Published by Siemens Canada, *Siemens Limited Power Product Catalogue, Canadian Edition 2019. Section 18 – Technical, Contents: Harmonics / K-factor Ratings (18-16, 18-17) *

**Non-Linear Loads**

When a sinusoidal voltage is applied to a linear load, the resultant current waveform takes on the shape of a sine wave as well. Typical linear loads are resistive heating and induction motors. In contrast, a non-linear load either:

- Draws current during only part of the cycle and acts as an open circuit for the balance of the cycle,

or

- Changes the impedance during the cycle, hence the resultant waveform is distorted and no longer conforms to a pure sine wave shape

In recent years, the use of electronic equipment has mushroomed in both offices and industrial plants. These electronic devices are powered by switching power supplies or some type of rectifier circuit. Examples of these devices used in offices are: computers, fax machines, copiers, printers, cash registers, UPS systems, and solid-state ballasts. In industrial plants, one will find other electronic devices such as variable speed drives, HID lighting, solid-state starters and solid-state instruments. They all contribute to the distortion of the current waveform and the generation of harmonics. As the use of electronic equipment increases and it makes up a larger portion of the electrical load, many concerns are raised about its impact on the electrical power supply system.

**Harmonics**

As defined by ANSI / IEEE Std. 519-1992, harmonic components are represented by a periodic wave or quantity having a frequency that is an integral multiple of the fundamental frequency. Harmonics are voltages or currents at frequencies that are integer multiples of the fundamental (60 Hz) frequency: 120 Hz, 180 Hz, 240 Hz, 300 Hz, etc. Harmonics are designated by their harmonic number, or multiple of the fundamental frequency. Thus, a harmonic with a frequency of 180 Hz (three times the 60 Hz fundamental frequency) is called the 3rd harmonic. Harmonics superimpose themselves on the fundamental waveform, distorting it and changing its magnitude. For instance, when a sine wave voltage source is applied to a non-linear load connected from a phase-leg to neutral on a 3-phase, 4-wire branch circuit, the load itself will draw a current wave made up of the

60 Hz fundamental frequency of the voltage source, plus 3rd and higher order odd harmonic (multiples of the 60 Hz fundamental frequency), which are all generated by the non-linear load. Total Harmonic Distortion (THD) is calculated as the square root of the sum of the squares of all harmonics divided by the normal 60 Hz value.

This yields an RMS value of distortion as a percentage of the fundamental 60 Hz waveform.

Therefore, it is the percentage amount of odd harmonics (3rd, 5th, 7th ,…, 25th,…) present in the load which can affect the transformer, and this condition is called a “Non-Linear Load” or “Non-Sinusoidal Load”. To determine what amount of harmonic content is present, a K-Factor calculation is made instead of using the THD formula. The total amount of harmonics will determine the percentage of non-linear load, which can be specified with the appropriate K-Factor rating.

**Typical Symptoms of Harmonic Problems**

- Distribution / lighting transformers overheating even when measured load current is within transformer rating
- Neutral cable / bus overheating even with balanced load
- Fuses blowing and circuit breakers tripping at currents within rating

**Effect Of Harmonics On Transformers**

Non-sinusoidal current generates extra losses and heating of transformer coils thus reducing efficiency and shortening the life expectancy of the transformer. Coil losses increase with the higher harmonic frequencies due to higher eddy current loss in the conductors. Furthermore, on a balanced linear power system, the phase currents are 120 degrees out of phase and offset one another in the neutral conductor. But with the “Triplen” harmonics (multiple of 3) the phase currents are in phase and they are additive in this neutral conductor. This may cause installations with non-linear loads to double either the size or number of neutral conductors.

**Measurement of Harmonics**

**Table A.3 K-Factor Ratings**

**Sizing Transformers for Non-Linear Loads**

ANSI / IEEE C57.110-2008 has a procedure for de-rating standard distribution transformers for non-linear loading. However this is not the only approach. A transformer with the appropriate K-Factor specifically designed for non-linear loads can be specified.

**K-Factors**

K-Factor is a ratio between the additional losses due to harmonics and the eddy losses at 60 Hz. It is used to specify transformers for non-linear loads. Note that K-Factor transformers do not eliminate harmonic distortion; they withstand the non-linear load condition without overheating.

**Calculating K-Factor Loads**

- List the kVA value for each load category to be supplied. Next, assign a K-factor designation that corresponds to the relative level of harmonics drawn by each type of load. Refer to Table A.4
- Multiply the kVA of each load or load category times the Index of Load K-rating (I
_{LK}) that corresponds to the assigned K-factor rating. This result is an indexed kVA-I_{LK }value. KVA x I_{LK}= kVA-I_{LK}. - Tabulate the total connected load kVA for all load categories to be supplied.
- Next, add-up the kVA-I
_{LK}values for all loads or load categories to be supplied by the transformer. - Divide the grand total kVA-I
_{LK}value by the total kVA load to be supplied. This will give an average I_{LK}for that combination of loads. Total kVA-I_{LK}/ Total kVA = average I_{LK}. - From Table A.4 find the K-factor rating whose I
_{LK}is equal to or greater than the calculated I_{LK}

**Measurement of Harmonics Table A.3 K-Factor Ratings**

For existing installations, the extent of the harmonics can be measured with appropriate instruments commonly referred to as “Power Harmonic Analyzers”. This service is offered by many consulting service organizations. For new construction, such information may not be obtainable. For such situations, it is best to assume the worse case condition based on experience with the type and mix of loads.

**Table A.4 Estimating K-Factor Loads ^{①}**