Battery Time-of-Use Arbitrage Value
What a time-of-use spread actually pays a grid-tied battery.
Example
You enter
- Battery nameplate (kWh) 13.5
- Depth of discharge (0-1) 0.9
- Round-trip efficiency (0-1) 0.9
- On-peak price ($/kWh) 0.45
- Off-peak price ($/kWh) 0.15
- Cycles per year 365
You get
- Usable energy per cycle 12.15 kWh
- Charge (kWh) 13.5
- Daily arbitrage value $3.44/day
- Annual value $1257/yr
- Break-even price ratio 1.11111
No published worked example is on file for this calculation. It is checked against a hand-worked derivation of its method and an independent reference test.
Details, formula, and sources
ScopeCharge 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 barely above that nets almost nothing: on a 13.5 kWh battery at 90% round trip (break-even 1.11x), a 1.12x spread is worth about $6 a year, 1.56x about $299, and 3x about $1,257. The NREL round-trip framing; RTE is AC-to-AC, DoD is warranty-usable. A gross spread-value aid, not a financed payback.
Formula or tableusable_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.
Source and editionThe 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.
Free accessThe arbitrage-value arithmetic and the round-trip-efficiency relation are public; NREL storage cost/performance data is free at nrel.gov.
What governsEstimate. AHJ and licensed professional govern.
API field namesnameplate_kwh, dod, rte, peak_price, offpeak_price, cycles_per_year, usable_kwh, charge_kwh, daily_value, annual_value, breakeven_ratio
- Arbitrage value daily = usable energy at the peak price minus the larger charge energy at the off-peak pricefirst principles
- Round-trip loss charge energy = usable / RTE; break-even requires peak > offpeak / RTE (AC-to-AC efficiency)NREL battery round-trip framing
- Usable energy usable = nameplate x depth of discharge (the warranty-usable fraction)manufacturer warranty