Title Battery Sizing Calculation Physics Physics & Mathematics Battery (Electricity) Electrical Components 234.7 KB 11
##### Document Text Contents
Page 1

How to determine the Size of the Battery array that will work well for

The first thing that you will have to decide on is the operating voltage of your system,
whether a 36Volt of 48Volt system. The higher voltage systems is slightly more effective,
but a little more expensive. We found that independent home owners mostly prefere the
36Volts packages, while the communication industry rather the 48Volts systems.

Sizing your battery bank and inverter is elementary math's. Power is measured in Watts.
The formula to determine watts is as follows: (Watts = amps x volts. ) Appliances wattage
is usually listed on the manufacturer's label. After you've collected this information about all
the items that you want to power off your system, you are ready to determine the battery
size you will need.

STEP 1:
Determine your daily energy budget. Make a list of all the appliances that you want to
serve with power. List their Watt ratings and list an estimate of the number of hours that
each item will be used per day. Multiply the watt ratings with the hours used per day, to
determine the daily watt-hours per items. Add these values together, to arrive at a total
budgeted watt-hour needed per day.

STEP 2:
Multiply total daily Watt hours needed by the number of anticipated days of autonomy, to
determine you basic battery size requirement. (For excellent wind conditions choose 1. For
poor wind conditions choose 3.) This figure we call you basic battery size.

STEP 3:
Multiply this basic battery size by 2, to determine safe battery size.

STEP 4:
Now, convert this safe battery size, to amp-hours as follows: Safe battery size expressed
in Amp-hours = Watt hours / DC volts. (DC volts is the operating voltage you've chosen
for the battery bank. For small systems it is normally either 36 volts or 48 volts. For larger
system is can be 110 Volt, 240 volt or 600 volt.) With this figure for a Safe battery size,
expressed in amp=hours, you can go and shop around for a suitable battery bank.

STEP 5:
To determine the correct inverter size, total the wattage requirements for all the
appliances you plan to run simultaneously. Add at least 25% to this perceived requirement.
The final check is to look for surge watts of any item of you appliances that might exceed
your inverter size. Choose an inverter size to suite this requirement.. and if in doubt, go for
one size up.

Page 2

Introduction

Stationary batteries on a rack (courtesy of Power Battery)

This article looks at the sizing of batteries for stationary applications (i.e. they don't move).
Batteries are used in many applications such as AC and DC uninterruptible power supply (UPS)
systems, solar power systems, telecommunications, emergency lighting, etc. Whatever the
application, batteries are seen as a mature, proven technology for storing electrical energy. In
addition to storage, batteries are also used as a means for providing voltage support for weak
power systems (e.g. at the end of small, long transmission lines).

Why do the calculation?

Sizing a stationary battery is important to ensure that the loads being supplied or the power system
being supported are adequately catered for by the battery for the period of time (i.e. autonomy) for
which it is designed. Improper battery sizing can lead to poor autonomy times, permanent damage
to battery cells from over-discharge, low load voltages, etc.

When to do the calculation?

The calculation can typically be started when the following information is known:

• Battery loads that need to be supported
• Nominal battery voltage
• Autonomy time(s)

Calculation Methodology

http://www.openelectrical.org/wiki/index.php?title=File:Batteries_Rack.JPG
http://www.openelectrical.org/wiki/index.php?title=File:Batteries_Rack.JPG

Page 5

12V 6 9-10

24V 12 18-20

48V 24 36-40

125V 60 92-100

250V 120 184-200

However, the number of cells in a battery can also be calculated to more accurately match the
tolerances of the load. The number of battery cells required to be connected in series must fall
between the two following limits:

(1)

(2)

where is the maximum number of battery cells

is the minimum number of battery cells

is the nominal battery voltage (Vdc)

is the maximum load voltage tolerance (%)

is the minimum load voltage tolerance (%)

is the cell charging voltage (Vdc)

is the cell end of discharge voltage (Vdc)

The limits are based on the minimum and maximum voltage tolerances of the load. As a
maximum, the battery at float voltage (or boost voltage if applicable) needs to be within the
maximum voltage range of the load. Likewise as a minimum, the battery at its end of discharge
voltage must be within the minimum voltage range of the load. The cell charging voltage depends
on the type of charge cycle that is being used, e.g. float, boost, equalising, etc, and the maximum
value should be chosen.

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 most appropriate).

Step 5: Determine Battery Capacity

Page 6

The minimum battery capacity required to accommodate the design load over the specified
autonomy time can be calculated as follows:

where is the minimum battery capacity (Ah)

is the design energy over the autonomy time (VAh)

is the nominal battery voltage (Vdc)

is a battery ageing factor (%)

is a temperature correction factor (%)

is a capacity rating factor (%)

is the maximum depth of discharge (%)

Select a battery Ah capacity that exceeds the minimum capacity calculated above. The battery
discharge rate (C rating) should also be specified, approximately the duration of discharge (e.g. for
8 hours of discharge, use the C8 rate). The selected battery specification is therefore the Ah
capacity and the discharge rate (e.g. 500Ah C10).

Temperature correction factors for vented lead-acid cells (from IEEE 485)

An explanation of the different factors:

http://www.openelectrical.org/wiki/index.php?title=File:IEEE_485_Table1.jpg
http://www.openelectrical.org/wiki/index.php?title=File:IEEE_485_Table1.jpg

Page 10

equipment / room layouts. Preliminary budget pricing can also be estimated based on the
calculation results.

Causes of electric hum

Electric hum around transformers is caused by stray magnetic fields causing the enclosure and
accessories to vibrate. Magnetostriction is a second source of vibration, where the core iron
changes shape minutely when exposed to magnetic fields. The intensity of the fields, and thus the
"hum" intensity, is a function of the applied voltage. Because the magnetic flux density is strongest
twice every electrical cycle, the fundamental "hum" frequency will be twice the electrical
frequency. Additional harmonics above 100 Hz or 120 Hz will be caused by the non-linear
behavior of most common magnetic materials.

Around high-voltage power lines, hum may be produced by corona discharge.

In the realm of sound reinforcement (as in public address systems and loudspeakers), electric hum
is often caused by induction. This hum is generated by oscillating electric currents induced in
sensitive (high gain or high impedance) audio circuitry by the alternating electromagnetic fields
emanating from nearby mains-powered devices like power transformers. The audible aspect of this
sort of electric hum is produced by amplifiers and loudspeakers.

The other major source of hum in audio equipment is shared impedances; when a heavy current is
flowing through a conductor (a ground trace) that a small-signal device is also connected to. All
practical conductors will have a finite, if small, resistance, and the small resistance present means
that devices using different points on the conductor as a ground reference will be at slightly
different potentials. This hum is usually at the second harmonic of the power line frequency
(100 Hz or 120 Hz), since the heavy ground currents are from AC to DC converters that rectify the

In vacuum tube equipment, one potential source of hum is current leakage between the heaters and
cathodes of the tubes. Another source is direct emission of electrons from the heater, or magnetic
fields produced by the heater. Tubes for critical applications may have the heater circuit powered
by direct current to prevent this source of hum. 

http://en.wikipedia.org/wiki/Mains_hum#cite_note-0
http://en.wikipedia.org/wiki/Vacuum_tube
http://en.wikipedia.org/wiki/Ground_loop_(electricity)
http://en.wikipedia.org/wiki/Rectifier
http://en.wikipedia.org/wiki/AC_to_DC_converter
http://en.wikipedia.org/wiki/Harmonic
http://en.wikipedia.org/wiki/Ground_(electricity)
http://en.wikipedia.org/wiki/Electrical_impedance
http://en.wikipedia.org/wiki/Amplifier
http://en.wikipedia.org/wiki/Electromagnetic_field
http://en.wikipedia.org/wiki/Sound
http://en.wikipedia.org/wiki/Gain
http://en.wikipedia.org/wiki/Electric_current
http://en.wikipedia.org/wiki/Electromagnetic_induction
http://en.wikipedia.org/wiki/Loudspeaker
http://en.wikipedia.org/wiki/Corona_discharge
http://en.wikipedia.org/wiki/Magnetostriction
http://en.wikipedia.org/wiki/Transformer

Page 11

Prevention

It is often the case that electric hum at a venue is picked up via a ground loop. In this situation, an
amplifier and a mixing desk are typically at some distance from one another. The chassis of each
item is grounded via the mains earth pin, and is also connected along a different pathway via the
conductor of a shielded cable. As these two pathways do not run alongside each other, an electrical
circuit in the shape of a loop is formed. The same situation occurs between musical instrument
amplifiers on stage and the mixing desk. To fix this, stage equipment often has a "ground lift"
switch which breaks the loop. Another solution is to connect the source and destination through a
1:1 isolation transformer, called variously audio humbucker or iso coil. Another extremely
dangerous option is to break contact with the ground wire by using an AC ground lift adapter or by
breaking the earth pin off the power plug used at the mixing deck. Depending on the design and
layout of the audio equipment, lethal voltages between the (now isolated) ground at the mixing
desk and earth ground can then develop. Any contact between the AC line live terminals and the
equipment chassis will energize all the cable shields and interconnected equipment.

Humbucking

Humbucking is a technique of introducing a small amount of line-frequency signal so as to cancel
any hum introduced, or otherwise arrange to electrically cancel the effect of induced line frequency
hum.

Humbucking is a process in which "hum" that is causing objectionable artifacts, generally in audio
or video systems, is reduced. In a humbucker electric guitar pickup or microphone, two coils are
used instead of one; they are arranged in opposing polarity so that AC hum induced in the two
coils will cancel, while still giving a signal for the movement of the guitar strings or diaphragm. 

In certain vacuum-tube radio receivers, a winding on the dynamic speaker field coil was connected
in series with the power supply so as to tend to cancel any residual hum.

Some other common applications of this process are:

• Humbucking transformers or coils used in video systems.
• Telephone (and other audio) system and computer communications wiring.

http://en.wikipedia.org/wiki/Mains_hum#cite_note-1
http://en.wikipedia.org/wiki/Humbucker
http://en.wikipedia.org/wiki/Utility_frequency
http://en.wikipedia.org/wiki/AC_power_plugs_and_sockets#Grounding
http://en.wikipedia.org/wiki/Cheater_plug
http://en.wikipedia.org/wiki/Humbucker
http://en.wikipedia.org/wiki/Ground_lift
http://en.wikipedia.org/wiki/Ground_loop_(electricity)