Random load fluctuations and collapse probability of a power system operating near codimension 1 saddle-node bifurcation

For a power system operating in the vicinity of the power transfer limit of its transmission system, effect of stochastic fluctuations of power loads can become critical as a sufficiently strong such fluctuation may activate voltage instability and lead to a large scale collapse of the system. Considering the effect of these stochastic fluctuations near a codimension 1 saddle-node bifurcation, we explicitly calculate the autocorrelation function of the state vector and show how its behavior explains the phenomenon of critical slowing-down often observed for power systems on the threshold of blackout. We also estimate the collapse probability/mean clearing time for the power system and construct a new indicator function signaling the proximity to a large scale collapse. The new indicator function is easy to estimate in real time using PMU data feeds as well as SCADA information about fluctuations of power load on the nodes of the power grid. We discuss control strategies leading to the minimization of the collapse probability.Comment: 5 pages, 1 figure, submission to IEEE PES General Meeting 201

Critical slowing-down as indicator of approach to the loss of stability

We consider stochastic electro-mechanical dynamics of an overdamped power system in the vicinity of the saddle-node bifurcation associated with the loss of global stability such as voltage collapse or phase angle instability. Fluctuations of the system state vector are driven by random variations of loads and intermittent renewable generation. In the vicinity of collapse the power system experiences so-called phenomenon of critical slowing-down characterized by slowing and simultaneous amplification of the system state vector fluctuations. In generic case of a co-dimension 1 bifurcation corresponding to the threshold of instability it is possible to extract a single mode of the system state vector responsible for this phenomenon. We characterize stochastic fluctuations of the system state vector using the formal perturbative expansion over the lowest (real) eigenvalue of the system power flow Jacobian and verify the resulting expressions for correlation functions of the state vector by direct numerical simulations. We conclude that the onset of critical slowing-down is a good marker of approach to the threshold of global instability. It can be straightforwardly detected from the analysis of single-node autostructure and autocorrelation functions of system state variables and thus does not require full observability of the grid.Comment: Shorter version submitted to IEEE SmartGridComm 2014; 6 pages, 4 figures, discussion of autostructure functions adde

Equation of state and Beginning of Thermalization After Preheating

We study the out-of-equilibrium nonlinear dynamics of fields after post-inflationary preheating. During preheating, the energy in the homogeneous inflaton is exponentially rapidly transfered into highly occupied out-of-equilibrium inhomogeneous modes, which subsequently evolve towards equilibrium. The infrared modes excited during preheating evolve towards a saturated distribution long before thermalization completes. We compute the equation of state during and immediately after preheating. It rapidly evolves towards radiation domination long before the actual thermal equilibrium is established. The exact time of this transition is a non-monotonic function of the coupling between the inflaton and the decay products, and it varies only very weakly (around 10^(-35) s) as this coupling changes over several orders of magnitude. This result is applied to refine the relation between the number of efoldings N and the physical wavelength of perturbations generated during inflation. We also discuss the implications for the theory of modulated perturbations from preheating. We finally argue that many questions of the thermal history of the universe should be addressed in terms of pre-thermalization, illustrating this point with a calculation of perturbative production of gravitinos immediately after chaotic inflation. We also highlight the effects of three-legs inflaton interactions on the dynamics of preheating and thermalization in an expanding universe.Comment: 15 pages, 13 figure

The Enhancement of Asphalt Concrete Surface Rigidity Based on Application of Shungite-Bitumen Binder

Physical interaction of organic binder depends on bituminous film ability to absorb the mineral particles on the surface. The thick film formation begins with the bitumen amalgamation with mineral powder grains and finishes during the processes of application, seal arrangement and cooling down of asphalt concrete. Active surface centers are on every mineral material and they supply their reactive ability and interaction with bitumen. For proving experimentally and to study the physical and mechanical properties in real operation conditions that were arranged, the blanket was arranged from stone-mastic asphalt with shungite bituminous binder of 500 m long. The monitoring conducted during 3 years indicates that asphalt concrete with shungite binder is subjected to calibration to a lesser degree in comparison with asphalt concrete based on standard powder. For operation reliability of nonrigid road base, it is necessary to estimate and prognosticate asphalt concrete fatigue properties in a blanket. The characterized property appears in such a way that the effect of loads which is significantly smaller than the destructive ones leads to the gradual degradation of fatigue and destruction of the blanket. The results proved that asphalt concrete with shungite bituminous binders has higher operation characteristics

Surprising phenomena in a rich new class of inflationary models

We report on a new class of fast-roll inflationary models. In a huge part of its parameter space, inflationary perturbations exhibit quite unusual phenomena such as scalar and tensor modes freezing out at widely different times, as well as scalar modes reentering the horizon during inflation. In another, narrower range of parameters, this class of models agrees with observations. One specific point in parameter space is characterized by extraordinary behavior of the scalar perturbations. Freeze-out of scalar perturbations as well as particle production at horizon crossing are absent. Also the behavior of the perturbations around this quasi-de Sitter background is dual to a quantum field theory in flat space-time. Finally, the form of the primordial power spectrum is determined by the interaction between different modes of scalar perturbations.Comment: 12 pages, 5 figures, 1 table, references + comments added, errors corrected, conclusions unchanged, version published in JCA