# Thread:

1. ## optimization with time dependent constraints, need help please~

Dear all,

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

Minimize F = 100Ppv + 2Pdg

subject to:
$Ppv(t) + Pdg(t) \geq PL(t)$
$\sum Ppv(t) \leq 0.4 \times \sum PL(t)$

t is from 1 to 24 and

PL is given as below:
$PL(t) = 2 for 1\leq t \leq 6$
$PL(t) = 8 for 7\leq t \leq 18$
$PL(t) = 4 for 19\leq t \leq 24$

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

2. 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:
$Ppv(t) + Pdg(t) \geq PL(t)$
$\sum Ppv(t) \leq 0.4 \times \sum PL(t)$

t is from 1 to 24 and

PL is given as below:
$PL(t) = 2 for 1\leq t \leq 6$
$PL(t) = 8 for 7\leq t \leq 18$
$PL(t) = 4 for 19\leq t \leq 24$

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
There is something wrong with this question. First you do not say how the time dependednce of F is to be dealt with. Also are you sure that you can demand any power you want from the solar panel at any hour?

As it stands it looks like three independednt optimisation problems.

CB

3. ## Optimization with time dependent constraints

Hi, thank you for the reply.

The pv power is available during day time only and the rest of the time output from the panel is zero and the summation of this pv power is limited to supply a portion of the load demand.

Do you have any suggestion where can I find a reference or example with time dependent constraints? Thanks.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9355834126472473, "perplexity_flag": "middle"}