Christopher L. DeMarco

Point of collapse methods applied to AC/DC power systems

The authors describe an extension of the point of collapse method developed for studies of AC systems to the determination of saddle-node bifurcations in power systems including high voltage direct current (HVDC) transmission. Bus voltage profiles are illustrated for an AC/DC test system. They significantly differ from the profiles of pure AC systems for typical system models. In particular, voltage dependent current order limits are shown to affect the voltage profiles and the loadability margin of the system. It is also shown that Hopf bifurcations, which are possible in purely AC lossless systems with second-order generator models, become plausible when the dynamics for the HVDC system are included. >

An energy based security measure for assessing vulnerability to voltage collapse

A security measure is defined to indicate vulnerability to voltage collapse based on an energy function for system models that includes voltage variation and reactive loads. The system dynamic model, the energy function, and the security measure are first illustrated in a simple radial system. Application of the security measure and its computational aspects are then examined in a standard 30-bus example (New England System). The security measure captures nonlinear effects such as VAR limits on generators that can influence the systems vulnerability to collapse. The behavior of the index with respect to network load increases is nearly linear over a wide range of load variation, facilitating prediction of the onset of collapse. >

Examining the limits of the application of semidefinite programming to power flow problems

The application of semidefinite programming (SDP) to power system problems has recently attracted substantial research interest. Specifically, a recent SDP formulation offers a convex relaxation to the well-known, typically nonconvex “optimal power flow” (OPF) problem. This new formulation was demonstrated to yield zero duality gap for several standard power systems test cases, thereby ensuring a globally optimal OPF solution in each. The first goal of the work here is to investigate this SDP algorithm for the OPF, and show by example that it can fail to give a physically meaningful solution (i.e., it has a nonzero duality gap) in some scenarios of practical interest. The remainder of this paper investigates an SDP approach utilizing modified objective and constraints to compute all solutions of the nonlinear power flow equations. Several variants are described. Results suggest SDPs promise as an efficient algorithm for identifying large numbers of solutions to the power flow equations.

Improved techniques for power system voltage stability assessment using energy methods

An improved method of assessing power system voltage stability using energy techniques is presented. The concept of an energy function providing a localized measure of voltage security in a particular portion of the system is developed. A crucial factor in the use of the energy function method is the ability to rapidly determine the appropriate low-voltage solution to use in the energy measure calculation. Also, an improved method of locating power alternative solutions with low associated energy measures is presented. Techniques are demonstrated on the IEEE 118 bus system and a 415-bus system. >

Implementation of a Large-Scale Optimal Power Flow Solver Based on Semidefinite Programming

The application of semidefinite programming to the optimal power flow (OPF) problem has recently attracted significant research interest. This paper provides advances in modeling and computation required for solving the OPF problem for large-scale, general power system models. Specifically, a semidefinite programming relaxation of the OPF problem is presented that incorporates multiple generators at the same bus and parallel lines. Recent research in matrix completion techniques that decompose a single large matrix constrained to be positive semidefinite into many smaller matrices has made solution of OPF problems using semidefinite programming computationally tractable for large system models. We provide three advances to existing decomposition techniques: a matrix combination algorithm that further decreases solver time, a modification to an existing decomposition technique that extends its applicability to general power system networks, and a method for obtaining the optimal voltage profile from the solution to a decomposed semidefinite program.

Stability Analysis of Interconnected Power Systems Coupled with Market Dynamics

The use of market mechanisms to determine generation dispatch, and the natural tendency to seek improved economic efficiency through rapid market updates, raises a critical issue. As the frequency of market-based dispatch updates increases, there will inevitably be interaction between the dynamics of markets determining the generator dispatch commands and the physical response of generators and network interconnections. This paper examines questions of stability in such coupled systems by means of numeric tests using various market update models (including detailed generator/turbine/governor dynamics) for the New England 39 bus test system. The results highlight the nature of potential instabilities and show the interaction modes between physical and market quantities through eigen-analysis. Understanding of potential modes of instability in such coupled systems is crucial both for designing suitable rules for power markets and for designing physical generator controls that are compatible with market-based dispatch.

Q-V curve interpretations of energy measures for voltage security

Energy methods have shown promise as measures for quantifying the vulnerability of power systems to problems of voltage instability and collapse. However, to make such measures more useful as a security assessment tool in an operational environment. It is important to provide physical interpretations of the quantitative measure. This paper demonstrates that for certain basic load models, the energy based security measure is equal to the area enclosed by a familiar Q-V curve, with a change of scale on the voltage axis. This interpretation has the added benefit of providing easily computed approximations to the maximum real and reactive power loadability both at individual buses and for the system as a whole. Results are demonstrated in detail on the IEEE 118 bus system, with additional tests on a 415 bus sample system. >

Sensitivity of Hopf bifurcations to power system parameters

Formulas for the sensitivity of the Hopf loading margin with respect to any power system parameter are presented. These first-order sensitivities determine an optimum direction in parameter space for changing parameters to increase the loading margin. The Hopf bifurcation sensitivities of a simple power system with a voltage regulator and a dynamic load model are computed. Parameter sensitivities of the Hopf and saddle node bifurcations are compared. An idea for eliminating some Hopf bifurcations is presented.<<ETX>>

A phase transition model for cascading network failure

We consider a special structure of dynamic system model that admits a very tractable inclusion of element failure phenomena, for which a global system Lyapunov function can be constructed. This class includes Hamiltonian systems as a special case, with a wide class of R-L-C circuits and mechanical spring-mass-damper systems in which branch failures are induced by exceeding thresholds of inductor current or spring force magnitude. Using a detailed R-L-C circuit as our illustrative example, this article describes how geometric features of the global Lyapunov function constructed, along with partial trajectory information from time domain simulations, can be used to more efficiently predict which branches are subject to failure in a specific disturbance scenario. The underlying concepts are closely related to techniques of merging families of Lyapunov functions in hybrid system analysis. It is hoped that these techniques will add to the set of tools available for predicting and preventing cascading failure in large scale networks.

The minimal dimension of stable faces required to guarantee stability of a matrix polytope

Considers the problem of determining whether each point in a polytope n*n matrices is stable. The approach is to check stability of certain faces of the polytope. For n>or=3, the authors show that stability of each point in every (2n-4)-dimensional face guarantees stability of the entire polytope. Furthermore, they prove that, for any k >