Gustavo Revel

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...

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.

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.

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.

BIFURCATION ANALYSIS IN A POWER SYSTEM MODEL

Abstract The dynamics of a 3-bus power system model is analyzed using bifurcation theory. This model has been widely studied concerning voltage collapse. This paper presents some additional results in this topic. It is shown that the cascade of period doubling bifurcations preceding the voltage collapse verifies the Feigenbaums universal constant. In addition a Lorenz map for the chaotic attractor is derived resembling a one-dimensional unimodal curve. A two parameter bifurcation analysis reveals the presence of a Bogdanov-Takens codimension-two bifurcation for a positive value of the active power. Several dynamical scenarios, not directly related to the Bogdanov-Takens unfolding, have been detected. The presence of homoclinic, cyclic fold and period doubling bifurcations curves may indicate the existence of an organizing centre of global dynamics on the two parameter plane.

A Degenerate 2:3 Resonant Hopf--Hopf Bifurcation as Organizing Center of the Dynamics: Numerical Semiglobal Results

In this paper a degenerate case of a 2:3 resonant Hopf--Hopf bifurcation is studied. This codimension-four bifurcation occurs when the frequencies of both Hopf bifurcation branches have the relation 2/3, and one of them presents the vanishing of the first Lyapunov coefficient. The bifurcation is analyzed by means of numerical two- and three-parameter bifurcation diagrams. The two-parameter bifurcation diagrams reveal the interaction of cyclic-fold, period-doubling (or flip), and Neimark--Sacker bifurcations. A nontrivial bifurcation structure is detected in the main three-parameter space. It is characterized by a fold-flip (FF) bubble interacting with curves of fold-Neimark--Sacker (

Soluciones Cuasiperiódicas en un Circuito Eléctrico Resonante

FNS

Numerical semi-global analysis of a 1:2 resonant Hopf–Hopf bifurcation

), generalized period-doubling (GPD), 1:2 strong resonances (

Multi-parameter bifurcation analysis of subsynchronous interactions in DFIG-based wind farms

R_{1:2}