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TMS320F28377D: SVGEN Library maths

Part Number: TMS320F28377D


Hi, 

I am currently working with the SVGENDPWM library from the control_suite motor control libraries. I understand how it is producing bus clamped SVM, however I am unaware of how this maths was actually derived. I am aware of the maths behind calculating Ualpha and Ubeta on a typical 2 level space vector hexagon however I do not understand how they have managed to obtain the equations for finding the sector number and timing periods without using the overall angle or sector angle. Clarification on this fact would be much appreciate, I have checked the documentation, however they do not explain the maths behind the algorithm.

I have pasted the algorithm from the control_suite library below. 

Thank-you