On Participation Factors for Linear Systems

Participation factors are nondimensional scalars that measure the interaction betweenthe modes and the state variables of a linear system. Since their introduction byVerghese, P'erez-Arriaga and Schweppe, participationfactors have been used for analysis, order reduction and controller design in a variety of fields.In this paper, participation factors are revisited, resulting in new definitions. The aim ofthese definitions is to achieve a conceptual framework that doesn't hinge on anyparticular choice of initial condition. The initial condition is modeled as an uncertainquantity, which can be viewed either in a set-valued or a probabilistic setting.If the initial condition uncertainty obeys a symmetry condition, the new definitionsare found to reduce to the original definition of participation factors

New Results on Modal Participation Factors: Revealing a Previously Unknown Dichotomy

The final version of this paper appeared in IEEE Transactions on Automatic Control, Volume 54, Issue 7, July 2009, pp. 1439-1449.This paper presents a new fundamental approach to modal participation analysis of linear time-invariant systems, leading to new insights and new formulas for modal participation factors. Modal participation factors were introduced over a quarter century ago as a way of measuring the relative participation of modes in states, and of states in modes, for linear time-invariant systems. Participation factors have proved their usefulness in the field of electric power systems and in other applications. However, in the current understanding, it is routinely taken for granted that the measure of participation of modes in states is identical to that for participation of states in modes. Here, a new analysis using averaging over an uncertain set of system initial conditions yields the conclusion that these quantities(participation of modes in states and participation of states in modes) should not be viewed as interchangeable. In fact, it is proposed that a new definition and calculation} replace the existing ones for state in mode participation factors, while the previously existing participation factors definition and formula should be retained but viewed only as mode in state participation factors. Examples are used throughout the paper to illustrate the issues addressed and results obtained.National Science Foundation, Office of Naval Research

Problems in Selective Modal Analysis and Control

In this dissertation, we develop monitoring and control systems for improving the performance of systems that are required to operate at the edge of their stability envelopes. The concept of modal participation factors, which is an essential construct in the theory of Selective Modal Analysis, is used extensively in this work. The basic definition of modal participation factors that was originally given for unforced linear time-invariant systems is revisited, and related notions of output participation factors and input-to-output participation factors are introduced, studied and applied to models of electrical power systems. A signal-based approach for real-time detection of impending instability in nonlinear systems is considered. The main idea pursued involves using a small additive white Gaussian noise as a probe signal and monitoring the spectral density of one or more measured states or outputs for certain signatures of impending instability. Input-to-state and input-to-output participation factors are used as tools to aid in selection of locations for probe inputs and states or outputs to be monitored, respectively. Since these participation factors are model-based, the work presented combines signal-based and model-based ideas toward achieving a robust methodology for instability monitoring. Case studies from power systems are used to illustrate the developed monitoring system, one of which involves the WSCC 3-generator, 9-bus network. Feedback algorithms are developed for assigning modal participation factors in general linear time-invariant systems using eigenvector assignment-based techniques. The goal is to reduce the interaction between a selected group of states (the high-value group) and an undesirable mode (for example a critical mode, i.e., one corresponding to an eigenvalue or pair of eigenvalues approaching the imaginary axis in the complex plane). In particular, we address two cases, one in which the mode of interest corresponds to a real eigenvalue approaching zero, and the other in which the mode involves a complex conjugate pair of eigenvalues that may be approaching the imaginary axis. A novel procedure for computing the desired closed-loop right eigenvector(s) associated with the critical mode (based on given constraints on the desired closed-loop participation factors) is presented. An example from power systems is presented to demonstrate the effectiveness of the controller. The example used is the WSCC 3-generator, 9-bus network

Nonlinear control design for stressed power systems using normal forms of vector fields

Large stressed interconnected power systems exhibit complicated dynamic behavior when subjected to disturbances. This nonlinear complex behavior is not well analyzed with present tools, and a complete theoretical analysis of this is not feasible in large systems. In stressed power systems, due to the presence of increased nonlinearity and the existence of nonlinear modal interactions, there exist some limitation to the use of conventional linear control design techniques. Therefore there is a need to understand the nature of nonlinear modal interactions and their influences on control performance for optimal controller setting;This work deals with control design in power systems using the method of normal forms. The objective of this work is to understand the effect of the nonlinear modal interaction on control performance and to develop a procedure to design controls incorporating the nonlinear information. For power systems equipped with fast exciters, the exciter gains have crucial influence on the system dynamic behavior. In order to be able to tune the exciter gains for optimal system performance, one has to understand, how the system response changes with different gain settings. In linear analysis, this consists of determining the eigenvalues for various gains, and computing the sensitivity of the eigenvalues under gain variations. If one takes into account the influence of the second order normal forms on the system response, then the corresponding interaction coefficients and their sensitivity with respect to gain variations has to be studied as well. This is the topic of the study presented here;The concept of nonlinear participation factors, and sensitivity of the normal forms coefficient, together with linear participation factors and eigenvalue sensitivity are used to vary control settings. The control settings are varied to obtain improved stability and to reduce the nonlinearity in the system. The proposed procedure was applied to the 50-generator IEEE test system. The results on a test system, demonstrate the importance of including the effect of the second order nonlinear terms in the analysis. The results provided also indicate some of the shortcomings of the linear approach, and illustrate the nature of the added information provided by the higher order terms. The control modes interacting with the inertial modes are identified, and the use of the nonlinear participation factors provides information regarding the states participating in the interacting modes. The sensitivity of the nonlinear coefficients to the identified control parameters provides information on the changes to the settings to reduce nonlinearity and improve stability;In this work we conduct a detailed testing of the proposed gain tuning procedure on the same 50-generator IEEE test system to show the validation of proposed method and to observe the effects of controller setting changes. A metric to measure the effect of the control tuning on the nonlinearity introduced is used to select the appropriate control setting. In addition the results dealing with the design of the controller are given and verification of the controller design using nonlinear time simulation is provided

Women's political leadership participation around the world: An institutional analysis.

Understanding institutional systems is critical for the advancement of women's participation in leadership in varying contexts. A unique and global analysis of the contextual factors that affect women in political leadership, this paper extends prior research in the field. This is a cross-country study where we ask, “How are societal-level institutional forces related to women's participation in political leadership?” We collected data from 8 secondary sources on 181 countries and conducted linear regression analyses with six institutional influences: the business environment, societal development, the economic environment, physical and technological infrastructure, political freedom, and culture. Results indicate that to increase the political leadership participation of women, we need to evaluate the following: customs and trade regulations, graft, the gender gap in political empowerment, public spending on education, the economic viability of the country, access to power and the internet, political freedom, and cultural variables like performance orientation, collectivism, and power distance

Student characteristics and PISA science performance: Portugal in cross-national comparison

Concurso aberto por um ano para projectos sobre o sucesso escolar.Problem Statement: PISA 2006 indicates that Portuguese students’ performance in science, although improving, is still lower than in most OCDE countries. What is the role of student characteristics, interests, gender and economic, social, cultural, status (ESCS) on scientific literacy scores? How does Portugal compare with some other selected countries? Purpose of Study: The study compares Portuguese students’ performance in PISA 2006 scientific literacy with that of students from the OECD, Spain, France, the United Kingdom, Turkey, Greece, and the USA. The study also examines students’ science interests, self-efficacy and beliefs about their own competences. Furthermore, the study identifies which student variables may help to explain performance in science. Research Methods: Our data are selected from the PISA 2006 student: (a) science performance and (b) interests and beliefs measured by the student questionnaire. In order to answer our research questions, we performed secondary analyses using hierarchical linear modeling. The 2006 PISA sample in Portugal consisted of 5109 students in 173 schools, all between the ages of 15;3 and 16;2. Findings: Change-in-score coefficients in the fitted model indicate that the ESCS effect is strongest in the USA, Finland and UK. The school-wide ESCS effect is superior to that of student ESCS and is a performance factor for all countries with the exception of Finland. Mean differences in performance tend to favor boys but, in several countries, gender does not contribute a significant change in score in the fitted models. For all countries, the general value of science, enjoyment of science and science selfefficacy are positively associated with performance. A negative association between personal value of science and performance was observed. The association of “participation in non-school science activities” with performance is either negative or non-significant. Conclusions: The constellation of associated factors differs from country to country but a few of these factors stand out as cross-nationally valid. Knowledge of both kinds of factors can be useful for the improvement of teaching/learning systems. Cross-national factors can simplify general models while the country-specific factors can help identify and target local concerns.FCT/ME

Continuing nursing education: An analysis of the relationship between benefits, participation and socialization of registered nurses in southeastern Virginia

There has been limited research on the benefits nurses\u27 derive from participation in continuing nursing education (CNE). Researchers have investigated sociodemographic and attitudinal characteristics of CNE participants or the effects of CNE on nursing practice.;The purpose of this study was to determine what factors influenced registered nurses in the Southeastern region of Virginia to participate or not to participate in CNE. Specifically, this study investigated the relationship of socialization (defined as level of nursing education, reading of professional nursing journals and professional nursing memberships), benefits (defined as either personal or social/professional type) derived from CNE attendance, the importance or non-importance of these derived benefits and participation or nonparticipation in CNE. Respondents\u27 socialization was characterized as either high or low for the purposes of this study.;The theoretical framework used in this study was the Expectancy Valence Model of Participation (Rubenson, 1977). Valence was described as anticipated satisfaction (i.e. the benefits accrued); it was viewed as the positive and negative values of the effects of participation. Expectancy was defined as an expectation that particular actions would lead to certain outcomes; it related to individuals\u27 perceptions of themselves as successful participants.;Data for the study were collected through the use of two questionnaires which were mailed to a sample of 400 registered nurses selected by systematic sampling. One hundred and fifty-five responses were received (38.75%). Data were analyzed by Statistical Analysis Systems (SAS) software using descriptive statistics, Chi square analysis and log linear analysis.;Findings indicated that level of socialization and participation in CNE were positively related. The importance of benefits derived from CNE participation and participation in CNE were not related. Level of socialization, importance of benefits derived from CNE participation and participation in CNE were positively related. High levels of socialization were related to participation in CNE while benefits of CNE were not related