Power System Harmonics, True Power Factor & DPF Measure

Displacement Power Factor (DPF) is the power factor as we know at fundamental system frequency (50Hz in UK). However, True Power Factor (PF) or just Power Factor is the product of the distortion power factor and DPF. Check out the Wikipedia article on this  topic. The following equation related components:

Where,  is the total current harmonic distortion at the point of measurement, and are fundamental and total harmonic RMS currents, and  is the distortion power factor (in other words distortion factor associated with power factor).

The above equation leads to the following conclusions:

• PF≤DPF, True Power Factor is always less than or equal to Displacement Power Factor.
• PF = DPF, True Power Factor equals Displacement Power Factor when there are current harmonics at the point of measurement;
• PF<DPF, suggests presence of harmonics, take it easy: awareness is good.
• PF<<DPF, means its time to take action.

The above observations, comparing DPF and PF will give you a quick assessment of harmonic severity, however if detail assessment is required then you will need to monitor both and .

As I understand, most meters or monitoring equipment that display PF and DFC also may have the ability to calculate both current and voltage total harmonic distortion factors: and , sometimes including individual harmonics levels as numbers and/or as a harmonic spectrum bar chart. Now if have measured these values, i.e. both THD for current and voltage, and individual harmonics levels in %, then compare them against the harmonics standards that govern your electric network, and you will know the severity of the harmonic problem.

In UK, DNOs are required to comply with EN50160 Std. and consumers with G5/4-1 Std.

Per Unit Formulae and Conversions

Even the best of the power systems Geeks sometime stumble at the basics. Here are some per unit formulae to brush up if you are one of them or among those willing to learn like me.

A per unit value is a scaled factor of the measured system parameter to the chosen system base value. In other words, the chosen value becomes by which all other values for consider system parameter will be compared. It’s a ratio and is a unit less quantity.

Most common approach, for most studies, is to choose a system apparent power base (typically 100MVA) and system local network voltage (line to line voltage) base values and base values for all other parameters can be estimated there after.

Base Value Calculation:

         (1)

        (2)

        (3)

Per Unit Calculation:

        (4)

        (5)

         (6)

Per Unit Conversion:

        (7)

References:

1. Wikipedia, Per Unit System, Wikipedia. [online]. Available: http://en.wikipedia.org/wiki/Per-unit_system. [Accessed: Sep. 19, 2009].
2. W. D. Stevenson, Jr., Elements of Power System Analysis, 3rd ed. New York: McGraw-Hill, 1994.

Power System Analysis

J. Grainger, W. Stevenson, Power System Analysis, 1ed,  McGraw Hill, 1994.