I dont see a reply here... but De-rate is a term that means the engine will lower its maximum output power in order to try and save itself if an over-heat condition occurs..
unless the cooling system has failed.. broken fan or belt, busted hose, etc.. the most common reason for an engine to over-heat and turn on a warning light is because it is being worked too hard.. you have your foot to the floor climbing a long mountain grade.. and its hot outside.. the radiator and fan arent designed for continuous usage like this on a school bus or maybe the fasn is not working as strong as it should.. so the engine gets hotter.. the driver ignores the temp gauge and keeps pushing.. the computer senses the hotter and hotter and starts reducing fuel going to the engine.. after all burning fuel is what makes things hot.. if it continues to heat up it will keep reducing fuel.. you will slow down and the fan / radiator have a better chance of keeping up.. typically the computers monitor the coolant and engine oil temperature.. some of the newest engines even monitor the transmission temperature..
not syaing your bus was over-heating, but de-rate is something that usually makes the warning light come on, to tell you "hey dude im sweating over here!"...
OK now onto the inverter.. your inverter is apparently over-taxing the alternator and dropping the voltage in your electrical system.. 400 watts really shouldnt kill off a good solid high amp bus alternator.. however if you have too small and too long of wires feeding from the batteries to the inverter it can greatly increase the current needed t orun the inverter and make the alternator hot... newer alternators lower their output if they get too hot.. which then drains the batteries as you drive..
the low voltage will turn on the engine warning light... fuel injectors require certainb voltages to operate.. as qwell the computer does too.. if you think about a flashlight as the batteries get low... it gets dimmer and dimmer and doesnt do its job very well giving you light as its batteries go flat.. your engine computer is the same way.. it cannot operate correctly with low voltage..
I dont know what size wire you ran to your inverter or what your alternator output is... and how much other stuff you are running to know why the 400 watt inverter is taxing things so much...
-Christopher