## Harmonic voltages

Non-linear loads, such as power electronic devices, such as variable speed drives on motor systems, computers, UPS systems, TV sets and compact fluorescent lamps, cause harmonic currents on the network.

Harmonic voltages are generated in the impedance of the network by the harmonic load currents.

Harmonics increase both load and no-load losses due to increased skin effect, eddy current, stray and hysteresis losses. The most important of these losses is that due to eddy current losses in the winding; it can be very large and consequently most calculation models ignore the other harmonic induced losses. The precise impact of a harmonic current on load loss depends on the harmonic frequency and the way the transformer is designed.

In a transformer that is heavily loaded with harmonic currents, the excess loss can cause high temperature at some locations in the windings. This can seriously reduce the life span of the transformer and even cause immediate damage and sometimes fire. Reducing the maximum apparent power transferred by the transformer, often called de-rating.

To estimate the required de-rating of the transformer, the load’s de-rating factor may be calculated.

This method, used commonly in Europe, is to estimate by how much a standard transformer should be de-rated so that the total loss on harmonic load does not exceed the fundamental design loss. This de-rating parameter is known as “**factor K**”.

The factor K is given by:

**where:**

**e** – the eddy current loss at the fundamental fre-quency divided by the loss due to a DC current equal to the RMS value of the sinusoidal current, both at reference temperature.

**n** – the harmonic order

**I** – the RMS value of the sinusoidal current includ-ing all harmonics given by

**In** – the magnitude of the n-th harmonic

**I1** – the magnitude of the fundamental current

**q** – exponential constant that is dependent on the type of winding and frequency.

Typical values are **1.7** for transformers with round rectangular cross-section conductors in both windings and **1.5** for those with foil low voltage windings.

Developing special transformer designs rated for non-sinusoidal load currents. This process requires analysis and minimising of the eddy loss in the windings, calculation of the hot spot temperature rise, individual insulation of laminations, and/or increasing the size of the core or windings. Each manufacturer will use any or all of these techniques according to labour rates, production volume and the capability of his plant and equipment. These products are sold as ‘K rated’ transformers.

During the transformer selection process, the designer should estimate the K factor of the load and select a transformer with the same or higher K factor.

**K factor is defined as:**

As an example **IEC 61378-1** deals with the specification, design and testing of power transformers and reactors, which are intended for integration within semiconductor converter plants; it is not designed for industrial or public distribution of AC power in general.

The scope of this standard is limited to applications of power converters, of any power rating, for local

distribution, at moderate rated converter voltage, generally for industrial applications and typically with a highest voltage for equipment not exceeding 36 kV. The converter transformers covered by this standard may be of the oil immersed or dry-type design.

The oil-immersed transformers are required to comply with **IEC 60076**, and with **IEC 60726** for dry-type transformers.

**Resource:** Selecting Energy Efficient Distribution Transformers by Intelligent Energy Europe

During our college days, our Professors taught that the Magnitude of Harmonics is as follows.

1. Even Harmonics – opposite in nature at 180 Degrees apart, hence annulled or cancelled.

2 Odd Harmonics magnitude is 1/n^2 where n is the Harmonic of 3rd, 5th, 7th 11th, 13th 15th and so on. Hence 5th Harmonic is 1/5^2 = (1/25) x 100 = 4% and so on. But the present scenario – the above formulae is not correct.and what are the correct level.

3. Does the Harmonic Magnitude and Harmonic Penetration mean the same.?

DHAYANANDHAN.S

I want more automation and electrical knowledge . Therefore I like ur website.

Thanks , this was helpful. However information about harmonic current testing on transformers would have been great. Maybe for your next article hopefully , yes?

CAN ANYONE EXPLAIN HOW ONE CAN CALCULATE ENERGY LOSSES DUE TO HARMONICS PRESENT IN THE SYSTEM?

IS THERE ANY METHOD TO CALCULATE THE SAME

Please can you tell me what is 7th, 5th,3rd harmonics in induction motor?

And what is plugging in DC motor?

I’m unsure what you mean about plugging a DC motor. About the only place I’m aware that you would plug a DC motor is on the long travel and trolley drives of DC cranes, and with these, currents are limited by resistors and step timing is done by flux decay timers. Usually, the motors are mill duty (= almost indestructable)

I have not known plugging on motors using a DC drive package. Deceleration is controlled by reducing the terminal voltage to below the back EMF, and regulating that voltage using SCR’s.

Uncontrolled plugging would leave to flashovers

Hi Edvard,

this is the information that i am busy doing my research on, but i concentrated more on the effect of harmonics on power transformers.

thanks Brother

Busy or not, now you can use this technical article for your research! :)

Glad you find it usefull!