In power system identification problems using synchrophasor measurements, we frequently encounter the question, whether the model responses match well with actual system responses or not. In power system model validation problems, we need to assess whether the simulated model response matches recorded system behavior. In ringdown analysis, we have to decide whether the model order is sufficient to capture critical system modes in the system measurements, again by comparing model responses with system measurements. In this paper, we propose quantitative indicators founded in rigorous theory to assess such quality of fit problems. Two different indicators, based on frequency domain and time domain formulations respectively, are proposed and are illustrated on power system identification problems.

As background, we describe frequently used feedforward wide-area discontinuous power system stability controls. Then we describe online demonstration of a new response-based (feedback) Wide-Area stability and voltage Control System (WACS). The control system uses powerful discontinuous actions for power system stabilization. The control system comprises phasor measurements at many substations, fiber-optic communications, real-time deterministic computers, and transfer trip output signals to circuit breakers at many other substations and power plants. Finally, we describe future development of WACS. WACS is developed as a flexible platform to prevent blackouts and facilitate electrical commerce.

The power grid is not only a network interconnecting generators and loads through a transmission and distribution system, but is overlaid with a communication and control system that enables economic and secure operation. This multilayered infrastructure has evolved over many decades utilizing new technologies as they have appeared. This evolution has been slow and incremental, as the operation of the power system consisting of vertically integrated utilities has, until recently, changed very little. The monitoring of the grid is still done by a hierarchical design with polling for data at scanning rates in seconds that reflects the conceptual design of the 1960s. This design was adequate for vertically integrated utilities with limited feedback and wide-area controls; however, the thesis of this paper is that the changing environment, in both policy and technology, requires a new look at the operation of the power grid and a complete redesign of the control, communication and computation infrastructure. We provide several example novel control and communication regimes for such a new infrastructure.

The paper provides an extensive analysis of local and global bifurcation phenomena in studying the voltage-angle dynamic interactions of a minimal power system model. Using nonlinear analysis and normal form theory, it is proved that this system will experience quasi-periodic motions near certain degenerate local bifurcations which are explicitly characterized. The results in the paper provide strong analytical evidence for the possible occurrence of complicated behavior in the general power system from the interactions of voltage and angle instability mechanisms.

This paper reports on the latest developments in taxonomy theory originally developed for dynamic systems represented by ordinary differential equations constrained by algebraic equations (DAEs). It gives some new results on the behavior of a second order state constrained system. It shows that the interplay between an unstable system and the hard limit can result generically in stable non-smooth limit cycles. These results are of particular importance for Hopf bifurcations which occur near the state limit since they point towards the possibility of stable operation even after a subcritical Hopf bifurcation has occured.

This paper provides an overview of the taxonomy theory which has been proposed as a fundamental platform for solving practical stability related problems in large constrained nonlinear systems such as the electric power system. The theory reveals a two-level intertwined cellular nature of the constrained system dynamics which serves as a unifying structure, a taxonomy, for analyzing nonlinear phenomena in large system models. These broadly divide into the state space aspects (related to dynamic stability issues among others) and the parameter space aspects (connected with bifurcation phenomena among others). In the state-space formulation, the boundary of the region of attraction for the operating point is shown (under certain Morse-Smale like assumptions) to be composed of stable manifolds of certain anchors and portions of the singularity surface. Such boundary characterization provides the foundation for rigorous Lyapunov theoretic transient stability methods. In the parameter space analysis, the feasibility region which is bounded by the feasibility boundary provides a safe opening region for guaranteeing local stability at the equilibrium under slow parametric variations. The feasibility boundary where the operating point undergoes loss of local stability is characterized in the form of three principal bifurcations including a new bifurcation called the singularity induced bifurcation.

This paper presents a time-delay formulation of the large power system dynamics which includes modeling the fast distributed parameter transmission system dynamics from within the familiar phasor domain of the equipment dynamics. The notion of fast time-varying phasors proposed recently for the balanced power system leads to explicit solutions in the form of time-delayed algebraic equations for the transmission system dynamics which is represented by a large interconnected set of partial-differential wave equations, under certain assumptions.>