Battery Runtime and Backup Power Calculator

Average AC power is $P_{avg}=\sum P_j d_j$; all-load running power includes every enabled load with nonzero duty. Battery current in an on/off state is $I=(P_{AC}/\eta+P_{idle})/V$. Inverter efficiency excludes the separate DC idle draw.

Victron BMV-712 Smart manual, attached PDF pages 48–49 (printed 44–45), gives Peukert's constant-current model and the 100 Ah C20 / 75 Ah C5 example. The reference current is $I_r=Q/H_r$. We express Peukert depletion as $g(I)=I\max[1,I/I_r]^{k-1}$. Above the rated current this reproduces $t=H_r(I_r/I)^k$ for a fresh, fully discharged bank; below it we cap capacity gain at the nominal Ah.

Duty fractions alone do not specify timing. The conservative model aligns on periods as much as possible, sorts their duty boundaries, and sums $\bar g=\sum \Delta d\,g(I_{state})$. For a convex depletion function this maximally coincident schedule has at least the depletion of any other overlap pattern with the same duties. The constant-average comparator uses $g(I_{avg})$. These are model-based planning estimates; physical recovery is not included.

Usable charge is $Q_u=Q\,f_T\,f_{health}\,[SOC_0-(1-DOD)]$. Runtime is $Q_u/\bar g$. Trojan's AGM guidance gives 50% capacity at -18 °C and 100% at 27 °C; the tool linearly interpolates those endpoints and caps the factor at 1 above 27 °C. This interpolation is our approximation. A manufacturer factor replaces it when selected.

A bracketed scalar root solves the Ah needed for the target duration, recomputing the rated current as bank capacity changes. The final minimum is the larger of that root and $I_{on}/C_{limit}$. The enlarged bank's modeled duration is also calculated.

Honda's generator guidance distinguishes running watts from total starting watts. Each load slot is one starting group: motors entered together start together. The default two-fan group gives 400 W before headroom, or 500 W with 25% headroom. Splitting the two 70 W fans into separate slots gives 330 W before headroom, or 412.5 W with the same allowance. With $\Delta P_j=P_j(s_j-1)$, sequential starting needs $P_{all}+\max\Delta P_j$; simultaneous starting needs $\sum P_j s_j$. Both running and starting ratings receive the entered headroom, then divide by the entered conservative power factor for VA. Headroom is a user design choice. These load aggregation, overlap-bound and sizing equations are derived here.

Individual-battery entry uses $N_s=V_{DC}/V_b$ (a whole number), $Q=N_p Q_b$, and $V=V_{DC}$. For the selected load, $N_{p,req}=\lceil Q_{required}/Q_b\rceil$ and $N_{total}=N_s N_{p,req}$. The tool recomputes runtime using $N_{p,req}Q_b$. Current divides equally between parallel strings: $I_{string}=I_{on}/N_p$. These topology equations follow Victron Wiring Unlimited, section 3.1. A numerical tolerance of 1e-10 in the Ah ratio prevents an exact integer root being rounded upward through floating-point noise.

Full-inverter mode replaces the appliance list with a constant load equal to the selected continuous watt rating. It does not assume motor starting or claim a surge capability. Actual W and VA are compared independently with inverter continuous ratings. Generator sizing still applies the chosen headroom. Only the inverter manufacturer's DC voltage is suitable; changing the example voltage represents choosing a different inverter.

The 150/200 Ah C20 examples are based on Exide IT500/IT750 capacity ratings. The 900 VA example uses Luminous Zolt 1100 ratings (756 W, 12 V); the 1500 VA example uses Power Sine M 1700 ratings (1260 W, 24 V). The shared efficiency, idle draw, DOD, Peukert exponent and C-rate limit are illustrative assumptions, not those products' measured values. Generic 3000 W / 3750 VA examples are design scenarios, not named products.

The runtime curve excludes continuous operating points beyond entered equipment limits. The battery permits $P_{bat}=\max[0,\eta(V Q C_{limit}-P_{idle})]$ AC watts. In individual-battery mode the permitted coincident running load is $P_{max}=\min(P_{bat},P_{inv},PF\,S_{inv})$. Complete-bank mode checks only the entered battery current limit because no inverter rating is specified there. With all enabled powers multiplied by $a$, require $aP_{all}\leq P_{max}$; apply this to coincident running power, not the duty-averaged power. The curve stops at the smaller of this bound and twice the entered load powers. Its displayed average-load boundary is $P_{max}P_{avg}/P_{all}$. Every plotted point is also checked directly; infeasible points are omitted. If idle draw consumes the entire current allowance, the curve is empty and an input message explains how to change the system. This is a continuous-operation screen: headroom, starting surge and pulse-current capability remain separate checks.

• AC input watts are measured or nameplate values while on. All enabled nonzero-duty devices can overlap; zero-duty devices are excluded from source sizing.
• Loads cycle repeatedly over the outage, so the entered duty fractions represent their long-term usage. Very short outages may depend on the initial on/off state.
• Bank voltage, inverter incremental efficiency and DC idle draw stay constant. The inverter remains on during off periods.
• Capacity uses the entered rating period. Presets use C20. In individual-battery mode, parallel strings add Ah and series batteries add voltage. In complete-bank mode, enter the whole bank voltage and Ah; individual-battery result cards are unavailable.
• Temperature and aging multiply available charge without changing the rated-current reference. This is an engineering approximation; measured discharge curves are preferable.
• Peukert exponent is between 1.00 and 1.50. The 1.25 default follows Victron's lead-acid starting estimate; lithium users should normally use 1.00 and a manufacturer temperature factor.
• Source sizing assumes the same conservative power factor for starting and running. The 25% default headroom is illustrative. Starting transients affect ratings but their short energy consumption is excluded.
• Default loads are assumed: one group of two fans totaling 140 W, lights totaling 40 W and a TV at 80 W, all continuously on. Both fans in the first group start together. The group starting multiplier of 2 is also an assumption; replace it with measured data or separate motors into individual slots.
• The home examples assume 85% incremental inverter efficiency, 10 W DC idle draw, 50% discharge allowance, full initial charge and health, a 100% temperature capacity factor, and a 0.25C continuous limit. These are editable engineering examples, not manufacturer guarantees.
• Identical batteries are permitted to connect in the chosen series/parallel arrangement, remain balanced, and share parallel current equally. A whole string must be added each time. Verify battery/BMS connection limits and matching condition.
• Required count is the total number of batteries for the selected duration and continuous current, not the number to add. Startup current is approximate and is not checked against a battery pulse-current limit.

Use for preliminary AC backup planning, not a guaranteed autonomy or motor-starting result. Peukert's fixed exponent becomes unreliable at very high currents. Check the battery's constant-power or constant-current discharge data at the actual cutoff voltage, temperature and load.

The built-in temperature interpolation is limited to -18…50 °C (-0.4…122 °F), with no capacity bonus above 27 °C. It represents Trojan lead-acid guidance and is not a universal lithium model. A custom factor is permitted only where the battery manufacturer allows discharge. Charging temperature limits are separate.

Runtime ignores changing terminal voltage, internal resistance, wiring losses, inverter low-voltage cutoff, BMS trips, self-discharge and recovery. The maximally coincident duty model is conservative only within this simplified depletion model; short outages and startup energy can give shorter real autonomy. There is no charger or generator fuel calculation.

Check inverter and generator continuous W/VA ratings, surge W/VA and duration, motor starting power factor, waveform, voltage dip and generator derating for altitude or temperature. Include battery-charger watts as another load if charging from a generator. For boilers, verify waveform and earthing/neutral compatibility. Installation work belongs to a qualified person; this schematic is functional, not a wiring design.

Do not treat the calculated battery count as approval of a wiring arrangement. Victron cautions against large lead-acid banks with more than about three or four parallel strings. Consider larger individual batteries or a compatible higher-voltage inverter when the arithmetic needs more strings. Check permitted series counts for lithium and BMS systems, pulse-current limits, battery balancing, protection and cable ratings with a qualified person.