Basics for power factor correction

Basics for power factor correction

Fig.: Active power formula
Fig.: Active power formula

Active power

If one connects an effective resistor, e.g. a heating device, in an alternating current circuit then the current and voltage are in phase.The momentary power values (P) are determined with alternating current through the multiplication of associated momentary values of current (I) and voltage (U). The course of the active power is always positive with doubled mains frequency.

The AC power has the peak value P = U x I. Through area conversion it can be converted into the equivalent DC power, the so-called active power P. In the event of effective resistance, the active power is half the size of the peak power value.

In order to determine the AC power, one always calculates using the effective values.

Fig.: AC power with purely ohmic load
Fig.: AC power with purely ohmic load

Active and reactive power

A purely ohmic load rarely arises in practice. An inductive component usually also arises. This applies to all loads, which require a magnetic field in order to function (e.g. motors, transformers, etc.). The current used, which is required in order to generate and reverse the polarity of the magnetic field, is not dissipated but flows back and forth as reactive current between the generator and the load.

Phase shifting arises, i.e. the zero point transitions for voltage and current are no longer congruent. With an inductive load the current follows the voltage, with a capacitive load the relationship is precisely the opposite. If one now calculates the momentary power values (P = U x I), negative values will always arise if one of the two factors is negative.

Example:
Phase shifting φ = 45° (equates to an inductive cos φ = 0.707). The power curve overlaps in the negative range.

Fig.: Calculation of the effective power with ohmic and inductive load
Fig.: Calculation of the effective power with ohmic and inductive load
Fig.: Voltage, current and power with mixed ohmic, inductive load
Fig.: Voltage, current and power with mixed ohmic, inductive load

Reactive power

Inductive reactive power arises for example in motors and transformers – without consideration to line, iron and friction losses.

If the phase shifting between current and voltage is 90°, e.g. with "ideal" inductance or with capacity, then the positive and negative area portions are of equal size.The effective power is then equal to the factor 0 and only reactive power arises. The entire energy shifts back and forth here between load and generator.

Fig.: Voltage, current and power with pure reactive load
Fig.: Voltage, current and power with pure reactive load
Fig.: Voltage, current and power with pure reactive load
Fig.: Voltage, current and power with pure reactive load


Apparent power

The apparent power is the electrical power that is supplied to or is to be supplied to an electrical load.The apparent power S is derived from the effective values of current I and voltage U.

In the event of insignificant reactive power, e.g. with DC voltage, the apparent power is the same as the active power. Otherwise this is greater. Electrical operating equipment (transformers, switchgear, fuses, electrical lines, etc.), which transfer power, must be appropriately configured for the apparent power to be transferred.

Fig.: Power diagram
Fig.: Power diagram
Fig.: Apparent power without phase shifting
Fig.: Apparent power without phase shifting

Apparent power with sinusoidal variables

With sinusoidal variables the offset reactive power Q arises, if the phases of current and voltage are shifted by an angle φ .

Fig.: The apparent power is the result of the geo- metric addition of active and reactive power.
Fig.: The apparent power is the result of the geo- metric addition of active and reactive power.

Power factor (cos φ and tan φ)

The relationship of active power P to apparent power S is referred to as the effective power factor or effective factor. The power factor can lie between 0 and 1.

With pure sinusoidal currents, the effective power factor concurs with the cosine (cos φ). It is defined from the relationship P/S.The effective power factor is a measure through which to determine what part of the apparent power is converted into effective power. With a constant effective power and constant voltage the apparent power and current are lower, the greater the active power factor cos φ.

The tangent (tan) of the phase shift angle (φ) facilitates a simple conversion of the reactive and effective unit.

Fig.: Determination of the power factor over effec- tive and apparent power
Fig.: Determination of the power factor over effec- tive and apparent power
.: Calculation of the phase shifting over reactive and effective power
.: Calculation of the phase shifting over reactive and effective power

The cosine and tangent exist in the following relationship to each other:

Fig.: Relationship to cos φ and tan φ
Fig.: Relationship to cos φ and tan φ

In power supply systems the highest possible power factor is desired, in order to avoid transfer losses. Ideally this is precisely 1, although in practical terms it is around 0.95 (inductive). Energy supply companies frequently stipulate a power factor of at least 0.9 for their customers. If this value is undercut then the reactive energy utilised is billed for separately. However, this is not relevant to private households. In order to increase the power factor, systems are used for power factor correction. If one connects the capacitor loads of a suitable size in parallel then the reactive power swings between the capacitor and the inductive load. The superordinate network is no longer additionally loaded. If, through the use of PFC, a power factor of 1 should be attained, only the effective current is still transferred.

The reactive power Qc, which is absorbed by the capacitor or dimensioned for this capacitor, results from the difference between the inductive reactive power Q1 before correction and Q2 after correction.

The following results: Qc = Q1 – Q2

Fig.: Power diagram with application of power factor correction
Fig.: Power diagram with application of power factor correction
Fig.: Calculation of the reactive power for the improvement of the power factor
Fig.: Calculation of the reactive power for the improvement of the power factor

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