A method for preventing an emergency over-speed condition in a rotating machine, the method comprising: receiving a speed and an acceleration of a rotating component in the rotating machine; determining whether at least one of the speed and the acceleration of the rotating component exceeds a non-trip operating space in a speed-acceleration plane, wherein the NTO space is defined by a boundary on the speed-acceleration plane that is representative of a maximum speed and acceleration for preventing the rotating component from exceeding a design speed limit and reaching an emergency over-speed condition and is based on a trip overshoot model of the rotating machine, wherein the trip overshoot model is defined by one or more differential equations that predict the behavior of the rotating component after tripping the rotating machine; and sending a notification for tripping the rotating machine in response to determining that at least one of the speed and the acceleration of the rotating component exceeds the NTO space, the method further comprising: receiving the design speed limit of the rotating component; calculating one or more overshoot values (215, 220, 225) of the rotating component based on the trip overshoot model; and determining an initial boundary representing an initial NTO space by subtracting the one or more overshoot values (215, 220, 225) from the design speed limit of the rotating component; determining the NTO space by further restricting the initial NTO space based on a maximum acceleration threshold; determining the NTO space by further restricting the initial NTO space based on a maximum speed threshold; and the method further comprising determining whether the speed and the acceleration of the rotating component is within a maximum speed space, wherein the maximum speed space is a region beyond the maximum speed threshold and within the initial boundary representing the initial NTO space in the speed-acceleration plane. receiving a speed and an acceleration of a rotating component in the rotating machine; determining whether at least one of the speed and the acceleration of the rotating component exceeds a non-trip operating space in a speed-acceleration plane, wherein the NTO space is defined by a boundary on the speed-acceleration plane that is representative of a maximum speed and acceleration for preventing the rotating component from exceeding a design speed limit and reaching an emergency over-speed condition and is based on a trip overshoot model of the rotating machine, wherein the trip overshoot model is defined by one or more differential equations that predict the behavior of the rotating component after tripping the rotating machine; and sending a notification for tripping the rotating machine in response to determining that at least one of the speed and the acceleration of the rotating component exceeds the NTO space, the method further comprising: receiving the design speed limit of the rotating component; calculating one or more overshoot values (215, 220, 225) of the rotating component based on the trip overshoot model; and determining an initial boundary representing an initial NTO space by subtracting the one or more overshoot values (215, 220, 225) from the design speed limit of the rotating component; determining the NTO space by further restricting the initial NTO space based on a maximum acceleration threshold; determining the NTO space by further restricting the initial NTO space based on a maximum speed threshold; and the method further comprising determining whether the speed and the acceleration of the rotating component is within a maximum speed space, wherein the maximum speed space is a region beyond the maximum speed threshold and within the initial boundary representing the initial NTO space in the speed-acceleration plane. receiving the design speed limit of the rotating component; calculating one or more overshoot values (215, 220, 225) of the rotating component based on the trip overshoot model; and determining an initial boundary representing an initial NTO space by subtracting the one or more overshoot values (215, 220, 225) from the design speed limit of the rotating component; determining the NTO space by further restricting the initial NTO space based on a maximum acceleration threshold; determining the NTO space by further restricting the initial NTO space based on a maximum speed threshold; and the method further comprising determining whether the speed and the acceleration of the rotating component is within a maximum speed space, wherein the maximum speed space is a region beyond the maximum speed threshold and within the initial boundary representing the initial NTO space in the speed-acceleration plane.