 Why UPS power factor is Important in electrical power system, including UPS measuring efficiency?

Engineers using external power supplies are no stranger to efficiency measurements. However, as their applications typically run on dc power, common mistakes can be made when measuring the power on the ac side of the UPS power supply. These common pitfalls include incorrectly measuring or completely omitting power factor when calculating the power input to the supply, which results in incorrect efficiency measurements. In this blog post, we will review the basics of power factor and efficiency, then provide guidance on how to incorporate power factor when measuring ac-dc power supply efficiency.

## UPS Power Factor and Efficiency

Efficiency (η) is the ratio of output power to input power:

Calculating the output power of an EPS, which is dc, is simply the output voltage multiplied by the output current:

A common mistake is to apply this same calculation to obtain the input power. This presents a problem because the volt-ampere product in ac circuits does not always equal the real power, and in fact, in the case of external adapters, the volt-ampere product will never equal the real power. In ac circuits, the volt-ampere product is equal to the apparent power (S), which is related to the real power through a term called Power Factor (PF):

By definition, power factor is the ratio of real power to apparent power, where apparent power is the product of the rms voltage and rms current. Only when the power factor equals 1 does the volt-ampere product equal the real power:

If UPS power factor is considered when calculating the efficiency, it must be calculated correctly. Many engineers have to rewind all the way back to their early engineering classes to remember what power factor is and how to measure it. However, in school they often focus on a linear case where both the voltage and current are pure sinusoids of equal frequency. In this case the power factor is simply the cosine of the phase difference between the voltage and current and is more accurately known as the displacement power factor:

Many engineers are familiar with the power triangle, which visually represents the relationship. By definition, the cosine of θ is equal to the ratio of the adjacent side to the hypotenuse. In the power triangle this equals the ratio of real power to apparent power, which matches our definition in Equation: Power Factor. On the other hand, when it comes to non-linear systems, of which ac-dc power supplies are one example, this does not present the whole picture.

What is missing is the distortion power factor, which adds a third dimension to the power triangle. This point is critical because in power supplies the distortion factor is the major contributor to reducing power factor since the displacement factor tends to be close to unity.

Fourier analysis shows that this non-linear current waveform can be broken down into a series of harmonic components of various magnitudes. These harmonics decrease the power factor, but are not accounted for in Equation Displacement Power Factor. To calculate the distortion power factor, Total Harmonic Distortion (THD) is introduced. THD takes into account the current associated with each harmonic as highlighted in the following equation:

When the THD is equal to 0, the distortion power factor is equal to 1, which would be the case for a linear system:

The UPS power factor picture is completed by multiplying the displacement power factor and distortion power factor, which results in the True Power Factor:

## Why power factor is important?

Considering an inductive load, the power factor will be lagging due to which the current is lagging behind the voltage. While in capacitive load the angle goes opposite, the applied current angle is now leading before the voltage and consider as leading power factor.

The power factor plays an important role in ac circuits depending upon the load. As we know that lower the power factor, higher is the load current and vice-versa. *Lagging power factor has some disadvantages like large KVA rating because the KVA is inversely proportional to the power factor.

• Similarly in lagging power factor the transmission lines must have greater conductor size due to which at low power factor the conductor carries a large amount of current.
• Another demerit is the large copper losses, at low power factor the conductor carries large current
• causes more IRlosses. This results in poor efficiency.
• The large current at low power factor causes greater voltage losses in alternator and transmission lines and with this effect, the system might reduce loading handling capacity as well.

## Power factor improvement

The low power factor is mainly due to the inductive loads. In order to overcome this situation, we must connect a capacitor in parallel with the loads which can somehow stabilize the power factor. Power factor improvement can be achieved by using the following types of equipment.

### Static capacitor

The power factor can be improved by connecting a capacitor in parallel with the inductive load. As we know that capacitor draws a leading current which can neutralize the lagging power factor produced by the inductive loads. For three phase loads, the capacitors can be connected in star or delta.

### Synchronous condenser

Synchronous motors take the leading current when they are over excited and therefore they behave like capacitors. So an overexcited synchronous motors running at no load is called synchronous condenser. When such machines are connected in parallel with the supply, it takes the leading current which partially neutralizes or tend to minimize the low power factor. Hence the power factor is improved.