Selective Modal Analysis (or SMA) is a physically motivated framework for understanding, simplifying and analyzing complicated linear time-invariant models of dynamic systems, see [1,2]. SMA can accurately and efficiently focus on selected portions of the structure and behavior of the system. the part of the model that is relevant to the dynamics of interest is singled out in a direct manner, and. the remainder of the model is collapsed in a way that leaves the selected structure and behavior Intact. The paper heuristically presents basic concepts and results of SMA and lays the foundations for their application to a number of problems in analysis of power system dynamics. The approach is illustrated with several examples, including a 60-machine model of a dynamic instability occurrence in an actual power system. A companion paper [3] elaborates on specific applications of SMA to power systems, particularly to the Dynamic Stability problem.

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Selective Modal Analysis with Applications to Electric Power Systems, PART I: Heuristic Introduction

Engineers in the power industry, face the problem that, while stability is increasingly a limiting factor in secure system operation, the simulation of system dynamic response is grossly overburdening on present-day digital computing resources. Each individual response case involves the step-by-step numerical solution in the time domain of perhaps thousands of nonlinear differential-algebraic equations, at a cost of up to several thousand dollars. A high premium is thus to be placed on the use of the most efficient and reliable modern calculation techniques. This paper is a critical tutorial-review of the calculation methods used routinely or investigated for use by the industry. It concentrates on solution concepts and computational techniques rather than on the analysis of the numerical methods. Details of system modeling are only emphasized when they affect the choice of solution method. The paper concludes with a view of the state of the art and a prediction of future directions of development.

Power system dynamic response calculations

Transient stability analysis of a power system is concerned with the system's ability to remain in synchronism following a disturbance In utility planning, transient stability is studied by numerical simulation The long CPU run times for simulation preclude their use for on-line security analysis Interest has therefore shifted toward the Lyapunov direct method of stability analysis This paper provides a critical review of research on direct methods since 1970 Considerable progress has been made on both theoretical properties of energy functions and on criteria suitable for on-line implementation Current theory provides a satisfactory treatment of voltage-dependent reactive power demand, transfer conductances, and flux decay However, it cannot incorporate the exciter control Proposed on-line criteria appear to work very well on sample examples; but, they still lack rigorous justification Finally, recent work has shown that power systems can exhibit chaotic behavior This surprising fact demonstrates that our understanding of the dynamics of power systems remains incomplete

Direct methods for transient stability analysis of power systems: Recent results

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.

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

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 >

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

An experience of dynamic instability was analyzed. The oscillations occurred on a large turbine generator that was operating radially on a long transmission line. The method of analysis was to determine stability by the calculation of the eigenvalues of the system.

Analytical Investigation of Dynamic Instability Occuring at Powerton Station

The transient stability problem has grown to enormous size due to the large number of interconnections of power systems. As the problem size has grown, so has the computational effort required for solution. This paper investigates the large scale parallelism available in the problem because of the sparsity of the equations and the algorithms used for solution. Multiprocessors are proposed to exploit this parallelism, and the gains achievable by these multiprocessors are predicted.

A feasibility study for the solution of transient stability problems by multiprocessor structures

A network of computers arranged in a modified ring structure has been designed for solving in parallel the equations describing dynamic disturbances on large power systems. The operation of this network when solving a 1732-bus, 398-generator system using an algorithm based on the Bonneville Power Administration's Transient Stability Program has been simulated on a CDC 6600. The purpose of the simulation was to determine how efficiently the algorithm can be executed in parallel on this multiprocessor configuration. The critical part of the algorithm is the forward and back substitution passes through the LDU decomposed I = YE equations. Parallel execution times for various combinations of processors and the corresponding gains over a conventional serial solution are given.

Simulation of a Multiprocessor Network for Power System Problems

This paper examines the possibility of using a dedicated multiprocessor network to do the step-by-step computations needed in the digital simulation of the dynamic response of a large power system. This multiprocessor network would use a general purpose digital computer for the input and output. It is found that over 97% of the computations for a typical 1723-bus, 396-machine, stability study could be done in parallel. Approximately 30% of the computation time is spent solving the network equations, I = YE. Various algorithms for this part of the solution and ways of scheduling the work assignments to the processors are discussed.

http://ieeexplore.ieee.org/iel4/5788/15447/00720086.pdf

The Use Of A Multiprocessor Network For The Transient Stability Problem

A network of computers arranged in a modified ring structure has been designed for solving in parallel the equations describing dynamic disturbances on large power systems. The operation of this network when solving a 1723-bus, 398-generator system using an algorithm based on the Bonneville Power Administration's Transient Stability Program has been simulated on a CDC 6600. The purpose of the simulation was to determine how efficiently the algorithm can be executed in parallel on this multiprocessor configuration. The critical part of this algorithm is the forward and back substitution passes through the LDU decomposed I = Y E equations. A scheduling algorithm that assigns tasks to the processors taking into account the precedence relationships necessary in the solution, the communication requirements, and the loadings on the individual processors has been developed to minimize the computing time for this part of the solution. This method gives better results than were obtained with other methods tried earlier.

F.M. Brasch

Papers

Analytical Investigation of Dynamic Instability Occuring at Powerton Station

A feasibility study for the solution of transient stability problems by multiprocessor structures

Simulation of a Multiprocessor Network for Power System Problems

The Use Of A Multiprocessor Network For The Transient Stability Problem

Design of multiprocessor structures for simulation of power-system dynamics. Final report