Which institution's logo to add to research poster when research was done at institution different to main affiliation as student?

If both institutions have supported your project, you should acknowledge both in your poster.

To save space, you have a variety of options:

• Make the logos smaller by scaling them.
• If available, use a small, square version of the logo rather than a larger rectangular version.
• Put the logos in a part of the poster that is underutilized. (For example, left-align the title and authors, and put the logos over to the right side next to the author list.)

There is no formal protocol. The general protocol is to ask your supervisor or colleagues. This is usually a question that depends on the particular group or institution, and where usually the "group's habits" is the precedence that you want to follow.

The general protocol that probably suit you well is the one ff524 answered, namely, acknowledge both.

Just one question: Who paid?

If they

• paid you to do the work
• paid for you to present the work
• bought the equipment or the consumables
• paid the mentor who guided you through the work

they you should be recognizing them.

And there is nothing wrong with having multiple logos, but no pressing need to have any at all. (In my business—particle physics—it is common to have everyone from the group display a logo on their slides/posters as part of establishing a brand, but those were always small because everyone was concerned about space.)

If someone asks you can tell them how it happened that you got support from multiple sources.