Various systems and methods are provided for a turbocharger system. In one example, a system for use with a power generator having a rotary machine including a combustor comprises: a heat exchanger positioned to receive exhaust gases from the combustor; and a turbocharger system, comprising: a low pressure compressor fluidly coupled to the heat exchanger and adapted to supply gases to the heat exchanger; a low pressure turbine and a high pressure turbine each fluidly coupled to the heat exchanger and adapted to receive gases from the heat exchanger; a high pressure compressor fluidly coupled to the rotary machine and the low pressure compressor, adapted to receive gases from the low pressure compressor and supply compressed air to the rotary machine; and a water injector adapted to inject water into a flow path between the low pressure compressor and the heat exchanger.