Robust optimization for energy transactions in multi-microgrids under uncertainty

Independent operation of single microgrids (MGs) faces problems such as low self-consumption of local renewable energy, high operation cost and frequent power exchange with the grid. Interconnecting multiple MGs as a multi-microgrid (MMG) is an effective way to improve operational and economic performance. However, ensuring the optimal collaborative operation of a MMG is a challenging problem, especially under disturbances of intermittent renewable energy. In this paper, the economic and collaborative operation of MMGs is formulated as a unit commitment problem to describe the discrete characteristics of energy transaction combinations among MGs. A two-stage adaptive robust optimization based collaborative operation approach for a residential MMG is constructed to derive the scheduling scheme which minimizes the MMG operating cost under the worst realization of uncertain PV output. Transformed by its KKT optimality conditions, the reformulated model is efficiently solved by a column-and-constraint generation (C&CG) method. Case studies verify the effectiveness of the proposed model and evaluate the benefits of energy transactions in MMGs. The results show that the developed MMG operation approach is able to minimize the daily MMG operating cost while mitigating the disturbances of uncertainty in renewable energy sources. Compared to the non-interactive model, the proposed model can not only reduce the MMG operating cost but also mitigate the frequent energy interaction between the MMG and the grid

Quantum Markov chains: Description of hybrid systems, decidability of equivalence, and model checking linear-time properties

© 2015 Elsevier Inc. In this paper, we study a model of quantum Markov chains that is a quantum analogue of Markov chains and is obtained by replacing probabilities in transition matrices with quantum operations. We show that this model is very suited to describe hybrid systems that consist of a quantum component and a classical one. Indeed, hybrid systems are often encountered in quantum information processing. Thus, we further propose a model called hybrid quantum automata (HQA) that can be used to describe the hybrid systems receiving inputs (actions) from the outer world. We show the language equivalence problem of HQA is decidable in polynomial time. Furthermore, we apply this result to the trace equivalence problem of quantum Markov chains, and thus it is also decidable in polynomial time. Finally, we discuss model checking linear-time properties of quantum Markov chains, and show the quantitative analysis of regular safety properties can be addressed successfully

Systemic risk in dynamical networks with stochastic failure criterion

Complex non-linear interactions between banks and assets we model by two time-dependent Erd\H{o}s Renyi network models where each node, representing bank, can invest either to a single asset (model I) or multiple assets (model II). We use dynamical network approach to evaluate the collective financial failure---systemic risk---quantified by the fraction of active nodes. The systemic risk can be calculated over any future time period, divided on sub-periods, where within each sub-period banks may contiguously fail due to links to either (i) assets or (ii) other banks, controlled by two parameters, probability of internal failure $p$ and threshold $T_h$ ("solvency" parameter). The systemic risk non-linearly increases with $p$ and decreases with average network degree faster when all assets are equally distributed across banks than if assets are randomly distributed. The more inactive banks each bank can sustain (smaller $T_h$), the smaller the systemic risk---for some $T_h$ values in I we report a discontinuity in systemic risk. When contiguous spreading becomes stochastic (ii) controlled by probability $p_2$---a condition for the bank to be solvent (active) is stochastic---the systemic risk decreases with decreasing $p_2$. We analyse asset allocation for the U.S. banks.Comment: 7 pages, 7 figure

Corrections to the thermodynamics of Schwarzschild-Tangherlini black hole and the generalized uncertainty principle

We investigate the thermodynamics of Schwarzschild-Tangherlini black hole in the context of the generalized uncertainty principle. The corrections to the Hawking temperature, entropy and the heat capacity are obtained via the modified Hamilton-Jacobi equation. These modifications show that the GUP changes the evolution of Schwarzschild-Tangherlini black hole. Specially, the GUP effect becomes susceptible when the radius or mass of black hole approach to the order of Planck scale, it stops radiating and leads to black hole remnant. Meanwhile, the Planck scale remnant can be confirmed through the analysis of the heat capacity. Those phenomenons imply that the GUP may give a way to solve the information paradox. Besides, we also investigate the possibilities to observe the black hole at LHC, the results demonstrate that the black hole can not be produced in the recent LHC.Comment: 12 pages, 6 figure

Temporal and Spectral Correlations of Cyg X-1

Temporal and spectral properties of X-ray rapid variability of Cyg X-1 are studied by an approach of correlation analysis in the time domain on different time scales. The correlation coefficients between the total intensity in 2-60 keV and the hardness ratio of 13-60 keV to 2-6 keV band on the time scale of about 1 ms are always negative in all states. For soft states, the correlation coefficients are positive on all the time scales from about 0.01 s to 100 s, which is significantly different with that for transition and low states. Temporal structures in high energy band are narrower than that in low energy band in quite a few cases. The delay of high energy photons relative to low energy ones in the X-ray variations has also been revealed by the correlation analysis. The implication of observed temporal and spectral characteristics to the production region and mechanism of Cyg X-1 X-ray variations is discussed.Comment: 17 pages, 6 figures included, to appear in Ap

Approach to accurately measuring the speed of optical precursors

Precursors can serve as a bound on the speed of information with dispersive medium. We propose a method to identify the speed of optical precursors using polarization-based interference in a solid-state device, which can bound the accuracy of the precursors' speed to less than $10^{-4}$ with conventional experimental conditions. Our proposal may have important implications for optical communications and fast information processing.Comment: 4 pages, 4 figure