Bernard C. Lesieutre

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.

An improved transformer top oil temperature model for use in an on-line monitoring and diagnostic system

In this paper, the authors examine dynamic models of power transformer top oil temperature for use in an online monitoring and diagnostic system. Data taken from large transformers in the field indicate that the IEEE model of top oil temperature rise over ambient temperature does not adequately account for daily variations in ambient temperature. The authors propose a modification that accurately predicts top oil temperature and can be implemented in an online system. This model is verified using data from a large power transformer in service.

The influence model

This article describes what we have termed the influence model, constructed to represent in a tractable way the dynamics of networked and interacting Markov chains. The constraints imposed on the influence model may restrict its modeling ability but permit explicit and detailed analysis and computation and still leave room for rather richly structured and novel behavior. We focus on the dynamic evolution of the system. The influence matrix H, in both the homogeneous and general cases, bears further study as an interesting generalization of familiar stochastic matrices. The influence model may also find use as a representation for stochastic signals of various kinds. The influence model is evidently related to other models of networked stochastic automata in the literature, but the details of the relationships remain to be worked out more explicitly in many cases. The generalizations embodied in the influence model could prove to be important degrees of freedom in particular applications.

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.

Evaluation of uncertainty in dynamic simulations of power system models: The probabilistic collocation method

This paper explores the use of a new technique, the probabilistic collocation method (PCM), to enable the evaluation of uncertainty in power system simulations. The PCM allows the uncertainty in transient behavior of power systems to be studied using only a handful of simulations. The relevant theory is outlined here and simple examples are used to illustrate the application of PCM in a power systems setting. In addition, an index for identification of key uncertain parameters, as well as an example with a more realistic power system, are presented.

Optimization Strategies for the Vulnerability Analysis of the Electric Power Grid

Identifying small groups of lines, whose removal would cause a severe blackout, is critical for the secure operation of the electric power grid. We show how power grid vulnerability analysis can be studied as a bilevel mixed integer nonlinear programming problem. Our analysis reveals a special structure in the formulation that can be exploited to avoid nonlinearity and approximate the original problem as a pure combinatorial problem. The key new observation behind our analysis is the correspondence between the Jacobian matrix (a representation of the feasibility boundary of the equations that describe the flow of power in the network) and the Laplacian matrix in spectral graph theory (a representation of the graph of the power grid). The reduced combinatorial problem is known as the network inhibition problem, for which we present a mixed integer linear programming formulation. Our experiments on benchmark power grids show that the reduced combinatorial model provides an accurate approximation, to enable vulnerability analyses of real-sized problems with more than 16,520 power lines.

Load modeling in power system studies: WECC progress update

This paper provides an update on a composite load model development in Western Electricity Coordinating Council (WECC). A composite load model structure is described. The two salient features of the new load model are: (a) the model recognizes electrical distance between the transmission bus and the end-uses and (b) the model represents the diversity in composition and dynamic characteristics of various electrical end-uses. The load model data includes (a) data for a distribution equivalent model, (b) load component model data and (c) load component fractions. The paper presents tests and modeling of various electrical end-uses. The paper in particular focuses on modeling compressor motors in single-phase air-conditioners. Load composition methodology is also discussed. The model structure was implemented and tested in a production-level grid simulator.

Severe Multiple Contingency Screening in Electric Power Systems

We propose a computationally efficient approach to detect severe multiple contingencies. We pose a contingency analysis problem using a nonlinear optimization framework, which enables us to detect the fewest possible transmission line outages resulting in a system failure of specified severity, and to identify the most severe system failure caused by removing a specified number of transmission lines from service. Illustrations using a three-bus system and the IEEE 30-bus system aim to exhibit the effectiveness of the proposed approach.

Model reduction for analysis of cascading failures in power systems

In this paper, we apply a principal-orthogonal decomposition based method to the model reduction of a hybrid, nonlinear model of a power network. The results demonstrate that the sequence of fault events can be evaluated and predicted without necessarily simulating the whole system.

Identification of severe multiple contingencies in electric power networks

In this paper we propose a two-stage screening and analysis process for identifying multiple contingencies that may result in very severe disturbances and blackouts. In a screening stage we form an optimization problem to find the minimum change in the network to move the power flow feasibility boundary to the present operating point and that will cause the system to separate with a user-specified power imbalance. The lines identified by the optimization program are used in a subsequent analysis stage to find combinations that may lead to a blackout. This approach is applied to a 30-bus system with encouraging results.