Free and projective Banach lattices

We define and prove the existence of free Banach lattices in the category of Banach lattices and contractive lattice homomorphisms, and establish some of their fundamental properties. We give much more detailed results about their structure in the case when there are only a finite number of generators, and give several Banach lattice characterizations of the number of generators being, respectively, one, finite or countable. We define a Banach lattice P to be projective if, whenever X is a Banach lattice, J is a closed ideal in X, Q : X → X/J is the quotient map, T: P → X/J is a linear lattice homomorphism and ε > 0, there exists a linear lattice homomorphism : P → X such thatT = Q º and ∥∥ ≤ (1 + ε)∥T∥. We establish the connection between projective Banach lattices and free Banach lattices, describe several families of Banach lattices that are projective and prove that some are not.

Minimal Hilbert series for quadratic algebras and the Anick conjecture

We study the question on whether the famous Golod–Shafarevich estimate, which gives a lower bound for the Hilbert series of a (noncommutative) algebra, is attained. This question was considered by Anick in his 1983 paper ‘Generic algebras and CW-complexes’, Princeton Univ. Press, where he proved that the estimate is attained for the number of quadratic relations $d\leq n^2/4$
and $d\geq n^2/2$, and conjectured that it is the case for any number of quadratic relations. The particular point where the number of relations is equal to $n(n-1)/2$ was addressed by Vershik. He conjectured that a generic algebra with this number of relations is finite dimensional. We announce here the result that over any infinite field, the Anick conjecture holds for $d \geq 4(n2+n)/9$ and an arbitrary number of generators. We also discuss the result that confirms the Vershik conjecture over any field of characteristic 0, and a series of related
asymptotic results.

Finite dimensional semigroup quadratic algebras with the minimal number of relations

A quadratic semigroup algebra is an algebra over a field given by the generators x_1, . . . , x_n and a finite set of quadratic relations each of which either has the shape x_j x_k = 0 or the shape x_j x_k = x_l x_m . We prove that a quadratic semigroup algebra given by n generators and d=(n^2+n)/4 relations is always infinite dimensional. This strengthens the Golod–Shafarevich estimate for the above class of algebras. Our main result however is that for every n, there is a finite dimensional quadratic semigroup algebra with n generators and d_n relations, where d_n is the first integer greater than (n^2+n)/4 . That is, the above Golod–Shafarevich-type estimate for semigroup algebras is sharp.

Characterization of Transmission Losses

In this paper, characterizing transmission losses according to their origin is carried out. Transmission loss is decomposed into three components. The first is due to the current flow from generators to loads. The second is due to the circulating current between generators. The third represents the contribution of network structure and controls to increasing or decreasing transmission losses. Analytical proofs of the proposed loss decomposition are presented along with methods of allocating each component to the parties contributing to it. Illustration on simple dc and ac systems is presented. Results of application of the proposed method compared with other methods are also presented.

Rapid design of application specific FFT cores

Methods are presented for developing synthesizable FFT cores. These are based on a modular approach in which parameterized commutator and processor blocks are cascaded to implement the computations required in many important FFT signal flow graphs. In addition, it is shown how the use of a digital serial data organization can be used to produce systems that offer 100% processor utilization along with reductions in storage requirements. The approach has been used to create generators for the automated synthesis of FFT cores that are portable across a broad range of silicon technologies. Resulting chip designs are competitive with ones created using manual methods but with significant reductions in design times.

Systolic VLSI compiler (SVC) for high performance vector quantisation chips

An overview is given of a systolic VLSI compiler (SVC) tool currently under development for the automated design of high performance digital signal processing (DSP) chips. Attention is focused on the design of systolic vector quantization chips for use in both speech and image coding systems. The software in question consists of a cell library, silicon assemblers, simulators, test pattern generators, and a specially designed graphics shell interface which makes it expandable and user friendly. It allows very high performance digital coding systems to be rapidly designed in VLSI.

Synthesizable FFT cores

Methods are presented for developing synthesizable FFT cores. These are based on a modular approach in which parameterizable blocks are cascaded to implement the computations required across a range of typical FFT signal flow graphs. The underlying architectural approach combines the use of a digital serial data organization with generic commutator blocks to produce systems that offer 100% processor utilization with storage requirements less than previous designs. The approach has been used to create generators for the automated synthesis of FFT cores that are portable across a broad range of silicon technologies. Resulting chip designs are competitive with manual methods but with significant reductions in design times.

Analysis of Two-Speed Wind Farm Operation From Grid-Side Measurements

This paper analyzes data captured by a phasor measurement unit at a wind farm, employing two-speed induction generators, and investigates aspects of the control system's interaction with the power system. Composite superimposed transient events are proposed as a method to improve the quality of the analysis and reduce errors caused by unknowns, such as wind speed variation. A Mathworks SimPowerSystems model validates the inertia contribution of the wind farm, which is an important parameter in power systems with high wind penetration. Transients caused by turbine speed transitions are identified and explained. The analysis also highlights areas where wind farm control should be improved if useful inertia contribution is to be provided.

Comparison of Wavelet Transform and Time-Domain Analysis of Second Trimester Uterine Artery Doppler Waveforms in Screening for Pre-Eclampsia

The aim of this study was to compare time-domain waveform analysis of second-trimester uterine artery Doppler using the resistance index (RI) with waveform analysis using a mathematical tool known as wavelet transform for the prediction of pre-eclampsia (PE). This was a retrospective, nested case-cohort study of 336 women, 37 of whom subsequently developed PE. Uterine artery Doppler waveforms were analysed using both RI and waveform analysis. The utility of these indices in screening for PE was then evaluated using receiver operating characteristic curves. There were significant differences in uterine artery RI between the PE women and those with normal pregnancy outcome. After wavelet analysis, significant difference in the mean amplitude in wavelet frequency band 4 was noted between the 2 groups. The sensitivity for both Doppler RI and frequency band 4 for the detection of PE at a 10% false-positive rate was 45%. This small study demonstrates the application of wavelet transform analysis of uterine artery Doppler waveforms in screening for PE. Further prospective studies are needed in order to clearly define if this analytical approach to waveform analysis may have the potential to improve the detection of PE by uterine artery Doppler screening.

Blown Jet Vortex Generator Control of a Separated Diffuser Flow

The application of blown jet vortex generators to control flow separation in a diffuser with an opening angle of 10° has been studied using the computational fluid dynamics (CFD) code Fluent 6™. Experimental data is available for the uncontrolled flow in the diffuser. The section of the duct upstream of the diffuser has a height H equal to 15 mm; its length and breadth are 101H and 41H respectively; the diffuser has an expansion ratio of 4.7:1. Fully developed flow is achieved upstream of the diffuser. Pipes of diameters equal to 1.5%, 2.5% and 5% of H were considered; pitch angle was constant at 45° and yaw angle was fixed at 60°; velocity ratio was varied from 1.7 to 8.0; both co-rotating and counter-rotating arrays were studied. The best results were obtained with a counter-rotating array of generators with a hole diameter of 5% of H and a velocity ratio of 3.7.

Capability Curve Based Enhanced Reactive Power Control Strategy for Stability Enhancement and Network Voltage Management

Reactive power has become a vital resource in modern electricity networks due to increased penetration of distributed generation. This paper examines the extended reactive power capability of DFIGs to improve network stability and capability to manage network voltage profile during transient faults and dynamic operating conditions. A coordinated reactive power controller is designed by considering the reactive power capabilities of the rotor-side converter (RSC) and the grid-side converter (GSC) of the DFIG in order to maximise the reactive power support from DFIGs. The study has illustrated that, a significant reactive power contribution can be obtained from partially loaded DFIG wind farms for stability enhancement by using the proposed capability curve based reactive power controller; hence DFIG wind farms can function as vital dynamic reactive power resources for power utilities without commissioning additional dynamic reactive power devices. Several network adaptive droop control schemes are also proposed for network voltage management and their performance has been investigated during variable wind conditions. Furthermore, the influence of reactive power capability on network adaptive droop control strategies has been investigated and it has also been shown that enhanced reactive power capability of DFIGs can substantially improve the voltage control performance.

Day-Ahead Optimal Charging/Discharging Scheduling for Electric Vehicles in Micro-Grids

A micro-grid is an autonomous system which can be operated and connected to an external system or isolated with the help of energy storage systems (ESSs). While the daily output of distributed generators (DGs) strongly depends on the temporal distribution of natural resources such as wind and solar, unregulated electric vehicle (EV) charging demand will deteriorate the imbalance between the daily load and generation curves. In this paper, a statistical model is presented to describe daily EV charging/discharging behaviour. An optimisation problem is proposed to obtain economic operation for the micro-grid based on this model. In day-ahead scheduling, with estimated information of power generation and load demand, optimal charging/discharging of EVs during 24 hours is obtained. A series of numerical optimization solutions in different scenarios is achieved by serial quadratic programming. The results show that optimal charging/discharging of EVs, a daily load curve can better track the generation curve and the network loss and required ESS capacity are both decreased. The paper also demonstrates cost benefits for EVs and operators.

Determination of Power System Response during Small Load Fluctuations

This paper proposes a calculation method to determine power system response during small load perturbations or minor disturbances. The method establishes the initial value of active power transient using traditional reduction technique on admittance matrix, which incorporates voltage variations in the determination. The method examines active power distribution among generators when several loads simultaneously change, and verifies that the superposition principle is applicable for this scenario. The theoretical derivation provided in the paper is validated by numerical simulations using a 3-generator 9-bus benchmark model. The results indicate that the inclusion of voltage variation renders an independent and precise measure of active power response during transient conditions.

Measurement-based Method for Wind Farm Power System Oscillation Monitoring

The global increase in the penetration of renewable energy is pushing electrical power systems into uncharted territory, especially in terms of transient and dynamic stability. In particular, the greater penetration of wind generation in European power networks is, at times, displacing a significant capacity of conventional synchronous generation with fixed-speed induction generation and now more commonly, doubly-fed induction generators. The impact of such changes in the generation mix requires careful monitoring to assess the impact on transient and dynamic stability. This paper presents a measurement based method for the early detection of power system oscillations, with attention to mode damping, in order to raise alarms and develop strategies to actively improve power system dynamic stability and security. A method is developed based on wavelet transform and support vector data description (SVDD) to detect oscillation modes in wind farm output power, which may excite dynamic instabilities in the wider system. The wavelet transform is used as a filter to identify oscillations in different frequency bands, while SVDD is used to extract dominant features from different scales and generate an assessment boundary according to the extracted features. Poorly damped oscillations of a large magnitude or that are resonant can be alarmed to the system operator, to reduce the risk of system instability. Method evaluation is exemplified used real data from a chosen wind farm.

Impact of Wind Generation Mix on Transient Stability for an Interconnected Power System

The rapid growth of wind generation in many European countries is pushing power systems into
uncharted territory. As additional wind generators are installed, the changing generation mix may
impact on power system stability. This paper adopts the New England 39 bus system as a test
system for transient stability analysis. Thermal generator models are based on a likely future plant
mix for existing systems, while varying capacities of fixed-speed induction generators (FSIG) and
doubly-fed induction generators (DFIG) are considered. The main emphasis here has been placed
on the impact of wind technology mix on inter-area oscillations following transient grid
disturbances. In addition, both rotor angle stability and transient voltage stability are examined, and
results are compared with current grid code requirements and standards. Results have shown that
FSIGs can reduce tie-line oscillations and improve damping following a transient disturbance, but
they also cause voltage stability and rotor angle stability problems at high wind penetrations. In
contrast, DFIGs can improve both voltage and rotor angle stability, but their power output
noticeably oscillates during disturbances.