  We present a detailed analysis of classical solutions in the bosonic sector
of the electroweak theory which describe vortices carrying a constant electric
current ${\cal I}$. These vortices exist for any value of the Higgs boson mass
and for any weak mixing angle, and in the zero current limit they reduce to Z
strings. Their current is produced by the condensate of vector W bosons and
typically it can attain billions of Amperes. For large ${\cal I}$ the vortices
show a compact condensate core of size $\sim 1/{\cal I}$, embedded into a
region of size $\sim{\cal I}$ where the electroweak gauge symmetry is
completely restored, followed by a transition zone where the Higgs field
interpolates between the symmetric and broken phases. Outside this zone the
fields are the same as for the ordinary electric wire. An asymptotic
approximation of the large ${\cal I}$ solutions suggests that the current can
be {arbitrarily} large, due to the scale invariance of the vector boson
condensate. Finite vortex segments whose length grows with ${\cal I}$ seem to
be perturbatively stable. This suggests that they can transfer electric charge
between different regions of space, similarly to thunderbolts. It is also
possible that they can form loops stabilized by the centrifugal force --
electroweak vortons.
