Energy Function Method Research Articles

Design and performance evaluation of SSSC supplementary modulation controller in power systems using SPEF method

Controllable series line compensation is a cornerstone to increase the transmittable power, improve the transient stability and power oscillation damping. The initiative of FACTS allows for fast and vernier control of series compensation using static synchronous series compensator (SSSC). This paper presents the control laws and location index proposed for a SSSC based on a circuit analogy of the electro-mechanical system. The signals which are used can be synthesized using locally available measurements. A detailed study of small signal analysis is carried out to study the effectiveness of the control law and strategic location of the damping controller. With the objective of damping oscillations, a nonlinear constrained optimization technique has been presented for tuning the controller parameters. Transient stability analysis has then been performed with SSSC for a multimachine power system. A path independent structure preserving energy function method (SPEF) is derived for the SSSC. Direct evaluation of the effect of SSSC on transient stability is investigated. Case studies considered illustrate the effect of SSSC on transient stability and its accurate prediction. Comparison of results of the proposed approach with that of the method proposed by M.H. Haque, clearly indicate that there is a good enhancement in the system stability.

GLOBAL STABILITY OF A THREE-SPECIES FOOD-CHAIN MODEL WITH DIFFUSION AND NONLOCAL DELAYS

In this paper, a three species reaction-diffusion food-chain system with nonlocal delays is investigated. Sufficient conditions are derived for the global stability of a positive steady state and boundary steady states of the system by using the energy function method. Numerical simulations are carried out to illustrate the theoretical results.

Image Compression using Haar and Modified Haar Wavelet Transform

Efficient image compression approaches can provide the best solutions to the recent growth of the data intensive and multimedia based applications. As presented in many papers the Haar matrix–based methods and wavelet analysis can be used in various areas of image processing such as edge detection, preserving, smoothing or filtering. In this paper, color image compression analysis and synthesis based on Haar and modified Haar is presented. The standard Haar wavelet transformation with N=2 is composed of a sequence of low-pass and high-pass filters, known as a filter bank, the vertical and horizontal Haar filters are composed to construct four 2-dimensional filters, such filters applied directly to the image to speed up the implementation of the Haar wavelet transform. Modified Haar technique is studied and implemented for odd based numbers i.e. (N=3 & N=5) to generate many solution sets, these sets are tested using the energy function or numerical method to get the optimum one.The Haar transform is simple, efficient in memory usage due to high zero value spread (it can use sparse principle), and exactly reversible without the edge effects as compared to DCT (Discrete Cosine Transform). The implemented Matlab simulation results prove the effectiveness of DWT (Discrete Wave Transform) algorithms based on Haar and Modified Haar techniques in attaining an efficient compression ratio (C.R), achieving higher peak signal to noise ratio (PSNR), and the resulting images are of much smoother as compared to standard JPEG especially for high C.R.A comparison between standard JPEG, Haar, and Modified Haar techniques is done finally, which approves the highest capability of Modified Haar between others

Determination of Critical Generator Group Using Accelerating Power and Synchronizing Power Coefficient in the Transient Energy Function Method

This paper proposes an algorithm for determining critical generator lists using accelerating power and synchronizing power coefficient (SPC), and critical generator group (CGG) from CGG candidates, which is a combination of critical generators. The accurate determination of CGG provides a more accurate energy margin while providing system operator with information of possible unstable generator group. Classical transient energy function (TEF) method selects the critical generators with big corrected kinetic energy of each generator at the moment of fault removal. However, the generator with small acceleration after fault, that is, the generator with small corrected kinetic energy, is also likely to belong to CGG if the generator has small synchronizing power. The proposed algorithm has been verified to be effective compared with the classical TEF method. We utilized the power system of Korean Electric Power Corporation(KEPCO) as a test system.

Allocating the cost of transient stability constraint relief in bilateral electricity markets

In this study, the issue of allocating the cost of transient stability relief in a bilateral electricity market is investigated. The results of a constrained generation scheduling problem can be utilised in two ways to price the cost of a constraint. In the first method, which is the basis of nodal pricing, the Lagrange multipliers of the nodal power balance constraint are used as the price of electricity at various buses. In the second method, which is used in this study, the constraint relief scheme is based on a bid-based adjustment market of increments and decrements offered by generators to be involved in the constraint relief process. In the scheme used in this study, the cost of transient stability relief is first allocated to the individual constraints by different methods and the allocated costs are then allocated to the transactions in proportion to the degree of involvement in that constraint. Three methods are proposed and discussed for allocation of cost to the constraints and the results are compared and commented. The transient energy function (TEF) method is used to calculate the contribution of transactions in the constraints.

An ILC scheme for a class of nonlinear continuous‐time systems with time‐iteration‐varying parameters subject to second‐order internal model

AbstractIn this paper, a new iterative learning control (ILC) scheme is proposed to deal with unknown time‐iteration‐varying parameters for a class of nonlinear continuous‐time systems. The parametric non‐repetitiveness in the iteration domain is described by a second‐order internal model, which includes systems with iteration‐invariant parameters as a subset. By incorporating the internal model into the parametric learning law, the proposed ILC scheme can handle more generic systems with parametric uncertainties, and includes existing ILC schemes as a special case with the first‐order internal model. The conditions under which the new ILC scheme can guarantee learning convergence are delicately explored. Utilizing the information of the previous two iterations and the method of composite energy function (CEF), it is able to derive pointwise convergence along the time axis and asymptotic convergence along the iteration axis. The controller design is further extended to the case for systems with mixed parameters and unknown time‐varying input gain. Copyright © 2010 John Wiley & Sons, Ltd.Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

A High-Order Internal Model Based Iterative Learning Control Scheme for Nonlinear Systems With Time-Iteration-Varying Parameters

In this technical note, we propose a new iterative learning control (ILC) scheme for nonlinear systems with parametric uncertainties that are temporally and iteratively varying. The time-varying characteristics of the parameters are described by a set of unknown basis functions that can be any continuous functions. The iteratively varying characteristics of the parameters are described by a high-order internal model (HOIM) that is essentially an auto-regression model in the iteration domain. The new parametric learning law with HOIM is designed to effectively handle the unknown basis functions. The method of composite energy function is used to derive convergence properties of the HOIM-based ILC, namely the pointwise convergence along the time axis and asymptotic convergence along the iteration axis. Comparing with existing ILC schemes, the HOIM-based ILC can deal with nonlinear systems with more generic parametric uncertainties that may not be repeatable along the iteration axis. The validity of the HOIM-based ILC under identical initialization condition (i.i.c.) and the alignment condition is also explored.

Rescheduling of power systems constrained with transient stability limits in restructured power systems

This paper investigates various approaches to relieve the transient stability constraint in restructured power systems. The approaches adopted fall into two broad categories: those based on eliminating the constraint in the least-cost way and those based on eliminating with the least possible rescheduling. The latter group can, on the other hand, emerge in the form of a pool-protected policy in which the bilateral contracts are rescheduled to maintain the stability or in the form of a contract-protected policy in which the realizable bilateral contracts are maximized while minimizing the rescheduling in pool market. Transient energy function (TEF) method is used as a tool to calculate the sensitivity of energy margin to the variations in the magnitude of generation and load. The effectiveness of the method is illustrated by case studies on Western System Coordinating Council (WSCC) 3-machine 9-bus power system and on the 10-machine 39-bus New England test system and the results are compared. The results are also verified by time domain simulations.

Asymptotic behavior of positive solutions of semilinear elliptic equations in ℝ n , II

In this paper, we will analyze further to obtain a finer asymptotic behavior of positive solutions of semilinear elliptic equations in ℝn by employing the Li’s method of energy function.

Transient stability output margin estimation based on the energy function method

AbstractIn this paper, a new method of estimating the critical generation margin (CGM) in power systems is proposed based on transient stability diagnostics. The proposed method can directly compute the stability limit output for a given fault based on the transient energy function method (TEF). Since CGM can be directly obtained by the limit output using estimated P‐θ curves and is easy to understand, it is more useful than the conventional critical clearing time (CCT) of the energy function method. The proposed method can also estimate CGM as a negative value, which means instability in the present load profile, and so a negative CGM can be directly used as a restriction on generator output.The accuracy and fast solution ability of the proposed method are verified by applying it to a simple 3‐machine model and IEEJ EAST10‐machine standard model. Furthermore, the usefulness of the method for severity ranking of transient stability for various fault cases is discussed by using CGM. 2010 Wiley Periodicals, Inc. Electr Eng Jpn, 173(3): 10–19, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ eej.21035

Determination of SMES capacity to enhance the dynamic stability of power system

This paper proposes the principle of SMES capacity determination for power system stable operation. Adopting the energy function method, the mechanism of SMES damping power oscillation in the classical single-machine infinite-bus (SMIB) system is analyzed. The released kinetic energy during disturbance is the original of power system oscillation, which is taken as the principle of SMES capacity determination. Then, the influence of fault type, fault position, and fault clearing time on the SMES capacity determination are discussed. Using MATLAB simulation, the principle of SMES capacity determination is evaluated.

Iterative approach to generator maintenance schedule considering unexpected unit failures in restructured power systems

This paper proposes an iterative generator maintenance scheduling (GMS) scheme in power markets, considering the influence of unexpected unit failures. It is built on the different objectives of power producers and the independent system operator (ISO) as well as the variable availability of generating units. Individual producers solve the GMS problems by optimizing their payoffs within the entire scheduling horizon, whilst the ISO determines the outage periods as the coordinated benchmark by minimizing the system operating costs. Based on the difference of the system costs between the producers' schedules and the benchmark, the ISO synthesizes the corrective signals of generating units, which direct producers to reschedule their outage planning and resubmit them to the ISO. Through iterations among power producers and the ISO, an appropriate schedule can be obtained to balance the producers' benefits and the system operating costs. Note that the system operating costs consist of three terms of the reliability cost, the production cost, and the maintenance cost. The former two are analyzed by the system probabilistic production simulation with the equivalent energy function (EEF) method. Finally, a 21-unit system is utilized to demonstrate the proposed GMS issue. Copyright © 2010 John Wiley & Sons, Ltd.

Thermodynamics analysis of oxidation wear behavior of cemented carbide tools in high speed machining

The essence of oxidation wear machanism of cenmented carbide tool was studied based on thermodynamics. Standard Gibbs free energy of possible reactions in cutting process at different temperature was calculated using substance Gibbs free energy function methods, and the sequence of reaction possibility order was researched as well as characteristics of every reaction. Theoretical calculation shows that WO3, Co3O4, TiO2 and CoWO4 are the main resultants, which are proved with the experiment results.

Particle-number restoration within the energy density functional formalism

We give a detailed analysis of the origin of spurious divergences and finite steps that have been recently identified in particle-number restoration calculations within the nuclear energy density functional framework. We isolate two distinct levels of spurious contributions to the energy. The first one is encoded in the definition of the basic energy density functional itself whereas the second one relates to the canonical procedure followed to extend the use of the energy density functional to multi-reference calculations. The first level of spuriosity relates to the long-known self-interaction problem and to the newly discussed self-pairing interaction process which might appear when describing paired systems with energy functional methods using auxiliary reference states of Bogoliubov or BCS type. A minimal correction to the second level of spuriosity to the multi-reference nuclear energy density functional proposed in [D. Lacroix, T. Duguet, M. Bender, arXiv:0809.2041] is shown to remove completely the anomalies encountered in particle-number restored calculations. In particular, it restores sum-rules over (positive) particle numbers that are to be fulfilled by the particle-number-restored formalism. The correction is found to be on the order of several hundreds of keVs up to about 1 MeV in realistic calculations, which is small compared to the total binding energy, but often accounts for a substantial percentage of the energy gain from particle-number restoration and is on the same energy scale as the excitations one addresses with multi-reference energy density functional methods.

Design and Implementation of on‐line dynamic security assessment

AbstractDespite possible changes in energy sources, the importance of maintaining the stability of interconnected power systems will not change. Technologies for maintaining power system stability must evolve with renewable energy technology. As renewable energy increases, analysis and control methods for transient stability assessment must be reexamined and improved. This paper presents an overview of on‐line dynamic security assessment (DSA) systems and related direct methods. The controlling unstable equilibrium point (UEP) method and the boundary of the stability‐region‐based controlling UEP (BCU) method are briefly described in order to provide a framework of understanding the concept of a transient stability‐screening program for DSA systems. The integrated package TEPCO‐BCU, a very advanced practical program based on the theory of the controlling UEP method, BCU method, energy function method, and BCU‐guided time‐domain method, is described from the viewpoint of on‐line performance. Finally, the importance of validating the assessment results of the BCU method is discussed. Copyright © 2009 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

A quasistatic crack propagation model allowing for cohesive forces and crack reversibility

While the classical theory of Griffith is the foundation of modern understanding of brittle fracture, it has a number of significant shortcomings: Griffith theory does not predict crack initiation and path and it suffers from the presence of unphysical stress singularities. In 1998, Francfort and Marigo presented an energy functional minimization method, where the crack (or its absence) as well as its path are part of the problem's solution. The energy functionals act on spaces of functions of bounded variations, where the cracks are related to the discontinuity sets of such functions. The new model presented here uses modified energy functionals to account for molecular interactions in the vicinity of crack tips, resulting in Barenblatt cohesive forces, such that the model becomes free of stress singularities. This is done in a physically consistent way using recently published concepts of Sinclair. Here, for the consistency of the model, it becomes necessary to allow for crack reversibility and to consider local minimizers of the energy functionals. The latter is achieved by introducing different time scales. The model is solved in its global as well as in its local version for a simple one-dimensional example, showing that local minimization is necessary to yield a physically reasonable result.

Study of Exponential Decay and Exact Solution of Evolution System via Energy Perturbation and Decomposition Methods

Energy functional and Adomian Decomposition Methods (ADM) are employed, respectively, in order to investigate the stability of a system of connected wave equations in parallel via internal feedback controllers. Numerical computations have also been attempted for confirmation purposes.

Study on power system transient instability detection based on wide area measurement system

AbstractIn this paper, a method, which is essential in initiating emergency control measures, is proposed for fast and accurate online detection of transient instability based on real‐time measurement. Under a certain disturbance, the candidate critical cluster (CC) of power system is predicted and refreshed at each sampling step. The method identifies the loss of synchronism at each time step by observing the geometric characteristic of the post‐fault trajectory of the generalized one‐machine equivalent system. Unlike the previous extended equal‐area criterion method, it is unnecessary to calculate the unstable equilibrium point (UEP) during instability detection in this method and some limitations caused by the time‐invariant assumption are also eliminated. Simulations are carried out on the IEEE 50 generator test system and a real power system. The simulation results indicate that the proposed method has the features of reliability and effectiveness in identifying the loss of synchronism with inter‐area mode. Copyright © 2008 John Wiley & Sons, Ltd.

Stability treatments of wave system in [formula omitted] with coupling controllers via energy functional and decomposition methods

In this paper, the stabilizability conditions of a system of wave equations, coupled in parallel with distributed springs and viscous dampers, are investigated via energy perturbation and decomposition methods for different wave propagation speeds.

Application of Differential Evolution Algorithm for Transient Stability Constrained Optimal Power Flow

Consideration of transient stability constraints in optimal power flow (OPF) problems is increasingly important because modern power systems tend to operate closer to stability boundaries due to the rapid increase of electricity demand and the deregulation of electricity markets. Transient stability constrained OPF (TSCOPF) is however a nonlinear optimization problem with both algebraic and differential equations, which is difficult to be solved even for small power systems. This paper develops a robust and efficient method for solving TSCOPF problems based on differential evolution (DE), which is a new branch of evolutionary algorithms with strong ability in searching global optimal solutions of highly nonlinear and nonconvex problems. Due to the flexible properties of DE mechanism, the hybrid method for transient stability assessment, which combines time-domain simulation and transient energy function method, can be employed in DE so that the detailed dynamic models of the system can be incorporated. To reduce the computational burden, several strategies are proposed for the initialization, assessment and selection of solution individuals in evolution process of DE. Numerical tests on the WSCC three-generator, nine-bus system and New England ten-generator, 39-bus system have demonstrated the robustness and effectiveness of the proposed approach. Finally, in order to deal with the large-scale system and speed up the computation, DE is parallelized and implemented on a Beowulf PC-cluster. The effectiveness of the parallel DE approach is demonstrated by simulations on the 17-generator, 162-bus system.