The power factor is a concept that is needed to be very clearly understood by electrical engineers. It is studied in the first or second year of the engineering courses when the students are not fully ready to grasp all the bits and pieces of this concept. Here I tried to write down the necessary details in a very easy manner so that it can be used as a reference study material in the student life as well as in professional life.

Power Factor

In simple terms, the power factor is just a ratio of real power and apparent power. But by this definition, it can be hardly realized. To understand we have to go back to the old analogy of the Wine glass.

Power Factor Calculator

How to Calculate Reactive Power

It is possible to improve the power factor by installing a capacitor bank in parallel. The capacitor bank will inject capacitive reactive power which is leading reactive power,. Before that, we have to calculate how much KVar we have to introduce into the system. In this case, the capacitor bank will introduce the leading reactive power to suppress the lagging reactive power.

Way of Generating Reactive Power

• synchronous alternators;
• synchronous compensators (SC);
• static var compensators (SVC);
• banks of static capacitors

Synchronous alternators

Synchronous alternators are the main machines used for the generation of electrical energy. They are intended to supply electrical power to the final loads through transmission and distribution systems. Besides, without
going into technical details, by acting on the excitation of alternators, it is possible to vary the value of the generated voltage and consequently to regulate the injections of reactive power into the network, so that the voltage profiles of the system can be improved and the losses due to the Joule effect along the lines can be reduced.

Synchronous compensators

They are synchronous motors running no-load in synchronism with the network and having the only function to absorb the reactive power in excess (under-excited operation) or to supply the missing one (over-excited operation).

E : e.m.f. induced in the stator phases
V: phase voltage imposed by the network to the alternator terminals
I: stator current
Xs: stator reactance

These devices are used mainly in definite nodes of the power transmission and sub-transmission network for the regulation of voltages and of reactive power flows. The use of synchronous compensators in power distribution networks is not favorable from an economic point of view because of their high installation and maintenance costs.

Static var compensators

The considerable development of power electronics is encouraging the replacement of synchronous compensators with static systems for the control of the reactive power such as for example TSC (thyristor switched capacitors) and TCR (thyristor controlled reactors). These are an electronic version of the reactive power compensation systems based on electromechanical components in which, however, the switching of the various capacitors is not carried out through the opening and closing of suitable contactors, but through the control carried out by couples of antiparallel thyristors.

TSC allow a step-by-step control of the reactive power delivered by groups of capacitors, whereas with TCR a continuous control of the reactive power drawn by the inductors is possible.

By coupling a TSC with a TCR it is possible to obtain a continuous modulated regulation of the delivered/drawn reactive power.

From the point of view of applications, these devices are used above all in high and very high voltage networks.

Static Capacitor Bank

A capacitor is a passive dipole consisting of two conducting surfaces called plates, isolated from one another by a dielectric material.

The system thus obtained is impregnated to prevent the penetration of humidity or of gas pockets which could cause electrical discharges.

The last generation capacitors are dry-type and undergo a specific treatment which improves their electrical characteristics. Using dry-type capacitors there is no risk of pollution because of the incidental leak of the impregnating substance.
According to the geometry of the metal plates, it is possible to have:
• plane capacitors;
• cylindrical capacitors;
• spherical capacitors.

The main parameters which characterize a capacitor are:

• Rated capacitance Cn: the value obtained from the rated values of power, voltage, and frequency of the capacitor;
• Rated power Qn: the reactive power for which the capacitor has been designed;
• Rated voltage Un: the r.m.s. value of the alternating voltage for which the capacitor has been designed;
• Rated frequency fn: the frequency for which the capacitor has been designed.

When an alternating voltage is applied across the plates,
the capacitor is subjected to charge and discharge cycles, during which it stores reactive energy (capacitor charge) and injects such energy into the circuit to which it is connected (capacitor discharge).

Such energy is given by the following relation:

where:
• C is the capacitance;
• U is the voltage applied to the terminals of the capacitor.
Because of their capability of storing and delivering energy, capacitors are used as a basic element for the realization of PF correction banks (for all voltage levels) and of static devices for the regulation of reactive power. Particularly, the PFI capacitors used for low voltage, applications are constituted by single-phase components of metalized polypropylene film and can be of the self-healing type. In these capacitors, the dielectric part damaged by a discharge is capable of self-restoring; in fact, when such situations occur, the part of the polypropylene film affected by the discharge evaporates due to the thermal effect caused by the discharge itself, thus restoring the damaged part.

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