Where is Jesus's Soul according to tripartite theology? When Lord Jesus came to the earth, He was fully God and fully human. 
Many Christians believe that the human has three parts – body, soul and the spirit – and the word says He came in flesh.  Then we read in Luke 23:46: 


  And when Jesus had cried with a loud voice, he said, Father, into
  thy hands I commend my spirit: and having said thus, he gave up the
  ghost. (KJV)


My question is: Are there references in the Bible that indicate what happened to the Lord's soul when He died or when He resurrected?

My question is directed to those that believes the Human has three parts (body, soul, and spirit).
The soul is the conscious part of you, and Jesus. His soul went to hell with His Body; returned to the surface of the earth at his resurrection; and to heaven at His ascension:

Men and brethren, let me freely speak unto you of the patriarch David, that he is both dead and buried, and his sepulchre is with us unto this day. Therefore being a prophet, and knowing that God had sworn with an oath to him, that of the fruit of his loins, according to the flesh, he would raise up Christ to sit on his throne; He seeing this before spake of the resurrection of Christ, that his soul was not left in hell, neither his flesh did see corruption. This Jesus hath God raised up, whereof we all are witnesses. Therefore being by the right hand of God exalted, and having received of the Father the promise of the Holy Ghost, he hath shed forth this, which ye now see and hear. [Acts 2:29-33 KJV]

Jesus' soul is whever Jesus is.