Patterns and bifurcations in low-Prandtl number Rayleigh-Benard convection

We present a detailed bifurcation structure and associated flow patterns for low-Prandtl number ($P=0.0002, 0.002, 0.005, 0.02$) Rayleigh-B\'{e}nard convection near its onset. We use both direct numerical simulations and a 30-mode low-dimensional model for this study. We observe that low-Prandtl number (low-P) convection exhibits similar patterns and chaos as zero-P convection \cite{pal:2009}, namely squares, asymmetric squares, oscillating asymmetric squares, relaxation oscillations, and chaos. At the onset of convection, low-P convective flows have stationary 2D rolls and associated stationary and oscillatory asymmetric squares in contrast to zero-P convection where chaos appears at the onset itself. The range of Rayleigh number for which stationary 2D rolls exist decreases rapidly with decreasing Prandtl number. Our results are in qualitative agreement with results reported earlier

Role of Bulk flow in Turbulent Convection

In this paper we present scaling of large-scale quantities like Pecl\'{e}t and Nusselt numbers, and the dissipation rates of kinetic energy and entropy. Our arguments are based on the scaling of bulk quantities and earlier experimental and simulation results. We also present the inertial-range properties of spectra and fluxes of kinetic energy and entropy.Comment: 15 pages, to Appear in the proceedings of "Senfest, International Conference on Complex Processes in Plasmas and Nonlinear Dynamical Systems

Online monitoring of voltage stability margin using PMU measurements

With the growing smart grid concept it becomes important to monitor health of the power system at regular intervals for its secure and reliable operation. Phasor Measurement Units (PMUs) may play a vital role in this regard. This paper presents voltage stability monitoring in real time framework using synchrophasor measurements obtained by PMUs. Proposed approach estimates real power loading margin as well as reactive power loading margin of most critical bus using PMU data. As system operating conditions keep on changing, loading margin as well as critical bus information is updated at regular intervals using fresh PMU measurements. Simulations have been carried out using Power System Analysis Toolbox (PSAT) software. Accuracy of proposed Wide Area Monitoring System (WAMS) based estimation of voltage stability margin has been tested by comparing results with loading margin obtained by continuation power flow method (an offline approach for accurate estimation of voltage stability margin) under same set of operating conditions. Case studies performed on IEEE 14-bus system, New England 39-bus system and a practical 246-bus Indian power system validate effectiveness of proposed approach of online monitoring of loading margin

Adaptive Control of Unknown Pure Feedback Systems with Pure State Constraints

This paper deals with the tracking control problem for a class of unknown pure feedback system with pure state constraints on the state variables and unknown time-varying bounded disturbances. An adaptive controller is presented for such systems for the very first time. The controller is designed using the backstepping method. While designing it, Barrier Lyapunov Functions is used so that the state variables do not contravene its constraints. In order to cope with the unknown dynamics of the system, an online approximator is designed using a neural network with a novel adaptive law for its weight update. In the stability analysis of the system, the time derivative of Lyapunov function involves known virtual control coefficient with unknown direction and to deal with such problem Nussbaum gain is used to design the control law. Furthermore, to make the controller robust and computationally inexpensive, a novel disturbance observer is designed to estimate the disturbance along with neural network approximation error and the time derivative of virtual control input. The effectiveness of the proposed approach is demonstrated through a simulation study on the third-order nonlinear system