Swing Curves Research Articles

Estimation of parameters in transient stability output swings using autoregressive models

This paper presents a data processing technique for the analysis of output waveforms from transient stability programs. The method is an autoregressive process based on an extension of Prony's method. Using this approach an algorithm is proposed to determine the main parameters that identify a particular waveform. These parameters include the amplitude, frequency, damping constant and phase angle of each mode of oscillation in the swing curve. The algorithm incorporates these variables in the solution and there is no need for further numerical analysis. The effectiveness of the algorithm is verified by tests on both artificial waveforms and actual swing curves from a stability program. In the cases tested, the method has demonstrated satisfactory results with an acceptable degree of accuracy. The computational complexity, necessary precautions, other applications and improvements are also presented.

Analysis of transient stability swings in large interconnected power systems by Fourier transformation

A novel technique to analyze transient stability program swing curves is developed which uses the Fourier transformation. This approach generalizes the swing characteristics to specific frequency components over the range of time. The frequency components of the power system swings are identified in the frequency spectrum. These components can then be selected for further analysis. The mathematical process to determine the amount of damping in the respective frequency components is outlined. The damping constants can be obtained by comparing the magnitudes of the respective frequency components in different time windows. Good correlations of the results with conventional linear eigenvalue analysis have been observed. Advantages and necessary precautions in applying the method are presented. >

Coherency identification by the method of weak coupling

A computationally efficient method for identifying groups of slowly coherent machines in an interconnected power system is presented. The method is based on the concept of weak coupling and uses a linearized representation of the total system. An algorithm is developed that rearranges the synchronous machines of the power system in order of their relative coupling. The machines are grouped into slowly coherent areas corresponding to the point of least coupling using a ‘coupling graph’. The method is illustrated by a case study on an 18-machine system. The results are validated by comparison with swing curves obtained from a transient stability simulation of the total system. It is shown that the proposed method identifies coherent groups that are independent of fault location.

Coherency Based System Decomposition into Study and External Areas Using Weak Coupling

The transient stability studies of large power systems are normally obtained, by dividing the system into study and external areas. In this paper, a systematic procedure is proposed via the joint application of the concepts of weak coupling and small perturbation. The suggested procedure determines weakly coupled areas in the system which are seen to contain weakly coherent machines. The procedure also identifies strongly coherent machine groups within weakly coherent areas. The technique has been applied for a system decomposition for the power grid of northern India containing 50 machines. The accuracy of the method is tested by comparing the swing curves obtained via a simulation study. This comparison validates the coherent behaviour of the machines in the predicted groups.

Conversion of transient stability problems to equivalent systems employing an infinite bus

The classical two machine system conversion to an equivalent system of one finite machine and an infinite bus has been used widely in calculation of swing curves and critical clearing angles. This letter describes direct calculation of equivalent-system swing curves extended to the general (m - 1)-machine system and one infinite bus.

Power System Modal Identification from Large Scale Simulations Using Model Adaptive Reference Control

The major objective of this paper is the identification of the dominant modal responses of large scale power system dynamic simulations. The results of simulations are the angle-time responses of synchronous machine rotors. The rotor inertias coupled via transmission lines produce second order responses, whose damping factors and undamped natural frequencies are identified by a Model Adaptive Reference Control (MARC) system. The MARC identification system is applied successfully to the swing curves of a 1700 bus power system simulation to identify the local and intertie mode parameters. Specifically the sensitivity of modal damping due to power modulation of an HVDC tie is quantified. The low frequency interarea mode damping ratio (¢) is increased from 0.12 to 0.17 by the use of Frequency Sensitive Power Modulation, whereas the other parameters of the two modes were not affected significantly. Thereby the effectiveness of an External Control system on an HVDC transmission line is quantified. Previous evaluations had yielded only qualitative results.

Transient stability analysis of multimachine power systems by the method of hyperplanes

This paper describes a new method for estimating critical clearing times for multimachine systems which dispenses with the calculation of post-fault swing curves. The theoretical basis of the method involves a study of trajectories in the post-fault state space near unstable equilibrium points. Results for a 15- machine system are described and a comparison is made with Lyapunov's direct method. Also described are some results concerning the modes of instability of a multi-machine system.

Stability analysis of power systems using Lie series and pattern-recognition techniques

This paper concerns the estimation of stability domains for transient stability problems in power systems. Lieseries methods are used for generating a solution to Zubov's partial differential equation and pattern recognition algorithms are applied to obtain the boundary defining a region of stability. Critical clearing times for representative problems are obtained using the analytical expression for the stability boundary, and these values are verified by observing the nature of the swing curves obtained by numerical integration.

Control configurations for a synchronous machine with dual excitation†

Abstract This paper describes some digital computer studies of the influences of various control-loop parameters and configurations on the performance of a synchronous machine with two field windings. The basic excitation control is provided by angle and voltage regulators. The effects of using stabilizing transformers to obtain subsidiary feedback within the main control loops is examined. Derivative regulators, with additional feedback signals proportional to rotor velocity and acceleration, are used on both field windings. The rotor-angle transducer is also considered. Steady-state stability is investigated by means of regulation curves, and the Domain separation method is applied in the case of derivative regulators. Transient performance is assessed in terms of swing curves, which indicate stability, and also by voltage recovery characteristics. It is shown that both steady-state and transient stability can be significantly improved by derivative regulators on both axes, and that stabilizers can prev...

Stability of synchronous machines with 2-axis excitation systems

The paper describes analogue- and digital-computer studies of a synchronous machine with various 2-axis-excitation control systems. The steady-state and transient performances of the same machine are analysed, assuming different control schemes, such as rotor-angle control and asynchronised operation, and are compared with a conventional machine. The effects of damper windings, regulator time constants and stabilising circuits on the steady-state performance are shown by regulation curves. It is confirmed that the voltage-regulator loop gain has virtually no effect on steady-state stability, provided the winding with a.v.r. control is aligned with the flux axis by an angle regulator. The improved transient-stability limits obtained with high gains are shown. The fundamentally different transient behaviour of unregulated doubly excited and conventional synchronous machines is explained, and confirmed using accurate mathematical models of the machines. The method of ‘small oscillations’ is applied to determine the speed stability of an asynchronised synchronous machine, and the transient performances of three different control schemes are compared in terms of swing curves and switching-time curves.

Analysis of Natural Half-Wave-Length Power Transmission Lines

This paper provides additional theoretical information on half-wave-length power transmission. The analysis is rendered more general by consideration of a natural half-wave line instead of a short line tuned to half-wave. The effects of line loading and its power factor on the voltage and current profiles of the line and ganerator excitation have been included. Some of the operating problems such as charging of the line and synchronization of the half-wave system are also discussed. The inevitability of power-frequency overvoltages during faults is established. Stability studies have indicated that the use of switching stations is not beneficial. Typical swing curves are also presented.

Routh-Hurwitz conditions and Lyapunov methods for the transient-stability problem

In this paper, Lyapunov functions are generated to determine the regions of asymptotic stability of power systems under transient disturbances. With suitable assumptions, the swing equations of the synchronous machines connected to a power system are second- or third-order nonlinear autonomous differential equations. The Lyapunov functions V, employed to determine the domains of asymptotic stability of these nonlinear differential equations, are simple quadratic forms, whose coefficients are chosen so that the Routh-Hurwitz criteria are satisfied for the corresponding linear differential equations. For a synchronous machine swinging against an infinite bus, three typical Lyapunov functions are generated, taking transient saliency and positive-sequence damping into account. The application of Aizerman's method to the same problem leads to a fourth Lyapunov function. The domains of stability given by these Lyapunov functions are compared with the actual stability region obtained by numerical integration. Consideration of one time constant of the prime-mover governor leads to a third-order differential equation. A Lyapunov function is generated, and the stability surface obtained is verified by computing the swing curves numerically for various initial conditions. Finally, it is explained how some of these techniques could be extended for generating Lyapunov functions for multimachine systems.

Damping in transmission systems under transient conditions

The general practice of neglecting the damping introduced by transmission networks during power-system transient-stability investigations is questioned, and a method is presented for calculating swing curves to include the influence of instantaneous frequency variations on the transmission network. In this consideration, although the system loads are treated as fixed impedances to isolate the effects of the transmission network, the approximation involved still enables the nature and significance of the effects to be demonstrated. An example illustrates that negative damping may be exhibited by a system when account is taken of instantaneous frequency variations in the network, and that consequently not only are the voltage and current distribution less favourable than when assessed by the usual calculations which neglect damping, but the system may be unstable, even though it has been calculated to be stable by conventional methods. As certain power systems, particularly those containing long transmission lines with series-capacitor compensation, have elements which tend to promote negative damping, it is suggested that consideration should be given to the introduction of instantaneous-frequency-deviation effects in transmission networks for transient-stability studies.

Generalized Swing Curves

Generalized Swing Curves

An Experimental Technique for Direct Recording of Machine Swing Curves

An Experimental Technique for Direct Recording of Machine Swing Curves

Effect of Turbine-Generator Representation in System Stability Studies

The effect of increasingly detailed turbine-generator representation on calculated system stability limits is discussed. A new computer program which permits transient saliency, flux linkage variation caused by armature current, saturation, machine and system damping, the speed-governor system, and the excitation system to be represented is compared to previous computing methods. Swing curves and permissible loading limits for an example system obtained by using varying degrees of detail in machine representation are compared. The advantage of a complete machine representation in permitting a single study approach to transient, dynamic, and steady-state stability is brought out.

Simplified Swing Curves

Simplified Swing Curves

Concept of synchronous generator stability

The conventional ideas concerning power-system stability are briefly outlined. Some ways in which the automatic voltage regulator and velocity-sensitive governor have modified these ideas by showing their effects qualitatively on alternator swing curves are indicated. They indicate that overall stability cannot with certainty be assessed from the first rotor swing, and the paper concludes by showing how, for some particular system conditions, the machine control devices modify transient stability.

Automatic Recording Device of Transient Swing Curves in Electronic A C Network Analyzer

Automatic Recording Device of Transient Swing Curves in Electronic A C Network Analyzer

The automatic solution of power-system swing-curve equations

The paper details the problem of transient stability in electrical power systems and divides the methods used to date into four categories. These categories, with the relevant literature, are briefly reviewed.The paper then describes the theory, method of construction and mode of operation of an automatic step-by-step computer for power-system swing curves; the machine has facilities for two generators only but may be extended in scope by the addition of equipment similar to that already employed. The limitations of this machine are discussed and a direct-analogue method for use with the generator units of a network analyser is then described.The procedure for calibration of the direct analogue is given, and difficulties in the setting up of the analogues of damping power and inertia constant are mentioned. Comparison of the results of a simple swing-curve problem by integraph, step-by-step and analogue appears at the end of the paper.Automatic generator-unit operation on a network analyser is possible with this type of direct-analogue equipment.