Energy Storage
• Distributed resources (DR) and distributed generation (DG):
• DG can be defined as “a subset of DR” [T. Ackermann, G. Andersson, and L. Söder, “Distributed
generation: A definition.” Electric Power Systems Research, vol. 57, issue 3, pp. 195-204, April 2001]
• DR are “sources of electric power that are not directly connected to a bulk
power transmission system. DR includes both generators and energy
storage technologies” [T. Ackermann, G. Andersson, and L. Söder, “Distributed generation: A definition.”
Electric Power Systems Research, vol. 57, issue 3, pp. 195-204, April 2001]
• DG “involves the technology of using small-scale power generation
technologies located in close proximity to the load being served” [J. Hall, “The new
distributed generation,” Telephony Online, Oct. 1, 2001 http://telephonyonline.com/mag/telecom_new_distributed_generation/ ]
• Microgrids are electric networks utilizing DR to achieve independent
control from a large widespread power grid
• Prevailing technologies:
• Batteries
• Flywheels
• Ultracapacitors
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© Alexis Kwasinski, 2012
Energy Storage
• Uses of energy storage devices in DG:
• Power buffer for slow, bad load followers, DG technologies.
• Energy supply for stochastic generation profiles.
• Power vs. Energy
dE
P
dt
• Power delivery profile: short, shallow and often energy exchanges.
• Flywheels
• Ultracapacitors
• Energy delivery profile: long, deep and infrequent energy exchanges.
• Batteries
• For the same energy variation, power is higher in short exchanges.
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© Alexis Kwasinski, 2012
Battery technologies
• Batteries stores energy chemically.
•Main technologies:
• Lead Acid
• Nickel-Cadmium
• Nickel-Metal Hydride
• Li-ion
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© Alexis Kwasinski, 2012
Battery technologies
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© Alexis Kwasinski, 2012
Lead-acid batteries
• Lead-acid batteries are the most convenient choice based on cost. The
technology that most of the users love to hate.
• Lead-acid batteries are worse than other technologies based on all the other
characteristics. Disposal is another important issue.
• In particular, lead-acid batteries are not suitable for load-following power buffer
applications because their life is significantly shortened when they are
discharged very rapidly or with frequent deep cycles.
http://polarpowerinc.com/info/operation20/operation25.htm
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© Alexis Kwasinski, 2012
Lead-acid batteries life
• Lead-acid batteries are very sensitive to temperature effects. It can be
expected that battery temperature exceeding 77°F (25°C) will decrease
expected life by approximately 50% for each 18°F (10°C) increase in average
temperature. [Tyco Electronics IR125 Product Manual]
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© Alexis Kwasinski, 2012
Lead-acid batteries
• Positive electrode: Lead dioxide (PbO2)
• Negative electrode: Lead (Pb)
• Electrolyte: Solution of sulfuric acid (H2SO4) and water (H2O)
H 2O
PbO2
Pb
H 2O
H 2O
H 2O
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H 2O
© Alexis Kwasinski, 2012
Lead-acid batteries
• Chemical reaction (discharge)
2H2O H SO
2
4
2eO22PbO2
Pb2+
2H+
2H+
SO4
2-
SO42H2SO4 PbSO4
Pb2+
Pb
2e-
PbSO4
H2O
H2O
H2O
H2O
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H2O
© Alexis Kwasinski, 2012
Lead-acid batteries
• Chemical reaction (discharge)
• Negative electrode
• Electrolyte
• Positive electrode
Pb
Pb2+ + 2e-
Pb2+ + SO42-
PbSO4
2H2SO4
PbO2 + 4H+ + 2ePb2+ + SO42-
•Overall Pb + PbO2 + H2SO42-
4H+ + 2SO42-
Pb2+ + 2H2O
PbSO4v
2PbSO4 + 2H2O
• The nominal voltage produced by this reaction is about 2 V/cell. Cells are
usually connected in series to achieve higher voltages, usually 6V, 12 V, 24 V
and 48V.
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© Alexis Kwasinski, 2012
Lead-acid batteries
• As the battery discharges, sulfuric acid concentration decreases.
• At the same time, lead sulfate is deposited on the electrode plates.
• Charging follows the inverse process, but a small portion of the lead sulfate
remains on the electrode plates.
• Every cycle, some more lead sulfate deposits build up on the electrode plates,
reducing the reaction area and, hence, negatively affecting the battery
performance.
• Electrode plates sulfatation is one of the primary effects that affects battery
life.
• To avoid accelerating the sulfatation process, batteries need to be fully
charged after every discharge and they must be kept charged at a float voltage
higher than the nominal voltage. For lead acid batteries and depending their
technology the float voltage is between 2.08 V/Cell and 2.27 V/cell. For the
same reasons, lead-acid batteries should not be discharged below 1.75 V/cell
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© Alexis Kwasinski, 2012
Lead-acid batteries models
“A New Battery Model for use with Battery Energy Storage
Systems and Electric Vehicles Power Systems”
H.L. Chan, D. Sutanto
“A New Dynamic Model for Lead-Acid Batteries”
N. Jantharamin, L. Zhangt
• All models imply one issue when connecting batteries of different capacity in
parallel: since the internal resistances depend on the capacity, the battery with
the lower capacity may act as a load for the battery with the higher capacity.
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© Alexis Kwasinski, 2012
Lead-acid batteries models
• Most circuit parameters depend on:
• State of charge
• Charge / Discharge rate
• Temperature
http://www.mhpower.com.au/images/tecfig23.gif
SONNENSCHEIN
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“Internal Resistance and Deterioration of VRLA Battery Analysis of Internal Resistance obtained by Direct Current
Measurement and its application to VlRLA Battery
Monitoring Technique”
Isamu Kurisawa and Masashi Iwata
© Alexis Kwasinski, 2012
Lead-acid batteries capacity
• Battery capacity is often measured in Ah (Amperes-hour) at a given discharge
rate (often 8 or 10 hours).
• Due to varying internal resistance the capacity is less if the battery is
discharged faster (Peukert effect)
• Lead-acid batteries capacity ranges from a few Ah to a few thousand Ah.
http://polarpowerinc.com/info/operation20/operation25.htm
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© Alexis Kwasinski, 2012
Lead-acid batteries capacity
• Battery capacity changes with temperature.
http://polarpowerinc.com/info/operation20/operation25.htm
• Some manufacturers of battery chargers implement algorithms that increase
the float voltage at lower temperatures and increase the float voltage at higher
temperatures.
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© Alexis Kwasinski, 2012
Lead-acid batteries discharge
• The output voltage changes during the discharge due to the change in internal
voltage and resistances with the state of charge.
Coup de Fouet
Patent 6924622
Battery capacity measurement
Anbuky and Pascoe
Tyco Electronics 12IR125 Product Manual
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© Alexis Kwasinski, 2012
Lead-acid batteries charge
• Methods:
• Constant voltage
• Constant current
• Constant current / constant voltage
• Cell equalization problem: as the number of cells in series increases, the
voltage among the cells is more uneven. Some cells will be overcharged and
some cells will be undercharged. This issue leads to premature cell failure
• As the state of charge increases, the internal resistance tends to decrease.
Hence, the current increases leading to further increase of the state of charge
accompanied by an increase in temperature. Both effects contribute to further
decreasing the internal resistances, which further increases the current and the
temperature….. This positive feedback process is called thermal runaway.
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© Alexis Kwasinski, 2012
Lead-acid batteries efficiency
• Consider that during the charge you apply a constant current IC, a voltage VC
during a time ΔTC. In this way the battery goes from a known state of charge to
be fully charged. Then the energy transferred to the battery during this process
is:
Ein = ICVC ΔTC
• Now the battery is discharged with a constant current ID, a voltage VD during a
time ΔTD. The final state of charge coincides with the original state of charge.
Then the energy delivered by the battery during this process is:
Eout = IDVD ΔTD
• So the energy efficiency is  E 
VD I D TD
 VC
VC I C TC
• Hence, the energy efficiency equals the product of the voltage efficiency and
the Coulomb efficiency. Since lead acid batteries are usually charged at the
float voltage of about 2.25 V/cell and the discharge voltage is about 2 V/cell, the
voltage efficiency is about 0.88. In average the coulomb efficiency is about
0.92. Hence, the energy efficiency is around 0.80
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© Alexis Kwasinski, 2012
Lead-acid batteries calculations
• Most calculations are based on some specific rate of discharge and then a linear
discharge is assumed.
•The linear assumption is usually not true. The nonlinearity is more evident for faster
discharge rates. For example, in the battery below it takes about 2 hours to discharge
the battery at 44 A but it takes 4 hours to discharge the battery at 26 A. Of course, 26x2
is not 44.
• A better solution is to consider the manufacturer discharge curves and only use a linear
approximation to interpolate the appropriate discharge curve.
• In the example below, the battery can deliver 10 A continuously for about 12 hours.
Since during the discharge the voltage is around 12 V, the power is 120 W and the
energy is about 14.5 kWh
10 A continuous
discharge curve
approximation
Discharge
limit
Nominal curve
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© Alexis Kwasinski, 2012