This is a simple battery example, showing how a battery voltage depends on both the discharge current and time.

As the battery is discharged, the voltage drops. This is primarily because a battery is an electro-chemical reactor. As the reactants are used up, the product of the reaction (electrical energy) is reduced.

Counter-intuitively, though, if you allow the battery to 'rest' for a bit, the voltage goes back up! This is because the reactor is still working, albeit somewhat slower, due to the reduction in available reactants.

Battery charging circuit for lithium ion battery. This is derived from a www.Silego.com GreenPak 2 application note.

Includes model of lithium ion battery.

This circuit will model a NaS cell voltage. The model is a circuit created by Darrell Teegarden for LiFePO4 battery and will be or has been altered to model and NaS battery system.

Based off of the model described in:

Advanced materials for sodium-beta alumina batteries: Status, challenges and perspectives; 2009, Xiaochuan Lu, Guanguang Xia, John P. Lemmon, Zhenguo Yang∗

Retrieved 1-18-2015 from Journal of Power Sources 195 (2010) 2431–2442 (via PSU Library).

parameters: (below params for LiFePO4, need params for NaS)

initial SOC [no units] (0.0 - 1.0) (

initial charge capacity [Coulombs] (> 0.0)(

Battery charging circuit for lithium ion battery. This is derived from a www.Silego.com GreenPak 2 application note.

Battery charging circuit for lithium ion battery. This is derived from a www.Silego.com GreenPak 2 application note.

Application circuit using a GreenPak 2 configurable mixed-signal array. This array has been configured to implement a voltage-to-PWM function. This is then used to control a lamp, powered by a Lithium Ion battery.

This circuit models a LiFePO4 cell voltage.

Based off of the model described in:

Liao Chenglin; Li Huiju; Wang Lifang, "A dynamic equivalent circuit model of LiFePO4 cathode material for lithium ion batteries on hybrid electric vehicles," Vehicle Power and Propulsion Conference, 2009. VPPC '09. IEEE , vol., no., pp.1662,1665, 7-10 Sept. 2009

doi: 10.1109/VPPC.2009.5289681

see also http://www.systemvision.com/design/dynamic-equivalent-circuit-model-lifepo4-batteries

parameters:

initial SOC [no units] (0.0 - 1.0)

initial charge capacity [Coulombs] (> 0.0)

This circuit models a Li-Ion (LiFePo4) battery

Based on the following paper:

Marek MICHALCZUK1, Bartłomiej UFNALSKI2, Lech M. GRZESIAK2, Piotr RUMNIAK2

Politechnika Warszawska, Instytut Automatyki i Robotyki (1), Instytut Sterowania i Elektroniki Przemysłowej (2)

Power converter-based electrochemical battery emulator

http://pe.org.pl/articles/2014/7/3.pdf

Status:

This model replicates figure 6 in the above paper, with the addition of modeling a variable number of cells.

The number of cells modeled can be changed by modifying the blocks:

NCELLS_const & NCELLS_reciprocal_const

Modify the values of these blocks to the number of cells and reciprocal of the number of cells, respectively.

The model is calibrated for a single 40Ah battery cell (specifically, WB-LYP40AHA). This 40Ah calibration is represented by parameters values of 4 different blocks:

I_meas

Rsn_const

C1_const

R1_const

To calibrate for a given cell capacity, Capacity_cell [Ah], modify the parameters according to these relationships:

I_meas.K =

1/(Capacity_cell[Ah]*3600[s])

Rsn_const.OUTPUT_LEVEL =

3.1E-3[Ohm]*Capacity_cell[Ah]/40[Ah]

R1_const.OUTPUT_LEVEL =

1.9E-3[Ohm]*Capacity_cell[Ah]/40[Ah]

C1_const.OUTPUT_LEVEL =

22.75E3[Farad]*Capacity_cell[Ah]/40[Ah]

The battery models the anode as a porous substrate that is plated with a metal and then filled with lithium. The resistance of the metal is calculated from the resistivity of the metal (an input parameter). The battery capacity is calculated assuming that the lithium is the limiting reactant.

The open circuit voltage is modeled as a function of state-of-charge (Nerst equation).

Three loss mechanisms are included:

(1) Activation voltage drop (Tafel equation)

(2) Ohmic losses (resistivity of substrate and plating)

(3) Transport losses (empirical)

surface charge storage is modeled as a time delay between the instantaneous activation voltage and the effective activation voltage.