### Stationary UPS Sizing Calculations – Part Three

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

1. The UPS sizing calculations,
2. Rectifier/Charger sizing calculations,
3. Inverter & Static Switch sizing calculations,
4. The Battery sizing calculations.

We explained the UPS sizing calculations in the above article and we explained in article “Stationary UPS Sizing Calculations -Part Two, the following calculations:

- Rectifier/Charger sizing calculations,

- Inverter & Static Switch sizing calculations,

- The Battery sizing calculations, which includes:

First: The Manufacturers’ methods, which include:

• Method#1: Watts per cell method,
• Method#2: Watts per bank method,
• Method#3: Ampere per cell method.

Today, we will explain the Second methods of Battery sizing calculations; The IEEE methods.

 Second: The IEEE Methods of Battery Sizing Calculations

 The IEEE methods include: Method#1: The IEEE 485 method,Method#2: The IEEE 1184 method.

 Method#1: IEEE Standard 1184 Batteries for Uninterruptible Power Systems

 This method is intended to assist engineers who select and design battery systems for uninterruptible power systems (UPS) from the two main battery types: Lead-acid batteries, which include both vented (flooded) and valve-regulated (sealed) constructionsNickel-cadmium batteries

Important Terminology

1- Equalizing charge - Nickel-cadmium cells

Recommended equalizing voltages range from 1.47-1.65 V/cell. To achieve reasonable end-of-discharge voltages, the equalizing voltage attainable in a specific application is normally restricted by system voltage limitations to about 1.55 V/cell.

Generally, equalizing is used for a fast recharge after a discharge, and to assist in electrolyte mixing after water addition (two rate chargers are generally recommended by the manufacturers). Depending on the float voltage chosen, routine periodic equalizing may be unnecessary.

All batteries are affected by high temperatures. However, nickel-cadmium cells can sustain high temperatures more easily than most other systems because the chemistry in the active materials is relatively stable.

For example, at 32 °C (90 °F) the normal life of a nickel-cadmium cell is diminished by about 20%, compared with a reduction of approximately 50% for a lead-acid cell.

Moreover, a nickel-cadmium battery will not be destroyed by low temperatures or freezing. With a normal electrolyte, the battery will operate at temperatures as low as 30 °C (86 °F) to 40 °C (104 °F); with a higher specific gravity electrolyte, it will operate at even lower temperatures. The available capacity is reduced at low temperatures, but at 40 °C (104 °F) a nickel-cadmium battery can deliver 60% or more of rated capacity.

Operating batteries at temperatures below 25 °C (77 °F) decreases performance. Note that temperature derating factors (see IEEE Std 485-1983) apply to the discharge rate and not the discharge time.

For example, a temperature derating factor of 1.11 for a certain cell type at 15.6 °C (60 °F) indicates that battery performance is approximately 10% less than at 25 °C (77 °F). If this battery can supply, say, 100 kW for 15 min at 25 °C (77 °F), it will be capable of delivering 90 kW for 15 min at 15.6 °C (60 °F). Conversely, the battery may be able to supply the same 100 kW load for only 10 min at 15.6 °C (60 °F), because of the decrease in battery efficiency at higher discharge rates. The extent of this effect varies with cell construction.

4- Battery Capacity

The ampere-hour (AH) capacity is the unit used in specifying the storage capacity of a battery. While a battery that can deliver 10 A for 10 hours can be said to have a capacity of 100 AH, that is not how the rating is determined by the manufacturers.

A 100 AH rated battery most likely will not deliver 10 A for 10 hours. Battery manufacturers use a standard method to determine how to rate their batteries. Their rating is based on tests performed over 20 hours with a discharge rate of 1/20 (5%) of the expected capacity of the battery per hour. So a 100 ampere-hour battery is rated to provide 5 A for 20 hours.

The efficiency of a battery is different at different discharge rates. When discharging at 5% an hour, the battery's energy is delivered more efficiently than at higher discharge rates. To calculate the 5% discharge rate of a battery, take the manufacturer's ampere-hour rating and divide it by 20.

5- C-rate

C-rate is a measure of the rate at which a battery is discharged relative to its maximum capacity. 1C rate means that the discharge current will discharge the entire battery in 1 hour; 0.1C means 10% transfer in one hour, or full transfer in 10hours; 5C means full transfer in 12 minutes, and so on.

6- State of Health

The state-of-health of a battery is the percentage of its capacity available when fully charged relative to its rated capacity. For example, a battery rated at 30 AH, but only capable of delivering 24 AH when fully charged, will have a state-of-health of 24/30 x100 = 80%. Thus, the state-of-health takes into account the loss of capacity as the battery ages.

7- Voltage Rating

The voltage rating is based on the number of cells connected in series and the nominal voltage of each cell (2.0 V for lead-acid type and 1.2 V for nickel-cadmium). Twelve-volt lead-acid batteries will have six cells in series.

8- Reserve Capacity (RC)

This is defined as the time in minutes for the battery voltage to fall to 10·5 volts with a constant load of 25 Amps at a temperature of 25°C.

9- Cycle Life

The cycle life of a battery is defined as the number of discharge-charge cycles the battery can experience before it fails to meet specific performance criteria. Cycle life is estimated for specific charge and discharge conditions. The actual operating life of the battery is affected by the rate and depth of cycles and by other conditions such as temperature and humidity.

10- State of charge

The concentration (strength) of sulfuric acid within the electrolyte varies with the state of charge. This changes the density or specific gravity of the electrolyte, which can be measured with a hydrometer. A hydrometer is a scale that indicates the density readings of an electrolyte.

 State Of Charge Density Fully Charged 1.280 Half Charged 1.200 Discharged 1.120

Since temperature also has a small effect on density, the graph below would be a more accurate way of finding the state of charge.

 The design steps for The IEEE 485 method    Step#1: calculate Battery Total load Step#2: calculate the corrected Battery Total load Step#3: calculate the maximum number of cells Step#4: calculate the end voltage Step#5: calculate the Minimum number of cells Step#6: Cell selection   Note: For each battery type, the design steps are described in order to facilitate the selection. Noting that each design has advantages and disadvantages, all of which should be considered when selecting a battery.

 Initial assumptions and limiting factors Battery discharge voltage range: 1.67- 2.10 V/cell Battery equalizing charge range: 2.30- 2.50 V/cell   Step#1: calculate Battery Total load   Battery Total load (W) = UPS Load (W) / inverter efficiency Or Battery Total load (W) = UPS Load (W) + inverter losses (W)   Example#1: System size: 500 kVA at 0.80 PF, 400 kW System output voltage: 3 ph, 120/208 Vac (not required for calculation) Inverter efficiency: 0.92 efficiency at full load (dc input to ac output)   Solution: Battery Total load (W) = 400 kW/0.92 = 435 KW   Note: The very latest generation of on-line UPS have inverter efficiencies of up to 97%, producing longer battery autonomies than could previously be achieved from the same battery connected to a UPS with a less efficient inverter.

 Step#2: calculate the corrected Battery Total load   Corrected Battery Total load = Battery Total load × ageing factor × temperature correction factor x design Margin   Where: - Ageing factor Since the battery capacity does not remain at its nameplate rating throughout its life, a 25% margin will be included as an aging factor for the 435 kW.   - Temperature correction factor Also, since it is expected that the operating temperature will drop to a low of 15.6 °C (60°F), the battery capacity should be increased by another 11% (per IEEE Std 485-1983) to ensure that it will provide rated load at reduced temperature.   - Design Margin A design margin is taken into account for any inaccuracies in the load’s estimation. Generally, a design margin ranges between 10% and 15% is suggested. And sometimes it will be ignored.   Then, in continued example#1: Corrected Battery Total load = 435 KW * 1.25 *1.11 = 604 KW

 Step#3: calculate the maximum number of cells   In Continued example#1: It is assumed that the manufacturer recommends an equalizing voltage of 2.40/cell.   The maximum number of cells = Maximum system voltage / Recommended equalizing V/cell Then, The maximum number of cells = 432/2.40 = 180 cells   Note: In this case no adjustment is made for the voltage losses in the cables and cell connectors. In the final stages of battery recharge the current drops to a point where the voltage drops are insignificant on the large cables that have been sized for the final discharge currents.

 Step#4: calculate the end voltage   Note: In order to take full advantage of the battery’s usable capacity, the lowest possible end-of-discharge cell voltage should be used. This is subject to the limits imposed by the minimum allowable system voltage and the battery manufacturer’s stated minimum cell voltage for the discharge time in question. More important, the battery must first be capable of being charged in accordance with the manufacturer’s recommendations and within the maximum system voltage limit.   The final voltage per cell = Minimum battery voltage/Number of cells   In Continued example#1: Allowing for the planned 2 V loss in the cables, the minimum battery voltage of 292 V is then used to calculate the final voltage per cell: The final voltage per cell = Minimum battery voltage/Number of cells = 292/180 = 1.62 V /cell

 Step#5: calculate the Minimum number of cells   Note: In most cases, the calculated number of cells and minimum voltage per cell would be used directly in the remainder of the battery sizing exercise. However, in this example, it is assumed that the battery manufacturer states a minimum discharge voltage of 1.67 V/cell for a 20 min discharge. Since the calculated minimum voltage is 1.62 V/cell and the manufacturer’s minimum voltage is 1.67 V/cell, it is necessary to adjust the number of cells to reflect the higher value of the minimum discharge voltage.   Minimum number of cells = Minimum battery voltage/ Minimum discharge V/cell   Therefore, In Continued example#1: Minimum number of cells = Minimum battery voltage/ Minimum discharge V/cell = 292/1.67 = 175 cells

 Step#6: Cell selection   At this point it has been determined that the battery required is one with 175 cells that can deliver 604 kW for 20 min and not drop below 1.67 V/cell. Each cell shall then deliver: 604 kW/175 cells = 3.45 k W/cell   Now there is complete information with which to consult the manufacturer’s performance charts and select the proper cell for the application (20 min, 1.67 V/cell, and 3.45 kW/cell).   It may be beneficial to repeat the calculation to optimize the number of cells for a particular cell type. For example, if there is a cell that can provide 3.40 kW/cell, it would probably be more economical to increase the number of cells, rather than using 175 of the next larger cell size. In this case, the new number of cells would be:   604 kW/3.40 = 178 c ells   Notes: - Changing the number of cells will affect both: The equalizing Voltage andThe end-of-discharge voltages.   - Increasing the number of cells allows a lower end-of-discharge voltage per cell (more usable capacity) within the lower system limit, but may result in a required equalizing voltage that is higher than the upper system limit. - Decreasing the number of cells will not impose any constraints on the maximum voltage limit, but will result in a higher end-of-discharge voltage per cell (less available capacity). - In this particular example, it is already known that 180 cells can be accommodated within the upper system voltage limit. At the lower voltage limit, the use of 178 cells would allow discharging to 1.64 V/cell, but would fail to meet the battery manufacturer’s stated minimum of 1.67 V/cell. - Battery selection, then, is a process of finding the best fit between the maximum charge voltage and the minimum operating point of the UPS that will allow the maximum use of the available battery capacity.

 Initial assumptions and limiting factors Battery equalizing voltage 1.52 V/cell Battery discharge voltage 1.00 - 1.10 V/cell   Step#1: calculate Battery Total load As in example#1

 Step#2: calculate the corrected Battery Total load   Since the design life (assumed to be 15 years) is well within the life expectancy of vented nickel-cadmium batteries, a 10% margin will be included as an aging factor for the 435 kW. Typically, temperature factors are used in nickel-cadmium battery sizing only when there is a considerable deviation from room temperature. In this example, the 15.6 °C (60°F) minimum temperature typically would give rise to a capacity reduction of only 3% or so. This figure would generally be incorporated into the overall battery sizing margins to give a combined figure for both aging and low temperature operation.   Then, Corrected Battery Total load = Battery Total load × ageing factor × temperature correction factor x design Margin    Corrected Battery Total load = 435 kW x 1.10 = 479 kW

 Step#3: calculate the maximum number of cells   Selection of number of cells (cell type) and end voltage point The most economical battery choice results from using the lowest end-of-discharge voltage and the largest possible number of cells that will satisfy the manufacturer’s recommendations. The first step in the battery calculation is to ensure that the battery can be properly charged. For this example, it is assumed that the manufacturer recommends a minimum equalizing voltage of 1.52 V/cell. The maximum number of cells is therefore:   The maximum number of cells = Maximum system voltage / Recommended equalizing V/cell  Then, The maximum number of cells = 432/1.52 = 284 cells

 Step#4: calculate the end voltage   Note: In this case no adjustment is made for voltage losses in the battery cables and cell connectors. In the final stages of battery recharge the current drops to a point where the voltage drops are insignificant on the large cables that have been sized for the final discharge currents.   Allowing for the planned 2 V loss in the cables, the minimum battery voltage of 292 V is then used to calculate the final voltage per cell:   The final voltage per cell = Minimum battery voltage/Number of cells    Then, The final voltage per cell = 292/284 = 1.03 V/cell

 Step#5: calculate the Minimum number of cells     Minimum number of cells = Minimum battery voltage/ Minimum discharge V/cell   Then, Minimum number of cells = 292/1.1 = 266 cells

 Step#6: Cell selection   At this point it has been determined that the battery required is one with 284 cells that can deliver 479 kW for 20 min and not drop below 1.03 V/cell.   Minimum discharge V/cell = 479/284 = 1.69 k W/cell Now there is complete information with which to consult the manufacturer’s performance charts and select the proper cell for the application. When using tabular data, it may be necessary to interpolate between published values. For instance, in the example the cell type required is one that will supply 1.69 kW/cell for20 min to a final voltage of 1.03 V/cell. In this case it would probably be necessary to interpolate between values given for a final voltage of 1.05 V/cell and 1.00 V/cell. Since most manufacturers offer high, medium, and low rate cell ranges, it may be advisable to determine cell sizes for two or more of the ranges. The most economical option meeting the above parameters can then be chosen. Battery selection then, is a process of finding the best fit between the maximum charge voltage and the minimum operating point of the UPS that will allow the maximum use of the available battery capacity.

 Method#2: IEEE 485 Lead Acid Batteries for Stationary Applications

 This standard details methods for defining the dc loads and for sizing a lead-acid battery to supply those loads in full float operation The IEEE 485 design method has the five steps as follows:   Step#1: develop the overall connected load list that the battery requires to supply Step#2: Develop a load profile Step#3: Calculating the Design Load & Energy Demand Design Load Step#4: Choose the type of battery and determine the cell characteristics Step#5: On the basis of design loads, calculate the desired Ampere-hour (Ah) battery capacity

 Step#5: calculate the Desired Ampere-Hour (Ah) Battery Capacity   The battery capacity desired to accommodate the total designed load over the determined back up (autonomy) time can be calculated using the following formula:   Cminimum= Ede(kaf×ktcf×kcrt) /( Vdc×kmdod×kse)   Where: Ede, total designed energy over back up time (VAh) kaf, Battery Aging Factor (%) ktcf, Temperature Correction Factor (%) kcrt, Capacity Rating Factor (%) Vdc, Battery Voltage (Nominal) kmdod, Maximum depth of Discharge (%) kse, System Efficiency (%)   Choose a battery capacity (Ampere-Hour) that surpasses the minimum capacity calculated using the above battery sizing formula.   An explanation of the various elements:   - Aging Factor: It actually represents the reduction in battery performance with the passage of time. To ensure the battery can meet the design requirements throughout its life the standard suggestions the initial capacity should be 125% of the design capacity.   - Temperature correction factor: The battery cells capacity is generally provided for a standardized temperature which is 25oC and if it varies, the battery cells capacity will vary as follows:   Temperature decreases, the battery cells capacity decreases And vise verse as the temperature increases, the battery cells capacity increases   So, a correction factor is needed to implement and this correction factor we can get it from the below table.  Temperature correction factor Table   - Capacity rating factor This factor accounts for voltage reduction during the discharge of the battery. In Lead-acid batteries, a voltage dip occurs in the early phases of battery discharge followed by certain recovery.   There are two ways of expressing capacity: Term Rt The term Rt is the number of amperes each plate can supply for t minutes, at 25oC to a defined minimum cell voltage. Ct = Rt   Term Kt The term Kt is the ratio of ampere-hour capacity, at a standard time rate, at 25oC and to a defined minimum voltage which can be delivered for t minutes. Ct = 1/Kt   Rt is not equal to 1/Kt because each factor is expressed in different units.   - System efficiency It accounts for battery losses (coulombic efficiency) as well as power electronics losses (such as charger and inverter).   - Design Margin  It accounts for unexpected circumstances (increased loads, poor maintenance, recent discharge, etc.) it is common to allow a design margin of 10% to 15%.   - Depth of discharge (DOD) Consider shallow DOD (max 20% recommended) and occasional deeper DOD (max 80%)   Example#4: calculate for the minimum battery capacity using the given energy demand of 4020 VAh, battery aging factor (kaf) = 25%, temperature correction factor at 30 deg C (ktcf) = 0.956, capacity rating factor (kcrt) = 10% and depth of discharge (kmdod) = 80%, system efficiency (kse) = 95%   Cminimum = Ede(kaf×ktcf×kcrt) /( Vdc×kmdod×kse)   Cminimum = [4020 VAh X (1.25 X 0.956 X 1.1)] / (120 V X 0.8 X0.95) Cminimum = 57.94 Ah Use a VRLA battery with a 60 Ah capacity.

 Very important Note   Mixing different battery sizes or types in a system is generally not recommended due to variations in voltage, capacity, and charging/discharging characteristics. It is best to use batteries of the same type, capacity, and age to maintain optimal performance and balance within the system.

In the next Article, we will explain the following:

• UPS Backup time calculation
• Selection and sizing of UPS protective devices (CBs or Fuses)
• Selection and sizing of UPS Cables
• Sizing a generator set for UPS system
• UPS room ventilation calculation

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)

### Stationary UPS Sizing Calculations – Part One

2- Rectifier/Charger Sizing Calculations

3- Inverter sizing calculations & Static Switch Sizing

4- The Battery sizing calculations

First: The Manufacturers’ methods, which include:

• Method#1:Watts per cell method
• Method#2:Watts per bank method
• Method#3:Ampere per cell method

Stationary UPS Sizing Calculations – Part Two