Towards a theory of voltage collapse in electric power systems

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

Transient stability analysis of a power system is concerned with the system's ability to remain in synchronism following a disturbance In utility planning, transient stability is studied by numerical simulation The long CPU run times for simulation preclude their use for on-line security analysis Interest has therefore shifted toward the Lyapunov direct method of stability analysis This paper provides a critical review of research on direct methods since 1970 Considerable progress has been made on both theoretical properties of energy functions and on criteria suitable for on-line implementation Current theory provides a satisfactory treatment of voltage-dependent reactive power demand, transfer conductances, and flux decay However, it cannot incorporate the exciter control Proposed on-line criteria appear to work very well on sample examples; but, they still lack rigorous justification Finally, recent work has shown that power systems can exhibit chaotic behavior This surprising fact demonstrates that our understanding of the dynamics of power systems remains incomplete

Direct methods for transient stability analysis of power systems: Recent results

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

Motivated by transient stability analysis of power systems, a framework for study of Lyapunov stability of equilibria in differential/algebraic (DA) systems is presented. Following a basic result on existence and uniqueness of solutions, it is easy to state general stability results. Several useful stability criteria for special DA structures are derived. One result for a Hamiltonian-type structure is applied to the study of undamped power systems. >

Stability theory for differential/algebraic systems with application to power systems

In this paper, an "energy function" is derived for transient stability analysis of power systems. The main contribution of this paper is the generality of the model for the loads. The loads are modeled as constant real power loads but the reactive part of the loads are modeled as arbitrary function of the load bus voltage. This model accounts for the voltage transients of the load busses and for this general model, it is shown that the system satisfies the law of conservation of energy. An efficient algorithm for determining the stability of the system for a given disturbance is described. Results of simulation of the system studied by El-Abiad and Nagappan [2] are included and it is shown that due to the fluctuations in the system voltages, the commonly used energy function over estimates the energy of the system during system transients.

A generalized energy function for transient stability analysis of power systems

A technique for extracting filled-in information in form documents is presented. The transformation that is required to convert a filled-in form to match the master (blank form) is derived using results from projective geometry. Experimental studies with several forms indicate the proposed technique to be accurate and robust.

Document registration using projective geometry

An algorithm for determining surface shapes from intensity measurements is presented. Assuming a point-surface illumination and a Lambertian surface, a model that allows for the estimation of the normals at any point on the surface as well as the depth at any point in the image plane along the viewer (camera) direction is developed. Explicit shape descriptors are derived for local characterization of the surface at any point. Studies with synthetic and natural scenes indicate that surface-shape descriptors are shown to provide a reliable local characterization of the surface at any point on the surface within the occluding boundaries. >

http://ieeexplore.ieee.org/iel1/31/3188/00103219.pdf

Shape determination from intensity images-a new algorithm

The load flow equations of a loss less transmission system has the same structure that of a nonlinear resistive network. By utilizing the minimum loss property of nonlinear resistive networks [9], the solution to the load flow equation can be characterized as the minimum of a suitably defined function. This characterization is utilized in solving the problem of scheduling power for economic operation of power systems, while taking account the transient stability margin of the resulting operating point. For the model used in this paper it is shown that the solution is essentially a load flow problem of a suitably modified system.

http://ieeexplore.ieee.org/iel5/31/23523/01085099.pdf

Application of minimum loss property of resistive networks to power scheduling

A novel algorithm for the determination of surface shapes from intensity measurements is presented. The proposed model allows the estimation of the normals at any point on the surface and of the depth at any point in the image plane along the viewer (camera) direction. Simple shape descriptors for characterizing most developable surfaces are derived. It is shown that the principal curvatures of the surface are simply eigenvalues of the restriction of the shape matrix to the tangent space. The proposed algorithm allows incorporation of prior information obtained from stereopsis and other vision processes. Tests with intensity images have shown the algorithm to be convergent, robust, and accurate. >

N. Narasimhamurthi

Papers

A generalized energy function for transient stability analysis of power systems

Document registration using projective geometry

Shape determination from intensity images-a new algorithm

Application of minimum loss property of resistive networks to power scheduling

Shape determination from intensity images-a new algorithm