You can run Rail lighting, a long way from one powerpoint especially since LED will keep wattage down, you can also remote the transformer for low voltage in a closet, an have the rail start from a wall power point... Do a 2 curiut rail so you and choose 2 light settings. ... this can work but I am really not clear from your explanation, bc the entry looks far from the kitche on the plan....... or do you mean the entry to the actual kitchen.. I can help you with this but I need to be more clear on where power can come from and where you want/ need light.

Thank you. I mean the entrance to the kitchen area (between the island and fridge) - there is a flush mount there now and a new one can be placed near there in its stead. On the other side of the beam, the electric would come from the wall and accross a lowered portion between the beam and ceiling (here is where i was considering 120v les track the same color as the ceiling. There is also a ceiling light centered over the open dining area of the kitchen that i am keeping with 6 bulbs).

Is this the area in question?

mostly yes. but the lighting could extend as far as the fridge, the range, and the pantry wall.

So where is the power source? I only need one.

And are you talking about running with this beam?

The red line you drew is the ceiling. The beam i mention is the large center low hanging beam over the middle of the island, with the center pendant shown that will/ can/ should not be there. There is already power to the right of that beam (between the island and the sink). But, on the other side of that beam, the power has to come from the wall (up the wall and accross the ceiling (I am suggesting firing out where that beam meets the ceiling.

ok so just use the power source that is between the island and sink, you dont need to drag power up to run a U or L shaped thack/rail, Im not sure you need pendants anywere...... how far does the beam hang down? I cant make out that measurement.

Or you can combine to L shape to make a square using 2 power sorces.

power From the sink side would require going over the beam (already lowers ceiling over a foot? Thinking of skipping tracks. area that I am trying to light (this is the "work area of a kitchen, will also have under cabinet lighting, and opens up to a 12' x 10' area, which is separated by a beam) 12' x 9' It seems like a flush mounted led fixture without opaque sides may work beat and would allow more light (through the bottom and sides).

Like this https://www.lightology.com/index.php?module=prod_detail&prod_id=804626&cat_id=9

That being said, oval or horizontal may be better but I see few online. maybe two round or square led lights

Any additional ceiling lights on the other side of the large beam would require fir out the ceiling, which I want to avoid, so on the other side i plan to keep the ceiling fixture that is centered there (which has 5 75 watt incandescent bulbs) and add a wall sconce above the pantry on the right facing wall. Ceilings are max 9' tall.