Edison Revisited: Should we use DC circuits for lighting in
commercial buildings?
(under review at Energy Policy)
a
Brinda A. Thomasa, b, Inês Azevedoa, Granger Morgana
Department of Engineering and Public Policy, Carnegie Mellon University, Pittsburgh, PA
Abstract
This research examines the economic feasibility of DC circuits for commercial building lighting
systems that are powered either by central power supplies and traditional AC grid electricity or
by on-site solar photovoltaic (PV) arrays, with or without battery back-up. Using DOE research
and development targets for light-emitting diodes (LEDs) and solar PV, our results show that
with present fluorescent and LED efficacies, fluorescent lighting systems are still the lowest
annualized cost lighting option. Using DC circuits with LEDs has a considerable range of effects
on levelized annual cost (LAC), from an increase of 3% to a decrease of 19%, if a DC voltage
standard was developed so that individual drivers in each LED fixture could be eliminated. DC
circuits in grid-connected solar PV-powered LED lighting systems can lower the total
unsubsidized capital costs of the system by 8 to 24% and LACs by 4 to 24% compared to a PVAC lighting system. Grid-connected PV-DC LEDs may match the LAC of grid-powered AC
fluorescent lighting systems by ~2014, with limited differences between DC and AC systems’
LACs. Further work is needed to better understand potential safety risks with DC distribution
and to remove design, installation, permitting and regulatory barriers.
Keywords
Direct current distribution, light emitting diodes, energy efficiency
1. Introduction
In 1891, the board for the Chicago World’s Fair received two bids to illuminate the world’s
first all-electric fair: General Electric proposed a $1.8 million (later reduced to $554,000) direct
current (DC) generator and distribution network, while the Westinghouse Electric Company
submitted the winning bid of $399,000 for an alternating current (AC) system (all costs in 1891
dollars) (Larson, 2003). The years that followed saw the decline of Thomas Edison’s pioneering
110 V DC distribution systems. AC long-distance transmission and distribution became standard
1
because the AC transformer made it possible to step voltage up for long distance power transfer
and then back down for end use. This achieved much greater efficiency, since resistive power
losses grow as the square of the current, while the amount of power transferred is proportional to
the product of voltage and current.
In recent decades, new semiconductor materials and devices have been developed that can
function as a “DC transformer” with efficient (>80%) and reliable designs (80plus.org, 2010).
Today, high-voltage DC (HVDC) (200-800kV) has become the most cost-effective option for
point-to-point electricity transmission across distances greater than 500-600 miles (e.g.
connecting hydropower in the Pacific Northwest to loads in Los Angeles). At these distances, the
cost savings from using two conductors for HVDC transmission versus three conductors for AC
transmission outweigh the higher cost of DC power electronics compared to AC transformers
(Schavemaker and van der Sluis, 2008). However, the economics is such that AC remains the
norm for all local transmission and distribution systems.
Today, the fact that many commercial and residential loads, such as computers, consumer
electronics, and LED lighting, use DC power has led to a proliferation of power supplies that
convert from AC to various DC voltages. Many small inefficient "wall warts" have efficiencies
as low as 40% (Caldwell and Reeder, 2002). Fortunately the performance of such devices is
improving as they become increasingly subject to national (and international) energy efficiency
standards, such as the minimum efficiency standards programs established by the Energy Policy
Act of 2005 and Energy Independence and Security Act of 2007 in the U.S. (DOE, 2010), and
similar programs run by the California Energy Commission and Australian Greenhouse Office
(Mammano, 2007).
2
Though he did not use the term, another Edison-era concept, distributed generation (DG), has
also seen a rebirth since the 1970s due to converging goals of greater overall efficiency in the use
of primary energy, divestiture of large generation by some utilities that have been restructured as
“wires companies” (Strachan, 2000), growing consumer concerns about supply reliability, and
concerns about lowering greenhouse gas emissions. Some DG technologies such as solar
photovoltaics (PV) and fuel cells inherently produce DC power, which is then converted to AC.
Other DG sources such as microturbines (30 kW – 1 MW) can also produce DC power. In both
cases, after power is distributed via AC circuits, it must be converted back to DC by power
supplies in many household or office loads. This has led some analysts to propose the use of
building-level DC distribution to reduce the cost and improve the efficiencies of power
conversion (Babyak, 2006). In this paper we evaluate the use of DC building distribution circuits
for lighting systems, especially with DC light-emitting diodes (LEDs) and solar PV, to achieve
cost and efficiency improvements by reducing or eliminating the need for power supplies and
inverters.
1.1 Modern Applications of DC Distribution
Much previous research has focused on DC distribution system design, the economics and
feasibility of DC in specific applications, and the integration of DC building circuits with DG
(Kaipia et al., 2006; Nilsson and Sannino, 2004; Sannino et al., 2003; George, 2006). Initial
engineering-economic analysis of a DC distribution system to residential customers shows that
medium voltage DC (± 750 V) may have lower total costs than 400 V AC due to lower capital
costs and outage repair costs (Kaipia et al., 2006). However, medium and low-voltage DC
distribution systems have higher energy losses on scales of more than a few kilometers (Kaipia et
al., 2006; Nilsson and Sannino, 2004). Sannino et al. (2003) have shown that 326 V DC
3
distribution is feasible and more efficient than 48 V DC for a mid-size commercial building in
Sweden.
DC circuits are cost-effective in some applications which use energy storage such as batteries
or uninterruptible power supplies (UPSs) that serve power plant auxiliary systems,
telecommunications facilities, and data centers (Pratt et al., 2007; Ton et al., 2008; Jancauskas and
Guthrie, 1995; Yamashita et al., 1999; Belady, 2007). In these applications, greater power
conversion efficiency can be achieved with DC by eliminating the UPS DC to AC inverter
between building circuits and batteries, the AC to DC rectifiers in load power supplies, and any
intermediate AC transformers or DC-DC converters that may be used. DC distribution might also
be economical in the face of environmental or other policy mandates. These may include
renewable portfolio standards (RPSs) that result in the adoption of solar PV or fuel cells. The
Electric Power Research Institute (EPRI) reports that using DC distribution with PV systems can
reduce PV system capital costs by up to 25% by eliminating the inverter and increasing system
efficiency with the result that a downsized PV array can provide the same electricity service
(Jimenez, 2005; DTI, 2002). Using a different definition of efficiency, Hammerstrom’s (2007)
analysis of an average household with various loads shows that with fuel cells and DC circuits, a
3% efficiency improvement is possible, while without fuel cells, DC distribution imposes a 2%
energy efficiency penalty. Given other uncertainties, whether these differences are significant is
unclear. Laboratory tests at EPRI have demonstrated that many household devices can readily
accept DC power (George, 2006).
While electrical safety is not the focus of this paper, we note that higher voltage DC circuits
pose a greater arc hazard than AC circuits and require specialized circuit breakers and protection
(Salomonsson and Sannino, 2007). AC circuit breakers function by opening the circuit, which
4
typically forms an arc that is extinguished when the voltage waveform passes through zero. Arcs
in high voltage (>50 V) DC wiring systems can occur through a loose wiring connection or
damaged insulation between cables of different polarity or between an electrical circuit and
ground (Dargatz, 2009). DC wiring can cause arcing even at currents under the threshold at
which the circuit protection operates. Thus, some DC wiring may need additional arc-quenching
insulation and fault-detection. The potential safety risks with DC circuits require further study.
2. Methodology
While DC building distribution circuits are feasible with existing power supply and circuit
breaker technologies, are they cheaper than AC if used to power building lighting systems? We
address this question for a commercial building by estimating levelized annual costs, or LACs,
using a commercial discount rate of 12 percent. While our analysis is limited to lighting, the
approach is applicable to other DC building applications and could be used for a overall DCpowered system analysis, and to DC distributed generation or energy storage.
We constructed a model that compares several lighting circuit scenarios: 1) a base case of 277
V AC fluorescent fixtures, 2) 249 V DC fluorescent fixtures (i.e. rectified 277 V AC), 3) 277 V
AC LED fixtures, and 4) 249 V DC LED fixtures. These four cases are examined with solar PV,
with and without battery storage. Given a specification of building geometry and lighting system
parameters, we estimate the number and wattage of ambient and task lighting fixtures needed.
This is used to determine the wire lengths and diameters (gauges) for the ambient and task
lighting systems. We then estimate levelized annual cost (LAC) for each scenario. For each
scenario, we hold constant the lighting services, i.e., the number of lumens (lm) provided by the
lighting fixtures. We also hold constant the number of fixtures – the wattage is therefore the free
variable. As an illustrative case-study, we examine a hypothetical four-story, 48,000 ft2 (4,400
5
m2) commercial building for 672 occupants, where lighting requirements are based on
Illumination Engineering Society of North America (IESNA) illuminance requirements for office
spaces (Navigant Consulting, 2002). Model specifications can easily be changed for alternate
case studies. We do not consider the use of daylighting or lighting controls, although in some
settings these can be highly cost-effective approaches to achieving higher lighting efficiency
(Jennings et al., 2000).
2.1 Lighting System and Power Electronics Characteristics
The modeled lighting systems consist of a 1900-klm ambient lighting system with 366
recessed troffer fixtures with 5300 lm per fixture and a 330-klm task lighting system with 672
desk-level under cabinet fixtures with 490 lm per fixture, with technical and cost parameters
shown in Table 1. Details are provided in Appendix 1 of the online version. Costs, not including
retail mark-ups, were primarily obtained from DOE research and development (R&D) targets, as
shown in Table 2. DC fluorescent ballasts and LED driver efficiencies were assumed to be equal
to the respective AC ballast/driver efficiency divided by the efficiency of a rectifier. The DC
lighting system is modeled as a circuit connecting the 277 V AC distribution system to a fullbridge rectifier with a non-isolated buck converter which produces 249 V DC output for each
floor-level lighting system of the building. LED driver, centralized rectifier, and fluorescent
ballast technical parameters are shown in Table 3. We ignore issues of standby-mode and offmode power consumption for fluorescent ballasts and LED drivers in this analysis, although DOE
is in the process of developing energy efficiency standards for these usage modes (DOE, 2010).
Power supply cost assumptions are shown in Table 4.
For the base case, annual lighting electricity intensity for the AC fluorescent lighting system is
2.3 – 4.9 (base case: 3.6) kWh/ft2, assuming ambient lights operate between 2500 and 5600
6
hours/year and task lights operate between 1500 and 2500 hours/year. This lighting electricity
intensity is just over half the average values for U.S. commercial office buildings as reported by
the EIA (6.1 kWh/ft2) (1992), LBNL’s Lighting Market Sourcebook (5.2 kWh/ft2) (1997), and the
EIA’s 2003 Commercial Building Energy Consumption Survey (CBECS) (6.8 kWh/ft2). This
difference arises primarily from the assumption that an energy-conscious office building owner
would design lighting fixtures to provide the IESNA minimum lumen requirement of 40
lumens/ft2, while the EIA estimated that the average U.S. office has a mean illumination level of
45-91 lm/ft2 (1992) which arguably means that it is overlit (Dau, 2003). Varying the amount of
total lumens provided would change the absolute value of the estimated levelized annual cost in
the results section, but not the ordering from least to most expensive. In addition, the model
excludes less efficient incandescent lighting in the base case lighting system because, given the
voltages assumed, the efficiency of these resistive elements are not affected by the use of AC
versus DC. In addition, because replacing incandescent lamps with fluorescent or LED lamps can
lower levelized annual cost of lighting (DOE, 2009; Azevedo, 2007), including incandescent
lamps in the base case would artificially inflate the levelized cost benefits of DC circuits with an
LED or fluorescent lighting system. We exclude issues of color quality in the present analysis.
Table 1: Base-case Fluorescent and LED Lighting System Parameters
AC FL
Ambient
Task
11-27 1.5-2.5
DC FL
Ambient
Task
11-27 1.5-2.5
AC LED
Ambient Task
DC LED
Ambient Task
FL Lamp Cost: $/fixture
LED Lamp Cost: 2010$/klm
86-116
86-116
Lamp Efficacy (lm/W)
86
78
86
78
125-169
125-169
Fixture Efficacy (lm/W)
53
24
56
25
99
92
114
105
Fixture Efficiency (%)
72%
37%
72%
37%
87% 80%
87% 80%
Calc: Wattage (W)
99
20
94
19
53
5
46
5
Notes: The number of fixtures and wattages are calculated from building geometry and IESNA lumen requirements
of 40 lm/ft2 for office buildings (Navigant Consulting, 2002), holding fixture lumens constant across scenarios. For
details see Appendix 1 in the online version. Cost per fixture obtained from Grainger.com (2010). Fluorescent lamp
efficacies from Navigant Consulting (2002). LED ambient fixture efficiency and fluorescent fixture efficiencies are
from DOE (2009, 2007a). LED task fixture efficiency is from DOE (2009). LED fixtures have higher efficiencies
than their fluorescent counterparts due to the directional nature of LED lumen output.
7
Table 2: 2008-2030 LED, PV, and Battery Projections
2008
2010
2015
2020
2030
Min
Max
Min
Max
Min
Max
Min
Max
Min
Max
PV Module Cost ($/Wp)
2.5
6.5
2.3
6.1
1.9
5.3
1.2
3.9
0.6
2.6
Inverter Cost ($/W)
0.33
0.68
0.31
0.65
0.25
0.57
0.20
0.54
0.15
0.37
SSL Device Efficacy (lm/W)
92
124
125
169
160
216
228
240
228
240
SSL Int.-Lamp Cost ($/klm)
144
194
86
116
24
32
7.6
17
1.7
2.3
SSL Thermal Eff (%)
81
89
85
93
90
95
91
96
92
97
SSL Driver Eff (%)
81
89
83
91
87
92
89
92
90
92
SSL Driver Cost ($/W)
1.98
2.9
1.61
2.36
1.18
1.73
0.87
1.27
0.18
0.26
Battery Cost ($/Wh) 0.31 0.82 0.30 0.80 0.28 0.74 0.26 0.69 0.22
0.59
Notes: PV module costs and efficiencies are from Curtright et al. (2008) and DOE (2007b) and SSL costs (except
for drivers) are from R&D targets in DOE (2009). Inverter costs are from Navigant (2006). SSL Driver costs are
assumed to be 12-15% (Philips, 2009) of integrated lamp costs in 2008 and 2010, and then decline by 6% annually
from 2010-2030. Given that LAC is relatively insensitive to electricity prices (see Figure 4), they are held constant
at $0.10/kWh. Lead-acid battery costs are from a sample of Grainger.com products, assuming costs decline at 1.5%
per year.
Table 3: Lighting System Power Supply Parameters
AC-DC Central Power
Supply
DC-DC Load Power
Supply
LED
LED
Ambient
Task
Fluorescent Ballasts
FL
LED
AC
DC
Converter Type
Buck
Buck
Vin (V)
277
277
242
242
277
242
Vout (V)
242
242
Calc: Efficiency (%) 93 ± 1a%
93 ± 1a%
84-99b%
84-99b%
85-109c%
91-112d
-7
-6
Calc: L (H)
8x 10
2x 10
Calc: C (F)
10x 10-8
7.x 10-8
Calc: (RON, RL, RD) /Rload (%)
1%
1%
Calc: Rload (Ohm)
1 ± 0.1
2 ± 0.3
a
AC-DC central power supply efficiencies are calculated assuming a buck converter topology, see Table 4 for costs
and (Erickson, 2001) for efficiency analysis.
b
AC LED driver efficiencies are from R&D targets in (DOE, 2009).
c
Ballast Efficiency is defined as the ratio of rated lamp power over lamp and ballast power consumption. If the
ballast is designed to run lamps at less than their rated power, the ballast’s nominal efficiency will be greater than
100%, yet the lamp will produce fewer lumens than if run at rated power. Ballast efficiency, together with
ballast factor, determines the light output and power consumption of the fluorescent lamp and ballast system. AC
fluorescent ballast efficiencies are from GE, Philips, and Osram Sylvania lamp catalogs.
d
DC fluorescent ballast and DC driver efficiencies are assumed to be equal to AC ballast/driver efficiency divided
by rectifier efficiencies of 93-97% from (Pratt et al., 2007).
Table 4: Power Supply Costs
Output Power Rating (W)
Cost ($/W)
0 – 50
0.10
51 – 150
0.34
150 – 250
0.18
250 – 500
0.17
500 – 1,000
0.20
1,000 – 50,000
0.17
8
Source: Philips, 2009
2.2 Wiring and Circuit Protection
The wiring system is sized to meet lighting system current requirements, subject to copper
conductor current limits and National Energy Code maximum voltage drop limits of 5% per
string. These two constraints on the wiring system limit maximum wire lengths. Since we are
modeling a new commercial building, the LAC calculations include wiring costs. Cables that
provide a direct connection from the central power supply on each floor to the AC grid are
assumed to be common to all cases and are not included in the model. We assume four circuit
breakers per floor for the ambient lighting system; these costs were explicitly included in the
LAC calculations, with prices obtained from manufacturer datasheets (see details in Appendix 1
of the online version). Circuit breakers (switches) for the task lighting systems are assumed to be
integrated in the fixture design and are not explicitly included in the model.
2.3 Economic Metrics
LAC is a useful metric for evaluating AC versus DC lighting systems because it allows for the
comparison of the costs of a system with many components of varying lifetimes, taking into
account the time value of money. The LAC estimates, in 2010$/yr, are the sum of installation and
capital costs for the lighting system (CapLED/CapFL), solar PV system (CapPV), and wiring and
circuit breakers (W), levelized over their respective lifetimes, and annual lamp replacement labor
costs (maintenance, M) and annual grid electricity costs (E) with $0.10/kWh rates, is defined as:
1
2
where CRF is the capital recovery factor.
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2.4 Solar Photovoltaic System Design (Without Energy Storage)
For the solar PV scenarios, we model a grid-connected commercial building with a solar PV
array with fixed-tilt at latitude, that supplies supplementary electricity in a climate such as in
Pittsburgh, PA. We model polycrystalline silicon solar PV, since it is readily available in the
marketplace and subject to future R&D improvements. Hourly and monthly average solar
radiation data were obtained from the National Renewable Energy Laboratory (NREL)’s National
Solar Radiation Database. Using these data, the model estimates hourly and monthly grid- and
solar PV- electricity consumption. The choice of the building site should not affect the relative
levelized costs of DC versus AC distribution since parameters that vary by region such as
insolation and electricity prices are held constant across all scenarios. However, variations in
insolation do affect the size and total capital costs of the PV panel, which constitute a major
portion of the LAC in the PV-integrated scenarios. Since Pittsburgh is a relatively cloudy site
(NOAA, 2010), we estimate an upper bound on absolute LACs with DC circuits in the U.S.
Sizing the solar PV system is an important design consideration to minimize DC circuit LAC.
An oversized PV system that produces more electricity than daily load requirements could require
an inverter to sell the excess electricity to the electric grid, DC energy storage, or would waste
excess PV electricity. All these options would increase the levelized cost of the system (Jimenez,
2005). Sizing the PV panel to minimize LAC is a rational approach, but this would not allow a
comparison of scenarios with and without PV when PV LCOEs are greater than grid electricity
prices (since the optimal PV size would then be zero watts). Given our interest in exploring not
only the least cost scenarios but also those that would increase the environmental sustainability of
the overall system, we opted for a scenario where the solar PV array is sized to power the “base
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load” ambient lighting systems during the sunniest month of the year using the “peak hours
approach” (Masters, 2004), so that the PV panel provides equal energy end-use (lighting) service,
for the scenarios excluding energy storage using:
3
where L is the building lighting system electricity load (kWh), !PV is the module efficiency of
the solar panel which is between 12-18% (Curtright et al., 2008, DOE, 2007b), I is the daily
insolation (h/day of peak sun = 1 kW/m2) at the site location, inv is the inverter efficiency (8794%) for the AC cases (and obviously 100% otherwise) (George, 2006). In months with less
solar radiation, grid electricity supplies the part of the load not powered by solar PV. A
consequence of the model’s PV sizing rule is that each scenario has a different solar PV module
size and electricity production, holding delivered lighting in lm/ft2 constant.
2.5 Integrated Solar PV Array and Energy Storage Design
To demonstrate how the addition of energy storage (in the form of simple lead-acid batteries)
would influence the LACs of the four main lighting scenarios, we also explore the case where the
solar PV and energy storage system provides a fixed proportion of total lighting load; this
proportion is held constant across scenarios for comparison. We chose lead-acid batteries for
simplicity and since they are a mature battery technology. Load profiles and solar PV output for
the maximum, minimum and mean solar insolation levels in Pittsburgh, PA are shown in Figure 1.
In this case, the solar PV array is sized for a load of bL where b ! 1.0, corresponds to the fraction
of the lighting load served by the integrated PV-battery system. The lead acid battery bank is
sized according to:
4
11
where B is the battery size in Ah defined as the maximum state of charge needed to store any PV
output not used by the lighting load at a given hour over the year, PV is the size of the
photovoltaic array in kW, It is the hourly insolation, and V is the system voltage of the solar PV
array and lighting system, and !d is the battery discharge efficiency. In our model, we ignore the
excess electricity stored in the battery at the end of the year; it could be used for other end-uses
for the commercial building. For this design, we assume the same system voltage for the lighting
and power generation system to preclude the use of additional power electronics. We vary the
proportion of electricity provided by PV and energy storage for the AC and DC fluorescent and
LED lighting systems, and compare LACs with the base case AC fluorescent lighting system
without solar PV.
Figure 1: Load Profiles for LED Lighting system vs. solar PV output in Pittsburgh, PA. The lighting load includes
ambient and task lighting systems. Load profiles generated from PV-integrated DC LED lighting systems with
100% of the load electricity requirements (on average over the year) provided by PV and energy storage.
2.6 Monte Carlo Simulation
Lighting and PV systems have a range of possible costs given the range in the efficiencies and
costs of DC and AC circuit components. In addition, there is considerable natural and sitespecific variability in solar radiation, which is an important parameter in the size and cost of the
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solar PV module and overall LACs in the PV-integrated scenarios. To represent a range of LAC,
these metrics were calculated using a Monte Carlo simulation of 1,000 runs, which randomly
sampled from uniform distributions of input parameters to generate a range of output values from
which statistics are generated (details available in Appendix 1 of the online version).
3. Results
3.1 The Economics of Grid-powered DC LEDs
Figure 2 shows the results for the grid-powered scenarios. Today, fluorescent lamps (either
DC or AC) are the cheapest options. If an industry voltage standard were established -- no matter
the level of the standard -- and LED manufacturers designed the lamps accordingly, LED drivers
could be eliminated from DC LED lighting systems. In that case grid-powered DC LED lighting
systems would require a central DC power supply. The ranges in Figure 2 and results reported in
the paper all correspond to one standard deviation. As Figure 2 shows, removing the drivers and
adding the power supply for a DC LED lighting system would lead to a 8 ± 11% (or $6,000/yr)
reduction in annualized costs and a 8 ± 8% (or $36,000) reduction in capital costs compared to a
baseline AC LED lighting system in 2010. In addition, any of the options involving LEDs are
almost twice the LAC of fluorescent options and almost four times the capital cost due to the
high capital cost of LED lamps. A commercial building of this size would spend roughly
$26,000/year on lighting electricity costs, using EIA’s (2003) end-use energy consumption
estimates, due to overlighting (Dau, 2003) and the limited use of incandescent lamps. In
contrast, our base case AC fluorescent lighting system has an annual electricity cost of
$18,000/yr and we estimate that DC LEDs correspond to a reduction in overall electricity costs
of 66% (to $6,000/yr) compared to the AC fluorescent base case.
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Figure 2: Levelized Annual Costs for AC vs. DC fluorescent and LED lighting systems. These results assume that
DC circuits eliminate the need for LED drivers, and calculate LAC with a discount rate of 12% and electricity price
of $0.10/kWh. Error bars represent plus or minus one standard deviation of the LAC distribution. The LED cost of
$101/klm for an integrated lamp is from DOE’s 2010 R&D targets (2009). LED and fluorescent lamp and fixture
costs are listed in Appendix 1. AC FL = 277 V AC fluorescent lighting systems, DC FL = 250 V DC fluorescents,
AC LED = 277 V AC LEDs, DC LED = 250 V DC LEDs. Lum install = luminaire installation cost, lamps + fix =
lamp plus fixture equipment cost, ps = power supply.
From a policy perspective, it is more important to assure that manufacturers can, in fact,
produce LEDs that follow DOE’s lamp production-cost and efficacy targets than to reduce power
electronics costs with DC circuits and voltage standardization. This can be seen in our
simulations in Figure 3, in which both DC and AC LED lighting systems match AC fluorescent
lighting system levelized costs by ~2014, with the difference between AC and DC LED lighting
systems declining with time. Compared to AC LED lighting systems, DC LED lighting systems
reduce LACs by 8% (or $3,000) in 2015 and by 7% (or $2,000) in 2020.
3.2 Impact on Carbon Dioxide Emissions
DC and AC LED lighting systems allow for the reduction of annual electricity consumption
in the simulated office building by 66%, compared to a baseline AC fluorescent lighting system.
Assuming the average U.S. carbon intensities for electricity (EPA, 2007), it would take
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electricity prices higher than $0.45/kWh for DC LEDs and AC LEDs to be able to compete with
AC fluorescents on a levelized annual cost basis. These electricity prices are much higher than
electricity prices in the U.S. but approach feed-in tariffs for roof top solar PV installations in
Germany, which are over $0.75/kWh (57.4 euro cents/kWh) (Solarbuzz, 2010). If decisionmakers decide that programs should be implemented to foster the adoption of LEDs, then a
possible program design would be to provide a rebate or credit for LEDs. In 2010, this would
require an incentive to consumers of roughly $0.36/kWh (this corresponds to an implicit price of
$600/ton CO2-e avoided), assuming the national average commercial electricity retail price of
$0.11/kWh (EIA, 2010). If DOE’s R&D targets for LED cost and performance are met, no
incentives would be required for the rational commercial consumer by ~2014 (Figure 3). These
LAC calculations are sensitive to discount rate, LED prices and lifetimes, luminaire fixture
efficiencies, and the lighting requirements of the building.
Figure 3: LAC projections for grid-connected AC vs. DC fluorescent and LED lighting systems. AC and DC LEDs
match AC FL LAC by 2014 and 2015, respectively. DC LED+PVs match AC FL LAC by 2016, and AC LED+PVs
reach these costs by 2019. The electricity price assumed is $0.10/kWh, and the discount rate is 12%. LED
projections are from DOE R&D targets, (2009) and solar PV projections are from Curtright et al. (2008). These
results assume that DC circuits eliminate the need for LED drivers.
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3.3 The Economics of Grid-connected PV-powered DC LEDs
Using a PV array output with the same voltage as the lighting system, one can eliminate an
inverter (DC-AC) and other power electronics. Eliminating the inverter would improve power
conversion efficiencies by up to 10%, so that a 14% and 22% smaller PV array would be needed
to power the lighting system with DC fluorescents and LEDs respectively. Figure 4 shows that
using DC distribution with grid-integrated PV and an LED lighting system reduces LACs by 14
± 10% and capital costs by 16 ± 8% compared to a similar AC system. With a DC fluorescent
lighting system and grid integrated solar PV, 15 ± 11% LAC reductions and 19 ± 13% capital
cost reductions are possible. The main cost drivers for a grid-integrated PV array powering an
LED lighting system are the PV array and LED capital costs. The LACs of grid-integrated PVpowered AC fluorescents and DC LEDs are virtually identical in 2010, but still double the LAC
of grid-powered AC fluorescents.
Figure 4: Levelized Annual Costs (in 1000$ per year) for grid-connected PV-powered AC and DC lighting systems.
For these results, the discount rate = 12% and electricity price = $0.10/kWh. Error bars represent plus or minus one
standard deviation of the LAC distribution. These results assume that DC circuits eliminate the need for LED
drivers. The LED cost of $101/klm for an integrated lamp are from DOE’s 2010 LED R&D targets (2009), and
solar PV costs of $2.3-6.1/Wp are from Curtright et al. (2008). LED and fluorescent lamp and fixture costs are
listed in Appendix 1. AC FL+PV = 277 V AC fluorescents integrated with a 43 kW solar PV system, DC FL+PV =
249 V DC fluorescents integrated with a 37 kW solar PV system, AC LED+PV = 277 V AC LEDs with a 23 kW
16
solar PV system, and DC LED+PV = 249 V DC LEDs with an 18 kW solar PV system. Lum install = luminaire
installation cost, lamps + fix = lamp plus fixture equipment cost, ps = power supply.
3.4 The Economics of Grid-connected PV-powered DC LEDs with Battery Back-up
Using DC distribution with solar PV and batteries can eliminate the need for several power
conversion stages, enabling the battery to provide power when the sun is covered by clouds or at
night, instead of using electricity from the grid. Today, crystalline silicon solar PV, lead-acid
batteries, and LED lighting are far too expensive to compete with grid-connected AC fluorescent
lighting systems (Curtright et al., 2008). However, if LEDs follow DOE’s R&D targets for cost
reductions (2009) and solar PVs follow a path toward $0.60-2.60/Wp by 2030, which is the 95%
confidence interval for crystalline silicon PV capital costs estimated by experts in Curtright et al.
(2008), our simulations suggest that it will be cost-effective for a grid-connected PV with battery
back-up to power up to 15% of the load from a DC LED lighting system by 2020, and up to 40%
of DC LED lighting loads by 2030, compared to using grid-powered AC fluorescent lighting
systems as seen in Figure 5.
Figure 5: 2010 and 2030 Lighting system LAC projections vs. fraction of load provided by solar PV and batteries
4. Discussion and Conclusion
Simulations in this work suggest that DC circuits could lower the LAC and capital costs of
LED lighting systems by 8 ± 11% compared to AC LEDs, provided that a DC voltage standard
17
were established for building distribution and LED luminaires so that drivers in individual
fixtures could be eliminated. The specific DC voltage standard chosen has limited impact on
lighting system LACs because wiring energy losses and switch costs, which depend on
distribution voltage, are small compared to the LED lighting and solar PV capital costs.
DC circuits with solar-integrated LEDs (with grid power as needed and no battery storage)
may match the LAC of grid-powered AC fluorescent lighting systems by ~2014, although there
is a considerable range in the LACs for lighting systems. Near-term applications of DC systems
include federal installations, given the government’s lower cost of borrowing. If states with solar
provisions in state RPSs or states with PV subsidies (DSIRE, 2010) required all new construction
of commercial office PV applications to use DC circuits, the LACs of the installations in 2010
could decline by 14 ± 10% and capital costs could decline by 16 ± 8%, further stretching subsidy
dollars, whether in the form of electricity production or power capacity investment subsidies.
However, given the large cost barriers that PV have yet to overcome, it is not clear that such
subsidies would be good public policy.
There are several limitations to using DC distribution for LED lighting systems. First, there
is a considerable range in the capital costs and energy efficiencies of various models of central
AC-DC power supplies and drivers in individual fixtures. Detailed benchmarking of baseline
capital cost and energy efficiencies of LED luminaire drivers would be needed to design a set of
replacement central AC-DC power converters that provide cost savings. Second, the main cost
driver for the LAC for LED lighting systems is the capital cost of the LED itself, which is 53%
of the AC LED lighting system levelized annual cost, rather than LED driver or electricity costs,
which are 10% and 12% respectively in 2010. Although a 8 ± 11% levelized annual cost savings
may be realized by switching from an AC LED lighting system to a DC LED lighting system in
18
2010, these cost savings are non-significant and small relative to the Department of Energy’s
R&D targets that capital costs for LEDs (in $/klm) will decline by over 20% annually during
2010-2020 through research and development (R&D).
Despite these limitations, DC distribution requires little or no new technology and can be
designed to meet building safety codes and standards. However, the century-long lock-in to AC
systems poses a formidable barrier to the implementation of DC use in buildings. Power
supplies, circuit protection, and other components designed for AC systems enjoy economies of
scale in manufacturing, strong demand, and a large pool of trained engineers and technicians to
control design and installation costs. At present, the small market for DC systems and small pool
of qualified technicians results in high mark-ups for central AC-DC power supplies of kWoutput power capacity, DC circuit protection, and installation. These factors have been ignored
in our analysis. Standardization as well as training efforts would be essential if a transition to
DC building circuits were to occur.
Developing a DC voltage standard will be challenging because it requires the coordination
and consensus of a diverse set of manufacturers with competing design objectives. However,
industry groups such as Emerge Alliance have now been formed to promote a low-voltage DC
standard to enable “plug-and-play” installation of DC appliances and lighting systems and to
reduce installation costs.
Today using LEDs for commercial building lighting systems, whether powered by AC or
DC, does not appear to be cost-effective strategy for reducing CO2 emissions. However, if DOE
R&D cost and efficiency targets are met, DC circuits for commercial LED lighting systems may
be economically feasible in the next few years, especially with the use of solar PV.
19
5. Acknowledgments
We thank Jay Apt, Kevin Dowling, Clark Gellings, Ihor Lys, Fritz Morgan, and Le Tang for
useful discussions and references to relevant data and literature. This work was supported in part
by a National Science Foundation Graduate Research Fellowship, the Gordon Moore Foundation,
and the Climate Decision-making Center (CDMC), which was formed through a cooperative
agreement between the National Science Foundation (SES-0345798) and Carnegie Mellon
University.
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23
Appendix 1: Engineering Design and Economic Model Inputs and Outputs
Parameter
Symbol
Unit
Description/Equation/Reference
Minimum/
Nominal
Value
Maximum
Value
Engineering Model
Building Input Parameters
Office Width
Office Breadth
Office Height
Number of Floors
Square feet per person
Cube Rows
Desk space
w
b
h
nf
sqftpp
ft2
cr
dk
ft2
Building Output Parameters
ft
ft
ft
fs
ocp
cc
tls
ft2
Lumen Requirement
Floorspace
Number of occupants
Cube Columns
Task light space
Office building width
Office building breadth
Office building height
Number of floors
Square feet per office occupant, average value
from http://www.officespace.com/SpaceCalc.cfm
Number of cubicle rows
Desk space
100
120
8
4
75
6
12
ft2
fs=w*b*nf
ocp = fs/sqftpp
cc =ocp/(4*nf*cr), rounded
tls=dk*cc*cr*nf*4
48,000
672
7
8064
lmft
lm/ft2
Navigant Consulting, 2002
40
Ambient Lighting Annual
Operating Hours
Task lighting Annual Operating
Hours
Fluorescent (FL) Ballast Factor
aaoh
hrs
taoh
hrs
T8 FL Efficacy
FL Lamps per Ambient Fixture
FL Lamps per Task Fixture
LED Lamps per Ambient Fixture
LED Lamps per Task Fixture
T8 Watts
T12 FL Efficacy
T8 FL lifetime
t8efc
flpaf
flptf
lpaf
lptf
t8w
t12efc
t8lf
Lighting System Input Parameters
Bf
lm/W
W
lm/W
hrs
Annual operating hours for ambient lighting from
Navigant Consulting (2002).
Annual operating hours for task lighting from
Energy Solutions (2004).
From GE, Philips, and Osram Sylvania, Inc.
(OSI) Lamp Catalogs
From GE, Philips, and OSI Lamp Catalogs
From GE, Philips, and OSI Lamp Catalogs
T8 Fluorescent lamp lifetime in hours, From GE,
Philips, and OSI Lamp Catalogs
24
2500
5600
1500
2500
0.84
0.92
80
3
1
12
1
32
70
16000
92
86
24000
Parameter
Symbol
Unit
T12 FL lifetime
t12lf
hrs
T8 FL Ballast lifetime
t8blf
hrs
T12 FL Ballast lifetime
t12blf
hrs
Ac T8 FL Ballast Efficiency
acT8beff
%
AC T12 FL Ballast Efficiency
acT12beff
%
FL ambient fixture efficiency
FL task fixture efficiency
LED lifetime
LED driver lifetime
LED ambient fixture efficiency
LED tasklight fixture efficiency
Maximum LED Efficacy
Maximum FL Efficacy
afefffl
tfefffl
ledLf
ledDrvLf
afeffled
tfeffled
maxEfcled
maxEfcfl
%
%
hrs
hrs
%
%
lm/W
Lm/W
Description/Equation/Reference
Minimum/
Nominal
Value
T12 Fluorescent lamp lifetime in hours, From
GE, Philips, and OSI Lamp Catalogs
T8 Fluorescent ballast lifetime in hours, From
GE, Philips, and OSI Lamp Catalogs
T12 Fluorescent ballast lifetime in hours, From
GE, Philips, and OSI Lamp Catalogs
Ballast Efficiency equals the ratio of rated lamp
power over lamp-and-ballast power consumption.
From lamp catalogs
Ballast Efficiency equals the ratio of rated lamp
power over lamp-and-ballast power consumption.
From lamp catalogs
DOE, 2007a
DOE, 2007a
DOE, 2009
DOE, 2009
Average (.87) from DOE, 2007a
Average (.80) from DOE, 2009
Tsao, 2004
Derived from Tsao (2004), FL are 25% efficient
at 85 lm/W, max efficacy = 4*85 lm/W
16000
24000
32000
48000
32000
48000
0.85
1.09
0.9
0.98
0.65
0.3
40000
40000
0.77
0.70
400
340
0.8
0.5
60000
60000
0.97
0.90
Lpaf/(naf*ledEfc*thermEff*lpaf*afeffled); LED
efficacy and thermal efficiency R&D targets in
Table 2
(lpaf or flpaf)*(t8w)/(t8beff or drvEff); driver
efficiency R&D targets in Table 2.
thermEff*(t8- or led-Efc) *(afefffl/led)
*(ac/dc,T8beff or ledDrvEff)*(t8blf); thermal
efficiency R&D targets in Table 2.
round(lmft*fs/(afw*afefc))
Lpaf/(ntf*ledEfc*thermEff*lptf*tfeffled); LED
efficacy and thermal efficiency R&D targets in
Table 2
lmft*dk/tfefc
thermEff*(t12- or led-Efc) *tfefffl/led*(ac/dc,
Varies
Lighting System Output Parameters
Ambient LED lamp watts
alw
W
Ambient fixture watts
afwfl/led
W
Ambient fixture efficacy
afefcfl/led
lm/W
naf
tlw
W
tfwfl/led
tfefcfl/led
W
lm/W
Number of ambient fixtures
Tasklight LED lamp watts
Tasklight fixture watts
Tasklight fixture efficacy
Maximum
Value
25
Varies
Varies
360
Varies
Varies
Varies
Parameter
Symbol
Unit
Description/Equation/Reference
Minimum/
Nominal
Value
Maximum
Value
t12beff or drvEff)*(t12blf) ; thermal efficiency
R&D targets in Table 2.
Number of tasklight fixtures
ntf
ntf=cc*cr*nf*4
672
Central Power Supply Input Parameters
Input Voltage
Output Voltage
Diode forward Voltage drop
Switching period
Central power supply lifetime
Vg
V
VD
Ts
psLf
Vac
Vdc
V
sec
hrs
http://www.testequity.com/products/1691/
277
48, 60, 250
0.35
.0001
30000
1.7
40000
Central Power Supply Internal Parameters
Load resistance
Inductor resistance
Switch transistor on resistance
Diode resistance
Voltage ripple
Duty Cycle
D-prime
Inductor current
Capacitor
Inductor
Rload
RL
Ron
RD
!V
D
D’
IL
C
L
W
W
W
W
V
A
F
H
Rload = V/I
RL = 0.01*Rload
Ron = 0.01*Rload
RD = 0.01*Rload
!V = 0.05*V;
D = (V*(RL +RD +Rload) + VD*Rload)/(Rload*(Vg +
VD) + V*(RD - Ron))
D’ = (1-D)
IL = (D*Vg – D’VD)/(RL + D*Ron + Rload)
C = (D*Ts*(Rload*IL- V)/(2*DV*Rload));
L =(D*Ts*(Vg-IL*(Ron+RL)-V)/(2*D*IL));
Varies
Varies
Varies
Varies
Varies
Varies
Varies
Varies
Varies
Varies
Central Power Supply Output Parameter
Converter Efficiency
PS"
%
"= (1-D’*VD/(D*Vg))/(1+(RL+D*Ron+D’*RD)/
Rload)
93%
PV, Wiring, Electrical System Input Parameters
AC Operating Voltage
DC Operating Voltage
Wire Installation Time
acOpV
dcOpV
wit
Vac
Vdc
hrs/ft
Wire life
Inverter Efficiency
Inverter Lifetime
Rectifier Efficiency
wlf
invEff
invLife
rectEff
yrs
%
yrs
%
http://www.turtlesoft.com/constructioncosts/Electric-Rough/Romex_6_3.htm
George (2006).
Pratt et al. (2007).
26
277
249
0.026 ;
(1hr/38 ft)
25
0.87
10
0.93
.94
.97
Parameter
Symbol
Battery Lifetime
Battery Charge Efficiency
Battery Discharge Efficiency
Battery Cost
battLife
battChEff
battDEff
battCost
Unit
Description/Equation/Reference
yrs
%
%
$/Ah
Messenger and Ventre, 2003
Messenger and Ventre, 2003
Grainger.com products, assuming 1.5% cost
decline per year. See Table 2.
Minimum/
Nominal
Value
10
95
95
varies
PV, Wiring, Electrical System Internal Parameters
Ambient Fixture Current
Ambient Wire Current Rating
afc
awc
A
A
Ambient Wire Resistance Rating
awr
!/1000 ft
awvd
afwg
V
Tasklight Fixture Current
Tasklight Wire Current Rating
Tfc
twc
A
A
Tasklight Wire Resistance
Rating
Tasklight Wire Voltage Drop
Tasklight Wire Gauge
twr
!/1000 ft
twvd
tfwg
V
Ambient Wire Voltage Drop
Ambient Wire Gauge
Hourly Insolation by month
solRad
W/m
2
afw/(acOpV or dcOpV)
Min AWG table current s.t. (AWG table current
>= afc) & awvd <= 0.05*(acOpV or dcOpV))
Wire resistance corresponding to cable with
current rating awc in AWG Table
awl*afc*awr/1000
Wire gauge corresponding to cable with current
rating awc in AWG Table
tfw/(acOpV or dcOpV)
Min AWG table current s.t. (AWG table current
>= tfc) & twvd <= 0.05*(acOpV or dcOpV))
Wire resistance corresponding to cable with
current rating twc in AWG Table
twl*afc*awr/1000
Wire gauge corresponding to cable with current
rating awc in AWG Table
See Appendix 5.
Varies
(w*cr/4+b/2)*4*nf
Assumes central circuit box and radial cables to
each desk with varying length -- i.e.
for a=0, step w/cc, to w/2; for b=0,
step b/cr, to b/2
if DC, (naf*afwfl/led + ntf*tfwfl/led)/PS", else naf*
afwfl/led + ntf* tfwfl/led
See Equation 4.
pvkW*(.97*.96*invEff*(1-0.005*(celltemp25))*solRad/1000, calculated hourly, aggregated
to daily averages per month, See Appendix 5, 6
Varies
12
2.53
Varies
14
Varies
12
2.53
Varies
14
Varies
PV, Wiring, Electrical System Output Parameters
Ambient fixture wire length
Awl
Twl
ft
ft
Task fixture wire length
Lighting Load
PV Panel size
PV Electricity Output
LkW
kW
pvkW
pvkWh
kW
kWh
27
Varies
Varies
Varies
Varies
Maximum
Value
Parameter
Grid Electricity Consumption
Symbol
gridkWh
Unit
Description/Equation/Reference
kWh
For each month, hourly grid kWh for the avg day
= naf*afwfl/led – hrlyPVkWh, aggregated for aaoh
hours/year + ntf*atoh*tfwfl/led (tasklight
electricity consumption), if excess PV electricity,
assume used by exogenous loads
Minimum/
Nominal
Value
Maximum
Value
Varies
Economic Model Inputs
Lighting System Cost Input Parameters
T8 Lamp cost
Fluorescent Ambient Fixture
Cost
T12 Lamp cost
Fluorescent Tasklight fixture
cost
AC T8 ballast cost
AC T12 ballast cost
LED Ambient Fixture Cost
LED Tasklight Fixture cost
Technician Level I Labor Rate
Technician Level II Labor Rate
Fluorescent Ballast Installation
Time
Lamp Installation Time
Luminaire Installation Time
LED Driver Installation time
t8c
afcfl
$/3-lamps
$/fix
Assume ambient fixtures use three 4-foot t8
lamps in a recessed troffer fixture. Costs from
Grainger.com
Costs from Grainger.com
Assume tasklights use one 2-foot t12 lamp in an
undercabinet fixture
3.75
9
17
97
1.5
2.5
23
11
5
19
31
10
40
43
24
9
99
46
20
68
t12c
$/lamp
tfcfl
$/fixture
Costs from Grainger.com
t8balc
t12balc
afcled
tfcled
tech1
tech2
$/ballast
$/ballast
$/fixture
$/fixture
$/hr
$/hr
Costs from Grainger.com
Costs from Grainger.com
Costs from Grainger.com
Costs from Grainger.com
bInst
hr
0.5
lInst
lumInst
dInst
hr
hr
hr
0.25
0.5
0.5
Lighting System Cost Output Parameters
Luminaire Cost, lamp
Luminaire Cost, fixture
Luminaire Cost, ballast or driver
(a/t)LumC
-l
$
LumC-fx
LumC-lps
$
$
Same calculations for ambient or task lighting.
For LEDs: costPerKlm*ledEfc*(alw* lpaf*naf or
tlw* lptf* ntf)/1000; For FL: flpaf* t8c or flptf*
t12c
naf* afcfl/led or ntf* tfcfl/led
For FL: naf*t8balc or ntf*t12balc; For LEDs:
(naf*afwled or ntf*tfwled)* DrvCostPerW; Driver
28
Varies
Varies
Varies
Parameter
Symbol
Unit
Luminaire Cost, installation
Luminaire Cost, annual
maintenance
LumC-in
LumC-m
$
$
Description/Equation/Reference
cost per Watt estimates in Table 2.
Tech2*lumInst
lInst*tech1*(aaoh/t8lf or taoh/t12lf or aaoh/ledLf
or taoh/ledLf)+ tech2 *(aaoh/t8blf*bInst or
taoh/t12blf*bInst or aaoh/ledDrvLf*dInst or
taoh/ledDrvLf*dInst)
Minimum/
Nominal
Value
Maximum
Value
Varies
Varies
Central Power Supply Cost Input Parameter
Power Supply Installation Time
psInst
hrs
1
Central Power Supply Cost Internal Parameter
Output Power
Pout
W
LkW/nf
Varies
psC-eq
$
psC-in
$
psCostPerW*Pout, See Appendix 2 for power
supply costs
tech2*psInst
psC-m
$
Tech2*psInst*aaoh/psLf
Central Power Supply Cost Output Parameter
Central Power Supply Cost,
equipment
Central Power Supply Cost,
installation
Central Power Supply Cost,
maintenance
Varies
Varies
Varies
PV, Wiring, Electrical System Cost Input Parameters
Inverter Cost
PV Balance of Plant Cost
invC
bop
$/W
$/W
250 V DC Switch Cost
Sw250
$/switch
48 V DC Switch Cost
Sw48
$/switch
60 V DC Switch Cost
Sw60
$/switch
277 V AC Switch Cost
Sw277
$/switch
Navigant, 2006
Curtright et al., 2008
http://www.abb.com/product/seitp329/19130a558
33d8efdc1256e89004019e9.aspx; half list price;
assume 4 switches per floor, task lamp switches
built into fixture
http://www.abb.com/product/seitp329/19130a558
33d8efdc1256e89004019e9.aspx; list price
http://www.abb.com/product/seitp329/19130a558
33d8efdc1256e89004019e9.aspx; half list price
http://www.drillspot.com/products/43243/Maple_
Chase_ET1100_Electronic_Light_Switch
Varies
2.5
6.5
115
155
10
13
59
80
49
67
PV, Wiring, Electrical System Cost Output Parameters
ambWireCost , equip
ambWireCost,installation
aWireCeq
aWireC-in
wire cost/ft*awl + nf*4*(sw48 or sw60 or sw250
or sw277); wire costs in Appendix 6
awl*wit*tech2
29
Varies
Varies
Parameter
Symbol
Unit
TaskWireCost , equip
TaskWireCost,installation
PV Panel Costs
tWireC-eq
tWireC-in
pvC
$
R
!
E
Years
$/kWh
Description/Equation/Reference
wire cost/ft*twl
twl*wit*tech2
1000*pvkW*(bop +pvPanelCostPerW); PV panel
costs in Appendix 4
Minimum/
Nominal
Value
Varies
Varies
Varies
Economic Input Parameters
Discount Rate
Time Period
Electricity Price
0.12
20
0.1
Economic Output Parameters
Cap
pv cap
Lac
Npv
aLumC + LumC + aWireC+ tWireC + psC
PV panel +bop costs, see Appendix 4
See equations 1-2
See equation 3
Varies
Varies
Varies
Varies
Environmental Input Parameters
Electricity CO2 Intensity
Electricity SO2 Intensity
Electricity NOx Intensity
eCO2
eSO2
eNOx
Environmental Output Parameters
Cost of CO2 Conserved
Cost of SO2 Conserved
Cost of NOx Conserved
CO2C
SO2C
NOxC
Ton
CO2/kWh
Ton
SO2/kWh
Ton
NOx/kWh
EPA, 2007.
$/ton CO2
$/ton SO2
$/ton NOx
(lacscenario – lacacfl)/(CO2acfl – CO2-scenario)
(lacscenario – lacacfl)/(CO2acfl – SO2-scenario)
(lacscenario – lacacfl)/(CO2acfl – NOx-scenario)
0.001
EPA, 2007.
2.63*10-6
EPA, 2007.
9.68*10-7
Varies
Varies
Varies
Monte Carlo Parameter
n
Number of runs in simulation
30
1000
Maximum
Value
b
Corresponding author. Tel: 1-240-672-1419, Fax: 1-412 -268-2670, Mail: 5000 Forbes Ave., 129 Baker Hall, Pittsburgh, PA, 1521
31