I came across some interesting things that Berkhof has to say about the Trinity…
…it is…of…greatest importance to maintain the personality of God, for without it there can be no religion… no prayer, no personal communion, no trustful reliance and no confident hope.
Personality does not develop nor exist in isolation, but only in association with other persons. Hence it is not possible to conceive of personality in God apart from an association of equal persons in Him.
Berkhof also brings up a point that one can look at the Trinity as 3 modes, but not modes of manifestation as the modalist heresy contends. Rather, modes of actual existence.
It is also interesting to consider God eternally existing before He began creation. As a personal being, He would have been very lonely if it were not for the persons within the Godhead. Then one could argue that God had to create in order to cease from being lonely.