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of Lead-acid battery for UPS / CBS
Initial assumptions and limiting factors
Battery discharge voltage range: 1.67- 2.10 V/cell
Battery equalizing charge range: 2.30- 2.50 V/cell
Step#1: calculate Battery Total load
Battery Total load (W) = UPS Load (W) / inverter efficiency
Battery Total load (W) = UPS Load (W) + inverter losses (W)
Example#1:
System size: 500 kVA at 0.80 PF, 400 kW
System output voltage: 3 ph, 120/208 Vac (not required for calculation)
Inverter efficiency: 0.92 efficiency at full load (dc input to ac output)
Solution:
Battery Total load (W) = 400 kW/0.92 = 435 KW
Note: The very latest generation of on-line UPS have inverter efficiencies of up to 97%, producing longer battery autonomies than could previously be achieved from the same battery connected to a UPS with a less efficient inverter.
Step#2: calculate the corrected Battery Total load
Corrected Battery Total load = Battery Total load × ageing factor × temperature correction factor x design Margin
Where:
Ageing factor Since the battery capacity does not remain at its nameplate rating throughout its life, a 25% margin will be included as an aging factor for the 435 kW.
Temperature correction factor Also, since it is expected that the operating temperature will drop to a low of 15.6 °C (60°F), the battery capacity should be increased by another 11% (per IEEE Std 485-1983) to ensure that it will provide rated load at reduced temperature.
Design Margin A design margin is taken into account for any inaccuracies in the load’s estimation. Generally, a design margin ranges between 10% and 15% is suggested. And sometimes it will be ignored.
Then, in continued example#1: Corrected Battery Total load = 435 KW * 1.25 *1.11 = 604 KW
Step#3: calculate the maximum number of cells
In Continued example#1:
It is assumed that the manufacturer recommends an equalizing voltage of 2.40/cell.
The maximum number of cells = Maximum system voltage / Recommended equalizing V/cell
Then,
The maximum number of cells = 432/2.40 = 180 cells
Note: In this case no adjustment is made for the voltage losses in the cables and cell connectors. In the final stages of battery recharge the current drops to a point where the voltage drops are insignificant on the large cables that have been sized for the final discharge currents.
Step#4: calculate the end voltage
Note: In order to take full advantage of the battery’s usable capacity, the lowest possible end-of-discharge cell voltage should be used. This is subject to the limits imposed by the minimum allowable system voltage and the battery manufacturer’s stated minimum cell voltage for the discharge time in question. More important, the battery must first be capable of being charged in accordance with the manufacturer’s recommendations and within the maximum system voltage limit.
The final voltage per cell = Minimum battery voltage/Number of cells
In Continued example#1:
Allowing for the planned 2 V loss in the cables, the minimum battery voltage of 292 V is then used to calculate the final voltage per cell:
The final voltage per cell = Minimum battery voltage/Number of cells = 292/180 = 1.62 V /cell
Step#5: calculate the Minimum number of cells
Note: In most cases, the calculated number of cells and minimum voltage per cell would be used directly in the remainder of the battery sizing exercise. However, in this example, it is assumed that the battery manufacturer states a minimum discharge voltage of 1.67 V/cell for a 20 min discharge. Since the calculated minimum voltage is 1.62 V/cell and the manufacturer’s minimum voltage is 1.67 V/cell, it is necessary to adjust the number of cells to reflect the higher value of the minimum discharge voltage.
Minimum number of cells = Minimum battery voltage/ Minimum discharge V/cell
Therefore, In Continued example#1: Minimum number of cells = Minimum battery voltage/ Minimum discharge V/cell = 292/1.67 = 175 cells
Step#6: Cell selection
At this point it has been determined that the battery required is one with 175 cells that can deliver 604 kW for 20 min and not drop below 1.67 V/cell.
Each cell shall then deliver: 604 kW/175 cells = 3.45 k W/cell
Now there is complete information with which to consult the manufacturer’s performance charts and select the proper cell for the application (20 min, 1.67 V/cell, and 3.45 kW/cell).
It may be beneficial to repeat the calculation to optimize the number of cells for a particular cell type. For example, if there is a cell that can provide 3.40 kW/cell, it would probably be more economical to increase the number of cells, rather than using 175 of the next larger cell size. In this case, the new number of cells would be:
604 kW/3.40 = 178 c ells
Notes:
Changing the number of cells will affect both:
- The equalizing Voltage and
- The end-of-discharge voltages.
Increasing the number of cells allows a lower end-of-discharge voltage per cell (more usable capacity) within the lower system limit, but may result in a required equalizing voltage that is higher than the upper system limit.
Decreasing the number of cells will not impose any constraints on the maximum voltage limit, but will result in a higher end-of- discharge voltage per cell (less available capacity).
In this particular example, it is already known that 180 cells can be accommodated within the upper system voltage limit. At the lower voltage limit, the use of 178 cells would allow discharging to 1.64 V/cell, but would fail to meet the battery manufacturer’s stated minimum of 1.67 V/cell.
Battery selection, then, is a process of finding the best fit between the maximum charge voltage and the minimum operating point of the UPS that will allow the maximum use of the available battery capacity.