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Load Leveling Reduces T&D Line Losses
Ali Nourai, Senior Member, IEEE, V. I. Kogan, Senior Member, IEEE, and Chris M. Schafer, Member, IEEE
Abstract—The benefit of shifting load from the peak to the offpeak period is well known from the viewpoints of demand response
and deferral of capacity upgrade. However, the impact of load leveling on reducing transmission and distribution (T&D) losses is
often ignored or lightly mentioned in the literature. A detailed analysis of T&D loss reduction is very specific to the considered power
system and cannot be readily generalized. Therefore, the objective
of this paper is to identify the key parameters and quantify the
saved T&D losses as a function of the size or power of the energy
storage in a set of normalized charts to help assess the benefits of
energy storage as a means to level a utility load. This is a benefit of
utility-scale energy storage that is not fully recognized.
Index Terms—Dispersed storage and generation, energy management, energy storage, losses, peak shaving, power distribution,
power generation peaking capacity, power transmission.
NOMENCLATURE
Ratio of storage size to peak load.
G Ratio of off-peak to peak load (before load leveling).
k Ratio of transmission and distribution (T&D) losses to
peak load.
d Ratio of T&D resistance from off-peak to peak.
M Value multiplier = increase in the value of saved losses due
to an energy price differential between peak and off-peak
periods.
C Ratio of energy cost at peak to cost at off-peak.
I. INTRODUCTION
TILITIES are interested in load leveling because it allows them to defer investment on generation, transmission, and distribution assets. It also allows them to retire old
power plants with high emissions. Battery-based, large-scale
electricity storage devices are now commercially available and
can be located anywhere on the grid to level the load. It also enables utilities to sell low-cost off-peak energy during the peak
period to help pay for the cost of the energy storage [1].
As shown in Fig. 1, the flow of energy from central generation
sites to load centers throughout the grid involves some losses
due to the resistance of wires and other equipment at the transmission, subtransmission, and distribution levels [2], [3]. Since
these losses are proportional to the square of the current flow,
using energy storage to shift some of this current or load from
U
Manuscript received April 11, 2007; revised August 29, 2007. Paper no.
TPWRD-00189–2007.
The authors are with the American Electric Power, Columbus, OH 43215
USA (e-mail: anourai@aep.com).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TPWRD.2008.921128
Fig. 1. Sample of American Electric Power’s (AEP) transmission and distribution (T&D) resistive losses from generation to load.
the peak period to off-peak period decreases the net resistive
losses, which can offset some of the storage losses.
Besides the squared current relationship that helps reduce the
T&D losses by shifting a fraction of load from the peak to offpeak period, two other factors enhance this loss reduction and
increase its value.
1) The resistance of T&D wires and transformers is lower at
off-peak periods (lower temperature).
2) The cost of the energy (and losses) is generally lower
during off-peak periods.
II. REDUCTION OF T&D LOSSES
A. Factors and Assumptions
Since T&D losses are proportional to the square of the load
current, shifting any amount of load from peak to off-peak results in a net reduction of T&D losses. It should be noted that
this loss reduction is for central generation and only a small fraction, if any, may apply to distributed generation. Despite its exponential growth, distributed generation is still an insignificant
portion of the total utility generation and is expected to remain
so for another decade.
The reduction of the T&D losses is quantified in Section II-B.
The mathematical model also considers the impact of the following parameters on the saved losses:
1) storage efficiency;
2) ratio of peak to off-peak loads (before load leveling);
3) equivalent total T&D resistance (derived from known T&D
losses);
4) variation of the total T&D resistance from peak to off-peak
periods.
B. Calculation of T&D Ohmic Losses
This calculation of T&D losses is based on a simplified
(Thevenin equivalent) circuit as seen by a single load center
with local energy storage to shift load from peak to off-peak
periods (see Fig. 2).
The total (peak and off-peak) T&D loss for a time period with
and without load shifting may be approximated as
0885-8977/$25.00 © 2008 IEEE
(1)
(2)
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IEEE TRANSACTIONS ON POWER DELIVERY
Fig. 3. Drop in T&D losses as a percent of the peak load.
T&D losses and its drop due to shifting load can be approximated as
(4)
This savings in T&D losses may be expressed as a fraction of
the original losses (normalized)
(5)
Fig. 2. Shifting load from peak to off-peak time reduces T&D losses.
T&D losses are often expressed as a fraction of the system
load in terms of percent of demand or percent of delivered energy. The total loss for a power system like AEP’s is in the range
of 10%–15% of the load. Defining the ratio of the total T&D
losses to the load as a parameter, (5) may be rewritten to show
the ratio of the saved losses to the peak load (before shifting)
where
T&D losses without any load shift;
T&D losses with shifted load (energy storage);
,
,
equivalent T&D resistances during peak and
off-peak periods, respectively;
load current during peak and off-peak periods,
respectively;
current provided locally by the storage device;
net ac energy efficiency of the storage system;
storage discharge time during the peak period;
(6)
Fig. 3 shows dependence of saved T&D losses on the storage
size, both normalized to the peak load. The following values
have been assumed for this plot:
= storage charge time longer than discharge
time due to the storage inefficiency.
Now if the storage current
is set equal to zero in (2), the
T&D losses would be the same as the case without any storage.
The savings in T&D losses due to the load leveling effect of the
local storage can be written and simplified as
(3)
Substituting
The main conclusion from this chart is the savings in T&D
losses increases (losses decrease) with the storage size up to a
maximum value beyond which the losses increase again. Another observation from Fig. 3 is the savings in the T&D losses
is sensitive to the ratio of the off-peak to peak loads (G). The
equations of saved T&D losses could be written to use a more familiar parameter like load factor, instead of the ratio of off-peak
load to peak load (G), except load factor depends on the load
profile while (G) is independent of it.
The percent change in the T&D resistance from peak to offpeak periods is expected to follow the change in resistance from
small currents (25 C) to high currents (carrying 75% of its rated
capacity at 50 C). This ratio is between 88% to 92% range
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NOURAI et al.: LOAD LEVELING REDUCES T&D LINE LOSSES
3
Fig. 4. Largest storage size for maximum reduction in T&D losses.
for most aluminum cable steel reinforced (ACSR) conductors
at 60 Hz [4].
Since energy storage is considered at or near a load site and
parallel with it (AEP recommendation and practice), it virtually
sees the same voltage as the load and, therefore, the ratio of the
storage size to the peak load is the same as their current ratio,
in the above equations
which was defined as alpha
Fig. 5. Drop in T&D losses as a percent of the storage size.
Obviously, there is a maximum storage size (load shift) that
can be deployed before the T&D losses would start to increase
again. Considering that (6) is a parabolic function relative to
a, the location of its peak, that is the storage size for realizing
maximum T&D loss reduction, can be expressed as
(7)
Fig. 4 shows a plot of this maximum storage size before T&D
losses start to increase again. Note that this maximum storage
size is 50% of the gap between peak and off-peak load for an
energy storage device that is 90% efficient. This is due to considering a lower T&D resistance at off-peak periods (90%) than
peak periods. The maximum storage size decreases for storage
devices that are less efficient than 90%. The maximum storage
size of 50% is reached for all storage systems with an efficiency
.
that numerically equals the night/day resistance ratio
With an energy storage device present
, then (6) can
be rewritten to express saved losses as a fraction of the storage
size
(8)
A plot of this equation is shown in Fig. 5 where saved T&D
losses (as a percentage of the storage size) are plotted vs. the
storage size (as a percentage of peak load).
The main observation here again is that the ratio of saved
losses to storage size decreases with increased storage size. In
other words, the first MW of storage is more effective in offsetting T&D losses than the second additional MW of storage
located at the same site. The reason behind this characteristic
is that as more and more load is shifted from peak to off-peak
period, the gap between the peak and off peak loads decreases
Fig. 6. Relative size of reduced T&D losses to the storage losses.
and, therefore, the effectiveness of additional load shifting decreases at that location (see Fig. 2). The second observation, as
also observed in Fig. 3, is that the savings in the T&D losses is
sensitive to the ratio of the off-peak to peak loads G.
If the amount of reduced T&D losses would equal or exceed
the storage losses, one could claim that the load leveling application of storage devices near loads would effectively render
them as “lossless devices.” An obvious question is whether the
saved T&D losses would cover or exceed the losses of the energy storage device. Fig. 6 shows the ratio of saved T&D losses
to the energy loss of a storage device used to shift load. For the
range of parameters considered in this study, the saved T&D
losses are up to about 50% of the storage losses. Therefore, if
the reduction in the T&D losses is combined with the load leveling losses of an 80% efficient energy storage device, the net
efficiency of the storage device would then be effectively increased from about 80% to about 90%, at best.
As demonstrated in Appendix A, more T&D losses can be reduced if a number of smaller loads are shifted at multiple sites
rather than a larger load shift at a single site. The numerical example in Appendix A shows that the saved T&D losses would
double if the total load to be shifted is divided into four and
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IEEE TRANSACTIONS ON POWER DELIVERY
implemented at four different sites. The principle behind this
observation is as more load is shifted from peak to off-peak periods, the gap between the peak and off peak loads decreases
at that site and; therefore, the effectiveness of additional load
shifting decreases at that same location. While this principle is
believed to apply in general and regardless of the location, the
numerical value mentioned above may be limited to the storage
parameters and the specific location it was used on the AEP
system. A more detailed study is needed to generalize the numerical value of distributing the load leveling storage units.
TABLE I
NPV OF REDUCED T&D LOSSES DUE TO LOAD SHIFTING— =kW
(
,
=MWH)
$
Storage Eciency = 77% Energy Value = $35
C. Numerical Example
In 2006, AEP installed a 1.0-MW Sodium Sulfur (NaS)-based
energy storage system on a 12-kV distribution feeder at Chemical station in North Charleston, West Virginia, for peak shaving
[5]. Many of the values for the following parameters are taken
from this existing application
C
Fig. 7. NPV of reduced T&D losses due to load shifting with a 77% efficient
energy storage device.
Applying the above numerical values to Fig. 5, one concludes
that the decrease in T&D losses is around 7%–13% of the 1 MW
storage, which is 70 kW–130 kW. Therefore
kW
kW
Considering a discount rate of 7.4%, the net present value
(NPV) of this savings over the 15 year life of the energy storage
device would be
These are values of the saved T&D losses with a flat energy
value of $35/MWh. In many cases, however, the energy value
does change between peak and off-peak periods and, therefore,
the value of the saved T&D losses is higher when load is shifted
from the peak to off-peak period.
Appendix B demonstrates how to calculate the impact of an
energy price differential (between day and night) on the value of
the saved T&D losses. Fig. B1 shows this increase as a “value
multiplier” expressed in terms of the change in energy cost and
the ratio of off-peak to peak loads. These are the two most
volatile parameters affecting the saved T&D losses and their
value. For the range of numbers used in this example, the value
multiplier would be in the 3 to 6 range. While the principles behind the increased value of saved losses are generally valid, the
numerical range of the value multiplier may still be limited to
the storage parameters and the specific location it was used on
the AEP system. A more detailed study may be needed to generalize the impact of energy cost differential on the saved T&D
losses.
Table I and Fig. 7 show a summary of the NPV for saved T&D
losses per kW of a 7.2-h energy storage device similar to what
AEP has installed. The average NPV of the saved T&D losses
kW
for this example.
is around
III. CONCLUSION
Shifting any part of a load from the peak to the off-peak period
will reduce T&D losses. However, this drop in losses is very
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NOURAI et al.: LOAD LEVELING REDUCES T&D LINE LOSSES
5
sensitive to the ratio of peak to off-peak load. Following is a list
of conclusions and observation from this study that is based on
an actual operating energy storage device on AEP power system.
1) The drop in the T&D losses is equivalent to increasing
the efficiency of the energy delivery system by 1% to 3%
(Fig. 3).
2) The present value of the reduced T&D losses is a few hundred dollars per kW of the storage device used to shift
some load from peak to off-peak over several hours a day
(Table I).
3) When using a 75%–80% efficient energy storage system
to shift loads from the peak to off-peak period, the saved
T&D losses can compensate for up to 50% of the storage
losses (Fig. 6).
4) When the savings in T&D losses is combined with the
losses of a 75%–80% efficient storage device, the overall
efficiency increases by about 10–13%.
5) More T&D losses may be saved if load reduction (peak
shaving) is distributed at several locations rather that at a
single site (Appendix A).
6) The above benefits are not limited to energy storage and
would apply to demand reduction programs, in general.
The foregoing study applied some assumptions to demonstrate the nature and relative size of the T&D loss reduction and
its value due to shifting some load from peak to off-peak period. A more thorough investigation including system modeling
is needed to fine tune these conclusions to any particular power
system.
APPENDIX A
FURTHER REDUCTION OF T&D LOSSES BY USING MULTIPLE
SMALL STORAGE DEVICES AT SEPARATE SITES
At any given site, the amount of saved T&D losses diminishes
with an increase in the storage size. This is due to the gradual
improvement in the load profile and the decrease between peak
and off-peak loads. In fact, it could be more beneficial to use
multiple smaller load shifts at different sites rather than doing a
single large load shift at one site, assuming that the load shift in
one site would not change the load profile at the other sites.
To demonstrate this point, consider splitting a given load to be
shifted equally into “N” sites, with independent but similar load
profiles. Using the loss equations in Section II-B, the increase
in saved losses can be expressed as follows:
Fig. A1. Increase in saved T&D losses by distributing the load shift to multiple
sites.
As noted in Fig. A1, dividing the storage to four sites rather
than deploying it all at one site would double the amount of
saved T&D losses.
APPENDIX B
IMPACT OF ENERGY PRICE DIFFERENTIAL ON
THE VALUE OF SAVED T&D LOSSES
Since an energy storage device shifts part of the T&D losses
from the peak period to off-peak period, the energy cost differential between these periods increases the value of the load shift.
The “impact” of the energy cost differential may be defined as
a value multiplier, M.
where
Starting with (1) and (2) for losses with and without the storage
and simplifying the results with the previously defined parameters, one gets
To see this impact in a simple chart, let us consider some
average values for the following less significant parameters:
(A1)
where the parameters are the same as defined in Section II-B.
For a numerical example, consider having several sites, each
with a peak load of 30 MW. There is a need to shift a total of
10 MW from peak to off-peak. There is an option to shift that
entire load at one site or do several smaller shifts at different
sites. Fig. A1 shows the increase in the saved T&D losses due to
a multisite load shift for the following additional assumptions:
Using the above values in (4), the Value Multiplier
be simplified as
may
(B1)
Fig. B1 shows the dependence of the Value Multiplier
on
energy cost and load variation from off-peak to peak. It should
be noted that a price differential of 2:1 has more than just a
doubling effect as it impacts unequal decreased losses at peak
and increased losses at off-peak.
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[4] Anderson Electrical Connectors, “Square D Company Technical
Data—A Reference for The Electrical Power Industry,” 1964, p. 34.
[5] A. Nourai, “Installation of the First Distributed Energy Storage System
(DESS) at American Electric Power (AEP),” Sandia National Laboratories, SAND2007-3580, Jun. 2007.
Fig. B1. Value Multiplier as a function of the energy price and load variation
from peak to off-peak periods.
ACKNOWLEDGMENT
The authors would like to thank Dr. J. M. Schneider for his
ideas and guidance throughout this work.
REFERENCES
[1] A. Nourai, “Large-scale electricity storage technologies for energy
management,” in Proc. IEEE Power Eng. Soc. Summer Meeting, 2002,
vol. 1, pp. 310–315.
[2] G. Koeppel, M. Geidel, and G. Anderson, “Value of storage devices
in congestion constrained distribution networks,” in Proc. Int. Conf.
Power Syst. Technol.—POWERCON’04, Singapore, Nov. 21–24, 2004,
pp. 1–6.
[3] J. Eto et al., “Research, development and demonstration needs for
large-scale reliability-enhancing integration of distributed energy
resources,” in Proc. 33rd Annu. Hawaii Int. Conf. Syst. Sci., Jan. 4–7,
2000, p. 2.
Ali Nourai (M’73–SM’87) received the M.B.A. degree from The Ohio State
University, Columbus, in 1976 and the Ph.D. degree from Rensselaer Polytechnic Institute, Troy, NY, in 1978.
He is currently the Manager of the Distributed Energy Resources program in
American Electric Power (AEP), Columbus. During his 29 years of activities
in the utility industry, he has developed and applied many techniques to improve energy efficiency and performance of power systems. His latest project
was deployment of a 1.2-MW Sodium Sulfur (NAS) battery for load leveling in
a distribution substation in AEP.
Dr. Nourai received the Walter Fee Award from IEEE’s Power Engineering
Society in 1989. He is a member of the Board of Directors of Electricity Storage
Association (ESA).
V. I. Kogan (M’80–SM’83) received the B.S., M.S., and Ph.D. degrees in mathematics from Kharkov State University, Kharkiv, Ukraine.
His publications cover methods of theoretical and engineering reliability,
operations research, theory of statistical functions, numerical methods, applied
electrodynamics, and spectral theory of differential operations. He is currently
with American Electric Power (AEP), Columbus, where he has been able to
apply his mathematical skills to utility operations over the last 27 years.
Chris M. Schafer (M’03) received the B.S. degree from DeVry University,
Columbus, OH, in 2003. He is currently pursuing the M.S. degree at Franklin
University, Columbus, and will graduate in 2008.
Chris is currently with the Distributed Energy Resources program, American
Electric Power (AEP), Columbus. During his three years at AEP, hey has worked
at AEP’s research and development laboratory and has been involved with many
regulatory matters addressing distributed generation, demand management, and
energy efficiency.