1 © Alexis Kwasinski, 2012 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 , 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 , 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, ] Microgrids are electric networks utilizing DR to achieve independent control from a large widespread power grid Prevailing technologies: Batteries Flywheels Ultracapacitors

2 © 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 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.

3 © Alexis Kwasinski, 2012 Battery technologies Batteries stores energy chemically. Main technologies: Lead Acid Nickel-Cadmium Nickel-Metal Hydride Li-ion

4 © Alexis Kwasinski, 2012 Battery technologies

5 © 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.

6 © 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]

7 © Alexis Kwasinski, 2012 Lead-acid batteries Positive electrode: Lead dioxide (PbO 2 ) Negative electrode: Lead (Pb) Electrolyte: Solution of sulfuric acid (H 2 SO 4 ) and water (H 2 O) PbPbO 2 H2OH2O H2OH2O H2OH2O H2OH2O H2OH2O

8 © Alexis Kwasinski, 2012 Lead-acid batteries PbO 2 H2OH2O H 2 SO 4 Chemical reaction (discharge) Pb 2+ O H + SO e - Pb 2+ Pb SO H + H 2 SO 4 PbSO 4 2e - PbSO 4 H2OH2O H2OH2O 2H 2 O H2OH2OH2OH2O

9 © Alexis Kwasinski, 2012 Lead-acid batteries PbO 2 + 4H + + 2e - Pb H 2 O Chemical reaction (discharge) Negative electrode Electrolyte Positive electrode 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 Pb e- 2H 2 SO 4 4H + + 2SO 4 2- Pb 2+ + SO 4 2- PbSO 4 Pb 2+ + SO 4 2- PbSO 4v Pb + PbO 2 + H 2 SO PbSO 4 + 2H 2 O

10 © 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

11 © 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 “A New Dynamic Model for Lead-Acid Batteries” N. Jantharamin, L. Zhangt

12 © Alexis Kwasinski, 2012 Lead-acid batteries models Most circuit parameters depend on: 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 SONNENSCHEIN

13 © 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.

14 © Alexis Kwasinski, 2012 Lead-acid batteries capacity 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.

15 © 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 Patent Battery capacity measurement Anbuky and Pascoe

16 © 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.

17 © Alexis Kwasinski, 2012 Lead-acid batteries efficiency Consider that during the charge you apply a constant current I C, a voltage V C during a time ΔT C. 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: E in = I C V C ΔT C Now the battery is discharged with a constant current I D, a voltage V D during a time ΔT D. The final state of charge coincides with the original state of charge. Then the energy delivered by the battery during this process is: E out = I D V D ΔT D So the energy efficiency is 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 In average the coulomb efficiency is about Hence, the energy efficiency is around 0.80

18 © 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 10 A continuous discharge curve approximation