Learn about how to calculate the battery size for applications like Uninterrupted Power Supply (UPS), solar PV system, telecommunications, and other auxiliary services in power system along with solved example.
This 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 based on the IEEE guidelines. 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)
IEEE Battery Sizing Calculations
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 (Vdc)
${{V}_{\text{charging}}}$, charging voltage of cell (Vdc)
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 formula:
\[{{C}_{\text{minimum}}}=\frac{{{E}_{de}}\left( {{k}_{af}}\times {{k}_{tcf}}\times {{k}_{crt}} \right)}{{{V}_{dc}}\times {{k}_{mdod}}\times {{k}_{se}}}\]
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 battery sizing 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 25oC 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 = Ede = 3,245 Vah
Figure 1: Load Profile for the Battery Sizing 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.
Key Takwaways of Battery Sizing Calculation
- Battery sizing is crucial to ensure optimal performance and reliability of a system.
- Factors such as power demand, desired runtime, efficiency, and specific application requirements should be considered when determining battery size.
- Battery size is commonly expressed in ampere-hours (Ah) or kilowatt-hours (kWh).
- Renewable energy systems require careful consideration of daily energy consumption, available resources, efficiency, and system losses for accurate battery sizing.
- Temperature variations and safety considerations must be accounted for in the battery sizing process.
- It is generally recommended to use batteries of the same type, capacity, and age within a system for optimal performance.
- Consulting a professional can provide valuable guidance and ensure accurate battery sizing for specific applications.
Battery Sizing Calculation FAQs
Why is battery sizing important?
Battery sizing is important to ensure that a system has the appropriate battery capacity to meet its power requirements. Proper sizing ensures optimal performance, reliability, and longevity of the battery system.
How is battery size determined?
Battery size is determined by considering factors such as the power demand of the system, desired battery runtime, efficiency of the battery technology, and any specific requirements or constraints of the application. It involves calculating the required energy capacity and selecting a battery with matching specifications.
What units are used to express battery size?
Battery size is commonly expressed in ampere-hours (Ah) or kilowatt-hours (kWh). Ampere-hours represent the amount of charge a battery can deliver over a specific period of time, while kilowatt-hours indicate the energy capacity of the battery.
What factors should be considered when sizing batteries for renewable energy systems?
When sizing batteries for renewable energy systems, factors such as daily energy consumption, available solar/wind resources, charging and discharging efficiency, depth of discharge, and expected system losses should be taken into account. These factors help determine the battery capacity needed to store and supply energy effectively.
Can battery size be changed after installation?
Battery size can be changed after installation; however, it may involve additional costs and considerations. It is recommended to carefully plan and size the battery system during the initial design phase to avoid unnecessary modifications or expenses later on.
How does temperature affect battery sizing?
Temperature can significantly impact battery performance and capacity. It is essential to consider temperature effects on battery chemistry and account for temperature variations in the sizing process. Some batteries may require derating or adjustments to their capacity based on temperature conditions.
Are there any safety considerations when sizing batteries?
Safety is crucial when sizing batteries. It is important to follow manufacturer guidelines, local codes, and standards to ensure proper installation, ventilation, and protection against overcharging, overheating, or other potential hazards associated with battery systems.
Can I mix different battery sizes or types in a system?
Mixing different battery sizes or types in a system is generally not recommended due to variations in voltage, capacity, and charging/discharging characteristics. It is best to use batteries of the same type, capacity, and age to maintain optimal performance and balance within the system.
Should I consult a professional for battery sizing?
If you are unsure about the battery sizing process or have specific requirements for your application, consulting a professional, such as an electrical engineer or a renewable energy specialist, can provide valuable guidance and ensure accurate sizing for your needs.
