Power supply for Raspberry Pi
Add to your 2 V load at 1800 mWh the power consumption of the RPi. Find a good guess on that at RPi@SE. Given the amount the RPi consumes (20 to 45 Wh a day) your load seems to be negligible for your power supply. So the most simple solution would be to pick a suitable power supply for the RPi and use a switching step down regulator to provide the 2 V.

(Depending on the application the RPi might not be best suited for a portable solution.)