Stationary UPS Sizing Calculations – Part Four ~ Electrical Knowhow

As we stated in the previous article “Stationary UPS Sizing Calculations -Part One” That Stationary UPS Sizing Calculations include:

The UPS sizing calculations,
Rectifier/Charger sizing calculations,
Inverter & Static Switch sizing calculations,
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.

And in Article “Stationary UPS Sizing Calculations -Part Three”, we explained

The IEEE methods of Battery Sizing Calculations which includes:

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

Today, we will explain the following:

UPS Backup time calculation
Selection and sizing of UPS protective devices (CBs or Fuses)

UPS Backup time calculation (At Full Load)

The Backup time sometimes is called Autonomy Time or discharge time or running time. There are two different methods to calculate the UPS/Inverter battery backup time as follows:

Method#1: Using Battery Capacity and Load
Method#2: Using Battery Discharge Rate

Method#1: Using Battery Capacity and Load

The first method to calculate UPS/Inverter battery backup time is by using the battery capacity and the load.

The battery capacity is the amount of energy that the battery can store, while the load is the amount of energy that your appliances or devices consume.

To calculate the backup time using this method, follow these (3) steps:

Step#1: Determine the Battery Capacity in Ah
Step#2: Determine the Load Wattage in W
Step#3: Calculate the Backup Time

Step#1: Determine the Battery Capacity in Ah

To determine the battery capacity in Ah, check the battery label or manual.

For example, if the battery is labeled as 12V 100Ah, the battery capacity is 100Ah.

Step#2: Determine the Load Wattage in W

To determine the load wattage in W, add up the wattage of all the devices connected to the UPS/Inverter.

For example, if you have a computer with a power consumption of 150W and a monitor with a power consumption of 50W, the load wattage is 200W.

Step#3: Calculate the Backup Time

To calculate the backup time, use the following formula:

Backup Time (in hours) =Battery Capacity (in Ah) * Battery Voltage (in V) * Battery Efficiency (in %) / Connected Load (in W/h)

Notes:

If the Battery Efficiency is not given, take it as 0.7 to account for battery efficiency and other losses.

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.

Example#1:

A 1500VA UPS with a 12V 100Ah battery, and the total wattage of your load is 800W, calculate the backup time?

Solution:

The backup time can be calculated as follows:

Backup Time (in hours) =Battery Capacity (in Ah) * Battery Voltage (in V) * Battery Efficiency (in %) / Connected Load (in W)

Backup time = 100Ah x 12V x 0.7 ÷ 800W

Backup time = 1.05 hours = 1.05 x 60 minutes = 63 minutes

Example#2:

An inverter battery with a capacity of 150 Ah, an input voltage of 12 V and battery efficiency 0.9, and the loads are:

Three tube lights 40 W each,

Three fans 75 W each, and

A Wi-Fi router 20 W

Calculate the backup time of the inverter battery?

Solution:

The total load will be:

3 tube lights = 40 x 3 = 120 Watts

3 fans = 75 x 3 = 225 Watts

1 Wi-Fi router = 1×20 Watts = 20 Watts

So, the total load = 120 + 225 + 20 = 365 Watts.

Backup Time (in hours) =Battery Capacity (in Ah) * Battery Voltage (in V) * Battery Efficiency (in %) / Connected Load (in W)

Backup Time (in hours) = 150 Ah x 12 V x 0.9/ 365 = 4.44 hours

The inverter battery will last around 4.44 hours to keep the loads running.

Method#2: Using Battery Discharge Rate

The second method to calculate UPS/Inverter battery backup time is by using the battery discharge rate.

The battery discharge rate is the rate at which the battery discharges during a power outage.

To calculate the backup time using this method, follow these steps:

Step#1: Determine the discharge rate of the battery. This information can usually be found on the battery or in the product manual.

Step#2: Determine the capacity of your battery. To determine the battery capacity in Ah, check the battery label or manual. For example, if the battery is labeled as 12V 100Ah, the battery capacity is 100Ah.

Step#3: Calculate the backup time by dividing the capacity of the battery by the discharge rate.

Backup time (in hours) = battery capacity (in Ah) ÷ discharge rate (in A)

Example#3:

If the discharge rate of a battery is 10A, and the capacity is 100Ah, calculate the backup time.

Solution:

The backup time can be calculated as follows:

Backup time (in hours) = battery capacity (in Ah) ÷ discharge rate (in A)

Backup time = 100Ah ÷ 10A

Backup time = 10 hours

Important Note#1

If it is required to calculate the UPS Backup time calculation other % load other than full load use the following rule:

Backup Time (hours) at % load = Backup Time (hours) at full load / load%

For example#1, calculate the backup time at 50% load. It will be as follows:

Backup Time (hours) at 50% load = Backup Time (hours) at full load / 0.5 = 1.05/0.5 = 2.1 hours.

Important Note#2

If you have many batteries (and of course, all have the same voltage, capacity, and charging/discharging characteristics) then when calculating the Backup time, multiply by the number of batteries and the rule will be as follows:

Backup Time (in hours) =Battery Capacity (in Ah) * Battery Voltage (in V) * the number of batteries * Battery Efficiency (in %) / Connected Load (in W/h)

For example#1:

Calculate the backup time if we have 3 batteries of the same type.

Solution:

Backup Time (in hours) =Battery Capacity (in Ah) * Battery Voltage (in V) * the number of batteries * Battery Efficiency (in %) / Connected Load (in W/h)

Backup time = 100Ah x 12V x 3 x 0.7 ÷ 800W

Backup time = 3.15 hours = 3.15 x 60 minutes = 189 minutes

Backup Time Common Scenarios

The typical range generally proposed is:

Standard backup times of 10, 15 or 30 minutes
Custom backup times

Some loads may only be required to have enough backup time to shut down safely, while some critical systems may need to operate for as long as possible. So, the optimal battery backup time must suit the particular business or application. The most common backup time solutions are as follows:

Solution#1: UPS with 10-15 minutes of runtime and no generator

This solution allows time to safely shut down connected equipment and save work-in-progress.

Solution#2: UPS with 10-15 minutes of runtime and a generator

This solution will keep connected systems up and running until the generator powers on.

Solution#3: UPS with two or more hours of battery runtime

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.

Selection and sizing of UPS protective devices (CBs or Fuses)

The right selection and sizing of UPS protective devices has a very important role since the best sizing of UPS and the best choice of configuration can be compromised by a wrong choice of only one circuit-breaker.

We have 3 important circuit-breakers in the protection scheme of a UPS:

The UPS input breaker (CB1)
The static bypass switch input breaker (CB2)
Downstream Load breakers (CB3)

Usually, these breakers are given by the manufacturers. However, the below table and Figure show how to select the circuit-breakers in the protection scheme of a UPS

Breaker	Rating (In)	Breaking capacity & Notes
The UPS input breaker (CB1)	If the UPS loads given in KW P = Ʃ KW of UPS Loads and S = (P/(EffW) + 0.25P/W) / PF Then: Ib = S /(√3V) Where: P: UPS output active power [kW] S:UPS apparent peak power [kVA] Ib: load current [A] V: Nominal Voltage W:UPS input current distortion factor determined from the manufacturer O&M instruction Eff: UPS efficiency determined from the manufacturer O&M instruction PF: UPS power factor determined from the manufacturer O&M instruction Select the nominal current of CB1 (In) that verify the following conditions: Ib ≤ In ≤ Iz Iz ≥ K2*In/1.45 Where: In: nominal current of protective device CB1[A] Iz: required continuous current-carrying capacity of a cable [A] k2: multiple factor of a protective device rated current at which the protective device operates at the specified conventional time, equal: 1.6- 2.1 for fuse links 1.45 for overcurrent circuit breakers 1.2 for overcurrent selective circuit breakers and bimetallic relays	- Must withstand the short-circuit current of the most powerful source (generally the transformer), - must trip on a short-circuit supplied by the least powerful source - (generally the generator).
The static bypass switch input breaker (CB2)	If the UPS loads given in KW P = Ʃ KW of UPS Loads and S = P / PF Then: Ib = S /(√3*V) Then complete the steps as for CB1	- Must withstand the short-circuit current of the most powerful source (generally the transformer), - must trip on a short-circuit supplied by the least powerful source - (generally the generator). -SCR: silicon controlled rectifier device. SCR is mainly used as a component of the UPS to be inserted into the static transfer switch (STS), and has the ability to quickly cut off the fault current when an accident occurs. -If the let through energy (i²t) of CB2 is higher than what the SCR can handle, then the SCR will fail. To protect the loads, SCR and to have the proper discrimination of short circuit, the following rule has to be respected: i²t SCR> i²t CB2 -The Im current of CB2 must be calculated for simultaneous energizing of all the loads downstream of the UPS, - CB2 must protect the UPS static switch if a short circuit occurs downstream of the switch, - The overload capacity of the static switch is 10 to 12 In for 20 ms, where In is the current flowing through the UPS at full rated load.
Downstream Load breakers (CB3)	Same As CB2	- The trip unit of CB3 must be set not to trip for the overcurrent when the load is energized. - If bypass power is not used to handle overloads, the UPS current must trip the CB3 circuit -breaker with the highest rating. - For distant short-circuits, the CB3 unit setting must not result in a dangerous touch voltage. If necessary, install an RCD. - The breakers should be selective with the upstream circuit breakers.

Figure-1 shows how to select the circuit-breakers in the protection scheme of a UPS

Fig-1

Example#4:

A UPS feed two production lines each with Normal power load 125 KW and other loads are:

Compressor 11 KW

Water Treatment Plant 41 KW

And from the manufacturer data sheet:

UPS input current distortion factor =0.9

UPS efficiency =0.9

UPS power factor =0.9

Size the UPS input breaker?

Solution:

P = Ʃ KW of UPS Loads = 2*125 + 11 + 41 = 302 KW

and

S = (P/(Eff*W) + 0.25P/W) / PF

S = (302/(0.9*0.9) + 0.25*302/0.9) / 0.9 = 507.5 KVA

Then:

Ib = S /(√3*V) = 507.5*1000/(√3*400) = 732.5 A

Select the nominal current of the UPS input breaker (In) to the nearest higher standard Value 800 A and which verify the following conditions:

Ib ≤ In ≤ Iz --------------- 732.5 < 800 < Iz

Iz ≥ K2*In/1.45 ------------ Iz ≥ 1.45 * 800/1.45

Example#5:

From example# , Size the UPS Downstream Load breaker?

Solution:

S = P / PF

S = 302/ 0.9 = 335.56 KVA

Then:

Ib = S /(√3*V) = 335.56*1000/(√3*400) = 484.9 A

Select the nominal current of the UPS Downstream Load breaker to the nearest higher standard Value 630 A and which verify the following conditions:

Ib ≤ In ≤ Iz --------------- 484.9 < 630 < Iz

Iz ≥ K2*In/1.45 ------------ Iz ≥ 1.45 * 630/1.45

DC breaker selection

A DC breaker, which is fundamental to protect the battery cabinet in case of a fault in between the cabinet and the inverter inside the UPS.

The Energy storage connected to a UPS consists of battery strings in parallel. Each string has its own disconnection/protection method, such as switch disconnector, MCB, MCCB or a fuse, depending on its rating. The parallel strings are then connected to the UPS either through a switch disconnector (if the protection was already provided by a fuse or circuit breaker on a string level), or a DC circuit breaker to provide DC protection in the paralleling switchgear at the point of UPS connection.

To Size the battery circuit breaker, follow the below (4) steps:

Step#1: The battery charging current after a long period power outage=full charger output (N+1 rectifiers) = Rectifiers quantity * Rectifier ampere

Step#2: The maximum charging current of each string = the battery charging current/ string quantity

Step#3: The battery circuit breaker sizing current = 1.25 x the maximum charging current of each string

Step#4: Select the rating of DC circuit breaker to be next higher standard value.

Location and Number of battery overcurrent devices:

Notes for sizing DC breaker:

DC side isolated from ground
Maximum breaking capacity to be selected according to the prospective short circuit current for different installation
Circuit breaker size has been selected considering maximum voltage and maximum discharge current
Probability of fault occurring between the batteries and DC circuit breaker is not considered, and the circuit breaker shall be installed as close as possible to the batteries.
Ambient temperature up to +40°C
Maximum discharge current refers to 1.7V/cell as battery cut off voltage
Always refer to UPS technical data sheets for details on number of blocks vs autonomy and temperature

Example#6:

The telecom power system at 48VDC has one battery string of flooded lead-acid cells rated 800 ampere-hours at an 8-hour discharge rate, which equates to a final battery voltage of 1.75V per cell. The system requires four 100A rectifiers to provide 3+1 redundancy. The telecom equipment load is 60A.

The battery discharge current at an 8-hour rate and 1.75V/cell = 100A, per published data of the manufacturer. However, the maximum expected discharge current = 60A (same as the load demand). Size the battery circuit breaker.

Solution:

Step#1:

The battery charging current after a long period power outage=full charger output (N+1 rectifiers) - (load current) = (4×100)-60=340A.

However, the load demand current may be anywhere from 0A to 60A. Therefore, for conservative design, the maximum charging current=4×100=400A (for zero load demand).

Step#2:

From the above, we can determine that the maximum battery circuit current=charging current/ string quantity =400A/1 = 400A.

Step#3:

The battery circuit breaker sizing current = 1.25 x charging current = 1.25 × 400A =500A.

Step#4:

The standard rating of DC circuit breaker is 500A.

The battery short-circuit current, per published data for the battery = 9,050A

Therefore, the recommended circuit breaker in this example=500A, 65VDC, 10,000 AIC.

Moving on to the conductor, we know the cable sizing current=1.25×400A=500A. Therefore, two parallel conductor runs of 250kcmil each can be used, per NEC guidelines.

Note: The circuit conductor is large enough to limit the voltage drop and withstand the short-circuit current for the duration of a fault.

Example#7:

The telecom power system at 48VDC has four parallel battery strings of flooded lead-acid cells. Each string is rated 2,260 ampere-hours at an 8-hour discharge rate for a final battery voltage of 1.75V per cell. The design provides for one battery string to be disconnected for maintenance, while the remaining strings still support the full load current. The system requires sixteen 100A rectifiers to provide 15+1 redundancy. The telecom equipment load is 700A.

The discharge current of one battery string at the 8-hour rate for a 1.75V/cell= 283A, per published data of the manufacturer. Size the battery circuit breaker.

Solution:

Step#1:

The maximum expected discharge current of each battery string=700A ÷ 3 =233A (same as the load demand).

The battery charging current after a long period power outage=[full charger output (N+1 rectifiers)] - (load current) =(16×100A) - 700A=900A.

However, load demand current may be anywhere from 0A to 700A. Therefore, for a conservative design, the maximum charging current=16×100A=1,600A (for zero load demand).

Step#2:

This current value must be divided among three parallel battery strings (the fourth string is considered OFF). So the maximum charging current of each string=1,600A ÷ 3=533A.

From the above, we can see the maximum battery circuit current=charging current=533A.

Step#3:

The battery circuit breaker sizing current=1.25×charging current=1.25×533A=666A.

Step#4:

The standard rating of a DC circuit breaker is 700A.

The battery short-circuit current, per published data for the battery=14,750A.

Therefore, the recommended circuit breaker in this example=700A, 65VDC, 15,000 AIC.

Moving onto the conductor, we know the cable sizing current=1.25×533=666A. Therefore, two parallel conductor runs of 400kcmil each can be used, per NEC guidelines.

Note: The circuit conductor is large enough to limit the voltage drop and withstand the short-circuit current for the duration of fault.

Selectivity between UPS protective devices

Selectivity is defined in IEC 60947-2 “Low voltage Equipment – part 2: Circuit breakers”, and we can accordingly explain it as the selectivity during a fault between two protection devices (i.e., circuit breakers) connected in a series, where the protection device closer to the fault would trip without tripping the upstream protection devices.

This is mainly achieved to isolate the fault and maintain the supply for other circuits that are not directly connected to the fault, and if selectivity is not achieved between circuit breakers, the purpose of installing an expensive UPS system is defeated.

It is required that you trip the CB3 circuit breaker and isolate the faulty section before tripping CB2 and dropping the entire load supplied by the UPS. It is also important to isolate the fault as quickly as possible to restore the output voltage for the load bus supplied by UPS.

Selectivity tables are provided by all manufacturers to define the selectivity between its different products, as shown in the. Here, for example, if the load downstream was protected by ABB MCB S803 B 63, the upstream breaker could be Tmax XT2 100 A, which provides partial selectivity up to 4.5 kA only, or 160A, which provides total selectivity.

How to ensure the selectivity between UPS protective devices?

The table below indicates how to determine the Ir (overload; thermal or longtime) and Im (short-circuit; magnetic or short time) thresholds to ensure selectivity, depending on the upstream and downstream trip units.

Type of downstream circuit	Ir upstream / Ir downstream ratio	Im upstream / Im downstream ratio	Im upstream / Im downstream ratio
Downstream trip unit	All types	Magnetic	Electronic
Distribution	>1.6	>2	>1.5
Asynchronous motor	>3	>2	>1.5

Notes:

Time selectivity must be implemented by qualified personnel because time delays before tripping increase the thermal stress (I²t) downstream (cables, semi-conductors, etc.). Caution is required if tripping of CB2 is delayed using the Im threshold time delay