I have one question regarding the decreasing LCOE with increasing load size.

You perhaps remember I had done 1 exercise before where for fixed load factor I looked at ViPOR output for increasing no. of identical load points (identical load curve). The result shows LCOE decreases with increasing load.

It would be nice if you can through some light on why it is so. Since it is pure PV plant the capital cost increases with load. Only thing I can think of is that the fixed costs are changing disproportionately with load increase. I do not remember any other reason of economies of scale. In fact HOMER calculates the increase in capital cost for PV and inverters proportionately.

That would happen in real life because load aggregation would lead to a higher load factor with an increasing number of load points.  You can account for that in HOMER by making the load profile smoother as you scale it up, but that's harder than just scaling the load in a sensitivity analysis, so most people don't do it.

My guess is that even without this 'load aggregation effect' providing economy of scale, your generation costs data probably still shows some economy of scale.  It might be because of a system fixed capital cost, or just the fact that the PV array or the battery bank can only get so small.

You could verify whether this is true by opening your HOMER file and plotting COE versus load size.

Another possibility is that the distribution costs show economy of scale.

One would expect that if you are increasing load density, since denser loads can be connected with proportionately less wire.