Harry G. Kwatny

This paper describes the use of power spectral density and cumulative power functions in the examination of the electromyogram (EMG). The EMG signals were obtained with surface electrodes from two muscles, the flexor pollicis brevis and the extensor digitorum, in four subjects. Each muscle was studied at two levels of contraction, both before and during fatigue. The power spectral density functions are compared, using a cumulative power difference function and the mean frequency of the spectrum, to determine differences between loading conditions in an individual muscle, before and during fatigue, between different muscles, between individuals (same muscle), and combinations of these conditions.

This paper presents an analysis of static stability in electric power systems. The study is based on a model consisting of the classical swing equation characterization for generators and constant admittance, PV bus and/or PQ bus load representations which, in general, leads to a semi-explicit (or constrained) system of differential equations. A precise definition of static stability is given and basic concepts of static bifurcation theory are used to show that this definition does include conventional notions of steady-state stability and voltage collapse, but it provides a basis for rigorous analysis. Static bifurcations of the load flow equations are analyzed using the Liapunov-Schmidt reduction and Taylor series expansion of the resulting reduced bifurcation equation. These procedures have been implemented using symbolic computation (in MASYMA). It is shown that static bifurcations of the load flow equations are associated with either divergence-type instability or loss of causality. Causality issues are found to be an important factor in understanding voltage collapse and play a central role in organizing global power system dynamics when loads other than constant admittance are present.

This paper provides an of overview of local bifurcation theory and its application to power system voltage stability analysis. The qualitative behavior of power system dynamics as modeled by differential-algebraic equations is discussed, followed by a summary of the concepts and tools for the analysis of local bifurcation from equilibria. Computational methods for locating and classifying bifurcation points as they have been applied in power system analysis are reviewed. Several examples are given.

In this paper, we present an efficient algorithm to compute singular points and singularity-induced bifurcation points of differential-algebraic equations for a multimachine power-system model. Power systems are often modeled as a set of differential-algebraic equations (DAE) whose algebraic part brings singularity issues into dynamic stability assessment of power systems. Roughly speaking, the singular points are points that satisfy the algebraic equations, but at which the vector field is not defined. In terms of power-system dynamics, around singular points, the generator angles (the natural states variables) are not defined as a graph of the load bus variables (the algebraic variables). Thus, the causal requirement of the DAE model breaks down and it cannot predict system behavior. Singular points constitute important organizing elements of power-system DAE models. This paper proposes an iterative method to compute singular points at any given parameter value. With a lemma presented in this paper, we are also able to locate singularity induced bifurcation points upon identifying the singular points. The proposed method is implemented into voltage stability toolbox and simulations results are presented for a 5-bus and IEEE 118-bus systems.