Power factor is the ratio of the power that does work to the power the supply has to deliver. It is 1.0 for a heater and something like 0.7 for a lightly loaded motor. That gap is not a rounding error: it decides how much current flows for a given job, how hot the cables run, how much of a transformer or generator is left for other loads, and, for industrial and commercial consumers in Pakistan, whether a penalty appears on the bill.
The lag
A resistive load draws current in step with the voltage. A load with inductance, which means anything with a coil, such as motors, transformers, magnetic ballasts, welders and solenoids, draws current that lags the voltage: the magnetic field has to be built up each half-cycle before the current can rise, and energy stored in that field is handed back to the supply as it collapses. That energy sloshes back and forth without doing work, but the current carrying it is real and heats every conductor it flows through.
The lag is an angle, φ, and cos φ is the displacement power factor. The three powers involved are:
- Real power P (kW): the average over a cycle, the part that becomes heat, motion or light.
- Reactive power Q (kVAr): the amplitude of the part that sloshes.
- Apparent power S (kVA): voltage times current, the total the wires carry. S² = P² + Q², and PF = P ÷ S.
A 100 kW load at 0.75 power factor is 133 kVA with 88 kVAr of reactive power along for the ride. At 0.95 it would be 105 kVA and 33 kVAr. The guide to single- and three-phase power shows how these turn into line current.
What a low power factor costs
- Tariff penalties. The terms and conditions attached to Pakistan's industrial and commercial tariffs, as approved by NEPRA, require a monthly average power factor of at least 90 % and add a percentage penalty to the bill for each point below it. Distribution companies measure it from the kWh and kVArh registers of the meter. Check the current terms for your category; the mechanism has been stable for years but the figures can change.
- Demand charges. Where the tariff bills maximum demand in kVA rather than kW, a poor power factor raises the demand charge directly: 100 kW at 0.75 is billed as 133 kVA.
- Cable and transformer losses. Loss is I²R. Correcting the example above from 0.75 to 0.95 cuts current by 21 % and I²R loss by 38 % in every conductor between the correction point and the supply.
- Capacity. A 200 kVA transformer feeding loads at 0.75 is full at 150 kW. At 0.95 the same transformer carries 190 kW. Correction is often the cheapest way to add a production line without a new supply connection.
- Voltage. Reactive current through the source impedance depresses the voltage at the load; correction lifts it, which helps motors start and run cooler.
How capacitors fix it
A capacitor draws current that leads the voltage by 90°, the mirror image of an inductor. Connected in parallel with an inductive load, its reactive power cancels the load's: the sloshing energy moves between the capacitor and the motor locally instead of travelling to the utility and back. The kVAr to add is:
where φ1 and φ2 are the angles for the present and target power factors. From 0.75 to 0.95 on a 100 kW load that is 100 × (0.882 − 0.329) = 55 kVAr. The power factor correction calculator gives the figure for any pair and the capacitance per phase it implies.
Three ways to connect them:
- Central automatic bank at the main switchboard: a controller reads the power factor and switches capacitor steps in and out through contactors. Corrects the whole site as seen by the meter; does nothing for losses inside the plant.
- Fixed capacitors at individual motors, switched with the motor: corrects at the source and unloads the motor's own feeder. The capacitor must be kept below about 90 % of the motor's no-load magnetising kVAr, or a spinning motor can self-excite when disconnected and generate damaging over-voltage.
- Group correction at a distribution board feeding several motors, a compromise between the two.
Where capacitors make things worse
Capacitors correct displacement. They do not correct distortion. Variable-frequency drives, UPS rectifiers, switch-mode power supplies and LED drivers draw current in pulses; the fundamental may be nearly in phase with the voltage, yet the true power factor, which includes the harmonic content, is well below 1. Adding capacitors to such a system does little for the bill and can do harm:
- The capacitor bank and the supply transformer form a resonant circuit. If its resonant frequency lands near a harmonic the loads produce, typically the 5th (250 Hz) or 7th (350 Hz), the harmonic currents are amplified, capacitors overheat and fail, and voltage distortion rises across the site.
- Capacitors present a low impedance to harmonics anyway, so they absorb harmonic current they were never rated for.
The remedies are detuned banks (a reactor in series with each capacitor step, tuning the combination below the 5th harmonic, the standard choice when drives are more than about 15–20 % of the load), active harmonic filters, or fixing the source by specifying drives with line reactors or active front ends. A power quality survey with a logging analyser at the incomer for a working week tells you which case you are in before money is spent.
Reading the power factor from a bill
Industrial bills list kWh and either kVAh or kVArh for the month. Then:
A month with 60 000 kWh and 40 000 kVArh has a power factor of cos(arctan 0.667) = 0.83, below the 90 % line. This monthly average is what the penalty is assessed on, so a site whose power factor is fine during the day but poor at night, when only ventilation and a few compressors run at light load, can still be penalised. That is the case for an automatic bank rather than fixed capacitors sized for the full-load condition.
Practical notes
- Aim for 0.95–0.98, not 1.0. Over-correction produces a leading power factor, which raises the voltage and is also penalised by some utilities.
- Buy capacitors rated for the actual system voltage and, in Pakistan, for the ambient temperature of the switchroom; capacitor life falls steeply with temperature, halving for roughly every 7–10 °C above the rated class.
- Capacitors store charge after switch-off. Discharge resistors are built in but take a minute or more; wait before working on a bank.
- Contactors for capacitor switching are a special type with pre-charge resistors, because the inrush into a discharged capacitor is very large; ordinary motor contactors weld.
- Check the bank once a year: measure each step's current against its rating (a capacitor losing capacitance draws less), look for bulged cans and smell for overheating.
References
- IEEE Std 1459-2010, Definitions for the Measurement of Electric Power Quantities — displacement, distortion and true power factor
- IEC 60831-1:2014, Shunt power capacitors of the self-healing type for a.c. systems having a rated voltage up to and including 1 000 V
- IEEE Std 519-2022, Standard for Harmonic Control in Electric Power Systems
- IEC 61000-3-12:2011, Limits for harmonic currents produced by equipment connected to public low-voltage systems with input current > 16 A and ≤ 75 A per phase
- NEPRA, Schedule of tariff and terms and conditions for the distribution companies (power factor penalty clause) — the 90 % monthly average requirement for industrial and commercial consumers