4-Hour Battery vs Gas Peaker: Levelized Cost of Peak Capacity

Capital recovery is evaluated as the reciprocal of the discounted annuity sum to remain stable near zero interest. Equivalently, it uses $CRF=r/[1-(1+r)^{-L}]$, with $CRF=1/L$ at zero interest. Annual equivalent costs compare repeatable battery and peaker lives at a common real discount rate; initial capital is paid at time zero, operating costs at year end, and augmentation at the beginning of years 2…L. No terminal salvage is credited.

A representative 365-day year has $N=H/\bar d$ full-power peak-event equivalents. Durations follow a bounded uniform or symmetric triangular distribution on $\bar d(1\pm w)$; $w=0$ is a fixed duration. The mean supplied duration $E[\min(d,D)]$ and duration CDF have closed forms. Their time integrals follow the evolving usable capacity and determine annual supplied energy and fully covered events.

Usable capacity follows $d\ln Q=-k_{cal}dt-k_{cyc}dn_{EFC}$, with equivalent full cycles measured against initial usable energy. The nominal four-hour fleet integrates capacity, delivered energy and the complete-event fraction together. It splits time intervals at duration thresholds using capacity-coordinate quadrature. Fully supplied and fully energy-limited regions have closed-form updates; smooth intermediate regions use adaptive Dormand–Prince integration. The intervals-per-year input bounds uninterrupted integration intervals. For fixed-duration events, the complete-event crossing time is exactly $\ln(4/d)/(k_{cal}+k_{cyc}H/4)$ before annual restoration. With augmentation enabled, missing usable energy is restored annually and its installed energy cost discounted explicitly. All additions share the aggregate fade rate and retire with the project.

For the complete peak need, the solver installs $s\ge1$ parallel four-hour blocks per required peak kW and dispatches only the required power. Brent's method finds the smallest fleet whose worst usable duration covers the longest event; the fleet also meets the charge-power/window constraint. Here annual throughput is known exactly, so exponential fade and annual augmentation are evaluated in closed form. Without augmentation, sizing covers end-of-calendar-life fade. Battery cost includes power and energy capital, fixed and variable O&M, charging energy divided by round-trip efficiency, and augmentation.

Peaker annual cost is capital × CRF + fixed O&M + annual MWh × (variable O&M + HHV heat rate × delivered gas price + combustion CO₂ × carbon price) + event starts × cost per start. One start is charged per event. The crossover map is battery minus peaker cost per required kW-year; blue favours the battery, red favours gas, and the black curve is the directly calculated equal-cost gas price. Its white marker is the selected case. Cost per MWh divides annual equivalent cost by delivered energy; nominal battery energy is discounted consistently over its life.

All monetary inputs use a common 2025 real USD basis. Defaults are illustrative screening values, prepared 6 November 2026: the battery power/energy split, charging price and peaker costs are within Lazard's June 2025 assumption ranges (PDF pp. 37 and 43). They are editable scenarios, not 2026 vendor quotes. NREL ATB 2024 supplies the 85% efficiency and 15-year battery-life benchmarks. Its 2.5%-of-capital O&M allowance includes augmentation; do not enter that full allowance here on top of separate augmentation. Default fixed O&M excludes augmentation. The fade coefficients, augmentation price, discount rate, delivered gas price and start cost are explicit illustrative assumptions, not a fitted warranty model.

Each peak event is rectangular at required power and starts fully charged. The conservative scheduling screen assumes equally spaced starts, with room for the longest event plus the stated recharge window in every slot. Fractional event counts are annual expected equivalents. Duration shape affects nominal delivered energy; equal-service sizing depends on the longest supported duration. Capital and fixed O&M scale linearly with installed power, and energy cost with usable AC energy. Four hours is usable AC output duration at beginning of life, so no extra depth-of-discharge factor is applied. Charging energy price includes tariffs and any upstream carbon charge. Gas CO₂ covers combustion only, using EIA's 52.91 kg/MMBtu HHV factor.

This is a deterministic cost and duration-coverage comparison, not ELCC, capacity-market accreditation, chronological dispatch optimization or a loss-of-load reliability study. Peak plus recharge windows must fit the year, and the charge window must be long enough; this necessary feasibility screen cannot establish that an actual clustered event calendar is feasible. Both resources are assumed available; forced outages, weather derating, fuel interruptions and network constraints are omitted.

The equal-service battery may have installed MW above the required peak; its cells remain four-hour blocks at their own rating. The nominal option's $/MWh covers only energy actually delivered and must be read with coverage. If its recharge window is too short, its displayed costs, coverage and shortfall are unavailable; the feasible sized-fleet and gas comparison remains available. Nominal coverage and shortfall are equivalent annual values from discounted lifetime energy. A negative break-even gas price means the battery costs less even at zero gas price for the other selected assumptions.

The fade law is an aggregate exponential scenario with throughput and calendar terms. It excludes temperature, state-of-charge, depth-of-discharge and rate-dependent ageing, chemistry changes and cohort-specific ageing. Annual augmentation restores usable energy; power equipment is not replaced before the selected life. No salvage is assigned even to late augmentation, which can overstate cost. Equal-service sizing protects against end-of-year/end-of-life fade conservatively. Nominal fade uses 24 base intervals/year by default, exposed for refinement. Capacity-threshold crossings are integrated separately so fixed-duration event coverage is not determined by sampling a midpoint. Smooth intermediate fade uses an adaptive ODE solver; the numerical and fixed-duration analytical limits are checked independently.

The crossover colour field uses 49 × 39 solved points and smooth blending. Its equal-cost boundary is calculated directly at 321 points clustered near low run hours, rather than extracted as straight cell-edge contour segments. Utilization and duration curves use 161 solved points. A linear energy-cost axis also displays negative charging-price scenarios. Taxes, subsidies, debt structure, real escalation, ancillary-service and arbitrage revenues, reserve margins, connection upgrades and decommissioning are excluded. This unlevered real annual-cost method does not reproduce Lazard's levered tax/IRR model or Wood Mackenzie's proprietary regional scenarios.