A technique for measuring the current-voltage characteristics (IVC) of a nonlinear inertia-free element from the amplitude spectrum of a current curve obtained by decomposing it into a Fourier series is given. The initial data for the method are the curves of current and voltage on a nonlinear element, measured for different points in time. The IVC is represented as a ratio of power polynomials whose coefficients are determined by the Cholesky method. Examples of measurement of the current-voltage characteristics are given, estimates of the relative and absolute error of the approach are given. The advantage of the proposed approach in comparison with the existing ones is the better accuracy of the reproduction of the IVC.

A method for determining the optimal state of the electrical network according to the criterion of minimum active losses using a genetic algorithm is presented. The algorithm is implemented in the programming language Visual Basic. The advantages of the proposed approach in comparison with the brute force are the reduced brute force required to determine the optimal scheme, the flexibility of setting the user controlled values. The practical significance lies in the possibility of implementing the approach of a distribution grid company and solving optimization problems in a timely manner. The algorithm was tested on 10-35 kV electrical network diagrams.

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The technique of assessing the state of the power network with two independent nodes of the radial and magistral structure is given. The advantages of the proposed approach in comparison with numerical methods are the efficiency of calculations. The theoretical significance lies in the possibility of expanding the presented approach on networks with a large number of independent nodes. Practical significance lies in the possibility of applying the results obtained to calculate the parameters of the electric network during its preliminary decomposition. The obtained formulas are tested on models of the electric network of the radial and magistral configuration.

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