Engineering, 2013, 5, 1-5 Published Online September 2013 (
Copyright © 2013 SciRes. ENG
Capacity Worth of Energy Storage System in Renewable
Power Gener a tion Pl an t
Jinbin Li1,2, Yao Yao1,2
1Hubei Electric Power Research Institute, Wuhan, China
2Key Laboratory of High-Voltage Field-Test Technique of SGCC, Wuhan, China
Received May 2013
With the advance in renewable generation technologies, the cost of renewable energy becomes increasingly competitive
when compared to fossil fuel-based generation resources. It is economically beneficial to integrate large amounts of
renewable capacity in power systems. Unlike traditional generation facilities, however, using renewable resources for
generation presents technical challenges in producing continuous power. In this report, an Energy Storage System (ESS)
is integrated to smooth the variations in renewable power production and ensure the output power more controllable.
Since it requires capital investment for the storage devices, it is important to obtain reasonable estimate of the storage
capacities. This project is therefore for mulated as an optimization problem in determining the two dominating factors of
the capital cost for the ESS: the power capacity and the energy capacity. The objective is to make the renewable power
more reliable and simultaneously maximize the economic benefits that can be obtained from the scheme. To make the
results more convincing, analyses in this report start with wind generation, for wind has greater variability and unpre-
dictability than other renewable sources. Selection of ESS type is narrowed down to battery energy storage system
(BESS) in the scheme. However, the methods presented here are suitable for any type of energy storage methods and
are also useful for intermittent renewable energy resources other than wind.
Keywords: Wind Power; Energy Storage System; Power Capacity; Energy Capacity
1. Introduction
Economic growth and prosperity since the industrial rev-
olution have, in large part, been due to the utilization of
fossil fuels. The consumption of fossil fuels has nearly
doubled every 20 years since 1900 [1]. However, the
long-term large combustion of fossil fuels has caused
undesirable environment impacts. The burning process
emits large amount of carbon dioxide and other gases
which cause the “greenhouse effect” and pollution [2].
And, even if we set aside worries about the environment
problems fossil fuels have brought to us, it must be ac-
knowledged that continuous and economically-priced
fossil fuels are fast coming to an end.
One obvious wa y to solve the worldwide energy crisis
problem is to find new primary sources. Amongst the
alternatives, wind energy is very promising. Many coun-
tries have set goal for high penetration levels of wind
generations. The annual growth rate of global installed
wind power capacity has exceeded 26% since 1990s [3].
However, one down side of wind power is its variabil-
ity and relative unpredictability. The output of wind
power system depends highly on the local natural envi-
ronment which is hardly controllable. Hence this form of
electricity generation would introduce more uncertainty
into the power grid. This presents a challenge when inte-
grating large scale wind power into electrical power
networks. To counter this, a usual scheme is to use ener-
gy storage devices as an energy buffer. It leads to a re-
duction in the amount of spinning and standby power
reserve needed to mitigate system frequency and voltage
excursions due to the variations in the wind power output
2. Power in Wind and Wind Turbine Model
2.1. Power in the Wind
The power in the wind is closely related to the wind
speed, the relationship between them is presented as fol-
lows [5]:
Pw = 0.5ρA v3 (1)
where Pw is the power in the wind (W); ρ is the air den-
sity (kg/m3); A is the cross-sectional area through which
the wind passes (m2); and v is wind speed normal to A
One expression that is often used to characterize the
impact of height on wind speed is the following [5]:
J. B. LI, Y. YAO
Copyright © 2013 SciRes. ENG
v1/v2 = (H1/H2)α (2)
The friction coefficient α is a function of the terrain
over which the wind blows. Usually, for rough approxi-
mation in somewhat open terrain, the rule-of-thumb is to
take a value of 1/7 for α [5].
In research activities, the most commonly used func-
tion for characterizing the statistics of wind speed is the
Rayleigh probability density fun c tion, given by [5]:
( )
2exp[() ]
fv c
= −
(3 )
where c is called the scale parameter.
2.2. Idealized Wind Turbine Power Curve
To figure out how much energy the wind turbine can
obtain by harnessing the wind, the performance characte-
ristics of wind turbine must be known. The most impor-
tant technical information for a specific wind turbine is
its power curve, which shows the relationship between
turbine generator’s electrical output and wind speed. An
idealized power cure is shown in Figure 1.
The relationship between the output wind power and
the wind speed can be described as follows [5],
vv vv
PAvC vvv
Pv vv
≤≤ ≥
= ≤≤
where vc is the cut-in wind speed; vR is the rated wind
speed; vF is the furling wind speed; PR is the rated pow er
of the wind turbine generator. Cp is the rotor efficiency,
which is the faction of the wind’s power that is extracted
by the turbine blades.
3. Approach to Determine the Capacity
of ESS
Utilizing Equations (3) and (4), the probability distribu-
tion of the wind power outputted from the wind turbine
generator is thus available. Its profile is illustrated in
Figure 1. Ide alized wind tur bi ne power curve.
Figure 2. The probability increases sharply when the
power reaches the rated value. This is du e to the fact that
the output power is limited to the rated power. Therefore,
the probability increases sharply when one sums up all
the probabilities that the wind speed ranges from vR to vF.
The average of the generated power can be calculated as
( )
In this project, it is proposed that the average power
will be set as the constant delivered power dispatched
from the wind turbine station over the studied period. It
will caus e no net change in the stored energy in the ESS.
The stored energy in the ESS will return to the same
energy level at the end of the period. Generally, the av-
erage power in a short-term, say 24 hrs ahead, can be
estimated according to the local historical wind speed
data or forecasting techniques. Thus, the intention of the
constant delivered power is to ensure no net change in
the stored energy in the ESS at the end of the subsequen t
24 hrs.
The power capacity of the BESS can always be found
as long as the probability distribution of the wind power
is known and the average power is calculated. The power
capacity can be equal to the larger of either the maximum
charge power or the maximum discharge power, as
shown on Figure 2.
3.1. Method to Determine the Reduced Power
Capacity of ESS
Since the power capacity of the BESS is determined by
the larger of the maximum charge and discharge power,
therefore in certain situation, the power capacity may be
equal to the maximum discharge power. Compared to the
much higher probability at the rated power level, the
probabilities of the low generated wind power level are
much lower. While their contributions to the total gener-
ated energy are small, they have brought a notable in-
crease in the power capacity of the BESS.
Figure 2. Probability distr ibution of gene rat ed wind power.
W ind Speed
Delivered Power
Cut in Wind Speed
Shedding the wind
Rated Win d Sp eed
R ated Power
Furling Wind Speed
Generated Wi nd Power Pw
Probabilit y of Pw
Max Discharge Power
Constant Delivered
Max Char ge Power
J. B. LI, Y. YAO
Copyright © 2013 SciRes. ENG
It is now proposed that contributions from the low
generated wind power components are delivered to a
capacitor. This is because compared to the rated power,
the energy contained in these components can be ex-
pected to be small. Furthermore, these components will
cause frequent charge-discharge, it will not be desirable
for the battery to deal with these charges [6,7]. Therefore,
the author considers a capacitor a more suitable storage
medium for these low power components. For those
components of higher generated wind power levels, they
are still to be dealt with by the BESS. The power net-
work model is as shown in Figure 3.
By doing so, the lower limit of the BESS’s discharging
power would increase, and the average generated power
from the BESS will also decrease most possibly sligh tly.
Consequently the discharging capacity will decrease and
the specified power capacity of the BESS may be re-
duced simultaneously. This decrease in the BESS power
capacity will reduce the capital investment for the BESS,
and thus may lead to an overall reduction in the cost for
this wind power plant. This intention is illustrated in
Figure 4, the darkened area refers to those low generated
power instances which have been delivered to the capa-
citor storage.
The benefit of this method is a decrease in the amor-
tized cost for the BESS’s power capacity. Also, it can be
expected that the energy capacity, which is another do-
minating factor of the capital cost for the BESS, will vary.
To maximize the overall economic benefit that can be
Figure 3. Power network model (BESS + Capacitor).
Figure 4. Reduce the power capacity by delivering the low
power components to the capacitor.
obtained from this scheme, both the changes need to be
taken into account to examine the economic effect and
determine the optimal level of the low power compo-
nents that should be assigned to the capacitor.
An analysis based on an actual site measurement ra-
ther than relying on Rayleigh assumptions is provided to
examine the economic effects of this scheme.
3.2. Analysis Based on Actua l Site Measurement
Data used in the following case study was recorded in Le
Mars (Latitude 42.78, Longitude 96.2) at a reference
height of 10m on Nov 1st 2000 [8-10]. Figure 5 shows
the probability distribution of the wind speed during the
studie d pe riod.
To analyze the output power which can be harnessed
from the wind resource, a typical idealized wind pow-
er-wind speed curve is assumed for the wind turbine. The
parameters are set as vc = 3 m/s, vR = 12 m/s, vF = 25 m/s,
PR = 2000 kW, and the blade’s radius 38m. The wind
turbine is mounted with its hub at 50 m above the ground
surface. Utilizing E qu a tion s (2) and (4), the probability
distribution of the output power from the wind turbine is
thus calculated, as shown in Figure 6.
Figure 5. Probability distribution of the wind speed in Le
Figure 6. Probabili ty distribution of the gene rated power in
Le Mars.
510 15 20 25
W ind Speed at the Height of 10m (knots)
Probabili ty of the Wind Speed
500 1,000 1,500 2,00080
5x 10
Generated Wind Power (kW)
Probabili ty of Pw
J. B. LI, Y. YAO
Copyright © 2013 SciRes. ENG
The average generated power is evaluated to be 1370.5
kW. Thus, the BESS power capacity is 1370.5 80 =
1290.5 kW (the probability of the generated power rang-
ing from 0 to 80 kW is zero), according to the maximum
discharge power.
Next, suppose the intention is to progressively deliver
those contributions when the generated power level is
low to the capacitor. The reason for doing so is to ob-
serve how by delivering the low power components to
the capacitor will affect the power capacity of the storage
element. The power level below which the contributions
are delivered to the capacitor is denoted as
. Figure 7
shows how the power capacity of the BESS
increases successively, owing to the slight
reduction in the average of the generated power, on one
hand, the discharging capacity of the BESS decreases, on
the other hand, the charging capacity increases simulta-
neously. It is reasonable to expect that at a certain
value, the maximum charging capacity will be equal to
the maximum discharging capacity, and beyond this val-
ue, the maximum charging capacity will exceed the
maximum discharging capacity and the latter starts to
dictate the BESS power capacity. This break point is
shown in Figure 7.
After the low generated power components are as-
signed to the capacitor, the change in the energy capacity
should be taken into account. Figure 8 shows how the
energy capacity Ce varies with
. The depth of the dis-
charge is assumed to be 20% [11].
Assuming the wind power farm has N identical wind
turbines, the life-time of the battery is T (year).
($/kW) and
($/kWh) represent the coefficien ts of the
amortized capital cost for the power capacity and energy
capacity of the BESS, respectively. Coefficient
($/kWh/year) is used to represent the maintenance cost
for the BESS each kWh of the energy capacity each year.
Since the cost for the capacitor is really negligible when
compared to the cost fo r the b at tery, the cap it al in vestmen t
Figure 7. Power capacity Cp of the BESS vs. Pc.
for the capacitor is not taken into account. Then the total
cost for the storage system can be described as:
( )
( )
( )
( )
( )
( )
ec ec
For a predetermined battery type,
, and
will be known. Thus, the total cost for the BESS of this
( )
can be evaluated, and the optimal power
will be found.
In this case study, the coefficients in (6) are selected in
the following way. Suppose the wind farm has N = 10
identical wind turbines. The amortized power capacity
cost of the BESS is such that
= 203$/kW. The amor-
tized energy capacity cost of BESS
= 116$/kWh.
The battery life is 2 years, and the maintenance cost for
the BESS per year is
= 29$/kWh [12]. Figure 9
shows a plot of
( )
based on these data.
According to the above figure, the capital cost for the
BESS has a gentle decrease at the beginning. In this case,
the best solution is to set
373 kW
, and then the
capital cost for the BESS is about $1.2513 × 107. Com-
pared to the capital cost of $1.2981 × 107 for the BESS
before assigning those low generated power components
to the capacitor, the method has resulted in a benefit of
about 4%.
Figure 8. Energy capacity Ce of the BESS vs. Pc.
Figure 9. Capital cost for the BESS F vs. Pc.
200 400 600 800 1000 1200 1400 1600 1800 2000
6 00
8 00
Pc ( kW)
Power Capacity of the BESS ( kW)
Cp vs. Pc
Break Poin t
200 400 600 800 1000 1200 1400 1600 1800 2000
11000 C e vs. Pc
Pc ( kW)
Energy Capacity of the BESS (kW h)
200 400600 80010001200 14001600 1800200080
2.1 x 10
Pc ( kW)
Cap ital Cost f or the BESS ( S)
F vs. Pc
J. B. LI, Y. YAO
Copyright © 2013 SciRes. ENG
Using a similar process, other wind power plants cou ld
be analyzed. The optimal
level can be found to mi-
nimize the capital cost for the BESS.
4. Conclusion
The methodology is proposed to assign those low gener-
ated power contributions to a capacitor. For those com-
ponents of higher generated wind power levels, they are
to be dealt with by the BESS to provide a constant deli-
vered power for the grid. By doing so, the power capaci-
ty of the BESS would drop, and thus the capital cost for
the BESS might probably decrease. The result from the
overall design demonstrated that utilizing this method
could create a considerable economic benefit.
5. Acknowledgeme nts
The author wish to express his deepest gratitude and ap-
preciation to his supervisor, Prof. Choi San Shing, for all
his invaluable suggestion and patient guidance through-
out the research period.
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