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AC UPS Sizing

Contents

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y 1 Introductiono 1.1 Why do the calculation?o 1.2 When to do the calculation?

y 2 Calculation Methodologyo 2.1 Step 1: Collect the AC UPS Loadso 2.2 Step 2: Load Profile, Design Load and Design Energyo 2.3 Step 3: Battery Sizing

2.3.1 Nominal Battery (or DC Link) Voltage 2.3.2 Number of Cells in Series

o 2.4 Step 4: UPS Sizing 2.4.1 Overall UPS Sizing 2.4.2 Rectifier / Charger Sizing 2.4.3 Inverter Sizing 2.4.4 Static Switch Sizing

y 3 Worked Exampleo 3.1 Step 1 and 2: Collect the AC UPS Loads and Construct Load Profileo 3.2 Step 3: Battery Sizingo 3.3 Step 4: UPS Sizing

3.3.1 Overall Sizing 3.3.2 Rectifier Sizing 3.3.3 Inverter and Static Switch Sizing

y 4 Computer Softwarey 5 What next?

Introduction

This calculation deals with the sizing of an AC uninterruptible power supply (UPS) system (i.e.

rectifier, battery bank and inverter). In this calculation, it is assumed that the AC UPS is a doubleconversion type with a basic system topology as shown in Figure 1.

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Figure 1 - AC UPS basic system topology

An external maintenance bypass switch and galvanic isolation transformers are other common

additions to the basic topology, but these have been omitted from the system as they are

irrelevant for the sizing calculation.

Why do the calculation?

An AC UPS system is used to support critical / sensitive AC loads. It is typically a battery-backed system which will continue to operate for a specified amount of time (called theautonomy) after a main power supply interruption. AC UPS systems are also used as stable

power supplies that provide a reasonably constant voltage and frequency output, independent ofvoltage input. This is particularly useful for sensitive electrical equipment on main power

supplies that are prone to voltage / frequency fluctuations or instability.

The AC UPS sizing calculation determines the ratings for the main AC UPS system components:1) rectifier, 2) battery banks and 3) inverter.

In some cases, the manufacturer will independently size the system and it is only necessary to

construct the AC UPS load schedule and load profile.

However the calculation results will alsohelp determine the indicative dimensions of the equipment (e.g. size of battery banks) for

preliminary layout purposes.

When to do the calculation?

The AC UPS sizing calculation can be done when the following prerequisite information is

known:

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y UPS loads that need to be supportedy Input / Output AC voltagey Autonomy time(s)y Battery type

Calculation Methodology

The calculation procedure has four main steps:

1) Determine and collect the prospective AC UPS loads2) Construct a load profile and determine the UPS design load (VA) and design energy

(VAh)3) Calculate the size of the stationary battery (number of cells in series and Ah capacity)

4) Determine the size of the inverter, rectifier/ charger and static switch

Step 1: Collect the AC UPS Loads

The first step is to determine the type and quantity of loads that the AC UPS system will beexpected to support. For industrial facilities, this will typically be critical instrumentation and

control loads such as the DCS and ESD processor and marshalling hardware, criticalworkstations and HMI's, telecommunications equipment and sensitive electronics. The necessary

load data should be available from the instrumentation and control engineers.

For commercial facilities, UPS loads will mainly be server, data / network and

telecommunications hardware.

Step 2: Load Profile, Design Load and Design Energy

Refer to the Load Profile Calculation for details on how to construct a load profile, calculate the

design load ( ) and design energy ( ). The "Autonomy method" for constructing load

profiles is typically used for AC UPS systems.

The autonomy time is often specified by the Client (i.e. in their standards). Alternatively, IEEE446, "IEEE Recommended Practice for Emergency and Standby Power Systems for Industrial

and Commercial Applications" has some guidance (particularly Table 3-2) for autonomy times.Sometimes a single autonomy time is used for the entire AC UPS load, which obviously makes

the construction of the load profile easier to compute.

Step 3: Battery Sizing

Refer to the Battery Sizing Calculation for details on how to size the battery for the AC UPS

system. The following sections provide additional information specific to battery sizing for ACUPS applications.

Nominal Battery (or DC Link) Voltage

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The nominal battery / DC link voltage is often selected by the AC UPS manufacturer. However,if required to be selected, the following factors need to be considered:

y DC output voltage range of the rectifier the rectifier must be able to output thespecified DC link voltage

yDC input voltage range of the inverter the DC link voltage must be within theinput voltage tolerances of the inverter. Note that the battery end of dischargevoltage should be within these tolerances.

y Number of battery cells required in series this will affect the overall dimensionsand size of the battery rack. If physical space is a constraint, then less batteries in

series would be preferable.y Total DC link current (at full load) this will affect the sizing of the DC cables

and inter-cell battery links. Obviously the smaller the better.

In general, the DC link voltage is usually selected to be close to the nominal output voltage.

Number of Cells in Series

The number of battery cells required to be connected in series must be between the two

following limits:

(1)

(2)

whereNmax is the maximum number of battery cells

Nmin is the minimum number of battery cells

Vdc is the nominal battery / DC link voltage (Vdc)Vi,max is the inverter maximum input voltage tolerance (%)

Vi,min is the inverter minimum input voltage tolerance (%)Vfis the nominal cell float (or boost) voltage (Vdc)

Veod is the cell end of discharge voltage (Vdc)

The limits are based on the input voltage tolerance of the inverter. As a maximum, the battery at

float voltage (or boost if applicable) needs to be within the maximum input voltage range of theinverter. Likewise as a minimum, the battery at its end of discharge voltage must be within theminimum input voltage range of the inverter.

Select the number of cells in between these two limits (more or less arbitrary, though somewhere

in the middle of the min/max values would be appropriate).

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Step 4: UPS Sizing

Overall UPS Sizing

Most of the time, all you need to provide is the overall UPS kVA rating and the UPS vendor will

do the rest. Given the design load ( in VA or kVA) calculated in Step 2, select an overallUPS rating that exceeds the design load. Vendors typically have standard UPS ratings, so it ispossible to simply select the first standard rating that exceeds the design load. For example, if the

design load 12kVA, then the next size unit (e.g.15kVA UPS) would be selected.

Rectifier / Charger Sizing

The rectifier / charger should be sized to supply the inverter at full load and also charge thebatteries (at the maximum charge current). The design DC load current can be calculated by:

where IL,dc is the design DC load current (full load) (A)

S is the selected UPS rating (kVA)

Vdc is the nominal battery / DC link voltage (Vdc)

The maximum battery charging current can be computed as follows:

where Ic is the maximum DC charge current (A)

C is the selected battery capacity (Ah)

kl is the battery recharge efficiency / loss factor (typically 1.1) (pu)tc is the minimum battery recharge time (hours)

The total minimum DC rectifier / charger current is therefore:

Select the next standard rectifier / charger rating that exceeds the total minimum DC current

above.

Inverter Sizing

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The inverter must be rated to continuously supply the UPS loads. Therefore, the inverter can besized using the design AC load current (based on the selected UPS kVA rating):

where IL is the design AC load current (full load) (A)

S is the selected UPS rating (kVA)Vo is the nominal output voltage (Vac)

Select the next standard inverter rating that exceeds the design AC load current.

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 theinverter sizing).

Worked Example

Step 1 and 2: Collect the AC UPS Loads and Construct Load Profile

Load profile for this example

For this example, we shall use the same loads and load profile detailed in the Energy Load

Profile Calculation example. The load profile is shown in the figure right and the following

quantities were calculated:

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y Design load Sd= 768 VAy Design energy demand Ed= 3,216 VAh

Step 3: Battery Sizing

For this example, we shall use the same battery sizes calculated in the Battery SizingCalculation] worked example. The selected number of cells in series is 62 cells and the minimumbattery capacity is 44.4 Ah. A battery capacity of50 Ah is selected.

Step 4: UPS Sizing

Overall Sizing

Given the design load of 768 VA, then a 1 kVA UPS would be appropriate.

Rectifier Sizing

Given a nominal dc link voltage of120Vdc, the design DC load current is:

A

Suppose the minimum battery recharge time is 2 hours and a recharge efficiency factor of1.1 is

used. The maximum battery charging current is:

A

Therefore the total minimum DC rectifier / charger current is:

A

A DC rectifier rating of40A is selected.

Inverter and Static Switch Sizing

Suppose the nominal output voltage is 240Vac. The design AC load current is:

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A

An inverter and static switch rating of5A is selected.

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