# Synthetical Modal Parameters Identification Method of Damped Oscillation Signals in Power System
## 1 Introduction  
The safety of the electric power supply affects national economy and social development, while the key to the safe operation of the power system lies in the stability of the system [1]. During the operation of the interconnected power system, oscillations frequently occur, where the low-frequency oscillation (LFO) is a detrimental fault threatening the stability of the system, which refers to the relative swing between the rotors of generators running in parallel in power systems under disturbance, and leads to an incessant oscillation within 0.1-2.5 Hz for lack of damping [2, 3]. The 1996 system blackout in the Western Electricity Coordinating Council (WECC) system makes people aware of the importance of monitoring and controlling the LFO [4]. The first step to analyze LFO is modal identification, which acquires the modal parameters of the oscillations for taking suitable measures to enhance the stability of the system. LFO mode identification methodology can be mainly divided into the analysis based on numerical solutions and that based on measured signals. The traditional linearization method is to identify these low-frequency modes through eigenvalue analysis, which requires a lot of information about the modeling of the system, lacking satisfactory precision. With the help of the wide area measurement system (WAMS) and phase measurement unit (PMU), the operation data of the power grid with a high-precision time scale can betransmitted to the control center, realizing the real-time data collection and monitoring of wide-area power grid [5]. The methods of analyzing the measured data and identifying the LFO mode primarily include fast Fourier transform (FFT) [6], wavelet transform [7], Prony [8], stochastic subspace identification (SSI) [9], auto-regressive and moving average (ARMA) [10], Hilbert-Huang Transform (HHT) [11], and so forth. FFT cannot analyze the damping characteristics and local characteristics, so it is not suitable for nonlinear and non-stationary signals. Wavelet transform has the problems of frequency overlap and adaptive basis selection and is only suitable for transient and non-stationary signals. Both Prony and SSI have problems with estimation of order and sensitivity to noise which bring in false modes when analyzing the oscillation signal of the non-stationary power system. The ARMA model method establishes a mathematical model for ordered discrete random data to obtain the inherent parameters of the system, whereas it is easily affected by noise and still has the problem of order determination as Prony and SSI. Although the HHT algorithm is suitable for non-stationary and nonlinear signals, it is affected by the end effect. These methods mentioned above have a certain ability to identify partial modal parameters, but the accuracy of identification is unacceptable yet. The damped low-frequency oscillation (DLFO) signal is one of the most common transient signal forms, which is often related to mechanical and circuit faults, especially in the power system. To solve the problems of insufficient precision and parameters in modal identification of DLFO, the synthetical modal parameters identification (SMPI) method, a comprehensive method, is presented by integrating the advantages of empirical mode decomposition (EMD), SSI, and Prony. In the SMPI method, the DLFO signals are, firstly, decomposed into several intrinsic mode functions (IMF) to filter high-frequency noise by EMD. Then, the Prony and SSI approaches are adopted to identify the modal parameters of the filtered signals after EMD, respectively. Lastly, the proposed parameters matching method is developed to match the accurate modal parameters of DLFO in line with the similar frequencies recognized by SSI and Prony and avoid the difficulty of estimation of model order. The proposed SMPI method is demonstrated by implementing case studies. In what follows, Section 2 introduces the theory and methods of SMPI including the EMD, SSI, and Prony algorithm.