Power Station Size Calculator: Runtime, Surge and Solar Recharge

Energy and runtime

Energy conservation is derived here. Total nameplate storage is $C=C_b+nC_e$. The available battery budget is $E_u=C f_h(s_0-s_r)$, where $f_h$ is the measured available-capacity fraction and $s_r$ is the displayed reserve.

For each appliance, $w_i(t)=\max(0,\min(t-b_i^{\rm on},b_i^{\rm off}-b_i^{\rm on}))$ is its elapsed scheduled time in hours, limited to the outage. AC energy is $E_{AC}(t)=\sum_i P_i d_i w_i(t)$ in Wh. Battery energy is $E_{DC}(t)=E_{AC}(t)/\eta_{inv}+P_{idle}t$. The reserve crossing is found by bisection, capped at the outage end. The chart includes schedule boundaries and the reserve crossing. Constant all-load runtime is $E_u/(\sum_i P_i d_i/\eta_{inv}+P_{idle})$ and ignores the schedule.

The complete schedule needs rated capacity $C_{need}=E_{DC}(H)/(f_h(s_0-s_r))$. The AC energy ceiling $E_u\eta_{inv}$ excludes idle losses; actual delivered AC energy integrates only to the reserve crossing. The Solar Lab explains the need for a separate idle term; Jackery's 60 W worked example checks the zero-idle 85% special case.

Running and startup ratings

At every schedule boundary, sum full running watts of all enabled appliances. Duty fractions affect energy only. One-start demand is running demand plus the largest active $(S_i-P_i)$ increment. Simultaneous demand sums all active $S_i$. Maxima are exact for these rectangular windows. Startup watts are not multiplied by duty and no startup energy is added.

Recharge

With outputs off, restore $\Delta E=C f_h(s_{to}-s_{from})$. Input-energy allowance is $E_{in}=\Delta E f_{taper}/\eta_{ch}$. Wall and car accepted watts are $\min(P_{limit},VI)$. Wall power factor is assumed near unity. Solar accepted watts are $\min(f_{PV}P_{array},V_{mp,array}I_{MPPT},P_{PV,max})$. Time is $E_{in}/P$ at that constant power. Solar Wh/day and recharge days use a constant-full-sun approximation: each day is treated as the entered peak sun hours at the accepted full-sun power. PV-side operating-current clipping differs from the absolute voltage and short-circuit-current limits.

Clipping is nonlinear. Actual daily battery energy requires integrating accepted power over an irradiance profile, applying the power/current caps at each time step before summing energy, as in the SAM clipping model (https://samrepo.nlr.gov/help/pv_inverter.html). Peak sun hours alone cannot specify this profile. For example, an 800 W array derated to 640 W with a 500 W input cap gives 2000 Wh for four hours at full sun, but 2560 Wh for eight hours at half sun, before charging losses and allowance. Both have four peak sun hours. This tool does not perform that daily integration and shows a warning whenever full-sun input power clips.

Cycle-life context

Cadex Battery University BU-808 Table 2 (11 October 2023) supplies approximate LFP and NMC cycles to 70% capacity, interpolated linearly only within 10–100% DoD. These historical trends are educational, not ratings for modern stations. A separate LFP product example from the attached Victron manual, page 38 (printed page 35), gives cycles to 80% capacity, only within 50–80% DoD. Outside that range its result is deliberately blank. These endpoints and test bases differ; do not compare their absolute counts as equivalent tests.

• Defaults are an illustrative 2 kWh station and user-editable appliance assumptions, not measured product specifications. No brand model is preset.
• All loads are on AC, use constant incremental conversion efficiency, and have one contiguous window. A duty fraction is an average, not simulated compressor switching. Combine appliances only when their windows and cycling match.
• The inverter remains on for the whole outage, including gaps. Input idle watts include all inverter, controller and expansion-pack standby loads. Startup energy is neglected; thermal surge duration and apparent-power limits need separate checking.
• Expansion packs are compatible, identical, share state of charge and capacity health, and add no output or input power.
• The available-capacity fraction covers aging, temperature or inaccessible energy only if known. Reserve is separate. A measured end-to-end AC fraction already includes loss; use zero separate idle draw in that approximation.
• Outage discharge has no recharge contribution. Recharge starts separately with outputs off; sources are alternatives, not added together. One MPPT port, matching panels/strings, fixed representative Vmp, charge efficiency and a user-set time multiplier are assumed.
• Solar Wh/day and recharge days assume H_sun hours per day at constant full-sun input. Peak sun hours summarize irradiation, but cannot determine daily yield when clipping occurs. The solar factor covers panel, orientation and wiring losses. No hourly irradiance profile, cloud timing, shading, dynamic MPPT or calendar completion time is modeled.

Use for preliminary energy and power sizing within the entered station and panel ratings. Schedule windows span 0–168 h; a disabled slot has zero running watts or duty. Runtime results assume the AC output passes both continuous and one-start rating checks. Simultaneous-start failure calls for staggered starts or a higher rating.

PV cold Voc must be strictly below the absolute maximum, hot Vmp must reach the startup/MPPT minimum, representative Vmp must stay within tracking limits, and design short-circuit current must be permitted. Current clipping and overpaneling are acceptable only if the actual manufacturer's instructions permit them. Check maximum Voc, irradiance allowances, connectors, polarity, per-port limits and supported combinations against the actual equipment manual.

No protection coordination, cable sizing, earthing, neutral bonding, transfer-switch design, UPS ride-through or guaranteed medical-equipment continuity is evaluated. Never backfeed a receptacle. Installation work and building-circuit connections belong to a qualified person using the rules in force.

Cycling data are dated illustrative datasets, not universal chemistry laws or remaining-life estimates. Temperature, mean state of charge, charge rate, calendar aging and the definition of a cycle can dominate; enter the actual model's warranty/test data when making a purchase or life commitment. Solar Wh/day and recharge days are constant-full-sun approximations. When input clips, use a time-resolved irradiance model for daily yield or recharge scheduling; the approximation can understate harvest during longer periods at lower irradiance. Solar days also exclude weather sequencing, night-time standby and concurrent loads.