Picture only because I had to via this comm’s posting rules. (???)

The verb run is only conjugated as “ran” in the simple past tense, as in:

• I ran a mile.
• He ran the company.

For literally every other conjugation of that verb, you should use “run.”

It baffles me that ran has somehow overtaken the other, much more (historically) common, much more appropriate, conjugation of “run,” which applies to most situations where you have a helper verb like to be or to have:

• I did run a mile
• He did run the company
• I have run a mile
• He has run the company
• I would have run…
• I might have run…
• I will have run…

This applies to a lot of other verbs with similar vowel changes like sing/sang/sung, ring/rang/rung, etc. In general, if you’re using an irregular/strong verb that has an “a” in it, it is only meant for simple past tense.

Now, all of this is really only appropriate for when you’re meaning to sound professional nowadays, since simple past tense is overtaking all those other verb conjugations. But for now, it’s still a good YSK.