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We propose an extended demand response program, based on ancillary service for supplying flexible electricity demand. In our proposed scheme, we suggest a broader management model to control the scheduling and power consumption of Bitcoin mining machines. The main aspect that we focus on is suppressing the power ramping and related transient effects. We extend previous works on the subject, that study the impact of incorporating cryptocurrency mining machines into existing power grid, and explore the potential profit of exploiting this flexible load in the Israeli electricity market. We analyze a trend based on historical data, of increasing electricity prices and ramping costs due to the increasing penetration of renewable energy sources. We suggest an extension to the unit commitment problem from which we obtain the scheduling scheme of the Bitcoin mining machines. We use simulation and the real-world data acquired from the "Noga" grid operator to verify the proposed ancillary service and test its practical limits for reducing the ramping costs, under changing ratio of energy production from renewable sources. Out results suggests that the machine price and ratio of production from renewable sources plays a significant role in determining the profitability of the proposed demand-response program., Comment: 8 pages, 7 figures

High shares of variable renewable energy necessitate substantial energy storage capacity. However, it remains unclear how to design a market that, on the one hand, ensures a stable and sufficient income for storage firms, and, on the other hand, maintains stable and affordable electricity costs for the consumers. Here, we use a game theoretic model to study storage competition in wholesale electricity markets. A main result is that these types of games are not necessarily stable. In particular, we find that under certain conditions, which imply a combination of a high share of variable renewable energy sources and low flexibility of conventional power plants, the system will not converge to an equilibrium. However, we demonstrate that a price cap on storage price bids can ensure convergence to a stable solution. Moreover, we find that when the flexibility of conventional power plants is low, while the storage usage for energy balancing increases with renewable energy generation, the profitability of using storage for the sole purpose of energy arbitrage decreases.

The flow of contracting systems contracts 1-dimensional parallelotopes, i.e., line segments, at an exponential rate. One reason for the usefulness of contracting systems is that many interconnections of contracting sub-systems yield an overall contracting system. A generalization of contracting systems is $k$-contracting systems, where $k\in\{1,\dots,n\}$. The flow of such systems contracts the volume of $k$-dimensional parallelotopes at an exponential rate, and in particular they reduce to contracting systems when $k=1$. It was shown by Muldowney and Li that time-invariant $2$-contracting systems have a well-ordered asymptotic behaviour: all bounded trajectories converge to the set of equilibria. Here, we derive a sufficient condition guaranteeing that the system obtained from the series interconnection of two sub-systems is $k$-contracting. This is based on a new formula for the $k$th multiplicative and additive compounds of a block-diagonal matrix, which may be of independent interest. As an application, we find conditions guaranteeing that $2$-contracting systems with an exponentially decaying input retain the well-ordered behaviour of time-invariant 2-contracting systems.

The flow of contracting systems contracts 1-dimensional polygons (i.e. lines) at an exponential rate. One reason for the usefulness of contracting systems is that many interconnections of contracting sub-systems yield an overall contracting system. A recent generalization of contracting systems is called $k$-contracting systems, where $k\in\{1,\dots,n\}$. The flow of such systems contracts $k$-dimensional polygons at an exponential rate, and in particular they reduce to contracting systems when $k=1$. Here, we analyze serial interconnections of $1$-contracting and $2$-contracting systems. We provide conditions guaranteeing that such interconnections have a well-ordered asymptotic behaviour, and demonstrate the theoretical results using several examples.

This paper proposes a very simple deterministic mathematical model, which, by using a power-law, is a \emph{non-integer power model} (or \emph{fractional power model (FPM)}). Such a model, in non-integer power of time, namely $t^m$ up to constants, enables representing at each day, with a good precision, the totality of the contaminated individuals. Despite being enriched with knowledge through an internal structure based on a geometric sequence "with variable ratio", the model (in its non-integer representation) has only three parameters, among which the non-integer power, $m$, that determines on its own, according to its value, an aggravation or an improvement of the viral spreading. Its simplicity comes from the power-law, $t^m$, which simply expresses the singular dynamics of the operator of non-integer differentiation or integration, of high parametric compactness, that governs diffusion phenomena and, as shown in this paper, the spreading phenomena by contamination. The proposed model is indeed validated with the official data of Ministry of Health on the COVID-19 spreading. Used in prediction, it well enables justifying the choice of a lockdown, without which the spreading would have highly worsened. The comparison of this model in $t^m$ with two known models having the same number of parameters, well shows that its representativity of the real data is better or more general. Finally, in a more fundamental context and particularly in terms of complexity and simplicity, a self-filtering action enables showing the compatibility between the \emph{internal complexity} that the internal structure and its stochastic behavior present, and the \emph{global simplicity} that the model in $t^m$ offers in a deterministic manner: it is true that the non-integer power of a power-law is well a marker of complexity.

As the share of renewable sources is increasing the need for multiple storage units appropriately sized and located is essential to achieve better inertial response. This work focuses on the question of "how to distribute constant number of storage units in the gird under transient events such that the inertial response of the maximum frequency deviation is minimized?". To answer this question, we provide a comprehensive modeling framework for energy storage units placement and size for frequency stability under spatial effects. The distributed storage units are modeled as grid supporting inverters and the total storage capacity in the grid is bounded based on the allowed steady-state frequency deviation after disturbances. The problem of finding the optimal distributions can be considered as combinatorial problem which consists of high dimensional solutions. In this light, we develop two numeric approaches based on Brute-force search and adaptation of the Cross-entropy method for finding the best distribution and examined it on a case study of the future Israeli grid. The results on the case study provide a new insight---the storage units should be placed around the area of the disturbances, including in sites with high inertia in accordance to the network topology., Comment: This article contains 20 pages and includes 7 figures

The response of a SERF atomic magnetometer to a repetitive short-pulsed pump was investigated. Quantum sub-resonances at a repetition rate of $1/n$ of the Larmor frequency of the magnetic field inside the shield are experimentally observed and theoretically explained. This is a type of synchronization phenomenon. Investigations in single alkali atoms cells as well as mixed alkali atoms of K and Rb are presented. In the later, one species is pumped while the probe is on the other specie polarized by spin exchange. The effect of spin destruction, spin exchange and collisions are studied in order to account for the width of the resonances. Quantum calculations of a three levels $\Lambda$ model for this phenomenon exhibit a dip at the resonance frequency in the absorption spectrum for both cases of pulsed and CW pump modes and an evidence for EIT., Comment: 14 pages, 11 figures