Hysteresis, Phase Transitions and Dangerous Transients in Electrical Power Distribution Systems

TL;DR

This study models the complex spatio-temporal dynamics of low-voltage power distribution systems with many asynchronous motors, revealing phase transition phenomena, hysteresis, and potential stability risks in the system.

Contribution

It introduces a spatially-extended 1+1 dimensional model of power distribution that uncovers phase transition behaviors and hysteresis effects in motor states, a novel insight for low-voltage grid stability.

Findings

Identification of coexistence of normal and stalled motor phases.

Observation of phase transition fronts propagating along feeders.

Detection of hysteresis effects in motor state transitions.

Abstract

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.