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.

Modelling of transient heat transfer in annealing furnaces

This is a study of heat transfer in a lift-off furnace which is employed in the batch annealing of a stack of coils of steel strip. The objective of the project is to investigate the various factors which govern the furnace design and the heat transfer resistances, so as to reduce the time of the annealing cycle, and hence minimize the operating costs. The work involved mathematical modelling of patterns of gas flow and modes of heat transfer. These models are: Heat conduction and its conjectures in the steel coils;Convective heat transfer in the plates separating the coils in the stack and in other parts of the furnace; and Radiative and convective heat transfer in the furnace by using the long furnace model. An important part of the project is the development of numerical methods and computations to solve the transient models. A limited number of temperature measurements was available from experiments on a test coil in an industrial furnace. The mathematical model agreed well with these data. The model has been used to show the following characteristics of annealing furnaces, and to suggest further developments which would lead to significant savings: - The location of the limiting temperature in a coil is nearer to the hollow core than to the outer periphery. - Thermal expansion of the steel tends to open the coils, reduces their thermal conductivity in the radial direction, and hence prolongs the annealing cycle. Increasing the tension in the coils and/or heating from the core would overcome this heat transfer resistance. - The shape and dimensions of the convective channels in the plates have significant effect on heat convection in the stack. An optimal design of a channel is shown to be of a width-to-height ratio equal to 9. - Increasing the cooling rate, by using a fluidized bed instead of the normal shell and tube exchanger, would shorten the cooling time by about 15%, but increase the temperature differential in the stack. - For a specific charge weight, a stack of different-sized coils will have a shorter annealing cycle than one of equally-sized coils, provided that production constraints allow the stacking order to be optimal. - Recycle of hot flue gases to the firing zone of the furnace would produce a. decrease in the thermal efficiency up to 30% but decreases the heating time by about 26%.

Nearwork-induced transient myopia (NITM) in anisometropia

Objective: To assess the magnitude of nearwork-induced transient myopia (NITM) under binocular viewing conditions separately in each eye of individuals with mild to moderate anisometropia to determine the relationship between NITM and their interocular refractive error. Methods: Forty-three children and young adults with anisometropia [cycloplegic spherical equivalent (SE) difference >1.00 D] were tested (ages 9-28 years). NITM was measured with binocular viewing separately in each eye after binocularly performing a sustained near task (5 D) for 5 min incorporating a cognitive demand using an open-field, infrared autorefractor (Grand-Seiko, WAM-5500). Data were averaged over 10 s bins for 3 min in each eye. Initial NITM, its decay time (DT), and its decay area (DA) were determined. A-scan ultrasound ocular biometry was also performed to determine the axial length of each eye. Results: The more myopic eye exhibited increased initial NITM, DT, and DA as compared to the less myopic eye (0.21 ± 0.16 D vs 0.15 ± 0.13 D, p = 0.026; 108.4 ± 64.3 secs vs 87.0 ± 65.2 secs, p = 0.04; and 17.6 ± 18.7 D*secs vs 12.3 ± 15.7 D*secs, p = 0.064), respectively. The difference in DA and the difference in SE between the more versus less myopic eye were significantly correlated (r = 0.31, p = 0.044). Furthermore, 63% (27/43), 56% (24/43), and 70% (30/43) of the more myopic eyes exhibited increased initial NITM, longer DT, and larger DA, respectively, than found in the less myopic eye. Conclusions: In approximately two-thirds of the anisometropic individuals, the initial NITM and its decay area were significantly increased in the more myopic eye as compared to the less myopic eye. NITM may play an important role in the development of interocular differences in myopia, although a causal relationship is yet to be established. Furthermore, the findings have potentially important implications regarding accommodative control and interocular accommodative responsitivity in anisometropia, in particular for anisomyopia. © 2013 The College of Optometrists.

Refractive error, cognitive demand and nearwork-induced transient myopia

Purpose. Whereas many previous studies have identified the association between sustained near work and myopia, few have assessed the influence of concomitant levels of cognitive effort. This study investigates the effect of cognitive effort on near-work induced transient myopia (NITM). Methods. Subjects comprised of six early onset myopes (EOM; mean age 23.7 yrs; mean onset 10.8 yrs), six late-onset myopes (LOM; mean age 23.2 yrs; mean onset 20.0 yrs) and six emmetropes (EMM; mean age 23.8 yrs). Dynamic, monocular, ocular accommodation was measured with the Shin-Nippon SRW-5000 autorefractor. Subjects engaged passively or actively in a 5 minute arithmetic sum checking task presented monocularly on an LCD monitor via a Badal optical system. In all conditions the task was initially located at near (4.50 D) and immediately following the task instantaneously changed to far (0.00 D) for a further 5 minutes. The combinations of active (A) and passive (P) cognition were randomly allocated as P:P; A:P; A:A; P:A. Results. For the initial near task, LOMs were shown to have a significantly less accurate accommodative response than either EOMs or EMMs (p < 0.001). For the far task, post hoc analyses for refraction identified EOMs as demonstrating significant NITM compared to LOMs (p < 0.05), who in turn showed greater NITM than EMMs (p < 0.001). The data show that for EOMs the level of cognitive activity operating during the near and far tasks determines the persistence of NITM; persistence being maximal when active cognition at near is followed by passive cognition at far. Conclusions. Compared with EMMs, EOMs and LOMs are particularly susceptible to NITM such that sustained near vision reduces subsequent accommodative accuracy for far vision. It is speculated that the marked NITM found in EOM may be a consequence of the crystalline lens thinning shown to be a developmental feature of EOM. Whereas the role of small amounts of retinal defocus in myopigenesis remains equivocal, the results show that account needs to be taken of cognitive demand in assessing phenomena such as NITM.