We discuss the computation of balanced truncation model reduction for a class of descriptor systems which include the semidiscrete Oseen equations with time-independent advection and the linearized Navier-Stokes equations, linearized around a steady state. The purpose of this paper is twofold. First, we show how to apply standard balanced truncation model reduction techniques, which apply to dynamical systems given by ordinary differential equations, to this class of descriptor systems. This is accomplished by eliminating the algebraic equation using a projection. The second objective of this paper is to demonstrate how the important class of ADI/Smith-type methods for the approximate computation of reduced order models using balanced truncation can be applied without explicitly computing the aforementioned projection. Instead, we utilize the solution of saddle point problems. We demonstrate the effectiveness of the technique in the computation of reduced order models for semidiscrete Oseen equations.

In this paper the empirical observability Gramian calculated around the operating region of a power system is used to quantify the degree of observability of the system states under specific phasor measurement unit (PMU) placement. An optimal PMU placement method for power system dynamic state estimation is further formulated as an optimization problem which maximizes the determinant of the empirical observability Gramian and is efficiently solved by the NOMAD solver, which implements the Mesh Adaptive Direct Search (MADS) algorithm. The implementation, validation, and also the robustness to load fluctuations and contingencies of the proposed method are carefully discussed. The proposed method is tested on WSCC 3machine 9-bus system and NPCC 48-machine 140-bus system by performing dynamic state estimation with square-root unscented Kalman filter. The simulation results show that the determined optimal PMU placements by the proposed method can guarantee good observability of the system states, which further leads to smaller estimation errors and larger number of convergent states for dynamic state estimation compared with random PMU placements. Under optimal PMU placements an obvious observability transition can be observed. The proposed method is also validated to be very robust to both load fluctuations and contingencies.

This paper describes an online dynamic security assessment scheme for large-scale interconnected power systems using phasor measurements and decision trees. The scheme builds and periodically updates decision trees offline to decide critical attributes as security indicators. Decision trees provide online security assessment and preventive control guidelines based on real-time measurements of the indicators from phasor measurement units. The scheme uses a new classification method involving each whole path of a decision tree instead of only classification results at terminal nodes to provide more reliable security assessment results for changes in system conditions. The approaches developed are tested on a 2100-bus, 2600-line, 240-generator operational model of the Entergy system. The test results demonstrate that the proposed scheme is able to identify key security indicators and give reliable and accurate online dynamic security predictions.Index Terms-Decision trees, online dynamic security assessment, phasor measurements, preventive control, transient stability.

In this paper the interactions between component failures are quantified and the interaction matrix and interaction network are obtained. The quantified interactions can capture the general propagation patterns of the cascades from utilities or simulation, thus helping to better understand how cascading failures propagate and to identify key links and key components that are crucial for cascading failure propagation. By utilizing these interactions a high-level probabilistic model called interaction model is proposed to study the influence of interactions on cascading failure risk and to support online decision-making. It is much more time efficient to first quantify the interactions between component failures with fewer original cascades from a more detailed cascading failure model and then perform the interaction model simulation than it is to directly simulate a large number of cascades with a more detailed model. Interaction-based mitigation measures are suggested to mitigate cascading failure risk by weakening key links, which can be achieved in real systems by wide area protection such as blocking of some specific protective relays. The proposed interaction quantifying method and interaction model are validated with line outage data generated by the AC OPA cascading simulations on the IEEE 118-bus system.Comment: Accepted by IEEE Transactions on Power System

System splitting, also called controlled system islanding, can effectively prevent blackouts. Following the OBDD-based three-phase method given in [3] for proper splitting strategies, which satisfy necessary steady-state constraints, this paper studies the feasibility of the proper splitting strategies by means of power system transient simulations on the IEEE 118-bus system. Simulation results show that a considerable proportion of proper splitting strategies can successfully split the power system into stable islands. Furthermore, considering a general knowledge that a controlled power system can easily maintain its stability after a small disturbance, this paper presents "threshold value constraint" to restrict the degrees of the disturbances caused by proper splitting strategies. An approach is proposed to select threshold values for the constraint. Further simulation results show that by checking the constraint for proper splitting strategies, feasible splitting strategies can be found, which can successfully split the system into islands satisfying transient stability constraints.