Sizing battery banks for switchgear and control applications is commonly performed using software designed specifically for that purpose. Just input the required load profile, and the program selects the optimum battery configuration. Although this is quite simple, an engineer should be capable of performing a straightforward hand calculation — either to confirm the results of a software-generated solution or to serve as an accurate design for a simple battery system. Do you know how to perform these calculations by hand? If not, then read on. This article will help you understand the basic premise of sizing switchgear battery systems and provide an example calculation for clarification of the concept. IEEE Standard 485-1997, “Recommended Practice for Sizing Lead-Acid Batteries for Stationary Applications,” also provides detailed guidelines for battery sizing.
Number of cells Battery banks for switchgear and control applications are made up of many cells. These cells are typically wired in series to achieve a desired voltage and may also be wired in parallel to achieve additional ampere capacity. Sizing of these battery banks, therefore, includes selecting the number and type of cells to be used. The terminal voltage per cell varies with the battery's chemical composition. The required number of series wired cells to achieve the more common DC control voltages for switchgear control is shown in Table 1. Selection of the type of cell is based on the required peak ampere output and total Ampere-hour (Ah) output capacity for the load and duration. Table 1
Load type IEEE Standard 485-1997 classifies individual DC loads as continuous, non-continuous, and momentary. Typical continuous loads include lighting, continuously energized coils, and power to protective relay and communications systems. Non-continuous loads are less common and include critical ventilation system motors and valve actuators with operating times exceeding 1 minute. Momentary loads do not exceed 1 minute in duration and include inrush currents and circuit breaker operations. The duty cycle imposed on switchgear batteries usually consists of momentary high ampere loading during charging of the respective tripping or closing springs, in addition to the small continuous load of powering protective relays and lights. While both motors for charging the tripping or closing springs can be DC, the more common switchgear design uses an AC closing motor and a DC tripping motor. Such a design reduces the total DC load because tripping is of the utmost importance — particularly when a fault occurs. However, this only allows one full operational cycle following a power failure because there is no AC to charge the closing spring.
Sizing guidelines Since the momentary load on a switchgear battery bank is much higher than the continuous load, the required 1minute (peak) ampere rate typically determines the battery cell type. However the Ampere-hour rate should also be checked. The battery cell type that meets the wors t-case condition between the two should be selected. These rates are tabulated in the manufacturer's standard literature at s everal final voltages. Use the rates published at a final voltage of 1.75 volts-per-cell for lead acid cells or 1.14 volts-per-cell for nickel cadmium cells. As an example, the data in Table 2 on page 43 is excerpted from a manufacturer's Web site. (The model designations are fictitious.) Table 2 To calculate the required 1-minute ampere rate, assume the peak rate to be equal to the sum of the loads (i.e. in-rush current for all breaker charging motors, load currents for all relays and other loads, and ignore pilot lights). Although momentary loads usually exist for much less than a minute — perhaps only a fraction of a second — it is common practice to use the full ampere value for an entire minute. Assign a required 1-minute rate equal to this peak rate divided by the ambient temperature derating factor, the battery aging factor, and a design margin as listed in Table 3 on page 43. Table 3 To calculate the required Ampere-hour rate, compute the average continuous load and divide by the ambient temperature-derating factor and battery-aging factor, as listed in Table 3. Use the manufacturer's data to select the battery cell type that meets both the ampere and Ampere-hour requirements.
Sample calculation To use a hypothetical real-world example, calculate the battery size for the 69kV substation loads listed in Table 4. The battery type shall be lead acid, operate the given loads for 8 hours at 125VDC, and be housed in a climatecontrolled building. Table 4 Step 1: Calculate the required 1-minute discharge rate. As can be seen in Table 4, the peak discharge rate is 96.2A. Divide this number by an ambient temperature factor of one for a 77°F room, by a 0.8 battery-aging factor, and by 0.85 for the design margin. Required 1-minute discharge rate = 96.2 A ÷ 0.8 ÷ 0.85 = 141.5A Step 2 : Calculate the required Ampere-hour (Ah) rate. As can be seen in Table 5, the total Ampere-hour rate is 27.1 Ah. Divide by an ambient temperature factor of one for a 77°F room, and by a 0.8 battery-aging factor. Required total Ah rate = 27.1 Ah ÷ 0.8 = 33.9 Ah Table 5 Step 3: Select the appropriate cell from the manufacturer's literature. Referring back to Table 2, a Model A battery has a 1-minute discharge rate of 177A and an 8-hour Ah rate of 180 Ah, down to 1.75V. This type of battery is, therefore, more than sufficient for this particular load. The 125VDC, 180 Ah battery bank would be composed of 60 Model A cells.
Back to basics So whether you're one of those people that refuses to trust a computer farther than y ou can throw it — or you simply feel more comfortable double checking calculations by hand — possessing the knowledge to size battery banks for
switchgear the old-fashioned way is a good skill for any engineer to master. Not only will you impress your peers, but you'll also feel more confident about recommending a rock solid switchgear solution. Hall is an electrical engineer based in the Las Vegas office of CH2M HILL, Inc. Table 1. String together 37 individual Ni-Cad batteries in series to achieve a control voltage of 48V. Battery Type Control Voltage Ni-Cad Lead acid 48VDC 37 cells 24 cells 125VDC 92 cells 60 cells 250VDC 184 cells 120 cells Table 2. Ampere-hour and ampere rates for four different battery models offered by one manufacturer. Nominal Rates at 77°F (25°C) Final Volts Models Ampere-Hours (Ah) Amperes (A) 8-hr 4-hr 3-hr 1.5-hr 1-hr 30 min 15 min 1 min 1.75V A 180 142 132 65 81 109 134 177 B 250 210 195 98 126 172 219 303 C 330 280 260 130 168 230 292 404 D 410 350 326 163 204 285 362 500 Table 3. Design factors to be used when calculating Ampere-hour rates for Ni-Cad and lead-calcium batteries. Battery Type Derating Function Ni-Cad Lead-Calcium Ambient temperature 77°F 1.0* 1.0* 32°F 0.7 0.67 0°F 0.5 0.8 Battery aging factor 0.8* 0.8* Design margin 0.85* 0.85* *Per IEEE Std. 485 recommended practice Table 4. Peak discharge rate for a hypothetical 69kV substation load. 125VDC Load Description Quantity Current (A) Subtotal (A) 69kV circuit switchers 2 15.0 30.0 69kV substation relays 8 0.2 1.6 5kV vacuum breakers 9 7.0 63.0 5kV switchgear relays 8 0.2 1.6 5kV switchgear indicating lights Ignore 0.0 0.0 Total 96.2A Table 5. Required Ampere-hour rate for a hypothetical 69kV substation load. 125VDC Load Description Quantity Current (A) Hours (h) Subtotal (Ah) 69kV circuit switchers 2 15.0 0.016* 0.5 69kV substation relays 8 0.2 8.0 12.8 5kV vacuum breakers 9 7.0 0.016* 1.0 5kV switchgear relays 8 0.2 8.0 12.8 5kV switchgear indicating lights Ignore 0.0 8.0 0.0 Total 27.1 Ah *0.016 hours = 1 minute
Definitions battery duty cycle - the load (including duration) the battery is expected to supply
cell size - rated capacity of the battery
equalizing charge - prolonged charge, at a rate higher than the normal float voltage
full float operation - operation with the batteries and load connected in parallel
period - time during which load is expected to be constant during sizing calculations
rated capacity - capacity of the battery cell (usually for a given discharge rate and end of cell voltage)
valve-regulated lead-acid (VRLA) cell - sealed lead-acid cell (with the exception of a valve that opens when the internal pressure exceeds the external pressure)
vented battery - battery in which the products of electrolysis and evaporation are allowed to escape freely to the atmosphere
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Battery Selection
The selection of the physical battery (cells) is dependant on several factors:
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type of battery (sealed, vented, lead acid, NiCad, etc.) expected life of the battery usage of the batter (number of charge/discharge cycles) dimensions and weight of the battery construction materials connectors and terminals ambient environment and conditions maintenance requirements seismic characteristics
Ampere-hour and Watts/cell
The Ah or Ampere-hour capacity is the current a battery can provide over a specified period of time. For example 100Ah @ C10 rate to end of discharge of 1.75 V/cell means the battery can provide 10 Amps for 10 hours to an end of discharge voltage of 1.75 V per cell.
Different battery manufacturers will use different Cxx rates depending on the market or application at which their batteries are targeted. Typical rates used are C3, C5, C8, C10 and C20. Because of this it is important, when comparing batteries from different manufacturers. Ah is used for sizing batteries based on constant current methods and watts/cell on constant power methods.
IEEE 485 Lead Acid Batteries for Stationary Applications
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This standard details methods for defining the dc loads and for sizing a lead-acid battery to supply those loads in full float operation. A brief description of the method presented by the standard follow. For a full and accurate description, refer to the full standard. [edit] Load Definition
Loads are classified as:
continuous - loads continually present noncontinuous - loads lasting for a specific period momentary - loads lasting for less than 1 minute Typical Loads
Continuous
Noncontinuous Emergency motors
Momentary Switchgear operations
Lighting Fire protection systems Valve operations ( < 1 min) Valve operations ( > 1 min) Isolating switch operations Continuous Motors Field flashing of generators Converters Motor starting currents Indicating Lights Inrush currents UPS Control Systems
Note: commonly momentary loads are assumed to last for 1 minute during battery sizing calculations.
[edit] Duty Cycle Diagram
The standard recommends a duty cycle be drawn showing the anticipated loads (in Amperes or power ) for the required duration of battery backup time.
IEEE 485 Std. Recommended Practice for Sizing Lead Acid Batteries for Stationary Applications - Typical Duty Cycle
Considerations
loads and times where known should be shown
random loads should be shown at the most critical times
[edit] Calculation of Battery Size
Number of Cells and Cell Voltage The mumber of cells is estimated based on the maximum battery voltage and float charge voltage:
The minimum battery voltage is the minimum system voltage (including voltage drops across cables). Given the minimum cell voltage the minimum cell voltage is given by:
Temperature Correction At temperature decreases the capacity of a cell decreases (and vise verse as the temperature increases). Manufacturers quote cell capacity at a given temperature and appropriate correction factors should be used for other temperatures. Aging Factor Battery performance is relatively stable through out its life, dropping of rapidly towards the end. To ensure the battery can meet the design requirements throughout its life the standard suggestions the initial capacity should be 125% of the design capacity. Design Margin To cater for unexpected circumstances (increased loads, poor maintenance, recent discharge, etc.) it is common to allow a design margin of 10% to 15%.
IEEE 485 Std. Recommended Practice for Sizing Lead Acid Batteries for Stationary Applications - Typical Duty Cycle
Sizing Methodology The required capacity of the cell F S is given by:
Where S can be any integer from 1 to N depending on the section being calculated and FS is expressed in watt-hours or ampere-hours depending on which Ct is used.
The required uncorrected cell size F, is then given by:
where:
F - is the uncorrected (temperature, aging and design margin) cell size
S - is the section of duty cycle being studied (containing all previous sections)
N - is the number of periods in the duty cycle
P - is the period being analyzed
AP - the amperes required for period P
t - the time in minutes from the beginning of period P through the end of Section S
Ct - is the capacity rating factor (for a given cell type, at the t minute discharge rate, at 25 °C, to a definite minimum cell voltage
FS - is the capacity required by each section
[edit] Capacity rating factor
There are two ways of expressing capacity: Term
R t
The term R t is the number of amperes each plate can supply for t minutes, at 25 o C to a defined minimum cell voltage.
giving:
Term
K t
The term K t is the ration of ampere-hour capacity, at a standard time rate, at 25 o C and to a defined minimum voltage which can be delivered for t minutes.
giving:
R t is not equal to 1/K t because each factor is expressed in different units. [edit]
References
IEEE Std. 485 'IEEE Recommended Practice for Sizing lead-Acid Batteries for Stationary Applications
