The variety generated by order algebras

Every ordered set can be considered as an algebra in a natural way. We investigate the variety generated by order algebras. We prove, among other things, that this variety is not finitely based and, although locally finite, it is not contained in any finitely generated variety; we describe the bottom of the lattice of its subvarieties

Virtual Induction Machine Strategy for Converters in Power Systems with Low Rotational Inertia

This paper presents a novel comprehensive control strategy for grid-connected Voltage Source Converters (VSCs) in power systems with low rotational inertia. The proposed model is based on emulating the physical properties of an Induction Machine (IM) and taking advantage of its inherent grid-friendly properties, i.e. self-synchronization, virtual inertia, power and frequency oscillation damping. For that purpose, a detailed mathematical model of the IMs working principles is derived, which includes the possibility of obtaining the unknown grid frequency without a dedicated synchronization unit, but rather via processing the voltage and current magnitude measurements at the converter output. This eliminates the need for an inherently nonlinear phase-locked loop, characteristic for virtual synchronous machines, while simultaneously preserving the synchronization and damping properties of a conventional electrical machine. Several case studies are presented that validate the mathematical principles of the proposed model and conclusions on VSC performance are drawn

Stability Performance of Power Electronic Deviceswith Time Delays

This paper deals with the impact of time delays on small-signal stability of power systems with an all converter-interfaced generation. For this purpose, a delay differential algebraic equation model of the voltage source converter and its control scheme is developed. The regulation is based on replicating the dynamical properties of a synchronous machine through appropriate controller configuration. Therefore, a virtual inertia emulation is included in the active power control loop. A transcedental nature of the characteristic equation is resolved by implementing the Chebyshev's discretization method and observing a finite number of critical, low-frequency eigenvalues. Based on the proposed approach, a critical measurement delay is evaluated. Furthermore, a bifurcation analysis of the droop gains and inertia constant is conducted. Stability regions and optimal parametrization of the voltage source converter controls are evaluated and discussed

Vertex routing models

A class of models describing the flow of information within networks via routing processes is proposed and investigated, concentrating on the effects of memory traces on the global properties. The long-term flow of information is governed by cyclic attractors, allowing to define a measure for the information centrality of a vertex given by the number of attractors passing through this vertex. We find the number of vertices having a non-zero information centrality to be extensive/sub-extensive for models with/without a memory trace in the thermodynamic limit. We evaluate the distribution of the number of cycles, of the cycle length and of the maximal basins of attraction, finding a complete scaling collapse in the thermodynamic limit for the latter. Possible implications of our results on the information flow in social networks are discussed.Comment: 12 pages, 6 figure

Fast Frequency Control Scheme through Adaptive Virtual Inertia Emulation

This paper presents a novel virtual inertia controller for converters in power systems with high share of renewable resources. By combining the analytical study of system dynamics and a Linear-Quadratic Regulator (LQR)-based optimization technique, the optimal state feedback gain is determined, adapting the emulated inertia constant according to the frequency disturbance in the system. The optimality is achieved through trade-off between the critical frequency limits and the required control effort, i.e. utilization of the internal energy storage. The proposed controller is integrated into a state-of-the-art converter control scheme and verified through EMT simulations. The results show a significant improvement in the frequency response compared to an open-loop system, while also preserving drastically more DC-side energy than a non-adaptive controller

Droop vs. virtual inertia: Comparison from the perspective of converter operation mode

Virtual Inertia Emulation (VIE) and traditional Active Power Droop Control (APDC) are among the most common approaches for regulating the active power output of inverter-based generators. Furthermore, it has been shown that, under certain conditions, these two methods can be equivalent. However, neither those studies, nor the analyses comparing the two control schemes with respect to their dynamical properties, have investigated the impact of the converter operation mode. This paper explores the subject by investigating the two control approaches under such conditions, and determining when this assumption does not hold. Using time-domain simulations with a detailed Voltage Source Converter model, we compare VIE and APDC qualitatively and reformulate the respective conditions for equivalence

Testing the Warm Dark Matter paradigm with large-scale structures

We explore the impact of a LWDM cosmological scenario on the clustering properties of large-scale structure in the Universe. We do this by extending the halo model. The new development is that we consider two components to the mass density: one arising from mass in collapsed haloes, and the second from a smooth component of uncollapsed mass. Assuming that the nonlinear clustering of dark matter haloes can be understood, then from conservation arguments one can precisely calculate the clustering properties of the smooth component and its cross-correlation with haloes. We then explore how the three main ingredients of the halo calculations, the mass function, bias and density profiles are affected by WDM. We show that, relative to CDM: the mass function is suppressed by ~50%, for masses ~100 times the free-streaming mass-scale; the bias of low mass haloes can be boosted by up to 20%; core densities of haloes can be suppressed. We also examine the impact of relic thermal velocities on the density profiles, and find that these effects are constrained to scales r<1 kpc/h, and hence of little importance for dark matter tests, owing to uncertainties in the baryonic physics. We use our modified halo model to calculate the non-linear matter power spectrum, and find significant small-scale power in the model. However, relative to the CDM case, the power is suppressed. We then calculate the expected signal and noise that our set of LWDM models would give for a future weak lensing mission. We show that the models should in principle be separable at high significance. Finally, using the Fisher matrix formalism we forecast the limit on the WDM particle mass for a future full-sky weak lensing mission like Euclid or LSST. With Planck priors and using multipoles l<5000, we find that a lower limit of 2.6 keV should be easily achievable.Comment: Replaced with version accepted for publication in PRD. Inclusion of: new figure showing dependence of predictions on cut-off mass; new discussion of mass function; updated refs. 18 pages, 10 Figure

Stability Analysis of Converter Control Modes in Low-Inertia Power Systems

This paper deals with the small-signal stability analysis of converter control modes in low-inertia power systems. For this purpose, a detailed differential-algebraic equation model of the voltage source converter and its control scheme is developed. Both grid-forming and grid-feeding concepts have been considered, as well as different active power controllers based on traditional droop and virtual inertia emulation. An eigenvalue analysis of the linearized state-space system is conducted and the performance of different control configurations is compared. Furthermore, various bifurcation studies have been completed and conclusions on stability margins have been drawn with respect to control sensitivity and robustness

Chloroplast pigments in post-fire-grown cryptophytes on Vidlič Mountain (Southeastern Serbia)

In this study the content of chloroplast pigments (chlorophyll a, b, a+b, and carotenoids) in the leaves of Geranium macrorrhizum L., Doronicum columnae Ten., Aegopodium podagraria L. and Tussilago farfara L. from a beech forest that had undergone fire on Vidlič Mountain was determined. The same species of plants from a place that had not been exposed to fire were taken as controls. Chloroplast pigments were determined from acetone extracts of these plants spectrophotometrically. In the first year after the fire the content of chlorophyll a, b and a+b in Geranium macrorrhizum L. and Doronicum columnae Ten. was greater than in the plants not exposed to fire. The results were the opposite for Aegopodium podagraria L. and Tussilago farfara L. These differences can be attributed to the different physiology of the plants and consequently their different adaptation patterns. The carotenoid content was higher in the plant species at the fire site than in the area not exposed to fire