## 3 Theoretical Analysis
### Algorithm Flow
However, the corresponding amplitudes are 50.6543 V and 36.9181 V, respectively, which greatly deviate from the actual values. In contrast, the proposed method detects the frequency components at 49.9946 Hz, 149.9963 Hz, 137.8659 Hz and 349.9532 Hz, respectively, all very close to the simulation signal. Meanwhile, the corresponding amplitudes of the four frequency components are 50.2379 V, 24.8951 V, 8.7083 V and 6.1268 V, and the corresponding phases are 71.7320\({}^{\circ}\), 107.1586\({}^{\circ}\), 141.9504\({}^{\circ}\) and 160.7258\({}^{\circ}\). The amplitudes and phases of the four frequency components are also significantly close to the actual parameters of the simulation signal. For the 10 dB noisy signal, the Prony algorithm only detects three frequency components close to the simulation signal, namely 49.9528 Hz, 150.1750 Hz and 350.1351 Hz. The corresponding amplitudes are 50.9132 V, 27.2627 V and 7.3542 V, which are significantly different from the actual values. By contrast, the proposed method detects four frequency components at 49.9963 Hz, 150.0043 Hz, 137.9901 Hz and 350.0049 Hz, which are very similar to those of the simulation signal. The corresponding amplitudes of the four frequency components are 50.4065 V, 25.1007 V, 8.6343 V and 6.2607 V, and the corresponding phases are 72.3173\({}^{\circ}\), 107.9841\({}^{\circ}\), 143.9876\({}^{\circ}\) and 160.4478\({}^{\circ}\). Hence, the amplitudes and phases of the four frequency components also closely aligned with the parameters of the simulation signal. As for the harmonic detection results of the 20 dB noisy signal, the Prony algorithm detects five frequency components similar to the simulation signal, namely 50.0017 Hz, 150.0270 Hz, 138.8344 Hz, 349.9924 Hz and 349.7109 Hz, but their corresponding amplitudes also significantly differ from the actual values. Meanwhile, the proposed method detects the components at 49.9994 Hz, 149.9997 Hz, 138.0054 Hz and 350.0015 Hz, all very similar to those of the simulation signal. The corresponding amplitudes of the four frequency components are 50.3869 V, 25.0419 V, 8.5718 V and 6.3054 V, and the corresponding phases are 72.0592\({}^{\circ}\), 108.0167\({}^{\circ}\), 143.8190\({}^{\circ}\) and 160.4092\({}^{\circ}\). The amplitudes and phases of the four frequency components are also significantly close to the parameters of the simulation signal. Finally, for the 30 dB noise signal, the Prony algorithm detects four frequency components similar to those of the simulation signal, namely 50.0016 Hz, 149.9883 Hz, 137.9193 Hz and 349.9786 Hz. The corresponding amplitudes are 49.8536 V, 24.6096 V, 11.9603 V and 5.9992 V. Except for 11.9603 V, other amplitudes are close to the actual values. The corresponding phases are 71.8437\({}^{\circ}\), 107.9125\({}^{\circ}\), 148.3649\({}^{\circ}\) and 161.4551\({}^{\circ}\), which are close to the actual values. In comparison, the proposed method detects the components at 49.9998 Hz, 150.0001 Hz, 137.9972 Hz and 350.0006 Hz, which are very similar to those of the simulation signal. The corresponding amplitudes of the four frequency components are 50.3943 V, 24.9830 V, 8.4957 V and 6.2310 V, and the corresponding phases are 72.0175\({}^{\circ}\), 107.9953\({}^{\circ}\), 144.1354\({}^{\circ}\) and 160.1573\({}^{\circ}\). The amplitudes and phases of the four frequency components closely match the parameters of the simulation signal. It can be noted that in the detection results of the 5 dB, 10 dB and 20 dB signals, the Prony algorithm detects false components far larger than those of the true amplitude, such as 368.3924 V and 149.8316 V in the detection results of the 5 dB signal, 292.7002 V, 83.3545 V in the 10 dB signal, and 85.2741 V in the 20 dB signal. All these false components have an impact on the selection of actual data. The detection result of the Prony algorithm deteriorates rapidly with increasing noise intensity, and the number of harmonics and related information in the signal cannot be effectively detected.