It is helpful to understand the difference between critiquing student writing and grading student writing. This link, Critiquing or Grading can help you create a rubric that achieves your goals.
Students will appreciate knowing how they are being assessed, too. So, I recommend clarifying the goals and allowing students to practice giving peer feedback to classmates using the different kinds of rubric. In-class Peer Feedback.
As they experience the thinking required to do each kind of assessing, they will be more likely to understand what is required of them when the write and how teacher comments can be used to improve their writing on the next assignment.