Theory 1 : Problem statement and difficulties

The failure of any sensitive equipment connected to a point of common coupling is broadly because of the interaction of two events. One the severity of voltage sag and the other  the tolerance of the sensitive equipment.  The voltage sag severity is decided in most of the cases from the electromagnetic exchange of energy from the supply to the load and vice versa. The literature asserts that the voltage sag events can be considered as stochastic events and thus assessment of voltage sag can be done by various already existing numerical methods.

However, the other event i.e. the tolerance of a sensitive equipment is something which has been a topic of discussion for a while among the experts of the subject matter. Is the occurrence of tolerance level of an equipment a stochastic event or a fuzzy event?

This conflict of viewpoint on the nature of the occurrence of tolerance level of an equipment has led to several research papers , each proposing a method which presents the very occurrence in a different context under the light of either stochastic event or a fuzzy event.

I have, for this paper, decided to take the course of fuzzy logic sets to quantify the amount of trips an equipment can have due to voltage sags.

Here are the problems I am facing as of now:
    1. Integrating fuzzy logic to quantify anything is not a convention as far as I have seen. Fuzzy logic has been used to present a subjective  view based on some expert opinion. But to quantify anything uncertain, probabilistic method is taken as the tool, in general.

   2. This brings me to the second problem, if probabilistic method is to be taken as the tool, then the methodology would become a stochastic process which is not at all considered by me. I am of the view that tolerance of an equipment is a fuzzy event and not a stochastic event. So how can I quantify the trips without using probabilistic method?


  3. I do not have any equipment or laboratory which can validate anything I would propose subsequently. How can I compare my results, if at all I happen to formulate a theory, with the experimental results?


These are the things I would need to read for better understanding of my work:

1. Fuzzy set theory- basics
2. Type 2 interval fuzzy set theory
3. Monte carlo simulaton method
4. Critical distance method for finding voltage sags

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