Battery Sizing - Open Electrical

Stationary batteries on a rack (courtesy of PowerBattery)

From Open Electrical

1 Introduction1.1 Why do the calculation?1.2 When to do the calculation?

2 Calculation Methodology2.1 Step 1: Collect the battery loads2.2 Step 2: Construct the Load Profile2.3 Step 3: Select Battery Type2.4 Step 4: Number of Cells in Series2.5 Step 5: Determine Battery Capacity

3 Worked Example3.1 Step 1 and 2: Collect Battery Loads and Construct Load Profile3.2 Step 3: Select Battery Type3.3 Step 4: Number of Cells in Series3.4 Step 5: Determine Battery Capacity

4 Computer Software5 What Next?

This article looks at the sizing of batteries for stationaryapplications (i.e. they don't move). Batteries are used inmany applications such as AC and DC uninterruptiblepower supply (UPS) systems, solar power systems,telecommunications, emergency lighting, etc. Whateverthe application, batteries are seen as a mature, proventechnology for storing electrical energy. In addition tostorage, batteries are also used as a means for providingvoltage support for weak power systems (e.g. at the endof small, long transmission lines).

Why do the calculation?

Sizing a stationary battery is important to ensure that theloads being supplied or the power system beingsupported are adequately catered for by the battery forthe period of time (i.e. autonomy) for which it isdesigned. Improper battery sizing can lead to poorautonomy times, permanent damage to battery cells fromover-discharge, low load voltages, etc.

When to do the calculation?

Battery Sizing - Open Electrical http://www.openelectrical.org/wiki/index.php?title=Battery_Sizing

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The calculation can typically be started when the following information is known:

Battery loads that need to be supportedNominal battery voltageAutonomy time(s)

The calculation is based on a mixture of normal industry practice and technical standards IEEE Std 485(1997, R2003) (http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=4899) "RecommendedPractice for Sizing Lead-Acid Batteries for Stationary Applications" and IEEE Std 1115 (2000, R2005)(http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6976) "Recommended Practice for SizingNickel-Cadmium Batteries for Stationary Applications". The calculation is based on the ampere-hour methodfor sizing battery capacity (rather than sizing by positive plates).

The focus of this calculation is on standard lead-acid or nickel-cadmium (NiCd) batteries, so please consultspecific supplier information for other types of batteries (e.g. lithium-ion, nickel-metal hydride, etc). Notealso that the design of the battery charger is beyond the scope of this calculation.

There are five main steps in this calculation:

1) Collect the loads that the battery needs to support2) Construct a load profile and calculate the design energy (VAh)3) Select the battery type and determine the characteristics of the cell4) Select the number of battery cells to be connected in series5) Calculate the required Ampere-hour (Ah) capacity of the battery

Step 1: Collect the battery loads

The first step is to determine the loads that the battery will be supporting. This is largely specific to theapplication of the battery, for example an AC UPS System or a Solar Power System.

Step 2: Construct the Load Profile

Refer to the Load Profile Calculation for details on how to construct a load profile and calculate the designenergy, , in VAh.

The autonomy time is often specified by the Client (i.e. in their standards). Alternatively, IEEE 446, "IEEERecommended Practice for Emergency and Standby Power Systems for Industrial and CommercialApplications" has some guidance (particularly Table 3-2) for autonomy times. Note that IEEE 485 and IEEE1115 refer to the load profile as the "duty cycle".

Step 3: Select Battery Type

The next step is to select the battery type (e.g. sealed lead-acid, nickel-cadmium, etc). The selection processis not covered in detail here, but the following factors should be taken into account (as suggested by IEEE):

Physical characteristics, e.g. dimensions, weight, container material, intercell connections,terminalsapplication design life and expected life of cellFrequency and depth of dischargeAmbient temperatureCharging characteristics


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Maintenance requirementsVentilation requirementsCell orientation requirements (sealed lead-acid and NiCd)Seismic factors (shock and vibration)

Next, find the characteristics of the battery cells, typically from supplier data sheets. The characteristics thatshould be collected include:

Battery cell capacities (Ah)Cell temperatureElectrolyte density at full charge (for lead-acid batteries)Cell float voltageCell end-of-discharge voltage (EODV).

Battery manufacturers will often quote battery Ah capacities based on a number of different EODVs. Forlead-acid batteries, the selection of an EODV is largely based on an EODV that prevents damage of the cellthrough over-discharge (from over-expansion of the cell plates). Typically, 1.75V to 1.8V per cell is usedwhen discharging over longer than 1 hour. For short discharge durations (i.e. <15 minutes), lower EODVs ofaround 1.67V per cell may be used without damaging the cell.

Nickel-Cadmium (NiCd) don't suffer from damaged cells due to over-discharge. Typical EODVs for Ni-Cdbatteries are 1.0V to 1.14V per cell.

Step 4: Number of Cells in Series

The most common number of cells for a specific voltage rating is shown below:

RatedVoltage

Lead-Acid Ni-Cd

12V 6 9-10

24V 12 18-20

48V 24 36-40

125V 60 92-100

250V 120 184-200

However, the number of cells in a battery can also be calculated to more accurately match the tolerances ofthe load. The number of battery cells required to be connected in series must fall between the two followinglimits:

(1)

(2)

where is the maximum number of battery cells

is the minimum number of battery cells is the nominal battery voltage (Vdc)

is the maximum load voltage tolerance (%)


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is the minimum load voltage tolerance (%)

is the cell charging voltage (Vdc) is the cell end of discharge voltage (Vdc)

The limits are based on the minimum and maximum voltage tolerances of the load. As a maximum, thebattery at float voltage (or boost voltage if applicable) needs to be within the maximum voltage range of theload. Likewise as a minimum, the battery at its end of discharge voltage must be within the minimum voltagerange of the load. The cell charging voltage depends on the type of charge cycle that is being used, e.g. float,boost, equalising, etc, and the maximum value should be chosen.

Select the number of cells in between these two limits (more or less arbitrary, though somewhere in themiddle of the min/max values would be most appropriate).

Step 5: Determine Battery Capacity

The minimum battery capacity required to accommodate the design load over the specified autonomy timecan be calculated as follows:

where is the minimum battery capacity (Ah)

is the design energy over the autonomy time (VAh) is the nominal battery voltage (Vdc)

is a battery ageing factor (%) is a temperature correction factor (%) is a capacity rating factor (%)

is the maximum depth of discharge (%)

Select a battery Ah capacity that exceeds the minimum capacity calculated above. The battery dischargerate (C rating) should also be specified, approximately the duration of discharge (e.g. for 8 hours ofdischarge, use the C8 rate). The selected battery specification is therefore the Ah capacity and the dischargerate (e.g. 500Ah C10).


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Temperature correction factors for vented lead-acid cells(from IEEE 485)

An explanation of the different factors:

Ageing factor captures the decreasein battery performance due to age.

The performance of a lead-acidbattery is relatively stable but dropsmarkedly at latter stages of life. The"knee point" of its life vsperformance curve is approximatelywhen the battery can deliver 80% ofits rated capacity. After this point,the battery has reached the end ofits useful life and should bereplaced. Therefore, to ensure thatbattery can meet capacitythroughout its useful life, an ageingfactor of 1.25 should be applied (i.e.1 / 0.8). There are some exceptions,check with the manufacturer.

For Ni-Cd batteries, the principlesare similar to lead-acid cells. Pleaseconsult the battery manufacturer forsuitable ageing factors, but generally, applying a factor of 1.25 is standard. For applications withhigh temperatures and/or frequent deep discharges, a higher factor of 1.43 may be used. Formore shallower discharges, a lower factor of 1.11 can be used.

Temperature correction factor is an allowance to capture the ambient installationtemperature. The capacity for battery cells are typicall quoted for a standard operatingtemperature of 25C and where this differs with the installation temperature, a correction factormust be applied. IEEE 485 gives guidance for vented lead-acid cells (see figure right), howeverfor sealed lead-acid and Ni-Cd cells, please consult manufacturer recommendations. Note thathigh temperatures lower battery life irrespective of capacity and the correction factor is forcapacity sizing only, i.e. you CANNOT increase battery life by increasing capacity.

Capacity rating factor accounts for voltage depressions during battery discharge. Lead-acidbatteries experience a voltage dip during the early stages of discharge followed by somerecovery. Ni-Cds may have lower voltages on discharge due to prolonged float charging(constant voltage). Both of these effects should be accounted for by the capacity rating factor -please see the manufacturer's recommendations. For Ni-Cd cells, IEEE 1115 Annex C suggeststhat for float charging applications, Kt = rated capacity in Ah / discharge current in Amps (forspecified discharge time and EODV).


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Load profile for this example

Step 1 and 2: Collect BatteryLoads and Construct Load Profile

The loads and load profile from the simpleexample in the Energy Load ProfileCalculation will be used (see the figureright). The design energy demandcalculated for this system is Ed = 3,242.8VAh.

Step 3: Select Battery Type

Vented lead acid batteries have beenselected for this example.

Step 4: Number of Cells in Series

Suppose that the nominal battery voltage isVdc = 120Vdc, the cell charging voltage is Vc = 2.25Vdc/cell, the end-of-discharge voltage is Veod =1.8Vdc/cell, and the minimum and maximum load voltage tolerances are Vl,min = 10% and Vl,max = 20%respectively.

The maximum number of cells in series is:

cells

The minimum number of cells in series is:

cells

The selected number of cells in series is 62 cells.

Step 5: Determine Battery Capacity

Given a depth of discharge kdod = 80%, battery ageing factor ka = 25%, temperature correction factor forvented cells at 30 deg C of kt = 0.956 and a capacity rating factor of kc = 10%, the minimum batterycapacity is:

Ah


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Some battery manufacturers (such as Alcad (http://www.alcad.com/) ) also provide software programs tosize batteries using basic input data such as load profiles, autonomies, etc. The software will size the batteriesand will often also provide details regarding different battery rack (or enclosure) dimensions.

Using the results of the battery sizing calculation, the approximate dimensions of the batteries can beestimated based on typical vendor information. This will assist in determining the size, number anddimensions of the battery racks or cabinets required, which can then be used as input into the equipment /room layouts. Preliminary budget pricing can also be estimated based on the calculation results.

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This page was last modified on 5 March 2011, at 10:39.


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