Solar PV, Batteries and Backup Power

Array and string sizing, yield, inverters, battery capacity, UPS and generators, with worked examples.

On this page

  1. How a PV system works
  2. Array size and energy yield
  3. Sizing strings for the inverter
  4. A day of generation and load
  5. Batteries
  6. UPS and generators
  7. Economics
  8. FAQ

How a PV system works

Photovoltaic (PV) cells turn sunlight directly into direct current: about 0.6 V per silicon cell, and 30 to 40 V from a module of 60 to 72 cells. Modules are wired in series (a string, to add the voltage) and strings in parallel (to add the current), and an inverter with a maximum power point tracker (MPPT) converts the DC to the 400 V AC of the grid (see Three-Phase Systems). A grid-tied system exports to the network and needs anti-islanding protection (it shuts down if the grid fails); an off-grid or hybrid system adds a battery and a charge controller.

Array size and energy yield

The energy comes from the array’s peak rating (kWp, measured at 1 000 W/m² and 25 °C cell temperature), the peak sun hours (the solar energy per day expressed in hours of full 1 000 W/m² sun: 3 to 6 over most populated regions) and a performance ratio PR that accounts for losses:

E (kWh) = kWp × peak sun hours × days × PR

LossTypical size
Temperature (cell 45 °C above ambient)− 8 %
Soiling and shading− 3 %
Module mismatch and DC wiring− 3 %
Inverter− 4 %
AC wiring and availability− 2 %
Combined performance ratio0.81

Temperature is the large one: a cell’s power falls about 0.35 percent per kelvin, so at a cell temperature of 70 °C (a hot day with the module 45 K above the ambient) the loss is 16 percent. Orientation and tilt also matter: a roof 30° off south with a poor tilt delivers about 85 percent of the optimum.

Worked example: a 4.8 kWp array

  • Modules of 400 W: 12 modules = 4.8 kWp.
  • Daily yield at 4.5 peak sun hours a day (a yearly average) and PR 0.78: E = 4.8 × 4.5 × 0.78 = 16.8 kWh a day, about 6 150 kWh a year.
  • This would cover the press motor’s 48 352 kWh a year (Power Factor, Harmonics and Energy) 13 percent, if the load matched the sun.
  • Carbon: at a grid intensity of 0.4 kg per kWh the array avoids about 2.5 tonnes of CO₂ a year.

Sizing strings for the inverter

The voltage of a string changes with temperature: Voc rises when it is cold (the worst case for the inverter’s maximum input voltage) and Vmp falls when it is hot (the worst case for the MPPT minimum voltage). Both limits must be met.

Worked example: modules of Voc 37 V and Vmp 31 V on a 600 V, 150 to 550 V MPPT inverter

  • Coldest day (−10 °C): Voc = 37 × (1 + 0.27% × 35 K) = 40.5 V per module; the largest string = ⌊600 ÷ 40.5⌋ = 14 modules.
  • Hot day (cell 70 °C): Vmp = 31 × (1 − 0.35% × 45 K) = 26.1 V; the smallest string = ⌈150 ÷ 26.1⌉ = 6 modules.
  • A single string of 12 modules lies between 6 and 14: open-circuit voltage at −10 °C = 486 V (below 600 V), operating voltage from 313 V (hot) to 418 V (cold), inside the 150 to 550 V window.
  • DC cable and fuse: module short-circuit current 10.9 A; NEC-style sizing uses 1.25 × 1.25 = 17.0 A (irradiance above 1 000 W/m² and a continuous-duty factor), so a 4 mm² solar cable and a string fuse or breaker of about 15 to 20 A.
  • Inverter size: a 4.0 kW inverter on a 4.8 kWp array has a DC/AC ratio of 1.20: the inverter clips the few hours of peak output, which wastes little energy and saves cost.

PV circuits need DC-rated isolators and fuses (DC arcs do not self-extinguish like AC arcs), a rapid-shutdown device where required, surge protection, earthing and bonding, and a type B or A RCD according to the inverter. Follow IEC 62548, IEC 60364-7-712 and the NEC Article 690, and always have the installation designed and inspected by a competent person.

A day of generation and load

Solar output and household load over a day0369121518212401234hour of the daypower (kW)solar array: 21.1 kWh a dayload: 16.5 kWh a dayMidday surplus 15.3 kWh, bought from the grid or battery 10.8 kWh. Array 5 kWp, performance ratio 0.78(temperature, wiring, inverter and dirt losses), a clear day.
A 5 kWp array on a clear day against a household load. The midday surplus is the part to export, store or use with a flexible load.

The peak of the sun (midday) rarely meets the peak of a household (morning and evening), so a PV system without storage self-consumes only 30 to 40 percent of its output in a home and more in a business that works in the day. A battery, a hot-water diverter, an electric vehicle charger or a heat pump shifts the use into the sunshine.

Batteries

TypeUsable depth of dischargeCycle lifeRound-trip efficiencyNotes
Lead-acid (flooded, AGM)50 %500 to 1 50080 to 85 %cheap; heavy; needs ventilation (flooded)
Lithium iron phosphate (LiFePO₄)90 to 100 %3 000 to 8 00092 to 96 %safe chemistry, the standard for home storage
Lithium NMC80 to 90 %1 500 to 4 00090 to 95 %compact; electric vehicles; thermal-runaway risk needs management
Flow batteries100 %10 000+65 to 75 %long duration; large and costly

Worked example: a battery for the evening

  • The evening load after sunset is 8 kWh (from the figure, about 5 pm to midnight).
  • Nominal capacity = E ÷ (DoD × one-way efficiency) = 8 ÷ (0.9 × 0.959) = 9.3 kWh; at 48 V that is 193 Ah.
  • The battery is limited by power as well as energy: a 1.6 kW evening peak needs a 5 kWh unit rated at least 2 kW, and the inverter must supply it.
  • The battery has to survive a cycle a day: 365 cycles a year, so a 6 000-cycle LiFePO₄ battery is good for over 15 years in theory; calendar aging and temperature limit it to 10 to 15.

UPS and generators

A UPS (uninterruptible power supply) carries a critical load through a short outage with a battery and an inverter, and can also condition the power. A generator supplies long outages but needs seconds to start, so a UPS bridges the gap. Sizing a generator is governed by motor starting, not by running power:

Sgen ≥ Sstart × X″d × (1 − ΔV) ÷ ΔV

Worked example: a generator for the press and a UPS for the controls

  • The 11 kW motor starts at 7 × 20.5 A = 144 A: 99.5 kVA. For X″d = 0.20 and a 15 percent dip the generator must be 113 kVA for DOL starting, 38 kVA with a star-delta starter and only 24 kVA with a drive (1.5 × rated current): the starting method (Induction Motors and Drives) changes the generator size by a factor of 5.
  • UPS: 2.0 kW of PLC, network and control loads for 15 minutes need 0.50 kWh of delivered energy; with a 0.9 inverter efficiency and 80 percent allowable discharge the battery is 0.69 kWh, about 14 Ah at 48 V.
  • Test the generator and the transfer switch regularly under load; the most common failure of backup power is a system that nobody has run for a year.

Economics

Worked example: does the array pay?

  • Installed cost 1 200 per kWp × 4.8 kWp = 5 760.
  • Of the 6 150 kWh a year, 60 percent (3 690 kWh) is used on site at 0.20 per kWh and 2 460 kWh is exported at 0.06: income 886 a year.
  • Simple payback = 5 760 ÷ 886 = 6.5 years (modules last 25 to 30 years, the inverter 10 to 15). Self-consumption is the biggest lever: raising it from 60 to 80 percent shortens the payback.

Related

FAQ

What does kWp mean?

Kilowatt-peak: the module power under standard test conditions (1 000 W/m², 25 °C). In practice the array rarely produces its kWp because of temperature and irradiance.

Why is the cold voltage the limit?

Voltage rises when cells are cold, so an array that is within the inverter’s limit in summer can exceed it on a frosty sunny morning and damage it. Always design on the lowest site temperature.

Can solar run my building in a power cut?

Not with a standard grid-tied inverter: it shuts down for safety. You need a hybrid inverter with a backup output and a battery, or a changeover system.

Is east–west better than south?

East–west arrays make less per kWp but spread the output across the day and fit the household load better and are used on flat roofs.

References

  • IEC 62548 (PV array design), IEC 60364-7-712 (PV systems), NFPA 70 (NEC) Article 690 and 705, IEC 61215 and 61730 (modules), IEC 62109 (inverter safety).
  • Messenger, R. A., Abtahi, A., Photovoltaic Systems Engineering, CRC Press; Masters, G. M., Renewable and Efficient Electric Power Systems, Wiley.
  • PVGIS (European Commission) and NREL PVWatts for site yield data; manufacturers’ datasheets for the module and inverter limits.

Last reviewed: October 2026. Yields, costs and tariffs are typical illustrations; use site data.