings [
22]. This work aims to evaluate and quantify the performance of AC and DC distribution in a residential building. The work addresses the gaps identified above by including measured efficiency characteristics of PECs and battery and evaluating the performance using a full-year data set of load usage and PV generation. The results include the relative effect of including DC sources (PV and battery) and challenge the assumption of using constant PEC efficiency. Furthermore, an examination of the daily and seasonal performance of the two topologies statistically determines when DC is a favourable option for loss reduction in the studied case. This study completes previous efforts and contributes to the current field with the following:
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.
The remainder of the work is outlined as follows:
Section 2 introduces the theoretical framework, and
Section 3 presents the case setup, including the residential building and modelled topologies.
Section 4 describes the PEC measurements and resulting efficiency characteristics, and
Section 5 presents the modelling approach and evaluation metrics. In
Section 6, the results are presented and discussed, and concluding remarks are presented in
Section 7.
5. System Modelling
System modelling was based on a power flow analysis using the PV generation and load usage time-series profiles from
Section 3.1 with 15-minute temporal resolution. The measured PV data are in AC quantity, and the gross yield generated by the PV array, that is, before MPPT and inverter, was calculated as
where
(s) is the inverter efficiency as a function of loading.
The battery control operated to minimize the grid interaction, as it has been identified in related studies that grid interaction disfavours the DC topology [
10,
20].
Figure 6 describes the battery charge and discharge conditions, where SOC(t) is the battery state of charge (SOC) in each time step and
(s) is the total efficiency of battery conversion, including losses of the battery cell [
10] and the converter for topology j (AC ∨ DC).
Here, the battery voltage level, u
(t), is adjusted for the next time step using the current and internal resistance, r
(i
), and the battery open-circuit voltage (OCV) as functions of its SOC, all adopted from previous work of the author [
10]. Lastly, the battery SOC level, SOC(t +
t), is adjusted for the next time step. The battery operating SOC range was set to 15–90% (SOC
and SOC
, respectively), and the variation in internal battery resistance was set as a function of the current adopted from [
10].
The case study was for a PV/battery system of 3.68 kWp and 7.5 kWh, respectively, and a charge/discharge limitation, P
, of 6 kW. The selected battery size was derived from a related study in [
43], which concluded that for the studied user case, limited additional gains in self-consumption were seen for battery sizes exceeding 7.5 kWh.
5.1. Loss Modelling
The following sections describe the conduction- and conversion-loss modelling methodology and introduce the evaluation performance metrics.
5.1.1. Cable Conduction Losses
For the modelling of the conduction losses, the feeder lengths defined based on the house drawings (see Appendix A in [
10]) were used together with the distribution voltage, U
, and (
3) and (
4). The cable cross-section area from
Table 1 was fixed for each appliance and set according to the maximum current of one year’s operation in each cable branch. For the lighting, it was assumed that the current to each room, being the sum of the current to all active lamps, was fed through one cable and then distributed to individual branches depending on the lighting layout [
10]. Each room consisted of 2–11 LED lights at 7 W each. The model treated individual room sockets similarly by distributing common current to the active socket(s) at each time step. In addition, stationary appliances has a fixed feeder length, and conduction losses were calculated using (
3) and (
4).
5.1.2. Converter Losses
Both the AC and DC topologies were operated with fixed main link voltage levels (230 VAC and 380 VDC, respectively). Therefore, the battery voltage had to be converted to the desired voltage using a converter, and these losses were calculated as
where
(s) is the load-dependent efficiency for topology j and p
(t) is the battery power. In addition to the losses of the battery converter, the losses of the battery cell—caused by the internal resistance—were included and modelled with varying resistance as a function of the current, r
(i
), as [
10]
where the relation between battery cell resistance and current, r
(i
), was taken from [
10].
The losses of the PV converter (PV inverter for the AC topology) were calculated using the gross yield, p
(t), from (
9) as
where the efficiency characteristics,
(p
), are dependent on the modelled topology, j.
A summary of the efficiency characteristics used in the modelling is given in
Table 2 for the four cases (AC, DC
–DC
).
Here, f(s) denotes efficiency varying with converter loading (s), and
and
are the load-side conversion efficiency values (see
Figure 1 and
Figure 3). The last DC/DC conversion for the low-power appliances,
, was present in both topologies and did not affect the relative comparison since they were treated equally. The losses of the grid-tied bidirectional converter were calculated using both load-dependent (DC
) and fixed (DC
) efficiency characteristics, as explained in
Section 3.3. The fixed efficiency was set to 97.6% to match the peak efficiency of the AC/DC converter from the measurements. The converter was modelled with a rated power to match the annual load peak, 6.2 kW, to always enable load coverage. The efficiency characteristics of the PV and battery converters in the AC case were extracted from the measurements in
Section 4.2 with a −1.5-percentage-point offset from the efficiency curve caused by extra-semiconductor crossing [
10]. In the AC topology, AC/DC conversions were performed with an H-bridge for each load, and the operation was binary (ON/OFF), with fixed efficiency of 97% [
10]. In DC
, the peak efficiency values from the measurements were used for the grid, battery, and PV converters.
5.2. Building Performance Metrics
In addition to loss savings, the topologies were evaluated for their PV utilisation factor,
, which defines the useful PV energy, with the losses of the PV converter (PV inverter for the AC topology) and battery storage (including battery cell losses) being taken into consideration. When battery charging is solely performed via PV surplus, PV utilisation is defined, in [
27], as
where p
are the losses of the battery converter; p
are the battery cell losses; p
are the losses of the PV converter, calculated with (
10)–(
12), respectively; and p
is the generated gross PV energy calculated with (
9). The numerator denotes the PV-associated losses. Another metric, defined in [
17] as the system efficiency, relates the annual losses to the total load demand as
where E
is the annual load demand, which is equal for all modelled topologies and cases. The total loss, E
, for topology j was calculated using (
3), (
6), and (
10)–(
12) as
where
p
(t) is the sum of all M load-side converter losses, and in the DC topology, these also include the grid-tied bidirectional converter.
6. Results and Discussion
This work quantified the loss savings of a DC topology and the resulting discrepancy when using load-dependent and fixed efficiencies. The analysis used the measured load and PV profiles presented in
Section 3.1 on the topologies in
Section 3.3.
Section 5 outlines the system modelling and includes the PEC measurement results in
Section 4.2.
The annual losses of the four topologies (
Figure 7) without PV and battery storage resulted in three observations:
The bidirectional converter losses significantly differed when modelled with fixed and load-dependent efficiency characteristics; see cases DC
and DC
. 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
) were 34% lower (or in absolute terms, an underestimation of 63 kWh) than those in the case implementing load-dependent efficiency (DC
). Using (
14), the system efficiency values of the respective systems (AC and DC
) were 95.3, 94.3, 95.8, and 93.7%, respectively.
Adding a DC sub-voltage level (DC
) 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
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
cases, respectively, which is in line with findings in previous works [
46,
47].
Without the inclusion of PV and battery, the DC topology did not present a favourable option in terms of loss reduction (excluding case DC
with the reasoning performed in 1). This result confirms the findings in previous works [
8,
9,
17,
22,
24].
Based on these observations, the continuing analysis only includes the AC reference case and the DC topology with load-dependent converter efficiency (DC).
The comparison presented in
Table 3 is for a system with a 3.7 kWp PV array and 7.5 kWh battery storage.
The generated PV energy was higher in the DC case, since it was fed directly to the DC link, with reduced conversion losses. With the inclusion of the DC sources (PV and battery storage), operation with the DC topology reduced the total annual losses by 15.8%.
Figure 8 shows a loss breakdown per source in the two cases.
The effect of adding the DC sources is confirmed in [
10,
12,
20]. The lowered losses through the bidirectional converter were due to the reduced grid interaction (see comparison with DC
in
Figure 7) when energy was generated and stored locally. Comparing the rectification losses in AC operation with the grid-tied converter in the DC case—having the same purpose (in addition to grid import rectification (AC/DC), the bidirectional grid-tied converter also inverts the grid export (DC/AC))—showed a 5.3% relative annual loss reduction with DC operation. The losses of the PV array and battery were lower in the DC case due to more efficient conversion (−41.4% and −27.3%, respectively), which affected the PV utilisation factor,
, as shown in
Table 3. In this case, the PV-associated losses of the PV converter, battery converter, and battery cells were 28.6% lower with the DC topology, resulting in a PV utilisation gain of 2.6% using (
13). The system efficiency values from (
14) were then 90.8 and 92.3% with the AC and DC topologies, respectively, thus resulting in a relative efficiency gain of 1.7%.
Figure 9 shows the power flow duration in annual operation as a function of respective converter loading. In
Figure 9a, the grid-interaction is shown for import and export, which highlight the necessity to account for the load-dependent efficiency characteristics when modelling the losses.
Fixed efficiency, thus, underestimated the accumulated losses by ignoring frequent operation under low loading (with poor efficiency; see
Figure 5). Similarly,
Figure 9b shows the duration of battery charge, battery discharge, and PV output. Again, the majority of occasions occurred under low converter loading, which further stresses the importance of adopting the complete PEC efficiency characteristics.
To determine under what circumstances DC is a favourable option for loss reductions,
Figure 10a shows a heat map of the loss difference in AC and DC operations sorted by daily hour (1–24) and month (1–12), where positive values indicate loss savings with DC operation.
When PV was present, DC operation resulted in lower losses, which correlates well with the results in
Figure 10b. In the presence of battery storage and with the battery control described in
Figure 6, the loss savings expanded to later in the day, when excess PV generation charged the battery (
Figure 10c) and discharged to cover load surplus (see
Figure 10d). Using Spearman’s rank coefficient of correlation [
48], the loss savings showed the highest correlation (0.59) with PV generation. The loss saving dependency on available PV generation is also confirmed in previous works [
27,
49,
50].
Figure 11 shows an expanded analysis of AC and DC
by varying the sizes of the PV array and battery storage.
Compared with the case without PV and battery in
Figure 7, the inclusion of PV (“1 PV”) reduced the annual loss difference from +22% to +6.7% but was not sufficient for the DC case to achieve annual energy savings comparable to those with AC. A doubling of the PV array (“2 PV”) resulted in a marginal improvement in the relative comparison with the AC topology (+5.3%/a). Doubling PV also added +18.3% to the grid-tied converter losses due to increased PV export (see
Figure 12).
The DC topology first achieved savings when including battery storage (“1 PV/10 kWh” and “2 PV/7.5 kWh”), as it reduced the interaction with the grid and thus the influence of the grid-tied converter. This reduction was due to the chosen battery control with the objective function to minimise the grid interaction, as presented in
Section 5. The annual loss reductions with a battery included ("1 PV/10 kWh" and "2 PV/7.5 kWh" in
Figure 11) were marginally greater than those in the case in
Table 3. This trade-off between PV array and battery size, and annual savings is further investigated in [
27], where it is concluded that the sizing of the PV array and the battery, for DC savings analysis, is important to avoid sub-optimisation.
This work, as well as several others, e.g., [
10,
17,
20], quantified the effect of the grid-tied converter on the system performance and highlighted it as a critical component of the DC topology. Measures to reduce this impact include parallel converter operation, as suggested in [
10,
25], and demand-side management of suitable loads. Two parallel converters, with one being designed for high-efficiency operation at low power, can boost the grid-tied converter performance. In addition, shifting loads and avoiding these low-power operations can further reduce losses. Furthermore, as proven in previous works [
27,
49,
50], the load and PV coincidence are decisive factors in DC operation loss savings. Awad et al. [
51] present a method to design the PV array (in terms of orientation(s) and tilt angle(s)) to match the load demand and suggest to include this in future works.
7. Conclusions
This work compared the performance of a residential building with AC and DC distribution using measured performance characteristics of power electronic converters (PECs) and battery storage. The results used load and PV profiles measured during one year’s operation. The analysis included quantifying the DC loss savings when adding solar photovoltaic (PV) and battery storage and varying their respective sizes. The results present a quantitative comparison of the DC annual loss discrepancy when using fixed and load-dependent efficiency characteristics of the PECs. Three DC topologies were studied and compared to AC distribution: 380 VDC with load-dependent PEC efficiency (DC), 380 VDC with fixed PEC efficiency (DC), and DC with an added sub-voltage level (DC).
Comparing DC and DC, which had identical topologies, revealed a significant loss discrepancy when using fixed and load-dependent efficiencies. In this study, the loss discrepancy was 34% in a case without PV and battery storage. Analysing the converter loading showed that most interactions occurred in the low-load region with poor efficiency, thus highlighting the importance of using load-dependent efficiency. Therefore, load-dependent efficiency is essential when modelling realistic scenarios with a wide operating range.
The results show that with load-dependent PEC efficiency, internal conduction and conversion losses were reduced by 15.8% when switching from AC to DC, with PV and battery included. Furthermore, the DC topology increased PV utilisation by 2.6% with a 28.6% reduction in PV-associated losses. The analysis of hourly and seasonal variations in DC savings showed that Spearman’s rank coefficient showed the highest correlation (0.59) between DC savings and available PV generation.
The extended analysis showed that more than only adding PV was needed to achieve savings in the DC case compared with the AC case. The DC topology marginally improved when doubling the PV size, from +6.7% to +5.4% annual loss increase. However, when adding a battery, DC operation achieved substantial savings (up to 17.7% reduction), as the effect of grid-tied converter operation was reduced. The battery objective function to minimise the grid interaction due to export and import is a prerequisite for grid reduction and DC loss savings.
Above all, the results from this work show the relevance of modelling the conversion efficiency characteristics with load dependence to account for the PEC efficiency characteristics. Using the assumption of constant efficiency has proven inaccurate in the studied case with frequent converter operations in the lower power ranges and, thus, high relative losses. The presented efficiency characteristics of the converters and battery offer an accurate way to assess the potential for DC distribution in future studies.