Waveform Analysis of Non-Sinusoidal Electrical Signals Using Cubic Spline Interpolation

The steady increase in nonlinear loads in modern electric power systems leads to distortion of electrical signal waveforms and, consequently, to deterioration of power quality. The presence of higher harmonics in the network adversely affects electrical equipment, especially capacitor banks. The classical harmonic analysis method based on the discrete Fourier transform has a number of drawbacks; therefore, the authors propose a new approach to analyzing voltage and current waveforms using cubic spline interpolation, which has not previously been applied as an independent method for analyzing electrical signals. The paper examines in detail the application of harmonic analysis and spline interpolation methods for standard equivalent circuits of loads: with a resistive-inductive load and with a connected capacitor bank. Computer simulation using Multisim software revealed that spline interpolation not only achieves accuracy comparable to that of harmonic analysis but also outperforms it when analyzing supply voltage waveforms at the connection point and current waveforms flowing through the capacitor bank, including when interharmonics are present in the network. Thus, the approach presented in the paper, based on the use of spline interpolation, can be recommended for application in the design, calculation, and reliability assessment of power supply systems, as well as in power quality monitoring and metering.