  The majority of dynamical studies in power systems focus on the high voltage
transmission grids where models consider large generators interacting with
crude aggregations of individual small loads. However, new phenomena have been
observed indicating that the spatial distribution of collective, nonlinear
contribution of these small loads in the low-voltage distribution grid is
crucial to outcome of these dynamical transients. To elucidate the phenomenon,
we study the dynamics of voltage and power flows in a spatially-extended
distribution feeder (circuit) connecting many asynchronous induction motors and
discover that this relatively simple 1+1 (space+time) dimensional system
exhibits a plethora of nontrivial spatio-temporal effects, some of which may be
dangerous for power system stability. Long-range motor-motor interactions
mediated by circuit voltage and electrical power flows result in coexistence
and segregation of spatially-extended phases defined by individual motor
states--a "normal" state where the motors' mechanical (rotation) frequency is
slightly smaller than the nominal frequency of the basic AC flows and a
"stalled" state where the mechanical frequency is small. Transitions between
the two states can be initiated by a perturbation of the voltage or base
frequency at the head of the distribution feeder. Such behavior is typical of
first-order phase transitions in physics, and this 1+1 dimensional model shows
many other properties of a first-order phase transition with the spatial
distribution of the motors' mechanical frequency playing the role of the order
parameter. In particular we observe (a) propagation of the phase-transition
front with the constant speed very long feeders; and (b) hysteresis in
transitions between the normal and stalled (or partially stalled) phases.
