How to Calculate of Backup Time and Capacity of Lead Acid Batteries in TeleCommunication

In telecommunication systems, lead-acid batteries are the core backup power source. Their core function is to provide continuous power supply to base stations and equipment in the computer room in the event of a power outage, avoiding communication interruptions. Its' backup time 'refers to how long it can last after the mains power is cut off, while' capacity 'refers to the total amount of electricity that the battery can release.

1.Battery capacity (unit: Ah, ampere hour) is commonly understood as the "storage capacity" of a battery, similar to the volume of a water bucket. For example, a 100Ah battery can theoretically discharge for 10 hours at 10A current (10A × 10h=100Ah), or discharge for 5 hours at 20A current (20A × 5h=100Ah). However, it should be noted that the larger the discharge current of lead-acid batteries, the less capacity they can actually release (during high current discharge, the internal reaction of the battery is not sufficient, which is equivalent to pouring a bucket too quickly and leaving residual water at the bottom that cannot be used).

2. Load current (unit: A, ampere) is commonly understood as the "power consumption" of communication equipment during normal operation, similar to the water output of a faucet. For example, a set of base station equipment consumes 50A of current per hour during operation, and the load current is 50A. If there are multiple devices, the total load current is the sum of the operating currents of all devices (excluding backup devices, only counting actual operating devices).

3. Discharge rate and temperature correction are the "correction terms" for calculation, because the actual power supply capacity of lead-acid batteries is greatly affected by discharge rate and environmental temperature, and cannot be directly calculated based on theoretical capacity:

Discharge rate: The ratio of discharge current to battery capacity (C). For example, if a 100Ah battery is discharged at 50A, the rate is 0.5C (50A/100Ah). The larger the rate (the faster the discharge), the greater the capacity discount. For example, if a 100Ah battery is discharged at 1C (100A), the actual capacity may only be 80Ah; if discharged at 0.1C (10A), the actual capacity is close to 100Ah.

Temperature correction: Lead acid batteries perform best at 25 ℃, and the capacity will change if the temperature deviates from 25 ℃. The lower the temperature, the less capacity (for example, at -10 ℃, the capacity may only be 70%); The higher the temperature (not exceeding 40 ℃), the slightly increased capacity, but it will shorten the battery life.

4. When the backup time is available, how to calculate battery capacity?

The required battery capacity (Ah)=total load current (A) × backup time (h) ÷ discharge rate coefficient ÷ temperature correction coefficient. 

Note: The "÷ coefficient" in the formula is to deduct the capacity loss caused by the discharge speed and temperature of the battery to ensure that the actual capacity can meet the demand.

Example: In a certain communication room, backup power supply is required for 4 hours after the mains power is interrupted. The total load current of the room is 60A, and the ambient temperature of the room is 15 ℃. A 12V lead-acid battery pack is selected to calculate the required battery capacity. 

Step 1: Determine the discharge rate coefficient. Backup time of 4 hours, discharge rate=load current/battery capacity (currently unknown, can be estimated by time factor). Industry common experience: discharge time is 2-10 hours, and the rate coefficient is set at 0.8-0.9 (the longer the time, the closer the coefficient is to 1); This case takes 4 hours and takes a coefficient of 0.85. 

Step 2: Determine the temperature correction coefficient. Check the lead-acid battery temperature correction table (simplified version): 25 ℃ coefficient 1.0, 20 ℃ 0.95, 15 ℃ 0.9, 10 ℃ 0.85, 0 ℃ 0.75, -10 ℃ 0.65. This case is at 15 ℃, with a coefficient of 0.9. 

Step 3: Substitute into the formula for calculation. Required capacity=60A × 4h ÷ 0.85 ÷ 0.9 ≈ 60 × 4 ÷ 0.765 ≈ 313.7Ah. 

Step 4: Select specifications. The common specifications for lead-acid batteries are 100Ah, 200Ah, and 300Ah. It is necessary to choose a specification greater than the calculated value. Here, a 300Ah battery pack is selected (if the load voltage is 48V, four 12V 300Ah batteries need to be connected in series, which does not change the capacity but only increases the voltage). 

Key reminder: If the load is power (unit: W, W), it needs to be converted to current first: current (A)=power (W) ÷ voltage (V). 

For example, a certain device has a power of 1200W, a working voltage of 48V, and a current of 1200 ÷ 48=25A.

5. When the battery capacity is available, how to calculate backup time?

The required battery capacity (Ah)=total load current (A) × backup time (h) ÷ discharge rate coefficient ÷ temperature correction coefficient.

Actual backup time (h)=actual available capacity of the battery (Ah) ÷ total load current (A), where: actual available capacity of the battery=nominal capacity (Ah) × discharge rate factor × temperature correction factor

Example: The computer room currently has a 12V 300Ah lead-acid battery pack (48V system, 4 in series), with a total load current of 60A and an ambient temperature of 15 ℃. Calculate the actual backup time. 

Step 1: Determine the discharge rate coefficient. The battery has a nominal capacity of 300Ah, a load current of 60A, a discharge rate of 60A/300Ah=0.2C, and a corresponding discharge time of about 5 hours (300Ah ÷ 60A). Check the coefficient table and take 0.85 (as before). 

Step 2: Determine the temperature correction coefficient. Take 0.9 at 15 ℃ (as before). 

Step 3: Calculate the actual available capacity. 300Ah × 0.85 × 0.9=229.5Ah. Step 4: Calculate the backup time. 229.5Ah ÷ 60A ≈ 3.82 hours, which is approximately 3 hours and 49 minutes (considering battery aging, the actual time may be further shortened by 10% -20%).

6.Practical precautions (key to avoiding pitfalls, even more important than formulas) 

1) The battery aging coefficient must be calculated based on the service life of lead-acid batteries, which is about 3-5 years. After aging, the capacity will decrease. For new batteries, it is calculated based on 100% capacity, 90% after 1 year of use, 80% after 2 years, and 70% after 3 years (specific adjustments can be made according to the battery testing report). For example, for a 3-year 300Ah battery, the actual usable capacity needs to be multiplied by 0.7. 

2) Reserve redundant capacity for communication systems to avoid extreme situations (such as unexpected power outages or temporary load increases), and reserve 10% -20% redundancy during calculations. For example, if 313.7Ah is required, a 400Ah battery can be directly selected, or the calculated value can be adjusted by multiplying it by 1.2. 

3. The impact of series/parallel connection on capacity. Series connection: Increasing voltage while maintaining capacity. For example, two 12V 300Ah batteries connected in series can be converted into 24V 300Ah (suitable for high-voltage loads). Parallel connection: increases capacity while maintaining the same voltage. For example, two 12V 300Ah batteries can be connected in parallel to become 12V 600Ah (suitable for high current and long-term loads). 

4. The discharge termination voltage cannot be ignored. Lead acid batteries have a minimum voltage limit for discharge (the termination voltage of a 12V battery is about 10.5V). After discharging to the termination voltage, it must be stopped, otherwise it will damage the battery. The actual backup time may be affected by the termination voltage, and if the device allows a small range of voltage fluctuations, the actual time may be slightly shorter.