Coherency-Based Dynamic Equivalents: Applications in Transient Stability Studies

R.W. DeMello, R. Podmore and K.N. Stanton, PAS 95, No.4, July/August 1976, p.1101 (abstracts)

The paper describes the development of a method for determining an equivalent dynamic representation of an external power system for use in transient stability studies. The resulting equivalent is composed of normal power system models element and therefore can be used with conventional transient stability programs. The approach used exploits generator coherency, which is the tendency for groups of generators to swing to gether.

The performance of of the coherency-based dynamic equivalents has been evaluated by tests on 10-generator, 39-bus system and a 295 generator, 732-bus system. Comparison of swing curves have demonstrated that the technique is accurate for both first and successive swings and that the accuracy is unaffected by the prevailing stability conditions. On the larger system, the method has archived greater than 10:1 reduction in the size of the external system representative.

The coherency-base dynamic equivalents have the potential for application as a production tool in planning studies and represent a key step in the future development of on-line transient security monitoring procedures

Dynamic Equivalents using operating Data and Stochastic Modeling

M.A.H. Ibrahim, O.M Mostafa, and A.H. El-Abiad, PAS 95, No.5 September /Oktober 1976, pp. 1713 – 1732

A method is developed to determine equivalent for extensive power systems external to an internal system equiooed with central control computer. These equivalents are needed for different system studies where the internal system is represented in detail, and the external system are represented by the equivalent to simulate the interaction effects of the external system on the internal system for disturbances originating in internal system.

The method uses a generalized Thevenin’s theory for representing the quasi-steady-state performance of the external system and stochastic linear differences equations to represent the dynamic changes in the internal equivalent voltage magnitudes and phase angels

The methods are demonstrated on two test systems

Dynamic Equivalents by combination of reduced order Models of System Component

HY Altalib and P.C. Krause, PAS 95 No.5, September/Oktober 1976 pp 1535 – 1544

Davidson,n Method is used to reduce the order of a one machine infinite bus system with excitation control from a tenth to a fourth order system. This is accomplished by first reducing the machine from seven to third order and excitation system from third to fisrt order and the combining these models to form the reduced order model of the one machine infinite bus system. It is shown that that eigens values which predict the natural and introduced rotor oscillation are accurately preserved by this method.

Also, a method of combining reduced order models of machine to form dynamic equivalents of multimachine system is set forth. Here, Davidson’s method is used to obtain a reduced order model of each machine where upon approximation are used to achieve a simple means of combining these reduced order models to form a dynamic stability investigations. It appears that the method of reduction presented in this paper may offer advantages in the analysis of power system

An External System Equivalent Model Using Real Time Measurement for System Security Evaluation

J.F. Dopazo, M.H. Dwarakanath, J.J. Li, and A.M. Sasson, PAS 96, No.2 March/April 1977, pp 431 – 466 A model for external system equivalent appropriate for real-time system security evaluations proposed. The model has two components, one which models the reaction of the external system to system changes in past time intervals and a second component for adjusting the equipment model to present operating levels. Decoupling techniques between P-δ and Q –V quantities at the boundaries are used in the model formulation and recursive system identification technique are employed to obtain the parameter of the model. Numerical Simulation studies made on the 1976 AEP-ECAR system show encourage results. Possible further improvement and the need for testing for the real time data are discussed, and it is hoped that the paper will encourage others to devote effort to these and other pertinent issues

Coherency Recognition for transient Stability Studies Using Singular Points

B.D. Spalding, H.Yee, and D.B Goudie, PAS 96, No.4 July/August 1977, pp. 1368-1375

This paper describes a new method for the recognition of coherent machines for use in transient stability studies. The machine angles are compares for both the stable operating point, and for the unstable singular or equilibrium point corresponding to the system instability excepted to result from the system instability expected to result from the particular fault under study. The technique requires the solution of n-1 non linier algebraic equation where a 25 machine and the method is shown to have advantages compared with existing technique.

A Computer based eigenvalue Approach for Power System Dynamic Stability Evaluation

H.M. Zein El-Din and ETH Alden, PAS 97 No 2 March April 1978, p. 318 (Abstract) This paper describes a highly efficient computer based procedure for determining system dynamic stability as a function of system parameters. The method is applicable in many practical situations where relatively small number of the system eigenvalue are known to be critical in describing stability. Once a base case, a full set a eigenvalue and eigenvector is determined, the movement of these critical eigenvalue is tracked over relatively wide parameter variations without recomputation of either the eigenvalue or the eigenvectors. The new values are estimated using first and second order eigenvalue sensitivity terms followed by an inverse iteration technique to refine the estimate. Results are presented by using a three generator, five bus by system simulation to illustrate the method.

An RMS Coherence Measure: A basic for Unification of coherence and modal Analysis Model Aggregation Technique

R.A. Schlueter, H. Akhtar, H. Modir, Paper A 78 533-2, 1978 Summer meeting, Los Angeles. Ca, July 1978.

The principal objective of this research is to show that modal analysis and coherency based aggregation procedures can be considered completely parallel model aggregation procedures. Thus it will be shown that modal analysis equivalents are coherency equivalents and that procedures for aggregating coherent group can be considered to be equivalent to the rules of mode elimination for the modal analysis procedure. These results depend upon first deriving a general probabilistic model of power system disturbance and an appropriate linearized model the power system. An rms measure of coherence is then defined that measures the expected value of a time average of differences in voltage angel deviations on generator buses for the probabilistically described disturbances. The modal analysis based equivalent is then shown to be a coherency based equivalent by showing that the rules of mode elimination for forming a modal analysis equivalent for the linearized system model considered can be derived by a modal analysis of this rms coherency measure evaluated over an infinite internal with the same linearized system model and a completely un certain disturbance model. The procedure for aggregating coherent groups of generator is shown to be equivalent to the rules of mode elimination for modal analysis procedures because it is shown that (1), Both methods of reducing model order can be based on an rms coherency measure and any particular form of the generalized model of disturbance desired and (2) both methods should produce equivalents as the unreduced system

Testing of the modal dynamic equivalent technique

W.W. Price, EM Gulachenski, P. Kundur, F.J Lange, G.C Loehr, B.A. Roth, and R.F. Silva, PAS 97, No.4, July/august 1978

Several technique have been proposed in the literature for constructing dynamic equivalent of power systems for used in stability studies. These techniques exist primarily as research tools and their applicability for use in large scale production studies has not been clearly established. One of technique that appears to be promising is the model analysis approach developed by general electric company for electric research council project RP90-4. This paper describes the investigation carried out to evaluate the effectiveness of this approach using a realistic power system model

The paper identifies the primary reason for the computational savings offered by the method and suggests modifications directed toward automating and simplifying the procedure. It is concluded that equivalencing method results in significant computational saving while retaining acceptable accuracy, and with proposed modifications could be practical for off line stability analysis.