# Power Triangle and Power Factor

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The subject of this article will be the power triangle and the power factor. More commonly called Direct Current or DC is a form of electric current or voltage that flows in only one direction around an electrical circuit, making it a "one-way" source.

In general, both DC currents and voltages are produced by power supplies, batteries, dynamo and solar cells, to mention a few. A DC voltage or current has a constant magnitude (amplitude) and a certain direction associated with it. For example, 12V represents 12 volts in a positive direction or 5 volts in a negative direction of -5V.

We also know that DC power supplies do not change their values over time, it is a constant value that flows in the direction of constant state. In other words, dc always maintains the same value, and a fixed one-way DC resource never changes or is negative unless its connections are physically reversed. An example of a simple DC or direct current circuit is shown below.

The impedance (Z) of an AC circuit is equivalent to the resistance calculated in DC circuits with the impedance given as ohm. Impedance for AC circuits is usually defined as the ratio of voltage and current phasers produced by a circuit component. Phasers are straight lines drawn to represent a voltage or current amplitude according to its length and angular position compared to other phasers and phase difference compared to other phaser lines.

AC circuits contain both resistance and reactaliate, which are combined to give a total impedance (Z) that limits the flow of current around the circuit. However, since an AC circuit impedance, pure resistance and pure reacquency are out of phase 90o with each other, they are not equal to the algebraic sum of resistant and reactive omic values. But we can use this 90-degree phase difference as the edges of a right-angled triangle called the impedance triangle, and the impedance becomes the hypotenuse determined by pythagorean theorem.

This geometric relationship between resistance, reassurance and impedance can be visually represented using an impedance triangle, as shown.

## Impedance Triangle

Note that impedance, which is the vector sum of resistance and recess, not only has a magnitude (Z), but also a phase angle (Φ) that represents the phase difference between resistance and reassurance. Also note that as the frequency changes (X), the triangle will change shape due to changes in the colorance. Of course, resistance (R) will always remain constant.

By transforming the impedance triangle into a power triangle representing three elements of power in an AC circuit, we can take this idea a step further. Ohm's Law tells us that in a DC circuit, power (P) equals the multiplication of the current in watts (I2) and the resistance (R). To achieve the corresponding power triangle as follows, we can multiply the three sides of our impedance triangle above with I2:

Real Power P = I2R Watt, (W)

Reactive Power Q = I2X Volt-amperage Reagent, (VAr)

Apparent Power S = I2Z Volt-amper, (VA)

## Real Power in AC Circuits

Real power (P), also known as real or active power, performs the "real work" within an electrical circuit. The actual power measured in watts defines the power consumed by the resistant part of a circuit. Then the actual power in an AC circuit is the same as the power in the (P) DC circuit, P. That is, as with DC circuits, it is always calculated as I2*R, where R is the total resistant component of the circuit.

Since resistors do not create any phase shift between voltage and current waveforms, all useful power is transmitted directly to resistance and converted into heat, light and work. Then the power consumed by a resistance is the real power, which is basically the average power of the circuits.

To find the corresponding value of real power, the cosine of the phase angle is multiplied by Φ, as shown by the rms voltage and current values.

Real Power P = I2R = VIcos(Φ) Watt, (W)

However, since there is no phase difference between voltage and current in a resistant circuit, the phase shift between the two waveforms will be zero (0). After:

## Real Power in AC Circuit

Where real power (P) is in watts, voltage (V) is in rms volts and current (I) is in rms amps.

Then the real power is the I2*R resistance element, which is measured in watts; this is what you read on your mains energy meter and has units in Watts (W), Kilowatts (kW) and Megawatts (MW). Notice that real power, P, is always positive.

## Reactive Power in AC Circuits

Reactive power (Q), (sometimes referred to as wattless power), is the power consumed in an AC circuit that does not do any useful work but has a major impact on phase shift between voltage and current waveforms. Reactive power depends on the reassurance produced by inductors and capacitors and resists the effects of real power. DC circuits do not have reactive power.

Unlike the real power (P) that does all the work, reactive power (Q) takes power from a circuit due to the creation and reduction of both inductive magnetic fields and capacitive electrostatic fields, thereby making it difficult for real power to provide power. directly to a circuit or load

When trying to control the power current stored in the magnetic field by an inductor, a capacitor tries to control the power voltage stored by the electrostatic field. The result is that capacitors "produce" reactive power and inductors "consume" reactive power. This means that they both consume and return to the source, so that none of the real power is consumed.

In order to find reactive power, the sine of the phase angle is multiplied by Φ as seen in the rms voltage and current values.

Reactive Power Q = I2X = VIsin(Φ) volt-amp reagent, (VAr's)

Since there is a 90o phase difference between voltage and current waveforms in a pure recess (inductive or capacitive), multiplying the V*I by sin(Φ) gives each other a vertical component of 90o out of phase, so:

## Reactive Power in AC Circuit

Where reactive power (Q) is reactive in volt-amps, voltage (V) is in rms volts and current (I) is in rms amps.

Then the reactive power represents the multiplication of volts and amps that are 90o out of phase with each other, but in general, any phase angle between voltage and current can be Φ.

Therefore, reactive power is the I2X reactive element with volt-amperage reagent (VAr), Kilovolt-amperage reagent (kVAr) and Megavolt-amperage reagent (MVAr) units.

Visible Power in AC Circuits
We found above that real power is expended by resistance and reactive power is given to a reassurance. As a result, current and voltage waveforms are not in the same phase due to the difference between the resistant and reactive components of a circuit.

Then there is a mathematical relationship between real power (P) and reactive power (Q), called complex power. The rms voltage applied to an AC circuit, the V and the rms current flowing into that circuit, the multiplication of I, the S symbol given and the magnitude of which is usually known as the visible power is called the "volt-amper product" (VA).

This complex Power is not equal to the algebraic sum of real and reactive forces added together, but instead the sum of the P and Q vectors given as volt-amp (VA). It is the complex power represented by the power triangle. The rms value of the Volt-amper product is known as the more widely visible power, since "apparently" this is the total power consumed by a circuit, even if the actual power doing the work is much less.

Since the visible power consists of two parts, we can show the addition of reactive power, vector, which is the actual power in intra-phase power or watts, and the out-of-phase power in volt-amps. These two power components are shaped like a power triangle. There are four parts of a power triangle: P, Q, S and ε.

The three elements that generate power in an AC circuit can be graphically represented by the three sides of a right-angle triangle, almost identical to the previous impedance triangle. The horizontal (adjacent) side represents the actual power of the circuit (P), the vertical (opposite) side represents the reactive power (Q) of the circuit, and the hypotenuse represents the resulting visible power of the power triangle (S), as shown.

## Power Triangle of AC Circuit

P is I2R or Real power, W Q, volt-amperage reagent, I2X or Reactive power measured in VAr,
S, volt-amper, I2*Z measured in VA or Visible power
is phase angle in Φ degrees. The larger the phase angle, the greater the reactive power
Cos(Φ) = P/S = W/VA = power factor, p.f.
Sin(Φ) = Q/S = VAR/VA
Tan(Φ) = Q/P = VAR/W
The power factor is calculated as the ratio of real power to visible power because it is equal to cos(Φ).

Power Factor In AC
Circuits The power factor, cos(Φ), is an important part of an AC circuit that can also be expressed as circuit impedance or circuit power. The power factor is defined as the ratio of real power (P) to apparent power (S), and is usually expressed as a decimal value, for example, 0.95 or percentage: 95%.

The power factor defines the phase angle between current and voltage waveforms, I and V are the magnitudes of the rms values of current and voltage. It does not matter whether the phase angle is different from the voltage of the current or whether the voltage is different from the current. The mathematical relationship is given as follows:

## Power Factor of AC Circuit

We have previously said that current and voltage waveforms are in the same phase in a purely resistant circuit, so the actual power consumed is the same as the visible power, because the phase difference is zero degrees (0o). Thus, the power factor will be as follows:

Power Factor, pf = cos 0o = 1.0

In other words, the number of watts consumed is the same as the number of volt-amps consumed, which produces a power factor of 1.0 or 100%. In this case, a unity power factor is referred to.

Above, we also mentioned that current and voltage waveforms are 90o out of phase with each other in a completely reactive circuit. Since the phase difference is ninety degrees (90o), the power factor will be as follows:

Power Factor, pf = cos 90o = 0

In other words, the number of watts consumed is zero, but there is still a voltage and current that feeds the reactive load. Then reducing the reactive VAR component of the power triangle will cause the power factor to decrease by one, and towards the union. It is also desirable to have a high power factor, since it provides the most efficient use of the circuit that transmits current to a load.

Then we can write about the relationship between real power, visible power and the power factor of the circuit as follows:

It is said that an inductive circuit where the current is "delayed" from voltage (ELI) has a delayed power factor, and a capacitive circuit in which the current "directs" the voltage (ICE) has a leading power factor.

## Power Triangle Example

A winding coil with 180mH inducing and 35Ω resistance is connected to the 100V 50Hz feed. Calculate: a) the impedance of the coil, b) the current, c) the power factor, and d) the visible power consumed.

Also draw the power triangle obtained for the coil above.

The data given is: R = 35Ω, L = 180mH, V = 100V and ε = 50Hz.

(a) Impedance of the coil (Z):

(b) Current consumed by the coil (I):

(c) Power factor and phase angle, Φ:

(d) Visible power consumed by the coil (S):

(e) Power triangle for coil:

As this simple example power triangle relationships show, in a power factor of 0.5263% or 52.63%, the coil requires 150 VA of power to produce 79 Watt useful work. In other words, in the 52.63% power factor, the coil receives about 89% more current to do the same work, which is a lot of wasted current.

Adding a power factor correction capacitor (a 32.3uF for this example) to the coil to increase the power factor above or above 0.95% will greatly reduce the reactive power consumed by the coil as these capacitors act as reactive current. generators, thereby reducing the total amount of current consumed.

 AC Devre Analizi AC Devre Analizi Sinüs Dalga Formları Faz Farkı ve Faz Kayması Fazör Diyagramı Karmaşık Sayılar AC Direnç ve Empedans Endüktans ve Endüktif Reaktans Kapasitans ve Kapasitif Reaktans Seri RLC Devresi Paralel RLC Devresi Seri Rezonans Devresi Paralel Rezonans Devresi RMS Değeri Ortalama Değer Reaktif Güç Harmonikler Pasif Bileşenler AC Devrelerde Güç Güç Üçgeni ve Güç Faktörü Güç Faktörü Düzeltmesi Empedans ve Kompleks Empedans True RMS Nedir?