Landau Zener scenario in a trapped atomic gas: multi-level multi-particle model

The paper investigates multi-level and multi-particle Landau-Zener problem applying the dynamic matrix approach. The Landau Zener transitions are observed to depend sensitively on the frequency, phase of interaction and number of levels and particles. The dynamic behaviour of atomic trapped gas is solved for one particle model that permits to deduce different probabilities for particular initial conditions. The generalization of the probabilities permits to solve any multi-level system with an arbitrary number of particles and controlled particle transitions

Backstepping Controller Design for Power Quality Improvement in a Two-Stage Grid-Connected Photovoltaic Systems with LCL Filter

In a grid-connected photovoltaic system, the quality of energy injected by the photovoltaic system into the grid is directly linked to the topology of the inverter used and to the efficiency of its control technique. This paper addresses this problem for a two-level grid-connected photovoltaic inverter operating under low irradiance conditions. The aim is to reduce the harmonic distortion on the electrical network and therefore improve its power quality. To achieve this goal, a control strategy was set up considering the nonlinearity of the dynamic system, and the high dimension of the system model. Thus, a nonlinear controller designed using the backstepping technique is proposed. The effectiveness of this control strategy was evaluated by simulation in MATLAB/Simulink. Results show that the proposed control technique significantly improves the power quality of the grid-connected photovoltaic system by minimizing the current harmonic distortion rates in low irradiance conditions. The current harmonic distortion rates obtained for solar irradiance of 1000 W/m2, 750 W/m2, 500 W/m2, and 250 W/m2 are 0.48%, 0.78%, 1.22%, and 2.16%, respectively. The power factor is 0.988, and the DC bus voltage is maintained at its reference voltage of 600 V with a very low response time during the transient phases. A comparison of our simulation results with those found in the literature on other control techniques such as proportional-integral-derivative (PID) and synergetic controls shows the efficiency, superiority, and satisfactory performance of the proposed control scheme to minimize harmonic distortion under low irradiance conditions. The robustness and better dynamic performance of the proposed backstepping controller under varying irradiance conditions have also been shown