Slow Coherency Identification and Power System Dynamic Model Reduction by Using Orthogonal Structure of Electromechanical Eigenvectors

Abstract

Identifying generator coherency with respect to slow oscillatory modes has numerous power system use cases including dynamic model reduction, dynamic security analysis, or system integrity protection schemes (e.g., power system islanding). Despite their popularity in both research and industry, classic eigenvector-based slow coherency techniques may not always return accurate results. The multiple past endeavors to improve their accuracy often lack a solid mathematical foundation. Motivated by these deficiencies, we propose an alternative consistent approach to generator slow coherency. Firstly, a new approach is introduced to accurately detect slow coherent generators by effectively minimizing generic normalized cuts. As a by-product, the new approach can also guide the choice of the number of slow coherent groups. Secondly, it is shown that the combination of the the proposed slow coherency approach and an enhanced version of the inertial generator aggregation method allows to produce accurate dynamic equivalents even if the selected number of generator groups is relatively low.

Review of Clustering Methods for Slow Coherency-Based Generator Grouping

“…the state of the art, tying to discover clustering algorithms most suitable for the structure of the problem with data available as time series. In a few cases (e.g., [37] and [54]), the proposed versions include come characteristics of the technical problem in the solution technique.…”

“…In this respect, with reference to the selected contributions shown in Table I: -The number of clusters has to be preliminarily defined in many classical methods, such as kmeans [55], hierarchical clustering [18,46,53], and fuzzy c-medoids [34]. -Methods that do not require the preliminary definition of the number of clusters include non-parametric clustering methods, such as support vector clustering [29,30], the mean shift spectral clustering [22], the affinity propagation clustering versions [6,21], the spectral clustering versions [32,54], the thresholdbased clustering [37], the subtractive clustering [19], and the density-based spatial clustering of applications with noise (DBSCAN) [36].…”

“…Close relations between the notion of slow coherency and the use of normalised graph cuts have been shown in [54]. Starting from the second-order electromechanical model with neglected damping, the matrix that contains the synchronising torque coefficients between the generators is simplified by neglecting the components associated with the transfer conductances.…”

WAMS-Supported Power Mismatch Optimization for Secure Intentional Islanding

“…To set up an additional protection barrier, a so-called intentional controlled islanding (ICI) scheme has been presented and researched recently [5][6][7][8][9]. ICI is a corrective measure scheduled for activation only when the remaining set of SIPSs is fully exhausted and not capable of stabilizing the system on its own.…”

“…The two most evident drawbacks of the latter approach are (i) the dependence of calculation results on the pre-incident equilibrium point and (ii) not considering topology changes. As an improvement of this approach, spectral clustering is often used in combination with the advances of the slow coherency approach [9]. Nevertheless, some of the drawbacks remain, such as ignoring the possibility of transient stability occurrence ( [5,17]).…”