Chapter 26 - Battery Sizing and Discharge Analysis

ETAP
PowerStation 4.0




User Guide
Copyright  2001
Operation Technology, Inc.
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Chapter 26
Battery Sizing & Discharge Analysis
Batteries are an essential part of a critical DC power system, serving as the backup power source under
emergency conditions. During normal operating conditions, a DC system is generally powered by AC
sources through chargers or other AC–DC interface components. However, the battery has to provide
power to the system under one of the following conditions:
1. Load on the DC system exceeds the maximum output of the battery charger
2. Output of the battery charger is interrupted
3. Auxiliary AC power is lost
The battery should be sized for the most severe of these conditions, which most likely is the third
condition. When the AC power is lost, batteries will provide power to critical loads and control circuits
for a specified time period so that the AC power source can be recovered or the critical equipment can be
adequately shut down. For example, in US nuclear power plants, it is required that batteries have
sufficient capacity to supply the required load during a loss of AC power for field flashing, control
circuits, DC fuel oil booster pumps, and DC lube oil pumps for a period of four hours. In order to meet
this requirement, battery sizing calculations need to be carried out to determine the appropriate battery
size.
The ETAP PowerStation Battery Sizing program provides you with a powerful tool to accomplish this
task. In complying with IEEE Standard 485, it determines the number of strings, number of cells, and
cell size of a battery for a designated duty cycle. The number of cells is determined to satisfy the
maximum system voltage during the battery charging period and the minimum system voltage during the
battery discharging period. The number of strings and cell size is determined to provide sufficient power
to the load cycle considering the minimum system voltage and the minimum operating temperature. It
also considers different factors that affect battery performance, such as design margin, aging
compensation, initial capacity, and temperature, etc.
The duty cycle for the battery can be a summation of the duty cycles of all the loads that the battery is to
supply power for. It can also be calculated using DC load flow, which considers different characteristics
of constant power load and constant impedance load, their variations to voltage changes, branch voltage
drops and losses. The battery duty cycle includes both random load and non-random load from individual
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Battery Sizing & Discharge Analysis

Study Toolbar

loads. In compliance with IEEE Standard 485, the load impulses in the battery duty cycle that are less
than one minute are automatically extended to one minute.
To verify the performance of an existing or a sized battery, ETAP PSMS also provides a Battery
Discharging Analysis program. The program calculates the battery capacity, voltage, current, and output
power as the battery discharges through a duty cycle. The battery duty cycle can be calculated from
either load current summation or load flow calculations. When the battery duty cycle is calculated from
load flow, the Battery Discharging Analysis also provides bus voltage and branch power along with
battery output results. Several correction factors used in battery sizing calculation, such as battery
temperature, aging and initial capacity, can also be considered in the battery discharge calculations.

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Study Toolbar

26.1 Study Toolbar
The Battery Sizing Study Toolbar will appear on the screen when you are in Battery Sizing Study mode.

Run Battery Sizing Calculation
Click on this button to initiate a battery sizing calculation. If the battery size is determined, a battery
discharging calculation will automatically follow to verify the battery capability. Note that PowerStation
will give you an error message indicating missing information if you have not entered all of the data
required for the calculation.

Run Battery Discharge Calculation
Click on this button to initiate a battery discharge calculation on an existing battery using the method
specified in the battery sizing info and discharge pages. Just like in battery sizing, PowerStation will give
you an error message if any required data is still missing.

Display Options
Click on this button to customize the information and results annotations displayed on the one-line
diagram in Battery Sizing mode.

Battery Sizing Report Manager
Click on this button to open the Battery Sizing Report Manager. You can also view output reports by
clicking on the View Output Report button on the Study Case Toolbar.

Battery Sizing Plots
Click on this button to view output plots.

Halt Current Calculation
Click on the Stop Sign button to halt the current calculation.

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Study Toolbar

Get Online Data
If the ETAP key installed on your computer has the online feature, you can copy the online data from the
online presentation to the current presentation.

Get Archived Data
If the ETAP key installed on your computer has the online feature, you can copy the archived data to the
current presentation.

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Study Case Editor

26.2 Study Case Editor
The Battery Sizing Study Case Editor contains parameter settings required to perform a battery sizing
calculation. The calculation results are dependent on these setting. When a new study case is created,
ETAP PowerStation provides the default parameters. However, it is important to set the values correctly
in the study case to meet your calculation requirements.
The Battery Sizing Study Case Editor includes three pages: the Information page, the Sizing page, and the
Discharge page. On the Information page, you specify the battery to be sized, select the duty cycle to be
considered, and enter the diversity factor that allows you to globally adjust system load.
On the Sizing page, you specify sizing requirements and correction factors for the calculation.
The Discharge page contains parameters for battery discharging calculations and will be available in
future versions of ETAP PowerStation.

26.2.1 Info Page

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Study Case Editor

Study Case ID
ID
Enter a unique alphanumeric ID with a maximum of 12 characters. PowerStation automatically assigns a
unique ID for a new study case.

Battery
ID
Select a battery to be sized from the drop down list.

Duty Cycle From
Specify the method for determining the battery duty cycle. For ETAP PowerStation 3.0, only the Load
Current Summation option is available.
Load Current Summation
Select this option to determine the battery duty cycle by using the load summation method. The battery
duty cycle will be equal to the sum of the load duty cycles for all the loads powered by the battery.
DC Load Flow Calculation
Select this option to determine the battery duty cycle by performing DC load flow calculations. This
method considers branch losses and voltage drops in determining battery duty cycle.

Correction Factor
Temperature
Click on this check box to specify the temperature to be used as correction factor in battery sizing and
discharge calculations. Once the box is checked, you have two choices for specifying the temperature:
using the battery minimum temperature from the Battery Editor or entering a desired temperature value.

Aging Compensation
Enter here the aging compensation correction factor in percent to be used in sizing and discharge
calculations.

Initial Capacity
Enter here the initial capacity correction factor in percent to be used for the battery sizing and discharge
calculations.

Load
Duty Cycle
Select the duty cycle from the dropdown list for battery sizing. Every load has five different duty cycles.

Duration
Select either the Hours or Duty Cycle Span option to specify the length of time to size the battery. You
must specify the length of duration (number of hours) if you use the Hours option by selecting a value
from the dropdown list or entering a value.

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Study Case Editor

Diversity Factor
Specify the load diversity factor in percent. The load used in battery sizing will be multiplied by this
diversity factor.

Remarks 2nd Line
You can enter up to 120 alphanumeric characters in this remark box. Information entered here will be
printed on the second line of every output report page header. These remarks can provide specific
information regarding each study case. Note that the first line of the header information is global for all
study cases and entered in the Project Information Editor.

26.2.2 Sizing Page

Voltage Requirements
Maximum System Voltage Deviation
Specify the maximum system operating voltage in percent based on the nominal voltage of the terminal
bus of the battery selected for sizing.

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Study Case Editor

Minimum. System Voltage Deviation
Specify the minimum system operating voltage in percent based on the nominal voltage of the terminal
bus of the battery selected for sizing.

Battery Charge Voltage
Specify the required voltage in V/Cell to charge the battery to be sized.

Battery Minimum Discharge Voltage
Specify the minimum discharge voltage in V/Cell for the battery to be sized.

Correction Factor
In this section, you specify the correction factors to be considered in battery sizing calculations.

Temperature
Click on this check box to use the temperature correction factor in battery sizing calculations. Once the
box is checked, the temperature value specified in the Info Page is displayed here.

Aging Compensation.
Click on this check box to use the aging compensation correction factor specified in the Info Page.

Initial Capacity
Click on this check box to use the initial capacity correction factor specified in the Info Page.

Design Margin
Click on this check box to use the design margin correction factor specified in the edit box.

Perform Discharge Calculation
This option will be available in future releases of ETAP PowerStation.

Update Battery Size
This option will be available in future releases of ETAP PowerStation.

Battery Library
Use Sizes Given in Library Only
Select this option to use only the sizes given in the library. For example, if the library has battery curves
for 11, 13, and 21 plates, then only these three sizes will be considered in the battery sizing calculation.

Use Sizes in Library as Min/Max Range
Select this option to use the sizes given in the library as the maximum and minimum limits. For example,
if the library has battery curves for 11, 13, and 21 plates, then it is assumed that batteries with 15, 17, and
19 plates are also available and the characteristic curves of these sizes are assumed to be the same as that
for the 21-plate battery.

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Study Case Editor

Options
Desirable Number of Cells
When this box is checked, in the battery sizing calculation, the value entered in the edit box will be the
number of cells for the battery, if this number is within the acceptable range determined based on the
voltage requirements. In case this number is outside the acceptable range, the number of the cells will be
selected so that the battery rated voltage is closest to the terminal bus rated voltage.

Update Battery Size
If this box is checked, when the battery sizing calculation has completed successfully, the program will
update the battery to the calculated size automatically. In order to make certain that a battery always has
corresponding library data for its size, this field is enabled only when the “Use Sizes Given in Library
Only” in the Battery Library section is checked.

26.2.3 Discharge Page

Vd Calc Parameters
Battery discharge calculation uses the information included in these fields in order to determine how the
voltage drop calculation will be performed.

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Study Case Editor

Time Step
The Time Step parameter is the time interval at which a plot point is to be generated. A plot point is also
generated at the times when load changes occur. This value will affect time of calculations, especially in
the case that the battery duty cycle is obtained by the load flow method.

Amax Limit
This feature allows the user to specify the maximum voltage value at the battery terminal. The default
value is 100% of the battery rated voltage. The calculated battery voltage will be limited at this value.

Correction Factors
This section of the battery discharge page provides a set of correction factors to be used during the battery
discharge cycle. Similar to battery sizing calculations, the adjusting factors have either a positive or a
negative effect on the battery AH capacity (Amp Hour) or the battery duty cycle. With these features, the
user is able to simulate the effect on the battery of operating temperature, battery maintenance conditions,
and aging factor. The user has the choice of applying the correction factors to the battery duty cycle or to
the battery initial AH capacity. The program calculates a total correction factor by multiplying the
temperature CF and the Aging Compensation CF and then divided by the initial Capacity CF.

Adjust Battery Capacity
If you select this feature, the correction factors are used to the battery capacity. The battery initial
ampere-hour capacity is as the rated capacity divided by the total correction factor.

Adjust Battery Duty Cycle
If this feature is used, the correction factor will used to modify battery duty cycle. The battery duty cycle
used in the discharge calculation is adjusted by multiplying by the total correction factor.

Temperature
Select this check box if you want the temperature correction factor to be used in battery discharge
calculations. This factor has the effect of either increasing or decreasing battery capacity. The
temperature correction factor is applied according to the IEEE method described in standard 485 for
correcting cell size in sizing calculations. The same standard applies for discharge calculations. IEEE
provides values between – 4°C and +52°C. Any value outside of this range is curve fitted using the IEEE
recommended curve-shifting method (PowerStation checks the temperature value and provides a user
message indicating that the entered temperature is out of normal range). When the box is not checked, the
temperature correction factor is assumed to be 100%.

Aging Compensation
Select this check box if you would like to use the aging compensation correction factor in battery
discharge calculations. When this factor is applied, the battery discharge simulation includes a decrease
in battery capacity due to aging. When the box is not checked, the aging correction factor is assumed to
be 100%.

Initial Capacity
Check this check box to use the initial capacity correction factor percent specified in the information
page. When the box is not checked, the initial capacity correction factor is assumed to be 100%.

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Study Case Editor

LF Parameters (Newton-Reason)
This section of the battery sizing discharge page becomes active if the Load Flow duty cycle calculation
method is selected form the info page. If the Current Summation method is used, this section remains
grayed out.

Maximum Iteration
Enter the maximum number for iterations. If the solution has not converged before the specified number
of iterations, a message will show up to flag the user.

Precision
Enter the value for the solution precision to be used to check for convergence. This value determines how
precise you want the final solution to be. A load flow solution is reached if, between two iterations, the
maximum bus voltage difference in per unit is less than the specified precision value.

Initial Condition
Similar to the LF Parameter Section, this part of the discharge page only has an effect if the Load Flow
method for battery discharge is selected from the Info Page. If the load flow method is indeed selected,
then the information entered in this area is used to initialize the Newton-Raphson load flow calculation.

Use Bus Voltage
The Newton- Raphson calculation method is highly dependent on initial conditions. If this radio box is
selected, the initial bus voltage will be set according to the bus nominal voltage multiplied by the initial
voltage entered in the Bus Editor. It should be noted that the DC Load Flow calculation performed for
battery discharge does not update the initial bus voltage values. If initial bus voltage values are required,
then the user should run a DC Load Flow study to update the initial bus voltages, then select this option to
run the discharge calculation using bus initial voltage values.

Use Fixed Value
When selecting this option, the voltage values used to initialize the Newton-Raphson calculation are equal
to the flat fixed voltage percent value specified here.

Motor Load
A motor normally behaves as a constant power load when its terminal voltage is close to its rated voltage.
However, as the battery terminal voltage deviates considerably from its rated voltage, its behavior
becomes similar to a static load. This section allows you to set the voltage range within which you want a
motor to be modeled as a constant power load.

Constant kW if V within Range
Click on this check box for setting VMin and VMax. When the motor terminal voltage is within this
range, it is represented as a constant power load. However, once the voltage is outside this range, it is
automatically converted to a constant impedance load.
If this box is not checked, all of the motor loads will be modeled as constant power loads regardless of
their terminal voltage. Please note that when there are only constant current sources in the system, this
may prohibit load flow calculations from reaching a solution.

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Study Case Editor

Vmin
Enter the minimum voltage in percent, below which the motor load will be modeled as a constant
impedance load.

Vmax
Enter the maximum voltage in percent, above which the motor load will be modeled as a constant
impedance load.

Report
Similar to DC Load Flow Calculations, If at any point during the specified battery discharge cycle (using
DCLF method) a bus voltage falls below the percent value specified in the Under Voltage field, this
information will be flagged in the One-Line diagram. The same is true for buses violating over voltage
limit.

Critical Voltage
Select this option and enter the minimum and maximum voltages that any bus may achieve before it is
flagged. The buses violating the critical voltage limits will be flagged in red color in the one-line
diagram.

Marginal Voltage
Select this option and enter the minimum and maximum voltages that any bus may achieve before it is
flagged as a marginally undervoltage or overvoltage bus. The buses violating the marginal voltage limits
will be flagged in pink color in the one-line diagram.

Bus Voltage
Calculated bus voltages displayed in the plot and one-line diagram can be given in kV or in percent of the
bus nominal voltages. Select your preference by clicking on Percent or V options.

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Battery Sizing & Discharge Analysis

Display Options

26.3 Display Options
The Battery Sizing Display Options consist of a Results page and three pages for AC, AC-DC, and DC
info annotations. Note that the colors and displayed annotations selected for each study are specific to
that study.

26.3.1 Results Page

Color
Select a color for displaying calculation results on the one-line diagram.

Voltage
Bus Display Unit
From the drop down list, select to display the bus voltage in percent or in volt.

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Display Options

Battery
Click on this check box to show the battery voltage in the one-line diagram.

Bus
Click on this check box to show the bus voltage in the one-line diagram.

Power Flows
Power Flow Display Units
Select the power flow to be displayed in kW or MW.

kW and Amp
Select kW to display power flow or select Amp to display the current in amperes.

Show Units
Check this box to show the unit with calculation results displayed on the one-line diagram.

Elements
Click on these check boxes to display load flow results for different types of elements, including Branch,
Source, Load, Composite Motor, and Composite Network.

24.3.2 AC Page
This page includes options for displaying info annotations for AC elements.

Color
Select the color for information annotations to be displayed on the one-line diagram.

ID
Select the check boxes under this heading to display the ID of the selected AC elements on the one-line
diagram.

Rating
Select the check boxes under this heading to display the ratings of the selected AC elements on the oneline diagram.

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Device Type
Gen. (Generator)
Power Grid (Utility)
Motor
Load
Panel
Transformer
Branch, Impedance
Branch, Reactor
Cable / Line
Bus
Node
CB
Fuse
Relay

Display Options

Rating
kW / MW
MVAsc
HP / kW
kVA / MVA
Connection Type (# of Phases - # of Wires)
kVA / MVA
Base MVA
Continuous Amps
# of Cables - # of Conductor / Cable - Size
kA Bracing
Bus Bracing (kA)
Rated Interrupting (kA)
Interrupting (ka)
50/51 for Overcurrent Relays

kV
Select the check boxes under this heading to display the rated or nominal voltages of the selected
elements on the one-line diagram.
For cables/lines, the kV check box is replaced by the
cable/line conductor type on the one-line diagram.

button. Click on this button to display the

A
Select the check boxes under this heading to display the ampere ratings (continuous or full-load ampere)
of the selected elements on the one-line diagram.
For cables/lines, the Amp check box is replaced by the
cable/line length on the one-line diagram.

button. Click on this button to display the

Z
Select the check boxes under this heading to display the rated impedance of the selected AC elements on
the one-line diagram.
Device Type
Generator
Power Grid (Utility)
Motor
Transformer
Branch, Impedance
Branch, Reactor
Cable / Line

Impedance
Subtransient reactance Xd”
Positive Sequence Impedance in % of 100 MVA (R + j X)
% LRC
Positive Sequence Impedance (R + j X per unit length)
Impedance in ohms or %
Impedance in ohms
Positive Sequence Impedance (R + j X in ohms or per unit length)

D-Y
Select the check boxes under this heading to display the connection types of the selected elements on the
one-line diagram.
For transformers, the operating tap setting for primary, secondary, and tertiary windings are also
displayed. The operating tap setting consists of the fixed taps plus the tap position of the LTC.

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Display Options

Composite Motor
Click on this check box to display the AC composite motor IDs on the one-line diagram, then select the
color in which the IDs will be displayed.

Use Default Options
Click on this check box to use PowerStation’s default display options.

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Display Options

26.3.3 AC-DC Page
This page includes options for displaying info annotations for AC-DC elements and composite networks.

Color
Select the color for information annotations to be displayed on the one-line diagram.

ID
Select the check boxes under this heading to display the IDs of the selected AC-DC elements on the oneline diagram.

Rating
Select the check boxes under this heading to display the ratings of the selected AC-DC elements on the
one-line diagram.
Device Type
Charger
Inverter
UPS
VFD

Rating
AC kVA & DC kW (or MVA / MW)
DC kW & AC kVA (or MW / MVA)
kVA
HP / kW

kV
Click on the check boxes under this heading to display the rated or nominal voltages of the selected
elements on the one-line diagram.

A
Click on the check boxes under this heading to display the ampere ratings of the selected elements on the
one-line diagram.
Device Type
Charger
Inverter
UPS

Amp
AC FLA & DC FLA
DC FLA & AC FLA
Input, output, & DC FLA

Composite Network
Click on this check box to display the composite network IDs on the one-line diagram, then select the
color in which the IDs will be displayed.

Use Default Options
Click on this check box to use PowerStation’s default display options.

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Display Options

26.3.4 DC Page
This page includes options for displaying info annotations for DC elements.

Color
Select the color for information annotations to be displayed on the one-line diagram.

ID
Select the check boxes under this heading to display the IDs of the selected DC elements on the one-line
diagram.

Rating
Select the check boxes under this heading to display the ratings of the selected DC elements on the oneline diagram.
Device Type
Battery
Motor
Load
Elementary Diagram
Converter
Cable

Rating
Ampere Hour
HP / kW
kW / MW
kW / MW
kW / MW
# of Cables - # of Conductor / Cable - Size

kV
Select the check boxes under this heading to display the rated or nominal voltages of the selected
elements on the one-line diagram.
For cables, the kV check box is replaced by the
type on the one-line diagram.

button. Click on this button to display the conductor

A
Select the check boxes under this heading to display the ampere ratings of the selected elements on the
one-line diagram.
For cables, the Amp check box is replaced by the
length (one way) on the one-line diagram.

button. Click on this button to display the cable

Z
Select the check boxes under this heading to display the impedance values of the cables and impedance
branches on the one-line diagram.

Composite Motor
Click on this check box to display the DC composite motor IDs on the one-line diagram, then select the
color in which the IDs will be displayed.

Use Default Options
Click on this check box to use PowerStation’s default display options.

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Calculation Methods

26.4 Calculation Methods
The ETAP PowerStation Battery Sizing and Discharging calculations comply with IEEE Standard 485,
the IEEE Recommended Practice for Sizing Large Lead Storage Batteries for Generating Stations and
Substations. Based on the characteristic curves from the Battery Library, it determines the number of
strings, number of cells, and cell size of a battery for a designated duty cycle.

26.4.1 Battery Duty Cycle
The duty cycle of a battery is the combination of the duty cycles of all the loads supplied by the battery.
The duty cycle of a battery can be determined by two different methods: load duty cycle summation and
load flow calculation. The first method simply sums up duty cycles for all the loads, with the conversion
of load current from the load rated voltage to the nominal voltage of the battery terminal bus. The load
flow calculation method runs a series of load flow calculations to determine battery load that considers
system losses and branch voltage.

Individual Load Duty Cycle
The individual load supplied by a battery can generally be classified into continuous and non-continuous
loads. Continuous loads are the ones that last for the whole duty cycle. Typical continuous loads include
lighting, continuously operating motors, inverters, indicating lights, continuously energized coils, and
annunciator loads, etc.
Non-continuous loads are on only during a portion of the duty cycle. Typical non-continuous loads
include emergency pump motors, critical ventilation system motors, communication system power
supplies, and fire protection systems, etc. Some of the non-continuous loads can occur repeatedly in a
duty cycle but are of short duration, less than one minute in any occurrence. These loads are called
momentary loads. Typical momentary loads include switchgear operations, motor-driven valve
operations, isolating switch operations, field flashing of generators, motor starting currents, and inrush
currents, etc.
If the time of occurrence of a non-continuous load cannot be predetermined, it is called a random load.
The random loads should be shown at the most critical time of a duty cycle. In battery sizing
calculations, these loads are treated differently from non-random loads.
In order to explain how the program determines the battery duty cycle, let us consider a sample case, in
which a battery supplies power to two loads: “Load 1” and “Load 2”. The following two tables list the
load duty cycle as entered in the Duty Cycle page of the Load Editor. Notice that the tables have two
columns: Non-random Load and Random Load. The Non-random load includes continuous, noncontinuous, and momentary loads.

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Calculation Methods

Item Name
L1
L2
L3

Load Items for “Load 1” Duty Cycle (Time in Seconds)
Non-Random Load
Random Load
Amp
St Time Duration
Item Name
Amp
Duration
280
0
12
Ld
100
60
60
60
7140
80
1800
1800

Item Name
Stage1
Stage2
Stage3
Stage4

“Load 2” Duty Cycle (Time in Seconds)
Non-Random Load
Random Load
Amp
St Time Duration
Item Name
Amp
Duration
40
0
1800
Ld1
50
120
140
1800
5400
40
7200
3540
120
10740
60

The load duty cycle for “Load 1” is plotted in the following figure. In figure A, it is plotted in load items
as entered in the Load Editor, while in figure B it is the combination of all load items plotted as a function
of time. Notice that the random load is also displayed in the curve.

Duty Cycle Diagram for “Load 1”
The following figure displays load duty cycle curve for “Load 2”.

Duty Cycle Diagram for “Load 2”
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Calculation Methods

Battery Duty Cycle – Current Summation Method
When using the summation method, the battery duty cycle is the sum of all load currents at every time
moment in the duty cycle, with the current value converted from the load rated voltage to the bus nominal
voltage of the battery terminal bus. This is equivalent to assume that the all loads are constant current
loads. The non-random loads and random loads are summed up separately, as shown in the figure below.

Battery Duty Cycle Diagram – “Load 1” Plus “Load 2”

Battery Non-Random Load
The summation of non-random loads for the battery duty cycle is straight forward, as seen in the battery
duty cycle diagram. It should be noted that at the beginning of the duty cycle, the duration for the 320ampere load section is extended from 12 seconds to one minute. According to IEEE Std 485, the load for
a one-minute period shall be assumed to be the maximum current at any instant. After summing up the
non-random loads from individual loads, the program searches through the duty cycle for current peaks.
If the duration for any peak is less than one minute, the peak current value will be used as the load for the
one-minute period from the beginning of the peak.

Battery Random Load
The summation of random loads for the battery duty cycle is different from that of non-random loads.
The duration of the battery random load is equal to the longest duration of all random loads from
individual loads. The random loads from individual loads are summed up so that they are aligned at the
end of the duration of the battery random load. This ensures that the maximum random load value occurs
at the end of the duration, to produce the severest duty cycle for the battery.
After summing up random loads, if there is any peak with duration less than one minute, it will also be
extended to a one minute time period, similar to the process applied on the non-random load.

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Calculation Methods

Battery Combined Duty Cycle
In the battery sizing calculation, the non-random and random loads are handled separately. The battery
total capacity is equal to the sum of the capacity that can provide power to the non-random load and
random load respectively. However, in the battery discharge calculation, the load applied on the battery
is the combined duty cycle, in which the random load is add on top of the non-random load. Per IEEE
Std. 485, to consider the worst case, the random load should be added to the non-random load at the time
where the battery has the lowest voltage value. In the example case, assuming that at 120 minutes the
battery has the lowest voltage value when the load consists of only the non-random load, the combined
battery duty cycle will be constructed by adding the random load backward at the 120-minute time, as
shown below.

Battery combined Duty Cycle Diagram

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Calculation Methods

Battery Duty Cycle – Load Flow Method
When using the load flow method to determine battery duty cycle, the load current at each moment is
determined by the DC load flow calculation, with the battery being the only constant voltage source. In
the battery sizing calculation, since the parameters are not available, the battery is modeled as a constant
voltage source at the nominal voltage of the terminal bus. In the battery discharging calculation, the
battery voltage is calculated based on the battery characteristic curves and duty cycle in previous steps.
The battery duty cycle determined based on the load flow method will give more accurate representation
of the actual load. With the load flow calculation, the load can be modeled as constant power or constant
impedance load depending the load type. As the responses of these two types of load with respect to
voltage variations are the very different, correctly modeling these loads provides more accurate battery
load current. In the load flow calculation, the battery load can also include losses on cables and other
branches. Additionally, when the load flow method is used in the discharge calculation, the program
calculates bus voltages and loads and branch flows for the whole system along with battery results.

26.4.2 Battery Library Data
The battery sizing calculation is based on the battery characteristics from the library of the battery to be
sized. Therefore, in order to size a battery, the battery has to be linked with the Battery Library, which is
done from the Battery Editor by clicking on the Library button in the Rating page and selecting a battery
from the Battery Library Quick Pick Editor. Once you have selected a battery from the library, the
battery is linked to the Battery Library and the battery type information appears in the Battery Type
section in the editor. The battery type information includes manufacturer, voltage per cell, resistance per
positive plates, etc. The same section also displays information on the selected size for the battery
including number of plates, cell capacity, and one-minute-discharge rate.
In the battery sizing calculation, the program retrieves the battery characteristic curves according to the
battery type information. Since this link between the battery and the library is dynamic, any changes you
make on the battery characteristics in the library may affect the battery sizing results afterward.
The ETAP PowerStation Battery Library provides two types of battery characteristic curves: Time vs.
Amp type and Time vs. Kt type. The following figure displays sample curves for both types, taken from
IEEE Std 485. On the left is the Time vs. Amp type and on the right Time vs. Kt type. The Time vs.
Amp type curves provide values for Rt, which is the number of amperes that each positive plate can
supply for a specified time, at 25° C and to a definite end-of-discharge voltage. Time vs. Kt type curves
provide values for Kt, which is the ratio of rated ampere-hour capacity (at a standard time rate, at 25° C,
and to a standard end-of-discharge voltage) of a cell, to the amperes that can be supplied by that cell for a
specified time, at 25° C and to a definite end-of-discharge voltage.

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Calculation Methods

In the above sample curves, the set of curves may apply to batteries of different sizes or to only one size.
In ETAP PowerStation, you specify a set of characteristic curves for a given size. If you want to use a
given set of curves for batteries of different sizes, you can indicate this in the Battery Sizing Study Case
Editor. Please see the Study Case Editor section for more information.

26.4.3 Battery Sizing Method
The battery sizing calculation includes determining the number of cells to meet the system voltage
requirement and determining the battery size and number of strings to meet the load duty cycle
requirement.

Number of Cells
The number of cells should be determined to satisfy system minimum and maximum voltage
requirements:
1. When charging the battery, the voltage to be applied to the battery should not be greater than the
maximum system voltage.
2. When discharging the battery, the battery minimum discharge voltage should not be smaller than the
minimum system voltage.

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Calculation Methods

Let N be the number of cells. The voltage requirements can be given in the following equation
V sys, min
V sys, max
≤N≤
V cell, disch
V cell, ch
Where
Vsys,min is the minimum system voltage that is equal to the nominal voltage of the battery terminal bus
multiplied by the minimum system voltage deviation entered in the Battery Sizing Study Case Editor.
Vsys,max is the maximum system voltage that is equal to the nominal voltage of the battery terminal bus
multiplied by the maximum system voltage deviation entered in the Battery Sizing Study Case Editor.
Vcell,ch is the battery charge voltage in V/Cell entered in the Battery Sizing Study Case Editor.
Vcell,disch is the battery discharge voltage in V/Cell entered in the Battery Sizing Study Case Editor.
It is clear that the number of cells of the battery is dependent on the four values for voltage requirement
entered in the Battery Sizing Study Case Editor. It can happen that for some incompatible values, we
cannot determine a value for N to satisfy the above equation. When this situation occurs, ETAP will
display a message indicating that it cannot determine the number of cells.
In practical cases, there is often a range of values that N can take to satisfy the above equation. In this
case, ETAP will select the value for N that results in the battery rated voltage being closest to its terminal
bus nominal voltage.

Cell Size
In determining the battery size, ETAP will find the smallest size that can provide sufficient power for the
specified duty cycle. The capacity of a battery can be increased either by using a larger size or by adding
more strings. Since ETAP allows you to enter different characteristic curves for different sizes of
batteries, in the battery sizing calculation, the program starts with one string and the smallest size
available for the calculation. If it fails to meet the load requirement, the program first increases the size
and performs calculations with the characteristic curves for the new size. When no available sizes can
meet the load requirement for the given number of strings, it then increases the string number and
performs the calculation with the smallest size again. This process continues until a battery size and a
string number are found to meet the load requirement.

Load Sections in Battery Duty Cycle
A battery duty cycle generally can be represented as a square waveform. It consists of a number of time
periods, with a constant current value during a period. The figure below shows a sample duty cycle for a
battery. It consists of six periods, designated as P1, P2, … P6. A load section Si is a combination of a
number of load periods, defined as:
S

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=

i

∑

j =1

P

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Calculation Methods

In the sample duty cycle there are six load sections.

Load Sections for A Sample Battery Duty Cycle

Determination of Cell Size Based on Battery Characteristic Curves
Based on a given set of battery characteristic curves, we can determine the required battery size for a
specified duty cycle. Let F represent cell size. It is equal to:
i=1,..Sm

F= Max Fi

where Sm is the total number of load sections and Fi is the size calculated for the ith load section. The
calculation of Fi depends on the type of battery library curves.
For the Time vs. Amp type battery library, the cell size Fi is the number of positive plates, which is
calculated as:
F

i

=

P =i

∑

P =1

A

p

− A
R

P −1

t

where Ap is the load current value in period P. RT is the value obtained from the battery characteristic
curve, which is the number of amperes that each positive plate can supply for t minutes, at 25° C, and to
the end-of-discharge voltage specified in the study case.

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Calculation Methods

For the Time vs. Kt type battery library, the cell size Fi is the capacity in ampere-hours, which is
calculated as:
Fi =

P =i

∑ (A
P =1

p

− A P −1 )∗ K

t

where Ap is the load current value in period P. Kt is the value obtained from the battery characteristic
curve, which is the ratio of rated ampere-hour capacity (at a standard time rate, at 25° C and to a standard
end-of-discharge voltage) of a cell, to the amperes that can be supplied by that cell for t minutes, at 25° C,
and to the end-of-discharge voltage specified in the study case.

Random Load and Non-Random Load
In general, the duty cycle for a battery consists of random loads and non-random loads. The program
determines the cells for random and non-random loads separately in the same way as described in the
previous section. The sum of the two cell size values is the uncorrected cell size for the given duty cycle.

Adjusting Factors
In the Battery Sizing Study Case Editor, you can select several adjusting factors to be considered in
calculating battery size. These factors include temperature factor, design margin factor, aging
compensation factor, and initial capacity factor. The uncorrected battery size is adjusted by multiplying
the first three factors and dividing that value by the initial capacity factor.

Calculation Cycle
It is clear from the equations for determining cell size that the cell size is calculated based on a given set
of battery characteristic curves, which is for a given cell size. If the calculated cell size is different from
the one corresponding to the characteristic curves used. We have to do the calculation again with the
battery characteristic curves for the calculated cell size, which may again result in a new size because of
different characteristic curves used. This process continues until the calculated size matches with the
curves used in the calculation. Sometimes the calculation may get into a cycle of changing cell size and
characteristic curves, especially if the curves were not entered correctly. ETAP PowerStation has
implemented a scheme to break the cycle.

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Calculation Methods

26.4.4 Battery Discharging Calculation Method
The purpose of battery discharge calculation is to determine battery performance for a specified duty
cycle. One of the key parameters for battery performance is the battery terminal voltage. When the
battery is supplying the load as the sole source, it should be able to maintain voltage level for the whole
period of the specified duty cycle.

Battery Characteristic Curves for Voltage Interpolation
The terminal voltage of a battery is dependent on the current drawing from the battery and the amperehour capacity contained in the battery. This relationship is described by the battery characteristic curve
and is very nonlinear. In ETAP, the battery characteristics are described in the battery library as discrete
points. Because no closed form equation is available to describe the battery characteristics, numerical
interpolation methods have to be used to find the points missing in the curves. Apparently, the more
curves are entered in the battery library, the more accurate the calculated results will be. The minimum
number of the characteristic curves entered in the library is two. ETAP will post an error message if the
number of curves in the library for the battery to be discharged is less than two.
In this release of ETAP, the discharge calculation is performed only when the battery is linked to the
“Time vs. Amp” type library. The Library data required by the discharge calculation for the characteristic
curves is described in section 24.6.2. The battery characteristic curves can be used to interpolate voltage
values in different ways. Because of the non-linearity of battery characteristics and often limited curves
available, voltage values interpolated from battery curves sometimes may not seem reasonable. For
example, the interpolated voltage value for a very small current at the beginning of discharging could be
larger than the rated voltage of battery. The method used in ETAP PowerStation first convert the curves
from “Time vs. Amp” curves to equivalent “AH vs. Amp” curves, and then interpolate for voltage values
at a fixed current value. This method is chosen for ETAP PowerStation due its consistent results for a
constant discharging current.

Battery Combined Duty Cycle
When the load powered by the battery includes random load, the random load should be added to the nonrandom load at the worst point, which is the time the battery has the lowest voltage value when only the
non-random load is considered. To identify this time moment, the program first performs battery
discharge calculation excluding the random load. It then determine the worst point, add the random load
to the non-random load and perform discharge calculation from the time when the random load takes
effect all the way to the end of battery duty cycle.

Battery Voltage Calculation
An iterative process is conducted to calculated battery discharge voltage values. A battery voltage value
is reported at each time step specified in the battery sizing study case and at each moment when there is a
change in the load duty cycle. By changing the step size from the battery sizing study case, the user can
adjust the level of detail information on discharge calculation to be reported.

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Calculation Methods

If the battery duty cycle is calculated by the load current summation method, the battery current will
change only when there is a change in any load duty cycle. When the load flow method is selected in the
study case, even if there is no change in the load duty cycle, the battery current will change due to
decrease in the battery voltage. In this case the battery current is calculated by a full load flow
calculation, considering different types of loads and system losses. In this load flow calculation, the
battery is modeled as a constant voltage source with the voltage calculated in the previous step. The
calculated battery current will be used in the current step for battery voltage calculation.
Along with battery voltage and current, the battery discharge program also calculates battery discharge
capacity. When there is change in the load current, two values of voltage and current are calculated, at t and t+, one for before the load change and one for after the load change.
When the battery is calculated using load flow method, the battery discharge calculation also provides a
lot of information on the system performance, including bus voltage, bus loading, branch power and
current, etc.

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Required Data

26.5 Required Data
26.5.1 Source
In battery sizing calculation, the only source is the battery to be sized. Batteries may only be
sized/discharged one at a time as specified in the study case. A UPS may be considered as a load to the
system when its input bus is not connected to an energized bus.

Battery
•
•
•

ID
Bus connection data
Battery library type data. This information is used to retrieve library data for calculations.

If only the battery discharge calculation is conducted, the following additional information is also
required:
•
•
•
•

Battery number of plates and Capacity.
Number of cells
Number of Strings
SC page battery external resistance.

26.5.2 Load
UPS
When a UPS is not connected to an energized input AC bus, it is considered a load in battery sizing
calculations.
•
•
•
•
•

ID
Bus connection data
DC rated voltage
kW and kVA.
Duty Cycle Page
If no duty cycle data is entered, this load will be assumed to be zero.

DC Motor
•
•
•
•
•
•

ID
Bus connection data
Quantity
Rated voltage
kW or HP and Efficiency.
Duty Cycle Page
If no duty cycle data is entered, this load will be assumed to be zero.

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Required Data

Lumped Load
•
•
•
•
•

ID
Bus connection data
Rated voltage
kW Rating
Duty Cycle Page
If no duty cycle data is entered, this load will be assumed to be zero.

Static Load
•
•
•
•
•

ID
Bus connection data
kW Rating.
Rated voltage
Duty Cycle Page
If no duty cycle data is entered, this load will be assumed to be zero.

Elementary Diagram (ED) Load
•
•
•
•
•

ID
Bus connection data
Rated voltage
kW Rating.
Duty Cycle Page
If no duty cycle data is entered, this load will be assumed to be zero.

Inverter
•
•
•
•
•

ID
Bus connection data
DC rated voltage
kVA, PF, DC kW rating
Duty Cycle Page
If no duty cycle data is entered, this load will be assumed to be zero.

26.5.3 Branch
DC Cable
•
•
•
•

ID
Bus connection data
Cable length
Resistance and Inductance and cable length units

DC Impedance
•
•
•

ID
Bus connection data
Resistance and inductance impedance information.

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Required Data

Tie PD (CB, Fuse, & Single-Throw & Double-Throw Switches)
•
•

ID
Bus connection data

DC Converter
•
•
•

ID
Bus connection data
kW Rating and Rated kV Input and output.

Library
•
•

Library type data
Battery characteristic curve data

Study Case
When you initiate a battery sizing calculation, PowerStation uses the study case currently selected from
the Study Case Toolbar. Every field in the Study Case Editor is set to its default value. However, it is
important to set the values in the study case correctly to meet your calculation requirements.

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Output Reports

26.6 Output Reports
The battery sizing calculation results are reported graphically on the one-line diagram, in plots and in the
Crystal Reports format. The graphical one-line display shows the number of cells, number of strings, cell
size, etc. You can use the Display Options Editor to specify the content to be displayed.
The Crystal Reports format provides you with detailed information for a battery sizing study. You can
utilize the Battery Sizing Report Manager to help you view the output report.

26.6.1 Battery Sizing Report Manager
To open the Battery Sizing Report Manager, simply click on the View Output File button on the Battery
Sizing Study Toolbar. The editor includes four pages (Complete, Input, Result, and Summary)
representing different sections of the output report. The Report Manager allows you to select formats
available for different portions of the report and view it via Crystal Reports. There are several fields and
buttons common to every page, as described below.

Output Report Name
This field displays the name to the output report you want to view.

Project File Name
This field displays the name of the project file based on which report was generated, along with the
directory where the project file is located.

Help
Click on this button to access Help.

OK / Cancel
Click on the OK button to dismiss the editor and bring up the Crystal Reports view to show the selected
portion of the output report. If no selection is made, it will simply dismiss the editor. Click on the Cancel
button to dismiss the editor without viewing the report.

Complete Report Page
In this page there is only one format available, Complete, which brings up the complete report for the
battery sizing study. The complete report includes input data, results, and summary reports.

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Output Reports

Input Page
This page allows you to select formats to view different input data, grouped according to type. They
include the following available formats:
Battery Characteristics
Branch Connection
Bus and Connected Load
Cable
Cover
DC Converter
Impedance
Inverter
Load Duty Cycle
UPS

Result Page
This page allows you to select formats to view the result portion of the output report, including
Calculation Results, Battery Load Profile, and Battery Characteristics. The Calculation Results portion
prints the uncorrected cell size for each load section in non-random load and random load. The Battery
Load Profile is the battery duty cycle generated based on load duty cycles. The Battery Characteristics
are mostly data entered by the user. However, if the characteristic data does not contain a curve
corresponding to the minimum discharge voltage specified in the Battery Sizing Study Case Editor, the
calculation program will generate a new curve based on data entered by the user. Therefore, the Battery
Characteristics portion is placed in both the Input and Results lists of the report manager.

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Output Reports

Summary Page
This page allows you to select available formats to view the result summary portion of the report. The
summary portion contains the final result for battery sizing calculations.

26.6.2 View Output Reports From Study Case Toolbar
This is a shortcut for the Report Manger. When you click on the View Output Report button,
PowerStation automatically opens the output report that is listed in the Study Case Toolbar with the
selected format. In the picture shown below, the output report name is BS-300A and the selected format
is Cable.

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Output Reports

26.6.3 Input Data
Input data are grouped together according to element type. The bus and branch connection data for
battery sizing are similar to DC load flow input data. The following are some samples of input data
specific for battery sizing calculations.

Load Duty Cycle
In battery sizing calculations, the load comes from the duty cycle of all the connected loads. In order for
a load to be considered in the study, you must enter load duty cycle data in the Duty Cycle Page of the
Load Editor.
In the sample below, there are duty cycles for a lump load, a static load, and an ED load. The lump load
and the static load are continuous load, maintaining constant load current over the whole duty cycle. The
ED load has both non-random and random loads. Notice that in the report the non-random load is the
combination of all load items entered in the Duty Cycle page, shown as a series of square waveforms as a
function of time. The random load is printed in load items, each with different load duration. Please note
that if you have entered two random load items that have the same load duration, they will be summed up
and shown as one item in the report.

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Output Reports

Battery Duty Cycle
The battery duty cycle is the total load used to size the battery. In this page, it prints the battery name, the
method used for obtaining the battery duty cycle, and the battery duty cycle. Notice that for the battery
duty cycle, both the non-random and random load profiles are printed as a function of time. In the load
profiles, any peaks that last less than one minute have been extended to one minute.

Battery Characteristics
In this page, the information from the Battery Library is printed. It starts with the library type information
including battery manufacturer, model, characteristic curve type, base temperature, V/Cell, resistance per
positive plate, etc. It is then followed by the information for the final battery size used. Note that in the
Battery Library there may be a set of characteristic curves for each battery size, but only one set of curves
is printed in the report, and it is the one used to determine the cell size. In this sample, curves for the
battery size with 21 plates are printed, including four curves with final discharge voltages at 1.75, 1.91,
1.84, and 1.88 volts, respectively. This page also prints the option you selected in the Battery Sizing
Study Case Editor on how to use the battery library data: as Sizes Given in Library Only or as Min/Max
Ranges. In this case, the Min/Max ranges option was selected.

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Output Reports

26.6.4 Results Report
Printed on this page are cell sizes for each load section. There are two columns, one for non-random load,
and one for random load. The maximum value from each column is selected and the sum of the two
values is the uncorrected cell size.
It is seen that for some load sections, such as sections 2 and 5, the cell size is printed as zero. This is
because the calculation skipped these sections. If the load current for the last load period of a load section
is less than the current of the next load period, the calculation for the load section is skipped, because its
size is surely smaller than the size for the next load section. In this sample case, it can be seen from the
Battery Load Profile in the Battery Duty Cycle section above that, for load periods 2 and 5, their load
currents are smaller than their next load period. Therefore, the calculation for load sections 2 and 5 are
skipped and the report prints zero for those sections.

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Output Reports

26.6.5 Load Flow Summary
This page summarizes the results of a battery sizing calculation. It shows the battery to be sized, the
requirements applied, and the final results.
The Correction Factors section prints the individual and total adjusting factors used in the calculation. If
you have indicated in the Study Case Editor not to use one or more adjusting factors, they will be printed
as 100 in this section.
The Cell Size section prints the curve used in the calculation. In this sample case, the curves for cell size
21 were used in the calculation. It also prints the cell sizes for maximum non-random and maximum
random load, as well as the uncorrected and the recommended sizes. Please note that, when the curves
used are the Time vs. Amp type, the first three values are the number of positive plates, while the last is
the total number of plates. When the curves used are the Time vs. Kt type, all four values are capacity in
ampere-hour.

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Output Reports

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One-Line Diagram Displayed Results

26.7 One-Line Diagram Displayed Results
PowerStation’s Battery Discharge Program displays the results from a battery discharge calculation on the
one-line diagram. The Battery Discharge Time Slider is a tool that may be used to change the displayed
results as they change throughout the discharge cycle. The user may click or move the time slider to any
desired position, and the results corresponding to that particular time are displayed on the OLV. The
range of the time slider is set from the beginning to end of the simulation time duration. If the pointer
position is clicked and dragged, the numerical time displayed is updated throughout the motion. The
numerical value displayed has units of minutes.

If the Current Summation Method for battery discharge is used, the displayed results are the discharged
Battery AH Capacity, Terminal Current (Amps), and the Terminal Voltage. These three results vary with
the time slider. Please note that when the time is equal to zero, the capacity displayed in the one-line
diagram as the sizing result is the rated capacity. Furthermore, the program will also display the number
of positive plates, strings, and cells it used for the discharge calculation. The following diagram provides
an example of how the parameters are displayed in the One-Line Diagram. The Battery Discharge Time
Slider displays the results at time equal to 59 minutes.

If the DCLF Method of Battery Discharge is used, branch flow results along with bus voltages may be
displayed on the One-Line Diagram. Branch flows displayed are Current (Amps) and Power (kW or
MW). Bus Voltage may be displayed in terms of kV or %Nominal Voltage.

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One-Line Diagram Displayed Results

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One-Line Diagram Displayed Results

26.8 Plots
PowerStation’s Battery Discharge Program provides Simulation Plots for the purpose of examining
calculation results graphically. To view the Battery Discharge plots, you may click on the Battery Sizing
Plots Icon located on the Battery Sizing toolbar. It will bring up a Battery Sizing Plot selection window.
Here you may select from one of several plots generated by the program. The device types currently
plotted by the program are Batteries, Buses, and Branches.

Modifying Plot Parameters
Plots generated for the battery includes:
•
•
•

Battery voltage, amp and discharged AH.
Battery duty cycle for non-random load, random load, and combined duty cycle.
Battery characteristic curves used for the discharge calculation.

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One-Line Diagram Displayed Results

If the load flow method is used to generate battery duty cycle, the program also generates plot for system
bus and branch, including.
•
•

Bus voltage and load.
Branch load current.

Plot parameters such as the plot line type, axis, legend, and text may be modified directly from the plot
view. For example, to modify the plot line type, double-click on the plot line and change the line type
from the Plot Parameter Editor.

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