God is a trinity on the 2nd level, insofar as each person of the Trinity has His own unique separate and distinct intellect, will, and power.
God is a unity for 3 reasons. First, the 3 levels in God are united into a single "thing."
Second, each person's intellect is an aspect of the intellect of God. The same is true for the wills and powers of the persons.
In particular, for God, His love of concupiscence, love of self, and love of friendship are numerically identical to each other. God loves Himself as a "consumer good" or object of contemplation; He loves His own self, such that the lover, the beloved, and the love (understood as everything God approves of and enjoys about Himself) are God Himself; and God manifests His love for the other through the relations of the Trinity.
Thus, the Father and the Son love each other through the Holy Spirit. But the effects of love are, as per St. Thomas, union, mutual indwelling, ecstasy, and zeal: "when a man loves another with the love of friendship, he wills good to him, just as he wills good to himself: wherefore he apprehends him as his other self, in so far, to wit, as he wills good to him as to himself. Hence a friend is called a man's 'other self'..., and Augustine says..., 'Well did one say to his friend: Thou half of my soul.'" (ST, II-I, 28) The Father and Son then indwell in each other perfectly and wholeheartedly together with the Holy Spirit, making them one. Each person is "another self" to the other two persons.
This relation may be also approached as follows: the lover unites with the beloved, is completed through this union, and rests in peace therefrom. The divine mind (Father) that thinks and through one comprehensive thought (Holy Spirit) understands itself (Son), while maintaining an identity of these three as simple pure act achieves precisely this sort of completeness and as its consequence, beatitude or happiness.
Third, the acts of the divine intellect, will, and power are in fact self-same single act.