My son has ran away from home. He changed his Apple ID password. Is there a way I can locate him?

If you did not have his Apple ID as part of a family sharing group, then you cannot use Find my iPhone or Find Friends. If he is a minor the police can get a court order to track him through his cell phone's IMEI and his carrier.

You're welcome, and good luck. As a parent emeritus my thoughts are with you.