Active Power in Solar PV: Formula, kW vs kVA, Output

Solar professionals read three power numbers all the time: kW, kVA and kWh. Active power is the first of them, and it is the one your customer is paid for or billed on. This guide explains how to calculate it and how it differs from the other two.

An inverter’s kW output, a site’s kVA demand and a monthly kWh reading are three different things. If you mix them up, your savings model can be wrong even when the math looks right.

Last updated: November 2026.

This guide shows how to find each quantity, how to check an inverter rating, and what curtailment means. Every number in the examples is made up for practice. None comes from a customer project, a utility or a product data sheet.

What are active, apparent and reactive power?

Yokogawa’s power-measurement guide names two kinds of power factor. Displacement power factor is the cosine of the angle between voltage and current, and it is correct for sine waves only. True power factor is real power divided by apparent power, and it works for every waveform. Use true power factor when harmonics (extra frequencies on top of 50 or 60 Hz) are present.

For sine waves, S² = P² + Q². P and Q are at right angles to each other, like the two short sides of a right triangle. You do not add them to get S. A power factor of 0.80 does not mean that 20% of the current is reactive. In that case, Q divided by S is 0.60, because √(1 − 0.80²) = 0.60.

Meters can calculate S and Q in different ways. Yokogawa lists two methods in its WT1800 and WT3000 analyzers. Type 1 works from RMS voltage, RMS current and active power. Type 3 also includes the harmonic parts of Q. Check which method a meter uses before you compare two readings. For more on the basics, see the glossary entry on active and reactive power.

How do you calculate active power?

For a single-phase circuit:

P = Vrms × Irms × true PF

For a balanced three-phase circuit:

P = √3 × VLL × IL × PF

VLL is the line-to-line RMS voltage. IL is the RMS line current. “Balanced” means all three phases carry the same load. Use watts with volts and amps, then divide by 1,000 for kW. Do not mix line-to-neutral and line-to-line voltage.

If the three phases carry different loads, measure each phase. Yokogawa says two-wattmeter shortcuts average two VA values and can give a wrong power factor on an unbalanced load. Its three-wattmeter method gives a correct power factor for balanced or unbalanced loads.

Also write down where you measure. The inverter terminals and the point of common coupling (the point where the site connects to the utility grid) can give different readings.

Single-phase example

Assume 230 V RMS, 15 A RMS and a true PF of 0.95.

• S = 230 × 15 = 3,450 VA, or 3.45 kVA.
• P = 230 × 15 × 0.95 = 3,277.5 W, or 3.2775 kW.
• For sine waves, Q = √(3.45² − 3.2775²) = 1.0773 kvar.

This Q result does not show whether the current leads or lags. That depends on the sign convention of your meter. Keep unrounded values until the last step.

Balanced three-phase example

Assume 400 V line-to-line, 25 A per line and PF = 0.90.

• S = √3 × 400 × 25 = 17.3205 kVA.
• P = S × 0.90 = 15.5885 kW.
• For sine waves, Q = S × √(1 − 0.90²) = 7.5498 kvar.

The reactive part is not “the other 10%”. P and Q are vectors at right angles to each other. Current is only one input to equipment choice. See AC disconnect sizing for the next step.

How do you turn power into energy?

Energy is active power times time. Say output averages 5 kW for two hours and 8 kW for one hour. The total is 5 × 2 + 8 × 1 = 18 kWh. One reading at noon cannot tell you the energy for the day.

Check your tariff before you turn a change in kW, kvar or power factor into money. Charges can include energy, demand and fixed fees. Put those inputs into your financial model.

What is active power curtailment?

Curtailment means the inverter sends out less active power than the array could make. Three common controls cause it.

NREL’s smart inverter presentation explains why. PV active power tends to raise grid voltage. Absorbing reactive power can lower voltage with little or no loss of active power, so it is generally preferred. Cutting active power loses PV energy. NREL says it is typically an option only when voltage is very high and reactive power is not solving the problem.

For frequency, NREL says advanced inverters can reduce power when frequency is high. This function is called frequency-watt control. Helping when frequency is low needs extra power, and that may not be possible unless the inverter is already running below its limit.

Curtailment example

Say a 10 MW plant is held at 85% for a steady half hour. Output is 10 × 0.85 = 8.5 MW. The lost energy is 1.5 MW × 0.5 h = 0.75 MWh. A real study needs time-series estimates of available power, the actual limits and a fixed comparison period. Do not turn this one example into a yearly loss percentage.

Clipping is different. Clipping happens when the array makes more DC power than the inverter rating allows. Track clipping, curtailment, shading and downtime as separate losses in your solar yield prediction.

How do you check an inverter’s kW and kVA rating?

An inverter has a kW rating and a kVA rating. Both matter. The DC array rating in kWp is a third number on a different basis.

Take a made-up inverter limited only by a 100 kVA rating. This table shows the most active power it can send out at each power factor.

Now turn the question around. To deliver 100 kW at a power factor of 0.90, you need 100 ÷ 0.90 = 111.11 kVA. For sine waves, the reactive power is 111.11 × √(1 − 0.90²) = 48.43 kvar. This is one operating point. It does not tell you which inverter size to buy.

Real inverters publish a capability curve. It shows how much kW and kvar the unit can give at your voltage and temperature. Read the curve on the data sheet for your exact model. Also check the current limit and the modes that are enabled. For how efficiency changes with load, read the inverter efficiency curve explained.

Power factor also changes cable current. Keep P and V the same in a balanced sine-wave case. Moving from PF 1.00 to PF 0.90 raises current by 1 ÷ 0.90 − 1 = 11.11%. Heat loss in the same cable (I²R) rises by 1.1111² − 1 = 23.46%. This is a comparison only. It does not pick a cable size.

Why does power factor drop at the meter after PV?

Here is a made-up snapshot for sine waves, with wiring losses ignored.

PV cut the imported active power, but the reactive demand stayed the same. So the power factor at the meter fell, even though the apparent demand also fell. That is not proof of a penalty or a fault. Look at interval data, your tariff and the meter’s sign convention. Also check whether the inverter’s reactive mode is on. For fixes, read power factor correction for solar inverters and reactive power compensation.

This example only covers imports. It does not cover the case where the site exports power. When import turns into export, the sign rules change.

What do the grid rules say?

Rules differ by country, utility and standard edition. The NLR summary of IEEE 1547-2018 says Clause 5 covers voltage and reactive power control. It lists four modes: constant power factor, voltage-reactive power, active power-reactive power and constant reactive power. Clause 6 covers how inverters respond to abnormal voltage and frequency, including ride-through.

The summary does not give settings for your site. Get the approved settings from the utility, and keep a record of the mode, limits, priority and who reviewed them. Never change a live inverter setting from a worked example.

Active power checklist for inverter commissioning

1. Pick the boundary: inverter output, load feeder or grid connection.
2. Write down units, phase and voltage basis, meter method, sign convention and interval.
3. Keep AC output, DC nameplate and energy separate.
4. Compare readings with the exact equipment limits.
5. Attach the tariff and the approved interconnection settings.
6. Track curtailment, clipping and other losses without counting the same energy twice.
7. Record open assumptions and the name of the qualified reviewer.

Use this record in your solar design workflow and your customer proposal. SurgePV supports 3D roof modeling, array layout, energy-yield modeling, financial modeling, electrical workflow support, bill-of-materials output and proposals. Book a demo to see these steps. SurgePV outputs support design and documentation. They do not replace approval by the responsible engineer, authority or utility.

Frequently Asked Questions

What is the output active power of a solar inverter?

It is the real power, in kW, that the inverter sends out at its AC terminals at a given moment. It is not the same as the apparent power in kVA or the energy in kWh. For single-phase AC, P = V × I × PF.

What is the difference between active power and reactive power?

Active power (P, in watts) does useful work. Reactive power (Q, in var) moves back and forth in the AC circuit and does no useful work. For sine waves, apparent power S follows S² = P² + Q². You cannot simply add P and Q.

How do you calculate active power in a three-phase solar system?

For a balanced system, P = √3 × line-to-line voltage × line current × power factor. If the three phases carry different loads, measure each phase. Yokogawa says its three-wattmeter method gives a correct power factor for balanced or unbalanced loads.

Why does power factor drop when solar PV is added to a site?

PV can cut the active power you import while the reactive demand stays the same. The ratio of active to apparent power then falls at the grid meter. In the example in this guide, it falls from 0.8944 to 0.6247. This is not a fault by itself.

What is active power curtailment in solar inverters?

Curtailment means the inverter sends out less active power than the array could make. Triggers include an export limit, high grid voltage (volt-watt) and high grid frequency (frequency-watt). NREL notes that cutting active power loses PV energy, so it is typically used only when voltage is very high.

How do you size a solar inverter for apparent power, not just active power?

Check both the kW and the kVA rating, and the maker’s capability curve. In this guide’s example, 100 kW at a power factor of 0.90 needs about 111.11 kVA. Use the real data sheet for your voltage and temperature.

What happens if available solar power exceeds the inverter output limit?

The extra power is not sent to the grid. If the cause is the inverter’s own rating, that is called clipping. If the cause is a limit set by a command or a rule, that is curtailment. Keep the two apart when you check energy yield.