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

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.

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

The calculation is based on a mixture of normal industry practice and technical standards IEEE Std 485 (1997, R2003) "Recommended Practice for Sizing Lead-Acid Batteries for Stationary Applications" and IEEE Std 1115 (2000, R2005) "Recommended Practice for Sizing Nickel-Cadmium Batteries for Stationary Applications". The calculation is based on the ampere-hour method for sizing battery capacity (rather than sizing by positive plates).

The focus of this calculation is on standard lead-acid or nickel-cadmium (NiCd) batteries, so please consult specific supplier information for other types of batteries (e.g. lithium-ion, nickel-metal hydride, etc). Note also that the design of the battery charger is beyond the scope of this calculation.

There are five main steps in this calculation:

1) Collect the loads that the battery needs to support 2) Construct a load profile and calculate the design energy (VAh) 3) Select the battery type and determine the characteristics of the cell 4) Select the number of battery cells to be connected in series 5) Calculate the required Ampere-hour (Ah) capacity of the battery

Step 1: Collect the battery loads

The first step is to determine the loads that the battery will be supporting. This is largely specific to the application of the battery, for example an AC UPS System or a Solar Power System.

Step 2: Construct the Load Profile

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

the design energy, , in VAh.

The autonomy time is often specified by the Client (i.e. in their standards). Alternatively, IEEE 446, "IEEE Recommended Practice for Emergency and Standby Power Systems for Industrial and Commercial Applications" has some guidance (particularly Table 3-2) for autonomy times. Note that IEEE 485 and IEEE 1115 refer to the load profile as the "duty cycle".

Step 3: Select Battery Type

The next step is to select the battery type (e.g. sealed lead-acid, nickel-cadmium, etc). The selection process is not covered in detail here, but the following factors should be taken into account (as suggested by IEEE):

Physical characteristics, e.g. dimensions, weight, container material, intercell connections, terminals

application design life and expected life of cell

Frequency and depth of discharge

Ambient temperature

Charging characteristics

Maintenance requirements

Ventilation requirements

Cell orientation requirements (sealed lead-acid and NiCd)

Seismic factors (shock and vibration)

Next, find the characteristics of the battery cells, typically from supplier data sheets. The characteristics that should be collected include:

Battery cell capacities (Ah) Cell temperature

Electrolyte density at full charge (for lead-acid batteries)

Cell float voltage

Cell end-of-discharge voltage (EODV).

Battery manufacturers will often quote battery Ah capacities based on a number of different EODVs. For lead-acid batteries, the selection of an EODV is largely based on an EODV that prevents damage of the cell through over-discharge (from over-expansion of the cell plates). Typically, 1.75V to 1.8V per cell is used when discharging over longer than 1 hour. For short discharge durations (i.e. <15 minutes), lower EODVs of around 1.67V per cell may be used without damaging the cell.

Nickel-Cadmium (NiCd) don't suffer from damaged cells due to over-discharge. Typical EODVs for Ni-Cd batteries are 1.0V to 1.14V per cell.

Step 4: Number of Cells in Series

The most common number of cells for a specific voltage rating is shown below:

Rated Voltage Lead-Acid Ni-Cd

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

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:

Ageing factor captures the decrease in battery performance due to age.

The performance of a lead-acid battery is relatively stable but drops markedly at latter stages of life. The "knee point" of its life vs performance curve is approximately when the battery can deliver 80% of its rated capacity. After this point, the battery has reached the end of its useful life and should be replaced. Therefore, to ensure that battery can meet capacity throughout its useful life, an ageing factor of 1.25 should be applied (i.e. 1 / 0.8). There are some exceptions, check with the manufacturer. For Ni-Cd batteries, the principles are similar to lead-acid cells. Please consult the battery manufacturer for suitable ageing factors, but generally, applying a factor of 1.25 is standard. For applications with high temperatures and/or frequent deep discharges, a higher factor of 1.43 may be used. For more shallower discharges, a lower factor of 1.11 can be used.

Temperature correction factor is an allowance to capture the ambient installation temperature. The capacity for battery cells are typicall quoted for a standard operating temperature of 25C and where this differs with the installation temperature, a correction factor must be applied. IEEE 485 gives guidance for vented lead-acid cells (see figure right), however for sealed lead-acid and Ni-Cd cells, please consult manufacturer recommendations. Note that high temperatures lower battery life irrespective of capacity and the correction factor is for capacity sizing only, i.e. you CANNOT increase battery life by increasing capacity.

Capacity rating factor accounts for voltage depressions during battery discharge. Lead-acid batteries experience a voltage dip during the early stages of discharge followed by some recovery. Ni-Cds may have lower voltages on discharge due to prolonged float charging (constant voltage). Both of these effects should be accounted for by the capacity rating factor - please see the manufacturer's recommendations. For Ni-Cd cells, IEEE 1115 Annex C suggests that for float charging applications, Kt = rated capacity in Ah / discharge current in Amps (for specified discharge time and EODV).

Worked Example

Load profile for this example

Step 1 and 2: Collect Battery Loads and Construct Load Profile

The loads and load profile from the simple example in the Energy Load Profile Calculation will be used (see the figure right). The design energy demand calculated for this system is Ed = 3,242.8 VAh.

Step 3: Select Battery Type

Vented lead acid batteries have been selected for this example.

Step 4: Number of Cells in Series

Suppose that the nominal battery voltage is Vdc = 120Vdc, the cell charging voltage is Vc = 2.25Vdc/cell, the end-of-discharge voltage is Veod = 1.8Vdc/cell, and the minimum and maximum load voltage tolerances are Vl,min = 10% and Vl,max = 20% respectively.

The maximum number of cells in series is:

cells

The minimum number of cells in series is:

cells

The selected number of cells in series is 62 cells.

Step 5: Determine Battery Capacity

Given a depth of discharge kdod = 80%, battery ageing factor ka = 25%, temperature correction factor for vented cells at 30 deg C of kt = 0.956 and a capacity rating factor of kc = 10%, the minimum battery capacity is:

Ah

Computer Software

Some battery manufacturers (such as Alcad) also provide software programs to size batteries using basic input data such as load profiles, autonomies, etc. The software will size the batteries and will often also provide details regarding different battery rack (or enclosure) dimensions.

What Next?

Using the results of the battery sizing calculation, the approximate dimensions of the batteries can be estimated based on typical vendor information. This will assist in determining the size, number and dimensions of the battery racks or cabinets required, which can then be used as input into the 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 mains waveform. See also ground loop.

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. [1]

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. [2]

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.