Implementation of polar form algorithms with the rectangular form complex number

Power system analysis algorithms under polar coordinates are traditionally implemented with the polar form complex number, which is abstracted as phase and magnitude. This paper addresses a method to implement the polar form algorithms with the common rectangular form complex number, which is abstracted as real and imaginary parts. The key points of the addressed method are to express the derivatives to polar components under rectangular coordinates, and to rotate and stretch a complex number under rectangular coordinates. With the addressed method, the polar form algorithms can be implemented with direct complex operations and will share more components with rectangular form algorithms.