Sodium-Ion vs LFP: Cold Storage Capacity and Lifetime Cost

Electrical model. Each reference cell is an Rint circuit, with $V_d=U(z)-I_dR(T)$ and $V_c=U(z)+I_cR(T)$. Resistance follows an Arrhenius law. Analytic OCV curves represent the sodium-ion slope and LFP plateau; they are not measured manufacturer OCV curves. Bisection locates voltage endpoints. Midpoint quadrature integrates charge, energy, loss and elapsed time over the selected SoC window.

Fixed capacity calibration. Capacity-temperature ratings and the reference resistance are calibrated together once: Na-ion uses 10 mΩ and 20 kJ/mol; LFP uses the assumed 0.5 mΩ and 25 kJ/mol. At each source temperature, the effective charge is the rated 0.5C delivered charge divided by the discharge span of that FIXED reference circuit. PCHIP joins those calibrated available-charge values. Editing resistance never changes this charge inventory. The resulting Na-ion cold-energy retention is checked against the independent 2026 HiNa measurement. Consistency guards reject resistance combinations that reduce reference warm or cold delivered charge below 95% of the source rating, or Na-ion cold-energy retention below 90% of the measured value. Available charge below 25 °C never exceeds its warm calibrated value.

Charging controls. HiNa uses its temperature-dependent current, voltage and upper-SoC limits. The CV current threshold is 0.1C at or below 0 °C and 0.05C above 0 °C (original HiNa p. 5). LFP uses EVE revision A §4.2.1's FULL-WINDOW constant-power envelope (attached s1 p. 23), including 0.12P at 5 °C. The alternative staged-power envelope is not used. P denotes rated cell energy per hour. Power limits are interpolated linearly between published temperatures. The applied current is the minimum of the requested current, allowed bulk current, power-limited current and CV current. The power-limited current solves $I(U+IR)=P_{max}$ using the simulated terminal voltage. CV stops at its source threshold; if bulk current is already below that threshold, charging stops at CV onset instead. SoC and voltage limits can stop charge sooner. LFP charging is blocked at and below 0 °C.

Seasonal ledger. Every sampled daily charge and discharge temperature is solved directly. One exact annual response is cached and reused for subsequent years; there is no interpolation across charging boundaries. The separate temperature-chart grid includes samples on both sides of discontinuities and does not determine annual dispatch. The ageing step is rounded down to whole monthly subdivisions. Available hours limit completed cycles. Cycle damage and calendar fade update capacity at each step; hot-cycle acceleration follows the datasheets' 25/45 °C life ratios. Calendar acceleration assumes 35 kJ/mol. Partial steps locate retirement.

Energy and cost. Purchased electricity equals AC delivery plus integrated resistance, converter and heater losses. Charge-only heating includes sensible warm-up per cycle and leakage during charge; continuous heating includes daily leakage and an initial warm-up. LCOS discounts installed cost, maintenance and purchased electricity against delivered energy. Cost per completed cycle is undiscounted. Zero delivery leaves that alternative's LCOS and cycle cost unavailable, preserves the other alternative's results, and disables break-even and lower-LCOS claims.

• Equal nameplate energy, continuous ideal cell scaling, and balanced cells. Each scheduled cycle uses the achievable SoC window; there is no independent load forecast.
• HiNa MP10: 10 Ah, 3.05 V, 270 g, Ø33.2 × 140 mm and 10 mΩ conservative DC resistance limit. EVE LF280K A: 280 Ah, 3.2 V, 5.42 kg and 173.7 × 72 × 207.2 mm. Its 0.5 mΩ DC resistance is assumed; the published ≤0.25 mΩ figure is AC impedance.
• OCV shape, reference activation energies, LFP DC resistance, calendar loss, thermal conductance, converter efficiency, pack overhead and prices are scenario assumptions. Temperature-capacity calibration remains fixed when resistance inputs change. Cycle-life defaults are 3000 cycles to 70% for HiNa and 6000 to 80% for EVE, at their stated test conditions.
• Ageing scales available charge and energy; resistance growth with age, SoC-dependent ageing, standby loads, self-discharge, availability outages and replacement are excluded. No low-temperature cycle-life bonus is assumed.
• Charge-only heating assumes cells cool back to the specified ambient before discharge. Daily ageing temperature is the mean of charge and discharge cell temperatures. Warm-up time and heater power are not resolved.

Use −20…45 °C cell ambient, 0.05…1C requested discharge and 0.05…0.5C requested charge. The charging envelope is chemistry- and temperature-specific. EVE's constant-power ratings apply across the full SoC window; they are converted using terminal voltage rather than treated as C-rates. Values between published power-map temperatures use linear interpolation. The heating setpoint assumes unlimited heater power; warm-up time is not resolved.

This is a comparative Rint model with a fixed reference capacity/resistance calibration, not a manufacturer-qualified pack simulation. Permissible resistance edits must stay consistent with its source discharge ratings and the HiNa cold-energy measurement. Changing OCV shape or the capacity data requires a new joint calibration. The Na-ion available-charge bound is its warm calibrated charge; the LFP warm calibration is about 1.0012 times its nominal charge because of the reference lower-voltage endpoint. Neither grows when resistance is increased.

Analytic OCV and isothermal discharge omit hysteresis, RC relaxation, diffusion and self-heating. Calendar and partial-cycle ageing remain assumptions. The 2026 HiNa cold-discharge test follows warm charging and is not a cold-charge guarantee. Its low-frequency EIS resistance is not substituted for DC resistance. CATL Naxtra and TENER announcements are context only; no CATL or BYD circuit preset is implied.

Annual dispatch solves actual sampled temperatures, including all permission and termination rules. Refining the ageing step checks seasonal time integration; refining SoC intervals checks the discharge and charging quadrature. Temperature-chart resolution does not affect annual energy. No interpolation is used across operating boundaries. Capacity curves stop at retirement.

A zero-delivery alternative has unavailable LCOS, cycle cost and break-even comparisons; its energy, size and mass remain visible. The operating-status result identifies blocked LFP charging or a voltage/SoC limitation. A warm-charged cold-test result can remain positive even when repeated unheated daily charging is impossible.

LCOS ends at the first retirement, so alternatives can have different service durations. Replacement, tax, financing, tariff escalation and salvage are excluded. Illustrative costs are constant 2026 USD scenarios. Equipment footprint excludes clearances, aisles and auxiliary equipment. Large BESS projects require discrete rack layouts and measured thermal performance.