## 3 Theoretical Analysis
### Algorithm Flow  
The overall process of this algorithm can be described as follows (Algorithm 1). ```
1: Obtain electric power signal \(X(i)=[x(1),x(2),\cdots,x(\text{N})]\). 2: Construct electric energy signal \(X(i)\) as Hankel matrix \(\mathbf{H}_{m\times n}\). 3: Perform SVD decomposition of matrix \(\mathbf{H}_{m\times n}\): \(\mathbf{H}_{m\times n}=\mathbf{U}_{m\times m}\mathbf{\Sigma}_{m\times n}\mathbf{V}_{n\times n} ^{T}\). 4: Select order \(k=2\) of the eigenvalue matrix \(\mathbf{\Sigma}_{m\times n}\) and set all eigenvalues after the second eigenvalue on the diagonal of matrix \(\mathbf{\Sigma}_{m\times n}\) to zero to obtain matrix \(\mathbf{\Sigma}_{m\times n}^{2}\). 5: Perform the reverse operation of SVD decomposition and reconstruct matrix \(\mathbf{H}_{m\times n}^{2}\) after denoising according to \(\mathbf{U}_{m\times n}\mathbf{\Sigma}_{m\times n}^{2}\mathbf{V}_{n\times n}^{T}=\mathbf{H}_{ m\times n}^{2}\). 6: Reconstruct one-dimensional signal \(X^{2}(i)\) according to matrix \(\mathbf{H}_{m\times n}^{2}\). 7: Calculate \(ESNR(2)\) of one-dimensional signal \(X^{2}(i)\) according to Equation (6). 8: Select order \(k=4\) of the eigenvalue matrix \(\mathbf{\Sigma}_{m\times n}\) and set all eigenvalues after the fourth eigenvalue on the diagonal of matrix \(\mathbf{\Sigma}_{m\times n}\) to zero to obtain matrix \(\mathbf{\Sigma}_{m\times n}^{4}\). 9: Perform the reverse operation of SVD decomposition and reconstruct matrix \(\mathbf{H}_{m\times n}^{4}\) after denoising according to \(\mathbf{U}_{m\times n}\mathbf{\Sigma}_{m\times n}^{4}\mathbf{V}_{n\times n}^{T}=\mathbf{H}_{ m\times n}^{4}\). 10: Reconstruct one-dimensional signal \(X^{4}(i)\) according to matrix \(\mathbf{H}_{m\times n}^{4}\). 11: Calculate \(ESNR(4)\) of one-dimensional signal \(X^{4}(i)\) according to Equation (6). 12: Calculate rate of change between \(ESNR(4)\) and \(ESNR(2)\) according to \(f(k)=0.5\times[ESNR(k+2)-ESNR(k)]\). 13: If rate of change does not meet \(f(k)<0.1\), order \(k=6\) of the eigenvalue matrix \(\mathbf{\Sigma}_{m\times n}\) is selected, and steps 8-12 are repeated to obtain \(ESNR(6)\); rate of change between \(ESNR(6)\) and \(ESNR(4)\) is calculated; order \(k\) is chosen by adding two to the previous \(k\) value. 14: When \(f(k)<0.1\) holds for the first time, the current \(k\) (i.e., optimal order for SVD denoising) and the one-dimensional signal \(X^{k}(i)\) corresponding to the current \(k\) (i.e., electric energy signal after denoising) are retained. 15: Apply the Prony algorithm for fitting analysis on \(X^{k}(i)\). 16: Calculate the dominant factors of each frequency component in the fitting results according to Equation (19) and screen fitting results through Equation (20) to obtain the final detection results of harmonic and interharmonic signal parameters in the electric power signal (i.e., amplitude, frequency and phase). The flowchart of this algorithm is shown in Figure 3.

## 4 Simulation Analysis

To verify the effectiveness of the proposed method for the detection of harmonics and interharmonics in power systems, a simulation analysis is carried out in this study. An electric power signal containing fundamental waves, harmonics and interharmonics is constructed according to literature [22]. \[ \begin{array}{ll}y(t)&=50.4e^{-0.095t}cos(100\pi t+0.4\pi)+25e^{-0.32t}cos(300 \pi t+0.6\pi)\\ &+8.5e^{-1.54t}cos(276\pi t+0.8\pi)+6.2e^{-0.34t}cos(700\pi t+0.89\pi).\end{array}  \tag{21}\]

The sample frequency is set as 4000 Hz, the number of sample points is set as 1200, and the order of the Prony model is set as 0.1 N, (i.e., \(p=120\)). The \"awgn\" function is used to apply 5 dB, 10 dB, 20 dB and 30 dB white Gaussian noise to the signals, respectively,

Figure 3: The flowchart of this algorithm. resulting in four groups of signals with noise. The waveforms of the four groups of signals with noise and the noiseless signal are shown in Figure 4. The harmonics and interharmonics of the four groups of noisy signals are detected by the Algorithm 1.