Average Power Facor Calculation
It was drawn to my attention that we are presently calculating the average daily power factor as the sum of the all the power factor measurements taken during that day divided by the total number of measurements {∑Pf1+Pf2+Pf3+…Pfn}/n. According to teachings on this subject this is entirely incorrect. Furthermore a document was written about this very theory some years ago by one Mr. Lampkin and it is apparent that no change was made to correct the calculations (please refer to). The following is a review of the general theory.
Power factor (Pf) is the ratio of real power (kW) to the apparent power (kVA). Power factor decreases with the installation of non-resistive loads, such as motors, transformers, lighting ballasts and other power electronics.
Under normal conditions, the current in a circuit can be split into a power component (Ip), and a reactive component (Ir). Because of the way these are related, the total current is calculated as follows:
And since the Pf is calculated as kW/kVA then the formula below can be used.
VIp is the real power, measured in watts, while VIr is the reactive power, measured in vars (volt-amps reactive). At the end of a measuring period, the average power factor is calculated as follows:
Some equipment draws current that is heavily distorted from the ideal sine wave. This generates harmonics, which increase the current by another component, the harmonic current Ih. These harmonic currents reduce the power factor to:
It is important to recall that the Pf is part of a complex component on our system and cannot be added linearly to give a true value. For example for a given system of n number of readings:
Total Real Power Pt= P1+P2+P3+…..Pn
Total Reactive Power Qt= Q1+Q2+Q3+…..Qn
But the total Apparent Power St= S1+ S2+S3+…..Sn? (This is incorrect)
Since S= P+jQ, it means that S has a real component and an imaginary component. So to calculate S we use the square root of the squares of Pt
Power factor (Pf) is the ratio of real power (kW) to the apparent power (kVA). Power factor decreases with the installation of non-resistive loads, such as motors, transformers, lighting ballasts and other power electronics.
Under normal conditions, the current in a circuit can be split into a power component (Ip), and a reactive component (Ir). Because of the way these are related, the total current is calculated as follows:
And since the Pf is calculated as kW/kVA then the formula below can be used.
VIp is the real power, measured in watts, while VIr is the reactive power, measured in vars (volt-amps reactive). At the end of a measuring period, the average power factor is calculated as follows:
Some equipment draws current that is heavily distorted from the ideal sine wave. This generates harmonics, which increase the current by another component, the harmonic current Ih. These harmonic currents reduce the power factor to:
It is important to recall that the Pf is part of a complex component on our system and cannot be added linearly to give a true value. For example for a given system of n number of readings:
Total Real Power Pt= P1+P2+P3+…..Pn
Total Reactive Power Qt= Q1+Q2+Q3+…..Qn
But the total Apparent Power St= S1+ S2+S3+…..Sn? (This is incorrect)
Since S= P+jQ, it means that S has a real component and an imaginary component. So to calculate S we use the square root of the squares of Pt