IEEE Power & Energy Society

Book Review

Coherency Theory

An Excellent Reference on the Subject

The book reviewed in this issue, Power System Coherency and Model Reduction, is an excellent reference on the subject, the reviewer states. The theme of coherency was also a topic of an earlier monohraph by the author, Time-Scale Modeling of Dynamic Networks with Applications to Power Systems.

Power System Coherency and Model ReductionPower System Coherency and Model Reduction

Joe H. Chow, editor

This is a timely monograph edited by Dr. Chow on an increasingly important topic. I learned a lot on the slow coherency theory of power systems from his previous book, Time-Scale Modeling of Dynamic Networks with Applications to Power Systems, published in 1982 by Springer. I was excited to read this new book.

Dr. Chow states at the beginning, “In the simulation of large power system dynamics for stability analysis on a digital computer, there is always a tug of war between capturing as much detail as possible in the simulation and completing the simulation in a reasonable amount of time so that the results can be useful.” For instance, power system engineers with the owners or operators of North American power transmission grids build their system models based on interconnection-wide models with 50,000 or more buses. The portions in their territories are modeled in greater detail while the portions from other territories or of lesser interest are usually represented by simplified equivalents to result in a customized overall equivalent model for daily use. Thus, an immediate challenge is to obtain an authentic equivalent model at a manageable scale.

Coherency, as a nature of power ­systems and other dynamic network ­systems, is found as key for model equivalencing and reduction, which is one of the themes of the 1982 monograph and of this new book as well. Today, coherency is becoming an even more attractive topic in power systems thanks to the increasing need for real-time power system situational awareness using wide-area synchrophasor measurements. ­Understanding the phenomena and nature of coherency is an approach to gain insights on power system dynamic patterns, oscillation modes, and potential stability issues. This book covers: 1) a summary of the original coherency and aggregation ­procedure and slow coherency theory, 2) recent applications of linear model reduction methods for power systems, 3) other methods for obtaining nonlinear reduced power system models, e.g., by artificial neural networks (ANNs), 4) application of synchrophasor measurements to create reduced-order models, and 5) tracing of interarea modes, i.e., phenomena of coherency.

The first chapter by Chow gives a brief literature review on power system coherency and model reduction. Model reduction techniques are introduced in two broad categories: 1) coherency and aggregation-based nonlinear power system model reduction and 2) input–output properties-based linear or nonlinear model reduction for external or less relevant parts of the system.

In Chapter 2, Podmore provides an overview of coherency and aggregation ideas, including key algorithms and engineering considerations for the identification of coherent generators, reduction of generator and load buses, and aggregation of generating unit models. EPRI’s DYNRED computer program is also introduced, which is one of the most widely used software tools for power system dynamic aggregation and reduction. Later in Chapter 7 by Morison et al., a practical case study is presented to illustrate how DYNRED is applied to create a reduced-order 7,000-bus model from a full WECC model to be used by BC Hydro’s EMS for online dynamic security assessment.

Chapter 3 by Chow gives an in-depth presentation of the theoretical and analytical basis of slow coherency and aggregation. The slow coherency theory arises from the fact that coherent groups of machines swing against each other at slower oscillatory frequencies, so-called interarea modes, than the local oscillation modes within individual groups. The chapter shows that the slow coherency phenomenon is attributed to the coherent areas being weakly coupled in the system. The singular perturbations theory is introduced to exploit the time-scale separation of the interarea and local modes, and then eigenvector-based grouping algorithms are presented for identification of coherent machines. Study results on an NPCC 48-machine system are presented to illustrate and compare aggregation algorithms. Chapter 4, by Chow et al., focuses on exciter aggregation and investigates a trajectory sensitivity method to tune parameters with aggregated nonlinear exciter models.

In Chapter 5, Vittal et al. introduce a hybrid dynamic equivalent consisting of both a coherency-based conventional equivalent and an ANN-based equivalent and test it on a system representing a portion of the WECC system. The idea behind the hybrid equivalent is to compensate for the discrepancy between the full system model and the reduced equivalent developed using, e.g., DYNRED, by providing appropriate power injections at all the boundary buses of the retained area.

Chapter 6 by Liu et al. introduces two mathematical approaches to model reduction based on Krylov subspace and balanced truncation methods, which focus on modeling the input–output behavior at the boundary buses of a study area. For example, the balanced truncation method, as an improvement of the Krylov subspace method, takes into account controllability and observability of the original models to obtain reduced-order models of the external system. Thus, it preserves key system characteristics while removing redundant information for handling a very large system. The system model is updated based on sensitivity analysis to ensure that the reduced-order model follows the actual system.

Chapter 8 by Chakrabortty et al. focuses on constructing simplified interarea models of large power systems by using dynamic measurements from synchrophasors installed at selected points on key power transfer paths. A measurement-based interarea model estimation method is introduced and illustrated using the WECC system, and its potentials in wide-area monitoring are investigated.

Chapter 9 by Rouco et al. introduces a selective modal analysis framework for the modeling, analysis, and control of selected dynamics of systems described by large linear time-invariant models. The roles of participation factors in the identification of dynamic patterns, design of damping controllers, and reduced-order eigen analysis are emphasized and discussed.

Chapter 10 by Vanfretti et al. demonstrates that the analysis on interarea oscillations observed from synchrophasor measurements of network variables, such as voltages and line currents, helps trace how electromechanical oscillations spread through the power network following a disturbance. The concept of “dominant inter-area oscillation paths” is developed to identify the passageways where the interarea modes of concern travel the most and is applied in feedback input signal selection for damping controller design.

In summary, I enjoyed reading this monograph and would highly recommend it. It is an excellent reference providing an overview of power system coherency, model reduction, and related problems by integrating analytical bases, engineering practices, emerging techniques, and insights, which would benefit both engineers and researchers in the fields of power system dynamics.

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