Load calculation formulae is different for Tubular and Lithium battery Inverter/UPS

Difference Between Backup Time of Lithium-Based Batteries and Tubular Lead-Acid Batteries: Formulae and Why Lithium Requires Smaller Size Batteries

Lithium Inverter/UPS

When designing a backup power system, understanding the backup time and capacity of batteries is crucial. Lithium-based batteries (such as Lithium-Ion or LiFePO4) and Tubular Lead-Acid batteries are two popular choices, but they differ significantly in terms of performance, capacity, and size. The key differences lie in their discharge characteristics, energy density, and the formulae used to calculate their backup time. Let’s explore these differences and why lithium-based batteries require smaller sizes for the same load.

1. Backup Time Formulae for Batteries

The backup time of a battery depends on its capacity (measured in Ampere-hours, Ah) and the load (measured in Watts or Amperes). The general formula to calculate backup time is:

Backup Time (hours)=Battery Capacity (Ah)×Battery Voltage (V)×EfficiencyLoad (Watts)Backup Time (hours)=Load (Watts)Battery Capacity (Ah)×Battery Voltage (V)×Efficiency​

However, the discharge rate (C-rating) of the battery plays a critical role in determining the usable capacity. This is where Lithium-based and Tubular Lead-Acid batteries differ significantly.

2. Discharge Rate and Capacity: C1 vs. C20

Tubular Lead-Acid Batteries

• Tubular Lead-Acid batteries are typically rated at the C20 discharge rate, meaning their capacity is measured when discharged over 20 hours. https://suvastika.com/how-to-calculate-backup-time-in-tubular-battery-inverter/
• For example, a 100Ah Tubular Lead-Acid battery can deliver 5A for 20 hours (C20 rating).
• If discharged at a higher rate (e.g., C1 or 1-hour discharge), the usable capacity drops significantly due to the Peukert Effect. This effect states that the effective capacity of a Lead-Acid battery decreases as the discharge rate increases.
• Formula for effective capacity at different discharge rates:Effective Capacity=Rated Capacity (Ah)k×(I)nEffective Capacity=k×(I)nRated Capacity (Ah)​Where:
  • $k$ = Peukert constant (typically 1.1 to 1.3 for Lead-Acid batteries)
  • $I$ = Discharge current
  • $n$ = Peukert exponent (typically 1.2 to 1.3 for Lead-Acid batteries)

Lithium-Based Batteries

• Lithium-based batteries are typically rated at the C1 discharge rate, meaning their capacity is measured when discharged over 1 hour.
• For example, a 100Ah Lithium battery can deliver 100A for 1 hour (C1 rating).
• Lithium batteries have a flat discharge curve and are less affected by the Peukert Effect. This means their usable capacity remains nearly the same even at higher discharge rates.
• Formula for effective capacity: Effective$$\text{Effective Capacity Rated}\text{Capacity (Ah) (}$$No significant reduction in capacity at higher discharge rates.) https://en.wikipedia.org/wiki/Lithium_iron_phosphate_battery

3. Why Lithium Requires Smaller Size Batteries for the Same Load

Higher Energy Density

• Lithium-based batteries have a much higher energy density compared to Tubular Lead-Acid batteries. This means they can store more energy in a smaller physical size.
• For example, a 100Ah Lithium battery is significantly smaller and lighter than a 100Ah Tubular Lead-Acid battery.

Higher Discharge Efficiency

• Lithium batteries can deliver their full rated capacity even at high discharge rates (C1), whereas Tubular Lead-Acid batteries lose capacity at higher discharge rates due to the Peukert Effect.
• For the same load, a Lithium battery can provide the required power with a smaller capacity because it doesn’t suffer from capacity loss at high discharge rates.

Example Calculation

• Load: 1000W
• System Voltage: 12V
• Required Current: 1000W12V=83.33A12V1000W​=83.33A

Tubular Lead-Acid Battery (C20 Rating):

• To deliver 83.33A, the battery must be oversized to account for capacity loss at high discharge rates.
• If the Peukert Effect reduces the effective capacity by 30%, you may need a 150Ah battery to deliver 83.33A for 1 hour.

Lithium Battery (C1 Rating):

• A 100Ah Lithium battery can deliver 83.33A for 1 hour without significant capacity loss.
• No need to oversize the battery.

Result

• A 100Ah Lithium battery can handle the same load as a 150Ah Tubular Lead-Acid battery, making the Lithium battery smaller and more compact.

4. Advantages of Lithium-Based Batteries

The Lithium Baterry has the inbuilt Battery Management System which keep the life of the battery maintained by equalizing each cell of the battery and we can monitor all the parameters of the battery through the Iot devices and all the protection features work through the BMS FOR THE Lithium battery which is missing in the Tubular Lead Acid battery.

• Smaller Size and Weight: Higher energy density allows for compact designs.
• Longer Lifespan: Lithium batteries typically last 3-5 times longer than Tubular Lead-Acid batteries.
• Faster Charging: Lithium batteries can be charged at a higher rate, reducing downtime.
• Maintenance-Free: No need for regular watering or maintenance.
• Better Performance at High Discharge Rates: No significant capacity loss at high loads.
• The Most of the manufacturers rate their product in VA capacity rather then Watt capacity which doesn’t give any clarity about the wattage of the Inverter/UPS. BIS has mandated that approved BIS product has to have the wattage written on the product.
• Always buy BIS approved product cgecking on the BIS site whether the product is approved by the Bureau of Indian Standards.

5. Conclusion

The backup time and capacity of a battery depend on its discharge characteristics and energy density. Tubular Lead-Acid batteries are limited by the Peukert Effect, which reduces their effective capacity at high discharge rates, necessitating larger battery sizes for the same load. In contrast, Lithium-based batteries have a flat discharge curve, higher energy density, and can deliver their full capacity even at high discharge rates (C1). This makes Lithium batteries more efficient, compact, and suitable for applications where space and weight are critical factors.

When designing a backup power system, choosing Lithium-based batteries can result in a smaller, lighter, and more efficient solution compared to Tubular Lead-Acid batteries, especially for high-power applications.