Congratulations, you have chosen to use lead batteries as the power supply to your energy storage system, now you must install it. Rick Tressler, President & CEO of Rick Tressler LLC, explores the basic steps for electrical sizing of a vented lead-acid battery for a data centre-type UPS with one module and single battery bank.
When utilising a standby battery as the primary energy source in a power system, proper electrical and physical sizing is very important. Of course, the cost must be considered. The system must be able to provide the required power to the critical load for a specific time throughout its service life.
That is if the run time on the battery is to be two hours, that applies to the overall battery service life. Additionally, a battery must operate within a defined voltage range to satisfy the DC input requirements of the uninterruptible power supply (UPS), while delivering rated power.
The physical size of the battery plays a role in its selection, which means an allowable footprint into which the battery will fit must be defined. The room itself must also be equipped to support adequate ventilation, maintenance clearances, wiring, cable trays, conduits, and racking/cabinet dimensions; all of which must comply with applicable codes.
UPS Battery Applications
Regardless of the specific type of UPS, the characteristic of the application is that of constant power (watts). That is, as the battery discharges, battery current (I) increases proportionately as voltage (E) decreases. At any point in time during a discharge, this can be proven by measuring battery voltage and current at multiple points during a discharge and calculating the power input to the UPS. P = I x E. The power figure will be constant (Fig 1).
Within the application, there are two distinct types of UPS in use: industrial and data centre. Industrial applications for UPS include— but are not limited to— oil, gas, petrochemical, and utility. In the industrial type, support time is frequently required from one to several hours or more, as opposed to data centre UPS.
In data centres, support time is generally less than 30 minutes. Many data centre UPS batteries are sized from 5 to 15 minutes as these sites are usually equipped with diesel generators that can be online in a matter of seconds. The difference between the two applications is important when selecting the battery. There is more to it than simply stating “I need a UPS battery”.
High rate, short duration applications such as those for data centre UPS typically require a battery capable of discharging to end-of-discharge voltage (EOD) as low as 1.60 volts per cell (VPC). Batteries designed for long-duration discharges are almost always limited to an EOD of 1.75VPC. Therefore, selecting a long-duration battery for a short-duration application and vice-versa is a misapplication and must be avoided.
With the previously discussed topics in the rear-view mirror, we’ll move to sizing considerations. It is assumed the battery room is equipped for the proper installation of a vented lead-acid (VLA) battery. The bullet list below summarises these considerations. A detailed discussion follows the considerations with an example sizing problem.
- Required support time on battery throughout life
- Minimum and maximum dc system operating voltage
- Ability to equalise the battery when needed
- Minimum battery discharge voltage
- Cable sizing
- The voltage drop from the battery terminals to the UPS input
- Expected operating temperature
- Design margin
- Ageing factor
The battery size is directly affected by not only the required load but the required support time for the load. This time is required throughout the expected service life of the battery. If two hours of run time is required, that must be accounted for in the sizing so when the battery is at end-of-life (EOL), the system will still meet the two-hour requirement. This is accounted for in the example sizing problem.
The minimum and maximum DC operating voltage parameters play a role in calculating the number of cells required for the battery. The system designer must know the minimum per-cell equalise/commissioning voltage needed to carry out such a charge when needed.
Accounting for sufficient ‘headroom’ so that the charging system voltage can be raised to properly equalise/commission charge a battery is important.
While a battery with too many cells may meet the power requirement, it can restrict the rectifier adjustment to achieve the necessary per-cell voltage needed. Be certain that the battery can be commissioned/equalised when needed. This applies even to VRLA batteries as they generally need to be initially charged at a higher-than-normal voltage during commissioning.
The minimum battery voltage parameter consists of the minimum battery operating voltage plus the voltage drop to the connected load. Voltage drop cannot be overlooked. This parameter, along with the number of cells, are both essential in calculating the minimum cell voltage. UPS batteries employed in data-centre applications are frequently sized to discharge down to as low as 1.60 VPC and generally no lower than 1.75 VPC for long-duration industrial UPS.
Unlike AC, cable voltage drop does occur in DC power circuits even when the cable run is short. This must not be overlooked as failure to calculate it will result in the appearance the battery has been undersized.
Cable ampacity must also be factored into sizing as the required cable size is needed to calculate the voltage drop. Voltage drop is calculated between the battery’s main positive and negative terminals and the UPS it is serving. Voltage drop is a function of the cable size, length, and the maximum load it will carry. Voltage drop is calculated using the maximum discharge current and EOD voltage.
Unless otherwise specified, a battery is sized for operation at the manufacturer’s stated normal temperature, also referred to as standard temperature. The stated temperature may be 77°F (25°C) or 68°F (20°C), depending on the manufacturer. In previous articles, I wrote about how battery temperature affects performance and service life. Lower than normal average temperature increases service life at the expense of recharge acceptance efficiency and capacity. Higher temperature has just the opposite effect, shortening service and reliability but increasing capacity a bit.
Never intentionally operate a battery at a higher than recommended temperature to achieve higher performance. However, if a battery is to be operated at other than standard temperature, (usually lower) this should be taken into consideration in the form of the Institute of Electrical and Electronics Engineers (IEEE) recommended temperature compensation factor. In the case of the lowered temperature, this will result in a larger battery compared to the standard temperature. Translation— lower temperature means a bigger battery at a higher cost and likely a larger footprint in the installation space.
UPS batteries are not normally sized with a design margin. When a user purchases a 500kVA module, for example, the expectation is the system will be loaded at or near 100% of the output rating. Therefore, a battery is sized accordingly. However, numerous applications exist where a design margin may be appropriate— such as adding more load later when it is needed.
The application of an ageing factor for any battery installation is common practice and necessary to ensure the sizing results in 100% capacity over the life of the battery. A battery should be replaced when its capacity reaches 80%. For a battery to accommodate the design requirements over its service life, the rated capacity should be at least 125% of the load at the end of its service life with an ageing factor of 1.25. This results in a rated capacity of more than what is needed initially. A battery will lose capacity over its service life, thus requiring more initial capacity (run time). Do not size a battery without an ageing margin.
Sizing— basic requirements
The sample problem that will be worked on here is for a single module, rated 450kVA with a unity power factor. Inverter efficiency is 97% with a required run time on a battery of 15 minutes at EOL. The voltage drop from the battery to the UPS may not exceed 3.0 volts. The minimum battery voltage input at the UPS may not be lower than 373 volts.
- KVA vs. KW
As the module is power factor corrected, kVA and kW are the same for the 450kW system. To determine the battery power required, the system AC output rating must be divided by the inverter efficiency of 97%. Therefore, 450 kW / .97 = 464 kW. However, if the UPS were to be rated with a power factor of .9, the full load AC power would then be 450 kVA x .9 = 405 kW and the battery sizing would be predicated on that figure.
- Determining number cells
Next is to determine the required number of cells. The UPS rectifier can be adjusted to a maximum of 560 volts. The minimum equalised voltage per cell needed for the battery is 2.40 VPC. The maximum bus voltage is divided by the minimum per-cell voltage. So, 560 V / 2.4 V = 233 cells.
- Discharge current calculation
To determine the discharge current at (EOD), divide the battery kW by the EOD voltage. Therefore, 464 kW / 373 V = 1244 amperes. Recall this is needed as the battery wire sizing is required based on maximum current through the cable.
- Sizing the wire to the load
The wire size and voltage drop can be determined when the EOD current and layout drawings are available. The latter is required so the length of the cable can be determined. In the example, the EOD current is 1,244 amperes, and the cable running from the battery to the UPS is 23.8 meters (80 feet).
For wire sizing, the EOD current is 1,244 amperes and is treated as continuous current. In the US, where this author works, the National Electrical Code (NEC) must be consulted (Table 2). The available wire on the shelf for the project is copper 750 and 500 kcmil (MCM). Both sizes are rated for 90°C (194°F).
Reviewing the table for copper wire rated 90°C, note the ampacity for 400 and 525 amperes for 500 and 750 MCM wire respectively. Since the EOD current is 1,244 amperes, neither wire will suffice for the duty as a single conductor per polarity, so multiple conductors are required. For both wire sizes, three conductors are required per polarity. Since the larger cable probably costs more, 500 MCM is selected as three conductors are rated for 1,290 amperes providing installation complies with the header text in Table 2.
It is worth noting that when 90°C wire is used, wire lugs and landing points must also be rated for this temperature. When landing points do not meet the requirement, lower temperature rated wire must be used.
Calculating voltage drop
Ampacity does not automatically indicate voltage drop specifications will be met, so using a simple formula is in order. There is more than one formula out there to calculate voltage drop. The one used in the article is one this author has used for years and has not been a problem when real-world measurements have been compared to calculations.
The formula is 11.1 x conductor loop in feet x load/wire size. Applying this to the example, 11.1 x 80 x 1244 / 1500 MCM = 0.736 volts, rounded up to 0.74 volts. The resulting calculation falls well within the maximum allowable drop of 3.0 volts. Note— when performing the calculation enter 1,500 kcmil as 1,500,000 or if entering 1,500, just move the decimal to the left of your answer by three decimal places.
Remember, minimum system voltage is the voltage at the battery minus the voltage drop in the cable serving the load. The calculation used here determines the minimum cell voltage at the battery main terminals.
It is suggested when an acceptance test is conducted, voltage measurements are taken at both the battery main terminal as well as the input to the UPS with calibrated digital voltmeters (DVM) if possible. As far as the battery manufacturer is concerned, the voltage measurement point needs to be at the battery’s main positive and negative terminals, not at the other end of the load wiring.
The minimum system voltage is divided by the cell count, therefore 373 volts/233 cells = 1.604 VPC. The value to use is 1.60 VPC. This is the EOD voltage per cell, which is applied to the battery manufacturer performance table for the candidate cell model.
The final step in the calculations before looking at battery performance data is the ageing factor. With a battery full load requirement of 464 kWb and 233 cells, the power requirement is 1991 watts per cell (WPC) or 1.991 kilowatts. To apply the ageing factor, multiply it by the full load battery power (kWb).
Therefore, 464 kWb x 1.25 = 580 kWb or 2.489 kW per cell at the 15-minute rate.
- A vented lead-acid calcium battery (VLA) required
- Required 15 minutes support time EOL
- 450 kVA UPS rating, power factor corrected
- Battery requirements is 464 kWb (1991 WPC) continuous
- Ageing margin 1.25 sized for 2489 WPC
- Final voltage at battery 373.74 volts (1.60 VPC)
- Wiring voltage drop at 23.8 meters (80 feet) .74 volts
- Cell requirement– 233
- Minimum equalisation voltage– 2.4 VPC (560 volts)
- Operating temperature– 25°C (77°F)
Selecting a battery can be time-consuming and for some, a bit of a headache especially if one does not know much about batteries from a selection and sizing perspective. Sizing a battery should be undertaken by persons with actual knowledge of the facts required. That said, to speed up the process for this article, the author has preselected a battery manufacturer and model meeting the requirements. Use of EnerSys product information is not an endorsement of EnerSys products and is not indicative this sizing example will work for all 450 kW UPS installations.
The battery model selected is a vented lead-calcium flat plate type designed for UPS applications (Fig 2). It is available in standard 1.215 specific gravity and optionally 1.250. The ES series battery is a single cell type. A total of 233 cells is required. Rack selection is beyond the scope of the article, but common arrangements include two- and three-tier racks depending on floor space and overhead clearance.
Referring to Table 3; this is the ES cell performance data for 1.250 specific gravity with an EOD of 1.60 VPC at 25°C (77°F). To find the cell needed, go to the 15-minute discharge rate column, then move down to find a WPC rating that meets or exceeds 2,489 watts. Once found, look left to read the Battery Type column. You should see the ES-25B. The purple dot between the 20 and 25-minute columns represents 1991 WPC. The battery should deliver 22 minutes when tested at full load when new. When the battery reaches EOL, the run time will be 15 minutes.
Referring to Table 4; the standard gravity ES cell is also a possible solution. However, due to its lower specific gravity, the ES-29 would be needed: a cell with four more plates than the ES-25B. The cell count remains 233. This product is just one of several offered that can meet the requirements of the job.
Readers may be thinking there has to be an easier method to sizing batteries than what has been presented in the article. The answer is yes. EnerSys and other manufacturers have been offering web-based sizing applications for several years. Originally, the software was on CDs and required periodic updates as product availability and performance changed. Online sizing is, in the author’s view, the preferred method. The onus is on the user and, be cautioned, mistakes can be made. It is suggested, that those who wish to use the applications should consult the manufacturer with their findings before submitting an order.
The author used the “old school” method to size the example battery, following up with the web-based EnerSys battery sizing program (BSP) to validate the manual process.
One of the goals of this article is to explain and illustrate the fundamentals behind how a battery is sized for a constant power application. Having this knowledge makes using software-based applications such as the web-enabled BSP easier to use, should a reader choose to take that path.
The applications can provide extensive reporting, such as sizing, sizing margin and estimated run-time reports, rack selection, hardware option selection and comprehensive line-by-line reporting for an entire system.