An eigensystem realization algorithm based data-driven approach for extracting electromechanical oscillation dynamic patterns from synchrophasor measurements in bulk power grids

Multichannel continuous wavelet transform approach to estimate electromechanical oscillation modes, mode shapes and coherent groups from synchrophasors in bulk power grids

The electromechanical dynamic patterns of the power system, which normally refer to electromechanical oscillation dominant modes, mode shapes, participation factors and coherent groups, are important for the study of power system dynamic behaviours. Different from the existing measurement-based methods which mainly estimate one or two facts of dominant modes, mode shapes or coherent groups, a holistic data-driven estimation approach is developed to estimate all the four electromechanical dynamic patterns from the measurements systematically and estimate the participation factors from measurements. In the developed approach, the multichannel continuous wavelet transform is firstly employed to dominant modes and mode shapes estimation. Besides, the estimated mode shapes are used to calculate the left eigenvalue vectors of the dominant modes. With the estimated mode shapes and left eigenvalue vectors, the participation factors are solved and coherent groups are separated. Finally, the proposed data-driven approach is evaluated by the 16-machine, 68-bus test system and China Southern Power Grid. The results validate that the proposed data-driven approach can accurately estimate all the four electromechanical dynamic patterns from synchrophasor measurements in a single way.

This study proposes a novel spatial‐temporal decomposition approach for systematically tracking dominant modes, mode shapes and coherent groups in bulk power systems using measurement data. First, components of the dominant oscillation modes, including frequencies and damping ratios, are identified from measurement data through a proposed recursive continuous wavelet transform. Second, cross‐wavelet transform is employed to estimate the mode shapes using the wavelet coefficient of the dominant modes. Furthermore, a reconstructed wavelet coefficient, which integrates the wavelet coefficients of all the estimated dominant modes, is used to identify the coherent groups of generators via the cross‐correlation coefficient. The proposed approach is evaluated on the simulation data from 16‐machine 68‐bus test system and China Southern Power Grid (CSG) as well as the field‐measurement data collected from phasor measurement units of CSG. It is demonstrated that the proposed approach performs with high accuracy, robustness and efficiency in tracking dominant modes, mode shapes and coherent groups in the bulk power systems.

Mode, mode shape, and participation factor are important modal parameters in small signal stability analysis. Most of the existing measurement-based methods focus on mode or mode shapes estimation, few of them explore the participation factors estimation. This paper proposes a multichannel modal analysis approach to estimate not only dominant modes and mode shapes, but also participation factors from synchrophasor measurements. The wavelet power spectrum is first applied to primary wavelet coefficient matrices of multichannel measurements to detect the critical scale ranges associated with the dominant modes, and new wavelet coefficient matrix with same critical scale in the detected scale ranges are constructed from the primary wavelet coefficient matrices. Applying singular value decomposition to these constructed matrices whose scales located in a range associated with one dominant mode, a maximum singular value vector is formed from each singular value matrix. Using the right and left singular value vectors of the maximum component in the formed maximum singular value vector, the dominant modes and mode shapes are all estimated. Meanwhile, the corresponding participation factors of the generators associated with the determined dominant mode are solved via the estimated mode shapes and their inverses. The proposed approach is tested and evaluated on a 16-machine 68-bus test system. The results demonstrate high accuracy and efficiency of the proposed approach in the estimation of dominant modes, mode shapes and participation factors utilizing synchrophasor measurements.

Synergistic data analytics for electromechanical oscillation in electric power systems

Power system inter-area oscillations curtail the power transferring capabilities of the transmission lines in a large interconnected power system. Accurate identification of dominant modes and associated contributing generators is important to avoid power system failures by taking appropriate remedial measures. This paper proposes a multi-channel Improved Dynamic Mode Decomposition (IDMD) algorithm-based modal analysis technique using Synchrophasors measurement. First, a reduced-order dynamic power system model is estimated and using this model dominant oscillation modes, corresponding modes shapes, damping ratio, coherent group of generators, participation factors are determined. To improve the accuracy data stacking technique is used to capture detailed information of the system. An optimal hard threshold technique is utilized to select the most optimal model order to avoid uncertainties due to the presence of high level of measurement noise. The study results show that the proposed algorithm gives an accurate and robust solution even in systems having high level of noise in the measurement data. The performance of the proposed technique is tested on simulated data from two-area four-machine system and wNAPS 41-bus 16-generator system with PMU measurements corrupted with different levels of measurement noise. To further strengthen the viewpoint, the proposed method is validated on real-time PMU measurement from ISO New England data to validate the accuracy of the proposed work.

Multi‐order stochastic subspace identification (MOSSI) has been extensively used to estimate the electromechanical oscillation modes from probing, ambient and ringdown data. It has been validated with good performances, while the computational burden is still a major obstacle. This study develops a fast iterative MOSSI (FSSI) approach for computational enhancement of MOSSI in mode estimation. In the proposed approach, an initial cluster of eigenvalues is formulated through FSSI with repetitive calculations (RCs), and electromechanical oscillation mode separation (EOMS) is utilised to discriminate the electromechanical modes. The RCs within the FSSI is calculated through changing the model order successively over the defined range given by a mean of singular values based order determination strategy. Additionally, the proposed approach is highly reliable against prevalent measurement noises owing to RCs and the EOMS. The performance of the proposed method is evaluated in Kundur's two‐area test system by comparing with MOSSI, Prony and autoregressive moving average exogenous. Its applicability for both the ringdown and ambient data is also demonstrated with the phasor measurement units field‐measurement data from the China Southern Power Grid. The results confirmed the accuracy, robustness and efficiency of the proposed approach for oscillation mode estimation.

This paper presents a general approach for coherency detection in bulk power systems using the projection pursuit (PP) theory. Supported by the concept of center of inertia (COI) in power systems, the PP theory is employed to model the wide-area coherency detection as an optimization problem. In the proposed method, the optimal projection direction in high dimensional orthogonal space is explored in order to detect the coherent groups via the data from synchronous phasor measurement units (PMUs). Two quantitative indices constructed with projection assessment index (PI), the objective of the optimization model, are then defined in order to determine the critical coherent group and the dominant coherent groups. The coherency detection criterion and the implementation framework for the proposed approach are also presented. Simulation data from the 16-machine 68-bus test system and China Southern power Grid (CSG), along with actual field-measurement data retrieved from WAMS database in the CSG, are employed to demonstrate the effectiveness and applicability of the proposed algorithm under different disturbances. It is shown that the proposed methodology successfully detects the dominant coherent groups of generators and buses in bulk power system via the wide-area field-measurement data.

This study proposes to extend the numerical algorithm for subspace state space system identification (N4SID) for power grid electromechanical dynamics monitoring using the multi‐channel noisy synchrophasor measurements. The oscillation modes, mode shapes, participation factors and coherent groups are estimated in a comprehensive manner. It consists of five key steps: (i) estimation of power system state subspace model via N4SID; (ii) electromechanical modes discrimination from the trivial modes by developing the generalised inverse and mode assurance criterion; (iii) calculations of the mode shapes using the estimated states and output subspace matrices; (iv) estimation of participation factors estimated by the calculated mode shapes and (v) the generator coherency identification by developing the direction cosine denoted coherency inductor. Test results on the IEEE 16‐machine 68‐bus test system and the practical China Southern power Grid using field synchrophasor measurements are performed. Comparison results with other existing methods show that the proposed method achieves better accuracy and efficiency for power system electromechanical dynamics monitoring in the presence of measurement noise.

Ambient-based oscillation modes extraction is an effective means of monitoring the small signal stability of a power system on-line. In this study, a data-driven approach based on output-only observer/Kalman filter identification (O3KID) combined with the eigensystem realisation algorithm (ERA) was proposed to extract electromechanical modes (frequency, damping ratio and mode shape) from synchronised ambient data. As a key for extracting a reduced-order state matrix using the ERA, the Markov parameters (impulse responses) are first estimated by employing O3KID on multi-channel ambient data. O3KID makes it possible to identify the modes with the ERA using only output ambient data, while ensuring the reliability of the extractions of frequencies, damping ratios and mode shapes. The performance of the proposed method was evaluated by employing the IEEE 16-generator 5-area system and measured data from a real power system. The estimation results in all cases as well as comparison results with the RDT-ERA method and NExT-ERA method indicate that the O3KID-ERA method is a promising method for ambient data-driven electromechanical oscillation modes extraction.

Technical analyses of several recent power blackouts revealed that a group of generators going out-of-step with the rest of the power system is often a precursor of a complete system collapse. Out-of-step protection is designed to assess the stability of the evolving swing after a disturbance and take control action accordingly. However, the settings of out-of-step relays are found to be unsatisfactory due to the fact that the electromechanical swings that occurred during relay commissioning are different in practice. These concerns motivated the development of a novel approach to recalculate the out-of-step protection settings to suit the prevalent operating condition. With phasor measurement unit (PMU) technology, it is possible to adjust the setting of out-of-step relay in real-time. The setting of out-of-step relay is primarily determined by three dynamic parameters: direct axis transient reactance, quadrature axis speed voltage and generator inertia. In a complex power network, these parameters are the dynamic parameters of an equivalent model of a coherent group of generators. Hence, it is essential to identify the coherent group of generators and estimate the dynamic model parameters of each generator in the system first in order to form the dynamic model equivalent in the system. The work presented in this thesis develops a measurement-based technique to identify the coherent areas of power system network by analysing the measured data obtained from the system. The method is based on multivariate analysis of the signals, using independent component analysis (ICA). Also, a technique for estimating the dynamic model parameters of the generators in the system has been developed. The dynamic model parameters of synchronous generators are estimated by processing the PMU measurements using unscented Kalman filter (UKF).

Spectral fitting approach to estimate electromechanical oscillation modes and mode shapes by using vector fitting

Fast and accurate identification of coherent generator groups is helpful in dynamic and transient stability analysis as well as other applications such as controlled islanding. In this study, a new method is presented for predicting the generators’ grouping scheme based on the data measured before and in a short time after the disturbance occurrence. To do that, a classifier model is trained using a training dataset. In the training dataset, the input is the attributes, which are obtained directly or indirectly from the data measured by phasor measurement units. On the other hand, the target in the training dataset is the generators’ grouping, which in this study is calculated using a new method called subtractive technique. In subtractive technique, coherent generator groups are determined based on the generator density values. When the classifier model is built using the training dataset, it can be used for online applications. In this study, the well‐known 68‐bus, 16‐machine power system as well as the Iranian 400 and 230 kV south east regional grid are used as the test systems for investigating the efficiency of proposed coherent group prediction method. Results show that the proposed method can predict the generators’ grouping scheme with high accuracy.

In this paper, a novel method that integrates the improved empirical mode decomposition (EMD) and signal energy algorithm is proposed to estimate the dominant oscillation parameters and corresponding mode shape. Firstly, the EMD with symmetrical extrema extension (SEE) is utilized to decompose the measured data from wide area measurement system (WAMS) into a finite set of intrinsic mode functions (IMFs). Then, the signal energy algorithm is used to calculate the approximate oscillation parameters of the IMFs. The nodes involved the dominant oscillation mode are classified based on the calculated frequency and reasonable threshold. Furthermore, for the dominant oscillation mode, the IMF with maximum mean amplitude is defined as the reference. Next, the relative phases (RPs) between the reference IMF and other IMFs are calculated in order to identify the negative and positive oscillation groups. According to the values of RPs, the coherent group and corresponding node contribution factor (NCF) can be identified, and the dominant approximate mode shape (AMS) can also be determined. The efficiency of the proposed approach is tested by applying it to synthetic signal and measured data from the simulation model.

Compared to traditional mode shape identification methods such as eigensystem realization algorithm (ERA), this article proposes a mode shape identification method based on estimated residues of measured data and the theoretical relationship between the estimated residues and the mode shapes from the state space model is obtained by defining a coefficient matrix. A mass-spring model with five degrees of freedom (DOFs) is utilized to demonstrate the approach. The numerical results indicate that the estimated residues are the mode shapes of structures, but with a coefficient matrix to maintain consistency with the mode shapes from the ERA. Using MATLAB a complicated numerical jacket platform is built to further study the proposed method. The results show that mode shapes consistent with those from the ERA could be obtained by taking the defined coefficient matrix into account, which is also demonstrated by a physical beam model that was built at Ocean University of China.