Originally Posted by

**lpy** Dear all,

I am trying to obtain the optimal solution from constraints that are represented in time function:

Minimize F = 100Ppv + 2Pdg

subject to:

$\displaystyle Ppv(t) + Pdg(t) \geq PL(t)$

$\displaystyle \sum Ppv(t) \leq 0.4 \times \sum PL(t)$

t is from 1 to 24 and

PL is given as below:

$\displaystyle PL(t) = 2 for 1\leq t \leq 6$

$\displaystyle PL(t) = 8 for 7\leq t \leq 18$

$\displaystyle PL(t) = 4 for 19\leq t \leq 24$

This is an electrical system optimization problem that need to find the optimal power supply from the solar panel (PV) and the diesel generator (dg) with a given load demand for 24 hours.

The first constraint is to ensure both power from pv and dg will meet the load demand at anytime. The second constraint is the total supply from the pv is limited to 40% of load demand only. The objective is to minimize the cost of this system. with the optimal Ppv and Pdg.

I have problem solving this question as most of the maths reference book examples show only decision variable x1, x2...etc that is time independent.

Your kind assistance is appreciated. Thank you