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 V_{i} for machine i 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.
[1]
P. Hartman.
Ordinary Differential Equations
,
1965
.
[2]
N. Rouche,et al.
Stability Theory by Liapunov's Direct Method
,
1977
.
[3]
M. Ribbens-Pavella,et al.
Direct Methods for Stability Analysis of Large-Scale Power Systems
,
1979
.
[4]
R. Podmore,et al.
A Practical Method for the Direct Analysis of Transient Stability
,
1979,
IEEE Transactions on Power Apparatus and Systems.
[5]
Naoto Kakimoto,et al.
Transient stability analysis of multimachine power system by Lyapunov's direct method
,
1981,
1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.
[6]
A.R. Bergen,et al.
A Structure Preserving Model for Power System Stability Analysis
,
1981,
IEEE Transactions on Power Apparatus and Systems.
[7]
A. Fouad,et al.
Transient Stability of a Multi-Machine Power System Part I: Investigation of System Trajectories
,
1981,
IEEE Transactions on Power Apparatus and Systems.
[8]
M. A. Pai,et al.
Power system stability : analysis by the direct method of Lyapunov
,
1981
.
[9]
Vijay Vittal,et al.
Power system transient stability using the critical energy of individual machines
,
1982
.