The short answer, I believe, is that there is nothing wrong with offering a prayer to the Holy Spirit since God the Spirit is, of course, fully God, just as is God the Father and God the Son. However, most prayers in the New Testament and in the church of the second and third centuries were to God the Father, with a few exceptions.
I recently read an article by Boris Paschke entitled: “Praying to the Holy Spirit in Early Christianity.” His conclusions include the following:
This article studied praying to the Holy Spirit in early Christianity, with the following results: while the New Testament neither contains prayers to the Holy Spirit nor references to such prayers, later early Christian sources from the Second and Third Centuries AD contain at the least a few passages that are relevant for the topic. In Tertullian’s De oration 12, spiritus sanctus is envisaged as addressee of Christian prayer. However, it remains unclear if this Latin term refers particularly to the third person of the Trinity or to God in general. In De baptism 8, Tertullian states that spirit epiclesis were components of the baptismal services he was familiar with. At the beginning of his homilies on the book of Leviticus, Origen encourages addressing not only Jesus but also the Holy Spirit in prayers asking for understanding the biblical text (Orig. Hom. Lev. I 1). In Jesus’s hymn and round dance (which is found in chapters 94-96 of the Acts of John) it is probably not the Holy Spirit but rather Jesus who is addressed with the epithet ‘Spirit’. The Acts of Thomas contain two prayers to the Holy Spirit, namely the spirit epiclesis in chapters 27 and 50. However, it is possible that these epiclesis not only ask the Holy Spirit but also Jesus Christ to come. In view of these findings, it seems (1) that prayers to the Holy Spirit were very rare in early Christianity; and (2) that the Holy Spirit was addressed either alone (Tertullian De baptism 8) or together with Jesus Christ (Orig. Hom. Lev. I 1).
So, what about our practice? My recommendation is that, following the biblical pattern and the pattern of the early church, we should normally address our prayers to God the Father, but still allow occasional addressing of prayers to Jesus, that is, to God the Son, as well as occasional prayers to the Holy Spirit, that is, to God the Spirit. But since the common pattern is to address God the Father in prayer, I would suggest that praying to God the Son and God the Spirit should focus more upon the works that are specifically connected in Scripture to those persons of the Godhead. Thus the occasional prayer to Jesus might look something like: “Jesus, thank you for dying as a substitute on the cross in our place,” or “Lord Jesus, we long for your second coming” (cf. 1 Cor. 16:22 “Our Lord, Come!”). The occasional prayer to the Holy Spirit could be: “Spirit, fill us with power to speak your word with boldness,” or “Illumine your Word as we read it, and help us know how to apply it.”
I would not take what I have written here as a rule, but rather as a suggestion that may bring you greater clarity and focus as you pursue a life of prayer.