  When providing frequency regulation in a pay-for-performance market,
batteries need to carefully balance the trade-off between following regulation
signals and their degradation costs in real-time. Existing battery control
strategies either do not consider mismatch penalties in pay-for-performance
markets, or cannot accurately account for battery cycle aging mechanism during
operation. This paper derives an online control policy that minimizes a battery
owner's operating cost for providing frequency regulation in a
pay-for-performance market. The proposed policy considers an accurate
electrochemical battery cycle aging model, and is applicable to most types of
battery cells. It has a threshold structure, and achieves near-optimal
performance with respect to an offline controller that has complete future
information. We explicitly characterize this gap and show it is independent of
the duration of operation. Simulation results with both synthetic and real
regulation traces are conducted to illustrate the theoretical results.
