This is a very interest topic for me. There are two terms that come to mind anytime you start limiting aircraft engine power - "De-Rating" and "flat-Rating" The differences between “flat-Rating” and “De-Rating” engines can be confusing. De-rating an engine means arbitrarily assigning a lesser output to an engine than it was designed to have. There are many ways to achieve the power output reduction – mechanically (for example a different fuel computer) or “on paper” (charts and graphs which limit output).
An engine derated to a particular thrust a SL will also be limited to that thrust at 40,000Ft. In other words, when they take away the power, you don’t get it back. There are many reasons to install de-rated engines. One of the major reasons is that they “loaf” – they’re operating at a certain reduced percentage of their design capability. This usually makes for increased engine life. Back about 35+ years ago, a race team (I’ve forgotten the driver’s name - I want to say it was A.J. Foyt) installed a P&W PT-6 in an Indy car and proceeded to eat everyone’s lunch. If it weren't for some bad luck, he would have won the Indy 500 the first time out with it. The following year the race officials forced them to de-rate the engines – by adding restrictor plates to the air inlet – to the point that they lost all of their previous advantage. Way back in the 60's, Piper decided that they needed an airplane co compete with Cessna's 150. Rather than design another aircraft, they simply removed the back seats from their Cherokee 150 and placed a restriction on the engine RPM - bingo... The New and Improved Cherokee 140. The first thing most folks did is get an STC to restore the RPM and get the 10 hp back. That’s de-rating.
Now, for flat-rating…
Generally speaking, it must be remembered that (in very simplistic terms) turbine engines are not supercharged, but rather normally aspirated - in other words, they lose power with altitude just like a Cessna 152. The percentage of N1 (on most turbofans) or EPR (many turbojets) required to obtain the engine's full rated thrust will vary significantly depending upon airport elevation and outside air temperature. For example, on the aircraft that I fly, on a cool day at a sea level airport the engines will develop their maximum rated thrust with an N1 somewhere in the upper 80's say for example 88.7%. Go to a higher elevation airport on a warm day and the N1 will be higher, for example 93.4%. (As I type this, I'm looking at the Static Takeoff Thrust Setting Chart for our aircraft. Depending on the airport elevation and outside air temperature, the N1 settings vary from a low of 84.2% to a high of 96.1%.) These numbers will, of course, vary from engine to engine, but you get my point. On most older generation engines, the flight crew is required to come up with a takeoff power setting from a set of charts or tables. In later generation engines with DEECs (Digital Electronic Engine Controllers) or FADECs, the pilots only have to set the power levers into the takeoff detent and monitor things while the computer takes care of the rest.
Just to make things a bit more interesting, some aircraft have larger engines installed than they were designed for. These engines are "flat-rated" back down to what the airframe was designed to handle. In other words, say for example, an airplane was designed to use a pair of 40,000 LB thrust engines, the aircraft designers might specify a pair of 50,000 LB thrust engines and limit their thrust to 40,000 LBS. Why would they want to do this? Simple, remember that turbine engines are "normally aspirated" and start loosing power the moment they start to climb. By using a larger engine, the aircraft can operate at higher altitudes or temperatures before it runs out of power. The engine never produces more than the “airframe-rated” thrust (in this example 40,000 lbs), it’s just able to do it to a higher altitude.
Turboprop engines are similar, only instead of N1 or EPR, they usually measure their power output in Percent Torque. For those guys it's a bit simpler, they simply advance the power levers until the engines reach either their torque limit or their temperature limit. Typically, with flat-rated engines, they will "torque" out at lower altitudes, then as the aircraft climbs higher they "temp" out as the max operating temperatures become limiting.
I hope it is all good.