A differential inequality approach is utilized to derive several stability conditions for synchronizing heterogeneous first-order forced coupled Kuramoto oscillator networks. First, we show that if either the amplitude of the external force is large enough or all natural frequencies equal to the external frequency, the heterogeneous first-order forced coupled Kuramoto oscillator network will reach the frequency synchronization for any initial condition. In particular, when all natural frequencies equal to the external frequency, a phase synchronization can be achieved when the amplitude of external force is not zero and the initial configuration is confined to a half circle. For non-identical cases, we show that if the average of all natural frequencies equals to the external frequency, the coupling strength is relatively large compared to the differences of natural frequencies and the amplitudes of external forces, and the initial configuration is confined to a half circle, the heterogeneous first-order forced coupled Kuramoto oscillator network still exhibit a frequency synchronization. Both quantitative and qualitative comparisons with existing synchronization conditions are examined by numerical simulations. These results indicate that these proposed criteria seem to be less conservative.

High penetration of distributed interface converters (DICs) in the isolated AC micro-grid (MG) may result in poor frequency and voltage response due to low inertia of conventional DICs. In order to overcome this difficulty, the concept of the virtual synchronous generators was proposed recently. meanwhile, in order to improve the convergence rate of the conventional consensus-based droop control and resilience to noises, new implementation of consensus-based distributed droop control by Alternating Direction Multipliers Methods (AD-MMs) is proposed. Possible extensions of the proposed method to two variants, including consensus ADMM with double message exchange and unique message exchange, are also discussed. Numerical experiments of a 14-bus/6-DIC micro-grid system on real-time digital simulators are performed to validate the effectiveness of the proposed distributed droop control mechanism.

Since distributed interface converters (DICs) embedded in the isolated micro-grid (MG) usually have low inertia, high penetration of DIC-based MGs may result in poor voltage and frequency response when the grid experiences large disturbances. The synchronverter is proposed recently in which the DIC mimics conventional synchronous generators (SGs) by designing parameters of the SG into the droop control mechanism of the DIC. In this paper, the concept of consensus-based droop control for DICs is extended to the consensus-based droop control for synchronverters. It will be shown that proper power sharing can still be achieved by the second-order consensus-based droop control. The stability of the closed-loop system is explored by the transient energy function (TEF) approach. Numerical experiments on real-time simulators will be performed to validate the effectiveness of the proposed control mechanism. Comparison studies about various existing droop control will also be studied.

With the increasing number of unpredictable accidents and power shortages on utility systems, the need to improve the reliability and security of electric power networks is imminent. Energy management systems that use traditional computer-aided tools to monitor and control generation and transmission systems using supervisory control and data acquisition (SCADA) actually have low sampling and update rates. In recent years, wide area monitoring system (WAMS) can possibly meet these challenges based on the state-of-the-art data retrieval technology. WAMS makes it possible to monitor power utility networks in a real-time dynamic manner using phasor measurement units. These sensor devices can provide synchronized measurements using global positioning satellite systems (GPS). In this paper, we study the power management problem under different scenarios. We present several multi-objective optimization models which can provide a deeper insight into operations on smart grid. We also consider contingency constraints and optimal allocation of these sensor devices on utility systems.

In order to provide autonomous power sharing of the conventional droop-control scheme for multiple power converters in isolated micro-grids, two consensus-based droop-control schemes will be examined. Since the conventional uniform droop gain ratio scheme requires identical droop gain ratio settings among all converters, applications to large-scale systems are restricted. An alternative scheme with the non-uniform droop gain ratio is proposed in this paper to simplify the droop gain setting while maintaining the perfect power sharing. Also, this new scheme is more robust since it is independent of particular gain settings. Real-time simulations of a micro-grid system are conducted to validate the effectiveness of this robust consensus-based droop control method.

We have developed a procedure for computing the probabilistic load margin of a power system when the main grid is embedded with various wind power generators. Three sub-tasks have been accomplished: (i) a distributed bi-directional sweep method for power flow computations when the main grid is embedded with wind power generators, (ii) a modified direct method for locating the collapse point has been proposed, and (iii) probabilistic load margin calculations by integrating the sensitivity method and Gram-Charlier expansions. Numerical demonstrations of IEEE 300-bus system have been performed to validate the correctness of the proposed computational methods.

The BCU method has been confirmed as an important on-line tool for direct transient stability assessment of power systems. The boundary property, which guarantees the controlling UEP of the original model and that of the reduced-state model, is a key issue in the BCU method. Instead of one-parameter transversality conditions proposed earlier, analytical results on the boundary property will be explored. We have applied the self-indexing energy function and the structural stability to analyze boundary properties of simple power systems. We have shown that, under certain mild conditions, the original system and the reduced-state system share the same UEPs on stability boundaries. Numerical studies confirm theoretical developments.

An energy function based unified power flow controller (UPFC) is developed for improving transient stability of network-preserving power systems. In order to consider model uncertainties, we also propose a forward neural networks controller to deal with such model uncertainties. This controller can be treated as neural network approximations of energy function control actions and provides online learning ability. Simulations on two power systems demonstrate that the proposed control strategy is very effective for suppressing power swing even under severe system conditions.

This paper proposes a technique for constructing dynamical equivalent networks of large-scale linearized power systems by using the Second-Order Arnoldi (SOAR) algorithm. Since the power system can be described by second-order swing equations, it is desired to construct a reduced-order model which can preserve its second-order structure. Inspired by the SOAR algorithm for single input systems, we will extend it with considering multiple inputs. Both block Arnoldi methods and global Arnoldi methods are investigated. System data of the reduced second-order system are obtained by the congruence transformation. Simulations about 50-machine power systems are performed to demonstrate the accuracy of the dynamical equivalent networks.

We apply the adaptive-order global Lanczos (AOGL) to generate the MIMO macromodel of high-speed VLSI interconnects. Theoretical foundations of the AOGL method for multiple point moment matching are investigated. In addition, the order selection of the reduced system was discussed. Experimental result on practical large-scale interconnect designs demonstrate that the reduced system generated by the AOGL method has better coherence to the original system both in time domain and in frequency domain. It has illustrated the feasibility and the efficiency of the AOGL method.

We present the global Lanczos algorithm for solving the RLCG interconnect circuits in this paper. This algorithm is an extension of the standard Lanczos algorithm for systems with multi-input multi-output (MIMO). A new matrix Krylov subspace will be developed first. By employing the congruence transformation with the matrix Krylov subspace, the two-side oblique projection-based method can be used to construct a reduced-order system. It will be shown that the system moments is still matched. The error of the 2q-th order system moment will be derived analytically. Finally, simulation results on both frequency domain and time domain will illustrate the feasibility and the efficiency of the proposed method.

We propose the global Arnoldi algorithm for MIMO RLCG interconnect model order reductions. This algorithm is an extension of the standard Arnoldi algorithm for systems with multi-inputs and multi-outputs (MIMO). By employing the congruence transformation with the matrix Krylov subspace, the one-sided projection method can be used to construct a reduced-order system. Two kinds of reduced systems using the global Arnoldi algorithm are proposed. The first q-th order of these reduced systems' moments is still preserved. The transfer matrix residual error of the reduced system is also derived analytically. Experimental results demonstrate the feasibility and the effectiveness of the proposed method.

In recent developments of direct methods for power system transient stability analysis, the task of finding the controlling unstable equilibrium point (u.e.p.) of the original system is performed on an artificial, dimension-reduction system for easily computing the controlling u.e.p. It has been shown that if the stable and unstable manifolds of a family of parametrized systems, which relates the original power system and an artificial, dimension-reduction system, satisfy the transversality condition as the parameter varies, then the artificial, dimension-reduction system contains the same set of u.e.p.'s on the stability boundary. In this paper, instead of direct verification of the transversality conditions, we show that under small mechanical power injections, the original power system model and the artificial, dimension-reduction system contain the same unstable equilibrium points on the stability boundary for one machine and two machine power system models.

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.

We propose a systematic method to find several local optimal solutions for a general nonlinear optimization problem. Analytical results for quasi-gradient systems and reflected gradient systems are developed and applied to explore the topological and geometric aspects of the critical points of the objective function. A mechanism is devised to escape from a local optimal solution and proceed into another local optimal solution by locating the decomposition point. By properly switching between quasi-gradient systems and reflected gradient systems, our proposed method can obtain a set of local optimal solutions and decomposition points. This algorithm also can find the global optimal solution. It depends on its ability to find all the decomposition points. The main algorithm contains two levels: the lower level is continuous while the upper level is discrete in nature. Further improvements in the algorithm to locate all decomposition points are desirable. The proposed method is applied to one test example with encouraging results.>