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newSchoolWorks.com › VoTechWorks › Building & Construction › Solar / PV Installation › Battery Storage Systems for PV Installations › Lesson 3
BLD-SOLA09-06 · Lesson 3 · 12 clock hours · theory

System Sizing: Load Analysis, Autonomy, and Battery Bank Design

Objective. Students will size a battery storage bank for a given residential backup application by calculating total critical load energy demand, required usable capacity, required nameplate capacity based on DoD limit, and selecting a battery model and configuration (series/parallel) that meets the design criteria.

⚠ Pending professional review

This lesson, its worked examples and its practice questions has not yet been verified by a licensed professional engineer or master tradesperson or by a certification or approval body. It is a study draft and may contain errors. Do not use it as instructions for work on a job site or on live equipment. Always follow your instructor, your supervising professional, and current official references and regulations.

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Why Battery Bank Sizing Matters

A battery bank that is too small will run out of energy before the backup window ends, leaving critical loads without power. One that is oversized wastes money and may never fully cycle, shortening its own life. Correct sizing starts with understanding exactly how much energy the system must deliver and then working backward through efficiency and depth-of-discharge limits to arrive at the nameplate capacity the battery bank must carry.

Step 1 — Critical Load Analysis

Not every load in a home needs to run during a grid outage. The first task is to identify critical loads: the appliances and circuits that must stay on. Common examples include a refrigerator, lighting circuits, a well pump, medical equipment, and a gas furnace blower.

For each critical load, record:

Multiply power by hours to get energy demand in watt-hours (Wh) or kilowatt-hours (kWh) per day per load. Sum all loads to get total daily critical load energy (E_load).

Then multiply by the number of backup days (autonomy) required:

> E_required = E_load × Autonomy (days)

Autonomy is a design decision made with the customer. Residential backup applications commonly target one to three days, but a medical or remote site may require more.

Step 2 — Accounting for System Losses

Energy is lost in the inverter, wiring, and the battery itself during charge and discharge. A round-trip efficiency factor is applied. A common overall system efficiency assumption for battery-backed systems is in the range of 90–95% depending on technology and inverter type; use the value specified in your design criteria or manufacturer documentation. Divide the required energy by this efficiency:

> E_usable_needed = E_required ÷ System Efficiency

Step 3 — Applying the Depth-of-Discharge Limit

Depth of discharge (DoD) is the percentage of a battery's nameplate capacity that is regularly used. Discharging a battery deeper than its design DoD degrades it faster.

To find the required nameplate capacity:

> Nameplate Capacity (kWh) = E_usable_needed ÷ DoD (as a decimal)

This is the total rated energy the bank must hold before any discharge occurs.

Step 4 — Temperature Derating (Lead-Acid)

Lead-acid batteries lose significant capacity in cold environments. If the battery enclosure is unheated, apply a derating factor from the manufacturer's temperature correction table. For example, at 30°F a flooded lead-acid battery may deliver only about 75–80% of its rated 77°F capacity. Divide the required nameplate capacity by the derating factor to find the derated nameplate capacity needed:

> Derated Nameplate = Nameplate Capacity ÷ Temp Derating Factor

Lithium chemistries also derate in cold, though the effect is generally less severe; always consult the manufacturer spec sheet.

Step 5 — Selecting Batteries and Determining Configuration

With the required nameplate capacity known, choose a battery model from an approved spec sheet. Note two key ratings: voltage (V) and capacity (Ah or kWh).

If using Ah-rated batteries:

> kWh = (Voltage × Ah) ÷ 1000

Series wiring increases voltage; total capacity (Ah) stays the same. Batteries must be identical.

Parallel wiring increases capacity (Ah); voltage stays the same.

Series-parallel combinations achieve both the required voltage and capacity.

The system DC bus voltage is set by the inverter/charger. Select the number of batteries in series to match that voltage, then add parallel strings until the total kWh meets or exceeds the derated nameplate requirement.

> Total strings needed = Required nameplate (kWh) ÷ kWh per string (round up to whole strings)

Safety Considerations

Battery work presents serious hazards. Follow these rules every time:

Putting It Together

Sizing follows a logical chain: identify loads → calculate energy demand → apply autonomy → correct for efficiency → correct for DoD → correct for temperature if needed → select battery model → calculate series/parallel configuration. Each step builds on the last, and an error early in the chain compounds. Always document your assumptions (autonomy days, DoD%, efficiency factor, temperature) so the design can be reviewed and updated as the project evolves.

Key terms10

Critical LoadA load that must remain energized during a grid outage; the starting point for backup system sizing.
AutonomyThe number of days a battery bank must supply the critical loads without any input from the grid or PV array.
Depth of Discharge (DoD)The percentage of a battery's nameplate capacity that is regularly drawn down during normal operation; exceeding the design DoD reduces cycle life.
Nameplate CapacityThe total rated energy or charge a battery can store under standard test conditions, expressed in kWh or Ah at a specified voltage.
Usable CapacityThe portion of nameplate capacity available for use, equal to nameplate capacity multiplied by the allowable DoD.
Temperature DeratingA reduction factor applied to battery capacity when the operating temperature is below the standard test temperature (typically 77°F/25°C for lead-acid); cold reduces available capacity.
Series ConfigurationConnecting batteries positive-to-negative so that voltages add while amp-hour capacity remains equal to that of one battery.
Parallel ConfigurationConnecting batteries positive-to-positive and negative-to-negative so that amp-hour capacity adds while voltage remains equal to that of one battery.
Round-Trip EfficiencyThe ratio of energy delivered by a battery to the energy put into it over one charge-discharge cycle; losses occur in both directions.
State of Charge (SoC)The current energy level of a battery expressed as a percentage of its nameplate capacity; 100% is fully charged.

Worked examples4

1. A homeowner wants a 1-day backup for the following critical loads: refrigerator 150 W running 8 h/day; LED lighting 200 W running 5 h/day; gas furnace blower 400 W running 3 h/day. The system uses LFP batteries with an allowable DoD of 80% and an overall system efficiency of 95%. What is the required nameplate battery capacity in kWh?
  1. Calculate energy per load: Refrigerator = 150 W × 8 h = 1,200 Wh; Lighting = 200 W × 5 h = 1,000 Wh; Blower = 400 W × 3 h = 1,200 Wh.
  2. Sum loads: Total daily critical load = 1,200 + 1,000 + 1,200 = 3,400 Wh = 3.4 kWh.
  3. Apply autonomy (1 day): E_required = 3.4 kWh × 1 = 3.4 kWh.
  4. Apply system efficiency: E_usable_needed = 3.4 kWh ÷ 0.95 = 3.58 kWh (rounded to two decimal places).
  5. Apply DoD to find nameplate capacity: Nameplate = 3.58 kWh ÷ 0.80 = 4.47 kWh. Round up to the next available battery size — the bank must provide at least 4.47 kWh nameplate.
Answer: Required nameplate capacity ≈ 4.47 kWh (design must select batteries totaling at least this value).
2. A designer selects a 48 V / 100 Ah LFP battery module for the system in Example 1 (required nameplate ≈ 4.47 kWh, 80% DoD). The inverter operates at 48 V DC. How many modules are needed, and how are they wired?
  1. Find kWh per module: 48 V × 100 Ah ÷ 1,000 = 4.8 kWh per module.
  2. Determine series string: The inverter bus is 48 V and each module is 48 V, so one module per string satisfies the voltage requirement (1 module in series = 48 V).
  3. Determine number of strings (parallel): Modules needed = 4.47 kWh ÷ 4.8 kWh per module = 0.93 → round up to 1 module (1 string).
  4. Verify: 1 module × 4.8 kWh nameplate × 80% DoD = 3.84 kWh usable. After applying 95% efficiency: 3.84 × 0.95 = 3.65 kWh delivered, which exceeds the 3.4 kWh daily requirement. Design is valid.
Answer: 1 module (48 V / 100 Ah LFP) wired as a single unit (no additional series or parallel connections needed) meets the design requirement.
3. An off-grid cabin requires 6 kWh/day of critical load energy, 2 days of autonomy, and uses flooded lead-acid batteries limited to 50% DoD. The battery enclosure is unheated and ambient temperature reaches 30°F; the manufacturer's table gives a capacity derating factor of 0.77 at that temperature. Overall system efficiency is 85%. What derated nameplate capacity must the battery bank provide?
  1. Apply autonomy: E_required = 6 kWh/day × 2 days = 12 kWh.
  2. Apply system efficiency: E_usable_needed = 12 kWh ÷ 0.85 = 14.12 kWh.
  3. Apply DoD: Nameplate at 77°F = 14.12 kWh ÷ 0.50 = 28.24 kWh.
  4. Apply temperature derating: Derated nameplate = 28.24 kWh ÷ 0.77 = 36.67 kWh. The bank must have at least 36.67 kWh of nameplate capacity rated at standard temperature to deliver the required usable energy at 30°F.
Answer: The battery bank must have a nameplate capacity of at least 36.67 kWh (at standard temperature) to meet the load after temperature derating.
4. A designer has 6 V / 200 Ah flooded lead-acid batteries available. The off-grid system from Example 3 requires at least 36.67 kWh nameplate and operates on a 24 V DC bus. How many batteries are needed, and how are they configured?
  1. Find kWh per battery: 6 V × 200 Ah ÷ 1,000 = 1.2 kWh each.
  2. Determine batteries per series string for 24 V bus: 24 V ÷ 6 V = 4 batteries in series per string. Each string = 4 × 1.2 kWh = 4.8 kWh nameplate.
  3. Determine number of parallel strings: Strings needed = 36.67 kWh ÷ 4.8 kWh per string = 7.64 → round up to 8 strings.
  4. Total batteries: 8 strings × 4 batteries per string = 32 batteries.
  5. Verify total nameplate: 32 × 1.2 kWh = 38.4 kWh ≥ 36.67 kWh required. Configuration is valid.
Answer: 32 batteries (6 V / 200 Ah each) wired as 8 parallel strings of 4 batteries in series, providing 24 V at 38.4 kWh nameplate capacity.

The math in this lesson2

Learners count series and parallel batteries to reach system voltage and capacity.
6.RP.3A-SSE.1
Brush up in the math halls at newSchoolWorks.com:
In class: Instructor works through a full sizing example on the whiteboard: students list critical loads (kW), multiply by backup hours to get kWh demand, divide by allowable DoD to get required nameplate kWh, then select a battery model from a spec sheet and determine the number of units and series/parallel configuration; students replicate the calculation in a guided worksheet. · Students complete two independent sizing problems of increasing complexity—one flooded lead-acid off-grid scenario with temperature derating and one LFP AC-coupled grid-tied backup scenario—using provided load lists, spec sheets, and a scientific calculator; peer-check answers before instructor review. · Introduction to software-assisted sizing: students use a free browser-based PV and storage sizing tool (instructor selects an available free platform such as PVWatts or a manufacturer sizing tool) to model the second scenario and compare software output to their hand-calculation results, noting any differences and explaining discrepancies in a short written reflection.
Materials: Scientific calculators, printed load-analysis worksheets, manufacturer spec sheets (matching those used in Lesson 1), laptop or tablet with internet access for sizing software, NABCEP PV Installation Professional Exam Prep Guide (energy storage section), whiteboard
Check: Both independent sizing problems graded by instructor; students must correctly calculate required nameplate capacity and select a valid battery configuration with no more than one arithmetic error per problem (75% accuracy across all numerical steps). Written reflection must identify at least one meaningful difference between hand calculation and software output.

Practice check8

Answer each question, then check it. Nothing is recorded; this is your own practice.

Energy Storage System Design
1. A critical load analysis lists a sump pump at 800 W that runs 2 hours per day and a refrigerator at 150 W that runs 10 hours per day. What is the combined daily energy demand of these two loads?
Energy Storage System Design
2. A battery bank has a nameplate capacity of 20 kWh and an allowable depth of discharge of 50%. What is the usable capacity of the bank?
Energy Storage System Design
3. A designer calculates that a backup system must deliver 8 kWh of usable energy. The selected LFP batteries have an allowable DoD of 80%. What minimum nameplate capacity must the battery bank have?
Energy Storage System Design
4. A flooded lead-acid battery bank is installed in an unheated garage where winter temperatures fall well below 77°F. Compared with the battery's rated capacity at standard temperature, what should the designer expect at low temperatures?
Energy Storage System Design
5. Four 6 V batteries are connected in series. What is the resulting bank voltage and amp-hour capacity if each battery is rated 200 Ah?
Safety and Safe Work Practices
6. A technician is about to replace a faulty cell in a flooded lead-acid battery bank. Which of the following is the MOST important first step before touching any battery terminal?
Energy Storage System Design
7. A system requires a 48 V battery bank with at least 9.6 kWh of nameplate capacity. A designer has 12 V / 100 Ah batteries (1.2 kWh each) available. How many batteries are needed, and how are they configured?
Energy Storage System Design
8. A student hand-calculates that a backup system needs 12.5 kWh of nameplate capacity. When the same scenario is entered into a browser-based sizing tool, the software recommends 14.2 kWh. Which explanation BEST accounts for the discrepancy?
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