BESS Degradation and Augmentation Planner: Fade, Top-Up and Cost

For a cohort of age $a$ years, linear retention is $S(a)=\max(0,1-ra)$; compounded retention is $S(a)=(1-r)^a$. The annual rate is an input, not an electrochemical fit. Initial capacity, new modules and per-kWh prices all use unfaded DC nameplate capacity; usable AC energy must first be divided by the actual SOC window and discharge efficiency to recover that basis. Required usable AC energy is $E_{req}=P\,h$ and the remaining DC requirement is $E_{DC}=E_{req}/(u\,\eta_d)$.

At each permitted year $y$, set $b=\min(y+K,N)$. Forecast existing DC energy at $b$ by summing each cohort's original nameplate times its own retention. Add $\max(0,E_{DC}-E_{existing}(b))/S(b-y)$ of new DC nameplate, then round upward to complete blocks if requested. This is a derived look-ahead sizing rule; it is not a global cost optimization. Original and added cohorts continue aging independently. No addition is made at $N$.

Each event costs its new DC kWh times the year-specific USD/kWh price, plus a fixed charge if capacity is added. Real battery prices follow $c_y=c_0(1-g)^y$; present cost is $\sum C_y/(1+d)^y$. Fixed event charges stay constant in real dollars. Money is represented as numerical USD amounts in labels because the engine does not define a currency unit.

The World Bank (2020), PDF pp. 30–31, supplies the energy-only degradation example and context for warranty-based annual rates. The HOMER public manual supplies the instantaneous capacity-shortfall reference. This planner uses its own cohort aging and window-sizing rule.

All cohorts are new at installation, share the selected fade law and rate, and remain connected throughout the horizon. The initial bank is new at year 0. New capacity does not rejuvenate older batteries. Fade is monotonic, independent of dispatch, and applies to DC nameplate energy. The usable SOC fraction and one-way discharge efficiency are constant. Power is used to define required energy and duration; power capability is assumed adequate.

Top-ups occur instantaneously at years 0, K, 2K, and so on before the project endpoint. There are no outages, construction lead times, site-space limits, or failed modules. Fractional sizing is available when block size is zero. Cost defaults are illustrative inputs dated 30 October 2026, not observed prices. All costs are USD in the same base-year purchasing power; no currency conversion is performed.

Use for preliminary capacity and augmentation budgeting with a supplier-supported aging assumption. The linear and compounded laws do not predict a capacity knee, chemistry-specific cycle damage, calendar/cycle interactions, temperature effects, resistance growth, or warranty behavior. The 60% original-cohort retention message is a screening flag chosen for this tool, not a retirement criterion. Cohorts are not retired or replaced even when their modeled capacity becomes very low.

No evaluation of inverter ratings, C-rate, DC voltage compatibility, control limits, auxiliary consumption, availability, charging losses, thermal behavior, fire protection, or structural space is included. Required AC energy is per discharge, not annual delivered energy. Discharge efficiency is not round-trip efficiency. Verify losses at the chosen delivery boundary. Augmentation costs exclude the initial bank, financing, taxes, incentives, routine O&M, replacements, decommissioning and salvage; this is not LCOS or project NPV. Installation design and work require qualified people.

Installation intervals must retain more than $10^{-6}$ (one part per million) of a new cohort’s capacity. Intervals at or below that numerical resolution floor are rejected; shorten the window spacing or horizon. Accepted intervals are sized using actual retention, with no denominator clamp. This numerical floor is separate from the original-bank retention screening flag.