TAHA Engineering Toolsby TAHA Knowledge Lab

Energy & Renewables

Solar Inverter Sizing Calculator

Inverter size in kW and kVA with motor surge and DC current, the DC/AC ratio, and a cold-weather string voltage check.

Inputs

Calculate from
A power triangle with P horizontal, Q vertical and S on the hypotenuse, and a bar chart of running and surge kVA.P (kW)Q (kvar)S (kVA)φPF = cos φ = P ÷ SrunningsurgeS(other) + k × S(motor)
Real power P (kW) and reactive power Q (kvar) add like the sides of a right triangle; the inverter must supply the apparent power S = √(P² + Q²) in kVA. A starting motor briefly draws k times its running kVA (the surge). Diagram not to scale.

Total real power (kW) of everything except the largest motor that may run at the same time.

1 for heaters and incandescent lamps; often 0.6–0.95 for motors, electronics and LED drivers (from the appliance data).

Running (not starting) power of the largest motor load, e.g. a pump, fridge or air-conditioner compressor. 0 if none.

Starting kVA ÷ running kVA, e.g. locked-rotor current ÷ rated current from the motor data. 1 to 8; no default is claimed.

Inverter ratings you can buy go in steps; the suggestion is rounded up to this step.

Result

Required continuous rating (with margin)
3.24133
Required continuous real power (with margin)
2.8125
Running apparent power S
2.59306
Running real power P
2.25
Running reactive power Q
1.289kvar
Overall power factor
0.8677
Surge while the motor starts
6.35417
DC input current (continuous)
50.4032A
DC input current during the surge (upper bound)
142.342A
Suggested continuous rating (next size step up)
3.5
Working
P = 1.5 + 0.75 = 2.25 kW; Q = P tan(cos⁻¹ PF) summed = 1.289 kvar S = √(P² + Q²) = 2.5931 kVA (PF 0.8677; adding kVA directly would give 2.6042 kVA) With 25% margin: 2.8125 kW and 3.2413 kVA Surge S = S_other + k × S_motor = 1.6667 + 5 × 0.9375 = 6.3542 kVA DC current = P ÷ (V × η) = 2,250 W ÷ (48 V × 0.93) = 50.403 A

An inverter of at least 3.24133 kVA (2.8125 kW) continuous with a surge rating of 6.35417 kVA is needed; the next size step is 3.5 kVA.

  • Choose an inverter whose continuous kW and kVA ratings both cover the required values, and whose surge rating and its duration (data sheet) cover the motor start. The surge figure adds kVA directly, which is a cautious upper bound because a starting motor has a low power factor.

Educational estimate — check the assumptions below.

About this calculator

An inverter must supply the real power (kW) of the loads, the apparent power (kVA) that their power factor demands, and the short surge when a motor starts. This calculator works these out from the loads you enter, with a design margin and the DC current drawn from the battery. Two more modes check a grid-tied array’s DC/AC ratio and the string voltage on the coldest morning.

Formula

Qi = Pi tan(cos⁻¹ PFi)    S = √[(ΣP)² + (ΣQ)²]    P = S × PF

Ssurge = Sother + k × Smotor    Smotor = Pmotor ÷ PFmotor    IDC = ΣP ÷ (Vbatt × η)

Voc,cold = Ns × Voc × [1 + βVoc (Tmin − 25 °C)]    Vmp,hot = Ns × Vmp × [1 + βVmp (Tmax − 25 °C)]

P = real power (kW), Q = reactive power (kvar), S = apparent power (kVA), PF = power factor, k = motor starting multiple, β = temperature coefficient (negative, per °C), Ns = modules in series. Loads are added as P and Q, not by adding kVA.

Worked example

  • Backup inverter: other loads 1.5 kW at PF 0.90, a 0.75 kW motor at PF 0.80 with starting multiple 5, margin 25%, 48 V, 93% → P = 2.25 kW, Q = 1.289 kvar, S = 2.593 kVA (PF 0.868); with margin 2.81 kW and 3.24 kVA; surge 1.667 + 5 × 0.938 = 6.35 kVA; DC current 50.4 A (up to 142 A during the start).
  • String check (example from IAEI magazine): Voc 45 V, β −0.36 %/°C, lowest temperature −10 °C → 45 × (1 + 0.0036 × 35) = 50.67 V per module; 11 modules = 557.4 V, below a 600 V limit.
  • DC/AC ratio: 6.6 kWp on a 5 kW inverter = 1.32.

Assumptions and limitations

  • Loads that run at the same time are entered as one total; the largest motor is entered separately for the surge.
  • Power factors and the motor starting multiple come from the equipment data; the calculator does not assume them for you.
  • The surge value adds kVA directly (cautious). Inverter surge ratings are given for a limited time (seconds); check the data sheet.
  • The string check uses the module data sheet coefficients and your temperatures. The applicable electrical code decides the official method; this is a check only.

References

  • Wiles, J. (2019), “PV Systems Math — Sample Calculations”, IAEI Magazine (NEC 690.7 cold-temperature Voc with the module coefficient).
  • NFPA 70 (NEC) Article 690.7 and IEC 62548 — maximum PV system voltage.
  • Dobos, A. P. (2014), PVWatts Version 5 Manual, NREL/TP-6A20-62641 (DC/AC ratio and inverter model).