The prediction and control of transients in thyristor values

This thesis describes an investigation of methods by which both repetitive and non-repetitive electrical transients in an HVDC converter station may be controlled for minimum overall cost. Several methods of inrush control are proposed and studied. The preferred method, whose development is reported in this thesis, would utilize two magnetic materials, one of which is assumed to be lossless and the other has controlled eddy-current losses. Mathematical studies are performed to assess the optimum characteristics of these materials, such that inrush current is suitably controlled for a minimum saturation flux requirement. Subsequent evaluation of the cost of hardware and capitalized losses of the proposed inrush control, indicate that a cost reduction of approximately 50% is achieved, in comparison with the inrush control hardware for the Sellindge converter station. Further mathematical studies are carried out to prove the adequacy of the proposed inrush control characteristics for controlling voltage and current transients during both repetitive and non-repetitive operating conditions. The results of these proving studies indicate that no change in the proposed characteristics is required to ensure that integrity of the thyristors is maintained.

Mathematical methods in power system stability studies

In this thesis various mathematical methods of studying the transient and dynamic stabiIity of practical power systems are presented. Certain long established methods are reviewed and refinements of some proposed. New methods are presented which remove some of the difficulties encountered in applying the powerful stability theories based on the concepts of Liapunov. Chapter 1 is concerned with numerical solution of the transient stability problem. Following a review and comparison of synchronous machine models the superiority of a particular model from the point of view of combined computing time and accuracy is demonstrated. A digital computer program incorporating all the synchronous machine models discussed, and an induction machine model, is described and results of a practical multi-machine transient stability study are presented. Chapter 2 reviews certain concepts and theorems due to Liapunov. In Chapter 3 transient stability regions of single, two and multi~machine systems are investigated through the use of energy type Liapunov functions. The treatment removes several mathematical difficulties encountered in earlier applications of the method. In Chapter 4 a simple criterion for the steady state stability of a multi-machine system is developed and compared with established criteria and a state space approach. In Chapters 5, 6 and 7 dynamic stability and small signal dynamic response are studied through a state space representation of the system. In Chapter 5 the state space equations are derived for single machine systems. An example is provided in which the dynamic stability limit curves are plotted for various synchronous machine representations. In Chapter 6 the state space approach is extended to multi~machine systems. To draw conclusions concerning dynamic stability or dynamic response the system eigenvalues must be properly interpreted, and a discussion concerning correct interpretation is included. Chapter 7 presents a discussion of the optimisation of power system small sjgnal performance through the use of Liapunov functions.

Feasibility studies of an on-line identification technique

This thesis is concerned with the study of a non-sequential identification technique, so that it may be applied to the identification of process plant mathematical models from process measurements with the greatest degree of accuracy and reliability. In order to study the accuracy of the technique under differing conditions, simple mathematical models were set up on a parallel hybrid. computer and these models identified from input/output measurements by a small on-line digital computer. Initially, the simulated models were identified on-line. However, this method of operation was found not suitable for a thorough study of the technique due to equipment limitations. Further analysis was carried out in a large off-line computer using data generated by the small on-line computer. Hence identification was not strictly on-line. Results of the work have shovm that the identification technique may be successfully applied in practice. An optimum sampling period is suggested, together with noise level limitations for maximum accuracy. A description of a double-effect evaporator is included in this thesis. It is proposed that the next stage in the work will be the identification of a mathematical model of this evaporator using the teclmique described.

Essential mathematics:a refresher course for business and social studies

Many students starting courses in business, accounting and similar areas want to update their mathematical skills, and are seeking a suitable text; this book addresses their needs. Written in an informal style, emphasising understanding and application of techniques rather than formal proofs, it covers all the mathematics needed by entrants to BTEC, undergraduate, MBA and related professional courses. Plentiful worked examples and exercises with solutions make the book a practical self-study aid for those wishing to revise before starting their course.

Studies of the drying of particulate slurries

The literature relating to the drying characteristics of pure liquid drops and particulate slurry drops has been reviewed. The experimental investigation was, therefore, divided into three parts: Pure water drops, Aqueous sodium sulphate decahydrate drops, and, Slurry drops from nine detergent formulations. The value of the constant,'Ψ, reported by Ranz and Marshall, was found to be temperature dependent. In the temperature range o 26.5≤T≤118.5°C,Ψ , for pure water drops, varied between 0.38 and 0.47. A revised correlation of the mass transfer coefficients is therefore proposed.  A mathematical model for estimating the variation of crust thickness, for aqueous sodium sulphate drops, with time is proposed: β = R _ {R3 - ( 1.5G/πCo ) ( ΔHD - ΔHU) Δ} 1/3 Experimental crust thickness evaluated from stereoscan micrographs showed good agreement with theoretical prediction. It has been shown that drying characteristics of detergent drops can be evaluated from the porosity:thickness ratio, {ε/\β}. Formulations having large {ε/β I-ratios dry better than those with smaller values. The agreement between the experimental and theoretical mass transfer coefficients shows, in addition to the above correlation, that the overall mass transfer coefficient can be predicted from the expression1/K = 1/K + β/DMε 1.5 The crust is the controlling resistance to transfer in particulate slurry drops. For aqueous sodium sulphate drops, the crust provides 64.2% of the total resistance while for detergents with thicker, but less porous crusts, the value is 97.5%.

Studies in organobismuth chemistry

Perturbations in the bismuth market resulted in Mining and Chemical Products Ltd., seeking further outlets in the market. Together with Manchem Ltd. they were anxious to evaluate the possibility of using bismuth compounds as a replacement for lead/calcium soaps in paint driers. A range of new organobismuth compounds were synthesised of the type RBiX2 and R3BiX2 (X= halogen, OOCR, dithiocarbamate). A variety of synthetic techniques were explored, including the use of mathematical reactions, phase-transfer catalysis and microwave energy. The preparation of a range of trivalent and pentavalent organobismuth carboxylates is reported and their infra-red , 13C, lH nmr spectra. The compounds were evaluated as paint driers and in cases found to enhance paint drying to a greater degree than the standard driers, to which they were being compared. The drying times of paint films containing the organobismuth compounds are reported, together with a comparison of the drying times with the addition of bismuth tris-diethyldithiocarbamate, which may promote the cross-linking reaction that occur in paint films during the drying process. Examples are reported to illustrate the great reductions in reaction times possible when using microwave energy. Reactions such as metallation of aromatic rings, ligand redistribution and synthesis were carried out in PTFE containers in a conventional domestic microwave oven. An X-ray diffraction study of (phenylazophenyl-C,N')mercury(II) chloride has shown it to be dimeric via long Hg-Cl bridging interactions of 3.367A. Its crystal structure is reported, together with its 13C nmr spectra and mass spectrum. The Lewis acidity of compounds of the type RBiX2 was investigated. The donor group being anchored to the organo group (R). The dithiocarbamates bis- (diethyldithiobarbamato)phenylbismuth(Ill) and [2-2-pyridyl)phenylbismuth(III) were synthesised, and their crystal structures, 14N, 13C nmr ar1d infra-red spectra are reported. Both compounds are pseudo-pentagonal bipyramidal in geometry, with two long Bi-S bonds and two short Bi-S bonds. The reaction of RBiBr2 (R= 2-(pyridyl) with various ligands is reported. The infra-red evidence suggesting that the coordination of extra ligands is accompanied by a reduction of the strength of the Bi-interaction.

Spray drier simulation and air flow pattern studies

The literature pertaining to the key stages of spray drying has been reviewed in the context of the mathematical modelling of drier performance. A critical review is also presented of previous spray drying models. A new mathematical model has been developed for prediction of spray drier performance. This is applicable to slurries of rigid, porous crust-forming materials to predict trajectories and drying profiles for droplets with a distribution of sizes sprayed from a centrifugal pressure nozzle. The model has been validated by comparing model predictions to experimental data from a pilot-scale counter-current drier and from a full-scale co-current drier. For the latter, the computed product moisture content was within 2%, and the computed air exit temperature within 10oC of experimental data. Air flow patterns have been investigated in a 1.2m diameter transparent countercurrent spray tower by flow visualisation. Smoke was introduced into various zones within the tower to trace the direction, and gauge the intensity, of the air flow. By means of a set of variable-angle air inlet nozzles, a variety of air entry configurations was investigated. The existence of a core of high rotational and axial velocity channelling up the axis of the tower was confirmed. The stability of flow within the core was found to be strongly dependent upon the air entry arrangement. A probe was developed for the measurement of air temperature and humidity profiles. This was employed for studying evaporation of pure water drops in a 1.2m diameter pilot-scale counter-current drier. A rapid approach to the exit air properties was detected within a 1m distance from the air entry ports. Measured radial profiles were found to be virtually flat but, from the axial profiles, the existence of plug-flow, well-mixed-flow and some degree of air short-circuiting can be inferred. The model and conclusions should assist in the improved design and optimum operation of industrial spray driers.

Studies of solar radiation and its measurement

A mathematical model has been developed for predicting the spectral distribution of solar radiation incident on a horizontal surface. The solar spectrum in the wavelength range 0.29 to 4.0 micrometers has been divided in 144 intervals. Two variables in the model are the atmospheric water vapour content and atmospheric turbidity. After allowing for absorption and scattering in the atmosphere, the spectral intensity of direct and diffuse components of radiation are computed. When the predicted radiation levels are compared with the measured values for the total radiation and the values with glass filters RG715, RG630 and OG530, a close agreement (± 5%) has been achieved under clear sky conditions. A solar radiation measuring facility, close to the centre of Birmingham, has been set up utilising a microcomputer based data logging system. A suite of computer programs in the BASIC programming language has been developed and extensively tested for solar radiation data, logging, analysis and plotting. Two commonly used instruments, the Eppley PSP pyranometer and the Kipp and Zonen CM5 pyranometer, have been compared under different experimental conditions. Three models for computing the inclined plane irradiation, using total and diffuse radiation on a horizontal surface, have been tested for Birmingham. The anisotropic-alI-sky model, proposed by Klucher, provides a good agreement between the measured and the predicted radiation levels. Measurements of solar spectral distribution, using glass filters, are also reported for a number of inclines facing South.

The mathematical modelling of the environmental performance of buildings as an aid in the design process

This thesis is a theoretical study of the accuracy and usability of models that attempt to represent the environmental control system of buildings in order to improve environmental design. These models have evolved from crude representations of a building and its environment through to an accurate representation of the dynamic characteristics of the environmental stimuli on buildings. Each generation of models has had its own particular influence on built form. This thesis analyses the theory, structure and data of such models in terms of their accuracy of simulation and therefore their validity in influencing built form. The models are also analysed in terms of their compatability with the design process and hence their ability to aid designers. The conclusions are that such models are unlikely to improve environmental performance since: a the models can only be applied to a limited number of building types, b they can only be applied to a restricted number of the characteristics of a design, c they can only be employed after many major environmental decisions have been made, d the data used in models is inadequate and unrepresentative, e models do not account for occupant interaction in environmental control. It is argued that further improvements in the accuracy of simulation of environmental control will not significantly improve environmental design. This is based on the premise that strategic environmental decisions are made at the conceptual stages of design whereas models influence the detailed stages of design. It is hypothesised that if models are to improve environmental design it must be through the analysis of building typologies which provides a method of feedback between models and the conceptual stages of design. Field studies are presented to describe a method by which typologies can be analysed and a theoretical framework is described which provides a basis for further research into the implications of the morphology of buildings on environmental design.

Characterisation of electrospun polystyrene scaffolds for three-dimensional in vitro biological studies

The purpose of this study was to produce a well-characterised electrospun polystyrene scaffold which could be used routinely for three-dimensional (3D) cell culture experimentation. A linear relationship (p<0.01p<0.01) between three principal process variables (applied voltage, working distance and polymer concentration) and fibre diameter was reliably established enabling a mathematical model to be developed to standardise the electrospinning process. Surface chemistry and bulk architecture were manipulated to increase wetting and handling characteristics, respectively. X-ray photoelectron spectroscopy (XPS) confirmed the presence of oxygen-containing groups after argon plasma treatment, resulting in a similar surface chemistry to treated tissue culture plastic. The bulk architecture of the scaffolds was characterised by scanning electron microscopy (SEM) to assess the alignment of both random and aligned electrospun fibres, which were calculated to be 0.15 and 0.66, respectively. This compared to 0.51 for collagen fibres associated with native tissue. Tensile strength and strain of approximately of 0.15 MPa and 2.5%, respectively, allowed the scaffolds to be routinely handled for tissue culture purposes. The efficiency of attachment of smooth muscle cells to electrospun scaffolds was assessed using a modified 3-[4,5-dimethyl(thiazol-2yl)-3,5-diphery] tetrazolium bromide assay and cell morphology was assessed by phalloidin-FITC staining of F-actin. Argon plasma treatment of electrospun polystyrene scaffold resulted in significantly increased cell attachment (p<0.05p<0.05). The alignment factors of the actin filaments were 0.19 and 0.74 for the random and aligned scaffold respectively, compared to 0.51 for the native tissue. The data suggests that electrospinning of polystyrene generates 3D scaffolds which complement polystyrene used in 2D cell culture systems.