WAZIPOINT WAZIPOINT Engineering Science & Technology: Variation of Efficiency with Power Factor

## Monday, February 6, 2023

### Variation of Efficiency with Power Factor

The efficiency of the transformer, the power factor of the transformer, and the efficiency variation due to the power factor are our discussion terms in this episode.

Earlier, we discussed transformer efficiency and power factors in another episode. So, we are not going to discuss what is transformer efficiency and what is the power factor.

## Relation between transformer efficiency variation and power factor

We are going to understand

How does the power factor affect transformer efficiency?
What is the variation in transformer efficiency?
What happens if the power factor increases- as the line current increases, the voltage drop in the conductor increases, resulting in a lower voltage at the equipment. With an improved power factor, the voltage drop in the conductor is reduced, improving the voltage of the equipment.

Factors That Affect the Efficiency of a Transformer
• The heating effect of current in a coil. Power is lost as heat I2R whereby I is the current flowing through the coil and R is the resistance of the coil,
• Heating effect of induced eddy currents. In the iron core,
• Magnetization of the Iron Core,
• Flux leakage.
The power factor affects transformer efficiency, because the lower the power factor, the less efficient the circuit, and the higher the overall operating cost. Poor power factor means that you’re using power inefficiently and the result becomes:

• Heat damage to insulation and other circuit components,
• Reduction in the amount of available useful power,
• A required increase in conductor and equipment sizes.

### The fact of Lower Power Factor

Low power factor is expensive and inefficient. A Low P.F. draws a higher internal current and the excessive heat generated will damage and/or shorten equipment life, Increased reactive loads can reduce output voltage and damage equipment sensitive to reduced voltage

### The fact of a higher Power Factor

If the power factor leads by too much, then a subsequent rapid voltage rise may cause equipment damage. The voltage rise can exceed the capacity of the electrical equipment or the capacitors themselves. In the case of a leading power factor, the load current leads to the load voltage.

### Transformer Efficiency

The variation in transformer efficiency is normally from 97 to 99 percent. The power supplied to the load plus resistive, eddy current, hysteresis, and flux losses must equal the input power.

Successful engineering is all about understanding how things break or fail.
Henry Petroski

The following formula is used to measure transformer efficiency:

$�=\frac{{�}_{���}}{{�}_{��}}$

where

η = transformer efficiency (in %)

POUT = transformer output power (in W)

PIN = transformer input power (in W)

Example: What is the efficiency of a transformer that has an output power of 1500 W and an input power of 1525 W?

Now we can draw the simple relationship between transformer efficiency and the load power factor:

eff=output/input

or, (1/eff)= (input/output)

or, (1/eff) = (output + losses)/output

or, (1/eff) = 1+ (losses/output)

output power or output=V2*I2*(load power factor)

so, (1/eff) - 1 = losses/(V2*I2**pf)

or, (1-eff)/eff =losses/(V2*I2*pf)

or, eff/(1-eff) =(V2*I2*pf)/losses

or, pf= [(losses/V2*I2){eff/(1-eff)}]