I think it is helpful to distinguish between two aspects of Charismatic experience. I like to find common ground on the MAJOR issue.
1. Do we experience the presence of God through our senses? Do believers have conscious contact with God? Does this conscious contact with God provide inspiration and can we know when this inspiration is happening? Edwards for example records David Brainard saying to his brother in a letter, “Reject fire without light”. By this he means reject experiences of God that do not include an intelligible inspiration. This quote shows that Brainard and certainly Edwards too believed in the work of the Holy Spirit as having a conscious element. This level of experience is the work of the Spirit that the Reformed Charismatic really has a passion to bring others into. In fact, I think this aspect of our life is what John Piper means by delighting in the Lord.
Also, the "light" (clarity regarding the mind of God) of this "fire and light" equation is what many Reformed-Charismatics mean when they say "prophecy". A good example of this is Lloyd-Jones who believed that the filling of the Holy Spirit was a heightened experience of assurance. Lloyd-Jones spends many chapters in his Romans 8 commentary giving illustration after illustration of the experiential aspect of many reformed divines spirituality. The point here is that this is the MAJOR work of the Spirit that leads to passion and love for God. Such passion and love leads and empowers a positive ethical response and is therefore very valuable. I believe it is vital that believers agree on this element of the "charismatic" experience. Such a work of the Holy Spirit in the believers life is life giving and worthy of being a defining element of one’s preaching and teaching in the church.
2. The second aspect is the Charismatic discussion is the issue of healing, tongues, and manifestations. These items, though important, involve a different problem and discussion. I would be willing to disagree on these matters so long as we can all labor together in promotion of the former experience of God and the illuminating work of the Holy Spirit stated above. Edward’s religious affections thesis is basically that affection (my #1) is the true sign of a work of grace in the believers life. In other words, like Edwards, one can be a cessationists (reject #2) but hold onto the vital issue of the conscious experience of God.
I believe it is a passion for the experience of the Glory of God as “seeing and savoring” as Piper says that compels many of us to consider oursleves both Reformed and Charismaic, for at the heart of the Reformed emphasis is a passion for the Glory of God and the experience of His glory in the life of the redeemed.