For 250KVA 11000/400V they used 31.5 Amps, if we upgrade to 500 KVA, same fuse can be used are we need to change the rating? 250KVA=HRC 31.5 AMPS? is there any formula?

I think you are talking about HT fuse, Fuse rating depends open the max. current capacity that can flow through phase of the transformer. For 250 KVA, 11000/400V we use the HRC fuse rating of 16 Amps per phase and if we upgrade to 500KVA, 11000/400 than HRC fuse rating be 31.5 on each phases.

If you are talking about HV fuse which is mounted in front of power transformer then I agree with sir Harish in aspect of selection of HT fuse.
You can use this expression for calculating current of fuse's acting during selection of appropriate fuse for protection of your power transformer:

Ifuse=1,2*Intr=1,2*Sntr/((sqrt(3))*Untr)

where are:

Ifuse-current of fuse's acting or minimum current under which your fuse will act
Intr-rated current of power transformer
Sntr-rated power of power transformer
Untr-rated voltage of power transformer

Comment: I multiplied rated current of your power transformer with 1,2 during selection of fuse for protection of your power transformer, because I wanted to include in calculation for selection of fuse for protection of your power transformer overloading of power transformer during which fuse will not act (recommended overloading is 20%).

Your primary fuse rating (11 KV) should not exceed 300% of the primary full load amps of the transformer.
Your secondary fuse rating (400 V) should not exceed 125% of the secondary full load amps of your transformer.
The above fuse ratings will provide your transformer adequate protection for overloads and short circuits.
You can choose lower settings but you should not exceed the thresholds in order to be adequately protected.

The availability of the following data (minimum) is required to achieve the appropriate Fuse ratings:-

a. Whether the intention of the protection against overload or short circuit or both.

b. Transformer Inrush current to be considered.

c. The required time coordinations / grading (discrimination).
d. The nearest available Standard rating.

e. Characterstic of the protective device as per manufacturer recommendation.

For you cases:-

Case one , the primary line current = 13.13 A. (delta connection)
Fuse rating = 31.5 A

Case two, the primary line current = 26.3 A.
I guess the Fuse rating (the neares standard) = 63A

Hi, you should just for the 500kva check the inrush when you enegize the transformer without any load on the secondary. As you know each fuse has a triggering curve, just check it versus the 500kva inrush.

As the Kva changes so does FLA.

Fuse can vary in range as an example on the primary between 150-300% depending on various factors.

Best is to get the damage curve for the respective transformer from the manufacture and plot the fuse curve to get the best fit with enough safety margin and without nuisance blowing on energization.

31.5A fuse for 250 KVA was on the higher side.Same fuse will not be adequate for 500 KVA transformer.These fuses don't provide overload protection.No back up protection for LV short circuits as well.I would recommend your going for 50 A fuse.
You may check that the HV cable/conductor is of adequate cross section.

This is the fast and approximate way to select the fuse:
You have 500kVA, 11kV transformer, then your primary FLC will be 26.24A. Transformer inrush current will be 20X26.24=524.8A. Assuming inrush current takes 0.1Sec. current @ 0.1Sec is 12X26.24=314.88A. You have to select the fuse which is above 524.8A @0.01Sec(energizing moment) and 314.88A@0.1Sec. As your existing fuse is 31.5A, I am assuming you are using "DIN rated" fuse rather than "E rated". Looking into "Melting Time Current Characteristics" for SIBA fuse manufacturer (as an example), the fuse selection will be 50A.

In my opinion there are not enough information to be sure about your installation. However i want to add some general comments:

1.- Most of the countries have its own electrical regulations and in many times those regulations are by law.

The comments posted are in compliance with your local regulations ?...be sure of that.

2.- Most of electrical regulations cover the basic elements of an Electrical Installation such as, overcurrent, grounding, etc, you only have to follows that rules.

I do not know what regulations you use but let me give some additional references:

IEC 7671 Requirements for Electrical Installations. May be read this reference can be complicated if you are not a design engineer the next book have a lot of examples based on IEC 7671 "Electrical Installation Calculation" by Marc Coates edited by Wiley.

If you are just a construction contractor all you have to do is install the specified transformer. Your job is done ! As per drawings.

When I was a contractor we bid on tendered jobs, complete with contract specifications and marked up drawings, similar to the one that was posted.

If the job entails switching out one 250 Kva transformer for 500 Kva, that would be the bid we submit for, including mobilization and econnection from supply side to load side, as per drawings.

Unless otherwise specified as in fusing, short circuit availability and perhaps other, that would be the responsibility of the design/project engineer or consultant engineer. Our job is to provide the labor to install the necesaary changes.

If it comes down to doing the job and a few things are indentified as in engineering defficiencies, then the original bid price is still in effect with added cost for scope change. This acan include enginering, installing new equipment what ever it take to make it work as long as the customer is paying for it.

Sort of like these discussion, many answer and which is the best solution .... we do not have enough detail.