A fast algorithm for coherency identification and dynamic equivalencing of power systems

In substations, shielded cables are widely used to reduce transient electromagnetic interference to the relay and control equipments due to the switch operation. Both the transfer impedance and transfer admittance are quantities for expressing numerically the mechanism that allows the passage of electromagnetic energy across the cable shield. Theoretical models to compute both the quantities often rely on simplifying assumptions. This, together with the fact that the transfer impedance and admittance can vary considerably between cable samples of the same type, means that measurements become necessary. In this paper, based on the transmission line theory we present a simple method to measure the transfer impedance and admittance of shielded cable in magnitude as well as in phase over the frequency range (0.1 MHz-10 MHz) which covers the main interference frequencies in power system. To illustrate this method a coaxial cable with a braided shield has been measured and compared with the existing method. As an application, the proposed method is used to predict the induced voltage and current on the shielded cable due to the switch operation in substation.

The development of the modern Global Positioning System (GPS) technique makes the real time monitoring of the generator status workable. However it is impractical and unnecessary to install GPS devices at all generators due to the high cost. Observations and calculations indicate that most of the generators in a large power system have some similar transient power angle characteristics. Therefore the generators can be grouped according to the similarity of their power angle characteristics, and within each group only one generator is required to install GPS device to monitor the real time status of all the generators in the group. Based on the coherence group theory, the coherence groups of the generators are irrelevant to the magnitude of disturbance and the details of the generator unit model. Therefore, by building a classical synchronous generator linear system model, an accessible Gram matrix model can be derived. Then according to the generator identification rule of ε-coherence (or coherent group), the generator coherence groups can be identified in a large power system. The methodology can facilitate the real time monitoring of generators' status and the real-time control based on the GPS technique.

A new approach for online coherency identification in power systems based on correlation characteristics of generators rotor oscillations

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.

The high complexity and long computation time in simulating dual‐active‐bridge (DAB)‐based parallel DC microgrid systems pose significant challenges. To address this, coherency identification and aggregation algorithms (CIAA) for multi‐DAB parallel DC microgrid systems (MDPDMS) are proposed. First, a correlation model between common DC bus voltage disturbances and measurable DAB output quantities is established. Using output current fluctuation similarity as the coherency criterion, a dynamic similarity index is derived. Coherent DAB groups (CDGs) are then adaptively identified using the K‐Medoids algorithm, with the clustering results refined by a defined cost function. Second, under the core constraints of power conservation and dynamic response equivalence, a mapping is established between the equivalent model (EM) and the internal topology and control parameters of the CDG to accurately aggregate parameter‐heterogeneous DABs. The proposed method maintains high fidelity to the dynamic characteristics of the detailed system (DS) while significantly improving simulation efficiency. The simulation time of the reduced‐order system (ROS) is only 56% of that required by the detailed system.

A novel nonparametric system identification (SI) algorithm is described, focusing on PID-based control loops for buck converters with effective series resistance (ESR) in the output filter. Dithering amplification effects on the control path are exploited during the steady-state converter operation. The noise injected is used to stimulate the loop reaction and to identify the output filter configuration. Oversampling-dithering features of third-order $\Delta \Sigma$ modulators are used to increase the DPWM resolution during the converter nominal operation and, moreover, as the core key to compute the SI algorithm. A modified structure of a noise shaper is used to handle the resolution of the SI algorithm over a range of the desired frequencies during the nonparametric identification. The SI algorithm comprises two steps: the first processing step extracts the resonant frequency, and the second extracts the ESR zero from the power spectrum density computation of the control feedback error. The SI method has been validated with different buck converter configurations, and has successfully been integrated and measured into a digitally controlled buck converters prototype for automotive safety application.

Model reduction techniques are often applied to large-scale complex power systems to increase simulation performance. The bottleneck of existing methods to get a high reduction ratio lies in: (1) Coherency identification is static and conservative. Some coherent generators are not detected when system topology or operating point changes. (2) Solitary generators outside any coherency group are not aggregated regardless of their importance. To overcome the first problem, a measurement-based online coherency identification method was used in this paper. By analyzing post-fault trajectories measured by phasor measurement units (PMUs), coherency generators were identified through principal component analysis. The method can track conherency groups with time-varying system topology and operating points. To address the second problem, sensitivity analysis was employed into model reduction in this paper. The sensitivity of tie-line power flows against injected active power of external system generators was derived. Those generators having minimal impacts on tie-line power flows were replaced with negative impedances. Case studies show that the proposed method can handle well these solitary generators and the reduction ratio can be enhanced. Future work will include generalization of the sensitivity method.

The fraction model has been widely used to represent a range of engineering systems. To accurately identify the fraction model is however challenging, and this paper presents a regularised fast recursive algorithm (RFRA) to identify both the true fraction model structure and the associated unknown model parameters. This is achieved first by transforming the fraction form to a linear combination of nonlinear model terms. Then the terms in the denominator are used to form a regularisation term in the cost function to offset the bias induced by the linear transformation. According to the structural risk minimisation principle based on the new cost function, the model terms are selected based on their contributions to the cost function and the coefficients are then identified recursively without explicitly solving the inverse matrix. The proposed method is proved to have low computational complexity. Simulation results confirm the efficacy of the method in fast identification of the true fraction models for the targeted nonlinear systems.

This paper presented a reduced-order method for swing mode eigenvalue calculating based on fuzzy coherency recognition. First, we recognize the coherent generator groups using the fuzzy clustering method. Then we aggregated the generators in a coherent group into a single equivalent generator that the dimension of the state equation reduced evidently. Using QR algorithm to the reduced-order state equation we calculated the eigenvalues of the inter-area mode. The eigenvalues of local mode calculated by using QR algorithm to the sub-state matrices corresponding to the coherent groups separately. Thus, all eigenvalues of swing mode can be calculated. We have given detailed results of both the coherent generator groups recognition and the eigenvalues calculating of the 10-machine New England power system. The results shows that the method for eigenvalue calculation is simple and practical.

Fast ℓ1-recursive total least squares algorithm for sparse system identification

The paper presents one reduced-order Multi-Input-Multi-Output (MIMO) identification approach, Principal Hankel Component Algorithm (PHCA), for power system modal analysis and damping controller design. The PHCA method is modified, using finite pulse for signal excitation, and applied to the power system identification. The identification results show that it approximates the original system with tolerable error. The proposed method has the similar identification results compared with conventional ERA (Eigensystem Realization Algorithm) method in terms of identification accuracy under different SNR conditions and computation time consumption. A two-area four-machine system case is validated for the idea.

Identification of coherent generators groups in multi-machine power systems is an important step for both operation and control needs. This paper presents a new identification method based on the generators' rotor angular positions. The methodology consists of extracting the time-domain dynamic responses of generators to build a relationship matrix indicating the degree of coherency between any pair of generators. Then, by applying the Fuzzy C Mean (FCM) clustering, coherent groups are determined. The Centre of Inertia (COI) is used to represent the coherent group in order to visualize the global oscillations of the rotor angle of that particular group following a disturbance. Applications on the 10-machine New England power system show the feasibility and the validity of the proposed methodology.

A wide variety of procedures have been proposed for identifying a finite impulse response (FIR) linear system from the input and output of the system. Most recently, a fast, efficient, least-squares method was proposed by Marple, and was shown to require less computation and storage than any other known procedure for identifying moderate to large FIR systems. In this paper we measure the actual performance of the newly proposed fast system identification algorithm by using it to estimate a variety of FIR systems excited by either white noise or a speech signal. It is shown that essentially theoretically ideal performance is achieved for white noise inputs; however, for speech signals poor performance was obtained because of the lack of certain frequency bands in the excitation. A simple modification to the estimation procedure is proposed and is shown to provide substantial performance improvements. Using the spectrally modified speech signal, the performance of the fast system identification algorithm was found to be acceptable for a wide variety of applications.

The variable step-size least-mean-square algorithm (VSSLMS) is an enhanced version of the least-mean-square algorithm (LMS) that aims at improving both convergence rate and mean-square error. The VSSLMS algorithm, just like other popular adaptive methods such as recursive least squares and Kalman filter, is not able to exploit the system sparsity. The zero-attracting variable step-size LMS (ZA-VSSLMS) algorithm was proposed to improve the performance of the variable step-size LMS (VSSLMS) algorithm for system identification when the system is sparse. It combines the $${\ell _1}$$ -norm penalty function with the original cost function of the VSSLMS to exploit the sparsity of the system. In this paper, we present the convergence and stability analysis of the ZA-VSSLMS algorithm. The performance of the ZA-VSSLMS is compared to those of the standard LMS, VSSLMS, and ZA-LMS algorithms in a sparse system identification setting.

The authors propose a two-dimensional direction-of-arrival (DOA) estimation for multi-path environments, in which there are uncorrelated, partially correlated and coherent signals. The inability to identify non-coherent signals from coherent ones results in a considerable waste of sensors. In this work, an adaptive and automated threshold is considered for the efficient separation of noise, non-coherent signals, and coherent groups. First, non-coherent signals, coherent groups, and noise subspace are separated using k-medoids clustering. After determining the number of sources, non-coherent signals and coherent groups, non-coherent DOAs are estimated separately. The number of coherent signals in each coherence group is determined by the minimum descriptive length criterion. Finally, coherent DOAs are estimated in each group by constructing a coherent estimation matrix. The proposed method does not require any prior information such as knowing the number of signals or the covariance matrix of uncorrelated signals. The simulation results show that the proposed method is able to distinguish between the non-coherent and coherent signals, even at low signal-to-noise ratios and a small number of snapshots. Also, in terms of detection probability and estimation accuracy, it shows an improvement of over 1.2 and 83%, respectively, compared with the conventional forward−backward spatial smoothing scheme.