A Quantification of the Energy Savings by
Conservation Voltage Reduction
Wendy Ellens, Adam Berry, Sam West
Abstract-The introduction of 'Smart grid' technologies in
the electricity supply industry has attracted new attention to
Conservation Voltage Reduction (CVR). CVR is a method that
the minimum voltage level, without exposing customers at the
end of the lines to under-voltage conditions [4].
aims to save energy by reducing the voltage level of the electrical
distribution network. However, not all devices consume less
electricity when exposed to lower voltage levels; some devices
keep energy consumption constant by extending their operating
time, while others increase the current, leading to higher line
losses.
This paper describes a model designed to calculate the energy
savings that can be reached through the use of CVR. The model
has been applied to the Australian residential sector, showing
that 0.4% of energy savings can be obtained for 1.0% of voltage
reduction. Besides a description of the model and the results,
the paper contains a thorough sensitivity analysis. Furthermore,
we present a simple but effective formula to predict the energy
savings by CVR.
Index Terms-energy conservation, power distribution, smart
grids, voltage control
I.
IN TRODUCTION
(CVR), also
or Conservation
Voltage Control (CVC), has been proposed as a method to save
energy by reducing the voltage level of the electrical distribu­
tion system [1], [2]. CVR is expected to have considerable
environmental benefits, because the reduction of the energy
consumption will lead to fewer CO2 emissions associated with
energy production'.
CVR is not a new energy conservation measure; tests have
been performed as early as in 1973 [1]. However, recent
developments in the field of smart grids have drawn new
attention to CVR [4], now also called voltage optimisation.
Integrated Volt-Var Control (also kwnown as VoltlVar manage­
ment), which is an important feature of the future grid, enables
the application of CVR. Traditionally, the substation voltage
is set to the maximum allowed voltage in order to guarantee
a minimum voltage level to customers at the end of the
distribution lines [4], [5]. In future energy networks, it will be
possible to control the voltage level along the distribution lines
in order to supply all customers with approximately the same
voltage, such that low-voltage substations can operate close to
ONSERVATION VOLTAGE REDUCTION
C called
Conservative Voltage Reduction
w. Ellens is with TNO Performance of Networks and Systems, P.O. Box
5050, 2600 GB Delft, The Netherlands (e-mail: wendy.ellens@tno.nl).
A. Berry and S. West are with CSIRO Energy Technology, PO
Box 330, Newcastle NSW 2300, Australia (e-mail: adam.berry@csiro.au.
sam. west@csiro.au).
1 Australia's greenhouse emissions totaled about 540 million tonnes of
carbon dioxide in 2010. Electricity generation accounts for 36 percent of
emissions [3].
A. The Effects of Conservation Voltage Reduction
Assuming that household devices require no reactive power,
the effect of CVR on energy consumption can be explained as
follows. By Joule's law, the power P, voltage V and current
1 in a resistive circuit satisfy P
VI. It follows from Ohm's
law V
1R that lowering the voltage level reduces the
power when the load consists of pure resistors with constant
2
resistance R, because in that case we have P
V / R.
In reality, this is true if loads are constant-resistance (hot­
water system, fridge, oven, incandescent lighting, pool pump,
etc.), but not if loads are constant-power (computer, TV,
etc.). If we have constant-power loads, dropping the voltage
will mean that the current has to increase, which leads to
higher energy loss in the lines, according to the power loss
formula llines
12 Rlines. Also, many constant-resistance
devices (hot-water system, fridge, oven, etc.) have a feedback
loop - mostly measuring the temperature - that extends
the operating time, leading to constant energy consumption
(the energy consumption U satisfies U
PT, where T
is the duration of the power consumption). Some lighting
technologies (compact fluorescent lighting) keep the current
constant. The power consumption of these devices decreases
linearly with the voltage according to P
VI. The savings
are therefore smaller than for constant-resistance devices, for
which the power consumption is quadratic in V. Because CVR
effectiveness depends on the type of device, we categorise
electrical devices into four load categories:
=
=
=
=
=
=
1) Constant-resistance loads without a feedback loop,
which we call constant-resistance loads, reduce the
energy consumption for both the loads and the lines;
2) Constant-resistance loads with a feedback loop, which
we call constant-energy loads, have a constant energy
consumption (for time-scales that are longer than the
duration of the feedback loop);
3) Constant-power loads increase the energy consumption,
because of increasing line losses due to increased current
draw caused by the lowered voltage.
4) Constant-current loads reduce the energy consumption
for the loads.
Table I lists some experimental results in the US. The list
shows that CVR savings for residential areas are generally
0.6% to 0.8% for each percent of voltage reduction, the savings
being higher for commercial areas and lower for industrial
areas. The average savings across the three market sectors
978-1-4673-2868-5/12/$3l.00 ©2012 IEEE
2
TABLE I
RESULTS OF CV R TESTS IN TERMS OF THE CV R FACTOR (RELATIVE
ENERGY SAVINGS PER PERCENT OF VOLTAGE REDUCTION)
Year
Source
Residential
Commercial
Industrial
Overall
0.62%
1973
[1]
0.61 %
0.89%
0.35%
1977
[9]
0.76%
0.99%
0.41%
1979
[2]
0.73%
0.84%
0.49%
1989
[10]
0.71%
0.62%
with equal source voltage Vsource and line resistance Rlines for
all devices. The energy consumption of a device consists of
energy consumed by the load and line losses. The calculation
of these for the different load categories is explained in
the subsections that follow. For an in depth discussion on
the assumptions that have been made during the modelling
proces, and also for the derivations of the formulas in the
next subsections, see [11].
A. Energy Consumption of Constant-Resistance Devices
are approximately 0.6% . The experimentally determined CVR
factors (relative savings per 1% voltage reduction) differ
substantially from utility to utility. As a result 'most utilities
feel that another utility's voltage regulation results are not
necessarily transferable to their own service territory' [6]. Al­
though the need for models assessing the factors that determine
CVR effectiveness is clear, no such models have been found
in the literature. For example [7], [8] describe results of CVR
modelling in their own region (Taiwan and Pacific Northwest
respectively), but do not discuss the sensitivity to the model
parameters necessary to verify the validity of the results for
other regions.
The load resistance of constant-resistance devices is derived
by applying the following formula to the power consumption
data:
Rload
=
2302
y.;:;- ,
load
where we have assumed that the nameplate power FI�ad is
measured at a voltage of 230 V. For constant-resistance devices
the actual power consumption Road at 230 V is somewhat
lower than the nameplate power, because the actual voltage
over the load is slightly less than 230 V (as the line resistance
is non-zero). It is
B. The Scope of this Research
As pointed out in Subsection I-A, long term benefits of CVR
are only obtained for constant-resistance and constant-current
loads. For constant-energy loads there are no energy savings
when reducing the voltage level, while reducing the voltage
for constant-power loads leads to higher energy consumption.
Therefore the question 'How effective is Conservation Voltage
Reduction; does it really save energy?' needs to be addressed.
Based on the breakdown of constant-resistance, constant­
energy, constant-power, constant-current loads and residential
consumption statistics, we will verify whether the energy
consumption in Australian households would be reduced when
setting the voltage to a lower level.
The paper is organised as follows. The next section, Section
II, explains how the model is built. Section III describes the
data used to calculate the energy savings by CVR in the
Australian residential sector. It is followed by Section IV ,
which contains the modelling results. Section V describes the
sensitivity analysis that is performed to point out the depen­
dency of the results on the modelling parameters. Finally,
Section VI summarises the main modelling results and some
theoretical results; describes the relevance of the research to
industry, science and society; and suggests subjects for further
research.
II.
DESCRI PTION OF T H E MODEL
The model takes the part of the electrical network into
account that is affected by CVR, i.e. the part of the network
from the low voltage substations to the consumers. The energy
consumption for a given voltage level is calculated as the sum
of the energy consumption of the devices. For all devices, the
circuit looks like a load in series with a resistor representing
the line resistance, together connected to the source voltage,
(1)
n
.Lload
=
J2Rload
=
��urce R
-R
-- load
tot
=
2302
(Rload + Rlines )2 Rload,
(2)
by which we divide the yearly energy consumption in order
to calculate the operating time of a constant-resistance device
(yearly, for all Australian households together). We can use (2)
also to calculate the power consumption at different voltage
levels:
.Fload
=
��urce
(Rload + Rlines )2 Rload,
(3)
Similarly we have for the line loss and the total power
consumption:
T>
.Llines
=
��urce
T>
(Rload + Rlines )2 Rlines and .Ltot
=
��urce
Rload + Rlines
(4)
The energy consumption of the load, the lines and the total
energy consumption of the device are now easily calculated by
multiplication by the operating time. For the standard voltage
of 230 V, the calculated energy consumption of the load will
be equal to the yearly energy consumption given in the data.
B. Energy Consumption of Constant-Energy Devices
The load consumption and line losses for constant-energy
devices are easier to calculate. For every voltage level the load
consumption is equal to the yearly energy consumption in the
data. The line loss can be calculated by
Ulines
=
UloadRlines
Rload
(5)
The load resistance is derived by the nameplate power in the
same way as for constant-resistance devices.
TABLE II
RESIDENTIAL DEVICES AND ELECTRICITY CONSUMPTION IN AUSTRALIA,
2007. AIR-CONDITIONING GIVES THE SUM OF THE ENERGY USED FOR
SPACE HEATING AND SPACE COOLING.
Constant-resistance
Constant-energy
1
Water heater
21.7%
constant-energy
2
Lighting
13.6%
mostly constant-resistance
3
Air-conditioning
11.6%
constant-energy or constant-resistance
4
Refrigerator
11.0%
constant-energy
5
Television
7.0%
constant-power
Constant-current
Unknown
Constant-power
C. Energy Consumption of Constant-Power Devices
As for constant-energy devices, for constant-power devices
the energy consumed by the load is equal to the yearly energy
consumption data, regardless of the voltage level. The power
consumed by the lines is
llines = 12Rlines =
( Vsource - J"V;;�urce - 41loadRlines ) 2
.
4R hnes
(6)
where lload is the nameplate power of the device. The line
energy consumption is a product of the line power consump­
tion and the operating time, which is simply the yearly energy
consumption divided by the power consumption.
D. Energy Consumption of Constant-Current Devices
For constant-current devices, the current through the load
and lines and the power consumption by the lines are constant:
1= ��ad
23 0
and
Rlines =
12Rlines·
(7)
The total and load power consumption are given by
Ptot= Vsource1
and
lload= Ptot - llines'
(8)
The operating time of a constant-current device is calculated
as follows:
T=
Ul�ad
Ul�ad
=
Road
23 01 - 12Rlines )
(9)
with Ul�ad the given yearly power consumption, which is used
to find the energy consumption for the load, lines and the total
energy consumption.
III.
RESEARCH DATA
In this section we briefly describe the data that we have used
in the application of our model to the Australian residential
sector. For the complete set of data see [11]. The most
important input for the model is information about the yearly
energy consumption of devices, their power consumption and
their load category.
For data on the energy consumption of residential electrical
devices we rely on the report Energy use in the Australian
residential sector 1986-2020 of the Australian Department
of the Environment, Water, Heritage and the Arts [12]. The
residential devices that consume the largest amount of energy
are given in Table II. Most of the typical power consumption
values have been taken from report [12] as well. Information
Fig. 1. Breakdown of the 2007 Australian residential electricity consumption
by load category. Constant-current devices are 1.4% of the energy consump­
tion. The category 'Unknown' consists of a group of miscellaneous devices
(8.6%) and pools (3.4%), which contain two load categories. This category
has not been included in the model.
about the reactive power of the devices was not available,
therefore we have not included it in the model. The cat­
egorisation of the residential devices in constant-resistance,
constant-energy, constant-power and constant-current devices
is based on experimental data. The proportion (in yearly
energy consumption, according to the 2007 energy data of
[12]) of constant-resistance, constant-energy, constant-power
and constant-current devices has been visualised in Fig. 1.
For the line resistance we have chosen the values 0, 0.1,
0.2, 0.5, 1.0 and 2.0 n because they lead to reasonable values
for the total line loss; between 0% and 5.5% of the total
energy consumption. The distribution and transmission losses
in reality are about 7.5% (in 2008 in Australia [13]). Therefore
5.5% of line loss for the modelled part of the network is almost
certainly an upper bound. Also important for our model is the
allowed lower and upper bound on the voltage. Since 2000
the standard voltage in Australia is 230 V with a tolerance of
+ 1 0% and -6% [14].
IV.
MODELLING RESULT S
In this section we discuss the outcome of the model. The
energy consumption at different voltage levels is given. The
results are analysed for different line resistance values and the
absolute and relative savings by CVR are quantified.
Fig. 2 gives the yearly Australian residential electricity
consumption (for different voltage levels and different values
of the line resistance). It turns out that the energy consumption
is almost linear in the source voltage with almost the same
slope for all line resistance values. The absolute electricity
savings (in the Australian residential sector, per year) are
approximately 0.09 . 109 kWh per 1 V voltage reduction
(independently of the line resistance).
The relative energy consumption (with respect to the con­
sumption at the standard of 230 V) can be found in Fig. 3. We
see that the relation between the relative energy consumption
and the relative voltage level (with respect to 230 V) is
approximately linear. The slope is again almost independent
of the line resistance. Hence, our conclusion does not depend
on the chosen line resistance (in the 0.0 to 2.0 n interval),
4
Energy(109 kWh)
Rlines
53
Rlines
52
Rlines
51
Rlines
Rlines
50
=
2.00
=
1.00
=
0.50
=
=
0.10
0.00
to determine the reference energy consumption, can be
different from 230 V.
While all of these modifications can be used to analyse the
sensitivity of our results with respect to errors in the input
data, all except for item 2) can also be used to model future
changes in the input data.
A. Modifying the Energy and/or Power Consumption
49
48
47
220
230
240
250
Voltage(V)
Fig. 2. Yearly Australian residential electricity consumption for the allowed
voltage levels and several values of the line resistance.
Rlines
Rlines
relative energy
2% -
=
0.00
=
2.00
1% relative voltage
Fig. 3. Yearly Australian residential electricity consumption relative to the
consumption at 230 V for the allowed voltage reduction levels relative to the
standard of 230 Y. The consumption has been plotted for two values of the
line resistance.
nor will it change if some devices are slightly further from
the substation (larger line resistance) than others. The savings
are about 0.4% per 1% voltage reduction for the Australian
households. Because of the linear relation, a 2.5% voltage
reduction (from 230 V to 224 V ) gives up to 1% energy
savings.
V.
SEN SITIV IT Y ANALY SIS
In this section we perform a sensitivity analysis in order
to point out dependencies of the described results on the
modelling parameters. In our model there are five types of
parameters that can be modified:
1) The yearly energy consumption of a device can change,
which means that the device is used more often;
2) The power consumption of a device can be modified, that
is, the power consumption data used were incorrect, but
the yearly energy consumption was correct;
3) The power and the yearly energy consumption of a
device can change, which means that the device requires
more power and thus consumes more energy;
4) Any device can change load category (e.g. from
constant-resistance to constant-power);
5) The standard voltage, used to calculate the resistance
of the constant-resistance and constant-energy devices,
the current of constant-current devices and also used
If the operating time (and thus the yearly energy consump­
tion) is increased by a certain factor, the energy consumption
of the load, the line loss and the total energy consumption
is increased by the same factor (for all load categories).
Increasing the (nameplate) power (but not changing the yearly
energy consumption) of a device increases the line loss linearly
(approximately in the case of constant-power and constant­
current devices) but does not affect the energy consump­
tion of the loads for all categories. It follows directly that
increasing the energy and power consumption by the same
factor (modelling a possible increase of power consumption of
devices) increases the load consumption and line consumption.
The load consumption is linear in the described parameter,
while the relation between the line consumption and the
energy/power consumption is (approximately) quadratic.
These observations show that, in order to give a good
approximation of the energy consumption for different volt­
age levels, it is much more important to know the energy
consumption of devices for the standard voltage, than to know
their power consumption.
B. Modifying the Load Category of a Device
In Fig. 4 we have analysed the energy consumption in four
extreme cases; the cases in which all loads are of the same
category. The graph shows that the constant-resistance loads
determine the change in energy consumption as the voltage
varies. Although the energy consumption of constant-power
devices increases by a small amount when the voltage is
reduced, the decrease in energy consumption of the constant­
resistance devices is much larger for the same voltage reduc­
tion. The influence of constant-current devices is very limited
because of their small share. As already stated, constant­
energy devices do not influence the effect of CVR.
It is important to know how large the share of constant­
power devices can be in order to still have benefits when
applying CVR. We have therefore taken linear combinations of
the graphs in Fig. 4. The results for the actual mixture of load
categories, the 10%/90% mixture and other mixtures have been
drawn in Fig. 5. The graph for the actual mixture matches the
graph in Fig. 2 (for a line resistance of 0.5 n). To generate this
curve no data about the load category of specific devices are
used. This fact shows again that the energy savings by CVR
heavily depend on the energy consumption for the different
load categories, while the power of the individual devices has
less influence. It is interesting to note that Fig. 5 indicates that
CVR will save energy if at least 2% of the constant-resistance
and constant-power devices are constant-resistance.
Energy(109 kWh)
constant-resistance
constant-current
54
TABLE III
T HE ENERGY CONSUMPTION OF THE LOADS, LINES AND THE TOTAL
ENERGY CONSUMPTION FOR SEVERAL VALUES OF THE SOURCE VOLTAGE
Vsource AND A SOURCE VOLTAGE REDUCED BY 1 % vsr;,eirce. THE LINE
RESISTANCE IS 1 0 .
53
52
Total consumption
51
Load consumption
50
constant-energy
49
Line consumption
constant-power
Voltage
Vsource
e
Vs� 1rce
1l0V
201.6
200.8
0.39%
230 V
179.8
179.0
0.42%
0.42%
Savings
llOV
174.7
174.0
230 V
174.7
174.0
0.42%
llOV
26.9
26.8
0.14%
230 V
5.1
5.1
0.14%
48
47
V I.
DI SCU S SION
A. Conclusions
46
,I
'I
220
'
,
230
,, I
I
,
'
240
250
Voltage(V)
Fig. 4. Yearly Australian residential electricity consumption for the allowed
voltage levels if all devices were of the same load category. The consumption
has been calculated for a 0.5 0 line resistance.
Energy(109 kWh)
actual mix
51
10%/90%
50 --
5%/95%
2%/98%
1%/99%
49 --
48
220
230
240
250
Voltage(V)
Fig. 5. Yearly Australian residential electricity consumption for the allowed
voltage levels for several load category mixtures. The consumption has been
calculated for a 0.5 0 line resistance. The actual mixture in Australia in
2007 was about 20% constant-resistance devices, 62% constant-energy, 17%
constant-power, 2% constant-current. The results have also been calculated
for other mixtures of constant-resistance and constant-power devices; x%/y%
stands for x% of constant-resistance and y% of constant-power devices.
C. Modifying the Standard Voltage
Table III shows that the results of Fig. 3 are almost
independent of the standard voltage (e.g. 240 V versus 110
V ). The savings on the load consumption are higher than the
savings on the line consumption. Together with the fact that
the proportion of line losses increases as the source voltage
decreases, this leads to slightly smaller savings on the total
energy consumption when a lower source voltage is applied.
Our model indicates that applying CVR in Australia would
indeed save energy. In the residential area, a 2.5% voltage
reduction (from 230 V to 226 V ) gives 1% energy savings,
implying up to 1% discount on the residential energy bills and
1% less greenhouse gas emissions associated with residential
electricity use. If CVR is applied in all residential areas in Aus­
tralia, the absolute savings are approximately 0.09· 1 09 kWh,
corresponding to 140 million Australian dollars (assuming a
linear tariff of 28 cents per kWh [15]), or 470 million kg of
CO2 (for electricity generated in Australia [16]) per year.
The CVR factor we found is 0.4% , which is smaller than the
CVR factors around 0.6% found during real-world tests. The
most likely explanation for this is that the number of constant­
resistance devices is decreasing over time, while constant­
power devices are used more and more. For the same reason, it
is expected that the savings by CVR will diminish in the future.
As CVR is beneficial also for constant-current devices, but less
than for constant-resistance devices, replacement of traditional
lighting by compact fluorescent lighting will decrease but not
cancel the positive effects of CVR.
According to our model, the CVR factor is almost inde­
pendent of the values of the source voltage. This means that
our results are valid also in countries with different standard
voltages and along distribution lines where voltages vary
between households. We found that savings do not depend
strongly on the line resistance, therefore further specifications
of the line lengths, material and diameter are not required.
An important conclusion of our sensitivity analysis is that
the savings by CVR are mainly determined by the load-mix,
or more precisely by the percentage of constant-resistance
devices. As a consequence (using (4)) the overall savings 6.u
can be easily approximated by the following formula:
6.u
=
(1 - (1 - Cred)2 ) Cresist;::::; 2CredCresist.
(10)
In this formula, Cred is the relative voltage reduction and
Cresist is the relative amount of constant-resistance devices
(in terms of yearly energy consumption). When the voltage
is reduced by 2.5% and 20% of the devices are constant­
resistance, the formula predicts a 1% energy reduction the same result as we found using the model. By taking
6
Gred 0.01 (a 1% voltage reduction) and Gresist 1 (100%
constant-resistance devices), (10) provides an upper bound on
the CVR factor that can be reached:
=
=
CVRf:S: 2%.
(11)
A second consequence of the fact that the increase of
energy consumption of constant-power devices is very small
compared to the energy savings by constant-resistance devices
is the following rule of thumb: as long as the energy consumed
by constant-resistance devices is at most fifty times smaller
than the energy consumed by constant-power devices, CVR
will reduce the energy consumption. This suggests that CVR
will continue to have benefits in the future and that savings can
be obtained also for commercial and, potentially, for industrial
areas - where more constant-power devices are used.
B. The Contribution of this Research
Conservation Voltage Reduction can be applied as a measure
to reduce carbon dioxide emissions, by reducing the electricity
consumption. The model described in this paper offers a
tool to quantify the effectiveness of CVR. While tests have
the same goal, the model is more sophisticated as it can
predict the energy savings when devices change load category
(for example a television becoming constant-power instead of
constant-resistance), when the power consumption of a device
(a television for instance) increases, or when consumers use a
device (such as an air conditioner) more often. In addition to
the calculation of future savings, the model can also used to
analyse regional and seasonal differences.
Aside from the numerical results (especially interesting for
the energy industry) the model offers, it also gives a deeper
theoretical understanding of CVR, showing how the results
depend (or do not depend) on the parameters. Additionally,
the modelling results have shown that the simple formula (10)
gives a tight approximation of the CVR factor. Other theo­
retical results include the fact that the savings are essentially
linear in the voltage reduction (see (10» - justifying the use
of the CVR factor as a measure of CVR effectiveness - and
the determination of an upper bound on the CVR factor (see
(11».
C. Further Research
Further research in the field CVR modelling may include lab
testing in order to determine the reactive power of household
appliances. However, it is expected that the reactive power
of residential devices is small compared to the real power,
because residential consumers generally have a power factor
close to 1 [17]. Nevertheless, quantifying the savings by
CVR on reactive power might be interesting as CVR factors
are shown to be larger for reactive power than for real
power. Lab testing could also give the current profile of
electrical devices and distribution lines (the load's response
to voltage variations). Embedding these results in our model
would provide a way to verify that the categorisation in
ideal constant-resistance, constant-energy, constant-power and
constant-current devices gives a good approximation.
As predictions of future residential energy consumption in
Australia are available [12], it would be interesting to use
these data to predict future savings by CVR. Extension of the
model to commercial and industrial areas would be necessary
to get an approximation of the total energy savings that can be
reached by applying CVR to the entire Australian electricity
network. The model for industrial application of CVR should
include an additional load category for induction motors. A
thorough cost analysis of CVR application in Australia is also
advisable to be performed in order to determine cost-benefit
trade-offs.
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