Battery Pack Design & Calculations
Read Electrical Basics before starting battery calculations
Battery Pack Calculations: Series, Parallel, and Hybrid Configurations
Series configuration: Voltage addition fundamentals
- Series connection increases voltage while maintaining current capacity.
- When cells connect in series (negative terminal of one cell to positive terminal of the next), voltages add while current remains constant throughout the string.
Mathematical relationships for series configuration:
Formulas
- Total voltage:
= - Current:
(same for all cells) - Capacity:
(limited by weakest cell)
Tesla Model Y example (simplified):
- Configuration: 96 cells in series (96S)
- Cell voltage: 3.7V nominal
- Pack voltage: 96 ร 3.7V = 355V
- This voltage level enables efficient motor operation and fast charging capability
Parallel configuration: Current and capacity addition
- Parallel connection increases current capacity and total energy storage while maintaining voltage.
- When cells connect in parallel (all positive terminals together, all negative terminals together), currents add while voltage remains constant.
Mathematical relationships for parallel configuration:
Formulas
- Current capability:
- Voltage:
(same for all cells) - Capacity:
Practical example:
- Module configuration: 4 cells in parallel (4P)
- Cell capacity: 72Ah each
- Module capacity: 4 ร 72Ah = 288Ah
- Voltage: 3.67V (same as single cell)
- Current capability: 4 ร single_cell_current
Series-Parallel combination circuits in real EVs
- Most EV battery packs use hybrid configurations combining series and parallel connections to achieve desired voltage, capacity, and power characteristics.
- Configuration notation uses "XsYp" format (X cells in series, Y groups in parallel).
Tesla Model Y Long Range detailed analysis:
- Configuration: 96S46P (96 series groups, 46 parallel strings)
- Total cells: 96 ร 46 = 4,416 cells
- Cell specifications: 21700 format, 4.8Ah, 3.7V nominal
- Pack voltage: 96 ร 3.7V = 355.2V
- Pack capacity: 46 ร 4.8Ah = 220.8Ah
- Pack energy: 355.2V ร 220.8Ah = 78.4kWh
- Weight: Approximately 478kg
Calculation verification using electrical laws:
Verification
- Power capability:
= 355.2V ร (46 ร 10A) = 163kW continuous - Energy density: 78.4kWh รท 478kg = 164 Wh/kg (competitive with industry standards)
Step-by-step battery pack design process
Complete design example: 400V, 75kWh battery pack for midsize SUV
Step 1: Define requirements
- Target range: 400km
- Energy consumption: 200Wh/km (realistic for SUV)
- Total energy needed: 400km ร 200Wh/km = 80kWh
- Pack energy (including losses): 75kWh usable
- System voltage: 400V (motor compatibility)
- Power requirement: 200kW peak
Step 2: Select cell specifications
- Cell choice: 18650 format (widely available)
- Cell voltage: 3.6V nominal (4.2V max, 2.5V min)
- Cell capacity: 3.5Ah
- Cell max discharge: 10A (2.86C rate)
Step 3: Calculate series requirement
- Series cells needed: 400V รท 3.6V = 111.1 โ 111 cells
- Actual pack voltage: 111 ร 3.6V = 399.6V
Step 4: Calculate parallel requirement
- Required pack capacity: 75,000Wh รท 399.6V = 187.7Ah
- Parallel groups needed: 187.7Ah รท 3.5Ah = 53.6 โ 54 groups
- Actual pack capacity: 54 ร 3.5Ah = 189Ah
- Actual pack energy: 399.6V ร 189Ah = 75.5kWh
Step 5: Verify power capability
- Max current per string: 10A per cell
- Total max current: 54 ร 10A = 540A
- Max power: 399.6V ร 540A = 215.8kW โ (exceeds 200kW requirement)
Step 6: Final specifications
- Configuration: 111S54P
- Total cells: 111 ร 54 = 5,994 cells
- Pack voltage: 399.6V nominal
- Pack capacity: 189Ah
- Pack energy: 75.5kWh
- Peak power: 215.8kW
Refer to Battery Pack Construction Techniques to learn more about how battery packs are built after calculating their cells in series and parallel
Conclusion
- Through this comprehensive exploration, several key insights emerge.
- Battery pack design relies heavily on series and parallel circuit analysis, with real-world examples like Tesla's 96S46P configuration showing how theoretical principles scale to practical applications.
- Cell-to-pack designs, structural battery packs, and advanced thermal management systems all require engineers who can apply Ohm's Law and Kirchhoff's Laws in addition to the Battery Pack Calculations to solve increasingly complex challenges.
Battery pack calculations practice
Go to Simple Calculator or Advanced Calculator to test your understanding and solve problems