As we stated in the previous article “Stationary UPS Sizing Calculations -Part One”, That Stationary UPS Sizing Calculations include:
- The UPS sizing calculations,
- Rectifier sizing calculations,
- Inverter sizing calculations,
- The Battery sizing calculations.
We explained the UPS sizing calculations in
the above article and Today, we will explain the other calculations.
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2-
Rectifier/Charger Sizing Calculations |
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The rectifier
should be properly sized to satisfactorily perform these two tasks:
Therefore, the
rectifier DC load current (Idc) is the sum of Ir and Ic. In equation form: Idc = Ir + Ic The inverter design DC full load current (Ir) can be computed as follows: Ir = S/Vdc Where: Ir = Design DC
full load current (A), the design DC load
current is the current drawn by the inverter from the rectifier at full
load. S = the
selected UPS VA rating Vdc = nominal
battery / DC link voltage Meanwhile, the maximum battery charging current can be computed as follows: Ic = (C X f)/t Where: Ic =
maximum DC charge current (A) C =
selected battery capacity (Ampere-hour or Ah) f =
battery recharge efficiency/Loss Factor (typically 1.1) t = minimum
battery recharge time (hours) Example#1: 1000 VA UPS with 60 Ah battery and recharge time of 2.25 hours and nominal battery voltage 120V. Calculate the Rectifier Size. Solution: Ir = S/Vdc Ir = 1000 VA /
120 V = 8.33 A. Ic = (C X f)/t Ic = (60 Ah X
1.1) / 2.25 Ic = 29.33 A Thus, the total
minimum DC rectifier/charger current is: Idc = 8.33 +
29.33 = 37.7 A Select the next standard rectifier
rating that exceeds the total minimum DC current above. Use
a 40-Ampere Rectifier. |
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Another Calculation Method Charger
size in Amps Ic = Ii+ Ia+ (Ib x Td x K)/ Tr Where: Ii = Inverter Current Required = Inverter VA
x Power Factor/ DC to AC Efficiency/ Float Voltage Ia = Any additional DC Loads in amperes Ib = Battery Current Required = Inverter VA x
Power Factor/ DC to AC Efficiency/ DCV Td = Battery Discharge (Run) Time in hours Tr = Battery Recharge Time in hours Example#2: Determine the charger required for a 20kVA
UPS with a 60 cell lead acid battery, no additional DC loads, 1 Hour backup
and 8 hour recharge time. Solution: Charger size in Amps Ic = Ii+ Ia+ (Ib x Td x K)/ Tr Ii = 20,000VA x 0.8 PF/0.86/130 V = 143A la = 0 Ib = 20,000VA x 0.8 PF/0.86/109 V = 171A Then: Ic= 143A + 0+171A x 1Hr x 1.15/8Hr = 143+24.6
= 167.6Amps |
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3- Inverter sizing calculations |
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The inverter must be rated to continuously supply the UPS loads. Therefore, the inverter shall be sized based on the selected UPS VA rating. For a three-phase UPS: Iac = S / (1.732 X Vo) For a single-phase UPS: Iac = S/Vo Where: Iac = design AC full load current (A) S = UPS VA rating Vo = nominal AC output voltage
(line-to-line voltage for a three phase UPS) Example#3: A single-phase 1000 VA UPS and
nominal UPS voltage 120V. Calculate inverter size. Solution: For a single-phase UPS: Iac = S/Vo Iac = 1000 VA / 120 V Iac = 8.33 A Select
the next standard inverter rating that exceeds the design AC load current. Use a 10-Ampere
Inverter. |
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Static Switch
Sizing |
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Like the inverter, the static switch must be
rated to continuously supply the UPS loads. Therefore, the static switch can
be sized using the design AC load current (as above for the inverter sizing) |
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4- The Battery
sizing calculations |
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Importance of Battery Sizing calculation Battery sizing calculation is very important for the following
reasons:
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Important terms for UPS Battery sizing (1)
Discharge rate: For
an UPS system battery, the discharge rate should correspond to the highest
inverter input power required to produce rated output at minimum input dc
voltage. The
end of discharge voltage should be equal to or higher than the minimum dc
input voltage required by the inverter to maintain rated performance. The
minimum dc voltage required by the inverter is normally published by the
manufacturer. The maximum dc power required by the inverter can be obtained
from the manufacturer or can be calculated. In addition, it is recommended to
include a margin of 30 percent for the required capacity to account for load
growth and battery aging. (2)
Lifetime: The
expected lifetime of batteries on UPS duty is usually stated in terms of
years of service on continuous charge to an end of life defined as the
failure to be able to deliver a certain percentage of rated capacity. Initial
capacity (unless specified as 100 percent capacity) is usually in the range
of 90 to 95 percent of rated capacity. This will rise to 100 percent capacity
in normal service after several charge-discharge cycles. IEEE
450 recommends that a battery be replaced when its actual capacity drops to
80 percent of rated capacity; however, some manufacturers rate
"end-of-life" at 50 percent of rated capacity. Obviously, the user
needs to check the initial capacity rating, the service life period, and the
aging characteristics given in the battery guarantee so as not to be
unpleasantly surprised.  (3)
End of discharge voltage: UPS
batteries are not sized on so many ampere-hours of capacity for an 8-hour
period. Battery voltage is not constant, so if the load requires a constant
power output, which most UPS applications do, the current must increase as
the voltage decreases. Consequently, the battery is sized to supply a
specific kW rate (usually the maximum inverter kW requirement without
recharging) for a specific period of time (usually 5 to 15 minutes) to a minimum
specific end voltage and, for lead-acid types, at a maximum specific gravity
(measured at 77°F). (3)(a)
Lead-acid cells A
nominal system design may utilize minimum end voltage of 1.67
to 1.75 volts per cell and a maximum specific gravity of 1.215 at 77°F. The
actual end voltage should be the voltage which the UPS manufacturer, battery
manufacturer, or the system design requires, whichever is higher. In some
cases, designs provide higher end voltages to meet design concerns. A higher
specific gravity may result in a battery installation needing less space, but
results in shorter life spans and higher cell losses and float voltages. The
lower end voltage that manufacturers recommend may cause the UPS to go to
static bypass or, by overstressing battery plates, shorten the life of the
battery. (3)(b)
Nickel-cadmium (ni-cad) cells: A
nominal system design for ni-cad units will be to a minimum end voltage of
1.14 volts at 77°F with the actual end voltage to meet both manufacturers'
and system design requirements. The specific gravity of a new cell will vary
between 1.160 and 1.190 at 77°F, depending upon the manufacturer. Lower
specific gravities are generally used in cells with larger electrolyte
reserves. Higher specific gravities are typically used for low-temperature
applications. The specific gravity will decrease slowly over the years
because of evaporation and other effects, even though the surface of the
electrolyte is probably covered with a protective layer of oil. Renewal will
be necessary if the specific gravity decreases to 1.130 to 1.160, depending
upon the manufacturer's instructions. (3)(c)
Temperature correction: Ratings
are at 77°F (25°C). Therefore, to determine specific gravity, which is
temperature sensitive, a temperature correction factor must be applied. For both lead-acid and nickel-cad batteries, add one point (.001) to the hydrometer reading for every 3°F above 77°F and subtract one point for every 3°F below 77°F. The
battery is rated in watts/cell at an ambient temperature of 25-27deg C. When
the operating temperature or battery is less the capacity of the battery will
be reduced and when the temperature is higher than the design temperature,
the capacity of the battery increases. Elevated
temperature operation will shorten battery life. A general rule of thumb for
lead-acid batteries is that the prolonged use at elevated temperatures will
reduce the battery life by approximately 50% for every 8 ºC above 25 ºC  (4)
Ambient temperature: The
usual controlled environment provided for batteries should eliminate
temperature correction while a 100 percent UPS inverter capacity normally
allows an adequate kW design margin. The life of a battery in comparison with
an UPS system (which may be outdated and replaced in much less time) may mean
that the aging factor is not of such great importance. (5) Battery protection time: Battery protection time depends on the load type and functions. Generally, a battery with a minimum protection time of one minute is necessary for the initial operation of the inverter without support from the power supply source, i.e., during the walk-in time. There is no upper limit for the protection time. However, other considerations may limit the length of battery protection time. Examples are the loss of the environmental control support, which could limit the length of a computer operation time with power loss to 5, 10, or 15 minutes. In such a case, there is no need to select a battery protection time which can extend computer operating time beyond the time for which a computer system can operate before it must shutdown due to overheating. The battery protection time shall
not be less than one minute and shall not exceed the maximum time the load
can be operated with the loss of the environmental support equipment as
specified by the equipment manufacturer (normally in the range of 1 to 15
minutes). (6)
Battery Back-up time or Autonomy Time or discharge time: This
is the time that the battery must support the load and is often called
autonomy or discharge time – typical systems are sized for 5 to 10 minutes
autonomy. Battery
manufacturers supply run-time charts that can be used by knowledgeable
persons to calculate the run time given in your specific situation. For certain application, Consider the following solution scenarios
for Battery Back-up time:
This
solution allows time to safely shut down connected equipment and save
work-in-progress.
This
solution will keep connected systems up and running until the generator
powers on.
In
some cases, generators may not be practical and organizations that wish to
remain up and running during an extended outage must rely solely on UPS
batteries |
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Common Battery types used in UPS
systems Typically
the following battery types are used in UPS systems:
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Relations between battery cells,
battery, battery bank, battery block & battery string Batteries
consists of nos. Of cells in series (total battery voltage = nos. of cells *
cell voltage) Common
battery configurations:
Note:
Multiple batteries can be connected in series for higher system voltage
From
above, when you Select the Battery Type (nos. of cells per battery) Then, Nos.
of batteries = Total nos. of cells / nos. of cells per battery Total
battery voltage = nos. of cells * cell voltage W
per battery = W per cell * nos. of cells per battery W
per battery = Battery Total load (W) / Nos. of batteries W
per String = W per battery * nos. of batteries per string Nos.
of strings required = Adjusted Battery Load in W per Battery / Watts the battery
can deliver (from battery
manufacturer datasheet) |
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Methods for UPS Battery Sizing |
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Various
methods exist to enable the correct selection of batteries for UPS
applications, these methods are: First: The Manufacturers’ methods, which include:
Second: The IEEE methods, which include:
The battery sizing can be
initiated once we have the following information:
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First: The Manufacturers’ Methods |
Method#1: Watts per cell method
Normally
information supplied for lead acid batteries designed for short discharge
times (5-120 minutes) is in the form of kilowatts per cell tabulated for
various back-up times. The required [Watts] per cell are given by: W per cell = AS + (VA x PF)/ (EFF x
Number Of Cells) Where: AS
= Additional loads expressed in amperes VA
= VA of the load or UPS PF
= Power factor of load EFF
= Efficiency of the UPS at the given load No.
Cells = Number of cells required. Example#4: Select the battery model number and quantity (using the typical
watts per cell table) for a 300 kVA UPS, 94% efficiency, power factor of 0.8,
for a backup time of 15 minutes. The UPS battery bus voltage is 480 V. The typical table is for
12 V batteries (six cells of 2 V each). Solution: Quantity of batteries per bank = 480/12 = 40 batteries Number of cells per bank = 40 x 6 = 240 cells Watt
per cell = (VA x PF)/ (EFF x Number of Cells) Watt per cell =
(300*1000*0.8)/(0.94*240) = 1063 w/cell  Looking at the capacity in the table, we see that the required
watt/cell is too much for one bank. However, various options are available,
for example if we decided to use three banks in parallel: Watt per cell (three banks in parallel) = 1063/3 = 354 w/cell Select a S12V370(F) battery with watts per cell = 372 Total number of batteries required = 40 (per bank) x 3 (banks) =
120 Example#5: Determine the battery required for a
20 kVA UPS operating at full load with an efficiency of 86%, a load power
factor of 0.8 and no additional DC loads. The UPS is a 130 VDC system
requiring 60 cells of lead acid batteries and requiring 30 minutes of back-up
time. Solution: W / cell = (VA x PF)/ (EFF x Number
of Cells)= (20,000 x 0.8) / (0.86 x60) = 310 W/Cell = 0.310 KW/cell The UPS manufacturer will also
recommend the battery be discharged to a specific end voltage per cell. For a
60 cell lead acid battery, this will normally be 105V per bank or 1.75
volts/cell. Utilizing the battery manufacturer’s
supplied information, such as that in below table for this 20 kVA UPS, 60 cells
of from the type CX-11 are required which will supply 19.4 kW (0.324kW x 60
cells = 19.4 KW) for 30 minutes  |
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Method#2: Watts per Bank Method In
this method, Normally information supplied for lead acid batteries from
manufacturers is in the form of kilowatts per bank tabulated for various
back-up times. The required [Watts] per bank are given by: W/bank = W/cell * Number of cells per bank Example#6: A 30 KVA UPS operating at 20KVA/16KW Load with an efficiency of
93%, a load power factor of 0.8 and no additional DC loads. The UPS is a 432
VDC system with 216 cells of lead acid batteries and requiring 20 minutes of
back-up time. The typical table is for 12 V batteries (six cells of 2 V
each). Calculate the nos. of battery banks/strings required. Solution: Quantity of batteries per bank = 432/12 = 36 batteries Number of cells per bank = 36 x 6 = 216 cells Calculated W/cell = (VA x PF)/ (EFF x Number Of Cells) = (30000
x 0.8) /(0.93 x 216) = 79.649 W/cell Calculated W/block = 79.649 W/cell x 6 = 477.894 W/block Calculated W/String = 79.649 W/cell x 216 cells = 17,204.184
W/String Or Calculated W/String = 477.894 W/block x 36 block = 17,204.184
W/String The UPS manufacturer will also recommend the battery be discharged
to a specific end voltage per cell. As per the manufacturer’s datasheet, this will normally be 378V
per bank or = 378 V/216 cell = 1.75 volts/cell.  Utilizing the Fiamm Battery
manufacturer supplied information, such as that in Figure 1, Select a FG20721
battery with watts per block
= 119.4 w Total number of batteries
required = 17,204.184 / 119.4 = 144 battery Nos, of strings required = 144 / 36 = 4 or Required nos. of Strings = Calculated W/block / selected w/block
= 477.894/119.4 = 4 Actual W/String = 119.4 w * 36*4 = 17,193.6 w Autonomy
Calculation as per Fiamm battery manufacturer supplied information at
constant power discharge of 17,204.184 W: T1
= 20 min (As per Column 5 of figure-1: Fiamm Battery Discharge Data) & T2
= ?? (Actual obtained Back-up Time) I)
As per supplied information: W α 1/ T1 => 119.4 W α 1 /20 minute II)
As per demand load calculation: W α 1/ T2 => 119.4 W α 1 / T2 minute Hence,
(119.4 W α 1 /20 minute = 119.4 W α 1/ T2 minute) then
(119.4 x 20 = 119.4 x T2) T2 = 119.4 x 20/119.4 = 2388/119.4 = 20 Minutes (Required Backup) Example#7:
A
15 mins backup on a 500KVA UPS with an output power factor of 0.9 and following
data:
Calculate the nos. of battery banks/strings required. Solution: Step
1: Arrive
UPS output power rating in watts = UPS output in volts-amperes × power factor =
500 X 0.8 KW = 400KW Step
2: Arrive
the nominal battery load in W Nominal
battery load in W = UPS output power in kW X1000 / Inverter efficiency = Answer
of Step 1 / Inverter efficiency = 400 X 1000 / 0.95 = 421053 W Step
3: Arrive
the nominal battery load in W per Battery Nominal
battery load in W/Battery = Answer of step 2 / No of Batteries = 421053 W /
50 = 8421 W/Battery Step
4: Arrive
at the adjusted battery power required by taking into consideration design
margin, ageing
factor and TCF (Temperature correction factor) Adjusted
nominal battery load in W/Battery = Answer of Step 3 X Design Margin X Ageing
Factor X TCF =
8421.05 X 1 X 1.25 X 1 =10526
W/Battery As
the maximum available AH is 200AH Battery in 12V SMF VRLA battery, we need to
parallel multiple strings of battery to achieve the desired backup time. Step
5: No
of strings required = Watts/Per battery required (Answer of step 4) / Watts
the battery can deliver (from battery manufacturer datasheet) A
160AH battery can deliver 3552 W at end cell voltage of 1.75V/Cell for 10
mins =
10526 W / 3552W = 2.96 strings = 3 strings Hence
in this scenario, 3 strings of 160AH battery with 50 battery in each string
will provide 10 mins backup at end cell voltage of 1.75V/Cell. |
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Method#3: Amperes per Cell Long term discharge lead acid batteries and
most nickel cadmium batteries are sized using charts expressed in available
amps for specified periods of time. The required [Amperes] per cell is: Ampere per cell = AS + (VA x PF)/
(EFF x Vdc) Where: AS
= Additional loads expressed in amperes VA
= VA of the load or UPS PF
= Power factor of load EFF
= Efficiency of the UPS Inverter Vdc = Average discharge voltage Average Battery Voltage Battery voltage varies in use - starting high and then
decreasing to it's end of discharge voltage. Taking into account this
variation, makes calculation more complicated. More often, an average voltage value is taken and calculations
based on this. If unsure about what the average value to use, then the
end of discharge voltage could be used (as this is on the safe side). For these calculations, it is recommended
that one calculate battery current based upon 104% of the final end voltage
of the battery bank. For example, 60 cells with an end voltage of 1 .75V/cell
will equal 105V/Bank. Consequently, 104% of 105V equals 109V. An average
current will be calculated at this voltage. Example#8: Determine the battery required for a
20 kVA operating at full load with an efficiency of 86%, a load power factor
of 0.8 and 30 amps of additional DC loads. The UPS is 130 VDC system
requiring 92 cells of nickel cadmium batteries and requiring three hours of
back-up time. Solution: Utilizing the following formula: Ampere per cell = AS + (VA x PF)/
(EFF x Vdc) DC Amps = 30+ (20 x 0.8 x 1000) /
(0.86 x 109) = 200.68 Amps The UPS manufacturer has recommended
an end voltage of 105V per bank or 1.14V per cell for the 92 cell bank. Using below Figure for this 20 kVA UPS and additional 30 amp
DC load, 92 cells of HB705P are required which will supply 213 amps for three
hours.  |
In the
next Article, we will explain the IEEE Methods for battery sizing
calculations. So, please keep following.
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Subject Of Pervious Article |
Article |
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Applicable Standards for UPS Systems
Classification of UPS: 1-Voltage range, 2-No. of phases, 3- Mobility, 4- Technological design, |
Classification and Types of UPS – Part One |
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5- Physical Size/capacity, 6- Form factor/ configurations: 6.1- “N” System
Configuration |
Classification and Types of UPS – Part Two |
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6.2- “N+1” System
Configuration, which includes:
6.3- Parallel Redundant with Dual Bus Configuration (N+1 or 1+1) |
Classification and Types of UPS – Part Three |
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6.4- Parallel Redundant with STS Configuration
6.5- System plus System
2(N+1), 2N+2, [(N+1) + (N+1)], and 2N |
Classification and Types of UPS – Part Four |
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7- According to UPS Topology 7.1 Off-line or Standby UPS, 7.2 Line Interactive UPS, 7.3 Standby-Ferro UPS, 7.4 Online Double Conversion UPS, 7.5 The Delta Conversion On-Line UPS. |
Classification and Types of
UPS – Part Five |
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8- According to UPS Distribution
Architecture 8.1 Centralized UPS Configuration, 8.2 Distributed (Decentralized) UPS Configuration, 8.2.1 Distributed UPS-Zonewise Configuration 8.3 Hybrid UPS Configuration. Conventional (Monolithic) Vs Modular
UPS System:
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Classification and Types of UPS – Part Six |
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Three Basic Configurations Of Mains And Bypass For A UPS System:
9-According to Use of transformers with the UPS
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Classification and Types of
UPS – Part Seven |
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Transformer Arrangements in Practical UPS Systems: 1-Transformer options for the “single mains” configuration 2-Transformer Options for the “Dual Mains” Configuration |
Classification and Types of UPS – Part Eight |
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3-
Transformer options for “single mains without bypass” |
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Components of Online Double Conversion UPS: 1- Rectifier, 2- Inverter, 3- Energy Storage system: 3.1 Battery |
Components of Online Double Conversion UPS– Part One
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3.1.1 Battery
Configurations
3.1.2
Battery Size and Location 3.1.3
Battery Transition Boxes 3.1.4
Battery Monitoring 3.2
Energy Storage System – Flywheel 3.3
Energy Storage system – Super Capacitors 3.4
Hydrogen Fuel Cells 4- Static
switch Earthing
Principles of UPS Systems |
Components of Online Double Conversion UPS – Part Two |
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Evaluation Criteria for Selecting an UPS: Step#1:
Determining the need for an UPS, Step#2:
Determining the purpose(s) of the UPS, Step#3:
Determining the power requirements, Step#4:
Selecting the type of UPS, Step#5:
Determining if the safety of the selected UPS is acceptable, Step#6:
Determining if the availability of the selected UPS is acceptable, Step#7:
Determining if the selected UPS is maintainable, and Step#8:
Determining if the selected UPS is affordable. |
Evaluation Criteria for Selecting an UPS-Part One
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Example:
Selecting an Uninterruptible Power Supply (UPS) UPS
System Ratings and Service Conditions First:
from IEC 60146-4 Second:
according to American standards |
Evaluation Criteria for Selecting an UPS-Part Two |
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The
UPS sizing calculations steps: Step#1:
List All the UPS Loads Step#2: List for Each Equipment/Load, the Voltage,
Number of Phases, and Frequency Step#3: List the KVA for Each Equipment/Load Step#4: Determine The UPS Voltage, Number Of Phases,
and Frequency. Step#5: Segregate the Loads (Non-Motor Loads &
Motor Loads) Step#6: Determining Load Power Factor and KW Demand Step#7: Determining Load Inrush Current/KVA. Step#8: Determine Loads’ Sequence of Operation Step#9: Apply the Derating Factors (If Any) Step#10: Calculate the Design UPS Load KVA |
Stationary UPS Sizing Calculations – Part One
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