How to calculate Load chart of a Lithium Inverter/UPS

The load chart calculations become different if the INVERTER/UPS is installed with Lithium-ion or Lithium LifePO4 battery or Tubular Lead Acid battery as the TUBULAR LEAD ACID BATTERY has the capacity of C20 or C10 maximum which makes a big difference in the calculations of time. https://suvastika.com/load-calculation-formulae-is-different-for-tubular-and-lithium-battery-inverter-ups/

When calculating the load chart for an inverter with a Lithium Battery (which typically has a C1 rating), you need to consider the battery’s capacity, discharge rate, and the inverter’s efficiency. The Load chart will always be calculated in terms of wattage of the inverter/UPS and Energy Storage Systems. most of the players give the capacity in terms of VA which has no meaning as each company uses different VA for it’s backup and solar products. BIS has mandated for all the manufacturers to write the capacity in wattage so that customer is not taken for the ride. bureau of Indian Standard has made it mandatory for India to have the approval of BIS for each inverter/UPS model for the safety and backup purpose. The mark of BIS has to have the real wattage of the product written by approved manufacturer so that customer get the clarity. https://suvastika.com/why-should-you-choose-a-bis-certified-inverter-ups/

Here are the key formulae and steps:

1. Battery Capacity in Watt-hours (Wh)

Lithium batteries are often rated in Ampere-hours (Ah) and Voltage (V). Convert the battery capacity to watt-hours using the formula:

$$\text{Battery Capacity (Wh)}=\text{Battery Capacity (Ah)}\times \text{Battery Voltage (V)}$$

Example:

• Battery Capacity = 100 Ah
• Battery Voltage = 24V
• Battery Capacity (Wh) = 100 Ah × 24V = 2400 Wh

2. Usable Battery Capacity

Lithium batteries typically allow a Depth of Discharge (DoD) of 80-90%. Multiply the total capacity by the DoD to get the usable capacity.

$$\text{Usable Capacity (Wh)}=\text{Battery Capacity (Wh)}\times \text{DoD}$$

Example:

• DoD = 90% (0.9)
• Usable Capacity = 2400 Wh × 0.9 = 2160 Wh

3. Inverter Efficiency

Inverters are not 100% efficient. Typical efficiency is around 85-95%. Factor this into your calculations.

$$\text{ Capacity (Wh)}=\text{Usable Capacity (Wh)}\times \text{Inverter Efficiency}$$

Example:

• Inverter Efficiency = 90% (0.9)
• Effective Capacity = 2160 Wh × 0.9 = 1944 Wh

4. Total Load Calculation

Calculate the total load (in watt-hours) of all appliances you want to power during a backup. Use the formula:

$$\text{ Load (Wh)}=\sum \; (\text{Power of Appliance (W)}\times \text{Usage Time (hours)})$$

Example:

• LED Bulb: 10W × 4 hours = 40 Wh
• Fan: 50W × 4 hours = 200 Wh
• TV: 100W × 2 hours = 200 Wh
• Refrigerator: 200W × 8 hours = 1600 Wh
• Total Load = 40 + 200 + 200 + 1600 = 2040 Wh

5. Backup Time Calculation

To calculate the backup time, divide the effective battery capacity by the total load.

Backup Time (hours)=Effective Capacity (Wh)Total Load (Wh)Backup Time (hours)=Total Load (Wh)Effective Capacity (Wh)​

Example:

• Effective Capacity = 1944 Wh
• Total Load = 2040 Wh
• Backup Time = 1944 Wh ÷ 2040 Wh = 0.95 hours (57 minutes)

6. C1 Rating Consideration

Lithium batteries are often rated at C1, meaning they can deliver their rated capacity over 1 hour. If your backup time is less than 1 hour, ensure the battery can handle the higher discharge rate.

• If the backup time is less than 1 hour, the battery must support a higher discharge rate (e.g., C2, C3, etc.).
• Check the battery datasheet for its maximum discharge rate.

7. Inverter Sizing

Ensure the inverter can handle the total connected load (in watts) and any starting surges.

$$\text{ Capacity (W)}=\text{Total Connected Load (W)}\times \text{Safety Margin (1.2-1.3)}$$

Example:

• Total Connected Load = 10W + 50W + 100W + 200W = 360W
• Safety Margin = 1.3
• Inverter Capacity = 360W × 1.3 = 468W
• Choose an inverter of at least 500W.

Summary of Formulae:

1. Battery Capacity (Wh): Battery$$\text{Battery Capacity (Wh)}=\text{Battery Capacity (Ah)}\times \text{Battery Voltage (V)}$$
2. Usable Capacity (Wh): Usable$$\text{ Capacity (Wh)}=\text{Battery Capacity (Wh)}\times \text{DoD}$$
3. Effective Capacity (Wh): Effective$$\text{ Capacity (Wh)}=\text{Usable Capacity (Wh)}\times \text{Inverter Efficiency}$$
4. Total Load (Wh): Total$$\text{ Load (Wh)}=\sum (\text{Power of Appliance (W)}\times \text{Usage Time (hours)})$$
5. Backup Time (hours): Backup Time (hours)=Effective Capacity (Wh)Total Load (Wh)Backup Time (hours)=Total Load (Wh)Effective Capacity (Wh)​
6. Inverter Capacity (W): Inverter$$\text{ Capacity (W)}=\text{Total Connected Load (W)}\times \text{Safety Margin (1.2-1.3)}$$

• Battery Capacity: 100 Ah, 24V (2400 Wh)
• Usable Capacity: 2160 Wh (90% DoD)
• Effective Capacity: 1944 Wh (90% inverter efficiency)
• Backup Time: 0.95 hours (57 minutes)
• Inverter Capacity: 500W (with safety margin)

This will help you design a system with a lithium battery and inverter for your backup needs.

About the author — Kunwer Sachdev

Founder of Su-Kam and Kunwwer.ai, and mentor at Su-vastika — known as the "Inverter Man of India," with 30+ years building inverter, UPS, solar and lithium storage technology and 15 technology patents. Read more →

Disclaimer: It is important to note that while Mr. Kunwer Sachdev founded Su-Kam Power Systems, he is no longer associated with the company as of 2019. Any information regarding his involvement in the company's operations, strategies, or future plans reflects his tenure prior to that date. Therefore, any discussions or analyses of Su-Kam Power Systems should be considered in the context of his past contributions and not his current association with the company. He currently mentors Su-vastika.