This program related to calculate life time of battery energy storage. The syntax of calculation this life time considered as two step problem which in the first step this problem solved without considering effect of charge and discharge on life time with objective of maximization of profit. when this problem has been solved E energy level calculated the first step. By using energy level obtained we determine adjacent local extreme points plot E.l(t) from lines 104-108 of program attached. K(t) defined as dynamic. set k contain of adjacent local extreme points.

where Em(k) is the amount of energy stored at the adjacent local extreme point.

Now Im going to calculate dk_half = (Em(k) – Em(k-1))/E_max for every two adjacent local extreme points.(referenced to line 125 /$ontext to $offtext)

and dk_half is different levels energy between two local adjacent local extreme points divided whole capacity of energy storage.

dk_half= abs ( (Em(k) - Em(k-1))/E_max)

neq,day= sum(k , 0.5 * (dk_half) 0.8

Tcycle = N_fail/w * neq,day

Untitled_36.gms (6.22 KB)