# Model development according to increase in the active resistance of the conductor to ac current at the surface effect

## Authors

• V.M. Prokuda Dnipro University of Technology, Ukraine
• N.YU Rukhlova Dnipro University of Technology, Ukraine

## Keywords:

cable line, heating, higher harmonics, regression, coefficient of determination, MATLAB Simulink, active resistance, surface effect

## Abstract

Purpose. When alternating current with higher harmonics passes through the cable, heating is carried out by the root mean square value of all harmonics. Taking into account the different resistance of the cable depending on the frequency due to the effect of the surface effect, it is advisable to calculate the coefficient of increase in the total current resistance, assuming the action of each harmonic as independent. However, there are prerequisites to consider existing calculation models difficult for algorithmic implementation in software packages. Therefore, the purpose of the work is to develop a calculation model to take into account the increase in the active resistance of the conductor to alternating current due to the surface effect for further use in simulation modeling packages such as, for example, MATLAB.

Methodology. Methods of linear algebra, linear regression, defining the coefficient of determination.

Findings. Dependencies for determining the resistance value of high-voltage cable lines to high-frequency currents, which take into account the cross-section and harmonic composition of the current, have been obtained. According to the existing and substantiated graphs (dependencies) obtained on the basis of classical expressions from the literature, new simplified calculation dependencies were obtained (for the cross-section of copper cable lines 240 - 1000 mm2) when current harmonics above the fifth at a base frequency of 50 Hz. Such calculated ratios will allow taking into account several harmonic components of the current during line heating in the MATLAB Simulink software environment.

The obtained values of the coefficient of determination in defining the calculated dependencies are close to 1, which indicates the correctly selected type of equation and the correctly selected coefficient k for different cross-sections of the cable line.

Originality.  The scientific novelty lies in the development of a new dependence, justified by the high value of the multiple correlation coefficient, the correction factor for the increase in the resistance of the cable core from the harmonic number and the empirical coefficient of the regression model, taking into account the cross section of the cable line.

Practical value.  The practical value of the work consists in obtaining dependencies that can be used in analytical and simulation models when determining the amount of heating of cable lines taking into account the current of harmonics above the fifth at a base frequency of 50 Hz. Such an application will allow in many cases to replace the physical experiment with a simulation in the MATLAB Simulink software environment, which will reduce the necessary human and material costs.

## Author Biographies

### V.M. Prokuda, Dnipro University of Technology

Ph.D, in Technology, assistant of the Electrical Power Engineering Department of the Dnipro University of Technology, Dnipro

### N.YU Rukhlova, Dnipro University of Technology

PhD, in Technology assistant of the Electrical Power Engineering Department of the Dnipro University of Technology, Dnipro

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2022-10-30

## How to Cite

Prokuda, V., & Rukhlova, N. (2022). Model development according to increase in the active resistance of the conductor to ac current at the surface effect . Electrical Engineering and Power Engineering, (3), 7–14. https://doi.org/10.15588/1607-6761-2022-3-1

Electrotechnics