Please help on time interval chart

Appreciate any assistance please - Struggling with this.
I have a number of pieces of equipment running over the day. I am trying to determine the peak demand at any 15 minute interval over a 24hr period. It is easy but time consuming to manually update (per attached) however I want to auto populate the time interval chart with the corresponding electrical demand (column F) over the time range.

Take Activity 1 for example - I can say that there is a constant electrical demand of 2 between 00:30 and 08:30 therefore the time interval chart identifies a value of 2 for every cell from 00:30 - 08:30

Also..
In some cases the start time is greater or equal to the finish time implying over night (over midnight demand)

In the attached I was trying =IF(AND(H2>=$D3,H2<=$E3),$F3,"") but it doesn't work

Appreciate any ideas...

Bernie.... Thank you so much... I have not used IFERROR (or even considered it in this context).
I have dropped into the schedule and it is 99% there.
I have what is probably a silly consideration where if the start time = the finish time, it is a 24hr operation and as such starting at 01:00 and finishing at 01:00 is exactly the same as starting at 00:00 and finishing at 24:00. Is it possible to make the formula consider at start time that is equal to the finish time but can be 01:00(s)-01:00(F) or 03:00 to 03:00 (for example). (I see that you already feature($D3=$E3)*$F3) in your formula..

If not possible, its perfectly fine... I am really grateful with what you have provided

=IFERROR(1/(1/(($D3<$E3)*($D3<=H$2)*($E3>=H$2)*$F3 +($D3>$E3)*($E3>H$2)*$F3+ ($D3>$E3)*($D3<=H$2)*$F3)+($D3=$E3)*$F3),"")

AS a sidenote (only if you have a minute) can you tell me why
1. You use 1/1 initially at the beginning of the formula
2. I assume that "$D3<$E3", "$D3<=H$2", "$E3>=H$2" etc... are conditions. I wasn't aware that you use an * between conditions... Perhaps I need to jump back to beginner level!!

Again Bernie.... Thanks for your kind assistance... Worked perfectly