# Calculation of voltage to ground along a three-phase power transmissionline

Posted 9 years ago
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 Hi , all ! I hope you may help me. I am trying to solve a (3x3) system of differential equations of second order. It allows me to obtain the voltage to ground for each of the three phase system (with two grounding wires. Thus, original 5 x 5 system becomes in a 3x3 after a matrix reduction) along a power transmission lines.Well, I started by solving it step by step through Laplace transform in relation to x (length) and the result was not good, because both side conductors should have the same voltage (modulus) along line lenght, whereas voltage of the central conductor should be different. However, obtained results were side conductorswith different voltages (which is right), whereas the central one is another value (maybe its ok).Thus , I tried through Laplace with shorter calculations a new family of results(even more incoherent than before) came. At last, I tried to solve it in the time domain and a third family of results came (much more incoherent).I believe I may be failing but I don´t know where and how...I´ve just bought a personal version of Mathematica
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Posted 9 years ago
 Now, after some go-and-come, with a complete support from Wolfram team I find myself astonished and completely satisfied with Mathematica. Everything is running very well along my postodoc project and I am very glad!
Posted 9 years ago
 Files to be taken into acoount...matrizes_início is the step by step version (Laplace), Laplace Tranform is its short version and Time Domain is self explanable... Attachments: