Or HaChaim on Exodus 15:2/אור החיים על שמות ט״ו:ב׳

1 עזי וזמרת כה, "The Lord is my strength and song." The normal procedure when one composes a song for G'd, praises Him or prays to Him, is to mention first how G'd relates to oneself before mentioning how G'd related to one's ancestors. Thus we find that the men of the Great Assembly who edited our major prayers began the עמידה by first referring to G'd as "our G'd," i.e. the G'd of the petitioner and only afterwards did they define G'd as also the G'd of the patriarchs. The Israelites were similarly motivated when they first referred to what G'd meant to them (each individual Jew), how G'd had proven a Saviour for them in their present situation acting as the merciful G'd (tetragram). They concluded the statement referring to their personal relationship with G'd by saying זה אלי ואנוהו, "this is my G'd and I will glorify Him," and only afterwards did they describe the same G'd in His capacity as the G'd of their fathers. Our sages copied this pattern when they formulated our prayers where we say אלוקינו ואלוקי אבותינו, "our G'd who was already the G'd of our ancestors." I have already explained why the Israelites in this instance chose to describe G'd in the singular as "my G'd" instead of as "our G'd."