Extended Equal Area Criterion Research Articles

98/02160 A novel approach to large scale system load flows Newton-Raphson method using hybrid bus

Another version of the extended equal area criterion (EEAC) method for fast transient stability analysis is presented. First, an efficient method of identifying the critical cluster by a two-step gap-ranking process of rotor angles is devised to decompose the multimachine system into two coherent groups. Then, the recently developed EEAC method is revised to circumvent some of its major difficulties. The main appeal of the presented method lies in that the empirical corrective factors compensating for the truncation error in the Taylor series expansion are completely eliminated. Moreover, the iterative procedure involved in evaluating the critical clearing angle can be precluded. Another attractive feature to be emphasized is the considerable curtailment in solution time in identifying the critical cluster. Finally, the proposed method is tested on the Taipower system, which is the only power system in Taiwan. The results obtained agree rather well with those from the conventional step-by-step method. It is significant that the presented method is superior to the most prevailing direct method, the potential energy boundary surface method, in its rapidity with comparable accuracy.

98/02154 Fuzzy logic based voltage control for a synchronous generator

Another version of the extended equal area criterion (EEAC) method for fast transient stability analysis is presented. First, an efficient method of identifying the critical cluster by a two-step gap-ranking process of rotor angles is devised to decompose the multimachine system into two coherent groups. Then, the recently developed EEAC method is revised to circumvent some of its major difficulties. The main appeal of the presented method lies in that the empirical corrective factors compensating for the truncation error in the Taylor series expansion are completely eliminated. Moreover, the iterative procedure involved in evaluating the critical clearing angle can be precluded. Another attractive feature to be emphasized is the considerable curtailment in solution time in identifying the critical cluster. Finally, the proposed method is tested on the Taipower system, which is the only power system in Taiwan. The results obtained agree rather well with those from the conventional step-by-step method. It is significant that the presented method is superior to the most prevailing direct method, the potential energy boundary surface method, in its rapidity with comparable accuracy.

Practically Negative Effects of Emergency Controls

Although apparently erroneous, negative effects on transient stability of emergency controls, such as generator tripping, load shedding and rapidly increasing excitation, follow natural laws. These important phenomena are uncovered, and their mechanisms are studied with extended equal-area criterion (EEAC) in this paper. The effects are quantitatively assessed, and their necessary and sufficient conditions are derived as well.

Hybrid Extended Equal-Area Criterion for Fast Transient Stability Assessment with Detailed Power System Models

The use of fast direct methods to evaluate the stability of power systems can benefit planning studies and operation planning. The existing Extended Equal-Area Criterion (EEAC), developed in 1988, enabled calculation much faster than timedomain simulations, but failed to deal with large and detailed dynamic systems. Based on it, we propose a new method, which is a Hybrid Extended Equal-Area Criterion (HEEAC), where time-domain simulations are used with a stability assessment provided by EEAC. HEEAC discriminates critical from non-critical machines, and yields a set of stability indicators such as critical clearing times, power transfer limits or power generation limits. The method has been applied to the French EHV system, with detailed generator and load models. The perfonnances are good both in tenns of computing speed and accuracy.

Practical and Flexible Incorporation of AVR into Extended Equal Area Criterion

Automatic voltage regulator (AVR) models, additions to transient salicncy, are incorporated into extended equal area criterion (EEAC) for transient stability assessment of power systems in this paper. This is a further development of a previous paper where the EEAC has been successfully extended to constant Eq' models to consider transient saliency. The present paper further defines two equivalent machines with equivalent AVRs, which arc likely responsible for the possible separation. The transient stability of multimachine systems of any size, where machines may have various AVR parameters or no AVRs, can always be represented by only six first order differential equations. To these, instead of to multimachine state equations of high dimension, implicit integration is applied. With parametrizing AVR's effects on transient stability, renewed parameters of a one—machine infinite—bus system arc applied to the energy function with classical models, which contains only two items, i.e. kinetic and potential energy. Un-like in other literature, angle diffcrcncc between E' and Eq' and that between Vtand Eq' are neither neglected nor treated as constant in this study. Besides, transient saliency of individual machine, being usually excluded in the literature on direct methods with AVRs, is preserved here. Extensive test results on several practical power systems, concerning the accuracy and robustness with respect to various faults, transient saliency and AVR profiles, are reported in this paper. These fully confirm the significance of this extension and validate the feasibility of its practical applications.

A mixed direct method for transient stability assessment

Abstract A mixed direct method taking the advantages of both the potential energy boundary surface (PEBS) method and the extended equal area criterion (EEAC) method for transient stability analysis of multimachine power systems with detailed models is presented. The mixed direct method first computes the approximate critically cleared trajectory using the critical clearing time which is fast estimated by the EEAC method. Then, the critical energy is evaluated along this trajectory by the PEBS method to access the transient stability. The proposed method overcomes the problem of the variance of potential energy at the boundary crossing and remedies the effect due to the fast dynamics contained in the detailed model. The fast dynamics destroys the assumption that a sustained fault can be used to approximate the critically cleared trajectory and its corresponding critical energy. Moreover, an efficient classifying criterion based on an interaction index for simplifying the power system modeling with reasonab...

Critical-cluster identification in transient stability studies

A method is proposed for identifying the critical cluster of machines, i.e. the machines responsible for loss of synchronism in a power system following a large disturbance. It is based on the conjecture that the loss-of-synchronism condition can be recognised by, first, considering ‘near-critically cleared trajectories’ of the machines and, secondly, observing how they are organised near the system's unstable equilibrium point. The term ‘near-critically cleared trajectories’ is meant to imply the swing curves of the system in the postfault-phase and is computed for a fault-clearing time that is slightly larger than the actual critical clearing time. To realise the above, the method uses the extended equal-area criterion. This direct criterion makes it possible to assess a convenient clearing time for computing the swing curves; to determine the system's unstable equilibrium point with great ease; and to select the critical machines by observing them at the time corresponding to this unstable equilibrium point. It also makes the speed of critical-cluster identification compatible with real-time requirements. Examples are given using the IEEE test system to illustrate the essential features: reliability in correctly identifying the critical clusters, robustness with respect to its capacity to do so under very stringent conditions, and effectiveness concerning its ability automatically to identify critical clusters of any size, i.e. irrespective of the number of machines that they contain.

Another version of the extended equal area criterion approach to transient stability analysis of the Taipower system

Another version of the extended equal area criterion (EEAC) method for fast transient stability analysis is presented. First, an efficient method of identifying the critical cluster by a two-step gap-ranking process of rotor angles is devised to decompose the multimachine system into two coherent groups. Then, the recently developed EEAC method is revised to circumvent some of its major difficulties. The main appeal of the presented method lies in that the empirical corrective factors compensating for the truncation error in the Taylor series expansion are completely eliminated. Moreover, the iterative procedure involved in evaluating the critical clearing angle can be precluded. Another attractive feature to be emphasized is the considerable curtailment in solution time in identifying the critical cluster. Finally, the proposed method is tested on the Taipower system, which is the only power system in Taiwan. The results obtained agree rather well with those from the conventional step-by-step method. It is significant that the presented method is superior to the most prevailing direct method, the potential energy boundary surface method, in its rapidity with comparable accuracy.

Robustness Improvement of the AESOPS Algorithm by Means of a Multimachine State-Space based Correction Formula

Although the sequential computation methods of obtaining eigenvalues associated with electromechanical modes, such as AESOPS, PEALS and III, may solve some eigenvalue problems of very large power systems, their convergence is very sensitive to both initial estimate of eigenvalues and guess at a machine to be disturbed. The lack of a systematic way of having proper starting conditions and the absence of well justified iteration formulas make these methods too fragile to fully identify critical modes.This paper reveals some inherent similarities between dynamic and transient stabilities, and presents two important improvements to overcome the above fatal weakness. First, analytical ways of providing good initial eigenvalues is proposed based on the “partial center of angles” equivalence concept, and of identifying the relevant machines based on the EEAC (Extended Equal Area Criterion). A second improvement is a reasonable and very simple Newton-Jacobian with analytic scalar formula derived in the multimachine state space to replace a heuristic one which has been followed in literatures with no way out. This significantly relieves the final convergence from its dependence on initial values. Thus the iteration procedure robustly, if not uniquely, converges to the mode in which the disturbed machine group participates most. Simulation results and comparisons are given to verify the effectiveness and robustness of these improvements.

Extended equal area criterion revisited (EHV power systems)

A study was conducted on the extra high voltage (EHV) French power system in order to explore the extended equal-area criterion and test its suitability as a fast transient stability indicator. The assumptions underlying the method are reexamined, causes liable to invalidate them are identified, and indices are devised to automatically circumvent them. The selection of candidate critical machines is also reconsidered, and an augmented criterion is proposed. The various improvements were developed and tested on about 1000 stability scenarios, covering the entire 400 kV system. The severity of the scenarios, resulting from the combination of weakened pre and post-fault configurations, subjected the method to particularly stringent conditions. The simulation results are summarized. >

Direct Transient Stability Assessment with Two-Axis Generator Models

The recently developed Extended Equal Area Criterion (EEAC) method has proved to be an accurate and extremely fast transient stability assessment method for the classical model. This model may be too rough for some practical engineering uses. In this paper, the EEAC method is successfully extended to managing the two-axis generator model, i.e. the constant Eq’ model, which may be accepted by more utilities for both planning and operation purposes. The proposed EEAC(Eq’) method has been extensively tested for hundreds cases with faults at all buses in the GREEK system and a Chinese regional system; and very promising results have been obtained. This generalization of EEAC method preserves its accuracy and extremely fast speed.

Extended equal-area criterion: an analytical ultra-fast method for transient stability assessment and preventive control of power systems

A unified approach to transient stability assessment of multimachine power systems is presented. It originates from the equal-area criterion applied to a two-machine equivalent of the system, combined with an analytical procedure totally free from any step-by-step numerical integration. The extended equal-area criterion thus devised provides analytical tools for transient stability analysis and sensitivity assessment. In turn, the latter furnishes transient stability limits and paves the way to control. Means to embed these transient stability techniques in a unified security assessment context are developed. Applications to system planning, operation planning and real-time operation are investigated and many practical uses are suggested. The method is scrutinized by a systematic exploration of 10 different power systems and many contingency scenarios, resulting in over 2500 simulations.

Extended equal area criterion justifications, generalizations, applications

The extended equal area criterion (EEAC) for online transient stability analysis is considered with the following objectives. The first is to state systematically its main hypotheses and key conditions, justify the former, and suggest means to guarantee the latter. The identification and error analysis of critical machines are among the investigated issues. The second is to scan all possible types of instabilities likely to arise in practice and devise means to treat them. The extension of the EEAC to cases beyond the so-called first-swing stability makes it more robust than all direct methods developed up to now. The third objective is to extract essential information out of a large body of simulations and show that the above improvements and extensions enhance the EEAC accuracy and its capability to work properly even under stringent conditions. Possible EEAC applications are also discussed, and uses of the method as such or as an auxiliary technique for more sophisticated approaches are suggested. >