  Power systems dominated by renewable energy encounter frequently large,
random disturbances, and a critical challenge faced in power-system management
is how to anticipate accurately whether the perturbed systems will return to
the functional state after the transient or collapse. Whereas model-based
studies show that the key to addressing the challenge lies in the attracting
basins of the functional and dysfunctional states in the phase space, the
finding of the attracting basins for realistic power systems remains a
challenge, as accurate models describing the system dynamics are generally
unavailable. Here we propose a new machine learning technique, namely balanced
reservoir computing, to infer the attracting basins of a typical power system
based on measured data. Specifically, trained by the time series of a handful
of perturbation events, we demonstrate that the trained machine can predict
accurately whether the system will return to the functional state in response
to a large, random perturbation, thereby reconstructing the attracting basin of
the functional state. The working mechanism of the new machine is analyzed, and
it is revealed that the success of the new machine is attributed to the good
balance between the echo and fading properties of the reservoir network; the
effect of noisy signals on the prediction performance is also investigated, and
a stochastic-resonance-like phenomenon is observed. Finally, we demonstrate
that the new technique can be also utilized to infer the attracting basins of
coexisting attractors in typical chaotic systems.
