The DTC P2413 OBD2 code setting implies that the Powertrain Control Module (PCM) has encountered a malfunction in the Exhaust Gas Recirculation (EGR) system.
The EGR system is designed to reduce nitrogen oxide in the engine exhaust. This system has a valve that is electronically controlled by a voltage signal from the PCM. This signal indicates when the valve should open, allowing part of the exhaust gases to return to the engine’s induction system. In this place, the excess nitrogen oxide vapors are burned.
The EGR system valve uses an electronically controlled solenoid to divert the intake vacuum to the valve. The solenoid is commanded by the PCM to allow the vacuum to pass through and reach the EGR valve. To accomplish this, it opens the valve to the desired degree. When the PCM commands the EGR valve to open and does not observe the expected degree of change, this code is stored.