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So don't worry so much about how to use  had had  as a unit of grammar, they will come together naturally when you want to express the verb ' to have ' in the past perfect. Let's consider a different verb for a moment like  to want .
In the first sentence here, using had, the sentence is fine. But using have had, the sentence is ungrammatical, because last year is always a completed event that is not connected to the present. But, as we know, the present perfect tense means that there is a connection to the present.