Study Of Transient Stability By Transient Energy Function

Large-scale AC-DC hybrid power systems have become a basic pattern for power transmission in China. Currently, time-domain simulation is widely used for transient stability analysis, which has the disadvantages of high computational burdens and lack of system stability margin information. An alternative method for transient stability analysis is the direct method, which assesses transient stability from the energy point of view. Direct method requires much less computation efforts. In addition, the stability margin of the system can be obtained. Due to the challenges in system modelling, energy function construction, and determination of critical energy value, it is challenging to apply direct method for transient stability analysis of AC-DC hybrid power systems. This paper is a step in exploring the application of direct method in AC-DC hybrid power systems.

This paper presents an overview about the main advances which occurred in the application of a direct method for transient stability analysis. The text is mainly focused on the potential energy boundary surface (PEBS) and boundary controlling unstable (BCU) method. The author's opinion about future perspectives and research areas of interest are given at the end of the text.

Transient stability domain estimation of AC/DC systems considering HVDC switching characteristics based on the polynomial Lyapunov function method

The method of generalized equal-area criterion (GEAC) for transient stability analysis of power systems and its recent generalization to cover a wider range of faults are explained. The method is based on an exact mathematical transformation of the time-invariant dynamical equations of an n-machine system into an equivalent single-machine-infinite-bus (SMIB) system equation with time-varying parameters. Further approximations are made to assign appropriate constant values to the SMIB parameters, thus enabling the use of a modified version of the well-known equal-area criterion. An approximate stability index is then defined to yield the degree of stability/instability. GEAC and time simulation results showed excellent agreement in the majority of cases; in the worst case the difference did not exceed 7%. Some tests results are presented. Potential applications of the GEAC method for online transient stability assessment are discussed. >

Attempts to complement the theoretical foundation of direct methods for transient stability analysis of structure preserving models made by H.D. Chiang et al. (see IEEE Trans. Circuits Syst., vol.CAS-34, p.160-73, 1987) by treating the model as a set of differential-algebraic equations that are not reduced to a set of pure differential equations. The implications of stability analysis on structure preserving models of power systems are explored. The model includes nonlinear load models and exciter dynamics. A practical controlling unstable equilibrium point method tailored to structure preserving models is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Recent efforts to apply direct methods of transient stability analysis to multimachine power systems have used the so-called "energy functions." These functions describe the system transient energy causing the synchronous generators to depart from the initial equilibrium state, and the power network's ability to absorb this energy so that the synchronous machines may reach a new post-disturbance equilibrium state. Recent results have shown that not all the transient energy contributes to system separation. Indeed it has become increasingly evident that system separation depends on the energy of certain individual machines or groups of machines, which comprise the critical group, and which tend to separate from the rest of the machines (which make up the noncritical group). Thus there is a need for generating energy functions for individual machines (or for groups of machines). Using a center of inertia frame of reference, the energy function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V_{i}</tex> for machine <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</tex> is derived. A procedure for first swing transient stability assessment is developed using the energy function of individual machines and groups of machines. The method is tested extensively on two realistic power networks (the 20-generator IEEE System and the 17-generator reduced Iowa System). An analytical justification for using the critical energy of individual machines in stability assessment is provided using an invariance principle for ordinary differential equations. Power system transient stability is analyzed using the energy function of the critical group of machines. This energy function is dependent on all state variables of the power system, and satisfies the hypotheses of the invariance theorem of La Salle, enabling us to deduce the asymptotic stability of the post-disturbance equilibrium of the entire power system. It also enables us to obtain an estimate of the domain of attraction of this equilibrium of the entire power system. The methodology advanced herein, which combines computer-aided techniques with analytical tools, yields less conservative results than were obtained in previous works that used total system energy. It is to be noted that the present results are preliminary in the sense that the mechanism of separation of the critical group of machines from the rest of the system needs further investigation.

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.

This paper proposes a decoupling based direct method to analyze the post-contingency transient stability for a general multi-machine power system. A linear decoupling transformation is used to construct the same number of independent single machine infinite bus (SMIB) power systems as oscillation modes. Each SMIB system carries stability information regarding one oscillation mode of the original system at the equilibrium. Then, the transient energy function method is applied on all decoupled SMIB systems to calculate stability margins, the smallest of which indicates the stability margin of the original system. Case studies on an IEEE 9-bus power system and a WECC 179-bus power system demonstrate the validity of the proposed method.

Direct stability analysis using an energy function has recently been widely used for angular and voltage stability analysis in electric power systems. Considerable efforts have concentrated on seeking energy functions for lossy power systems, accomplished only for the simple two-bus system. A new approach is presented to derive an energy function by using the complex integral of bus current equations with respect to bus voltages. Under an assumption that all transmission lines have a uniform R/X ratio, it is shown that the energy function can be developed for multimachine power systems with losses. The proposed energy function is tested on sample systems by comparing the time simulation method, which shows the validity of the proposed method.

The wide application of WAMS (Wide Area Measurement System) provided a new thinking for transient stability analysis of power system. Based on real-time measurement information from WAMS, a method to quickly analysis power system transient stability that does not depend on network structure, model and parameters of power system is proposed in this paper. Firstly, the parameters of system are identified online by improved least squares method on basis of that the multi-machine power system is equivalently reduction to one machine infinity bus system. The equilibrium point and stability margin of equivalent system are rapidly computed, and then the stability of system is quickly judged. The simulation results show that the algorithm can accurately judge transient stability of system and has better antidisturbance ability and robustness. The issue of dependence of transient stability analysis on system model and parameter is solved. The adverse influences of data lose and measurement errors in actual measurement of the WAMS on analysis results are avoided effectively. Keywords-power system; wide-area measurement system; parameter identification; energy function; transient stability analysis

Consistent formulations of direct and iterative methods of pile group analysis are presented. The iterative methods are derived from the same equilibrium and compatibility equations as the direct methods but are cast in different forms. These new iterative methods highlight the shortcomings of some existing iterative methods of analysis, although conceptually they are similar. Unlike the direct methods of analysis in which the stiffness matrix of the pile group system is generally fully coupled, the individual pile stiffness matrix can be uncoupled in the iterative methods and requires only a minimal amount of computer core storage. The accuracy of the iterative methods is compared with that of the direct method, and generally good agreement can be obtained. Field tests on the axial and flexural response of pile groups are studied and show that, in general, the computed response compares favourably with the field measurements. L'article présente des formulations logiques de méthodes directes et itératives pour l'analyse des groupes de pieux. Les méthodes itératives découlent des mêmes équations d'équilibres et de compatibilité que les méthodes directes, mais elles prennent des formes différentes. Ces nouvelles méthodes itératives accentuent les insuffisances de quelques méthodes itératives d'analyse à présent disponibles, malgré une certaine ressemblance de conception. En contraste avec la méthode directe d'analyse, dans laquelle les matrices de rigidité du système représenté par le groupe de pieux sont en général pleinement couplées, la matrice de rigidité du pieu individuel peut être découplée dans les méthodes itératives et n'a besoin que d'une quantité minimale de mémorisation par tores magnétiques dans l'ordinateur. Une comparaison de la précision des méthodes itératives avec celle de la méthode directe indique qu'en général l'accord est bon. Une étude des essais in situ sur la réponse axiale et de flexion des groupes de pieux démontre que généralement la réponse calculée s'accorde bien avec les mesures en place

This paper proposes a method for power system stability monitoring and analysis through Phasor Measurement Units' (PMUs) measurements (i.e., bus voltage magnitudes and angles). Real-time stability monitoring can be achieved by observing the behavior of the measurement data's frequency spectra. In addition, a modified Thevenin equivalent-based model is proposed to analyze the system small-signal stability and transient stability. The model's parameters are estimated based on the phasor measurements. We verify our proposed method through simulations on a RTDS/PMU/PDC testbed and perform analyses on real PMU data.

Practical applications of Lyapunov's direct method to transient stability analyses of multimachine power systems have been obstructed by the well-known conservative nature and the computational difficulty accompanying the usual critical value of Lyapunov function. These problems have been solved in this paper by introducing a new critical value for the first swing stability, and by developing a efficient method of calculating it as well as one of taking account of transfer conductances. These methods have been applied to a transient stability analysis of a 10-machine power system, and yielded results of practical significance.

A direct matrix method for the elastic stability analysis of plates

Both Angle and voltage stability are discussed in the context of the energy function approach. It is shown that complete decoupling of the two phenomena is not possible in general, particularly in stressed systems. It is demonstrated that the UEP (unstable equilibrium point) concept is a valid one for both types of stability analysis. >