Hi Caroline,
See the discussion at the end of Section 2, "Methods" in Cole (2019) "Cost Projections for Utility-Scale Battery Storage" for some insight into the reasons for expressing battery costs in $/kWh vs $/kW. That is available as a PDF here:
www.nrel.gov/docs/fy19osti/73222.pdf
For SAM's default costs, we mostly use data from the NREL Annual Technology Baseline at
atb.nrel.gov/. The battery costs are at
atb.nrel.gov/electricity/2019/index.html?t=st. Note that SAM's default costs are for a complete installed system, so they account for more than just the purchase price of the equipment. (And, as always, SAM's default costs are intended as a reasonable starting point for your analysis rather than as a reference for the current state of the market.)
SAM allows you to enter the battery cost in $/kWh, which scales with the rated storage duration (rated kWh capacity / rated kW maximum discharge rate = rated hours of storage), and $/kW, which scales with the battery's rated maximum discharge rate, so you can use either method for your analysis in SAM.
The market for batteries is rapidly evolving, so the costs in these published reports are likely to vary from each other and to change as new versions are published over the near term.
Best regards,
Paul.