Hello @ali checkout the attached pdf lecture. Your question is very difficult to answer without getting into a lot of details. On page 47 of the PDF, the author gives formulas for the Newton Raphson method. These formulas are very similar to the "Power Flow Equations" that was discussed (here). On Page 53, the author provides a very specific example of Power flow using the same equations. The manual results are shown on Page 57... and the computer simulation results are shown on page 58. As you can see, the the manual/hand-written results match the computer simulation one. But this is a very specific example.
I'm currently working on two video tutorials that will shed some light on Ybus matrix as well as the Newton Raphson method... The first part of the video will be release in a couple days. I'll post the link here.