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Automotive EngineeringEnergy Storage

EV Battery & Thermal Workspace

Determine pack voltage, total energy (kWh), discharge C-rate, internal resistance, heat generation, and steady-state cooling effectiveness based on cell topology.

Joule Heating (I²R)Cell-To-Pack ScalingSteady-State Thermal Model

Engineering Schematic

Thermal & Structural Hierarchy (Cell → Module → Pack → Cooling)

PACK ARCHITECTUREBATTERY PACK (96S4P)V_nom = 345.6 VMODULE 1MODULE 2MODULE 3SINGLE CELL50 Ah | 3.6 VLIQUID COLD PLATETHERMAL DYNAMICSQ = 1440 WT_ss ≈ 42.3 °C

Topology & Cell Data

Architecture
V

Individual cell voltage

Ah

Individual cell capacity

-

Series string length

-

Parallel branches

Electrical Load

Operating Point
A

Discharge rate

DCIR per cell

Thermal Environment

°C

Coolant or air inlet

°C/W

Pack to coolant efficiency

Calculated Results

Electrical Capability

Pack Nom. Voltage

345.6V

384 total cells

Energy Capacity

69.1kWh

200 Ah nominal

Power Output

69.1kW

At 200 A

C-Rate

1.00C

60 min runtime

Pack DCIR

36.00

Excludes busbar parasitics

Voltage Sag

7.20V

Operating: 338.4 V

Thermal Equilibrium (Steady State)

Joule Heating (I²R)

1440W

Continuous thermal load

Estimated Steady Temp

42.3°C

ΔT = 17.3 °C over ambient

Engineering Check

Nominal Operation

The calculated parameters indicate a stable design under the given continuous load. Steady-state temperature remains within acceptable EV limits. Note that transient peak loads (e.g., hard acceleration) may exceed these values.

Engineering Relations

Governing Formula

E = (Ns·Vcell) · (Np·Ccell)
EWh

Energy

Ns-

Series Cells

Np-

Parallel Cells

Governing Formula

Rpack = Rcell · (Ns / Np)
RpackΩ

Pack Resistance

RcellΩ

Cell Resistance

Ns,Np-

Topology

Governing Formula

Q = I² · Rpack
QW

Heat Gen.

IA

Pack Current

RpackΩ

Resistance

Governing Formula

Tss = Tamb + (Q · Rth)
Tss°C

Steady Temp

Tamb°C

Ambient

Rth°C/W

Thermal Res.

Fundamentals of EV Battery Pack Thermal Management

Designing a high-voltage battery pack for electric vehicles involves complex scaling from individual electrochemical cells up to modules, and finally to the complete pack structure. A critical aspect of this scaling is managing the electrical and thermal loads simultaneously to prevent accelerated degradation or catastrophic thermal runaway.

Series and Parallel Topologies (NsNp)

The topology of the battery pack determines its overarching electrical characteristics. Cells placed in series (Ns) increase the nominal Pack Voltage, crucial for driving high-power traction motors efficiently. Cells placed in parallel (Np) increase the Pack Capacity (Ah). The total pack energy in kWh is essentially the product of the scaled voltage and capacity. Understanding this cell-to-pack ratio directly dictates the overall internal resistance of the system.

Heat Generation and Steady-State Temperature

As current flows through the battery pack, the inherent internal resistance of the cells (Rcell) leads to Joule heating (I²R). During high C-rate discharging or fast charging, this heat generation (Q) can be immense. The pack's cooling system—often utilizing liquid cold plates—is quantified by its Thermal Resistance (Rth). By evaluating the heat generation against the thermal resistance, engineers can estimate the Steady-State Temperature (Tss). Maintaining this temperature below 45-50°C is strictly required in modern EV design to ensure longevity and safety.

Frequently Asked Questions

What does C-rate mean for battery performance?

C-rate is a measure of the rate at which a battery is discharged relative to its maximum capacity. A 1C rate means the discharge current will empty the entire battery in 1 hour. A 2C rate means it takes 30 minutes. High C-rates generate significantly more heat and typically lower the lifespan of lithium-ion cells.

How is the Pack Internal Resistance determined?

The total pack resistance is determined by multiplying the single cell's internal resistance by the number of cells in series, and then dividing by the number of cells in parallel. Busbars and connections also add parasitic resistance, but cell resistance is the primary driver of pack-level Joule heating.