Ignacio J. Pérez-Arriaga

On sensitivities, residues and participations

This paper presents techniques for the evaluation and interpretation of eigenvalue sensitivities, in the context of the analysis and control of oscillatory stability in multimachine power systems. These techniques combine the numeric power of modal analysis of state-space models with the insight that can be obtained from transfer function descriptions. Relationships with tools from Selective Modal Analysis (namely, participations) are stressed. Examples of applications to a detailed multimachine power system model are given.

On sensitivities, residues and participations: applications to oscillatory stability analysis and control

Techniques are presented for the evaluation and interpretation of eigenvalue sensitivities, in the context of the analysis and control of oscillatory stability in multimachine power systems. These techniques combine the numeric power of model analysis of state-space modals with the insight that can be obtained from transfer-function descriptions. Relationships with tools from selective model analysis (namely, participations) are stressed. Examples of applications to a detailed multimachine power system model are given. >

Selective Modal Analysis With Applications to Electric Power Systems, Part II: The Dynamic Stability Problem

Selective Modal Analysis (or SMA) is a physically motivated framework for understanding, simplifying and analyzing complicated linear time-invariant (or LTI) models of dynamic systems [1,2,3]. SMA allows one to focus on any prespecified dynamic pattern of intrest in the model. In particular, One can efficiently and accurately compute the eigene values and eigenvectors of the natural modes of interest and their sensitivities, and also determine physically meaningful reduced order models containing these natural modes. SMA is particularly suitable for dealing with composite models, i.e. models consisting of several dynamic subsystems interrelated by static constraints. An introduction to the basic concepts of SMA pertinent to the applications being considered here is presented in the companion paper [3]. This paper concerns the application of SMA to the Dynamic Stability problem in electric power systems; it is shown how SMA is well suited to meet the demanding requirements of Dynamic Stability analysis. This is illustrated in [3] with examples, including a 60-machine model of a dynamic instability occurrence in an actual power system.

The Impact of Bidding Rules on Electricity Markets With Intermittent Renewables

The cycling regime of thermal power plants significantly increases in the presence of intermittent renewables, increasing fuel and operation and maintenance costs from startups. Some regional electricity market operators adopt complex bidding mechanisms to account for nonconvex cost components that are not reflected in the marginal cost of energy, while other markets rely solely on simple bids with revenue sufficiency conditions. This paper compares the impacts of different bidding rules on wholesale prices and on the remuneration of units in power systems with a significant share of renewable generation. We distinguish the effects of bidding rules from the effects of regulatory uncertainty that can unexpectedly increase renewable generation by considering two distinct situations: 1) an “adapted” capacity mix, which is optimized for any given amount of renewable penetration, and 2) a “nonadapted” capacity mix, which is optimized for zero renewable penetration, but operated with different nonzero levels of renewables. We show that, although in the transitory state the impact on remuneration of having a nonadapted system dominates over the effect of the startup remuneration mechanisms explored, in equilibrium, bidding rules play an important role in making power plants whole while impacting on the cost borne by consumers.

The role of participation factors in reduced order eigenanalysis of large power systems

The authors present a family of variable transformations which are aimed at improving the performance of selective modal analysis (SMA) algorithms. The value of such transformations has been assessed with participation factors and participation ratios. These transformations are applied at two subsystem levels: generator and area level. It is shown that their successive application allows an important order reduction while maintaining convergence of SMA algorithms. Emphasis is on a specific feature of a family of simple and physically meaningful variable transformations: the feasibility of accumulating the participation of the modes of interest on a few state variables.<<ETX>>

Measuring State Variable Participation for Selective Modal Analysis 1

Abstract A simple scale-invariant criterion is proposed for picking out state variables that significantly participate in the construction of selected modes of a linear time-invariant dynamical system. The criterion is of value in such approaches to modal reduction as Davisons method, singular perturbation methods, and our Selective Modal Analysis framework (which in several respects extends the former two methods, and in which the proposed criterion arises in a natural way). Application to sampled-data systems is also considered.

The Transmission of the Future: The Impact of Distributed Energy Resources on the Network

The Massachusetts Institute of Technology (MIT) study The Future of the Electric Grid, published in December 2011, examined challenges for power systems and concluded with a number of findings and recommendations. The study carefully separated recommendations for transmission from those meant for distribution. Transmission analysis focused on the lack of comprehensive planning at interconnected system levels, siting governance shortcomings, new technologies to enhance grid observability and security, and cybersecurity issues. It also stressed the additional flexibility requirements imposed by the growing presence of intermittent wind and solar generation in the generation mix. At the distribution level, in addition to concerns related to privacy and cybersecurity, recommendations focused on the need for a transition to dynamic pricing for end consumers, promotion of innovation in network design and management, data availability and ownership, and tariff reforms to support distribution network cost recovery.

Selective Modal Analysis

Selective Modal Analysis (SMA) is a comprehensive methodology for the modeling, analysis, and control of selected parts of the dynamics of systems described by large linear time-invariant (LTI) models. The main components of SMA are sensitivity tools and algorithms for reduced-order eigenanalysis. Sensitivity tools developed within the SMA framework include participation factors, which measure the participation of the state variables in the eigenmodes and vice versa. Participation factors play a central role in SMA developments. This chapter shows the role of participation factors in the identification of dynamic patterns, design of damping controllers, and reduced-order eigenanalysis.