A Linearization of DFT Spectrum for Precision Power Measurement in Presence of Interharmonics

TL;DR

This work addresses accurate power metering in systems with interharmonics by introducing a linearization of the DFT spectrum that decomposes power into fundamental, harmonic, interharmonic, and cross terms. By expressing the DFT lines as $S_l(k)=\alpha_l/(\beta_l-k)$ and solving a derived linear system through eigen-decomposition and generalized Vandermonde mappings, the method recovers genuine frequency components and computes band-specific powers with high precision. Across extensive tests involving frequency shifts, noise, and closely spaced interharmonics, the proposed approach consistently outperforms FFT-based methods and MP-SVD in total and cross-power accuracy, while maintaining competitive computational efficiency (~6–8 ms per component) suitable for real-time metering. The results demonstrate improved robustness to asynchronous sampling and interharmonics, offering practical impact for accurate power measurement in modern grids with renewable integration.

Abstract

The presence of interharmonics in power systems can lead to asynchronous sampling, a phenomenon further aggravated by shifts in the fundamental frequency, which significantly degrades the accuracy of power measurements. Under such asynchronous conditions, interharmonics lose orthogonality with the fundamental and harmonic components, giving rise to additional power components. To address these challenges, this paper introduces a linearization algorithm based on DFT spectrum analysis for precise power measurement in systems containing interharmonics. The proposed approach constructs a system of linear equations from the DFT spectrum and solves it through efficient matrix operations, enabling accurate extraction of interharmonic components near the fundamental and harmonic frequencies (with a frequency interval $\geq$1 Hz). This allows for precise measurement of power across the fundamental, harmonic, interharmonic, and cross-power bands, as well as total power. Test results demonstrate that the proposed method accurately computes various power components under diverse conditions--including varying interharmonic/fundamental/harmonic intervals, fundamental frequency deviations, and noise. Compared to existing methods such as fast Fourier transform (FFT), Windowed interpolation FFT, and Matrix pencil-Singular value decomposition, the proposed technique reduces estimation error by several times to multiple folds and exhibits improved robustness, while maintaining a computational time of only 7 ms for processing 10-power-line-cycle (200 ms) data.

Figures (12)

• Figure 1: Division of power bands. Four categories of power bands are classified: the fundamental power band, the harmonic power bands, the interharmonic power bands, and the cross power bands.
• Figure 2: An example of spectrum leakage of a signal containing 50 Hz, 54 Hz, and 100 Hz components with amplitudes of 1, 0.1, and 0.1, respectively. (a) compares the real spectrum and the leaked spectrum. (b), (c) and (d) present spectrum leakage details.
• Figure 3: General metering process of the proposed algorithm.
• Figure 4: The average errors in frequency, amplitude and phase. From (a) to (c), $f_s$=5000 Hz, $N$=1024, and SNR= 60 dB.
• Figure 5: The average computation time. ($f_s$=5000 Hz, $N$=1024, and SNR= 60 dB.) The shaded region delineated by the dashed lines represents one standard deviation from the mean, calculated from 1000 iterations.