PW-B2 · Power and power factor

Power-factor correction: erasing reactive power with a capacitor

In B1 reactive power did no work yet swelled the apparent power and tied up equipment. Cancel the lagging reactive of a coil load with the leading reactive a capacitor supplies, and the triangle gets shorter. Grow the capacitor yourself to learn how the same work is sent with less current.

Grow the capacitor and shrink the triangle

The base, active P, is fixed (the same work). Drag the handle to grow the capacitor reactive Q_C. Subtracting Q_C from the load lagging reactive Q_L leaves less net reactive, and the hypotenuse, apparent S, and the line current shrink together.

Drag the handle up and down to set the capacitor size.

Power factor cosφ and line current (vs before)

cosφ ≈ 0.800

I ≈ 100%   S ≈ 1.25   Q_net ≈ 0.75

Why reactive power is a loss

Coil loads like motors and transformers draw a lagging reactive Q_L to build their magnetic fields. This reactive does no real work, yet it flows as current in the line and swells the apparent power S. Wires and transformers must withstand that S, and the line loss I²R grows with it. This is why utilities charge for a low power factor.

A capacitor supplies leading reactive

A capacitor is the opposite of a coil: its current leads the voltage, supplying a leading reactive Q_C. Being exactly opposite in direction to the load lagging reactive, the two erase each other on the spot. Q_net = Q_L − Q_C. Put the capacitor right next to the load and the reactive only shuttles between load and capacitor, never down the line. It is borrowing reactive on site instead of hauling it from afar.

Just enough, not too much

As the reactive Q falls, the apparent S = √(P² + Q²) falls too, and so does the line current I = S/(√3 V_L) carrying the same active P. Wires and transformers gain margin, and losses and bills drop. To reach a target power factor cosφ2 you need Q_C = P(tanφ1 − tanφ2). At pf = 1, Q_C = Q_L erases the reactive entirely. But add more and it tips into a leading power factor toward the capacitor and worsens again — just enough.

ObserveQ_net = Q_L − Q_C

Net reactive = load reactive minus capacitor reactive.

ChooseQ_L = P · ?

Load reactive is active times tanφ1.

Fill inQ_C = P (tanφ1 − ?)

The target leaves only tanφ2.

On your ownpf = 1 → Q_C = ?

Full cancellation (pf=1) means capacitor equals load reactive.

Back to the first screen

Raising the handle to grow the capacitor shrank the height Q_net, and the hypotenuse S and line current shrank with it. The base, active P, stayed the same from start to finish — the same work sent with less current. Where B1 had reactive swell S, B2 erases that reactive on site with a capacitor and pulls S back toward P. When the handle reaches the height of P, the reactive is zero and the power factor is one.

A power-factor correction cancels the lagging reactive Q_L of a coil load with the leading reactive Q_C of a capacitor. As the net reactive Q_net = Q_L − Q_C falls, the apparent S and the line current fall, sending the same active P with less current. The capacitor needed for a target factor is Q_C = P(tanφ1 − tanφ2). At pf = 1, Q_C = Q_L (full cancellation); beyond that, a leading power factor.

The next step

So far we handled the power of a single load. A real system has many loads switching on and off at different times. The next unit (PW-B3) looks at load and demand factors: why the actual peak demand is smaller than the sum of all installed capacity (demand factor), and the margin that appears when the peaks of many loads fall at different times (diversity factor).