Battery storage: an overview

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Sandra Spencer
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1 Battery storage: an overview S. Keshav March 18, 2015! (several slides are borrowed from Dr. Yashar Ghiassi-Farrokhfal)

2 Overview Why storage? Lithium-Ion battery modelling Simple model A more realistic model

3 Why storage Many reasons Our focus: it allows us to decouple supply and demand

consumption Prioritizes solar over grid Prevents power peaks Up to 8kW power

6 Example: Schneider Conext SW inverter/charger Integrates with existing solar panel Supplies 120/240 VAC from inverter Works with a diesel genet Allows self consumption Prioritizes solar over grid Prevents power peaks Up to 8kW power Works with an external battery

7 What does it cost per KWh?Source: Mr. Franz-Josef Feilmeier, FENECON Component Cost in Euros Cell Module - safety certified (depends on size of cell and safety architecture to deal with over currents. This can be removal of failed cells (with many cells) or valves (for large cells) Battery unit BMS, cables, sensors, cabinet ~ depending on quality Inverter Charger for PV or inverter 100 Electronics Sensors, cables, terminals, relays, cabinet, manufacturing cost Warranty 7 years 500 3%/year 21%-40% Transportation, customs ~10% Distributor/wholesaler margin ~10-15% Installer margin includes certification ~20% Total cost for 1C rate systems

8 Battery basics A battery stores energy (like bits) measured in Joules or Watt-hours Energy is the product of power and time Power is measured in Watts (like bits/sec) 1 Joule = 1 Watt * 1 second 1 kwh = 1000 W * 3600 s = 3.6 million Joules Battery delivers a nominal voltage State of charge (SoC) is the fraction of energy capacity in use

9 Discharge To discharge a battery, we connect a load to it, which causes a current to flow This is the discharge current The higher the load, the lower the discharge current the longer it takes for the battery to discharged Load

10 Rated capacity The amount of energy a battery can hold usually measured in Ampere-hour (Ah) not Watt-hours Product of 20 hours multiplied by the discharge current that a new battery can consistently supply at 20 C, while remaining above a specified terminal voltage per cell a battery rated at 100 Ah can deliver 5 A over a 20- hour period Rated energy capacity = rated capacity * nominal voltage

11 C rate Measures the discharge current Actual discharge current divided by the theoretical discharge current under which the battery would deliver its nominal rated capacity in one hour. A 1C discharge rate delivers the battery's rated capacity in 1 hour. A 2C discharge rate means it will discharge twice as fast (i.e., 30 minutes).

12 5 hours Why does mah increase but Wh decline?

13 Battery voltage: a critical parameter A battery has a nominal voltage e.g. 1.5 V Actual voltage is slightly higher or lower when the battery is full, the voltage is higher, and as it empties, the voltage declines the change in voltage is very nearly linear with state of charge

14 Voltage vs. SoC SoC Voltage Figure 1: Mapping of SoC to voltage, provided by Mr. Kitzbichler of Landshut

15 Battery imperfections Maximum charge rate (scales with B) limits charge power Maximum discharge rate (scales with B) limits discharge power Self-discharge linearly proportional to the SoC Charge inefficiency only a fraction of input energy is stored Discharge inefficiency only a fraction of output energy is available Maximum depth of discharge (DoD) SoC must lie in the range [DoD, 1] = [0, DoD] 0 <= b(t) <= B* DoD DoD is MAX not MIN!

16 Simple storage model

18 Problem: voltage limits Voltage is a function of SoC, drain/charge current, and temperature To prevent irreversible damage: Battery cannot be charged above a voltage limit Battery cannot be discharged below a voltage limit

21 Updated model: Voltage limits -> SoC limits V = f(soc, I, T) Vmin <= V <= Vmax SoC = g(v, I, T) (reverting to traditional definition of DoD) B*SoCmin(Vmin, D(t),T) <= b(t) <= B*SoCmax (Vmax,C(t),T) SOCmin(D(t),T) is modeled as a linear function of D(t) - disregarding T

22 Battery state update equation with voltage limits Source: Mr. Kitzbichler, Landshut

23 The final model b(0) = init_charge_state b(t+t_u) = b(t) + eff_input - eff_output - self_discharge self_discharge = either \gamma*b(t)*t_u or constant eff_input = charge_rate * t_u * charge_efficiency eff_output = (discharge_rate * t_u) /discharge_efficiency! min(b, discharge_rate, temp) <= b(t) <= max(b, charge_rate, temp)! 0 <= charge_rate <= max_charge_rate(b) 0 <= discharge_rate <= max_discharge_rate(b) charge_rate * discharge_rate = 0 During t_u all variables are constant

24 Validation of battery state update equation 23 charge-discharge cycles on a Lithium-Titanate cell Charge rate: 1C, Discharge rates: 0.1-5C Simple model Final model

25 Conclusion Battery is not the same as a RAM several imperfections need to be modeled Need to take both SOC and voltage limits into account Final model is experimentally validated and can be made part of an optimization framework

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