Realtime Clock in Arduino
Internal
Arduino has an internal clock. Is shut down if Arduino loses power. Can use 3.7 battery for power. Library is RTC.h.
https://www.arduino.cc/en/Reference/RTC
Power draw for Arduino on standby on 3.7V is about 20ma. So uses about 1.5Whr every 24 hours.
See more about Relays#Power Draw
External
Module is cheap - [1]