AC vs. DC distribution: A loss comparison

Abstract

Environmentally friendly technologies such as photovoltaics and fuel cells are DC sources. In the current power infrastructure, this necessitates converting the power supplied by these devices into AC for transmission and distribution which adds losses and complexity. The amount of DC loads in our buildings is ever-increasing with computers, monitors, and other electronics entering our workplaces and homes. This forces another conversion of the AC power to DC, adding further losses and complexity. This paper proposes the use of a DC distribution system. In this study, an equivalent AC and DC distribution system are compared in terms of efficiency.

Full text

Page 1

Abstract--Environmentally friendly technologies such as
photovoltaics and fuel cells are DC sources. In the current power
infrastructure, this necessitates converting the power supplied by
these devices into AC for transmission and distribution which
adds losses and complexity. The amount of DC loads in our
buildings is ever-increasing with computers, monitors, and other
electronics entering our workplaces and homes. This forces
another conversion of the AC power to DC, adding further losses
and complexity. This paper proposes the use of a DC distribution
system. In this study, an equivalent AC and DC distribution
system are compared in terms of efficiency.

Index Terms-DC power systems, power system modeling,
power distribution, losses
I. INTRODUCTION
ncreasing demand and environmental concerns have
forced engineers to focus on designing power systems
with both high efficiency and green technologies. Green
technologies are those that conserve natural resources such as
fossil fuels while reducing the human impact on the
environment through a reduction in pollution [1]. The most
well-known green technologies include photovoltaics and
wind turbines. Although fuel cells are not considered a green
technology, fuel cells have low emissions compared to other
forms of energy and are deemed more environmentally
friendly. Unfortunately, the prevailing power system
infrastructures are based on alternating current (AC) while
two of the leading environmentally friendly energies, fuel
cells and photovoltaics, produce direct current (DC).
Currently, power system infrastructures that wish to
incorporate fuel cells and photovoltaics must first convert the
DC power produced by these energy sources to AC. This adds
complexity and reduces efficiency of the power system due to
the need of a power converter. Furthermore, an ever
increasing number of DC consuming devices such as
computers, televisions, and monitors are being incorporated
into our buildings. The power supplied to these devices must
be converted again from AC back to DC adding further losses
and complexity to the power system.
Instead of using multiple converters to convert DC to AC
and then AC to DC, the power system could solely be based
on DC. This would eliminate the need for two sets of
converters for each DC load, reducing the cost, complexity,
and possibly increasing the efficiency. However, a definitive
analysis on a DC distribution system is needed to determine
the net benefits of eliminating the converters. In this paper, a
large steady state analysis of an existing AC grid is
constructed along with a DC counterpart. These models are
compared in terms of efficiency.
II. BACKGROUND
Since the development of electricity, AC has been depicted
as the better choice for power transmission and distribution.
However, Thomas Edison one of the founders of electricity
supported the use of DC. No method at that time existed for
boosting and controlling DC voltage at the load, so that
transmission of DC power from generation to load resulted in
a large amount of losses and voltage variations at the different
load locations. To resolve this issue, Westinghouse proposed
AC distribution. Nikola Tesla had only recently at that time
developed the transformer which had the capability of
boosting voltage in AC. This allowed for efficient
transmission of power from one location to another resulting
in a complete transformation of the power systems to AC [2].
Although many things have changed since the invention of
electricity, AC is still the fundamental power type of our
power infrastructure. However, due to the development of
power converters and DC energy sources, interest in DC has
returned.
Several studies have investigated the use of a DC
distribution system. In [3], a small-localized DC distribution
system for building loads is investigated. This power system
is supplied by a DC distributed energy source for the DC
loads and has a separate AC grid connection for the AC loads.
The author relates that this methodology leads to a higher
efficiency compared to a system solely based on AC through
avoiding the use of the rectifier. The author notes that power
rectifiers have a relatively low efficiency compared to
inverters and DC-DC converters.
In [4], a DC zonal distribution system for a Navy ship is
investigated to provide electrical isolation, reduce cost, and
increase stability. Essentially each zone has a separate
distribution system providing protection to the overall ship
power systems when an attack has occurred. Due to the need
of multiple levels of DC voltage, a DC system was deemed
superior to a AC system in terms of efficiency and cost. The
AC system would need an inverter and then DC-DC converter
for each DC bus voltage level, while a DC system would only
implement DC-DC converters.
AC vs. DC Distribution:
A Loss Comparison
Michael Starke1, Student Member, IEEE, Leon M. Tolbert1,2, Senior Member, IEEE,
Burak Ozpineci2, Senior Member, IEEE,
1University of Tennessee,
2Oak Ridge National Laboratory
I
978-1-4244-1904-3/08/$25.00 ©2008 IEEE

Page 2

Nevertheless, several investigations in DC have suggested
that DC distribution is not as efficient. In [5], the authors
investigate DC distribution for a small-scale residential
system. The authors note that although conduction losses in a
DC system appear to be lower, the efficiency of power
converters during partial loading is a concern and can
ultimately lead to higher losses in DC. In [6], the author
compares several AC and DC systems for data centers. Based
on the results, the author concludes that a high voltage (HV)
DC distribution system is more efficient than AC, but no
components need this high voltage. The author constructed
another DC system, coined a hybrid DC system, which
contained multiple DC voltages. However, the author
observed that the converter losses reduced the efficiency to
that below what is found in an equivalent AC system.
In all of these cases, a DC distribution system was
employed at systems below what is deemed the power
distribution level of the utility. Furthermore, the loads were
either assumed to be fully AC or DC. In this study, the utility
level distribution is considered, and efficiencies of the AC
and DC power systems are compared. The power system is
also adjusted for partial loading of AC and DC components.
The goal is to relate an AC power system to DC in terms of
efficiency.
III. MODEL
To best represent the differences in AC and DC power
infrastructures, two models were created, one implementing
the actual AC devices and components of the grid and a
second model implementing DC devices. The DC model
adopts some of the AC components along with necessary DC
components to represent a direct conversion from an AC
system to a DC system.
The AC model is a representation of a large existing power
distribution system with thousands of loads in a variety of
sizes. The loads range in size from several watts to several
hundred kW and come from industrial motors, lighting,
computers, air conditioners, and other devices. Due to the
sheer number, the loads are not measured for each device
within the building, but instead are measured at the building
level. This results in a power system consisting of 235 loads
or buildings.
The loads employed have two sets of recorded data, a
maximum and an average. During a one year span, daily
maximum and average building loads of the power system in
question were measured. At the end of the year, the daily
averages were averaged and the maximum was found for the
whole year. The average and maximum instantaneous power
usage for the entire distribution system for the year are
31.9MVA/27.1MW and 42.6MVA/36.2MW, respectively.
The AC distribution power system under investigation is
divided into three voltage divisions, two medium
voltages(MV) and a low voltage(LV). For the AC power
system the HV and MV are 13.8kV and 2.4kV. The LV
magnitude is dependent on the building loads.
The DC model was constructed with the AC model in
mind. Any location where voltage was increased or decreased
with a transformer in AC, a DC/DC converter was
implemented in the DC model. AC components that are
deemed applicable in DC power systems were implemented in
the DC model and include the distribution lines and some
fault interrupting devices.
Both of these models were inserted into the SKM power
system analysis software package for analysis. This program
is a used extensively by the Oak Ridge National Laboratory
(ORNL) for AC power system power flow verification. This
software package accepts the input data from the user and
implements several numerical analysis techniques to
determine the voltage, current, and power levels at different
locations in the power system. The following subsections
describe the model in more detail.
A. AC Model
The components in the AC portion of the model that are
implemented in the load flow analysis are the distribution
line, transformer, AC load, and capacitor for Var
compensation as seen in Fig. 1. These components account
for more than 900 components in the model. Buses are also
necessary for analysis of the data and are placed in between
each load flow component. The total number of buses in the
model were determined to be 714. The fault interruption
devices in the model were ignored due to the negligible
resistance these devices add to the overall power system.
The characteristic data used to determine the load flow and

Transformer
losses for the different components is described in Table I.
This data comes primarily from manufacturer-supplied data
with missing information supplied by test data.

TABLE I
AC DISTRIBUTION SYSTEM CHARACTERISITIC
COMPONENT DATA
Distribution Line
Positive sequence impedance
Zero sequence impedance
Load Apparent Power
Power Factor
Voltage Rating
Zero Sequence impedance
Positive Sequence Impedance
Power Rating
Input/Output Voltage Rating
Zero sequence capacitance
Positive sequence capacitance
Transformer
Capacitor Bank
Load
0800 AREA
POLE 41A325 FTD
0800 AREA
0855 AREA
41-S47 41-F4741-47
9321-41-47-SEC
LOAD-41-47
XLN-41-48
41-S4841-F48
9330-41-48-PRI
41-48
9331-41-48-SEC
LOAD-41-48
41-S5141-F5141-51
9341-41-51-SEC
LOAD-41-51
Bus
Distribution Line


Fig. 1. Portion of AC distribution system.

Page 3

B. AC Model Equations
The basic methodology behind the SKM program is the use
of Ohm’s law. In matrix form this is:

[ ] [ ][ ]
I =

where I represents the currents, V the voltages, and Y the
admittance matrix. The admittance matrix represents the
different admittance values that interconnect the buses in the
power system. These admittance values can come from a
number of sources, line impedance, impedance within a
transformer, or even shunt admittance from a capacitive
source. Consider the three bus example provided in Fig. 2.

VY
(1)
The three bus example is composed of 3 lines that could be
considered as either a distribution line or a transformer. In
either case, a characteristic series impedance is associated
with these lines. Fig. 3 shows the admittance model.

Using Fig. 3, equations for the injected current at each bus
can be constructed in terms of the voltage and series and
shunt admittance values. The following equations represent
the injected current for the three different buses.

322112112 13
)()()(VYVYVYYYJJ
sha
×−+×−+×++=+
(2)

3323111 2321
)()()(VYVYYYVYJJ
shb
×−+×+++×−=+
(3)

×
32323123231
)()()(VYYYVYVYJJ
shc
×+++−+×−=+
(4)

Manipulation of these equations into matrix form results in
the formation of the admittance matrix as shown below [7-8].

⎡
+−=
⎥
⎦
⎢
⎣
2
3
YYJ

Since the voltages and current values are the unknown
values in the system, another equation must be adopted to
resolve the equations. The following equation relates the real
and reactive power to current and voltage:

⎥
⎦
⎥
⎥
⎤
⎢
⎣
⎢
⎢
⎡
⎥
⎦
⎥
⎥
⎤
⎢
⎣
⎢
⎢
++−−
−+
−−++
⎥
⎥
⎤
⎢
⎢
⎡
3
2
1
323
3311
2121
2
1
*
V
V
V
YYY
YYYYY
YYYYY
J
J
shc
shb
sha
(5)
i
ii
i
V
jQP
I
)(
+
=
(6)

Combining equations 1 and 6 results in a nonlinear
equation as shown:

[ ][ ]
Y
⎥⎦
⎤
⎢⎣
⎡
+
V
=
*
)(
jQP
V
(7)

This equation contains the variables of real and reactive
power, voltage (including magnitude and phasor angle), and
the admittance. Depending on the unknown and known
variables in this equation, the names swing bus, load bus, and
voltage control bus are provided as descriptions of the bus
type as shown in Table II.

TABLE II
AC BUS TYPES
Specified
Swing Bus Pl, Ql
V = 1 pu
δ = 0o
Load Bus Pg, = Qg = 0
Pl, Ql
Voltage Control
Bus
Pg = real power generated
Qg = reactive power generated
Pl = real power consumed
Ql = reactive power consumed
V = voltage magnitude
δ = voltage angle


Since the base equation is nonlinear, an iterative numerical
technique must be implemented to solve for the solution. The
numerical analysis method implemented by SKM has been
coined the “double current injection” method. In this method,
the losses are originally assumed to be zero, and the current is
determined through calculation from the load and nominal
voltage values. The losses are then included and the voltage
drop at each load and bus is determined. The new voltages
lead to a recalculation of the current and another iteration is
begun. This process is repeated to a minimum error has been
reached.
Free
Pg, Qg
V, δ
Pg, Qg, Pl, V Qg, δ

Y1
Y3
Y2
Yshc
BUS 1
V1
BUS 2
V2
BUS 3
V3
J12
J21
J13
J31
J32
J23
Yshb
Ysha


Fig. 3. Impedance schematic of 3 bus example
BUS 1
BUS 2
BUS 3

LINE 1
LINE 2LINE 3

Fig. 2. Schematic of 3 bus example.

Page 4

C. DC Model
The components of the DC load model implemented in
load flow include the distribution line, DC/DC converter, and
DC load as seen in Fig. 4.



For this model several assumptions had to be made:

1)
As with AC, the fault interruption devices were
deemed negligible in terms of losses and were
ignored in the model.
2)
One current problem with DC-DC converters is that
the efficiency tends to fall when operated below the
rating. In the model implemented, the DC-DC
converter efficiency was assumed fixed for all
operating conditions.
discussed in [9] describes a design that allows DC-
DC converters to operate close to the maximum
operating efficiency until as low as 10% of operation
as seen in Fig. 5.
A paralleling topology

3)
The distribution lines used in the DC model are the
same as the AC model. Hence, the resistance values
employed come from the manufacturer specifications
of the AC distribution lines. The values used
represent the DC resistance of the conductor at a
temperature of 25oC.
4)
Since DC is only composed of two cables instead of
the three used in AC, an extra cable exists for DC.
This extra cable is to be applied as a DC negative.
This provides DC with a positive, neutral, and
negative thereby doubling the apparent voltage [10].
Since no reactive power is produced or consumed in
a DC power system, the loads modeled in DC were of
the same real power magnitude. This power value
was determined by multiplying the apparent power of
the AC load by the power factor.
5)

The characteristic data for the DC model involves purely
resistive elements. SKM uses the equations in Table III to
convert the data supplied to a DC resistance. Since the DC-
DC converter model resistance is based on the rated power,
the simulation results must be verified to ensure that the
actual efficiency input was actually implemented.

TABLE III
DC COMPONENT CHARACTERISTIC EQUATIONS
Distribution Line
lrcable×
V2
Load
P
DC-DC Converter
P
V2
)1 (
η−

rcable – resistance/ft
l – length of cable in ft
V – rated voltage
P – rated power
η - rated efficiency


D. DC Model Equations
The DC load flow calculations are similar to those of the
AC power system with a few differences. The DC power
system uses a conductance matrix instead of an admittance
matrix since no reactance exists in DC:

[ ] [ ][ ]
I =

This embodies the DC system with a much simpler overall
equation and characterization of the buses. Table IV shows
the distinct bus types of a DC type. Unlike the AC system, the
DC system only has 2 bus types with 2 unknown variables.
SKM implements Newton Raphson to solve for these
variables.

TABLE IV
DC BUS TYPES
Specified
Swing Bus Pl
V = 1 pu
Load Bus Pg, Pl
VY
(8)
Free
Pg
V


0 10 203040 506070 8090 100
0
10
20
30
40
50
60
70
80
90
100
Efficiency (%)
Converter Rating(%)
Single Converter
4 Converters

Fig. 5. Efficiency curves for DC-DC converter.


0800 AREA
POLE 41A
0800 AREA
0855 AREA
41-S47 F-41-008
41-S48F-41-009
41-S51 F-41-010
dcCBL-41-013
dcBUS-41-020
dcCNV-41-008
dcBUS-41-019
dcCNV-0009
dcBUS-41-021
dcCNV-41-010
dcBUS-41-023
dcCLD-41-007
dcCLD-41-008
dcCLD-41-009
DC Load
DC/DC Converter
DC Cable


Fig. 4. Portion of DC distribution system.

Page 5

E. Difference in AC and DC
In terms of the basic power system equations, AC and DC
power systems have quite a contrast. In an AC system, power
flow is often determined by the equation:

3
3
φ
×=
RMS
VP)cos(
θ××
RMS
I
(9)

where VRMS, IRMS, and θ are the respective voltage in RMS,
current in RMS, and power factor angle. In DC, the power
flow is calculated by:

PDC

Upon examination, these equations can have a substantial
difference in power flow. Depending on the power factor,
AC can have three times more power flow when the same
RMS voltage and current are implemented in an AC and DC
system as shown:

P
IV
×=
(10)
)cos(3
3
θ
φ=
DC
P
(11)

The voltage and currents in the DC system must be
adjusted to overcome this difference. If we now consider the
difference in losses for AC and DC:

IP
×=
3
3
φ
P
×=
2
ACRMS
I
AC
R
×
×

2
(12)
(13)
DCDC DC
R
2
and if we wish the systems to have the same losses:

I
82.
3
2≈=
DC
RMSAC
I
(14)

where the AC and DC resistance values are assumed to be the
same, a noticeable gain in DC can be seen. This result shows
that the DC current can be 1.22 times larger than the AC
current and the system will have the same conduction losses.
If a DC neutral is implemented as previously discussed,
and the equations (9),(10), and (14) are combined:

V
)cos(
82.
2
θ
=
DC
RMS
AC
V
(15)

and if we convert the voltages from RMS to peak:

)cos(
15
θ
. 1
2
≈
DC
AC
V
V
(16)

This illustrates that if the same peak voltages in both the
AC and DC systems are implemented, DC should have a
small advantage over AC in terms of transmission losses
when implementing AC
transmission losses tend to only account for a small
cables. Nevertheless, the
percentage of the system losses. The power conversion
devices have a more significant impact.
In AC, the power conversion devices employed are
transformers. The efficiency of the transformer over the years
has improved dramatically, particularly in upper level power
systems. These devices now have efficiency upwards of 98%.
Unfortunately to convert back to DC, AC power systems use
rectifiers that are much lower in efficiency. In this study the
rectifiers are assumed to be 90% efficient [3].
DC on the other hand employs DC-DC converters with
overall efficiencies that tend to be below 95% and as
mentioned, suffer from decreased efficiency when operated
below rating unless special implementation of the converter is
performed. To convert back to AC, inverters are necessary. In
this study, the inverters are assumed to have efficiencies of
97%.
Based on the varying efficiencies of the power converting
technologies, and the use of multiple converters in each
system, it is difficult to distinguish one type of power over the
other based on a simple calculation. Instead a power system
must be analyzed to determine the system that has the better
results.
The following section relates the outcome of the
comparison of the power systems.

IV. RESULTS
For the comparative study, the efficiency rating of the DC-
DC converters were assigned to three different efficiencies,
95%, 97%, and 99.5%. The voltages of the DC system were
varied to represent the I2R losses and the total losses are
provided in kW. The data for a power system supplied by a
DC source, with DC components, and DC loads based on
maximum operation is shown in Fig. 6.


The equivalent AC system with an AC source, AC
components, and AC loads resulted in 800 kW of losses.
Table V shows the results. Based on a straight comparison of
0.00
500.00
1000.00
1500.00
2000.00
2500.00
3000.00
3500.00
1214161820 2224 262830
System Voltage (kV)
Losses (kW)
99.5% 97%95%


Fig 6. DC power system efficiency for maximum operation.