Battery Pack Configuration Calculator

For matched cells, Kirchhoff's laws give $N=N_sN_p$, $V_{pack}=N_sV_{cell}$, $Q_{pack}=N_pQ_{cell}$ and $W_{nom}=V_{pack,nom}Q_{pack}$. Current in one cell is $I/N_p$; a cell C-rate in reciprocal hours gives $I_{limit}=cQ$. Cell-body volume is $\pi d^2h/4$ or $wbh$. Mass and occupied-volume allowances are explicit planning inputs. These network and geometry equations are derived here.

The local two-RC equivalent circuit follows Chen & Rincón-Mora (2006), attached source s1, p. 3, Fig. 2: an OCV source, series resistance, and two parallel RC networks in series. For an initially relaxed cell during a current pulse, $v_k=(I/N_p)R_k[1-\exp(-t/\tau_k)]$ with $\tau_k=R_kC_k$. After switch-off each branch decays from its end-pulse voltage as $\exp[-(t-T)/\tau_k]$. Pack terminal voltage is $N_s(V_{oc}-v_1-v_2)-IR_{0,pack}$, with $R_{0,pack}=N_sR_0/N_p$. The ohmic drop disappears immediately at switch-off. The analytic solution avoids numerical time stepping.

$P_0=I^2R_{0,pack}$ is R0 heating, and $P_0T$ its pulse energy. The long-time loss limit uses the sum of all three resistances; it is not the instantaneous heat of a finite pulse. Nominal energy is not integrated delivered energy.

Transient chart points are concentrated near pulse application and switch-off using uniform increments no larger than 0.02 in $\log(1+t/\tau_{fast})$, where only branches with positive polarization resistance select the active time constants. The pulse endpoint is exact and is repeated on the resting side to retain the voltage discontinuity. Automatic pulse detail limits the displayed recovery to the smaller of five active slow time constants and three pulse durations; with inactive RC branches it shows one pulse duration of rest. Full recovery uses five active slow time constants, and a custom recovery duration is also available. Verification compares linear chart interpolation with the analytic response at three interior points in every interval for fast, slow, short-pulse and widely separated RC cases.

• Cells have identical capacity, voltage, resistance, state of charge and temperature; parallel current sharing is ideal.
• Default cell electrical and physical values come from the Molicel P28A datasheet v1.3 (s2, p. 1). Its 20 mΩ DC figure at 10 A / 1 s is an ohmic proxy, not an identified instantaneous two-RC resistance. The default discharge C-rate is its 35 A maximum divided by 2.8 Ah; the selected charge rate is the standard 2.8 A.
• Both polarization resistances start at zero. Enter measured fits together with a fitted R0 before using two-RC results as predictions. No P28A RC parameters or OCV–SOC curve are inferred.
• The starting OCV is a user input. OCV, resistance and time constants remain fixed during the pulse and recovery; initial polarization is zero.
• Packaging fractions and starting OCV are editable engineering assumptions, not manufacturer specifications. The circuit drawing is schematic; repeated cells and groups are abbreviated.
• The playback is independent of precomputed curves. At the exact switch-off time, playback shows the open-circuit side; the loaded end-pulse result shows the instant immediately before switch-off.

Use for preliminary matched-cell configuration and short constant-current discharge pulses at nearly constant SOC and temperature. A warning appears above 5% nominal capacity removed per pulse; that threshold is a practical local-model guideline, not a universal accuracy guarantee. Pulses exceeding the entire nominal capacity are rejected.

The loaded voltage must remain positive; falling below the cell cutoff or exceeding the selected cell current limit prompts a warning. The plotted pulse continues as a hypothetical imposed load and does not simulate BMS disconnection. Recovery approaches the initial OCV because SOC-dependent OCV drift is omitted. Change all cell inputs consistently for LiFePO4 or another chemistry.

No balancing, mismatch, ageing, thermal feedback, reversible heat, self-discharge, charger CC/CV timing, busbar losses, fuse coordination, protection design or regulatory approval is calculated. Cell-rating ceilings do not establish an assembled pack's usable continuous rating. Check actual manufacturer's limits at the intended temperature and application. A qualified person must perform any fixed electrical installation work.

The X-engineer reference cases verify its published cell-based sizing results with rounding tolerances. Their nominal powers use a 400 V target; this calculator uses the actual rounded series count times cell voltage. Their integrated or target-based power values are therefore not used as references.