  Battery storage is essential for the future smart grid. The inevitable cell
degradation renders the battery lifetime volatile and highly dependent on
battery dispatch, and thus incurs opportunity cost. This paper rigorously
derives the marginal degradation cost of battery for power system dispatch. The
derived optimal marginal degradation cost is time-variant to reflect the time
value of money and the functionality fade of battery and takes the form of a
constant value divided by a discount factor plus a term related to battery
state of health. In case studies, we demonstrate the evolution of the optimal
marginal costs of degradation that corresponds to the optimal long-term
dispatch outcome. We also show that the optimal marginal cost of degradation
depends on the marginal cost of generation in the grid.
