In Delighting in the Trinity, Michael Reeves explains how God’s triune nature relates to His love and wrath. As three Persons eternally in communion, God is love. It’s essential to His nature. Expressions of wrath, on the other hand, are not essential to His nature. Rather, He did not express any wrath until after creation and the fall, when His love reacted to sin and evil in the world.
With this [triune] God, it is not as if sometimes he has love and sometimes he has wrath, as if those are different moods so that when he’s feeling one he’s not feeling the other. No, for all eternity the Father was loving his Son, but never once was he angry. Why? Because there was nothing to be angry with until Adam sinned in Genesis 3. So God’s anger at evil from Genesis 3 onward is a new thing: it is how the God who is love responds to evil.
Like God’s holiness, then, his wrath is not something that sits awkwardly next to his love. Nor is it something unrelated to his love. God is angry at evil because he loves. Isaiah speaks of the pouring out of God’s wrath as his “strange work,” his “alien task” (Is 28:21), because it is not that God is naturally angry, but that evil provokes him: in his pure love, God cannot tolerate evil. That makes complete sense to me as a father: if I could twiddle my thumbs and yawn while my daughters suffered, it would prove I didn’t really love them; but precisely because I so love them I hate the thought of anything evil befalling them. How much more is it so with the Father of lights, in whom there is no darkness at all. Love cares, and that means it cannot be indifferent to evil. “Love must be sincere. Hate what is evil; cling to what is good” (Rom 12:9). Only such love is sincere...
[W]ith the God who is eternally love [as a result of His triune nature], his anger must rise from that love. Thus his anger is holy, set apart from our temper-tantrums; it is how he in his love reacts to evil. The Father loves his Son, and so hates sin, which ultimately is rejection of the Son; he loves his children, and so hates their being oppressed; he loves his world, and so hates all evil in it. Thus in his love he roots out sin in his people, even disciplining them that they might be freed from their captivity to it. In his love he is patient with us. And in his love he promises finally to destroy all evil as light destroys darkness.
If, when you think of God, you picture a being who is primarily angry with sinful human beings, you have missed the Christian God. His triune nature makes Him different from all other conceptions of gods. He is love because He is three Persons who love, without beginning and without end. And we see His love interact and react in all sorts of ways with those who are outside Himself. His wrath is simply what happens when He, a being of love, encounters our evil.