  We construct a compactification of the space of circular planar electrical
networks studied by Curtis-Ingerman-Morrow and De Verdiere-Gitler-Vertigan,
using cactus networks. We embed this compactification as a linear slice of the
totally nonnegative Grassmannian, and relate Kenyon and Wilson's grove
measurements to Postnikov's boundary measurements. Intersections of the slice
with the positroid stratification leads to a class of electroid varieties,
indexed by matchings. The partial order on matchings arising from electrical
networks is shown to be dual to a subposet of affine Bruhat order. The
analogues of matroids in this setting are certain distinguished collections of
non-crossing partitions.
