Showing papers in "IEEE Transactions on Circuits and Systems in 1982"
TL;DR: A steady-state security region is a set of real and reactive power injections (load demands and power generations) for which the power flow equations and the security constraints imposed by equipment operating limits are satisfied.
Abstract: A steady-state security region is a set of real and reactive power injections (load demands and power generations) for which the power flow equations and the security constraints imposed by equipment operating limits are satisfied. The problem of determining steady-state security regions is formulated as one of finding sufficient conditions for the existence of solutions to the power flow map within the security constraint set. Explicit limits on real and reactive power injections at each bus are obtained, such that if each injection lies within the corresponding limits, the system is guaranteed to operate with security constraints satisfied.
213 citations
TL;DR: In this paper, a technique for designing recursive digital filters to approximate simultaneously given magnitude and linear phase characteristics is presented. But the linear phase is specified in terms of a desired constant group delay and the constraints of the linear program become a function of desired group delay.
Abstract: A technique is presented whereby a class of recursive digital filters can be designed to approximate simultaneously given magnitude and linear phase characteristics. The underlying approach is to linearize the inherently nonlinear approximation problem, and thereby use linear programming to carry out the approximation. The linear phase is specified in terms of a desired constant group delay. Therefore, the constraints of the linear program become a function of desired group delay. Thus the design algorithm consists of carrying out a univariant search within a range of group delay values to obtain a minimum error of approximation. Several examples of design are presented to illustrate the usefulness of the method.
172 citations
TL;DR: In this paper, chaotic motions occurring on certain energy surfaces of the conservative two-degree-of-freedom (three-machine) swing equations used as models in transient stability analysis of electric power systems are analyzed.
Abstract: We analyze chaotic motions occurring on certain energy surfaces of the conservative two-degree-of-freedom (three-machine) swing equations used as models in transient stability analysis of electric power systems, and we note the implications of this chaotic behavior for first swing stability predictions using these equations. In the particular parameter range chosen for study the swing equations may be thought of as a perturbation of the equations of a forced oscillator; the parameter range bears the same relation to the general swing equations as does a special case of the restricted three body problem to the equations of motion of celestial mechanics. We also give a simplification of Melnikov's method for detecting chaotic motions which may prove useful in other examples.
141 citations
TL;DR: A modified Bezout technique is used which allows for very explicit results regarding the number of stable load flows for a given network topology and set of power injections and shows that for systems describing an n -machine network with n \geq 4 , this result cannot be directly applied because the solutions contain solution components of positive dimension "at infinity."
Abstract: Electric utility analysts today face an increasingly difficult task of formulating both long and short term operating plans which will provide at the same time efficient and economical operation while delivering reliable and uninterrupted service to electricity users. One of the key ingredients in this planning is a set of large scale simulations of the steady-state network performance under various anticipated operating conditions. Central to these analyses are the classical "load flow" equations which are the equilibrium equations for the "swing equations" which are a physically based model of the dynamic operation of an n -node power system. Despite the long standing and widespread use of these equations, there remain a number of very basic open questions: What are the number and nature of the equilibria of the swing equations? How many stable equilibrium operating points are there in an n -node electric power grid? In this paper some powerful analytical tools from topology and geometry are used to answer certain of these questions. It is well documented that the load flow equations comprise a formidable large scale system but what is interesting, and perhaps surprising, is that even for a small number of buses, these equations possess a rather rich and intricate qualitative behavior which has heretofor been only partially understood. Indeed, until now there was no complete statement in the literature concerning the number of load flows in a general three-bus network. In Theorem 2.7, we state that for the "generic" three-bus network there are, for sufficiently small power injections, either four or six real load flows and that, in either case, exactly one of those load flows is stable. This is a special case of the results we derive for a general n -bus powergrid. Our method consists in first transforming the load flow equations for a lossless electric power network by trigonometric substitutions into algebraic equations. This makes it possible to apply some deep and powerful results from algebraic geometry and intersection theory to study these equations. An obvious tool for determining the number of solutions is provided by the classical theorem of Bezout, but it is shown that for systems describing an n -machine network with n \geq 4 , this result cannot be directly applied because the solutions contain solution components of positive dimension "at infinity." A major result in this paper is a modified Bezout technique which allows us to compute the number of complex (and a fortiori an upper bound on the number of real) solutions to the load flow equations. Combining this with the classical Morse inequalities, we obtain very explicit results regarding the number of stable load flows for a given network topology and set of power injections. The cases of three and four machine networks are considered in detail.
117 citations
TL;DR: It is shown that causality puts rather severe constraints on the frequency mappings that can be realized by stationary linear systems, and a recently proposed generalized sampling method is analyzed by means of the concepts discussed in this paper.
Abstract: A comprehensive review of representations of linear timevarying systems is given, both in the time and in frequency domains. Subsequently a definition is given of a stationary deterministic signal. Based on this definition the notion of stationary systems is introduced. These systems have the useful property that the spectral relation between input and output has a simpler form than the corresponding relation for arbitrary time-varying systems. It is shown that causality puts rather severe constraints on the frequency mappings that can be realized by stationary linear systems. An extension of the theory of linear time-varying systems to the case of discrete-time and hybrid systems (analog input, digital output, or vice versa) is discussed. Examples of stationary systems are given, such as a decimator, a periodic sampler, and a bilinear A/D converter. Also, a recently proposed generalized sampling method is analyzed by means of the concepts discussed in this paper.
111 citations
TL;DR: In this paper, the results on linear slow coherency and aggregation are extended to nonlinear electromechanical models of power systems and similar dynamic networks and conservation and equilibrium properties are used for the derivation of nonlinear singular perturbation models with explicit separation of time scales.
Abstract: Recent results on linear slow coherency and aggregation are extended to nonlinear electromechanical models of power systems and similar dynamic networks. Conservation and equilibrium properties are used for the derivation of nonlinear singular perturbation models with explicit separation of time scales.
92 citations
TL;DR: In this article, a power system operating state is defined to be dynamically secure with respect to a given disturbance if the system, starting in that state maintains transient stability after experiencing the disturbance.
Abstract: A method for deriving dynamic security regions of power systems is developed. A power system operating state is defined to be dynamically secure with respect to a given disturbance if the system, starting in that state maintains transient stability after experiencing the disturbance. Specifically, these are regions of prefault angles such that the post-fault system is asymptotically stable. The proposed approach is to construct affine approximations to the nonlinearities in the transient stability model and then derive quadratic bounds on the errors between the nonlinearities and their approximation. These are then used to derive sufficient conditions for a polytope of operating states to be dynamically secure.
89 citations
TL;DR: Using a novel approach, the amplitude and frequency of nearly sinusoidal nonlinear oscillators can be calculated by solving two algebraic nonlinear equations using a recursive algorithm based on Volterra series.
Abstract: Using a novel approach, the amplitude and frequency of nearly sinusoidal nonlinear oscillators can be calculated by solving two algebraic nonlinear equations. These determining equations can be generated to within any desired accuracy using a recursive algorithm based on Volterra series. Our method inherits many desirable features of the harmonic balance method, the describing function method, and the averaging method. Our technique is analogous to, but is much simpler than, the classic approach due to Krylov, Bogoliubov, and Mitropolsky. Unlike conventional techniques, however, our approach imposes no severe restriction on either the degree of nonlinearity, or the amplitude of oscillation. Moreover, the accuracy of the solution can be determined by a constructive algorithm.
84 citations
TL;DR: Novel circuits, based on the N -path (or pseudo-N -path) configuration, are described for the design of narrow-band switched-capacitor (SC) bandpass filters, providing stable passband responses and low sensitivities to element-value variations even for extremely narrow relative bandwidths, where other design approaches fail.
Abstract: Novel circuits, based on the N -path (or pseudo- N -path) configuration, are described for the design of narrow-band switched-capacitor (SC) bandpass filters. For noncritical applications very simple and economical circuits, based on the simulation of passive or active RC circuits, can be used; for high-accuracy filtering tasks, more elaborate circuits (obtained from doubly terminated reactance ladders) are proposed. The resulting filters provide stable passband responses and low sensitivities to element-value variations even for extremely narrow relative bandwidths, where other design approaches fail.
80 citations
TL;DR: In this article, a primitive factorization algorithm which produces a primitive matrix over an arbitrary field K is presented and the use of this algorithm is illustrated by a nontrivial example.
Abstract: Morf, Levy, and Kung and Youla and Gnavi presented a primitive factorization algorithm which extracts in some sense the content of a (full rank) matrix A with entries in the ring K[z,\omega] of bivariate polynomials over some field K . However, the algorithms presented in both cases specify and require the coefficient field K to be algebraically closed-typically the field of complex numbers. It is desirable, from theoretical and computational standpoints, to have no such restriction on K ; so, for example, one could do the factorization over the real field or even the field of rational numbers, provided the coefficients start out in these fields. Here an algorithm which produces a primitive factorization over an arbitrary field K is presented and the use of this algorithm is illustrated by a nontrivial example. Several related results leading to a general factorization theorem are stated and proved. Scopes for applying the results in various problems of scientific and engineering interest are mentioned.
78 citations
TL;DR: In this article, a new approach to design centering is presented, which starts at the initial nominal values of the circuit parameters and improves these nominal values by maximizing the circuit yield step by step with the aid of a yield prediction formula.
Abstract: Design centering is an appropriate design tool for all types of electrical circuits to determine the nominal component values by considering the component tolerances. A new approach to design centering will be presented, which starts at the initial nominal values of the circuit parameters and improves these nominal values by maximizing the circuit yield step by step with the aid of a yield prediction formula. Using a variance prediction formula additionally, the yield maximization process can be established with a few iteration steps only, whereby a compromise between the yield improvement and the decrease in statistical certainty must be made in each step. A high-quality interactive optimization method is described which allows a quantitative problem diagnosis. The yield prediction formula is an analytical approximation based on the importance sampling relation. This relation can also be used to reduce the sample size of the necessary Monte Carlo analyses. Finally the efficiency of the presented algorithm will be demonstrated on a switched-capacitor filter.
TL;DR: In this article, a fast procedure is given to design equiripple minimum-phase FIR filters following the technique proposed by Herrmann and Schuessler [1]: use is made of cepstral deconvolution, carried out through FFT, to avoid the polynomial root-finding problem inherent in the method.
Abstract: A fast procedure is given to design equiripple minimum-phase FIR filters following the technique proposed by Herrmann and Schuessler [1]: Use is made of cepstral deconvolution, carried out through FFT, to avoid the polynomial root-finding problem inherent in the method.
TL;DR: In this article, enumerative techniques are introduced for establishing a clustered semidecoupled dynamic model for a class of autonomous linear systems exemplified by the electromechanical dynamics of the electric power system.
Abstract: Simple, computationally efficient, enumerative techniques are introduced for establishing a clustered semidecoupled dynamic model for a class of autonomous linear systems exemplified by the electromechanical dynamics of the electric power system. Such a model consists of intercluster (usually slow) dynamics and intracluster dynamics (usually fast) which are respectively weakly coupled. The process starts by selecting the point in frequency where intracluster and intercluster dynamics tend to separate. The sorting technique then identifies the number of clusters, the width of separation in frequency, the specifics of the dynamic components and the coupling between them. No matrix manipulations like finding eigenvalues or inverses are required.
TL;DR: A complete stability analysis of a new power system model is presented that facilitates a dynamic representation directly in terms of the network structure and the multivariable Popov criterion is used to obtain general Lure-Postnikov type Lyapunov functions which rigorously allow for the presence of real loads.
Abstract: This paper presents a more complete stability analysis of a new power system model which was presented in [1]. The essential feature of the model is the assumption of frequency dependent loads. This facilitates a dynamic representation directly in terms of the network structure. Consequently, concepts and results from circuit theory can play a strong role in the stability analysis of the model. The multivariable Popov criterion is used to obtain general Lure-Postnikov type Lyapunov functions which rigorously allow for the presence of (frequency dependent) real power loads. This has not been possible with the previously used model. Results are given for both local (dynamic) stability and for determination of regions of asymptotic (transient) stability.
TL;DR: This paper shows how to select the set of weighting coefficients in the currently used PI's for analyzing either the real power flow or node voltage magnitude problems in order to circumvent some of the contingency ranking problems.
Abstract: This paper presents the theory and method for systematically finding the performance index (PI) which is used in Automatic Contingency Selection (ACS) algorithms. Since the ACS problem is a binary decision problem, then the choice of the PI is equivalent to the selection of a decision function which measures the impact of each contingency on the system performance in terms of giving out-of-limit conditions. This paper shows how to select the set of weighting coefficients in the currently used PI's for analyzing either the real power flow or node voltage magnitude problems in order to circumvent some of the contingency ranking problems. Even more important, it is shown how to select the threshold values of the PI which guarantee proper classification of the contingencies in terms of minimizing the probabilities of missing critical contingencies and false alarms. The approach taken is a set theoretic one which allows us to develop a method for finding the PI as a volume maximization problem which can be solved using standard SUMT methods. One such algorithm is given together with an illustrative example.
TL;DR: A simulation-after-test algorithm for the analog fault diagnosis problem is proposed in which a bound on the maximum number of simultaneous failures is used to minimize the number of test points required.
Abstract: A simulation-after-test algorithm for the analog fault diagnosis problem is proposed in which a bound on the maximum number of simultaneous failures is used to minimize the number of test points required. The resultant algorithm is applicable to both linear and nonlinear systems with multiple hard or soft faults and can be used to isolate failures up to an arbitrarily specified "replaceable chip or subsystem."
TL;DR: In this article, the trajectories of an interconnected power system are described by their swing equations and loads are treated as PV buses, and it is shown that' oscillations can never occur.
Abstract: The paper presents some asymptotic properties of the trajectories of an interconnected power system. Generators are described by their swing equations, loads are treated as PV buses. It is shown that' oscillations can never occur. Moreover, for small levels of injected power, all trajectories converge.
TL;DR: In this article, the qualitative nature of the time evolution in a piecewiselinear lossy resonant circuit driven by a sinusoidal voltage source is investigated by computer-aided analysis using exact analytical formulas.
Abstract: The qualitative nature of the time evolution in a piecewiselinear lossy resonant circuit driven by a sinusoidal voltage source is investigated by computer-aided analysis using exact analytical formulas. A surprising wealth of different nonlinear phenomena is discovered. They are: stable and unstable harmonics, subharmonics, and even apparently completely disordered aperiodic "chaotic" motions. In the latter case, the hyperbolicity, strange attractor, and broad-band frequency spectrum normally associated with chaotic motions have all been observed using nearly exact piecewise-linear solutions. These results represent the most reliable numerical confirmation to date of chaotic motions in a real physical circuit.
TL;DR: In this paper, the authors considered the application of linear programming to the design of two-dimensional recursive digital filters, where the desired specification consists of both magnitude and phase, the design procedure is restricted to the case where the phase specification is linear (i.e., constant group delay).
Abstract: This paper considers the application of linear programming to the design of two-dimensional recursive digital filters. Although the desired specification consists of both magnitude and phase, the design procedure is restricted to the case where the phase specification is linear (i.e., constant group delay). A stability constraint that is linear in form and which enables the design of a class of stable nonsymmetric half-plane (NSHP) and quarter-plane filters (QP) is proposed and proof of the sufficiency of the stability constraint is also provided. Examples of NSHP and QP stable filter designs using linear programming that incorporate the linear stability constraint are presented. Some examples of applications to image processing are also provided.
TL;DR: In this paper, the authors consider two fundamental techniques for large-scale circuit analysis, one-way macromodels and time waveform techniques, where the subcircuits are integrated for the total analysis time in contrast to the conventional incremental time approaches where all circuits are integrated simultaneously by small incremental time steps.
Abstract: In this paper we consider two important fundamental techniques for large-scale circuit analysis. In the first technique, unilateral subcircuit models are considered which we call one-way models. With these models, the independent time integration of the subcircuits can be accomplished. The second technique which is called a time waveform technique is based on the one-way macromodels. In this approach the subcircuits are integrated for the total analysis time in contrast to the conventional incremental time approaches where all circuits are integrated simultaneously by small incremental time steps.
TL;DR: In this paper, a new Z domain continued fraction expansion is presented which proceeds in terms of z - 1 and 1 - z^{-1} factors, and is proved to be always convergent for polynomials whose roots all lie within the unit circle.
Abstract: A new Z domain continued fraction expansion is presented which proceeds in terms of z - 1 and 1 - z^{-1} factors. It is proved to be always convergent for polynomials whose roots all lie within the unit circle. The procedure involves a unique decomposition of the given polynomial into a mirror image polynomial (MIP) and an antimirror image polynomial (AMIP) whose degrees differ by unity. The ratio of these polynomials is shown to possess the properties of a digital reactance function. The continued fraction expansion developed here-due to the fact that z - 1 and 1 - z^{-1} are the inverse transmittances of digital accumulators, as well as of switched capacitor integrators-has application to the synthesis of digital and switched capacitor ladder filters.
TL;DR: In this paper, the authors present some experimental results on known circuits and a new configuration which allows the electronic control of the absolute bandwidth of a biquad circuit with operational transconductance amplifiers.
Abstract: The design of voltage- or current-controlled active filters with operational transconductance amplifiers (OTA's) is much less expensive than with analog multipliers. This paper presents some experimental results on known circuits and a new configuration which allows the electronic control of the absolute bandwidth of a biquad circuit.
TL;DR: In this article, a technique for realizing a versatile operational floating amplifier by using a standard op amp is presented, which greatly extends op amp capabilities, especially in cases where grounded loads have to be current driven and where accurate low-noise termination impedances must be realized.
Abstract: A technique for realizing a versatile operational floating amplifier by using a standard op amp is presented. Such a building block greatly extends op amp capabilities. Especially in cases where grounded loads have to be current driven and where accurate low-noise termination impedances must be realized, this technique may be very useful.
TL;DR: In this article, a singular perturbation analysis of the synchronous machine equations in the (d, q) reference frame reveals that several reduced order models can be derived systematically from the fundamental machine equations.
Abstract: A singular perturbation analysis of the synchronous machine equations in the (d, q) reference frame reveals that several reduced order models can be derived systematically from the fundamental machine equations. Some inconsistencies in the classical approach to model reduction are eliminated, and some assumptions commonly overlooked in the literature are clarified. Ways of accounting for armature transients and amortisseur effects in the electromechanical equations of the reduced models are obtained directly from the theory.
TL;DR: In this paper, the analysis of complex dynamical systems (which may be of high dimension) is accomplished in terms of the qualitative properties of the free subsystems and the interconnections of such systems.
Abstract: In two recent papers, Brayton and Tong developed some significant results which are the basis of a constructive approach in the stability analysis of dynamical systems. Although their algorithm is powerful, it taxes the capabilities of most modern computers when the dimension of a system is high or even when the dimension is moderate in size. In this paper we remove these difficulties to a certain extent by generalizing the work of Brayton and Tong to interconnected dynamical systems. In our approach, the analysis of complex dynamical systems (which may be of high dimension) is accomplished in terms of the qualitative properties of the free subsystems and the interconnections of such systems.
TL;DR: In this article, the authors proposed a signal processor that can be implemented using only delay elements, analog gates, an unweighted summer and a low-pass filter or integrator.
Abstract: Signal processors are proposed which can be implemented using only delay elements, analog gates, an unweighted summer and a low-pass filter or integrator. It is shown that in some cases even the summer and the low-pass filter can be omitted. The transfer function coefficients depend on timing, and are independent of values or even value ratios of elements. The proposed filters can be made fully programmable by using programmable timing, and are suitable for integration using MOS technology; in fact, coefficient resolution improves with the advent of technology.
TL;DR: Band faults can be used to create a fault dictionary that is supposed to isolate single element catastrophic faults, and when applied to several example linear circuits nonetheless has yielded promising results.
Abstract: "Band faults," the approximate movements of nominal worstcase boundaries with catastropic faults, are much more efficiently computed than the "fault bands" that they approximate. Derived from a simulation before test, band faults can be used to create a fault dictionary that is supposed to isolate single element catastrophic faults. By no means general, the approach when applied to several example linear circuits nonetheless has yielded promising results.
NEC1
TL;DR: In this paper, a new infinite impulse response (IIR) Nyquist filter with zero intersymbol interference was proposed, and the necessary and sufficient conditions for the transfer function were obtained.
Abstract: A new infinite impulse response (IIR) Nyquist filter with zero intersymbol interference is proposed. The necessary and sufficient conditions for the transfer function are obtained. The proposed IIR Nyquist filter requires only frequency-domain optimization. Multistep optimization, using the iterative Chebyshev approximation, is proposed. This method is able to design a new kind of IIR Nyquist filter with the minimum order. Numerical examples for 30- and 15-percent rolloff rates are illustrated. From these examples, it is confirmed that the IIR approach can reduce the filter order and hardware size, compared with the conventional finite impulse response (FIR) Nyquist filters. Its efficiency becomes marked for high Q Nyquist filters.
TL;DR: In this article, a user-oriented method for checking error bounds for nonlinear elements with single valued and bounded slope was proposed. But this method is limited to single-valued nonlinear element characteristics.
Abstract: The describing function method is widely used without much attention being paid to the error analysis so vital in any approximate method. One reason for this is the lack of a straightforward user-oriented method for checking error bounds except when the nonlinear element characteristic is single valued and of bounded slope. This paper attempts to eliminate that defect. A far wider range of nonlinear elements is now amenable to straightforward, usually graphical treatment; discontinuities, hysteresis, and backlash characteristics are included. In addition, previous results for slope-bounded single-valued nonlinear characteristics may be substantially improved with a small additional computational effort.
TL;DR: This paper provides a rigorous foundation in the nonlinear domain for the two energybased concepts fundamental to network theory: passivity and losslessness and gives a rigorous justification for the various equivalent criteria in the linear case.
Abstract: This paper is the second in a two-part series [1] that aims to provide a rigorous foundation in the nonlinear domain for the two energybased concepts fundamental to network theory: passivity and losslessness. We hope to clarify the way they enter into both the state-space and the input-output viewpoints. Our definition of losslessness is modeled on that of a "conservative system" in classical mechanics; several examples are used to compare it with other concepts of losslessness currently found in the literature. We show in detail how this definition avoids the anomalies and contradictions that many other definitions produce. This concept of losslessness has the desirable property of being preserved under interconnections, and we extend it to one that is representation independent as well. It is applied to five common classes of n -ports, yielding explicit criteria for losslessness in terms of the state and output equations. In particular we give a rigorous justification for the various equivalent criteria in the linear case. A network realization and a new explicit canonical form of state representation are derived for a large class of lossless nonlinear systems.