Can there even be non-localised drought on a small island the size of New Zealand? The only significant geographical feature in the North Island (where most people live) is 3 mountains right in the middle.
New Zealand is small enough that a localized drought can have significant impact. Most of the people do indeed live in the North Island but most of the power is generated in the South Island, particularly around the Mackenzie Basin/Otago area (dry highlands).
https://en.wikipedia.org/wiki/List_of_power_stations_in_New_... - sort the hydroelectric by capacity - most of the major dams are in this area.