In his excellent and highly practical book Prayer: Experiencing Awe and Intimacy with God (Dutton, 2014), Tim Keller uses a great analogy to show that on their own, our prayers do not have power to make God listen to us or to earn us favor with him. Those who have trusted in Christ already have these things, and so prayer is more of the mechanism by which we connect our hearts to God and avail ourselves of the access to him that has been purchased by Christ, our great High Priest (Hebrews 4:14-16).
“When you flick on the light switch, the bulbs illuminate. Does the light switch provide the power for the bulbs? No – that comes from the electricity. The switch has no power in itself, but rather it connects the bulbs to the power. In the same way, our prayers have no virtue to procure us access to the Father. Christ has done that. Prayers that are in accord with a gracious God, however, can connect us to him.” (104)