Enhanced DC Building Distribution Performance Using a Modular Grid-Tied Converter Design

: This work quantifies the techno-economic performance of AC and DC residential building distribution. Two methods, utilising software and hardware configurations, are showcased to improve DC distribution: (i) a novel rule-based battery dual-objective operation (DOO) and (ii) a modular Master/Slave design of the grid-tied converter (GC). Both methods use the GC’s load-dependent efficiency characteristic, eliminating partial-load operation and enhancing energy efficiency. The work uses measured annual PV and load data to evaluate the performance of the methods compared to AC and DC references. The techno-economic analysis includes the annual net electricity bill and monetised battery degradation. The results show that the DOO eliminates GC partial-load operation at the cost of increased battery usage, resulting in marginal net savings. In contrast, the modular converter design significantly reduces losses: − 157 kWh/a ( − 31%) and − 121 kWh/a ( − 26%), respectively, relative to the DC and AC references. For a parametric sweep of electricity price and discount rate, the Lifetime Operating Cost (LOC) comparison shows savings from DC of up to USD 575 compared to AC.


Introduction
Historically, AC has had market momentum for building power distribution.Lately, however, DC distribution has gained interest following the market development of DC sources, i.e., solar photovoltaic (PV) [1] and battery storage [2].Advancements in power electronic technologies [3] and the availability of DC-ready and compatible end-user products [4][5][6] also incentivize DC distribution in buildings.Previous works have reported reduced energy losses [7,8], enhanced power quality [9], and cost savings [10] with DC distribution.
There are numerous comparative techno-economical studies of AC vs. DC distribution in buildings in the literature, e.g., [11][12][13].Several referred studies conclude that PV and battery storage are keys to achieving energy savings with a low-voltage direct current (LVDC) distribution system.Studies quantifying the respective loss sources for LVDC also conclude that the bi-directional grid-tied converter (GC) is the primary loss source, e.g., [13,14].In [14], the GC loss share exceeds 30% despite optimising the converter size.In other related works, the GC loss shares comprise 65% [7] or 60% [15] when accounting for the efficiency characteristics at partial loading.As acknowledged in [13], the GC is optimised for high powers but often operates at partial loading, resulting in poor efficiency.Gelani et al. perform a sensitivity analysis on the essential modelling parameters and a quantitative comparison of AC vs. DC distribution and conclude that the GC's efficiency has the highest effect on the relative comparison [16].

Related Works
A modular converter design for partial-load loss reduction is one measure to reduce the loss contribution of the GC suggested in [17,18].Several works on modular converter design exist.The work in [19] uses a genetic algorithm (GA) efficiency optimisation for current sharing among three parallel DC/DC converters in an LVDC application.Extrapolated results from simulations of the GA operation for a single day show annual savings of 143 kWh.The work in [20] compares linear droop operation for an islanded microgrid with an improved primary regulation using non-linear droop control.From an investigated day's operation, the proposed load sharing reduces the losses by 11.5%.Other parallel converter load-sharing examples in DC microgrids are [21,22], focusing on the converters' interplay and power qualities.The work in [23] applies hierarchical control management on parallel-operated DC/DC converters.A GA is integrated at the tertiary level to enhance the system's efficiency by solving an optimisation problem.A hardware-in-the-loop simulation on four converters demonstrates the potential system improvements.However, to the best of the authors' knowledge, studies of modular converter operation are lacking in applied cases of LVDC distribution systems targeting the GC's operation, including the effect of varying loading conditions and a quantified performance gain.A related approach for loss minimisation in an LVDC case is presented in [24], where the energy management system chooses the operation mode with the lowest losses.Real-time monitoring of the PV supply, load demand and battery status dictate the power flows.However, it does not describe how the power electronic converter (PEC) losses are accounted for, an essential aspect of loss analysis.
As concluded in previous works, the DC saving potential depends on the coincidence of load demand and PV generation [10,11] and thus the minimisation of grid interaction.Previous works, e.g., [13,25], including PV and battery storage, typically use a self-consumption (SC) maximisation battery dispatch objective to boost the PV and load correlation.However, using this dispatch algorithm while considering load-dependant efficiency characteristics for the GC could increase conversion losses through more frequent partial-load operations.As concluded in [26] and demonstrated in [27], a sole operation to maximise SC in a Nordic climate reduces the battery usage and increases idle time.Single-objective battery operation thus constrains the battery's technical and economic potential, as highlighted in [28][29][30].Additional compatible operating objectives can be added to the battery control to reduce idle periods and improve the system's operation.
Furthermore, the PECs in previous comparisons on AC and DC building distribution, e.g., [31,32], are typically modelled with constant efficiencies and thus neglect the load dependency, which is paramount for a fair comparison, as highlighted in [16].Other examples are studies using a range of fixed efficiencies; in [32] the distribution converter, efficiency is modelled in the range 90-95%, and the load-side converter at 85-95%.In [8], the inverter efficiency is set between 85 and 99% and the DC/DC converter between 80 and 90%.As highlighted in [33], the converters strongly influence the system's performance.Similarly, the battery's characteristic is often modelled with a constant-round-trip efficiency, e.g., [8,13], which neglects the dynamics in actual operation.
Previous works typically use synthetic load and PV data, based on average profiles [13,32] or modelled from building and occupancy-specific factors [14].Averaged data leave out peaks and power fluctuations while modelled data from key performance indexes may result in repetitive-and non-representative-profiles [33,34].Furthermore, the data temporal resolution affects the modelled performance, where the work in [12] acknowledges the limitation of hourly load and PV profiles.
To sum up, no works explicitly targeting the GC performance have been found in the available scientific literature, which is the critical component for building DC distribution loss-saving opportunity.Furthermore, this work also accounts for the identified needs of using measured high temporal load and PV profiles and accounting for the PEC and battery performance characteristics.

Aims and Contributions of the Present Work
This work presents methods to enhance the performance of DC distribution by addressing the bi-directional GC.It is a continuation of previous work [15] and uses the available data and modelling framework as a basis.It completes the effort in [15] through the addition of two DC enhancement methods: (i) a novel rule-based battery dual-objective operation (DOO) and (ii) a Master/Slave modular GC design.The enhancement methods are also assessed for the imposed battery degradation.The results of the proposed methods are compared against a DC reference case and conventional AC distribution for a residential building in Sweden using measured load and PV data with a 15-minute temporal resolution.An economic assessment of Lifetime Operational Cost (LOC) from net annual electricity billing and monetised battery degradation quantifies the added investment cost for the DC cases to break even with AC distribution.The specific contributions provided in this article are as follows: • A novel rule-based battery dual-objective operation (DOO) and modular GC design; • The importance and quantified effect on GC losses from a reduced partial-load operation are highlighted; • A quantified effect on battery degradation from the proposed battery controls; • An economic assessment of LOC for net annual billing and monetised battery degradation.

Methods
The studied case is a single-family residential building with a PV and battery system.Apart from the reference case (DC ⋆ ) adopted from [15], the DC distribution includes two proposed methods to minimise the GC losses.
Figure 1 shows the modelling outline, referencing the related sections and equations in this work.The outline includes the input from the measured load and PV time-series of the use-case, the measured PEC efficiency characteristics, the selection of the case study, and the techno-economic assessment.

Use-Case-Single-Family Residential Building
The modelling uses the AC load demand and PV generation from a single-family residential building in Sweden.Data are acquired with a 15-minute temporal resolution for a year's operation, with a total demand of 6354 kWh.The building has a ground-source heat pump covering the space heating and domestic hot water demands.The PV array has a rated peak power of 3.68 kWp and an annual generation of 3113 kWh.More information about the residential building and its blueprints are found in [17].

AC and DC Building Distribution
The modelled AC and DC topologies in Figure 2 come from [15], where it is assumed that all loads operate on DC at the final stage [4,5].The PV and battery system is AC-coupled in the AC topology (Figure 2a) via two separate inverters.Both topologies' loads are separated based on their rated powers.The smaller loads (≤100 W) in the AC topology need a two-step AC/DC conversion to the required DC voltage level [32] with a galvanic isolated DC/DC step.The proposed DC topology (Figure 2b) is commonly found in related studies [35] and effectively integrates the PV array, energy storage, and loads at a common side [36].Unlike the AC topology, the DC topology includes a three-phase bi-directional GC that links the AC grid and the main DC bus.The main DC link voltage is set to 380 VDC per previous conclusions on suitable DC levels [35,37], and all big loads operate directly on this voltage level.

Battery System and Operation
Related work on the studied residential building concludes that a 7.5 kWh battery is suitable given the load demand, PV generation, and battery control to maximise the SC [38].The battery control is taken from [15] for the AC and DC reference cases with the objective to maximise the PV self-consumption.The battery operates within the SOC boundaries 15-90%, SOC min and SOC max , respectively, and with a power converter constraint (P max ) of 6 kW (0.8 C).
Battery ageing consists of two parts: calendar and cycle ageing, where the former depends on time, temperature and SOC, and the latter also on the battery operation, e.g., the number of equivalent cycles, depth of discharge (DoD) and C-rate [39].Based on the power law equation in [40], the work in [41] developed a cycle degradation model for a graphite-LiFePO4 battery cell.The model considers the operating temperature, time, DoD, and discharge rate to calculate the cell's capacity fade and is widely used in the literature, e.g., [42][43][44].Derived from the power law equation, Wang et al. [41] replace the time dependency with Ah-throughput and define the percentage capacity loss as where R g is the gas constant, T is the absolute temperature (in K), and z is the power law factor.The pre-exponential factor, B, and activation energy, E a , are parametrised from experimental tests for different C-rates and operating temperatures in [41].The Ah-throughput (A h ) represents the amount of charge during the cycling and is calculated as where n(t) is the cycle number and Q batt is the cells nominal capacity (in Ah).In this work, the battery's capacity fade is accounted for using ( 1) and ( 2) and the parametrised values in Table 1.

Electrical Loss Modelling
Previous studies conclude the marginal effect of the cable conduction losses on the aggregated losses and the relative insignificance between the topologies [15,45,46]; a maximum of 0.9 percentage-point savings favouring DC.Thus, the present investigation excludes these losses, and the focus is on the PECs.The comparison also excludes the smaller loads' load-side DC/DC conversion as they are treated equally in both topologies [15].
Figure 3a depicts the layout for the efficiency measurements of the DC converters.A Norma D6100A power analyser was used for the battery and PV converter and the AC side of the GC, while the DC side of the GC was measured with a Yokogawa WT1600.Figure 3b shows the measurement installation with the solar emulator, power analyser, battery module, battery management system (BMS), and converter.To capture the complete efficiency characteristics, measurement points were obtained for the full PEC operating range (s ∈ 0-100%).
Figure 4 shows the converters' measured load-dependant efficiency characteristics.The efficiency characteristics for the equivalent AC converters are modelled with a −1.5% offset, accounting for an additional semiconductor in series with the current for rectification [17].The curve-fitted characteristics (solid lines) are used in the loss modelling with the methodology and coefficients obtained from [15].
The rated DC power of the bi-directional GC is set by the ampere rating (I RMS ) of the building's main fuse (ψ) as where ψ is set to 16 A for the reference case (DC ⋆ ).
The battery cell's losses are calculated from the quadratic current relation as [47] p cell,j loss (t) = r cell (i where the ohmic resistance's current variation, r cell (i j cell ), is taken from [47].The losses from the battery converter are calculated as where η j batt is the load-dependant efficiency and p j batt the battery power for topology, j.For the loss analysis, the measured PV AC quantity, p AC pv , is converted to gross generation, that is, before the inverter and MPPT, using the PV inverter efficiency, η AC pv as The equivalent PV DC generation (p DC pv ) is calculated from the gross yield in (6) as with η DC pv from Figure 4.The PV losses are calculated as where η j pv is the PV inverter/converter efficiency.In this work, all loads operate with DC in the final stage.The rectification in the AC topology uses the appliances' built-in load-side PEC(s) and the DC topology via the bi-directional GC.The rectification losses for each topology are calculated as where p m load is the power to load m, η grid conv the GC efficiency, and p g the power to/from the grid.In (9), the losses are summarised for all loads M assuming a fixed load-side H-bridge rectifier efficiency of 97% [17].

Battery Dual-Objective Operation
The battery DOO combines the SC dispatch [15] with an objective to minimise the GC's partial loading.The latter reduces the low-power import and export operations through the converter using a rule-based charge and discharge control with DoD = 100%.
The rule-based control compares the net demand with a power threshold value, P h lim .The P h lim is modelled as a share (β) of the rated power from (3) as The battery DOO completes the reference battery operation from [15] with two additional conditions: 1. Suppose net demand is lower than P h lim .In that case, a check is made whether the available charge content (or gap) can meet the net demand completely.The battery charge gap is defined as available storage capacity to 100% SOC.If true, the battery uses full DoD to charge or discharge to meet the net demand (P 1 ).If this is false, the battery either charges or discharges the extra amount so that the GC throughput equals P h lim (P 2 ). 2.
If the available charge content (or gap) can fully meet the net demand, it charges or discharges so that the power through the converter is zero, i.e., no grid interaction occurs (P 3 ).If this is false, the battery is not engaged for partial-load coverage and passes all net demands through the GC.

Modular GC Design
To reduce partial-load operation, a modular GC design is proposed, having two converters operate in a Master/Slave configuration [48] at the tertiary control level [49].Since this design targets the converters' load sharing, the battery dispatch remains the same as the reference operation.Figure 6 depicts the proposed load sharing (PLS).
With P aux.,k conv and P main,k conv as the rated powers of the auxiliary and main converter, respectively, calculated from (3) as Here, χ k is the ratio of the auxiliary converter, p g the import/export power, with p aux.,k g and p main,k g for the auxiliary and main converters, respectively.The PLS performance is benchmarked to an optimised load sharing for loss minimisation with the objective function expressed as min t∈T T ∑ p loss aux.(t) + p loss main (t) (15) and subject to the constraints for the benchmark operation as where ( 16) ensures load coverage and ( 17) and ( 18) the PECs' power constraints.Figure 7 shows the efficiency characteristics for grid import using the PLS and optimisation (both for χ = 15%) and the reference case with a single-converter operation.).The colour-coding follows the execution from Figure 6.
The PLS offers significant efficiency improvements at partial loading compared to the reference operation and performs similarly to the benchmark operation.

Combined Modular Design and Battery DOO Operation
To examine the effect of the combined operation of the proposed enhancement methods, the battery DOO is applied to the auxiliary converter (grey area in Figure 7), and the β condition restricts the partial-load operation of the auxiliary converter as The analysis include scenarios (S) with varying β and χ operations as ∀β = 1, . . ., 20% ∀χ = 2, . . ., 50%.

Economic Assessment
The economic assessment derive from the electricity bill and monetised battery degradation.The net electricity bill (C net ) is calculated as where C sell and C buy are the prices for sold and bought electricity, respectively, and e sell and e buy the hourly energies.The battery degradation from (1) can be monetised using the battery initial investment (C batt 0 ) as [50,51] The life-cycle cost (LCC) is calculated from the investment cost and the present worth value of the operational costs as where I C is the investment cost and the annual net operating cost (OC) is given from ( 21) and (22) as The uniform present value (UPV) for N years of equal cash flows and with a discount rate (r) is calculated as [52] UPV The product UPV×OC gives the Lifetime Operating Cost (LOC) for N years with a discount rate r.Due to the investment cost uncertainties [10], the economic assessment is performed to quantify the added cost to break even.By setting the LCC in ( 23) equal for all scenarios, the difference in LOC gives the cap for the added investment cost.The comparison assumes that the maintenance, replacement costs, and residual values are equal for all cases.

Results and Discussion
Two methods to enhance the energy performance of residential building DC distribution are analysed.The enhancement methods (PLS and battery DOO) are firstly compared to a DC reference case, denoted DC ⋆ , and the best performing cases are compared to conventional AC distribution for system losses using (11).The methods are also evaluated for their battery degradation.An economic assessment quantifies the added investment cost for the DC cases to break even compared to AC.

DC Distribution Enhancement Methods
The annual system losses, per source, is shown in Figure 8a  For DC ⋆ , most losses come from grid import (57%), with marginal (6%) export losses.Noticeably, DOO reduces the GC losses for all β by constraining the grid interaction above P h lim .Consequently, the battery operation increases substantially for β ≥ 5%, resulting in net savings only for β ≤ 5%.The net loss increase for β = 10 and 20% comes from the significant increase in battery throughput (+114% for β = 20% cf.β = 1%).Figure 8b shows the losses for DC ⋆ and modular GC designs.The PLS reduces the GC losses relative to DC ⋆ for all designs.Since the battery operation is the same, the difference in battery-associated losses is insignificant.Relative to DC ⋆ , annual savings from the PLS are 5-27%, with optimal savings for χ = 15-20%.

Effect on Battery Ageing from Battery DOO
Figure 9 shows the modelled battery degradation for DC ⋆ and battery DOO.For DC ⋆ , the battery degradation is 5% of the nominal capacity.A marginal difference for DOO with β ∈ 1-5% (<0.5 percentage points) is observed.However, a significant difference is observed for β ∈ 10-20%, with up to four percentage points for β = 20%.Since the DOO uses DoD = 100%, the battery operates more frequently at the SOC extremities than DC ⋆ .The most significant difference is observed at SOC < 15%, where DC ⋆ limits discharge to 15% (SOC min ), while DOO allows for complete battery depletion.Considering the findings in [53] that both cycling and calendar ageing are less prominent at lower SOC levels, and the empirical degradation in Figure 9, the effect of the DOO on battery ageing is negligible for β ∈ 1-5%.

Combined Modular and Battery DOO
To examine the combined effect of the proposed DC enhancement methods, Figure 10 shows the variation in loss savings from the scenarios (S) in (20) relative to modular operation (∀χ) with β = 0%.(20).Peak additional savings ( ) for β = 5% and χ = 50%.NB!The upper limit of ∆Loss is restrained at 0 for better visualisation.
Despite reducing the losses from the auxiliary converter, the net savings are marginal.Increased battery-associated losses (converter and cells) supersede the converter loss sav-ings, especially for higher β.At most, an additional −5.1 kWh/a is observed for β = 5% and χ = 50% (σ β5χ50 ).In absolute numbers, σ β3χ20 gives the lowest losses, and compared to the best-performing design in Figure 8b (χ = 15%); the difference is a mere −1.6 kWh/a.

Loss Comparison-AC vs. DC
From the results in Section 3.1, the best DC cases' performance is compared to conventional AC distribution.To examine the effect of the GC size, DC ⋆ is also modelled with a smaller (S) and bigger (B) GC.The GC size is determined from (3) for ψ = 10 and 20 A to 6.9 kW (DC S ) and 13.9 kW (DC B ), respectively.
Compared to AC distribution, DC ⋆ does not generate savings (+8% increase in annual losses), not even with the inclusion of PV and battery storage; see Figure 11.A bigger GC (DC B ) worsens the performance (+20%).However, a smaller GC (DC S ) reduces the annual losses (−10%) relative to AC.So, the sole inclusion of DC sources (PV and battery) to achieve loss savings with DC distribution-as concluded from previous works, e.g., [3,13,54]-contradicts these findings.Reducing the nominal power of the GC shifts the operating points to higher loading and thus increases the operationally weighted efficiency.
As for modular design and the PLS, χ = 15 and 20% result in 26% annual savings compared to AC distribution.The DC sources' (PV and battery) converters have −92 kWh lower losses with DC distribution, while the cells' losses in Figure 11 remain equal and independent of the topology.Suppose the import and export losses from the DC distribution are summed and compared with the rectification losses of the AC distribution.In that case, the DC reference cases (∀ψ) have higher losses, while the modular operation gives lower losses (−29 kWh/a).As aforementioned, the best-performing S scenario (σ β3χ20 ) marginally reduces the aggregated losses.Compared with χ = 20%, loss reductions occur for the auxiliary converter and the battery (converter and cells).

Life-Cycle Cost Comparison
Table 2 shows the LOC for varying electricity prices (C el ), with the buy and sell prices equal in (21), i.e., C el = C sell ≡ C buy .The net billing (C net ) strongly dominates the LOC and relative to AC, DC ⋆ does not give any cost savings (positive ∆C tot ).However, a modular GC design with χ = 15% presents savings in the range of USD 80-399 for the modelled electricity prices (0.1-0.5 USD/kWh).Figure 12 shows a sensitivity analysis of the LOC savings for χ = 15% relative AC operation and varying discount rates (r) and electricity prices (C el ) with N = 10 years.In the expanded analysis, the LOC savings for χ = 15% are in the USD 75-575 range relative to AC operation and are the most sensitive to the electricity price.Considering that these savings shall cover the costs for cabling, labour, converters and compatible appliances, a retrofit to DC distribution for this studied case is questionable from an economic perspective.

Conclusions
This work proposed two measures to enhance the performance of DC distribution in buildings by addressing the GC's performance.It quantified the annual energy loss savings compared to conventional AC distribution and a DC reference case.One measure was a novel rule-based battery dual-objective operation (DOO) that used DoD = 100% to eliminate partial loading of the GC.The other measure was a Master/Slave modular GC design.
The proposed DOO reduced the GC losses by eliminating the operation at partial loading.Consequently, the battery throughput and losses increased, resulting in varying net savings.Marginal savings were found for β = 1-5% (up to 16 kWh/a), and the empirical battery degradation showed that the relative effect on annual degradation is marginal (≤0.5 percentage points) compared to the reference battery operation.For β = 10-20%, the annual net losses increased compared to DC ⋆ despite the reduction in GC losses; due to the significant increase in battery-associated losses.Considering the significant battery degradation for β ≥ 10% (+1-4 percentage points relative to the reference operation), this operation was not preferred for the studied case.
The proposed Master/Slave GC design achieved savings of up to 157 kWh/a (−31% of the annual losses for DC ⋆ ) for χ = 15-20%.Upon combining the modular design and battery, DOO resulted in marginal additional savings: −5.1 kWh/a for σ β5χ50 relative β = 0%, and −1.6 kWh/a for σ β3χ20 compared with the best-performing case (χ = 15%).
The economic evaluation showed that the LOC for the DC reference operation (DC ⋆ ) was higher than for AC, meaning that the DC investment cost cannot exceed the one for AC to break even.The modular operation (χ = 15%) showed up to USD 575 lower LOC over 10 years than AC.A DC topology reduces the costs for converters and cabling, but the economic viability is still uncertain, considering the limited market of compatible appliances.Further work is suggested for the economic analysis to deepen the understanding of DC's viability.
Unlike previous findings, this work showed that the sole inclusion of PV and battery storage is insufficient to make DC a superior choice over AC for loss reduction due to the frequent partial converter operation.The results highlighted the importance of converter sizing and its effect on DC performance when using load-dependant efficiency characteristics: 83 kWh/a (−16%/a) for DC S relative to DC ⋆ .However, limiting the GC's nominal power also restrains the peak power load demand.
This work quantified the potential loss savings for the two proposed methods for an applied case of a single-family residential building.While the proposed modular GC design and its load-distribution operation generated significant operational improvements for the studied case, further assessment of its viability and operability is needed.These methods could be applied to other cases and more heterogeneous load and PV profiles to further assess the viability.Furthermore, including electric vehicles-as a native DC load and potential bi-directional storage-is interesting from a DC perspective.For such a case, an interesting analysis is the cooperation and synergies of the stationary and mobile storage.

Figure 2 .
Figure 2. Modelled building's electric schematic representations for (a) AC and (b) DC distribution.The loss modelling treats the dashed perimeters (DC/DC conversion to low-voltage DC) equally.

Figure 3 .
Figure 3. Measurement setup for the efficiency characterisation of the DC converters.Principle measurement scheme (a) and actual installation (b) with the solar emulator, power analyser, battery module, battery management system (BMS), and converter.

Figure 5 .
Figure 5. Operating principle of battery DOO with β = 5% and demonstration of P 1 -P 3 operations to eliminate grid-tied converter (GC) partial-load (grey area).

Figure 7 .
Figure 7. Efficiency characteristics for grid import with the PLS and benchmark (for χ = 15%), and single-converter operation (Ref.).The colour-coding follows the execution from Figure 6.

Figure 8 .
Figure 8. System losses from DC distribution per loss sources compared to DC ⋆ (Ref.) for (a) battery DOO, and (b) modular GC design using the PLS; see Section

Figure 9 .
Figure 9. Battery degradation for DC ⋆ and battery DOO.

Figure 11 .
Figure 11.System losses per source for AC distribution, DC with varying GC size, the PLS with χ = 15 and 20%, and combined PLS and DOO for σ β3χ20 ; see Section 3.1.2.

Figure 12 .
Figure 12.LOC savings for χ = 15% relative AC for varying discount rates (r) and electricity prices (C el ) with N = 10 years.

S
Scenarios from parametric sweep of β and χ A h Battery capacity throughput DC ⋆ DC reference (ψ = 16 A and χ = 0%) DC B DC with bigger GC (ψ = 20 A) DC S DC with smaller GC (ψ = 10 A) P h lim Grid-tied converter power threshold PLS Proposed load sharing
a Relative AC for the same electricity price (C el ).