kW, kVA and kVAR: The Power Triangle, Explained

Part 7 of 23 in Cobler's Electricity Fundamentals series. New here? Start with the course map.

Buy a standby generator rated at 1000 kVA and you might reasonably expect 1000 kW of usable power. You will not get it. Feed a normal factory load and that same machine delivers only about 800 kW. The other 200 kW of the nameplate is headroom you never get to spend, because the alternator is busy carrying a second kind of power the wires need but the meter that bills your energy will not charge you for directly. That gap between the number on the nameplate and the power you can actually use is the whole story of kW, kVA and kVAR.

Alternating current has three kinds of power, not one. Getting them straight explains why your transformer is sized the way it is, why TNB watches your power factor, and why the same load can look bigger to the grid than the work it actually does.

What are kW, kVA and kVAR?

Three different measures of AC power, and only one of them does work.

- Real power (kW) is the power that does something useful: turning a shaft, heating an element, lighting a lamp. This is what your kWh meter counts and what most people mean by "electricity used." Its unit is the watt.
- Reactive power (kVAR) is the power that builds and collapses the magnetic fields inside motors, transformers and ballasts. It does no net work over a full cycle, but AC machines cannot run without it. Its unit is the volt-ampere reactive, "VAR."
- Apparent power (kVA) is what the wires actually carry: the effective, or RMS, voltage multiplied by the effective current, with no regard for whether the current is doing work. Its unit is the volt-ampere.

Every inductive load (every motor, transformer and ballast, and a factory is full of them) pulls real and reactive power at the same time. The cables, switchboard and transformer have to carry the combination. That combination is the kVA.

The beer analogy, and where it lies to you

Picture a poured mug of beer. The liquid you drink is the real power (kW). The foam on top is the reactive power (kVAR). The full mug, beer plus foam, is the apparent power (kVA) you paid the bartender to pour. Power factor is the ratio: how much of your mug is actual beer.

It is a useful first picture, and it is genuinely wrong in two ways. First, the mug adds up in a straight line, but real and reactive power do not. They combine as a right triangle, which we will get to. Second, and more important, the analogy paints reactive power as useless froth you would rather not pay for. That is false. Foam is waste; reactive power is not. The magnetising current that "wastes" a mug of foam is exactly what lets an induction motor produce torque and a transformer step voltage. Take the reactive power away and the motor will not turn. We give that idea its own article in Part 8: reactive power is not wasted energy, because it is the single most misunderstood point in this whole subject.

What is the power triangle, and how does power factor work?

The power triangle is a right triangle where real power and reactive power are the two legs and apparent power is the hypotenuse. Because it is a right triangle, the three quantities obey Pythagoras:

`kVA² = kW² + kVAR²`

So the apparent power is always the vector sum, never the arithmetic sum. A load drawing 800 kW of real power and 600 kVAR of reactive power presents `√(800² + 600²) = 1000 kVA` to the grid, not 1400.

Power factor is the ratio of real to apparent power:

`Power Factor = kW ÷ kVA = cos θ`

where θ is the angle of the triangle, the phase shift between voltage and current. A power factor of 1.0 (unity) means every amp is doing work and the triangle collapses to a flat line: kVA equals kW. A power factor of 0.8 means only 80% of the apparent power is real work. Our 1000 kVA load above has a power factor of 800 ÷ 1000 = 0.8, and its angle θ is about 37 degrees.

This is why a poor power factor costs you. The grid has to deliver the full kVA even though you only do the kW of work, and TNB charges accordingly. We cover that bill in the power factor surcharge explainer.

kWh, kVAh, kVARh: which energy does your bill count?

Each of the three powers has an energy counterpart, and different countries bill different ones.

Integrate real power over time and you get kWh, the real energy every consumer knows. Integrate reactive power and you get kVARh, reactive energy. Integrate apparent power and you get kVAh, apparent energy. They relate the same way the powers do: `kVAh = √(kWh² + kVARh²)`.

Who bills what varies by regime:

- Malaysia (TNB) bills you on kWh for energy and on kW for maximum demand, then adds a power factor surcharge if your average power factor falls below the threshold. TNB requires a power factor of at least 0.85 for supply below 132 kV, and at least 0.90 at 132 kV and above (TNB power factor page). TNB meters do record kVARh, but only to work out that power factor. Malaysian bills are not raised on kVAh.
- Parts of India bill directly on kVAh, the apparent energy. Maharashtra's MSEDCL moved its high-tension consumers (and LT consumers above 20 kW) to kVAh billing effective 1 April 2020, and several other states followed (MSEDCL kVAh FAQ). Under kVAh billing a poor power factor inflates the bill automatically, with no separate penalty line, because you are charged for the full hypotenuse.

The mechanism differs but the incentive is identical everywhere: keep your current in phase with your voltage, and you pay for less apparent power.

Why are transformers and gensets rated in kVA, not kW?

Because their heating depends on current, and current follows kVA regardless of your power factor.

A transformer or a genset alternator fails in two ways: its windings overheat from the current flowing through them, and its insulation breaks down from the voltage across it. Neither cause cares about the phase angle between voltage and current. The copper losses that heat the windings scale with current squared, and current is set by apparent power, not real power (Schneider Electric).

The manufacturer also cannot know your power factor in advance. One customer's load might be resistive at unity, another's a bank of lightly loaded motors at 0.6. A 100 kVA transformer running 100 kW at unity produces the same winding heat as one running 60 kW at 0.6 power factor, because both draw the same current. So the only honest, power-factor-independent rating is the one tied to current: kVA.

This is exactly why the 1000 kVA generator from the opening delivers 800 kW at a power factor of 0.8. The alternator can carry 1000 kVA of current before it overheats. How much of that turns into real kW is set by your load, not by the machine. (Generators carry a kW figure too, because the engine driving the alternator has its own mechanical limit, usually quoted at an assumed 0.8 power factor. Both numbers matter when you size a set.)

The practical lesson for anyone sizing a switchboard, a transformer or a standby set: size it in kVA, then improve your power factor so more of that kVA is available as useful kW. A site running at 0.85 that lifts itself to 0.98 frees up roughly 15% more usable kW from the same iron, and shaves its demand and surcharge at the same time. That is the job of a capacitor bank, which we take apart in Part 23 on power factor correction. It is also money, because under RP4 medium-voltage sites pay maximum demand charges of RM89 to RM97 per kW every month, and a cleaner power factor means fewer kVA drawn for the same work.

This is Part 7 of 23 in Cobler's Electricity Fundamentals series. Previous: Why Is Power Measured in Watts? Blame the Steam Engine. Next: Reactive Power Is Not Wasted Energy.

Wondering how much of your transformer capacity is being eaten by reactive current, or what your real power factor is doing to your TNB bill? Book a demo and CobiNeural will show you the live kW, kVAR and power factor across your site.