Operational Amplifier IC1 is used as a precision voltage comparator to monitor the voltage level of the battery. Its Inverting input gets a reference voltage of 1.8 V from the junction of Red LED and R3 while the Non inverting input gets slightly higher voltage of 2 volts ( as set by VR1). This makes output of IC1 high. PNP transistor then remains off to keep the relay de-energized. Since the Neutral line is connected through the Comm and NO contacts of the relay, AC path remains cut off and no charging takes place.
When the battery voltage drops below 11.5 volts, voltage at the Non inverting input (pin3) drops below that of the Inverting input (pin2) and the output of IC1 turns low. T1 then conducts to actuate the relay. Relay contacts completes the neutral path and charging process starts. Green LED indicates the charging process.