A Bank That Was Never Big Enough: Battery Autonomy and DC Voltage Drop
A telecom operator's remote repeater site is fed by a −48 V DC plant with a 200 Ah VRLA battery bank rated at the 10-hour rate. The steady site load is 22 A. The grid fails daily for up to six hours. The bank is four years old, and a capacity test last year showed it delivering 82% of nameplate capacity. During the last outage the site dropped out after 4 h 40 min. Separately, a technician measured 53.5 V at the rectifier terminals but only 46.5 V at the load busbar while the load drew 22 A. The DC cable between them is a 25 m run of 16 mm² copper in each direction (resistivity 0.0172 Ω·mm²/m). Every terminal feels tight by hand. There is no spare battery on site and the next delivery is three weeks away. The site carries a district hospital's ambulance dispatch link.
1. Estimate the backup time the battery should give at 22 A, and compare it with the observed 4 h 40 min. State every derating assumption you use.
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Work from nameplate to usable ampere-hours, then to hours.
- End voltage of 1.75 V/cell is about 42 V for 24 cells; usable capacity to that point is roughly 80% of the 10-hour rating: 0.80 × 200 = 160 Ah.
- 22 A is about C/9, slightly faster than the 10-hour rate, so take off a few percent: about 152 Ah at 25 °C.
- Apply the measured state of health: 0.82 × 152 ≈ 125 Ah.
- 125 Ah ÷ 22 A ≈ 5.7 h.
So the site should have ridden through a six-hour outage with roughly 40 minutes in hand before the low-voltage disconnect. It actually delivered 4 h 40 min ≈ 103 Ah, about two-thirds of nameplate. That is worse than last year's capacity test, so either the bank degraded faster than a linear projection, or the real load is above the 22 A measured (fans, a heater, traffic peaks), or one block is weak and its cell reaches 1.75 V early and ends the discharge while the rest are still half full. A string average hides exactly that failure.
Action: log per-block voltage through a controlled discharge, find the weak block, and do not accept a string-average capacity figure as proof of health.
2. Check whether the 7 V drop between rectifier and load busbar is a design problem or a fault, and say how you would locate it.
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Expected drop: R = ρ × 2L/A = 0.0172 × (2 × 25)/16 = 0.0538 Ω, so V = IR = 22 × 0.0538 ≈ 1.18 V. The load bus should sit near 53.5 − 1.2 = 52.3 V.
The measured 7.0 V drop implies an effective 0.318 Ω, about six times the calculated value. At 22 A that is roughly 154 W being converted to heat somewhere in the run. A correctly sized 16 mm² cable cannot absorb that without becoming noticeably warm, so this is a fault, not a design limit.
Likely causes in order: a high-resistance terminal or crimp (hand-tight is not a measurement, since oxide and a partly seated lug can add tenths of an ohm); a fuse holder or breaker contact; a cable that is not actually 16 mm², since 4 mm² would give about 4.7 V and matches the symptom; or a poor joint inside a junction box.
Diagnose with the load connected: measure the voltage between the rectifier terminal and the lug, between the lug and the busbar, and across the fuse or breaker. Whichever element carries most of the 7 V is the fault. A micro-ohmmeter or thermal camera confirms it with the load off. Re-terminate with a proper crimp to the specified torque and re-measure; tightening by hand and walking away is how the site burns.
3. You have three weeks before a replacement bank arrives. Set out what you would do, in priority order, and what you would refuse to do.
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Rank by consequence. This is an ambulance dispatch link, so the aim is guaranteed ride-through for six hours, every day, for three weeks.
- Cut the load to what the link actually needs. Shed non-essential equipment and confirm the 22 A with a clamp meter over 24 hours, including the evening traffic peak.
- Add temporary generation. A small auto-start diesel set with a changeover contactor is cheaper than losing the link and covers outages of any length, including a multi-hour grid repair.
- Verify the low-voltage disconnect is set at 42 V. Lowering it buys minutes and destroys the string; raising it silently shortens autonomy.
- Rent or borrow a standby string (about 100 Ah is enough to bridge the deficit) and keep it on float from a separate charger, clearly labelled as temporary with a removal date.
What I would refuse: raising the end-voltage setpoint or disabling the disconnect to squeeze out more hours. The string already ends 1.3 h short, and a deep discharge will turn a degraded bank into a dead one.
Also size the replacement properly: for 8 h at 22 A with an 80% depth limit and a 1.25 ageing factor you need roughly 220 Ah at the 10-hour rate, so the existing 200 Ah was undersized for the new requirement even when new.