Mathematical modeling and computational principles for the analysis and simulation of long-distance energy systems

Methods for the modeling and simulation of long-distance energy systems are considered. Due to Kirchhoff's laws a special type of non linear equation is crucial for the steady state and the transient analysis. A reliable algorithm to solve these equations based on Newton's method is presented. The uniqueness of the solution and the convergence of the method are proved by the stability theory of Liapunov. To apply this method, the calculation of some derivatives is necessary. An approach for C++ to do this in an automatic way without rewriting a program is presented.