Stability analysis programs are a primary tool used by power system planning and operating engineers to predict the response of the system to various disturbances. Important conclusions and decisions are made based on the results of stability studies. This paper presents a theoretical foundation of direct methods for both network-reduction and network-preserving power system models. In addition to an overview, new results are offered. A systematic procedure of constructing energy functions for both network-reduction and network-preserving power system models is proposed. An advanced method, called the BCU method, of computing the controlling unstable equilibrium point is presented along with its theoretical foundation. Numerical solution algorithms capable of supporting online applications of direct methods are provided. Practical demonstrations of using direct methods and the BCU method for online transient stability assessments on two power systems are described. Further possible improvements, enhancements and other applications of direct methods are outlined.

Direct stability analysis of electric power systems using energy functions: theory, applications, and perspective

A boundary of stability region based controlling unstable equilibrium point method (BCU method) for direct analysis of power system transient stability is presented. Features distinguishing the BCU method from the existing direct methods are that it consistently finds the exact controlling unstable equilibrium point (UEP) relative to a fault-on trajectory and that it has a sound theoretical basis. Moreover, the BCU method appears to be fast. This method is based on the relationship between the boundary of stability region of a power system and that of a reduced system. The BCU method finds the controlling UEP of the original system via a reduced system whose controlling UEP is easier and cheaper to compute. Effective numerical schemes to speed up the presented method are also proposed. This method has been tested on several power systems with very promising results. Simulation results on a 50 generator, 145 bus system are presented along with a comparison between the results obtained using the BCU method and another existing method. >

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A BCU method for direct analysis of power system transient stability

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.

Power system transient stability using individual machine energy functions

The hybrid method of power system transient stability analysis, which combines the desirable features of both the time-domain simulation technique and the direct method of transient stability analysis, is presented. The hybrid method first computes the actual system trajectory using time-domain simulation, then evaluates the transient energy function in order to derive a stability index for fast derivation of transient stability limits. Proper criteria are proposed to stop the time-domain simulation of the system trajectory to reduce CPU time, once the status of the system has been identified. The method was successfully applied to three test systems varying in size from four generators to 50 generators. The method is shown to be a potential tool for online calculation of transient stability limits. >

Hybrid transient stability analysis (power systems)

Direct methods for studying dynamics of large-scale electric power systems-A survey

Direct methods of transient stability analysis of a multi-machine power system, using a function describing the system's transient energy, are discussed. By examining the trajectory of the disturbed system, the following fundamental questions are dealt with: the concept of a controlling unstable equilibrium point (u.e.p.), the manner in which some generators tend to lose synchronism, and identifying-the energy directly responsible for system separation. Resolving these issues will substantially improve transient stability analysis by a direct method.

Transient Stability of a Multi-Machine Power System Part I: Investigation of System Trajectories

This paper deals with transient stability analysis of a multi-machine power system using direct methods based on the transient energy of the system when subjected to a large disturbance. The component of the transient energy that does not contribute to system separation is identified, and is corrected for in the computation of the critical transient energy at clearing. The technique is validated by computing critical clearing times for two test systems and comparing the results with those obtained by time solutions.

Transient Stability of a Multi-Machine Power System. Part II: Critical Transient Energy

Nathan Cohn's newly proposed technique of coordinated, system-wide correction of time error and inadvertent interchange is examined and validated by computer simulations. Area and system performances are investigated for a sudden change in load or generation in a three-area power system. The following effects are examined: changing the time of correction; simultaneous versus individual correction of time error and inadvertent interchange; the type of disturbance; the governor delay time; and the presence of sustained errors.

A. A. Fouad

Papers

Transient Stability of a Multi-Machine Power System Part I: Investigation of System Trajectories

Transient Stability of a Multi-Machine Power System. Part II: Critical Transient Energy

Effect of Coordinated Correction of Tie-Line Bias Control in Interconnected Power System Operation