# Identification of Mode Shapes Based on Ambient Signals and the IA-VMD Method
## 5 Simulation
### Analysis of the Measured Signal  
To prove the effectiveness of the method proposed in this paper, the actual oscillation data of a real power grid are selected, and the method is used to identify and analyze the oscillation modes of the measured signal. The actual oscillation signal collected from the real power grid is shown in Figure 5. When the system runs to 130 s, an obvious oscillation signal appears. After 20 s, the oscillation diverges rapidly, and the power grid alarms at the same time. After 170 s, the oscillation begins to attenuate, later returning to normal. Before the obvious oscillation of the system occurs, there is a small amplitude fluctuation in the system between 70 and 120 s. However, at this time, the system considers that the ambient data are generated by the normal electrical operation of the power grid and does not give an alarm, and the system has a significant disturbance approximately 20 s after the noise-like attenuation. The data interval between the ambient signal and the obvious oscillation signal is shown in Figure 5. Considering the possibility of broadband oscillation, the sampling frequency of the signal is 100 Hz in this paper. The data can be classified into normal data and abnormal data. Ambient signals are a type of normal data, while oscillation signals are a type of abnormal data. The ambient signals of 65-110 s and the obvious oscillation signals of 165-210 s are selected as the research objects, and the operation characteristic modes are identified by the method proposed in this paper. The obvious oscillation signal is shown in Figure 6, and the ambient signal is shown in Figure 7.  
Figure 5: The actual oscillation signal collected. Figure 7 shows that the oscillation amplitude is small and the amplitude fluctuation is less than 10 MW. In addition, the signal-to-noise ratio (SNR) of this signal is low, so the signal is easily affected by environmental noise, and it is more difficult to identify the oscillation information from the ambient noise signal. We find that the characteristic of the ambient signal is not obvious. Observing Figure 6, we find that the oscillation signal has an obvious oscillation mode, and the oscillation amplitude is higher; the maximum value is over 100 MW, not less than 30% of the active power of the system. The signal has a high SNR, is less affected by environmental noise, and is easy to identify. The IA-VMD method is used to address the obvious oscillation signal, and the oscillation mode signals in each frequency band after the first decomposition are shown in Figure 8. Then, IMF4 is ignored by the signal energy method. So, three main oscillation modes are obtained from the obvious oscillation signal by the IA-VMD method. The parameters of the main oscillation modes are identified, and the LFO parameters are obtained, as shown in Table 2.  
Figure 8: Intrinsic mode functions (IMFs) extracted from the obvious oscillation signal. Figure 6: Obvious oscillation signal collected. Figure 7: Ambient noise signal collected. The main oscillation modes decomposed by the IA-VMD method were identified by the Prony algorithm and compared with the MF-Prony method and the EMD-Prony method. The results are shown in Table 2. Table 2 shows that when there are obvious oscillation signals in the processing system, the above three methods can identify a variety of oscillation modes. Relatively speaking, the identification results of this method are close to those of the EMD-Prony algorithm. It can be concluded that the oscillation caused by this accident consists mainly of two obvious oscillation modes. The dominant oscillation frequency is approximately 1.48 Hz, and the secondary dominant oscillation frequency is approximately 2 Hz. Compared with the two algorithms above, the MF-Prony algorithm has a certain deviation in identification results.