I have four 400v 50hz generators with capacity 1.5 mva per each
those generators are connected to 400/11000 v transformers and synchronized at medium voltage side with the utility

we have a problem which is when the utility feeder is switched off all circuit breakers of the generators transformers are tripping

Said, Until you determine what protective relays are causing the trip. Do you have any local load, do your control system(s) and/or governors support isolated/islanding operation?

Once the utility feeder is lost you have no frequency reference and the governors may be forced to trip unless you have some form of automatic switchover to isolated mode and governors with properly adjusted droop mode controls.

protective relays of the normal relays which means over current under voltage over/under frequency and other famous types of the protective relays as you see i am working on 11kv voltage level which do not need complicated protections
i was not there when it trips and i was taking only 250kw from the utility and generators overloading was not the reason

You indicated that your synchronizing set-up of the generators is with the medium voltage utility bus. You also indicated that you are tripping the generator when the utility feeder is switched off which means you are isolating with the utilty so there is no utility power and frequency to synchronize with, so I believe with Allan's view that once you lost the frequency and power to synchronize with, then your generators' circuit breaker will trip to protect your generators in parallel from running without load. Prolonged operation of generators underloaded even with loads under 35% is not a recommended. operation for generators.

Said, 11 kV can do plenty of damage! That being said, we have to rely on the information that you give us, so it would be very useful if you could tell us what relays did operate, and if there is any local load (250 kW??) that is fed from both the grid and your generators.

If you have no local load and you were taking 250 kW from the grid then your generators were operating as motors and you should consider yourself lucky that some form of relaying, reverse power perhaps, took you out.

Continuing what Meynardo said about reduced load operation, it's not the generators that care, they could operate and no load forever, if they do they're known as motors or synchronous condensers, it's the prime movers that are at risk. You did not say whether they are turbines or diesels, but each has its own minimum operating point.

Steam turbines, unless designed for low load operation, will experience blade erosion if they operate with low quality steam conditions that allow condensation and/or water droplets to enter the last stages of blading.

Diesels are generally meant to operate around their highest efficiency point, around 75-85% of rated load, otherwise they can experience significant carbon fouling, glazing, poor fuel economy, and increased maintenance costs.

To conclude, the more you tell us about your particular situation and the relays that operated, the more we may be able to help. At these power levels guessing is not an option.

What are your relay targets from each unit ?

Have you even studied the tripping or shutdown schematic ?

Have you looked into anything at all ? Please say yes and tell us what you know first before we try to help you ;

Not surprising! Once the utility feeder is switched off, the generators are driven to over frequency and/or over voltage. From your posts, it is understood that you do nit have a load shedding or a load-shading scheme for your generators. Suggest to introduce a time delay for your over voltage and over frequency relays.

Said: The tripping of your generators' circuit breakers when you disconnect the feeder from the utilty is not a problem but a properly designed protective relay function that is quickly isolating your generators to prevent the generators from being damaged. What is happening is not a problem but a quick reaction for protection. Probably you should make some refinements in your operating procedure of gradually unloading the generators before doing an abrupt disconnection of the utility feeder. Or some refinements / adjustments can be made in your time delay settings of the relays.

all of you help me very well thank you for every little information you support me with thank you