Instant UPS Battery String Sizing Calculator: Get Series/Parallel Counts & Target DC Bus Voltage

This guide explains sizing UPS battery strings for instant UPS using series and parallel configurations.

It covers target DC bus voltage, cell counts, runtime, and practical engineering calculations standards compliance.

UPS Battery String Sizing Calculator (Series / Parallel Counts for Target DC Bus Voltage)

Target DC bus voltage (V)

Single battery nominal voltage (V) 12 V (sealed lead-acid block) 6 V 2 V (industrial cell) Custom value

Custom single battery nominal voltage (V)

Single battery rated capacity (Ah)

UPS load active power (kW)

backup time (h)

Opciones avanzadas

DC system efficiency (%)

Usable depth of discharge (%)

Design energy margin (%)

Series count rounding method Ceiling (always round up) Nearest integer

Max DC bus deviation from target (%)

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Enter UPS and battery data to obtain the series and parallel battery counts.

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Calculation method and formulas (units in SI):

• Target DC bus voltage: V_target in volts (V) as specified by the UPS DC link.
• Single battery nominal voltage: V_batt in volts (V).
• Number of batteries in series (integer): Ns = round_method( V_target / V_batt ).
• Actual nominal DC bus voltage: V_bus = Ns × V_batt [V].
• UPS load active power: P_load in kilowatts (kW). Converted to watts: P_W = P_load × 1000 [W].
• Required backup time: t in hours (h).
• Load energy during backup: E_load = P_W × t [Wh].
• DC system efficiency: η_dc as a per-unit number, from DC bus to load (for example 0.92 for 92 %).
• Usable depth of discharge: DOD_pu as a per-unit value (for example 0.8 for 80 %).
• Design energy margin: M_pu as a per-unit oversizing factor (for example 0.10 for 10 %).
• Required battery energy: E_batt_req = E_load / (η_dc × DOD_pu) × (1 + M_pu) [Wh].
• Single battery capacity: C_batt in ampere-hours (Ah).
• Required ampere-hours at bus voltage: C_req = E_batt_req / V_bus [Ah].
• Number of parallel strings (integer): Np = ceil( C_req / C_batt ).
• Total number of batteries: N_total = Ns × Np.
• Total installed nominal energy: E_total = V_bus × C_batt × Np [Wh].

UPS application	Typical DC bus voltage (V)	Typical series count with 12 V blocks (Ns)	Example configuration
Small single-phase UPS	36 V to 96 V	3 to 8	4 × 12 V = 48 V DC bus
Medium single/three-phase UPS	192 V to 240 V	16 to 20	16 × 12 V = 192 V DC bus
Large three-phase UPS	360 V to 480 V	30 to 40	32 × 12 V = 384 V DC bus
Industrial DC systems (2 V cells)	110 V to 220 V	55 to 110 (2 V cells)	110 × 2 V = 220 V DC bus

Technical FAQ – UPS Battery String Sizing

How is the number of series batteries (Ns) determined?

The series count is calculated by dividing the target DC bus voltage by the nominal voltage of a single battery and applying a rounding method (typically ceiling) to ensure the resulting DC bus voltage is equal to or higher than the target.

How is the number of parallel strings (Np) determined?

The battery energy is computed from load power and backup time, corrected for DC system efficiency, usable depth of discharge and design margin. This energy is converted to ampere-hours at the DC bus voltage and divided by the single battery capacity. The result is rounded up to obtain the number of parallel strings.

Why do efficiency, depth of discharge and margin matter in sizing?

Converter and cable losses reduce the usable energy, while limiting depth of discharge and including a margin provides acceptable battery life and capacity at end of life. Ignoring these factors usually leads to underestimated battery capacity and insufficient backup time.

Can I use this calculator for lithium-ion UPS batteries?

Yes, provided you enter the correct single cell or module nominal voltage, rated capacity and suitable values for usable depth of discharge and efficiency that match the specific lithium-ion technology and UPS design.

Overview of Instant UPS Battery String Design

Designing battery strings for instant UPS systems requires deterministic calculation of series and parallel counts to meet DC bus voltage, runtime, and system reliability targets. A systematic approach reduces risk, ensures compliance with standards, and simplifies procurement and maintenance.

Key design parameters and constraints

• Target DC bus voltage: defines series count and open-circuit pack voltage range.
• Cell chemistry and nominal cell voltage: Li-ion, LiFePO4, VRLA, NiCd, NiMH typical values.
• Cell capacity (Ah) and stable capacity at required discharge rates.
• Depth of Discharge (DoD) policy and cycle life trade-offs.
• Inverter/rectifier efficiency and allowed DC bus voltage window.
• Temperature derating and ambient conditions impacting capacity.
• Redundancy, parallel string balancing, and equalization strategy.
• Standards and regulatory compliance (UL, IEC, IEEE, local rules).

Fundamental equations and variables

Below are the essential formulas used by an Instant UPS Battery String Sizing Calculator and detailed variable explanations with typical values.

1. Required energy and battery energy accounting

Variables and typical values:

• Load_Watts — continuous critical load in watts. Typical: 1000 W to 10000 W.
• Runtime_hours — desired backup time in hours. Typical: 0.08 (5 minutes) to 8 hours.
• Inverter_Efficiency — conversion DC→AC efficiency, typical 0.90–0.98 (95% common).
• System_Efficiency — battery-to-inverter system losses (wiring, BMS, contactors), typical 0.95–0.99.

2. Convert required energy to ampere-hours at DC bus

Variables and typical values:

• Required_Battery_Energy_Wh — from previous formula.
• Nominal_Pack_Voltage_V — expected pack nominal voltage (after series cells). Typical: 24V, 48V, 110V, 192V, 400V.

3. Available usable capacity with DoD

Variables and typical values:

• Single_String_Ah — capacity of a single series string measured in Ah (depends on chosen cell series-parallel configuration). Typical cell sizes: 20Ah to 400Ah.
• Depth_of_Discharge_fraction — fraction allowed per cycle (e.g., 0.8 for 80% DoD for Li-ion; 0.5 for VRLA in cyclic applications).

4. Number of parallel strings required

Note: ceil() indicates rounding up to next whole string.

5. Series cell count to meet DC bus

Variables and typical values:

• Nominal_Cell_Voltage_V — depends on chemistry: LiFePO4 3.2 V, Li-ion NMC 3.6–3.7 V, VRLA 2.0 V, NiCd/NiMH 1.2 V.
• round() — choose integer that keeps pack within inverter DC bus acceptable range and charger setpoints.

6. Practical pack voltage window and tolerance

Cell_OCV_min and Cell_OCV_max are the discharge and charge voltages per cell (e.g., LiFePO4: 2.5–3.65 V). Consider end-of-discharge and full-charge voltages when selecting series count.

Battery chemistry typical values table

Common DC bus voltages and series counts

Below are common instantaneous UPS DC bus voltages and representative series cell counts for common chemistries. For precision, use the previously provided formula to tune counts to acceptable charger/inverter ranges.

Algorithm flow for an Instant UPS Battery String Sizing Calculator

1. Input system parameters: Load_Watts, Runtime_hours, Target_DC_Bus_Voltage, Cell_Chemistry, Single_Cell_Ah (or typical cell pack Ah), Desired_DoD, Inverter_and_system_efficiencies, Ambient_temperature.
2. Calculate Required_Battery_Energy_Wh using the energy formula.
3. Determine Series_Cell_Count by dividing Target_DC_Bus_Voltage by Nominal_Cell_Voltage and rounding to a safe integer considering charge/discharge windows.
4. Choose Single_String_Ah based on selected cell/module (Single_Cell_Ah × parallel per module if preconfigured).
5. Compute Parallel_Strings needed using the Required_Ah and Usable_Ah formula; round up and verify current distribution and per-cell C-rate.
6. Check thermal and C-rate constraints: per-cell discharge current = (Load_Watts / Nominal_Pack_Voltage) / Parallel_Strings.
7. Validate charge and end-of-discharge voltages: ensure charge voltage across series cells does not exceed per-cell maximum.
8. Size fusing, busbars, contactors, balancing resistors, and BMS specifications accordingly.
9. Output final configuration: Series_Cell_Count × Parallel_Strings, pack nominal voltage, estimated runtime, margins, and recommended cell model numbers.

Important electrical checks and mechanical concerns

• Cell balancing strategy and passive/active balancing power budgets.
• Equalization cycles if VRLA or flooded lead-acid are used.
• Current distribution between parallel strings and fusing each string per standards.
• Temperature coefficient: capacity derating typically decreases ~0.5–1% per °C below optimal range for some chemistries.
• DC bus surge and transient handling: include precharge resistors to avoid inverter inrush.
• Mechanical layout for busbar impedance and thermal dissipation.

Thermal, safety, and standards references

Compliance with regional and international standards ensures safe installation, certification, and insurance coverage. Key references include:

• IEC 62040-1 / -3 (Safety and performance of UPS systems) — https://www.iec.ch
• UL 1778 (Uninterruptible Power Systems) — https://standardscatalog.ul.com/standards/en/standard_1778
• IEEE 1188 (Recommended Practice for Maintenance of VRLA Batteries) — https://ieeexplore.ieee.org
• IEEE 1491 (Recommended Practice for Selection and Use of Battery Systems) — https://www.ieee.org
• IEC 62619 (Safety requirements for secondary lithium cells and batteries) — https://www.iec.ch
• Battery Testing and Safety guidance from NREL and Sandia National Labs — https://www.nrel.gov and https://www.sandia.gov

Example 1 — 10 kW load, 30 minutes runtime, 48 V DC bus, LiFePO4 cells

Scenario: An instant UPS must support a 10 kW critical load for 0.5 hours (30 minutes). Target DC bus nominal is 48 V. Selected chemistry: LiFePO4 with nominal cell voltage 3.2 V. Choose typical single cell/module size of 100 Ah cells (prismatic modules).

Step-by-step solution

1) Determine required battery energy:

Assume Inverter_Efficiency = 0.95, System_Efficiency = 0.98.

2) Select nominal pack voltage and compute Required_Ah:

Choose nominal pack after series selection. Compute preliminary series count:

Consider charger headroom: 16s (51.2 V) common. We'll adopt 16s to provide charge headroom.

3) Account for DoD and select parallel strings:

Assume Depth_of_Discharge_fraction = 0.9 (90% for LiFePO4 in many UPS cycles).

Single_String_Ah = cell/module Ah = 100 Ah per 16s single string.

4) Verify discharge current per string and C-rate:

5) Final configuration and notes:

• Final pack: 16s2p using 100 Ah LiFePO4 modules → nominal 51.2 V, 200 Ah overall.
• Estimated usable energy = 51.2 × 200 × 0.9 = 9216 Wh; available margin vs required 5370 Wh is significant for safety and aging.
• Precharge resistor, string fuses (per string), BMS rated for peak currents, and thermal monitoring required.
• Recommendation: Use cell modules with 100 A continuous rating and adopt BMS balancing and temp compensation.

Example 2 — 1.5 kW critical load, 2 hours runtime, 240 V DC bus, VRLA 2V cells

Scenario: A telecommunications shelter requires 1.5 kW for 2 hours on a 240 V DC bus, using VRLA 2V cells commonly available at 100 Ah.

Step-by-step solution

1) Required battery energy:

Assume Inverter_Efficiency = 0.92, System_Efficiency = 0.97.

2) Series count for 240 V using 2 V VRLA cells:

3) Required Ah at nominal pack voltage:

4) Usable Ah per string with DoD:

For VRLA in cyclic operation, choose conservative DoD = 0.5 (50%).

Single_String_Ah = cell Ah = 100 Ah for a 2V cell string of 120 in series.

5) Parallel strings required:

6) Check discharge current and C-rate:

7) Final configuration and notes:

• Final pack: 120s1p of 2V, 100 Ah VRLA → nominal 240 V, 100 Ah overall.
• Usable energy = 240 × 100 × 0.5 = 12000 Wh, which far exceeds required 3362 Wh—this yields long life and headroom; verify float charge voltage limits and equalization cycles.
• It may be cost-effective to use a smaller Ah VRLA or fewer cells if continuous standby is the objective; however, OEM availability often dictates standard sizes.

Additional worked case: High-voltage NMC pack for larger UPS

Scenario: 50 kW instantaneous UPS, 15 minutes ride-through, target DC bus 400 V, chemistry NMC (3.6 V nominal cells) approximate.

Compute step-by-step

1) Required energy:

Runtime_hours = 0.25. Assume Inverter_Efficiency = 0.96, System_Efficiency = 0.98.

2) Series cell count:

Series_Cell_Count = round(400 / 3.6) = round(111.11) = 111s (399.6 V) or 112s (403.2 V).

3) Required Ah:

4) Select cell capacity: choose high-power cells at 50 Ah typical for large modules.

5) Check discharge current:

C_rate = 124.06 / 50 ≈ 2.48 C. This is high and may exceed continuous discharge rating; therefore parallel strings required to lower C-rate to acceptable level. If cells are rated 3C peak but want 1C continuous, then Parallel_Strings_target = ceil(124.06 / 50 / 1) = ceil(2.4812) = 3 strings

6) Recompute with 3 parallel strings:

Total_Ah = 50 × 3 = 150 Ah; Usable_Ah = 150 × 0.85 = 127.5 Ah; energy available = 403.2 × 127.5 ≈ 51408 Wh (sufficient)

Final configuration: 112s3p of 50 Ah NMC modules, pack nominal 403.2 V, 150 Ah, supports 50 kW for design ride-through with acceptable cell C-rate and reserve margin.

Design checklist for implementation

1. Verify inverter DC bus allowable voltage window (min–max) and ensure pack OCV_min and OCV_max lie within it.
2. Confirm charger/regulator setpoints are compatible with chosen series count and cell charging limits.
3. Design per-string fusing and mechanical isolation for serviceability; fuse per parallel string recommended.
4. Define BMS topology: per-module or per-cell monitoring, balancing method (active vs passive), and fault handling.
5. Confirm thermal management: airflow, heat sinks, and temperature sensors on high-current modules.
6. Plan for ambient derating curves and reserve margin for end-of-life capacity loss (typical design target: 70–80% of initial capacity after warranty period).
7. Establish maintenance and periodic testing per IEEE/IEC/UL guidelines.

Tables of common pack configurations and quick sizing references

Monitoring, diagnostics, and commissioning recommendations

• Commissioning tests: full discharge test under controlled load, capacity verification at design discharge rate, BMS validation and balancing verification.
• Monitoring: per-string voltage, per-cell temperatures, current sensors on each parallel string, SOC estimation algorithms.
• Periodic maintenance: capacity testing schedule per IEEE 1188 and manufacturer guidelines.
• Data logging for lifecycle analysis: track charge/discharge cycles, peak currents, temperature excursions, and capacity fade.

Regulatory links and authoritative references

• IEC 62040 series — Uninterruptible power systems (https://www.iec.ch/standards)
• UL 1973 — Batteries for use in stationary and motive auxiliary power applications (https://standardscatalog.ul.com)
• UL 9540 and UL 9540A — Energy storage systems and fire testing (https://www.ul.com)
• IEEE Std 1188-2005 — IEEE Recommended Practice for Maintenance, Testing, and Replacement of Valve-Regulated Lead-Acid Batteries (https://standards.ieee.org)
• Sandia National Laboratories — Battery Testings and Safety research (https://www.sandia.gov/ess)
• National Renewable Energy Laboratory (NREL) publications on storage systems (https://www.nrel.gov)
• Battery University — Practical articles on battery charging and care (https://batteryuniversity.com)

Frequently encountered pitfalls and mitigations

• Underestimating charge overhead: include charger inefficiencies and balancing losses in energy budget.
• Choosing series count solely on division yields out-of-range pack voltages—always verify charger and inverter setpoints and transients.
• High C-rate per cell: add parallel strings or select high-power cells to reduce stress and heating.
• Insufficient fusing per parallel string: fuse each string to ensure isolation during faults.
• Ignoring thermal gradients: thermally uniform layouts and active cooling for high-power packs.
• Poor BMS coverage: ensure per-cell or per-module monitoring for safety in large series counts.

Appendix — Quick calculation cheat-sheet

Use these equations as a checklist when using a sizing calculator or designing manually:

• Required_Battery_Energy_Wh = Load_Watts × Runtime_hours / (Inverter_Efficiency × System_Efficiency)
• Series_Cell_Count = round(Target_DC_Bus_Voltage / Nominal_Cell_Voltage)
• Nominal_Pack_Voltage = Series_Cell_Count × Nominal_Cell_Voltage
• Required_Ah = Required_Battery_Energy_Wh / Nominal_Pack_Voltage
• Parallel_Strings = ceil(Required_Ah / (Single_String_Ah × DoD_fraction))
• Load_current_DC = Load_Watts / Nominal_Pack_Voltage
• Current_per_string = Load_current_DC / Parallel_Strings

Variable typical default values to use in calculators

• Inverter_Efficiency: 0.95 (adjust by vendor datasheet)
• System_Efficiency (wiring/BMS): 0.98
• LiFePO4 DoD: 0.9 for short UPS cycles, reduce for longer service life
• NMC DoD: 0.8–0.85 (life/cost balance)
• VRLA DoD: 0.5 for cyclic use
• Safety margin: include 10–30% energy margin for aging and faults

Final engineering considerations

Accurate Instant UPS battery string sizing combines electrical calculation, thermal design, safety compliance, and lifecycle considerations. A robust calculator will allow input of cell models, charge/discharge efficiency curves, temperature derating, and aging factors. Always validate designs with prototype testing, integrate a qualified BMS, and consult applicable local codes and standards before deployment.

For authoritative standards documents and manufacturer datasheets, consult IEC and UL portals, IEEE Xplore, and reputable laboratory publications like NREL and Sandia for best practices and up-to-date safety guidance.