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One of the first steps to the successful application of a battery is to make sure the battery is correctly sized for the load it will be required to handle. Without this crucial step, it is very likely that your battery will be undersized for the application.
This article examines the elements involved in sizing a battery for an application. While loads can vary over time and be quite complicated, this article will focus on sizing batteries for single step or level loads. Single-level loads are typical in applications such as uninterruptible power supply (UPS) systems.
The three key types of battery connections are series, parallel and series-parallel, which are shown in Figure 1. In each case, four 2V lead acid cells are shown.
The electric power, voltage and current are related in a very simple way. The power in watts is equal to the product of the voltage and the amperes, as shown here: W = V x A.
Sizing for constant current load
The four pieces of information needed to size a battery are nominal system voltage, minimum system voltage, load (constant current or constant power) and desired backup time. Depending on the location of the battery installation, temperature range should also be considered, particularly if operation in cold weather will be required, as shown in Figure 2.
The following example illustrates the battery sizing exercise. The goal is to determine battery capacity for a nominal 48V system that requires a constant current of 9A for four hours to a minimum voltage of 42V.
- Step 1: The number of cells, N, is given by the nominal voltage (48V) divided by the nominal cell voltage, which is 2V for lead acid cells. Thus, in this case, the number of cells works out to 24.
- Step 2: The cell end voltage is found by dividing the minimum voltage (42V) by the number of cells calculated in Step 1. In this example, 42V/24 cells = 1.75 volts per cell (VPC).
- Step 3: Consult the battery manufacturer's constant current discharge table to 1.75 VPC and find the smallest battery that will deliver at least 9A for four hours.
If the manufacturer does not offer a battery that will support your load for the duration you want, repeat the process after cutting the load in half. In this example, the current that is required will be 4½ amps. Repeat the sizing exercise for this new load, remembering that you will have two parallel strings now—because the load has been cut in half, two strings are needed to support the full load.
Sizing for UPS loads
In general, UPS systems are rated in volt-amperes (VA) or kilovolt amperes (kVA), where 1kVA equals 1,000 VA. The kVA rating is always an AC rating and must be converted to a kW rating by multiplying the kVA by the power factor (PF) of the UPS. The UPS manufacturer must provide the PF value.
To determine the actual kW the battery must provide, the kW rating of the UPS must be divided by the efficiency (also provided by the UPS manufacturer). These two operations are shown by the two equations in Figure 3. The last equation calculates the watts per cell (WPC) the battery has to deliver.
The following is an example of battery sizing with power factor (PF) and efficiency involvement. Both numbers must be provided by the UPS manufacturer.
A nominal 120V system has to support an UPS load of 15kVA for 15 minutes. The UPS has a PF of 0.88 and an efficiency of 85 percent. The end of discharge voltage is 105V.
Steps 1 and 2 in this example are identical to the first two steps in the previous example, giving 60 as the number of cells and 1.75 VPC as the end voltage. Using the equation for the UPS kilowatts, kWUPS works out to 13.2kW; dividing this number by the efficiency (0.85) yields a battery kilowatt (kWBattery) of 15.53kW. By using the equation for the watts per cell (WPC) we can determine that the battery must be capable of delivering 258.8 WPC.
Then, look up the constant power discharge tables provided by the manufacturer to find the smallest battery that will support 258.8 WPC for 15 minutes, before its terminal voltage drops to 1.75 VPC.
Final comments
While the two examples illustrate the most common battery installation cases, there are special situations that require a more complex sizing exercise, particularly those applications that call for multi-step loads on the battery.
Allowances also should be made for factors such as battery end-of-life and design margin. These can be taken into account by multiplying the required load by an appropriate factor such as 1.1 to allow for a 10 percent safety margin.
A common technique to account for battery end-of-life (usually defined as a failure of the battery to deliver at least 80 percent of its rated capacity) is to multiply the load by 1.25. So, if the load is 10A, the battery will be sized to support a load of 12½ amps. When the battery reaches its end of life, it will still support 80 percent of 12½ amps, or 10A for the specified time. In other words, the battery will support 100 percent of the desired load even when it is at the end of its useful life.
Although typically a relatively low-cost component of any reserve power system, batteries are an important insurance policy for critical equipment when AC power is down. By sizing your battery properly, you will have adequate power provided to your equipment for the necessary duration.
Kalyan Jana is technical product manager at EnerSys, a battery manufacturer.
author: By Kalyan Jana