There are different types of relays and each type has specific applications. It looks that you are looking for overcurrent setting calculations, as can be seen from mentioning plug setting and time setting multipliers. This is a typical protection scheme in distribution systems, the story is different at transmission levels.
There are many commercial software packages available that can be used to do the calculations, but again you need to build fundamental knowledge in order to interpret the outcome of these packages.
Going to the 'basics' there are multiple possible reasons for a coordination study or a protection study in general. Reason 1 is protection of 'upstream' equipment -a fault conditions stresses equipment both thermally (I^2*time) and mechanically. Interrupting devices should 'clear' a fault before a device is damaged. Here is the US there are also safety concerns relating to both Arc Flash (heat exposure generated at the fault) and current exposure (limiting fault time in the event an employee is 'in' the fault path to prevent heart fibrillation. the other common goal is to ensure that the device that clears the fault interrupts the supply to the smallest area of the system so restoration is simplified-in simple terms this means the nearest 'upstream' device opens before any other device that would interrupt a larger part of the system.
A good working knowledge of the system and the devices on the system is necessary. You must start now to study and learn the fundamentals of relaying. Learn the basics and then continuously practice progressive sample calculations and time current characteristics curves. This is the best way to learn the logic and application. I did it this way even manually plotting the relay curves. You will realized that you will be more better in applying and justifying the logic of choosing your settings, your characteristic curves, and arguing with the electrical group. I learned it this way and I am still doing it on some smaller projects. I can even check other design analysis / calculations of big projects that were done using software programs. I can see their shortcomings. I can check the logic they used and the applicability to the objective of the over-all design. I even see justified un-coordinated protection curves. Practice will make you more versatile.
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