  This paper proposes a dynamic valuation framework to determine the
opportunity value of battery capacity degradation in grid applications based on
the internal degradation mechanism and utilization scenarios. The proposed
framework follows a dynamic programming approach and includes a piecewise
linear value function approximation solution that solves the optimization
problem over a long planning horizon. The paper provides two case studies on
price arbitrage and frequency regulation using real market and system data to
demonstrate the broad applicability of the proposed framework. Results show
that the battery lifetime value is critically dependent on both the external
market environment and its internal state of health. On the grid service side,
results show that second-life batteries can provide more than 50% of the value
compared to new batteries, and frequency regulation provides two times more
revenue than price arbitrage throughout the battery lifetime.
