Chlamydomonas, Chlorella are present in Kingdom Protista as well as Plantae under division algae.
In which kingdom they correctly belong to?
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It is generally accepted now that Chlorophyta are Plantae (see here). They are more closely related to plants than any other group of organism. Protist is a kind of basket term for any eukaryotic unicellular organism that is not an animal, fungi or a plant which is a rather exclusionary definition.
Personally, I think the kingdoms are pretty 'macro' oriented and do not really capture the diversity well of unicellular organisms. If you want to see a bunch of elderly scientist shout at each other over what appear to be arbitrary distinctions, I highly recommend attending the taxonomy session of any unicellular conference