Slide 1Distributed 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:
Power buffer for slow, bad load followers, DG technologies.
Energy supply for stochastic generation profiles.
Power vs. Energy
Flywheels
Ultracapacitors
Batteries
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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
© Alexis Kwasinski, 2012
Lead-acid batteries life
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Negative electrode: Lead (Pb)
Pb
PbO2
H2O
H2O
H2O
H2O
H2O
Chemical reaction (discharge)
Overall
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.
Pb Pb2+ + 2e-
2H2SO4 4H+ + 2SO42-
Pb2+ + SO42- PbSO4
Pb2+ + SO42- PbSO4v
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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.
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© Alexis Kwasinski, 2012
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.
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
N. Jantharamin, L. Zhangt
State of charge
Charge / Discharge rate
Temperature
“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
Battery capacity changes with temperature.
Some manufacturers of battery chargers implement algorithms that increase the float voltage at lower temperatures and increase the float voltage at higher temperatures.
http://polarpowerinc.com/info/operation20/operation25.htm
© 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.
Tyco Electronics 12IR125 Product Manual
Coup de Fouet
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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
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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
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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
Discharge limit
Nominal curve
dE
P
dt