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(Using the word psychological in the most-basic sense: pertaining to the human soul.)
St. Thomas did not invent the psychological analogy for the Holy Trinity. He inherited it from ancient theological tradition. St. Augustine also used the analogy 800 years earlier.
In one of my theology classes, I joked with the professor that the psychological analogy is actually more mystifying than the divine mystery of the Trinity itself. But it’s worth listening to this long chapter four or five times in order to begin to understand it. (It took me more than five tries to record it, believe me.)
For me, the most inspiring thing is St. Thomas’ utter humility. He does not propose grand theories. He merely correlates the words used in the Bible with the way that we generally use those words, and tries to find the most-consistent way of understanding it all.
Father Mark White Blog 
TABIV-Ch11: Love it! Will work through it a few more times!
TABIV-Ch11: I finally had a chance to give this one another go. I appreciate so much, the process TA uses to extrapolate or prove the one-ness of God/Jesus… Our beings can come to understand ourselves, and we can come to understand many things, we can even come to understand the divine to a certain degree. What makes God and Jesus different is that they understand without needing external assistance to understand. They simply understand their essence, their being, their Word, creation, incarnation, intent… they simply understand all things and are all things and were all things before all things.
And so it is… and so it shall be.