Battery Time-of-Use Arbitrage Value
What a time-of-use spread actually pays a grid-tied battery: charge cheap off-peak and discharge dear on-peak, but the round trip loses ~15 percent, so the daily value is usable energy at the peak price minus the larger amount bought at off-peak to store it (daily = usable x peak - usable/RTE x offpeak). The catch every arbitrage pitch skips is that the peak has to beat off-peak by more than the round-trip loss (break-even = 1/RTE) just to break even, so a spread that looks like a tempting 1.56x nets almost nothing. The NREL round-trip framing; RTE is AC-to-AC, DoD is warranty-usable. A gross spread-value aid, not a financed payback.
Formula and source
usable_kwh = nameplate_kwh x dod; charge_kwh = usable_kwh / rte; daily_value = usable_kwh x peak_price - charge_kwh x offpeak_price; annual_value = daily_value x cycles_per_year; breakeven_ratio = 1 / rte.
The standard energy-arbitrage value (daily = usable x peak - (usable / RTE) x offpeak, usable = nameplate x DoD, break-even when peak > offpeak / RTE) and the NREL battery round-trip / degradation framing, by name; the relations are public.
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