REDUNDANCY ALLOCATIONS IN ELECTRONIC RELAY CIRCUITS

Abstract

The thesis gives a detailed study of the problem of redundancy allocations in electronic circuits associated with the protective relay circuits. The approach has been kept general so that application to various fields is unrestricted. Operational reliability is the main concern of any electronic circuit associated with such protective relay circuits. Un less the electronic components are made absolutely reliable by tried and tested methods of manufacturing processes, the choice rests on duplicating the components or, in general, what is called as redundancy applications. The thesis begins with a. detailed study of the redundancy circuits and their modelling as far as the reliability evalu ation is concerned. Various types of redundant circuits are analysed to complete the study. Different approaches are devised for relia bility evaluation of such networks. In general, one may come across series and/or parallel or non series-parallel networks in practice. The non series-parallel networks usually present difficultywhen the problem is to evaluate the overall reliability of such networks. Flow-graph method has been developed wherein a method of inspection makes it all the more easy to calculate reliability of the redundant networks, quickly. If the network is large and complex, the reliability evaluation poses a problem; therefore an algorithm is present ed for straight and fast computation on a digital computer for any type of the redundant network. This has been possible by

correlating the properties of redundant networks with those of di-graphs. The thesis embodies optimisation techniques for maxi misation of the system reliability subject to linear or non linear constraints. Here again, various techniques have been applied, viz. gradient method, Kuhn-Tucker conditions of optimality, Dynamic programming, Variational method, Discrete maximum principle, Integer linear programming etc. Several new approaches and modifications of the existing methods have been proposed and they are tested on problems from various sources. One usually faces the problem of choosing proper values of Lagrangian multipliers when solving an optimisation problem with linear constraints. Attempts have been made to make proper selection of these and to solve such problems with ease. Dynamic programming formulation in 'summation' form has been developed and was found to be more convenient than usual 'product' formulation. An algorithm based on Lagrangian multipliers and general optimal condition is proposed in case of problems with linear constraints. A Variational method for multiple linear constraints is also developed and has been tried on several problems. Discrete maximum principle has been used for problems with linear and non-linear constraints. Discrete optimisation technique- is discussed in general perspective for reliability optimisation under'several constraints. In the end a comparative assessment of the methods embodied in the thesis is made to provide th'e merits and demerits of each so as to allow one to make his own choice of the method under limitations and advantages exposed.

In brief, a detailed mathematical analysis has been presented for the problem of reliability evaluation and opti misation of the redundant networks under conditions specified which will help to pave the way for making circuits or systems more reliable.