A non-transitory, computer readable medium stores instructions executable by a processor of an electronic device. The instructions include instructions to determine that a transient event is occurring in an electrical grid coupled to an EGR gas turbine system, wherein the transient event is an under-frequency or an under-voltage event. The instructions also include instructions to increase a flow rate of fuel to a combustor of the EGR gas turbine system in response to the transient event when the EGR gas turbine system is operating in a non-stoichiometric combustion mode. The instructions further include instructions to increase a flow rate of oxidant to the combustor before increasing the flow rate of fuel to the combustor, or to decrease a local consumption of the electrical power to increase a portion of the electrical power that is exported to the attached electrical grid, or both, in response to the transient event when the EGR gas turbine system is operating in a stoichiometric combustion mode.