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Oxford Advanced Leaner's Dictionary says:
You use "was/were able to" or "manage" (but not "could") when you are saying that something was possible on a particular occasion in the past.

However, I often hear the following conversation.
"Thank you for inviting me over."
"I'm glad you could come."
May I understand that "I'm glad you could come" is acceptable because it is an idiomatic expression?
Is it strange to use "I'm glad you were able to come" in the above case?

What about the following sentence? Must I use "was able to" instead of "could"?
"I ran fast and I could catch the bus."
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"I ran fast and I could catch the bus" is not idiomatic. (It's not acceptable.)
"I found that if I ran fast, I could catch the bus" is fine.

"I ran fast so I could catch the bus" is fine.
"I ran fast in order to catch the bus" is fine.
"I ran fast, and I was able to catch the bus" is fine.
"I'm glad you could come" is fine.
"I'm glad you were able to come" is fine.

<< May I understand that "I'm glad you could come" is acceptable because it is an idiomatic expression? >>

In my opinion, this is grammatical in its own right.
"I'm glad (that)" plus a clause is generally okay. "I'm glad (that) I found you."

I guess you're talking about "I'm glad you came" vs. "I'm glad you could come."

"I'm glad you were able to come" and "I'm glad you could come" definitely mean the same thing and are equally acceptable.

I'm beginning to see that it's tricky. Here, "To come" means "to come in the future."
"I'm glad you can walk" means you can walk now.
"I'm glad you can come" means you'll be able to come in the future.
"I'm glad you could walk" means I'm glad now that you could walk in the past.
"I'm glad you could come" means I"m glad now that you were able to come in the past, since the act of coming is complete (you have come)

Maybe it is an idiom. You had the ability in the past to come in the future, but now that future is also past.
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SnappyIs it strange to use "I'm glad you were able to come" in the above case?
It is not strange at all. In fact, it means the same thing as the example with could.

This is a statement about the possibility of complying with the invitation (and therefore doing so in the present), not about a past success.

The situation that your dictionary is cautioning against is like this:

*I was invited to a party, and I could [go / attend].

(used to mean that you succeeded in going/attending)

I don't see any reason why it should be considered a special idiom of any kind.

CJ