actually, all are correct, just there is a slight difference in the three sentences (like the manner of speaking/ emphasis..), but the meanings are almost the same. No. 1: the 了， emphasized the verb more than the whole fact, that is to say, it is intent to draw a line under the verb: went, the motion has already happened. No.2: the 了， emphasized on the place you went more. just like: I went to somewhere yesterday, the place is supermarket. No.3: this one is something like the past perfect tense, it emphasized the verb “go” and the place "supermarket" at the same time, the whole fact. So you might think "\了" can help to express the past time thng, not only just a verb, that depends on the location it is placed in. Hope that can help you

1 我昨天去了超市。 Yesterday,I went to supermarket, and I ....... 2 我昨天去超市了。 I didn't find you yesterday,where were you? I went to supermarket. 3 我昨天去了超市了。 have you been to the supermarket yesterday? yes, I've been there yesterday.

example 1 and 2 are correct, as for no.3, 了 usually don't repeat in a sentence it's absolutely correct to say "去了超市"

I think they are all correct.but we are used to using the first one. what do you mean "but also learned that sentences cannot be ended without 了 if objects are not specific."? Could you show me an example?

As you have the indication of time 昨天 you actually don't needed 了 just saying 昨天 我 去 超市 is enough