Adiabatic temperature rise for fully energy-matched 6S stacks across Prismatic (reference), Cylindrical 21700 (6S×nP), and PCC bipolar (parallel 6S mini-stacks). All three stacks carry identical Ah and Wh. C/2 rate · 20 complete cycles.
| Stack Type | S×P Config | Cell Count | Stack V (V) | Ah | Wh | Stack Mass (g) | I at C/2 (A) | R_stack (mΩ) | Q / cycle (J) | Total Q (kJ) | Cₚ (J/g·K) | ΔT (°C) | vs Prismatic |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
Prismatic
REF
300×200×25 mm · NMC |
— | — | — | — | — | — | — | — | — | — | — | — | Reference |
|
Cylindrical 21700
21 mm × 70 mm · NMC |
— | — | — | — | — | — | — | — | — | — | — | — | — |
|
PCC (Bipolar)
300×200 mm · 6S mini-stacks ∥ |
— | — | — | — | — | — | — | — | — | — | — | — | — |
The prismatic cell (300 × 200 × 25 mm) sets the Ah and Wh baseline for all stacks:
areal_capacity = AREAL_CAPACITY_MAH_CM2 = 4.0 mAh/cm² ← shared constant, all 3 formats
Ah_ref = areal_capacity × electrode_area × n_layers_inside_cell
Stack_Ah = Ah_ref (6S preserves Ah)
Stack_Wh = Stack_Ah × (6 × V_nom) = Stack_Ah × 22.2 V
Dimensions: 300 × 200 × 25 mm (L × W × H)
Casing: 1 mm Al on all sides
Electrode area: (L−2) × (H−2) mm per layer
Layer count: floor((W−2) / layer_pitch)
Areal capacity: 4.0 mAh/cm² (AREAL_CAPACITY_MAH_CM2)
Configuration: 6S × 1P → 22.2 V
All three stacks are built to match the prismatic stack's Ah and Wh exactly.
This ensures a fair thermal comparison — the same energy throughput (Wh × cycles) drives all stacks at C/2 rate.
Because Ah is matched, current I = Ah × C_rate is identical across all three stacks. The only difference in Q = I²Rt is the internal resistance R.
Ah_21700 = AREAL_CAPACITY_MAH_CM2 × electrode_area_from_jelly_roll_geometry / 1000
≈ 4.9 Ah (21 mm × 70 mm jelly-roll at 4.0 mAh/cm²)
nP_cyl = ceil(Ah_prismatic / Ah_21700)
Stack_Ah_cyl = nP_cyl × Ah_21700 ≥ Ah_prismatic
Stack_config = 6S × nP_cyl
21700 cell Ah is computed from its jelly-roll electrode area × AREAL_CAPACITY_MAH_CM2 (4.0 mAh/cm²) — the same constant used by prismatic and PCC. This produces ~4.9 Ah, consistent with Samsung 50E / LG M50 class cells. 6 in series gives the same 22.2 V. To reach prismatic Ah, parallel strings are added.
nP = number of parallel branches = ⌈Ah_ref / Ah_21700⌉
Total cell count = 6 × nP
Cell mass = electrode active material + stainless steel can (0.25 mm wall) + electrolyte (30% void fraction). Computed from first principles — no hardcoded mass.
Parallel resistance rule: nP parallel branches of identical 6S strings: R_stack = R_single_6S_string / nP
Stack current I = Ah_stack × C/2 = matched to prismatic current.
Ah_one_pcc_ministack = AREAL_CAPACITY_MAH_CM2 × electrode_area_cm2
= 4.0 × 600 cm² / 1000 = 2.4 Ah per mini-stack
nP_pcc = ceil(Ah_prismatic / Ah_one_pcc_ministack)
Stack_config = 6S × nP_pcc (parallel mini-stacks)
R_stack_pcc = R_one_ministack / nP_pcc
Footprint: 300 × 200 mm (matches prismatic X-Y)
Layers: 6S bipolar → 22.2 V
Ah per unit: 4.0 mAh/cm² × 600 cm² (AREAL_CAPACITY_MAH_CM2)
Zero tabs: current flows ⊥ through full electrode area
R model: R_plate_layer + R_electrode_layer (per layer)
Each mini-stack is an identical 6S bipolar unit. Stacking them in parallel multiplies Ah proportionally.
nP_pcc = ⌈Ah_ref / Ah_per_ministack⌉
R_stack = R_single_ministack / nP_pcc
No tab or busbar resistance between layers within each mini-stack — bipolar architecture. Only thin inter-stack parallel connectors at the top and bottom terminals.
R_plate_layer = R_sheet × t_plate² / A_electrode
R_elec_layer = (ρ_NMC×t_cath + ρ_sep×t_sep + ρ_graph×t_an) / A_electrode
R_ministack = 6 × (R_plate_layer + R_elec_layer)
Perpendicular current flow through full electrode area gives extremely low R per layer.
I = Stack_Ah × C_rate = Ah_ref × 0.5 [same for all three stacks]
Q_per_cycle = I² × R_stack × 2 × t_half_cycle
Q_total = Q_per_cycle × N_cycles
t_half_cycle = (1/C_rate) × 3600 = 7200 s
N_cycles = 20 → Q_total time = 288,000 s total
Because Ah is identical across stacks, I is identical. Only R_stack differs. This means Q ∝ R_stack — the thermal advantage is purely from resistance engineering.
Series stack resistance (prismatic/cylindrical):
R_6S_string = 6 × R_cell + 5 × R_busbar (0.5 mΩ per busbar)
Parallel combination (cylindrical/PCC):
R_stack = R_6S_string / nP
ΔT [K or °C] = Q_total [J] / (m_stack [g] × Cₚ_stack [J/(g·K)])
m_stack = total mass of all cells in the stack (n_series × n_parallel × m_cell for conventional; sum of all mini-stack mass for PCC)
Cₚ_stack = mass-weighted average Cₚ across all stack components
This is the adiabatic (worst-case) temperature rise. Real ΔT will be lower with thermal management.
Cₚ_stack = Σ (mᵢ × Cₚᵢ) / m_stack_total
| NMC cathode | 0.70 J/(g·K) |
| Graphite anode | 0.71 J/(g·K) |
| Separator (PP/PE) | 1.90 J/(g·K) |
| Electrolyte (LiPF₆) | 1.65 J/(g·K) |
| Cu current collector | 0.385 J/(g·K) |
| Al current collector | 0.897 J/(g·K) |
| Al casing | 0.897 J/(g·K) |
| Stainless steel can | 0.502 J/(g·K) |
| PCC polymer plate | 1.20 J/(g·K) |
Refs: Klett et al. (2014), Forgez et al. (2010), Pesaran et al. (2013)
| NMC cathode (ρ) | 1.0×10⁻³ Ω·m |
| Graphite anode (ρ) | 5.0×10⁻⁴ Ω·m |
| Separator (ρ_eff) | 5.0×10⁻² Ω·m |
| Cu (σ) | 5.96×10⁷ S/m |
| Al (σ) | 3.77×10⁷ S/m |
| Busbar R (per junction) | 0.5 mΩ |
Refs: Doyle et al. (1993), Bernardi & Carpenter (1995), Kim et al. (2012)
AREAL_CAPACITY_MAH_CM2 = 4.0 mAh/cm² ← single shared constant for all 3 formats
Prismatic Ah = 4.0 × (298×23 mm² per layer) × n_layers / 1000
Cylindrical Ah = 4.0 × (jelly-roll area from geometry) / 1000 [NOT hardcoded]
PCC Ah = 4.0 × (300×200 mm²) / 1000 per mini-stack
Electrode stack: Σ (areaₗ × tₗ × ρₗ × n_layers) for cathode/anode/sep/Cu/Al
+ Al casing shell mass (1 mm wall)
+ Electrolyte: 30% of inner cell volume × 1.2 g/cm³
Casing has excellent active:inactive ratio → lower mass/Wh
Electrode stack: same layer model over jelly-roll area
+ Stainless steel can: (V_outer − V_inner) × 7.85 g/cm³ (0.25 mm wall)
+ Electrolyte: 30% of jelly-roll volume × 1.2 g/cm³
Each 21700 carries its own can → higher mass/Wh than prismatic
Electrode stack: Σ (area × tₗ × ρₗ × n_layers) per mini-stack
+ PCC bipolar plates: 10 µm × 1.20 g/cm³ per layer
+ Terminal Al CCs (top + bottom only)
+ Electrolyte: 30% of stack volume × 1.2 g/cm³
No metal housing per mini-stack
📌 Key insight: A 21700 pack requires 50–100+ individual steel cans to match a single large prismatic can. The steel can mass overhead per Wh is ~5–10× higher for cylindrical than for prismatic. This is why cylindrical stacks are correctly heavier per Wh despite higher volumetric energy density of the jelly-roll itself.
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