Harmonics, Inter-harmonics, and Sub-harmonics

I knew instinctively what these terms meant, but I never knew the true harmonic terminology until I attended a harmonics training training course recently at The University of Manchester. So if you didn’t know like I did, here’s enlightenment for both of us.

Harmonics: A sinusoidal component of a periodic wave having a frequency that is an integer multiple of the fundamental frequency.

Inter-harmonics: Components with frequencies between two consecutive harmonics or those components whose frequencies are not integer multiples of the fundamental power frequency.

Sub-harmonics: A special subset of interharmonics that have frequency values that are less than that of the fundamental frequency.

Table below illustrate their usage with examples for a 50Hz system.

Note: Information presented here and illustration was taken from the Prof. A. Testa’s power quality course lecture held at the University of Manchester on the 26th Jan 2010. Some information was obtained through email exchange between Prof. V. Katic and I following my attendance of the course. Thank you Gentlemen.

Poor Harmonic Metering: Rewards Polluter, Penalizes Non-Polluter

Have you ever been in a situation or seen a situation where the system on the side of good rewards the bad guy for doing bad, and punishes good guy for doing good? Well, no worries if you haven’t experience it yet. If you at a power system network with watt/energy meters  that do not account for harmonics, you will get to see this first hand. Energy meters that do not account for harmonics will reward non-linear loads for injecting harmonic pollution into the network by showing less energy consumption reading, while penalising  linear loads for forced harmonics pollution absorption by showing high consumption reading even though they actually consume less useful power than the meter reading. Sounds very dodgy, doesn’t it? Here’s the reason why?

Imagine a power systems network with a linear load ( i.e. non-linear << linear) customer and non-linear load ( i.e. linear << non-linear) customer fed from the system busbar, with both customers’ utility watt meters that do not account for harmonics.

The non-linear load due to its non-linear voltage-current relationship will use part of the supplied power to generate and inject harmonic currents back into the supply system. And if there is sufficient impedance between the PCC (Point of Common Coupling, or the customer supply point) and the non-linear equipment, then this impedance will distort the supply voltage waveform, i.e. instantaneous voltage = voltage fundamental + sum of harmonic voltages (due to Ih*Zh, h is harmonic order). As the current harmonics are injected back into the supply, the powers (product of current and voltage in VA) at these injected frequencies, the meter will see the total effect as a reduced energy consumption reading, i.e. energy reading = supplied power to the non-linear customer – harmonic powers injected by the non-linear equipment into the supply system.

For the linear load customer, however, the effect will be opposite. The linear will absorb the harmonic currents along with the fundamental frequency current. The absorbed harmonic currents by the linear load will generate harmonic voltages at harmonic current frequencies. That powers absorbed by the load at the absorbed harmonic frequencies will add on to the actual useful power required to do the job, therefore penalising the linear load. The linear load energy reading = required power for the linear load to do the job + harmonic powers absorbed by the linear equipment from the supply system.

Lesson learnt: Install (for your own measurement) or check (if metered by a utility installed meter) a energy meter  that take harmonics into account, so the customer pays for what he consumes and not for all the pollution he is forced to consume.

Note: The discussion presented here and illustration was taken from the Prof. A. Testa’s power quality course lecture held at the University of Manchester on the 26th Jan 2010.

Hope you found it useful, interesting and fun as I did. Thanks for reading!

Power Quality Course at University of Manchester

University of Manchester’s power systems group is organising a power quality course between the 25th – 27th January 2010. The course seeks to provide attendees a thorough understanding of major Power Quality issues facing customers and electrical power system operators with substantial distributed generation penetration. The most interesting part of this course will be the presenters’ list, these are some of the finest academics and researchers in the field of Power Quality.

Download the brochure. The document includes course scope, schedule, and presenter biographies.

I have been a student at the university, completing a masters and a doctoral degree, between 2003-2008. Since leaving school  I’ve been in contact with the power system group staff and colleagues at the university. This comes as a surprise to me seeing the group organising this specialised Power Quality course inviting renowned researchers in this field.  Not that the group has’t invited people or has not been visited by top researchers before, but never to my knowledge was a course for 3days like this one. Well done Power Systems group.

Hope the attendees will find it useful. Good luck!

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.