How big of a PV system is needed?

The amount of energy from a given size system varies based on the site.  Using Mwanza, Tanzania as a typical site, a system to reliably supply 2 kWh of AC electricity per day would consist of two 320-340 Wp modules, an MPPT charge controller, a 2.5 kW inverter and some batteries.  Induction cooktops are typically rated at either 1,000W-AC or 1800-2200 W-AC.  The smaller unit will require longer cooking times (same overall energy) and will put less stress on the battery.

The batteries are a critical part of the system, as well as the most expensive component.  Lead-carbon batteries have excellent cycle life as well as high efficiency and relatively low cost.  The recommended battery size for this application would be two 12V-G31 units — 110 Ah / 220 Ah at 24 VDC