Diego M. Alonso

Bifurcation Analysis on a Multimachine Power System Model

In this article bifurcation analysis of the 9 bus power system model corresponding to the Western Systems Coordinating Council is performed. In order to use standard continuation packages like MATCONT, a full ordinary differential equations model, including the corresponding dynamics of the control loops and the transmission lines, is derived. Different loading conditions are studied by using the load demands as bifurcation parameters. For variations of one of the loads, it is shown that the equilibrium point undergoes Hopf and saddle-node bifurcations. Furthermore, the bifurcation analysis varying two loads simultaneously reveals the existence of a pair of double Hopf and a zero-Hopf bifurcations, acting as organizing centers of the dynamics. Finally, a power system stabilizer has been added in order to modify the location of a Hopf bifurcation curve.

A GALLERY OF OSCILLATIONS IN A RESONANT ELECTRIC CIRCUIT: HOPF-HOPF AND FOLD-FLIP INTERACTIONS

In this work, the dynamics of a coupled electric circuit is studied. Several bifurcation diagrams associated with the truncated normal form of the Hopf-Hopf bifurcation are presented. The bifurcati...

Controlling an Inverted Pendulum with Bounded Controls

The dynamical behaviour of a simple underactuated mechanical system with a bounded continuous control law is analyzed. The system consists of a pendulum with an inertia disk mounted on its free extreme. It is driven applying torques to the inertia disk by means of a DC motor. The closed-loop system exhibits a rich and complex dynamic when a control parameter is varied. A numerical analysis reveals Hopf, fold and homoclinic bifurcations as the main phenomena. It is shown that the pendulum can be stabilized in its inverted position with zero velocity of the disk if the controller’s gains are appropriately chosen.

Interactions between oscillatory modes near a 2:3 resonant Hopf-Hopf bifurcation.

In this paper, the dynamics near a 2:3 resonant Hopf-Hopf bifurcation is studied. The main result is the identification of a distinctive structure connecting 1:2 and 1:3 strong resonances of limit cycles. This structure is found near the Hopf-Hopf point revealing that it may be associated to the resonant case, and may provide useful information about the dynamics generated by this codimension 3 bifurcation.

DETECTION OF LIMIT CYCLE BIFURCATIONS USING HARMONIC BALANCE METHODS

In this paper, bifurcations of limit cycles close to certain singularities of the vector fields are explored using an algorithm based on the harmonic balance method, the theory of nonlinear feedback systems and the monodromy matrix. Period-doubling, pitchfork and Neimark–Sacker bifurcations of cycles are detected close to a Gavrilov–Guckenheimer singularity in two modified Rossler systems. This special singularity has a zero eigenvalue and a pair of pure imaginary eigenvalues in the linearization of the flow around its equilibrium. The presented results suggest that the proposed technique can be promising in analyzing limit cycle bifurcations arising in the unfoldings of other complex singularities.

ON SEMI-ANALYTICAL PROCEDURE FOR DETECTING LIMIT CYCLE BIFURCATIONS

This paper reports some computation of periodic solutions arising from Hopf bifurcations in order to build up a more accurate procedure for semi-analytical approximations to detect limit cycle bifurcations. The approximation formulas are derived using nonlinear feedback systems theory and the harmonic balance method. The monodromy matrix is computed for several simple nonlinear flows to detect the first bifurcation of the cycles in the neighborhood of the original Hopf bifurcation.

Frequency regulation and inter-area oscillation damping using variable-speed wind generators

This work explores the contribution of variable-speed wind turbines on two typical problems of multimachine power systems: the frequency regulation and the inter-area oscillations. Towards this end, a multimachine test system is augmented with a variable-speed wind farm. Two additional control loops are included in order to modify the active power delivered by the wind farm in response to frequency deviations and inter-area oscillations. Some guidelines are given to achieve a suitable tuning of the loop gains. In case of the inter-area oscillation compensator, the analysis is carried out for different loading conditions, measurement time delays and input signals.

Modelling an Inertia Wheel Pendulum Benchmark

In this paper, modelling and parameter identification of an inertia wheel pendulum benchmark is considered. This is an underactuated mechanical system useful for teaching and research. Attention is focused on deriving a simple but accurate model capable of reproducing large amplitude oscillations. Due to the particular design of the prototype, the friction forces on the actuated joint are noticeable. A simple friction model including dead-zone effects and viscous terms is proposed, and a compensation method for the dead zone is derived. The accuracy of the compensation strategy and the predictive quality of the derived model are analysed by comparing numerical simulations with experimental data.

Bifurcation Control in Feedback Systems

In this chapter the mathematical tools from bifurcation theory are used within the framework of feedback control systems. The first part deals with a simple example where the amplitude of limit cycles and the appearance of period-doubling bifurcations are controlled using a method derived from the frequency domain approach. In the second part, bifurcation theory is used to analyze the dynamical behavior of an inverted pendulum with saturated control. The main objective is to find appropriate values of the controller parameters to achieve the stabilization of the pendulum at the inverted position and, at the same time, to obtain the largest basin of attraction.

Bifurcation analysis on a detailed multimachine power system model

In this article the dynamics of a multimachine power system model is studied using bifurcation theory. The classical 9 bus WSCC power system model is considered. It is represented using a full differential ODE set, including the corresponding dynamics of the control loops and the transmission lines. The analysis is carried out using the load demands as bifurcation parameters, in order to reveal possible dynamical scenarios for different loading conditions. For variations of one of the loads, Hopf and saddle-node bifurcations were detected. Furthermore, the bifurcation analysis varying two loads simultaneously reveals the existence of a pair of double-Hopf and a zero-Hopf bifurcations, acting as organizing centers of the dynamics.