Energy functions, transient stability and voltage behaviour in power systems with nonlinear loads
TL;DR: In this article, the authors present preliminary results in a computer program aimed at energy function analysis of transient behavior of power systems with nonlinear loads, which preserves the network structure, is of a differential-algebraic type, and the concepts permit the establishment of a connection between transient stability, multiple stable equilibria, and voltage behavior.
Abstract: The authors present preliminary results in a computer program aimed at energy function analysis of transient behavior of power systems with nonlinear loads. The model, which preserves the network structure, is of a differential-algebraic type. This introduces some new analytical issues, but the concepts permit the establishment of a connection between transient (angle) stability, multiple stable equilibria, and voltage behavior. A practical method for determining and classifying the equilibrium points of the model is developed. >
Citations
More filters
11 Jun 2018
TL;DR: The challenges of such low-inertia power systems are reviewed, the solutions that have been put forward thus far are surveyed, and the topics of power system stability, modeling, and control are touched upon.
Abstract: The electric power system is currently undergoing a period of unprecedented changes. Environmental and sustainability concerns lead to replacement of a significant share of conventional fossil fuel-based power plants with renewable energy resources. This transition involves the major challenge of substituting synchronous machines and their well-known dynamics and controllers with power electronics-interfaced generation whose regulation and interaction with the rest of the system is yet to be fully understood. In this article, we review the challenges of such low-inertia power systems, and survey the solutions that have been put forward thus far. We strive to concisely summarize the laid-out scientific foundations as well as the practical experiences of industrial and academic demonstration projects. We touch upon the topics of power system stability, modeling, and control, and we particularly focus on the role of frequency, inertia, as well as control of power converters and from the demand-side.
621 citations
Cites background from "Energy functions, transient stabili..."
...short term voltage dips in the transient region [94];...
[...]
TL;DR: In this paper, the authors developed trajectory sensitivity analysis for hybrid systems, such as power systems, and proposed a hybrid system model which has a differential-algebraic-discrete (DAD) structure.
Abstract: 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.
512 citations
TL;DR: In this article, an approach for experimental determination of aggregate dynamic loads in power systems is described, which can be expressed as nonlinear differential equations or equivalently realised in block diagram form as interconnections of nonlinear functions and linear dynamic blocks.
Abstract: This paper describes an approach for experimental determination of aggregate dynamic loads in power systems. The work is motivated by the importance of accurate load modeling in voltage stability analysis. The models can be expressed in general as nonlinear differential equations or equivalently realised in block diagram form as interconnections of nonlinear (memoryless) functions and linear dynamic blocks. These components are parameterized by load indexes and time constants. Experimental results from tests in Southern Sweden on the identification of these parameters are described. >
442 citations
01 Nov 1995
TL;DR: In this article, a theoretical foundation of direct methods for both network-reduction and network-preserving power system models is presented, along with numerical solution algorithms capable of supporting online applications of the direct methods.
Abstract: 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.
412 citations
TL;DR: In this article, a framework for study of Lyapunov stability of equilibria in differential/algebraic (DA) systems is presented, motivated by transient stability analysis of power systems.
Abstract: 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. >
290 citations
References
More filters
TL;DR: In this paper, the authors describe the development and evaluation of an analytical method for the direct determination of transient stability, which is based on the analysis of transient energy and accounts for the nature of the system disturbance as well as for the effects of transfer conductances on systenmbehavior.
Abstract: This paper describes the development and evaluation of an analytical method for the direct determination of transient stability. The method developed is based on the analysis of transient energy and accounts for the nature of the system disturbance as well as for the effects of transfer conductances onsystenmbehavior. It has been evaluated on a 10 generator 39 bus system and on a 20 generator 118 bus system. The method predicts critical clearing times for first swing transient stability which agree very closely with the results of simulations.
929 citations
TL;DR: In this article, a new model for the study of power system stability via Lyapunov functions is proposed, which is an assumption of frequency-dependent load power, rather than the usual impedance loads which are subsequently absorbed into a reduced network.
Abstract: A new model for the study of power system stability via Lyapunov functions is proposed. The key feature of the model is an assumption of frequency-dependent load power, rather than the usual impedance loads which are subsequently absorbed into a reduced network. The original network topology is explicitly represented. This approach has the important advantage of rigorously accounting for real power loads in the Lyapunov functions. This compares favorably with existing methods involving approximations to allow for the significant transfer conductances in reduced network models. The preservation of network topology can be exploited in stability analysis, with the concepts of critical and vulnerable cutsets playing central roles in dynamic and transient stability evaluation respectively. Of fundamental importance is the feature that the Lyapunov functions give a true representation of the spatial distribution of stored energy in the system
641 citations
TL;DR: In this paper, it has been confirmed analytically and by simulations that the multiple load flow solutions are likely to appear under the heavy-loaded conditions, and that the individual solutions of the solution pair have different features from each other, from the standpoint of stability, although they are close to each other.
Abstract: There have been observed several voltage instability phenomena in electric power systems where receiving end voltages oscillate remarkably or get much lower than the nominal values. Those phenomena tend to occur in heavy loaded conditions and seem to be related to the multiple load flow solution problem for the following reasons. It has been confirmed analytically and by simulations that the multiple load flow solutions are likely to appear under the heavy-loaded conditions, and that the individual solutions of the solution pair have different features from each other, from the standpoint of stability, although they are close to each other.
377 citations
TL;DR: In this paper, the authors present a load model for power system stability studies, which is qualitatively different from generator load modeling in many aspects, such as reliability of load estimates, models of different components must be combined to obtain a reasonably manageable overall system model and field measurements are not at all easy.
Abstract: Proper representation of load is important in power system stability studies, but it is a difficult task. Load modeling is qualitatively different from generator modeling in many aspects. Composition of load needs to be reliably estimated, models of different components must be combined to obtain a reasonably manageable overall system model, and field measurements are not at all easy.
314 citations
01 Dec 1985
TL;DR: In this paper, the authors provide a critical review of the Lyapunov direct method of transient stability analysis of power systems and propose on-line criteria suitable for online implementation.
Abstract: 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
300 citations