A PHEV battery has a $100\%$ SOC of $36$ kWh$.$ The battery DOD is maintained

within a range of $20\%$ to $80\%.$ The simplified HEV battery pack model has the fol$-$

lowing parameters: open$-$circuit voltage is Vbp$($nl$)=360$ V at $20\%$ DOD, with an

internal ohmic resistance of Rb $=200$ m$$ and a constant of K $=0\mathrm{.}5$ V$/(\%$ DOD$).$

i$)$ Determine the battery terminal voltage if the battery is discharged to $80\%$ at a

constant $100$ A$.$

ii$)$ Determine the battery terminal voltage, current, and efficiency at DOD $=80\%$

for $($a$)+80$ kW discharge and $($b$)80$ kW charge.

iii$)$ If the battery has $96$ cells in series, at which charging power does the battery

hit a $4\mathrm{.}3$ V per cell limit at $20\%$ DOD?