Abstract: Methods and apparatus provide flexible allocation and regulation of scheduled energy transfers between energy storage devices (“batteries”) and a power grid. Piecewise mappings having at least one sloping segment enable gradual variations in scheduled energy transfers as cleared values of a medium of energy exchange deviate from predicted values of the medium of energy exchange. Thereby deviations from a battery's predicted energy transfer schedule can be reduced, and overall smoother operation of a power grid can be achieved. Two sloping linear segments can be separated by a dead band, a portion of the mapping in which the scheduled energy transfer amount is invariant. A dead zone can increase the likelihood of a battery meeting its predicted schedule.

Abstract: Methods and apparatus provide flexible allocation and regulation of scheduled energy transfers between energy storage devices (“batteries”) and a power grid. Piecewise mappings having at least one sloping segment enable gradual variations in scheduled energy transfers as cleared values of a medium of energy exchange deviate from predicted values of the medium of energy exchange. Thereby deviations from a battery's predicted energy transfer schedule can be reduced, and overall smoother operation of a power grid can be achieved. Two sloping linear segments can be separated by a dead band, a portion of the mapping in which the scheduled energy transfer amount is invariant. A dead zone can increase the likelihood of a battery meeting its predicted schedule.