Battery Sizing with Days of Autonomy and Depth of Discharge for JSS 1

System Sizing (Battery)

Performance Objectives

By the end of the lesson, students should be able to:

1. explain meaning of Days of Autonomy (DoA);
2. Use the battery depth of discharge (DoD) to determine the corrected battery size.
3. use system Days of Autonomy (DoA) to determine the total battery bank capacity.

Introduction to Battery Sizing in Solar PV Systems

Solar photovoltaic (PV) systems use batteries to store energy. This stored energy is used when the sun is not shining, such as at night or on cloudy days. To ensure a solar system works reliably, it is important to choose the right size of battery.

Choosing the correct battery size means making sure the battery can store enough energy to power all the appliances for the required time. It also means protecting the battery so it lasts for many years. Two important ideas for battery sizing are Days of Autonomy (DoA) and Depth of Discharge (DoD).

What is Days of Autonomy (DoA)?

Days of Autonomy (DoA) refers to the number of days a fully charged battery bank can supply power to a solar system’s electrical loads without any charging from the solar panels.

Imagine a situation where there are several cloudy days in a row, and the solar panels cannot generate enough electricity to charge the batteries. The Days of Autonomy tells you how long your battery system can continue to power your home or school appliances during such periods.

For example, if a system has 2 Days of Autonomy, it means the battery can power the connected appliances for two full days without receiving any charge from the sun. This is important for ensuring a continuous power supply, especially in areas with unpredictable weather.

What is Depth of Discharge (DoD)?

Depth of Discharge (DoD) is the percentage of a battery’s total capacity that has been used or discharged.

Batteries have a certain amount of energy they can store. When electricity is drawn from a battery, its charge level goes down. The DoD indicates how much of that stored energy has been taken out. For example, if a 100 Ampere-hour (Ah) battery has supplied 50 Ah of energy, it has been discharged by 50%. Its Depth of Discharge is 50%.

It is important not to discharge a battery completely (100% DoD) because this can damage it and shorten its lifespan. Most batteries, especially deep-cycle batteries used in solar systems, have a recommended maximum DoD. This recommended DoD helps to protect the battery and ensure it lasts longer.

Common recommended DoD values for solar batteries are often around 50% to 80%. For instance, if a battery has a recommended DoD of 70%, it means only 70% of its total capacity should be used before it is recharged. The remaining 30% should always stay in the battery to prevent damage.

Calculating Usable Battery Capacity using Depth of Discharge (DoD)

The total capacity of a battery is its nominal capacity, usually given in Ampere-hours (Ah). However, due to the Depth of Discharge (DoD) recommendation, not all of this capacity is actually usable. To protect the battery, only a certain percentage should be used.

Formula for Usable Capacity

The usable capacity of a battery can be calculated using the following formula:

Usable Capacity (Ah) = Nominal Battery Capacity (Ah) × Recommended DoD (%)

Remember to convert the percentage DoD into a decimal for the calculation. For example, 70% DoD becomes 0.70.

Worked Example 1: Calculating Usable Capacity

A solar system uses a 100 Ah battery. The manufacturer recommends a maximum Depth of Discharge (DoD) of 70%.

Determine the correct usable capacity of this battery.

1. Identify the Nominal Battery Capacity: 100 Ah
2. Identify the Recommended DoD: 70% (or 0.70 as a decimal)
3. Apply the formula:

Usable Capacity = 100 Ah × 0.70

Usable Capacity = 70 Ah

This means that out of the 100 Ah total capacity, only 70 Ah should be used to power the appliances before the battery needs recharging.

Calculating Total Battery Bank Capacity using Days of Autonomy (DoA)

To determine the total battery bank capacity needed for a solar system, you must consider the daily energy requirement of the appliances and the desired Days of Autonomy (DoA).

The daily energy requirement is the total amount of energy (in Watt-hours, Wh) that all the appliances in the system consume in one day. This value is usually obtained from a load sizing worksheet.

Steps to Determine Total Battery Bank Capacity

The procedure involves the following steps:

1. Determine the Total Daily Energy Requirement (Wh): This value is usually provided from a load sizing worksheet.
2. Calculate the Total Energy Needed for Autonomy (Wh): Multiply the daily energy requirement by the desired Days of Autonomy.
3. Convert Total Energy to Ampere-hours (Ah) at Battery Voltage: Divide the total energy needed by the battery voltage (e.g., 12V for a common solar battery).
4. Adjust for Depth of Discharge (DoD): Divide the result by the recommended DoD (as a decimal) to find the actual nominal battery capacity required.

Formula for Required Battery Capacity

Required Battery Capacity (Ah) = (Total Daily Energy Requirement (Wh) × Days of Autonomy (days)) / (Battery Voltage (V) × Recommended DoD (%))

For JSS1, we will assume a common battery voltage of 12 Volts (V) for our calculations.

Worked Example 2: Calculating Required Battery Capacity

A small solar system for a classroom has a total daily energy requirement of 600 Watt-hours (Wh). The system needs 2 Days of Autonomy (DoA) and uses 12V batteries with a recommended Depth of Discharge (DoD) of 50%.

Determine the total battery bank capacity needed for this system.

1. Identify the Total Daily Energy Requirement: 600 Wh
2. Identify the Days of Autonomy (DoA): 2 days
3. Identify the Battery Voltage: 12 V
4. Identify the Recommended DoD: 50% (or 0.50 as a decimal)
5. Apply the formula:

Required Battery Capacity (Ah) = (600 Wh × 2 days) / (12 V × 0.50)

Required Battery Capacity (Ah) = 1200 Wh / 6 V

Required Battery Capacity (Ah) = 200 Ah

Therefore, a battery bank with a total nominal capacity of 200 Ah is needed for this classroom solar system.

Sizing Solar Batteries: A Combined Approach

To correctly size solar batteries, both the Days of Autonomy (DoA) and the Depth of Discharge (DoD) must be considered. This ensures the battery bank is large enough to power the system for the required number of days and that the batteries are protected from damage.

Practical Steps for Sizing Solar Batteries

The procedure for sizing solar batteries involves the following steps:

1. Determine Daily Energy Requirement: Find the total Watt-hours (Wh) consumed by all appliances in one day from a load sizing worksheet.
2. Choose Days of Autonomy (DoA): Decide how many days the system should run without sunlight (e.g., 1, 2, or 3 days).
3. Identify Battery Voltage: Note the voltage of the battery (e.g., 12V).
4. Identify Recommended Depth of Discharge (DoD): Find the maximum DoD recommended by the battery manufacturer (e.g., 70% or 0.70).
5. Calculate Required Battery Capacity: Use the combined formula to find the nominal Ampere-hour (Ah) capacity needed.

Worked Example 3: Sizing a Battery Bank for a Home System

A small home solar system has a daily energy requirement of 900 Watt-hours (Wh). The owner wants the system to have 3 Days of Autonomy (DoA). The system will use 12V deep-cycle batteries with a recommended Depth of Discharge (DoD) of 60%.

Determine the total battery bank capacity needed for this home system.

1. Daily Energy Requirement = 900 Wh
2. Days of Autonomy (DoA) = 3 days
3. Battery Voltage = 12 V
4. Recommended DoD = 60% (or 0.60)
5. Apply the formula:

Required Battery Capacity (Ah) = (Daily Energy Requirement × DoA) / (Battery Voltage × DoD)

Required Battery Capacity (Ah) = (900 Wh × 3 days) / (12 V × 0.60)

Required Battery Capacity (Ah) = 2700 Wh / 7.2 V

Required Battery Capacity (Ah) = 375 Ah

Therefore, the home solar system requires a battery bank with a total nominal capacity of 375 Ah.

Worked Example 4: Usable Energy from a Given Battery Bank

A solar system uses a 200 Ah battery bank. It is designed for 2 Days of Autonomy (DoA) and has a recommended Depth of Discharge (DoD) of 70%. The battery voltage is 12V.

Determine the total usable energy (in Watt-hours) that this battery bank can provide over its 2 days of autonomy.

1. Nominal Battery Capacity = 200 Ah
2. Days of Autonomy (DoA) = 2 days
3. Battery Voltage = 12 V
4. Recommended DoD = 70% (or 0.70)
5. First, calculate the usable capacity in Ah:

Usable Capacity (Ah) = Nominal Capacity (Ah) × DoD (%)

Usable Capacity (Ah) = 200 Ah × 0.70

Usable Capacity (Ah) = 140 Ah

6. Next, calculate the total usable energy in Watt-hours (Wh) over the 2 days:

Total Usable Energy (Wh) = Usable Capacity (Ah) × Battery Voltage (V) × Days of Autonomy (days)

Total Usable Energy (Wh) = 140 Ah × 12 V × 2 days

Total Usable Energy (Wh) = 3360 Wh

This 200 Ah battery bank can provide a total of 3360 Wh of usable energy over its 2 days of autonomy, while respecting the 70% DoD limit.