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

Operation Technology, Inc. 26-1 ETAP PowerStation 4.0

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.



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.



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.


Battery Sizing & Discharge Analysis 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


Battery Sizing & Discharge Analysis 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.



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.



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.



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.


Battery Sizing & Discharge Analysis 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%.



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.



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.


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.



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 one-line diagram.



Device Type Rating Gen. (Generator) kW / MW Power Grid (Utility) MVAsc Motor HP / kW Load kVA / MVA Panel Connection Type (# of Phases - # of Wires) Transformer kVA / MVA Branch, Impedance Base MVA Branch, Reactor Continuous Amps Cable / Line # of Cables - # of Conductor / Cable - Size Bus kA Bracing Node Bus Bracing (kA) CB Rated Interrupting (kA) Fuse Interrupting (ka) Relay 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 button. Click on this button to display the cable/line conductor type on the one-line diagram.

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 button. Click on this button to display the cable/line length on the one-line diagram.

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 Impedance Generator Subtransient reactance Xd” Power Grid (Utility) Positive Sequence Impedance in % of 100 MVA (R + j X) Motor % LRC Transformer Positive Sequence Impedance (R + j X per unit length) Branch, Impedance Impedance in ohms or % Branch, Reactor Impedance in ohms Cable / Line 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.


Battery Sizing & Discharge Analysis 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.



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


ID Select the check boxes under this heading to display the IDs of the selected AC-DC elements on the one-line 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 Rating Charger AC kVA & DC kW (or MVA / MW) Inverter DC kW & AC kVA (or MW / MVA) UPS kVA VFD 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 Amp Charger AC FLA & DC FLA Inverter DC FLA & AC FLA UPS 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.




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


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 one-line diagram.

Device Type Rating Battery Ampere Hour Motor HP / kW Load kW / MW Elementary Diagram kW / MW Converter kW / MW Cable # 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 button. Click on this button to display the conductor type on the one-line diagram.

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 button. Click on this button to display the cable length (one way) on the one-line diagram.

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.



Battery Sizing & Discharge Analysis 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, non-continuous, and momentary loads.



Load Items for “Load 1” Duty Cycle (Time in Seconds) Non-Random Load Random Load

Item Name Amp St Time Duration Item Name Amp Duration L1 280 0 12 Ld 100 60 L2 60 60 7140 L3 80 1800 1800

“Load 2” Duty Cycle (Time in Seconds)

Non-Random Load Random Load Item Name Amp St Time Duration Item Name Amp Duration

Stage1 40 0 1800 Ld1 50 120 Stage2 140 1800 5400 Stage3 40 7200 3540 Stage4 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”



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 320-ampere 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.


Battery Sizing & Discharge Analysis 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



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.



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.


Battery Sizing & Discharge Analysis Calculation Methods Let N be the number of cells. The voltage requirements can be given in the following equation

≤ N ≤ V sys, max V cell, ch

V sys, min V cell, disch

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:

∑=

=i

jji PS

1


Battery Sizing & Discharge Analysis 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:

F= Max Fi i=1,..Sm 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:

∑=

=

−−=

iP

P t

Ppi R

AAF

1

1

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.


Battery Sizing & Discharge Analysis Calculation Methods For the Time vs. Kt type battery library, the cell size Fi is the capacity in ampere-hours, which is calculated as:

( )∑=

=− ∗−=

iP

PtPpi KAAF

11

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.



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 ampere-hour 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 non-random 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.


Battery Sizing & Discharge Analysis 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.


Battery Sizing & Discharge Analysis 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



Battery Sizing & Discharge Analysis Required Data Lumped Load • ID • Bus connection data • Rated voltage • kW Rating • Duty Cycle Page


Static Load • ID • Bus connection data • kW Rating. • Rated voltage • Duty Cycle Page


Elementary Diagram (ED) Load • ID • Bus connection data • Rated voltage • kW Rating. • Duty Cycle Page


Inverter • ID • Bus connection data • DC rated voltage • kVA, PF, DC kW rating • Duty Cycle Page


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.


Battery Sizing & Discharge Analysis 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.


Battery Sizing &Discharge Analysis 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.



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.



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.



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.



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.



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.



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.


Battery Sizing & Discharge Analysis 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.



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.


Battery Sizing & Discharge Analysis 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.


chapter 26 - battery sizing and discharge analysis

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