Bifurcation control deals with modification of bifurcation characteristics of a parameterized nonlinear system by a designed control input. Typical bifurcation control objectives include delaying t...

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Bifurcation control: theories, methods, and applications

This brief presents a novel control scheme to achieve fast fixed-time system stabilization. Based on fixed-time stability theory, a novel fixed-time stable system is presented. Using the proposed fixed-time stable system, a fast fixed-time nonsingular terminal sliding mode control method is derived. Our control scheme achieves system stabilization within bounded time independent of the initial condition and has an advantage in convergence rate over the existing result of the fixed-time stable control method. The proposed control strategy is applied to suppress chaotic oscillation in power systems, and its effectiveness as well as superiority is verified through numerical simulation. The proposed control strategy can be applied to address the control and synchronization problem for other complex systems.

Fast Fixed-time Nonsingular Terminal Sliding Mode Control and its Application to Chaos Suppression in Power System

The dynamics of a large class of physical systems such as the general power system can be represented by parameter-dependent differential-algebraic models of the form x/spl dot/=f and 0=g. Typically, such constrained models have singularities. This paper analyzes the generic local bifurcations including those which are directly related to the singularity. The notion of a feasibility region is introduced and analyzed. It consists of all equilibrium states that can be reached quasistatically from the current operating point without loss of local stability. It is shown that generically loss of stability at the feasibility boundary is caused by one of three different local bifurcations, namely the saddle-node and Hopf bifurcations and a new bifurcation called the singularity induced bifurcation which is analyzed precisely here for the first time. The latter results when an equilibrium point is at the singular surface. Under certain transversality conditions, the change in the eigenstructure of the system Jacobian at the equilibrium is established and the local dynamical structure of the trajectories near this bifurcation point is analyzed.

Local bifurcations and feasibility regions in differential-algebraic systems

This paper discusses various methods based on power network partitioning and voltage stability indices to accelerate the computation of voltage collapse points using continuation techniques. Partitioning methods derived from right eigenvector and tangent vector information are thoroughly studied, identifying limitations and probable application areas; a mixed partition-reduction technique is then proposed to reduce computational burden. Also, tangent vectors are used to define a clustering method for the identification at any operating condition of the critical area at the collapse point, and a new voltage stability index is defined based on the identification of this critical area. Finally, a predictor-corrector methodology based on this index and the continuation method is proposed for fast computations of voltage collapse points. All the different methods are compared based on the results obtained for the IEEE 300-bus test system, and a methodology is recommended based on its prospective computational savings.

New techniques to speed up voltage collapse computations using tangent vectors

This paper provides an overview of the taxonomy theory which has been proposed as a fundamental platform for solving practical stability related problems in large constrained nonlinear systems such as the electric power system. The theory reveals a two-level intertwined cellular nature of the constrained system dynamics which serves as a unifying structure, a taxonomy, for analyzing nonlinear phenomena in large system models. These broadly divide into the state space aspects (related to dynamic stability issues among others) and the parameter space aspects (connected with bifurcation phenomena among others). In the state-space formulation, the boundary of the region of attraction for the operating point is shown (under certain Morse-Smale like assumptions) to be composed of stable manifolds of certain anchors and portions of the singularity surface. Such boundary characterization provides the foundation for rigorous Lyapunov theoretic transient stability methods. In the parameter space analysis, the feasibility region which is bounded by the feasibility boundary provides a safe opening region for guaranteeing local stability at the equilibrium under slow parametric variations. The feasibility boundary where the operating point undergoes loss of local stability is characterized in the form of three principal bifurcations including a new bifurcation called the singularity induced bifurcation.

Dynamics of large constrained nonlinear systems-a taxonomy theory [power system stability]

Bifurcations occurring in power system models exhibiting voltage collapse have been the subject of several recent studies. Although such models have been shown to admit a variety of bifurcation phenomena, the view that voltage collapse is triggered by possibly the simplest of these, namely by the (static) saddle node bifurcation of the nominal equilibrium, has been the dominant one. The authors have recently shown that voltage collapse can occur "prior" to the saddle node bifurcation. In the present paper, a new dynamical mechanism for voltage collapse is determined: the boundary crisis of a strange attractor or synonymously a chaotic blue sky bifurcation. This determination is reached for an example power system model akin to one studied in several recent papers. More generally, blue sky bifurcations (not necessarily chaotic) are identified as important mechanisms deserving further consideration in the study of voltage collapse. >

Bifurcations, chaos, and crises in voltage collapse of a model power system

Dynamic bifurcations, including Hopf and period-doubling bifurcations, are found to occur in a power system dynamic model recently employed in voltage collapse studies. The occurrence of dynamic bifurcations is ascertained in a region of state and parameter space linked with the onset of voltage collapse. The work focuses on a power system model studied by Dobson & Chiang [1989]. The presence of the dynamic bifurcations, and the resulting implications for dynamic behavior, necessitate a re-examination of the role of saddle node bifurcations in the voltage collapse phenomenon. The bifurcation analysis is performed using the reactive power demand at a load bus as the bifurcation parameter. It is determined that the power system model under consideration exhibits two Hopf bifurcations in the vicinity of the saddle node bifurcation. Between the Hopf bifurcations, i.e., in the "Hopf window," period-doubling bifurcations are found to occur. Simulations are given to illustrate the various types of dynamic behaviors associated with voltage collapse for the model. In particular, it is seen that an oscillatory transient may play a role in the collapse.

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Dynamic bifurcations in a power system model exhibiting voltage collapse

Bifurcations are studied for a power system dynamic model which has previously been used to illustrate voltage collapse It is found that for this model, the nominal operating point undergoes dynamic bifurcations prior to the static bifurcation to which voltage collapse has been attributed These dynamic bifurcations result in a reduced stability margin in parameter space Moreover, a short oscillatory voltage transient typically occurs prior to voltage collapse for this model In addition, it is found that the model admits large-amplitude bifurcations, including cyclic fold and period-doubling bifurcations; the latter leading to period-doubling cascades and the resulting chaotic behavior >

/pdf/dynamic-bifurcations-in-a-power-system-model-exhibiting-2hzpo21vm2.pdf

A.M.A. Hamdan

Papers

Bifurcations, chaos, and crises in voltage collapse of a model power system

Dynamic bifurcations in a power system model exhibiting voltage collapse

Dynamic bifurcations in a power system model exhibiting voltage collapse