Motivated by recent interest for multiagent systems and smart grid architectures, we discuss the synchronization problem for the network-reduced model of a power system with nontrivial transfer conductances. Our key insight is to exploit the relationship between the power network model and a first-order model of coupled oscillators. Assuming overdamped generators (possibly due to local excitation controllers), a singular perturbation analysis shows the equivalence between the classic swing equations and a nonuniform Kuramoto model. Here, nonuniform Kuramoto oscillators are characterized by multiple time constants, nonhomogeneous coupling, and nonuniform phase shifts. Extending methods from transient stability, synchronization theory, and consensus protocols, we establish sufficient conditions for synchronization of nonuniform Kuramoto oscillators. These conditions reduce to necessary and sufficient tests for the standard Kuramoto model. Combining our singular perturbation and Kuramoto analyses, we derive ...

Synchronization and Transient Stability in Power Networks and Nonuniform Kuramoto Oscillators

A new model for the study of power system stability via Lyapunov functions is proposed. The key feature of the model is an assumption of frequency-dependent load power, rather than the usual impedance loads which are subsequently absorbed into a reduced network. The original network topology is explicitly represented. This approach has the important advantage of rigorously accounting for real power loads in the Lyapunov functions. This compares favorably with existing methods involving approximations to allow for the significant transfer conductances in reduced network models. The preservation of network topology can be exploited in stability analysis, with the concepts of critical and vulnerable cutsets playing central roles in dynamic and transient stability evaluation respectively. Of fundamental importance is the feature that the Lyapunov functions give a true representation of the spatial distribution of stored energy in the system

A Structure Preserving Model for Power System Stability Analysis

Stability analysis programs are a primary tool used by power system planning and operating engineers to predict the response of the system to various disturbances. Important conclusions and decisions are made based on the results of stability studies. This paper presents a theoretical foundation of direct methods for both network-reduction and network-preserving power system models. In addition to an overview, new results are offered. A systematic procedure of constructing energy functions for both network-reduction and network-preserving power system models is proposed. An advanced method, called the BCU method, of computing the controlling unstable equilibrium point is presented along with its theoretical foundation. Numerical solution algorithms capable of supporting online applications of direct methods are provided. Practical demonstrations of using direct methods and the BCU method for online transient stability assessments on two power systems are described. Further possible improvements, enhancements and other applications of direct methods are outlined.

Direct stability analysis of electric power systems using energy functions: theory, applications, and perspective

Nonlinearity is a hallmark of complex networks, but has generally been regarded as an obstacle to controlling their behaviour. Here Cornelius et al. show how nonlinear dynamics can be harnessed to control a network and drive it to desired states.

/pdf/realistic-control-of-network-dynamics-wqjegng46b.pdf

Realistic control of network dynamics.

A boundary of stability region based controlling unstable equilibrium point method (BCU method) for direct analysis of power system transient stability is presented. Features distinguishing the BCU method from the existing direct methods are that it consistently finds the exact controlling unstable equilibrium point (UEP) relative to a fault-on trajectory and that it has a sound theoretical basis. Moreover, the BCU method appears to be fast. This method is based on the relationship between the boundary of stability region of a power system and that of a reduced system. The BCU method finds the controlling UEP of the original system via a reduced system whose controlling UEP is easier and cheaper to compute. Effective numerical schemes to speed up the presented method are also proposed. This method has been tested on several power systems with very promising results. Simulation results on a 50 generator, 145 bus system are presented along with a comparison between the results obtained using the BCU method and another existing method. >

/pdf/a-bcu-method-for-direct-analysis-of-power-system-transient-1ekk48jlw8.pdf

A BCU method for direct analysis of power system transient stability

This paper describes the development and evaluation of an analytical method for the direct determination of transient stability. The method developed is based on the analysis of transient energy and accounts for the nature of the system disturbance as well as for the effects of transfer conductances onsystenmbehavior. It has been evaluated on a 10 generator 39 bus system and on a 20 generator 118 bus system. The method predicts critical clearing times for first swing transient stability which agree very closely with the results of simulations.

A Practical Method for the Direct Analysis of Transient Stability

IEEE 39-Bus System

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A Practical Method for the Direct Analysis of Transient Stability

IEEE 39-Bus System