## Figure P33

A 12 V battery is connected to a series RL load as shown in Figure P3.3. The battery has a rated capacity of 80 Ah. At t=0, the switch is closed, and the battery begins to discharge.

(a) Calculate and plot the battery discharge current, i(t), if the steady state discharge rate is C/2. Neglect battery voltage drop.

(b) Calculate and plot SoD(t) in Ah for 0<t<2 h.

(c) Calculate and plot SoC(t), assuming that at t=0 the battery is charged to rated capacity. Assume also that the rated capacity is the practical capacity.

(d) Calculate the time corresponding to 80% DoD.

Given below are constant power discharge characteristics of a 12 V lead-acid battery:

10 67.5

110 8

The battery characteristics are to be expressed in terms of Peukert's equation, which has the following form:

\S!'i [S!'.) ■■'/. hi l.iil: A,ir:j ai:^1 "'iUiiiL' ;.-u:lsU.il>)

(a) Derive the constants n and , assuming a linear relationship between log(SP) and log(SE).

(b) Find the capacity QT of the battery if the theoretical energy density is SET=67.5 Wh/kg, given a battery mass of15 kg.

An EV battery pack consists of four parallel sets of six series-connected 12 V, 100 Ah lead-acid batteries. One steady state motoring (discharge) cycle of battery current is shown in Figure P3.5a. The steady-state regenerative braking (charge) cycle of the battery is shown in Figure P3.5b.

## DIY Battery Repair

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