### Stationary UPS Sizing Calculations – Part Two

As we stated in the previous article “Stationary UPS Sizing CalculationsThat Stationary UPS Sizing Calculations include:

1. The UPS sizing calculations,
2. Rectifier sizing calculations,
3. Inverter sizing calculations,
4. The Battery sizing calculations.

We explained the UPS sizing calculations in the above article and Today, we will explain the other calculations.

 2- Rectifier/Charger Sizing Calculations

 The rectifier should be properly sized to satisfactorily perform these two tasks:  Supply the inverter at full load (Ir) and Charge the batteries at the maximum charge current (Ic).   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.

 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

 3- Inverter sizing calculations

 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.

 Static Switch Sizing

 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)

 4- The Battery sizing calculations

 Importance of Battery Sizing calculation Battery sizing calculation is very important for the following reasons: In order to ascertain that it can supply power to the connected loads for the time period it is designed.Unsuitable sizing of the battery can pose many serious problems such as permanent battery damage because of over-discharge, low voltages to the load, insufficient backup times.

 Common Battery types used in UPS systems   Typically the following battery types are used in UPS systems: Lead Acid/Plante BatteryLead Acid/Antimony BatteryLead Acid/Calcium BatteryLead Acid/Calcium, Maintenance-free Liquid Electrolyte BatteryLead Acid/Calcium, Maintenance-free Gelled Electrolyte, Sealed BatteryLead Acid (Special Alloy), Suspended Electrolyte, Maintenance-free, Sealed BatteryNickel Cadmium, Pocket Plate Liquid Electrolyte Battery

 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: 1 cell: 2 V3 cells: 6 V6 cells: 12 V   Note: Multiple batteries can be connected in series for higher system voltage   Battery block refers to a complete individual battery (block = battery)Battery string is a group of batteries (blocks) connected in series or parallelA battery bank is a group of batteries or strings connected together for a single application in parallel   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)

 Methods for UPS Battery Sizing

 Various methods exist to enable the correct selection of batteries for UPS applications, these methods are:   First: The Manufacturers’ methods, which include: Method#1:Watts per cell methodMethod#2:Watts per bank methodMethod#3:Ampere per cell method   Second: The IEEE methods, which include: Method#1:The IEEE 485 method Method#2:The IEEE 1184 method   The battery sizing can be initiated once we have the following information: Loads need to be supported by batteryMinimal voltage for battery (end of discharge voltage)Back up time(s)ambient temperature

 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:

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

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:

 UPS Rating (KVA) 500KVA Specified by Customer or Consultant Actual Load on UPS (KVA) 500KVA Specified by Customer or Consultant Output Power Factor 0.8 Specified by Customer or Consultant Inverter Efficiency (n) 95% Based on UPS Manufacturer’s data No of Batteries 50 Nos Based on UPS Manufacturer’s data End Cell Voltage (ECV) 1.75V Specified by Customer or Consultant Backup time required (in mins) 10 mins Specified by Customer or Consultant Ageing Factor 1.25 Specified by Customer or Consultant Design Margin 1 Specified by Customer or Consultant Temperature Correction Factor 1 Specified by Customer or Consultant

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.

In the next Article, we will explain the IEEE Methods for battery sizing calculations. So, please keep following.

Subject Of Pervious Article

Article

Applicable Standards for UPS Systems

• What is a UPS?
• Why do we need a UPS?
• UPS Rating

Classification of UPS:

1-Voltage range,

2-No. of phases,

3- Mobility,

4- Technological design,

5- Physical Size/capacity,

6- Form factor/ configurations:

6.1- “N” System Configuration

6.2- “N+1” System Configuration, which includes:

• Isolated Redundant Configuration (N +1)
• Parallel Redundant Configuration (1+1)
• Parallel Redundant Configuration (N +1)
• Parallel Redundant Configuration (N +2) and so on

6.3- Parallel Redundant with Dual Bus Configuration (N+1 or 1+1)

6.4- Parallel Redundant with STS Configuration

• Parallel Redundant Configuration (1+1) + STS
• Parallel Redundant Configuration (N+1) + STS

6.5- System plus System 2(N+1), 2N+2, [(N+1) + (N+1)], and 2N

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.

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:

• Deploy UPSs in parallel,
• Deploy UPSs in Series,
• Use modular UPS products.

Three Basic Configurations Of Mains And Bypass For A UPS System:

• Single mains,
• Single mains without bypass,
• Dual mains.

9-According to Use of transformers with the UPS

• Transformer based,
• Transformer less UPS,
• Transformer less UPS with external input/ output transformer.

Transformer Arrangements in Practical UPS Systems:

1-Transformer options for the “single mains” configuration

2-Transformer Options for the “Dual Mains” Configuration

3- Transformer options for “single mains without bypass”

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

3.1.1 Battery Configurations

• Serial Strings,
• Parallel Strings.

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

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

Example: Selecting an Uninterruptible Power Supply (UPS)

UPS System Ratings and Service Conditions

First: from IEC 60146-4

Second: according to American standards

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#6: Determining Load Power Factor and KW Demand

Step#8: Determine Loads’ Sequence of Operation

Step#9: Apply the Derating Factors (If Any)