Jure,
I'm sure some folks can give you even more detailed info, but let me share what I know.
Series I & II basses come with a rackmountable power supply that connects to the bass with a special 5 pin stereo cable. This is in addition to the battery; you can use them either way, when not using the stereo 5 pin jack( & the power supply) you have to use the 1/4 inch jack , which will give you a mono signal I believe. Also the battery runs down fairly quickly if you decide not to use the power supply. In short, the power supply will give you stereo sound and save you lots of money in batteries. Series I & II electronics are energy hogs so the power supply really helps.
Valentino