According to this Wiki article https://en.wikipedia.org/wiki/Comparison_of_single-board_computers#Physical_and_electrical_comparison, the Pi Zero is the lowest power consuming single-board computer at about 0.5W idle. A first test confirms that: 250mW for the charge controller plus 500mW for the Pi = 750mW (reading is 759mW.)
For USB communication between the Arduino and the Pi, we need to add a serial-to-USB adapter which results in 975mW power draw.
A USB hub to add a few USB ports adds another 100mW to 1076mW. (The Wifi adapter in the picture is not powered yet.)
With the Edimax Wifi adapter powered up and connecting, the power goes up to 1541mW.
When we run minicom on the Pi, the power fluctuates between 1.5 and 1.8Watts.
The more powerful Hawking Wifi adapter with the antenna has a much better connection, but it also uses more power (system power = 2346mW) than the Edimax.