There are many problems with your code.
There is a lowercase which. Anyway, you should use Piecewise, and not Which, for symbolic math.
The equation
v[k]'[t] == (i[k][t] - i[k + 1][t])/Cv[k][t]
involves i[k+1]. When k ranges from 1 to NN the last equation involves i[NN+1].
Qs[0][t] is not defined, but is needed for Qs[1][t]
The definition
Ip[k_][t] :=
Ip[k - 1][t] + Multi[[k]]*Sum[i[j][t], {j, k, NN}, {t, 0., tmax}]
uses t as both independent variable and iterator. What does it mean?
