The power in alternating current is the way to describe how energy is delivered, returned and transformed in AC circuits.
In resistive examples of direct current, the source delivered energy and the load transformed it continuously.
In Alternating Current, having coils and capacitors, a fascinating phenomenon occurs: part of the energy is not consumed, but rather “bounces” between the generator and the load.
To understand the Power Triangle, we must distinguish between consuming energy and borrowing energy.
Active Power (
This is the power that performs irreversible work. It is the energy that leaves the electrical grid and does not return. It is transformed into something else:
- In a resistor, it turns into Heat.
- In a light bulb, it turns into Light.
- On the shaft of a motor, it turns into Mechanical Movement.
It is the “useful” power from the user’s point of view.
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Symbol: 𝑃
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Unit: Watts (𝑊) or Kilowatts (k𝑊).
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Formula:
For sinusoidal voltage and current:
This is the power that your meter records and that you pay for as “energy consumed” on your bill.
Reactive Power (
Here is the key. Coils and capacitors do not dissipate energy (ideally). What they do is store it temporarily in the form of a magnetic or electric field.
Imagine the cycle of alternating current (50 times per second):
- First quarter cycle: The coil “asks” the grid for energy to create its magnetic field.
- Second quarter cycle: The current drops, the magnetic field collapses, and the coil returns that energy to the grid.
The net result is that the total work is ZERO. The energy goes back and forth like a tennis ball. This energy that oscillates without being consumed is called Reactive Power.
- Symbol: Q
- Unit: Volt-Amperes Reactive (VAR) or kVAR.
- Formula:
Is it useless? No. It is fundamental. Without this energy, the magnetic field of the motor would not exist, and it could not turn. It is the “magnetic fuel” that keeps the system standing, even though it produces no final work on the shaft.
Apparent Power (
Even though Reactive Power (Q) is returned to the grid, the electrons must physically travel through the wires to carry it back and forth.
This means that the cables, transformers, and switches must withstand the total current: the one that will work (P) plus the one that will oscillate (Q).
This total sum of electrical effort is called Apparent Power. It is the “total capacity” we must install.
- Symbol: S
- Unit: Volt-Amperes (VA) or kVA.
- Formula (Magnitude):
The power triangle
The complex power is written as
They form a right triangle where:
- Adjacent Side: Active Power (P - Watts).
- Opposite Side: Reactive Power (Q - VARs).
- Hypotenuse: Apparent Power (S - VAs).
Applying the Pythagorean Theorem, we obtain the fundamental relationship for sizing any installation:
Engineering Example
Imagine a transformer designed to handle S = 100 kVA.
- If we connect only heaters (only P, no Q), we can get 100kW of heat.
- If we connect highly inductive motors (lots of Q), we might be using 50kVA just for reactive energy (magnetization). This leaves less room for active power. The transformer will saturate “sooner” before having delivered all its real working capacity.
