Modelling of induction motors for system faults and transient stability studies

The research carried out in this thesis was mainly concerned with the effects of large induction motors and their transient performance in power systems. Computer packages using the three phase co-ordinate frame of reference were developed to simulate the induction motor transient performance. A technique using matrix algebra was developed to allow extension of the three phase co-ordinate method to analyse asymmetrical and symmetrical faults on both sides of the three phase delta-star transformer which is usually required when connecting large induction motors to the supply system. System simulation, applying these two techniques, was used to study the transient stability of a power system. The response of a typical system, loaded with a group of large induction motors, two three-phase delta-star transformers, a synchronous generator and an infinite system was analysed. The computer software developed to study this system has the advantage that different types of fault at different locations can be studied by simple changes in input data. The research also involved investigating the possibility of using different integrating routines such as Runge-Kutta-Gill, RungeKutta-Fehlberg and the Predictor-Corrector methods. The investigation enables the reduction of computation time, which is necessary when solving the induction motor equations expressed in terms of the three phase variables. The outcome of this investigation was utilised in analysing an introductory model (containing only minimal control action) of an isolated system having a significant induction motor load compared to the size of the generator energising the system.

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.

Short-term stability in refractive status despite large fluctuations in glucose levels in diabetes mellitus type 1 and 2

Purpose: This work investigates how short-term changes in blood glucose concentration affect the refractive components of the diabetic eye in patients with long-term Type 1 and Type 2 diabetes. Methods: Blood glucose concentration, refractive error components (mean spherical equivalent MSE, J0, J45), central corneal thickness (CCT), anterior chamber depth (ACD), crystalline lens thickness (LT), axial length (AL) and ocular aberrations were monitored at two-hourly intervals over a 12-hour period in: 20 T1DM patients (mean age ± SD) 38±14 years, baseline HbA1c 8.6±1.9%; 21 T2DM patients (mean age ± SD) 56±11 years, HbA1c 7.5±1.8%; and in 20 control subjects (mean age ± SD) 49±23 years, HbA1c 5.5±0.5%. The refractive and biometric results were compared with the corresponding changes in blood glucose concentration. Results: Blood glucose concentration at different times was found to vary significantly within (p<0.0005) and between groups (p<0.0005). However, the refractive error components and ocular aberrations were not found to alter significantly over the day in either the diabetic patients or the control subjects (p>0.05). Minor changes of marginal statistical or optical significance were observed in some biometric parameters. Similarly there were some marginally significant differences between the baseline biometric parameters of well-controlled and poorly-controlled diabetic subjects. Conclusion: This work suggests that normal, short-term fluctuations (of up to about 6 mM/l on a timescale of a few hours) in the blood glucose levels of diabetics are not usually associated with acute changes in refractive error or ocular wavefront aberrations. It is therefore possible that factors other than refractive error fluctuations are sometimes responsible for the transient visual problems often reported by diabetic patients. © 2012 Huntjens et al.