Wind Turbine Energy Storage 1

1 Wind Turbine Energy Storage

• Most electricity in the U.S. is produced at the same time it is

consumed.
• Peak-load plants, usually fueled by natural gas, run when de-
mand surges, often on hot days when consumers run air condi-
tioners.
• Wind generated power in contrast, cannot be guaranteed
to be available when demand is highest.
• The hourly electric power demand is relatively periodic on a 24
hour cycle with the peak demand occurring in the daylight hours.
• Wind power generation is not periodic or correlated
to the demand cycle.
• The solution is energy storage.

Figure 1: Example of a two week period of system loads, system loads minus wind generation,
and wind generation.

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• There are many methods of energy storage.

– electro-chemical energy storage such as batteries
– chemical storage such as electro-hydrogen generation
– gravitational potential energy storage such as pumped-storage
hydroelectric
– electrical potential storage such as electric capacitors
– latent heat storage such as phase-change materials
– kinetic energy storage such as flywheels
• Short-term energy storage vs very long-term storage
• maximum discharge rate
• possible number of charge-discharge cycles

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Figure 2: Wind turbine energy storage optimization flow chart.

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1.1 Electro-chemical Energy Storage

• Rechargeable batteries are the most common form of electric

storage devices
• Three main types: lead-acid batteries, nickel-based batteries,
and lithium-based
• Each consist of cells made up of positive and negative electrodes
that are immersed in an electrolyte

Figure 3: Illustration of an electro-chemical storage battery cell.

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Lead-acid Batteries.

• Lead-acid batteries are the oldest type of rechargeable battery,

and the most commonly used
• The rated voltage of a lead-acid cell is 2 volts.
• The energy density is around 30 W-h/kg, with a power density
of approximately 180 W/kg
• Lead-acid batteries have an energy efficiency between 80%-90%
• They are relatively low maintenance and initial investment cost
• A relatively low self-discharge rate of approximately 2% of the
rated capacity per month at 25◦C. (ideal for long-term stor-
age)
• Low cycle life and battery operational lifetime
– Typical lifetime between 1200 and 1800 charge/discharge cy-
cles, or approximately 5-15 years of operation
• The cycle life is negatively affected by the depth of discharge and
temperature.
– Fully discharging the battery can damage the electrodes, re-
ducing lifetime
– High temperatures, up to 45◦C (upper limit) improves bat-
tery capacity but reduces battery lifetime.

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Nickel-based Batteries.

• Consist of nickel-cadmium (NiCd), nickel-metal-hydride (NiMH)

and nickel-zinc (NiZn)
• Rated voltage per cell is 1.2 V (1.65 V for the NiZn type)
• Typical energy density is higher than that of lead-acid batteries:
50,W-h/kg for the NiCd, 80 W-h/kg for the NiMH and 60 W-
h/kg for the NiZn
• Operational life and cycle-life is also superior to that of the lead-
acid batteries
• Typical lifetimes range from 1500-3000 charge-discharge cycles
• Several disadvantages compared to the lead-acid batteries:

– NiCd battery may cost up to 10 times more than the lead-

acid battery
– Lower energy efficiencies between 65% and 70%
– Higher self-discharge rate, of 10% of rated capacity per month

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Lithium-based Batteries.

• Consists of two main types: lithium-ion and lithium-polymer

• Higher energy density and energy efficiency, lower self-discharge
rate, and extremely low required maintenance compared to NiCd
and lead-acid batteries
• Nominal cell voltage about 3.7 V
• Energy density from 80 to 150 W-h/kg
• Energy efficiencies from 90% to 100%
• Power density from 50 to 2000 W/kg
• Very low discharge rate of 5% per month
• Lifetime of up to 1500 cycles
– Depends on temperature, worse at high temperatures
– Severely shortened by deep discharges
• Very fragile, requiring a protection circuit to maintain safe oper-
ation that limits the peak voltage during charging and prevents
the cell voltage from dropping too low on discharge
• Cell temperature is monitored to prevent temperature extremes
• Cost is between $900 and $1300 kW-h.

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Figure 4: Specific energy, W − h/kg, versus energy density, W − h/kg, for the three types
of electro-chemical storage batteries.

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1.1.1 Additional Electro-chemical Storage Technologies

Sodium Sulfur Batteries.

• NaS battery consists of liquid (molten) sulfur at the positive

electrode and liquid (molten) sodium at the negative electrode
as active materials separated by a solid beta alumina ceramic
electrolyte.
• Highly energy efficient (89-92%)
• Inexpensive and non-toxic materials
• High operating temperatures, and highly corrosive nature of
sodium makes it only suitable for large-scale stationary ap-
plications
• Currently used in electricity grid related applications such as
peak shaving and improving power quality

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Redox Flow Battery.

• A type of rechargeable battery involving two liquid chemical

components contained within the system and separated by a
membrane
• Ion exchange (providing flow of electrical current) occurs through
the membrane while both liquids circulate in their own respective
space
• Cell voltage is chemically determined and ranges from 1.0-2.2V

Figure 5: Schematic drawing of a flow battery.

• Technically both a fuel cell and an electro-chemical accu-

mulator cell
• Significant advantages such as no self-discharge and no degrada-
tion for deep discharge
• Appealing only for long-duration stationary energy storage
• Scalable energy capacity: (measured in MW-h) basically requires
only an increase in the size of its liquid chemical storage reservoirs

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Metal-air Battery.

• An electro-chemical cell that uses an anode made from pure

metal and an external cathode of ambient air, typically with
an aqueous electrolyte
• Offers high energy density (compared to lead-acid batteries)
• Long shelf life
• Promising reasonable cost levels
• However, limited operating temperature range
• Other technical issues: difficulty in developing efficient, prac-
tical fuel management systems and cheap and reliable bifunc-
tional electrodes

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1.2 Supercapacitor Storage

• Supercapacitors (or ultracapacitors) are very high surface areas

activated capacitors that use a molecule-thin layer of electrolyte
as the dielectric to separate charge
• The supercapacitor resembles a regular capacitor except that it
offers very high capacitance in a small package
• The separation of charge interface is measured in fractions of
a nanometer, compared with micrometers for most polymer
film capacitors
• Energy storage is by means of static charge rather by an
electro-chemical process

Figure 6: Schematic a super capacitor.

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• Minimal degradation in deep discharge or overcharge

• Typical cycle life is hundreds of thousands of cycles – more
than 500,000 cycles at 100% depth of discharge
• The limiting factor may be the years of operation, with reported
lifetimes reaching up to 12 years.
• One limiting factor is the high self-discharge rate of 14% of
nominal energy per month.
• However, they can be easily charged and discharged in seconds,
thus being much faster than batteries.
• Energy efficiency is very high, ranging from 85% to 98%
• Low energy density, 5W-h/kg.
• Extremely high power density of 10,000 W/kg, which is a
few orders of magnitude higher than that of batteries
• As a result of the low energy density, this high amount of power
is only be available for a very short duration
• Significant cost of $20,000/kW-h, which is much higher than for
example, lead-acid batteries

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1.3 Hydrogen Storage

• Electricity is used with water to make hydrogen gas through the

process of electrolysis
• Approximately 50,kW-h of electric energy is required to produce
a kilogram of hydrogen
• The cost of the electricity clearly is crucial
– At $0.03/kW-h, which is the common off-peak high-voltage
line rate in the United States, hydrogen costs approximately
$1.50 a kilogram for the electricity

Figure 7: Illustration of the elements in the use of electricity for hydrogen production and
possible storage.

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• The two most mature methods of hydrogen storage are hy-

drogen pressurization and the hydrogen adsorption in
metal hydrides
• Pressurized hydrogen relies on materials that are impermeable
to hydrogen and mechanically stable under pressure
• Storage tanks with aluminum liners and composite carbon fi-
bre/polymer containers are being used to store hydrogen at 350 bar
providing a higher ratio of stored hydrogen per unit weight of up
to 5%
• Metal hydrides offer an excellent alternative to pressurized stor-
age
• Metal hydrides bind with hydrogen very strongly. As a result,
high temperatures around 120◦C are required to release their
hydrogen content
• Liquid hydrogen storage technology use is currently limited due
to the properties and cost of the materials used in the manu-
facturing of the container/tank and the extreme temperatures
required for such storage (-253◦C)
• Liquid Hydrogen self-discharge may reach 3% daily, which trans-
lates to a 100% self-discharge in 1 month!

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1.4 Mechanical Energy Storage Systems

• Involves the conversion of electric energy into potential or kinetic

energy
• Includes pumped storage hydroelectricity, compressed
air storage, and flywheel energy storage
• Pumped Storage Hydroelectricity. During times of low
electricity demand, the excess generation capacity is used to
pump water into a reservoir at a higher elevation, when the elec-
tric demand is higher, the water is released back into the lower
reservoir and passes through a turbine/generator

Figure 8: Illustration of pumped storage hydroelectric power plant.

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• Worldwide, pumped storage hydroelectricity is the largest

form of grid energy storage available, accounting for
more than 99% of bulk storage capacity, representing approxi-
mately 127,000 MW
• Accounting for evaporation losses from the exposed water surface
and conversion losses in the pump, turbine and piping, approx-
imately 70-85% of the electrical energy used to pump the water
into the elevated reservoir can be regained
• It is currently the most cost-effective means of storing
large amounts of electrical energy on an operating basis
• Issues:

– Capital costs and the presence of appropriate geography

– Relatively low energy density requiring either a very large
body of water, or a large variation in elevation

• They can be economical to flatten out load variations on the

power grid, permitting thermal power stations to provide base-
load electricity at peak efficiency, and reducing the need for peak-
load power plants that use costly fuels
– Pumped storage plants can respond to load changes within
seconds

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• Compressed Air Storage is another method of storing elec-

tric energy during off-peak demand and to be used later when
the demand is higher
• Electric energy is used to compress air which is typically stored
in underground caverns

Figure 9: Illustration of compressed air storage power plant.

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• Compressed air storage is generally made up of

1. a motor/generator that employs clutches to provide for alter-
nate engagement to the compressor or turbine power train,
2. an air compressor that may require two or more stages, inter-
coolers and aftercoolers to reduce moisture in the compressed
air, and to increase the power plant efficiency, and
3. high and low pressure turbines and a recuperator to again
increase the power plant efficiency.

Figure 10: Components of a basic compressed air storage power plant.

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• Involves multiple-staged compressors in which inter-stage heat

exchangers are used to remove heat resulting from compress-
ing the air
• The heat can be stored and utilized in a combined or recu-
perated cycle to improve the plant efficiency

Figure 11: Recuperated cycle compressed air storage power plant.

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• The compressed air is released to pass through the turbine

• The air is first heated by passing it through a recuperator that
makes use of the stored heat that was released during the air
compression
• Fuel is then injected into the air and heated further in a com-
bustor
• The hot gas then expands through the turbine, which is con-
nected to the synchronous motor/generator
• Waste heat from the turbines is used for inter-stage turbine heat-
ing or in the recuperator
• Apart from the pumped storage hydroelectric system, no other
storage method has a storage capacity that is as large as the
CAES.
• Typical capacities are from 50 to 300 MW
• The storage period is the longest of the other systems, easily
storing energy for more than a year
• Start-up times O9 min. in an emergency, and O12 min. under
normal conditions
– Conventional combustion turbine peak-load plants typi-
cally require 20-30 min. for a normal start-up

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• Flywheel Storage uses a mass rotating about an axis to store

energy mechanically in the form of kinetic energy
• An electric motor is used to accelerate the flywheel to its design
rotation speed
• The energy stored is
1
E = M r2ω 2 ∼ M ν 2 (1)
4
– M is the mass of the flywheel
– r is the radius of the flywheel
– ω is the rotation rate
– ν is the linear velocity at the outer rim of the flywheel

Figure 12: Illustration of a flywheel energy storage system.

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• Low-speed flywheels, operate at up to 6000 rpm

– Usually consist of steel rotors and conventional bearings
– Achieve specific energy of approximately 5 W-h/kg
• High-speed flywheels operating at up to 50,000 rpm
– Use advanced composite materials for the rotor along with
ultra-low friction bearing assemblies
– Achieve specific energies of 100 W-h/kg
– Come up to speed in a matter of minutes, rather than the
the hours needed to recharge a battery
– The enclosure is either evacuated or filled with helium to
reduce aerodynamic losses and rotor stresses
• Advantages of flywheel storage systems are their high charge and
discharge rate
• Energy efficiency is typically around 90% at rated power
• Operation lifetime is estimated to be 20 years
• Main disadvantages are their high cost, and the relatively high
standing loss
• Self-discharge rates are approximately 20% of the stored capacity
per hour!
• Thus they are not a suitable device for long-term energy storage.

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Figure 13: Comparison of different electric power storage systems with regard to power
rating and discharge rate.

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1.5 CAES Case Study

Figure 14: Thermodynamic representation of a CAES power plant.

• The thermodynamic cycle so depicted, is known as an Ericsson

cycle.
1-3 the “charging mode” where the electric motor compresses
the air using power either from the wind or from the grid at
low demand periods of time, and
3-7 the “discharge mode” in which the compressed air is ex-
panded through the turbines to drive the electric generator
during peak demand periods of time.
• The efficiency of the thermodynamic cycle is
wt
ηth ≡ wc (2)
ηex + qf

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– where ηex is the external efficiency of the base load power

plant, that is, the wind turbine efficiency source of
electricity used to power the electric motor for the air com-
pression

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• How do we improve the thermodynamic efficiency of a CAES

power plant?
• Considering air to be an ideal gas, and process such as compres-
sion or expansion to be polytropic
pV k = Constant (3)
so that
 k−1
T2  P 2 

k
= which for air, k = 1.4 (4)
T1 P1

• For the compression

C p T1  
wc = n σcR1/n − 1 (5)
ηcηelm
where

rmt = T5/T1 = maximum temperature ratio (6)

rst = T3/T1 = storage temperature ratio (7)
ηc = compressor efficiency (8)
ηelm = electro-mechanical efficiency (9)
ηt = turbine efficiency (10)
R = T2/T1 = terminal isentropic temperature ratio (11)
σ = pressure losses factor, with subscripts c and(12)
t
n−1 = number of intercoolers (13)
m−1 = number of reheaters (14)
(15)

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• The “energy storage effectiveness”, β = wt/wc is

 
ηtηcηelmrmtm 1 − Rσ1/m
t
β= (16)
n σcR1/n − 1
 

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• The economics of a CAES power plant depends on the instanta-

neous price of electricity, which in turn depends on the instan-
taneous demand
• A model for the cost of electricity, P (t) is
P (t) ' A0 + A1N (t) + A2N (t) (17)

• N (t) is the time variation in the electric power demand, and the
A’s are best-fit coefficients that relate the cost of electricity to
the demand.

Figure 15: Example of the electric power demand and corresponding consumer price of
electricity over a 24 hour period.

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• Given the price function, P (t), the charging and discharging

price functions, Cch, and Cd, can be developed
• These depend on the duration of the charging and discharging,
hch and hd

Figure 16: Charging and discharging price functions that correspond to the price function
shown in Figure 15.

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• The Cost Function estimates the costs associated with a CAES

plant
• It is broken down into fixed costs and variable costs
Ctot = C1K + Shd + Cf om [$/kW-yr] (18)
C1 = capital cost [$/kW installed] (19)
K = capital recovery factor [1/yr] (20)
S = specific variable cost [$/kW-h generated] (21)
hd = plant service factor [operating hrs/yr] (22)
Cf om = fixed operating & maintenance cost [$/kw-yr] (23)
(24)

• The specific variable cost includes the energy cost of charging,

Cch, and discharging, Cd, the energy reserve
S = Cch + Cd + Cvom (25)
with Cvom as the cost of Operation & Maintenance (O&M)
• The energy cost of charging is
wc
Cch = Pc = Pcβ −1 [$/kW-h generated] (26)
wt
where Pc is the charging price function with units of [$/kW-
h]
• The ideal situation (to generate capital) is the Pc < Pd where
Pd is the discharging price function with units of [$/kW-h]
• The coefficient for discharging, Cd is defined as
ṁf
Cch = Pf (27)
ẇt
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where Pf is the fuel price with units of [$/kg-fuel], and ṁf /ẇt
is the specific fuel consumption with units of [kg-fuel/kW-
h]

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• The capital costs, C1, include all of the costs of installation

C1 = rw Cc+Ct+rg Cg +rw Cin+Cr e+CR C+Cr +Cs [$/kW installed]
(28)
where the coefficients Cc, Ct, Cg , and Cin are the costs/kW
installed of the compressor, turbine, generator and intercoolers
• The discharge-charge ratio, rh is
hd
rh = hc (29)
ẇc wt
= ẇt wc (30)
= rw β (31)
(32)
where hd and hc are the hours per year of discharging and charg-
ing

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• The Net Benefit, B, represents a metric of merit

B = (Pd − S) hd − C1K − Cf om [$/kw-yr] (33)
where Pd = f (hd) is the discharging price which is a function
of the discharge duration
• B is a function of many variables:
B = f (rmt, R, rb, hd, RC , m, n) (34)
where
rst ≤ rmt ≤ 4.91 ; rmt = T4/T1 = max. temp. ratio (35)
; rst = T3/T1 = max. temp. ratio (36)
0 ≤ rh ; rh = discharge-charging duration ratio(37)
0 ≤ hd ≤ γ ; hd = discharge duration (38)
; γ = a constraint that prevents charging(39)
; discharging at the same time (40)
 
1
; therefore, hd 1 + r ≤ 8760 (41)
h
0 ≤ RC ≤ 1 ; RC = recuperator effectiveness (42)
1 ≤ m ≤ mmax (43)
1 ≤ n ≤ nmax (44)
0.01 ≤ PHF ≤ 0.1 ; heat price [$/kW-h] (45)

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Figure 17: Result of optimization based on a range of heat price for a CAES power plant.

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1.6 Battery Case Study

• Consider an electro-chemical battery energy storage with rated

energy stored given as
Erated = CratedVnominal [W − h] (46)
– Crated is the amp-hour capacity of the battery
– Vnominal is the nominal voltage of the battery
• There is a general restriction on the “depth of discharge” (DOD)
of 50% of capacity to ensure a long operating life
• The average lifetime battery efficiency is approximately 68%
– 80% at the start, 50% at the end
• Example. Consider a deep-cycle lead acid battery in which Vnominal =
60V, and Crated = 1200A-hr. The usable energy is then
Eusable = Erated · DOD (47)
= (1200)(60)(0.5) (48)
= 36[kw-h] (49)
We can define the efficiency for the battery “system” to include
the battery and the power inverter that converts A.C. to D.C.
for charging. Thus
ηbattery/inverter = ηbattery ηinverter . (50)
The average efficiency of a voltage inverter is approximately 85%.
Therefore the overall efficiency of the battery-inverter combina-
tion is
ηbattery/inverter = (0.68)(0.85) = 0.578 (57.8%) (51)

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1.7 Hydro-electric Storage Case Study

• Considers the energy that can be stored and the efficiency of

hydro-electric storage
• The energy generated in this process is
Ehydro = ρghV OLη (52)
where
V OL = water volume stored [m3] (53)
h = stored water elevation (pressure head) [m] (54)
ρ = water density [1000 kg/m3] (55)
g = gravitational constant [9.8 m/s2] (56)
η = ηtηpipe (57)
ηt = turbine efficiency (0.60) (58)
ηpipe = pipe flow efficiency (0.90). (59)

• Noting that 1J = 1W , the stored energy in units of [kW-h] is

gV OLhη
E= (60)
3600

• The required volume of water needed to supply a given amount

of energy is
3600E
V OL = (61)
ghη
– Note that 3600 s/hr is a conversion between hours and sec-
onds

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Figure 18: Schematic of a hydro-electric storage configuration.

• Example. Determine the volume of water at an elevation of 50 m.

that is needed to produce 100,kW-h of electric power.

3600E
V OL = ghη (62)
(3600)(100)
= 9.8(50)(0.60)(0.90) (63)
3
= 1359 m (64)
= 50 m by 20 m by 1.4 m deep (65)

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1.8 Buoyant Hydraulic Energy Storage Case Study

• Wind turbines in deep off-shore locations are supported by float-

ing structures
• This has led to a concept for storing electric energy that is similar
to pumped hydro-electric storage but instead used buoyant
hydraulic energy storage of the floating structures

Figure 19: Example of a floating off-shore platform supporting a wind turbine.

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• The buoyant energy is stored through the potential energy of the

mass of the floating structure

Figure 20: Example of a floating off-shore platform supporting a wind turbine.

1. The floating structure has an opening at its lowest point that

can allow water to enter an internal compartment
2. When the water enters the compartment, it passes through a
turbine to generate electricity, and the floating structure sinks
lower in the water
3. Electric power is used to pump out the compartment by reversing
the turbine to act as a pump, and the floating structure rises
higher in the water

• When the floating structure is at its highest elevation, it stores

the largest amount of energy

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Figure 21: Schematic representation of the buoyant energy storage.

• Consider the reservoir to be cylindrical in shape

• The maximum occurs when the compartment is half full, at
which point the immersion depth is h
• The maximum amount of stored energy is then
E = mg h2 (66)
= ρA h2 g h2 ηt (67)
2
= ρAg h4 ηt (68)
– A is the projected area of the floating structure
– A(h/2) is the volume of displaced water
– ηt is the efficiency of the turbine ('60%)
• Rearranging the previous equation,
m = ρA h2 (69)
= 2E
gh . (70)

• The gravimetric energy density is

E
ρgrav = m (71)
= g h2 . (72)
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• The volumetric energy density is

E
ρvol = hA (73)
= m2 Ag (74)
= ρg h4 . (75)

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Figure 22: Relation between the projected area of the floating structure and the immersion
depth for a given stored power level.

• A floating structure with a projected area of 40,000 m2 that can

change elevation by 20 m, can store 10 MW-h of energy
• Like the pumped hydro-electric system, the buoyant energy sys-
tem has a short response time, and an unlimited number of
charge-discharge cycles

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