This particular article talks about the battery sizing for certain applications such as Uninterrupted Power Supply (UPS), solar PV system, telecommunications, and other auxiliary services in power system. Whatsoever the practical application, batteries are proven technology to store an electrical energy. Other than storage purposes, batteries are extensively utilized in order to provide voltage support for weaker electric power systems such as very long transmission lines.

**Why Is Battery Sizing Essential?**

Battery sizing is crucial in order to ascertain that it can supply power to the connected loads for the time period it is designed. Unsuitable sizing of the battery can pose many serious problems such as permanent battery damage because of over-discharge, low voltages to the load, insufficient backup times.

The battery sizing can be initiated once we have the following information:

- Loads need to be supported by battery
- Minimal voltage for battery
- Back up time(s)

**Calculation Approach**

The calculations performed are based on “Recommended Practice for Sizing Lead-Acid Batteries for Stationary Applications” and “Recommended Practice for Sizing Nickel-Cadmium Batteries for Stationary Applications” IEEE standards. All the calculations in this article are established on conventional lead-acid or nickel-cadmium (NiCd) batteries. The outcomes presented here may not support other types of batteries, so the manufacturer’s guidance will require being conferred.

The methodological analysis has the five steps as follows:

Step 1: Collect the total connected loads that the battery requires to supply

Step 2: Develop a load profile and further compute design energy

Step 3: Choose the type of battery and determine the cell characteristics

Step 4: Choose the battery cells required to be linked in series fashion

Step 5: On the basis of design loads, compute the desired Ampere-hour (Ah) battery capacity

**Step 1: Collect the Total Connected Loads**

The first step is the determination of the total connected loads that the battery needs to supply. This is mostly particular to the battery application like UPS system or solar PV system.

**Step 2: Develop the Load Profile**

Generally, the “**Autonomy Method**” is utilized to establish a load profile for batteries.

The backup (autonomy) time is frequently provided by the customer. Instead, IEEE standard “Recommended Practice for Emergency and Standby Power Systems for Industrial and Commercial Applications” provides certain guidelines for autonomy (backup or discharge) times.

**Step 3: Choose the Type of Battery**

The following step is the selection of the type of battery (e.g. Lead-acid or nickel-cadmium). While choosing the battery type, the following elements should be considered as per IEEE guidance.

- Ambient temperature threshold
- Charging & discharging characteristics
- Maintenance & Ventilation requisites
- Cell orientation essentials
- Shock and vibration factors
- Anticipated cell life
- Physical properties like dimensions, weight, and battery terminals

Next step is to determine the battery cell characteristics which are generally provided in manufacturer’s data sheet. The primary cell characteristics that should be considered are:

- Ampere-Hour capacities of battery cell
- Temperature of battery cell
- Electrolyte density in case of lead-acid batteries at a full charge
- Cell float voltage of cell
- Cell end-of-discharge voltage (EODV) of cell

Battery’s Ampere-Hour capacities are provided by the battery manufacturer on the basis of various EODVs. For lead-acid type batteries, an EODV is principally based on an EODV value that prohibits cell damage by over-discharge. Generally, EODV ranging between 1.750V and 1.80Vis utilized per cell when discharging time is longer than 1 hour. For short discharging time (<15 minutes), an EODV of about 1.66V per cell may be utilized without cell damage.

**Step 4: Choose the Battery Cells Required To Be Linked In Series Fashion**

The number of cells required for a particular voltage rating is presented below:

Rated Voltage (V) | Cells (Lead-Acid Battery) |

12 | 6 |

24 | 12 |

48 | 24 |

125 | 60 |

Nevertheless, the number of cells required can be determined more precisely in order to match with the load tolerance more accurately. The number of battery cells expected to be linked in series fashion must fall between the two limits which are given below:

\[{{N}_{\text{maximum}}}=\frac{{{V}_{dc}}\left( 1+{{V}_{\text{load,max}}} \right)}{{{V}_{\text{charging}}}}\]

\[{{N}_{\text{minimum}}}=\frac{{{V}_{dc}}\left( 1-{{V}_{\text{load,min}}} \right)}{{{V}_{\text{eodv}}}}\]

Where

${{N}_{\text{maximum}}}$, Maximum battery cells required

${{N}_{\text{minimum}}}$, Minimum battery cells required

${{V}_{dc}}$, Battery Voltage (Nominal)

${{V}_{\text{load,min}}}$, Minimum load voltage tolerance in %

${{V}_{\text{load,max}}}$, Maximum load voltage tolerance in %

${{V}_{\text{eodv}}}$, Represents end of discharge voltage (V_{dc})

${{V}_{\text{charging}}}$, charging voltage of cell (V_{dc})

Choose the required number of cells within these two limits (although choosing cell numbers in the middle of minimum and maximum values would be most suited).

**Step 5: Compute the Desired Ampere-Hour (Ah) Battery Capacity **

The battery capacity desired to accommodate the total designed load over the determined back up (autonomy) time can be computed using the following equation:

\[{{C}_{\text{minimum}}}=\frac{{{E}_{de}}\left( {{k}_{af}}\times {{k}_{tcf}}\times {{k}_{crt}} \right)}{{{V}_{dc}}\times {{k}_{mdod}}\times {{k}_{se}}}\]

Where

${{E}_{de}}$, total designed energy over back up time (VAh)

${{k}_{af}}$, Battery Aging Factor (%)

${{k}_{tcf}}$, Temperature Correction Factor (%)

${{k}_{crt}}$, Capacity Rating Factor (%)

${{V}_{dc}}$, Battery Voltage (Nominal)

${{k}_{mdod}}$, Maximum depth of Discharge (%)

${{k}_{se}}$, System Efficiency (%)

Choose a battery capacity (Ampere-Hour) that surpasses the minimum capacity computed using the above formula.

An explanation of the various elements:

**Aging Factor:**

It actually captures the reduction in battery performance because of the age factor.

The lead-acid battery performance is comparatively stable but reduces with the passage of time.

**Temperature correction factor:**

The battery cells capacity is generally provided for a standardized temperature which is 25^{o}C and if it varies somewhere with the installation temperature, a correction factor is needed to implement.

**Capacity rating factor**

This particular factor accounts for voltage reduction during the discharge of the battery. In Lead-acid batteries, a voltage dip occurs in the early phases of battery discharge followed by certain recovery.

**System efficiency**

It accounts for battery losses (coulombic efficiency) as well as power electronics losses (such as charger and inverter).

**Battery Sizing Calculation Example**

**Step 1 and 2: Collect All the Connected Loads and Develop a Load Profile**

In this particular example, we will apply the same loads and load curve provided in the **Load Profile Calculation Example**. The load profile for this case is demonstrated in the figure right and the following parameters were computed:

Total Design Energy Demand = E_{de} = 3,245 Vah

Fig.1: Load Profile for the Example

**Step 3: Choose the Type of Battery**

For this particular example, a vented lead-acid battery has been chosen.

**Step 4: Choose the Battery Cells Required To Be Linked In Series Fashion**

We assumed the following values in order to calculate number of cells required:

${{V}_{dc}}=120V$

${{V}_{\text{load,min}}}=10%$

${{V}_{\text{load,max}}}=20%$

${{V}_{\text{eodv}}}=1.80V/cell$

${{V}_{\text{charging}}}=2.25V/cell$

Maximum number of cells required to be connected in series:

\[{{N}_{\text{maximum}}}=\frac{{{V}_{dc}}\left( 1+{{V}_{\text{load,max}}} \right)}{{{V}_{\text{charging}}}}=\frac{120\times \left( 1+0.2 \right)}{2.25}=64\text{ Cells}\]

Minimum number of cells required to be connected in series:

\[{{N}_{\text{minimum}}}=\frac{{{V}_{dc}}\left( 1-{{V}_{\text{load,min}}} \right)}{{{V}_{\text{eodv}}}}=\frac{120\times \left( 1-0.1 \right)}{1.80}=60\text{ Cells}\]

The number of cells chosen for this example is 62 cells which is in between the maximum and minimum limits.

**Step 5: Compute the Desired Ampere-Hour (Ah) Battery Capacity**

We assumed the following values in order to compute the battery capacity:

${{E}_{de}}=3245\text{ }VAh$

${{k}_{af}}=0.30$

${{k}_{tcf}}=0.96$

${{k}_{crt}}=0.12$

${{V}_{dc}}$, Battery Voltage (Nominal)

${{k}_{mdod}}=0.75$

Using the above mentioned parameters, we can compute the minimum battery capacity as:

\[{{C}_{\text{minimum}}}=\frac{{{E}_{de}}\left( {{k}_{af}}\times {{k}_{tcf}}\times {{k}_{crt}} \right)}{{{V}_{dc}}\times {{k}_{mdod}}\times {{k}_{se}}}\]

\[{{C}_{\text{minimum}}}=\frac{3245\times \left( 1.30\times 0.96\times 1.12 \right)}{120\times 0.75}=50.4\text{ Ah}\]

Choose a battery capacity (Ampere-Hour) that surpasses the minimum capacity computed using the above formula.