Power Factor Correction in Practice

The arithmetic of power factor correction fits on one line. The engineering does not. A capacitor bank that is the right size on paper can still overheat because of harmonics, trip a generator off line, push a lightly loaded plant to a leading power factor or leave the utility penalty exactly where it was. This guide works through the sizing calculation and then covers the practical decisions: where the capacitors go, fixed or automatic switching, harmonics and detuning, discharge, generators and the electricity bill.

Sizing the bank: Q = P (tan φ1 − tan φ2)

Capacitors supply reactive power locally, so the network upstream no longer has to carry it. The real power P does not change. Only the reactive part shrinks, from P tan φ1 at the existing power factor to P tan φ2 at the target:

Take a plant drawing 400 kW at PF 0.75 from a 400 V, three-phase main board, with a target of 0.95:

A standard 225 kVAr bank would be chosen. Line current falls by about 21 %, and because copper losses scale with the square of current, losses in the transformer windings and feeders fall by about 38 % ((421.1 / 533.3)² = 0.62). If the plant is supplied from a 630 kVA transformer, its loading drops from about 85 % to about 67 %, which frees capacity for new load. The power factor correction calculator runs these steps and gives the capacitance per phase. The kVA to kW converter solves the power triangle, and the transformer loading calculator shows the change in losses.

Size from the measured load profile, not a single number. A plant that swings between 100 kW at night and 400 kW by day needs very different correction at each end, which is why automatic banks exist.

Where to install the capacitors

There are three basic arrangements, and many sites combine them.

• Individual correction at the motor. A fixed capacitor is connected at the motor terminals and switched with the motor. The reactive current is removed from the whole route back to the source, including the final circuit, so cable losses and voltage drop fall the most. It suits large motors that run for long hours at steady load. It costs the most per kVAr, because each capacitor sits idle whenever its motor is off.
• Group correction. One bank serves a sub-distribution board feeding several loads. It relieves the feeder to that board and is cheaper per kVAr than individual units.
• Central correction at the main LV board. One automatic bank serves the whole installation. It has the lowest cost per kVAr and the best use of installed capacitors, because the diversity of the loads is shared. It does not relieve the internal cables, which still carry reactive current between the loads and the main board, but it fixes the power factor the utility measures and unloads the transformer.

Fixed versus automatic banks

A fixed bank is always connected while its supply is on. It suits a roughly constant reactive demand, such as a transformer's no-load magnetising demand. Sized for full load, it over-corrects when load falls.

An automatic bank is divided into steps, each switched by a capacitor-duty contactor or a thyristor switch. A power factor controller measures current and voltage, usually through one current transformer on the incoming supply, and switches steps in and out to hold a target power factor. Step sizes are often unequal, such as 1:2:2:2 ratios, so that a few physical steps give many combinations of total output. Thyristor-switched banks are used where load changes faster than contactors can follow, such as welding or cranes, because they switch without inrush and without wear.

Two controller settings deserve attention. The reconnection delay must be at least the capacitor discharge time, because closing onto a charged capacitor in phase opposition causes a large transient. And the CT must see the whole load with the correct polarity; a misplaced or reversed CT is a common reason a new bank seems to do nothing.

Fixed capacitors at motors: avoid self-excitation

When a motor with a capacitor connected directly across its terminals is switched off, it keeps turning for a while. If the capacitor supplies more reactive power than the motor needs to magnetise itself, the pair can behave as a self-excited induction generator. The terminal voltage can then rise above the supply voltage. The general rule is to keep the capacitor below the motor's no-load magnetising reactive power, which can be estimated from the no-load current as √3 × U × I0. Manufacturers publish recommended maximum kVAr for their motors, and that guidance takes precedence.

Two further cautions apply. Do not fit terminal capacitors to motors that are star-delta started, reversed, jogged or driven by a variable speed drive. A drive has its own DC link and should not see capacitors on its output. If the capacitor is connected downstream of the overload relay, the relay now sees a smaller current than the motor draws, and its setting must be reduced accordingly.

Harmonics and resonance

Variable speed drives, rectifiers, UPS systems and LED drivers draw non-sinusoidal current that contains harmonics. Capacitor reactance falls with frequency, so a capacitor attracts harmonic current and can overheat. A more serious problem is parallel resonance between the capacitor bank and the inductance of the supply transformer. An approximate resonant harmonic order is:

The estimate ignores upstream impedance and damping, but it shows the danger: a resonance near the 7th harmonic, next to the 5th and 7th that six-pulse drives produce. As steps switch, the resonant frequency moves and may land on a harmonic that is present, amplifying harmonic voltage and overheating capacitors.

The usual remedy in harmonic-rich installations is a detuned bank. Each step has a series reactor that tunes the capacitor-reactor combination below the lowest significant harmonic, so the step looks inductive at harmonic frequencies and cannot resonate with the transformer. The tuning is described by the tuning factor p, the ratio of reactor reactance to capacitor reactance at the fundamental frequency:

The appropriate p depends on the measured harmonic spectrum, especially on whether the 3rd harmonic is significant, so it is chosen from a harmonic survey and supplier guidance, not from a fixed rule. The reactor also raises the voltage across the capacitor to roughly U / (1 − p), so detuned banks use capacitors rated above the system voltage. A detuned bank is not a harmonic filter. Its job is to protect the capacitors and avoid resonance. Where harmonic levels must be reduced, a tuned or active filter is a separate design. IEC 60831 covers self-healing LV shunt capacitors, and IEC 61921 covers the LV power factor correction bank as an assembly.

Discharge and switching

A disconnected capacitor can stay charged at a dangerous voltage. IEC 60831-1 requires each capacitor unit to have a means of discharging it to 75 V or less within 3 minutes, usually built-in discharge resistors. Treat any capacitor as charged until it has been discharged and verified. When a discharged capacitor is energised, it draws a short, high inrush current, especially when other steps are already connected in parallel. Capacitor-duty contactors with early-make damping resistors, or thyristor switching, limit this inrush.

Over-correction and generators

If more kVAr is connected than the load needs, the power factor becomes leading. On a utility supply this wastes capacity, can raise the voltage and is charged by some tariffs. On a generator it is more serious. A synchronous generator's capability curve allows only a small amount of leading reactive load before the excitation becomes too weak for stable operation. With a lightly loaded generator, even a modest capacitor bank can push the alternator outside that limit and cause voltage rise or loss of excitation. The common practice is to interlock the automatic bank with the transfer switch so that it is disconnected, or limited to steps agreed with the generator supplier, whenever the site runs on its generator.

Reading the utility bill

Utilities that charge for reactive power meter it as kVArh alongside kWh. The average power factor for a billing period is:

Tariffs differ widely. Some charge for kVArh above a set fraction of kWh, some add a surcharge below a threshold power factor, and some bill maximum demand in kVA. Thresholds and rates depend on the utility and tariff class, so read them from your own tariff schedule. Note that a monthly average hides hours of poor power factor, while a kVA demand charge depends on the worst demand interval.

Measure before and after

Before buying a bank, record at least a week of kW, kVAr, power factor and harmonics at the main incomer with a power quality analyser. The record sets the step sizes and shows whether detuning is needed. After commissioning, measure again: the controller should hold its target across the load range without over-correcting at night, and harmonic voltage distortion should not have risen. The next few bills confirm whether the kVArh charges have actually fallen.

This guide is general education. Follow the manufacturer's data, the applicable standards and your utility's rules for any real installation.