fast.engineer
Sign in
[[ calculationForm.title || displayName ]] Page [[ pages.length ? activeIndex+1 : 0 ]] of [[ pages.length ]]

[[ dlg.mode === 'copy' ? 'Save a copy' : 'Save calculation' ]]

[[ dlg.error ]]

UPS SELECTION AND BATTERY SIZING

This report selects a standard UPS rating for the critical load with safety and growth margins (IEC 62040-3 rated output kVA and kW), and estimates the battery runtime from the string arrangement using Peukert's law at the actual discharge current with the IEEE 485 / IEEE 1184 capacity derating factors.

UPS Rating

Formula: $$ \cos\varphi = \frac{P_{load}}{S_{load}} $$
Substitution: $$ = \frac{2.50}{2.78} $$
Result: $$ = 0.899 $$

The load power factor 0.899 is at or below the UPS output power factor 0.9, so the kVA rating governs.

Formula: $$ S_{size} = \max\left(S_{load},\ \frac{P_{load}}{0.9}\right) $$
Substitution: $$ = \max\left(2.78,\ \frac{2.50}{0.9}\right) $$
Result: $$ = 2.78 \; \text{kVA} $$

The rating is the UPS output; efficiency sets the input and battery power, not the output rating.

Formula: $$ S_{req} = S_{size} \times k_{safety} \times k_{growth} $$
Substitution: $$ = 2.78 \times 1.25 \times 1.20 $$
Result: $$ = 4.17 \; \text{kVA} $$

Next standard three-phase rating.

Formula: $$ S_{UPS} \geq S_{req}, \quad P_{UPS} = 0.9 \times S_{UPS} $$
Substitution: $$ P_{UPS} = 0.9 \times 10 $$
Result: $$ S_{UPS} = 10 \; \text{kVA}, \quad P_{UPS} = 9.0 \; \text{kW} $$

60-80 % utilisation leaves headroom for transients and growth.

Formula: $$ U_S = \frac{S_{load}}{S_{UPS}}, \quad U_P = \frac{P_{load}}{P_{UPS}} $$
Substitution: $$ U_S = \frac{2.78}{10}, \quad U_P = \frac{2.50}{9.0} $$
Result: $$ U_S = 27.8\%, \quad U_P = 27.8\% $$

Battery String

Formula: $$ N_s = \frac{V_{dc}}{V_{block}} $$
Substitution: $$ = \frac{384}{12} $$
Result: $$ = 32 $$
Formula: $$ N = N_s \times N_p $$
Substitution: $$ = 32 \times 1 $$
Result: $$ = 32 $$
Formula: $$ E_{inst} = \frac{C_{10} \times V_{dc} \times N_p}{1000} $$
Substitution: $$ = \frac{100 \times 384 \times 1}{1000} $$
Result: $$ = 38.40 \; \text{kWh} $$

Battery Discharge and Runtime

UPS (inverter) efficiency in battery operation.

Formula: $$ P_{batt} = \frac{P_{load}}{\eta} $$
Substitution: $$ = \frac{2.50}{0.950} $$
Result: $$ = 2.63 \; \text{kW} $$

Average discharge voltage 364.8 V (0.95 of nominal).

Formula: $$ I = \frac{1000\,P_{batt}}{k_v\,V_{dc}\,N_p} $$
Substitution: $$ = \frac{1000 \times 2.63}{0.95 \times 384 \times 1} $$
Result: $$ = 7.2 \; \text{A} $$

Peukert exponent n = 1.3 for VRLA-AGM (5-10 year).

Formula: $$ t_{new} = 10\,\text{h} \times \left(\frac{C_{10}/10}{I}\right)^{n} $$
Substitution: $$ = 600 \times \left(\frac{10.00}{7.2}\right)^{1.3} $$
Result: $$ = 917.36 \; \text{min} $$

k_T at 25 °C; lead-acid takes no capacity credit above 25 °C (IEEE 485 cl. 6.2.2).

Formula: $$ k = DoD \times k_{EOL} \times k_T \times k_{age} $$
Substitution: $$ = 0.80 \times 0.80 \times 1.000 \times 0.90 $$
Result: $$ = 0.5760 $$

Target 15 min: met.

Formula: $$ t = t_{new} \times k $$
Substitution: $$ = 917.36 \times 0.5760 $$
Result: $$ = 528.40 \; \text{min} $$

Half the current: Peukert gives 2^n times the full-load runtime.

Formula: $$ t_{50} = t \times 2^{n} $$
Substitution: $$ = 528.40 \times 2^{1.3} $$
Result: $$ = 1301.08 \; \text{min} $$
Formula: $$ E_{use} = \frac{P_{load} \times t}{60} $$
Substitution: $$ = \frac{2.50 \times 528.40}{60} $$
Result: $$ = 22.017 \; \text{kWh} $$

With N strings each carries 1/N of the current.

Formula: $$ N_{p,req} = \left\lceil N_p \left(\frac{t_{target}}{t}\right)^{1/n} \right\rceil $$
Substitution: $$ = \left\lceil 1 \times \left(\frac{15}{528.40}\right)^{1/1.3} \right\rceil $$
Result: $$ = 1 $$

UPS System Configuration

UPS System Configuration UPS Utilization: 27.8% 80% Target 2.8/10.0 kVA Utility Input UPS 10 kVA Online/Double-C No Redundancy Battery 384V DC 32 Batteries Load 2.8 kVA System Specifications Input Voltage: 400 V Output Voltage: 400 V Frequency: 50 Hz Target Runtime: 15 minutes Actual Runtime (full load): 528.4 minutes Battery Configuration Technology: VRLA-AGM (5-10 year) Configuration: 32S × 1P Per Battery: 12V, 100 Ah Total Capacity: 38.40 kWh Usable Capacity: 22.02 kWh ✓

Runtime vs Load (% of UPS rating)

Runtime vs Load Chart Operating Point 28% load, 528 min 100% 75% 50% 25% 0% Load (% of UPS Rating) 607 455 303 152 0 Runtime (minutes) Battery: VRLA-AGM (5-10

Battery Life and Physical Estimates

VRLA-AGM (5-10 year): design life 7 years (float service), about 300 cycles at 80 % DoD. Estimated masses: batteries 384 kg, UPS 100 kg (indicative only). Availability for N redundancy: 99.0 %.

Scan to View Online

QR code will appear after save

Scan this QR code with your mobile device to view the calculation online.

Scan to access this calculation from any device