Battery Sizing Explained

Electric power has become one of the most significant requirements in the modern world. In the bid for clean and free energy utilization, engineers have come up with battery systems such as solar and electric vehicles, triggering growth in battery utilization. These batteries are designed to meet certain criteria, and engineers need to be able to size such batteries.

 

What Is Battery Sizing?

A battery is a hardware device employed to supply power to another device giving the device permission to work without being connected to the power cord. Such devices include laptops, cellphones, electric cars, and radios and can be classified as rechargeable or non-rechargeable. The battery can be categorized according to the material used, including lithium-ion, lithium polymer, nickel-cadmium, and nickel-metal hydride.

Battery sizing is balancing the power requirement of a given system and coming up with a battery that meets the client’s requirements. Sizing determines the number of kilowatt-hours stored in a particular battery. It is an important action that gives a product lifetime. Undersized batteries reduce the shelf life of an electrical product.

To size a battery, gather the following information:

• load that will be supported by the battery to be designed
• minimal voltage the battery should handle
• backup time

 

IEEE Sizing Calculations

Our calculations are based on the IEEE-provided standards for the sizing of both nickel-cadmium and lead-acid station application batteries. This is a directive to all users that the calculation here may not be used to design any other battery type unless you refer to the guides provided by the manufacturers of the other types.

The following should guide you during the sizing process:

• Collect the total loads that will be supported by the battery. This step will help the designer determine the total load the battery should supply.

• Develop a load profile. The load profile is determined using the autonomy method, and IEEE standards give the guidelines for the autonomy, discharge, or backup times.

• Select the type of battery to design. Choose the type of battery, for example, lead-acid and follow IEEE-provided guidance on characteristics of charging and discharging; essentials on cell orientations; the threshold for ambient temperature; cell life; ventilation and maintenance requirements; other physical properties such as battery terminals and weight.

Using the manufacturer’s datasheet, determine the battery cell characteristics, including cell temperature; cell floating voltage; end of discharge voltage (EODV, which in most batteries ranges between 1.75 V to 1.8 V per cell if the discharge time is more than one hour and 1.66 V if the discharge time is less than 15 minutes); AH battery cell capacity; electrolyte density in the case of lead-acid batteries.

Choose battery cells that can be linked in series method. For lead acid of a particular size, the list below shows the number of cells that can fit in them.

RATED VOLTAGE (V)	CELLS
6	3
12	6
24	12
48	24
120	60

Table 1. Table Showing Different Battery Voltage Ratings and The Number of Cells Required for The Lead Acid Battery

 

I would not advise designers to always stick to the list above because they can perform calculations and determine the required number of cells to match a specific load. The formulas here will guide designers in determining the number of cells required, which should not go below or above this limit:

\[N_{max}=\frac{V_{dc}(1+V_{load,max})}{V_{charging}}\]

\[N_{min}=\frac{V_{dc}(1-V_{load,min})}{V_{EODV}}\]

Where

N_max =  Maximum number of cells needed per battery

N_min =  Minimum number of cells needed per battery

V_dc =  Nominal voltage of the battery

V_charging =  Cell’s charging voltage

V_{load, max} =  Maximum battery load tolerance computed in %

V_{load, min} =  Minimum battery load tolerance computed in %

V_EODV =  End-of-discharge battery cell voltage

 

When choosing the number of cells between the two limits, always choose the average number of cells between the two limits for the best outcome.

 

Calculating Battery Capacity in Ampere-Hour

This can be computed by use of the following equation

\[C_{min}=\frac{E_{de}(k_{af}k_{tcf}k_{crt})}{V_{dc}k_{mdod}k_{se}}\]

Where

C_min  = Minimum battery desired capacity

E_de = Total required energy over the backup time (VAH)

k_tcf = Temperature correction factor

k_af = The aging factor of the battery

k_crt = Battery capacity rating factor

 k_se = System efficiency in percentage

k_mdod = Maximum discharge depth

V_dc = Nominal battery voltage

Make sure to choose the battery capacity which is more than the calculated minimum above.

Let’s take a quick look at the important elements of the formula above.

Battery Capacity Rating Factor. This factor represents the battery voltage reduction during the discharge process.

The Aging Factor of the Battery. This captures how the battery performance reduces based on how long it will be used.

System Efficiency. This represents the battery and electronic power losses.

Temperature Correction Factor. The battery cell is designed to work at a particular temperature and, if this temperature is violated, a correction factor has to be implemented.

 

Example of Battery Sizing Calculation

Collect all the connected loads and develop the load profile.

 

Figure 1.  Load powered by the battery to be sized. Image used courtesy of Simon Mugo

 

From the figure above, we can compute the total design energy demand. It is important to note that the figure represents energy rectangles piled on top of each other.

• Height represents load (VA)
• Width represents the time (autonomy)
• The rectangle area is the total energy of the load

 

From the graph, 

Design Energy Demand, E_tle = Total areas of the Rectangles in the graph = 2700 Vah

Design Energy Demand, E_de = E_tle(1+k_cont) (1+k_dm)

Let k_cont = 10% and k_dm = 10%

E_de = 2700(1+0.1) (1+0.1) = 3267 Vah

 

Battery Type 

For the design calculation example, we are working with the lead-acid battery.

Let’s assume some values as follows to calculate the battery’s number of cells

V_dc = 120

V_charging = 2.25V/cell

Vl_{oad, max} = 30

V_{load, min} = 15

V_EODV = 1.75V/cell

The maximum number of cells that should be required for series connection

\[N_{max}=\frac{V_{dc}(1+V_{load,max})}{V_{charging}}\]

\[N_{max}=\frac{120(1+0.3)}{2.25}=70\,cells\]

The minimum number of cells that should be required for series connection

\[N_{min}=\frac{V_{dc}(1-V_{load,min})}{V_{EODV}}\]

\[N_{min}=\frac{120(1-0.15)}{1.75}=58\,cells\]

The total number of cells is the average of the sum of maximum and minimum which is given by (70+58)/2 = 64 cells

 

Computing Ampere-Hour Battery Capacity 

Let’s assume the following values to compute ampere-hour battery capacity.

Cmin  = Minimum battery desired capacity

E_de = 3267VAh

k_tcf = 0.94

k_af = 0.2

k_crt = 0.15

k_mdod = 0.75

V_dc = 120V

By use of the parameters listed above, calculate the minimum battery using

\[C_{min}=\frac{E_{de}(k_{af}k_{tcf}k_{crt})}{V_{dc}k_{mdod}k_{se}}\]

\[C_{min}=\frac{3267(1.2\times0.94\times1.15)}{120\times0.75}=47.09\,Ah\]

From the above computation, choose a battery size with higher capacity than the calculated battery capacity above.

 

Key Takeaways of Battery Sizing

• A battery is the hardware used to supply power to electronic and electrical devices that need it.
• Battery sizing is the calculation determining the battery size that will sufficiently support the load.
• The reader has understood the steps that are approached during the sizing of the battery.
• Readers have been fashioned with the formula necessary for battery sizing and provided with a fully solved example.

 

Featured image used courtesy of Adobe Stock