Almost any house can be a net zero house, it just has to produce as much energy as it uses on an annual basis.  The easiest way to reach this goal is to not require the energy in the first place.  This is why net zero homes are usually built to be extremely efficient, the less energy the house consumes the less it has to produce.  The basic principles of the passive house standard would typically apply to to this type of energy efficient construction. 

Net Zero homes can be grid-tied or off-grid with battery backup.  Net Zero homes are typically all electric, including the heating.

Below is a diagram which illustrates the basic strategies of net zero homes and how the principles dovetail with those of passive houses.