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.

On the stress analysis of cracked bodies by means of finite elements

The work described in this thesis deals with the development and application of a finite element program for the analysis of several cracked structures. In order to simplify the organisation of the material presented herein, the thesis has been subdivided into two Sections : In the first Section the development of a finite element program for the analysis of two-dimensional problems of plane stress or plane strain is described. The element used in this program is the six-mode isoparametric triangular element which permits the accurate modelling of curved boundary surfaces. Various cases of material aniftropy are included in the derivation of the element stiffness properties. A digital computer program is described and examples of its application are presented. In the second Section, on fracture problems, several cracked configurations are analysed by embedding into the finite element mesh a sub-region, containing the singularities and over which an analytic solution is used. The modifications necessary to augment a standard finite element program, such as that developed in Section I, are discussed and complete programs for each cracked configuration are presented. Several examples are included to demonstrate the accuracy and flexibility of the technique.

Statin use in rheumatoid arthritis in relation to actual cardiovascular risk:evidence for substantial undertreatment of lipid-associated cardiovascular risk?

Background Cardiovascular disease (CVD) is partially attributed to traditional cardiovascular risk factors, which can be identified and managed based on risk stratification algorithms (Framingham Risk Score, National Cholesterol Education Program, Systematic Cardiovascular Risk Evaluation and Reynolds Risk Score). We aimed to (a) identify the proportion of at risk patients with rheumatoid arthritis (RA) requiring statin therapy identified by conventional risk calculators, and (b) assess whether patients at risk were receiving statins. Methods Patients at high CVD risk (excluding patients with established CVD or diabetes) were identified from a cohort of 400 well characterised patients with RA, by applying risk calculators with or without a ×1.5 multiplier in specific patient subgroups. Actual statin use versus numbers eligible for statins was also calculated. Results The percentage of patients identified as being at risk ranged significantly depending on the method, from 1.6% (for 20% threshold global CVD risk) to 15.5% (for CVD and cerebrovascular morbidity and mortality) to 21.8% (for 10% global CVD risk) and 25.9% (for 5% CVD mortality), with the majority of them (58.1% to 94.8%) not receiving statins. The application of a 1.5 multiplier identified 17% to 78% more at risk patients. Conclusions Depending on the risk stratification method, 2% to 26% of patients with RA without CVD have sufficiently high risk to require statin therapy, yet most of them remain untreated. To address this issue, we would recommend annual systematic screening using the nationally applicable risk calculator, combined with regular audit of whether treatment targets have been achieved.

Proliferative diabetic retinopathy (R3) referrals from the digital diabetic retinopathy screening program:urgency of appointment in the hospital eye service achieved and needed?

DESIGN. Retrospective analysis PURPOSE. To assess the clinical characteristics and outcomes of patients identified with proliferative diabetic retinopathy (PDR) referred from the screening program to the hospital eye services (HES) METHODS. a retrospective analysis of urgently referred PDR cases to Birmingham Heartlands HES from august 2008 until July 2010 RESULTS. 130 urgent diabetic retinopathy referrals were made and reviewed. 103 (68% male, 80% type 2 diabetes) were referred for PDR with a mean age of 59 years, mean diabetes duration of 17.8years. 69% were on insulin treatment at the time of the screening, with mean HbA1c of 10.4% (range-5.7 to 16.5%). 65% of the patients were offered appointments at HES within two weeks after referral from the screening. 50.5% of the patients were seen in the HES within 2 weeks, 22 and 16 % were seen 2-4 and 4-8 weeks after referral respectively. 6 patients never attended ophthalmology examination during the two years of review. Of all the attendees, 56% were booked for pan retinal photocoagulation (PRP) & 9(9.3%) for macular laser respectively on their 1st HES visit. 75% of the patients were newly diagnosed PDR and 26 had previous PRP laser but lost to follow up. 63 patients ( 66%) received either PRP or macular laser treatment (85.7% of which is PRP). 63% of the PRP treatment was performed within a month of first HES attendance. Retinopathy grading discrepancy between the screening program and HES was noted in 20% (21 patients). CONCLUSIONS. This data suggests that the digital screening programme is appropriately identifying high risk patients with PDR with timely PRP laser treatment in the majority of patients but raises concern over patients lost to follow up (hence failsafe tracking of appointment attendance), and review of grading discrepancies between the ophthalmology and screening service.