The thesis presents a theoretical analysis and development of an open-source program for calculating energy flows in the EES. The work begins with a description of the theoretical foundations of modeling network elements, consisting of an alternative Pi-model of a transmission line, transformers and synchronous generators. Based on these models, the composition of the network admittance matrix is presented, which enables a mathematical description of connections and interactions between system nodes. To solve the problem of energy flow in the EES, the multidimensional Newton–Raphson method is used, which enables fast convergence when solving nonlinear systems of equations. The work derives equations for calculating active and reactive power and describes in detail the composition of the Jacobian matrix. The practical part of the thesis includes the development of one's own program, which is based on previously processed theoretical starting points. The program allows the input of arbitrary topologies of power networks and their parameters, automatic generation of the admittance matrix and calculation of power flows on all network elements. The results of testing on a sample network confirm the correctness of the implementation and compliance with calculations using standard methods. Due to its open-source nature, the developed solution allows for further expansion and customization, making it suitable for both research and educational purposes in the field of electrical power engineering.
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