The development of trajectory sensitivity analysis for hybrid systems, such as power systems, is presented in the paper. A hybrid system model which has a differential-algebraic-discrete (DAD) structure is proposed. This model forms the basis for the subsequent sensitivity analysis. Crucial to the analysis is the development of jump conditions describing the behavior of sensitivities at discrete events, such as switching and state resetting. The efficient computation of sensitivities is discussed. A number of examples are presented to illustrate various aspects of the theory. It is shown that trajectory sensitivities provide insights into system behavior which cannot be obtained from traditional simulation.

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Trajectory sensitivity analysis of hybrid systems

The primary objective of any electric utility company in the new competitive environment would be to increase the market value of the services it provides with the right amount of reliability, and at the same time, lower its costs for operation, maintenance, and construction of new facilities in order to provide lower rates for customers. The electric utility company will strive to achieve this objective via many different means, one of which is to defer the capital distribution facility requirements in favor of a distributed generation (DG) solution by an independent power producer (IPP) to meet the growing customer load demand. In this case, the distribution capital investment deferral credit received by the IPP will be dependent on the incremental system reliability improvement rendered by the DG solution. In other words, the size, location and the reliability of the DG will be based on the comparable incremental reliability provided by the distribution solution under considerations. This paper presents a reliability model for determining the DG equivalence to a distribution facility for use in distribution system planning studies in the new competitive environment.

Reliability modeling of distributed generation in conventional distribution systems planning and analysis

A real-time performance monitoring system for monitoring an electric power grid. The electric power grid has a plurality of grid portions, each grid portion corresponding to one of a plurality of control areas. The real-time performance monitoring system includes a monitor computer for monitoring at least one of reliability metrics, generation metrics, transmission metrics, suppliers metrics, grid infrastructure security metrics, and markets metrics for the electric power grid. The data for metrics being monitored by the monitor computer are stored in a data base, and a visualization of the metrics is displayed on at least one display computer having a monitor. The at least one display computer in one said control area enables an operator to monitor the grid portion corresponding to a different said control area.

Wide-area, real-time monitoring and visualization system

The computation of an optimal operation point in power systems is a nonlinear optimization problem in functional space, which is not easy to deal with precisely, even for small-scale power systems. On the other hand, the emergence of competitive power markets makes optimal power flow (OPF) with transient stability constraints increasingly important because the conventionally heuristic evaluation for the operation point can produce a discrimination among market players in the deregulated power systems. Instead of directly tackling this tricky problem, in this paper, OPF with transient stability constraints (OTS) is equivalently converted into an optimization problem in the Euclidean space via a constraint transcription, which can be viewed as an initial value problem for all disturbances and solved by any standard nonlinear programming techniques adopted by OPF. The transformed OTS problem has the same variables as those of OPF in form, and is tractable even for the large-scale power systems with a large number of transient stability constraints. This paper also derives the Jacobian matrices of the transient stability constraints and gives two computation algorithms based on the relaxation scheme. The numerical simulation verified the effectiveness of the proposed approach.

Optimal operation solutions of power systems with transient stability constraints

In this paper, a new hybrid intelligent system is proposed for transient stability prediction. This intelligent system is composed of a preprocessor, an array of neural networks (NN) and an interpreter. The preprocessor partitions the whole set of synchronous machines into subsets, each one including only two generators. Each subset is assigned to one NN, which extracts the input/ output mapping function of that subset. Then, the interpreter combines the responses of the NNs in a voting procedure to determine the transient stability status of the power system. This mechanism can cover the probable errors of the NNs, increasing the accuracy of the final response of the hybrid intelligent system. In addition to the transient stability status, this intelligent system can determine tripped generators and islanded parts of the power system for unstable cases. The proposed method has been examined on the PSB4 and New England test systems. The obtained results indicate the efficiency of the hybrid intelligent system for transient stability prediction.

Transient Stability Prediction by a Hybrid Intelligent System

The transient stability of power systems is investigated using a new analytical tool. Instead of computing the sensitivities of energy margins, trajectory sensitivity functions of the post-fault system with respect to parameters are computed. The goal is to find how sensitive the trajectories of each state are to variations in system parameters. When the system becomes more stressed, the state trajectories become more sensitive to variations in parameters. Thus these trajectory sensitivities can be used as a measure of system security. This concept is illustrated on the IEEE single- and seventeen-machine systems, and it is shown that dynamic sensitivity functions can also be applied to systems of differential-algebraic equations where the TEF method has limitations.

A new approach to dynamic security assessment using trajectory sensitivities

All players in the US electricity industry must understand how specific generation decisions, wheeling arrangements, and legislative initiatives affect system operations. This article features PowerWorld, a comprehensive power system simulation package developed to help meet this need. The package is designed for the many new players in the power industry who will never operate an actual system but who must have a basic understanding of its operations. The package, which runs in the Microsoft Windows environment, is user friendly, interactive, and menu driven. It effectively uses visualization techniques to present the basics of power system operations and control simply, yet also with a level of detail to accurately model large-scale systems realistically and with the appropriate level of fidelity. The package has been demonstrated to policy makers, legislative analysts, small and large utilities, and regulatory decision makers both nationally and internationally. It has been found to be a very effective tool for communicating the many technical and economic impacts of third-party access.

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Visualizing power system operations in an open market

We propose a new approach to dynamic security analysis based on sensitivity theory. We compute the trajectory sensitivity of the system with respect to a pre-selected set of parameters such as generator output using different contingencies and clearing times. Initial condition sensitivity is also be examined. From this we find out which machines are critical, or for a given t/sub cl/, the level of stress in the system. Motivation through a single machine example followed by validations on the WSCC three generator and IEEE 17 generator test systems are presented.

Sensitivity theory in power systems: application in dynamic security analysis

Various proposals have been made for new paradigms for operating the restructuring electrical system. One of the key challenges associated with this restructuring is to effectively analyze and evaluate the effects these alternative paradigms may have on major aspects of power system operations, including the so called ancillary services. The paper provides preliminary results on the development of a simulation tool to perform this analysis. Since power systems are ultimately governed by the laws of physics, the heart of the tool is a power system simulation engine, valid over a simulated time frame of minutes to days. The modular structure of the tool then allows other packages to be superimposed on this structure to represent different proposed paradigms. Integration of effective visualization into an interactive simulation environment is then used to gain understanding and insights concerning the attributes of each paradigm.

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M.J. Laufenberg

Papers

A new approach to dynamic security assessment using trajectory sensitivities

Visualizing power system operations in an open market

Sensitivity theory in power systems: application in dynamic security analysis

A simulation tool for analysis of alternative paradigms for the new electricity business

Some clarifications in the transient energy function method