K-FACTOR/HARMONIC MITIGATION TRANSFORMERS

K-Factor transformers differ from standard transformers in that they have additional thermal capacity enabling them to tolerate the heating effects of harmonic currents generated by non linear loads. Winding eddy current losses are produced by these harmonic currents and we minimize this effect through the use of parallel conductors and other production techniques. In order to compensate for the increased core losses due to the harmonic currents our transformer cores are built from high quality grain oriented steel and the steel is run at a low flux density.

In the design of our K-Factor transformers we utilise the DZN0 connection which in addition to providing the user with a zero phase shift solution also mitigates the load Triplen harmonic currents in the secondary windings, dramatically reducing the effect of these currents when reflected through to the primary. The harmonic effects on the system are further mitigated by designing the transformers to have low impedance thus reducing voltage distortion.

We integrate Multi-Faraday screening into our transformers which improves the electrical noise attenuation and reduces the inrush current drawn from the supply at switch on.

Related Technical Data

The effect of harmonic distortion on supplies emanating from load sources has reached significant levels resulting from the present day usage of multiple IT work points, using switch mode techniques. Such switch mode devices create very high levels of harmonic distortion, which in turn have critical effects on the supply transformers. Appreciation of the situation is indicated by worldwide seminars, discussion papers, etc. devoted to the topic.

Considerable work has been undertaken particularly in the USA, which has led to the introduction of the term K factor, a term which unfortunately, seems to have several definitions. It is however an attempt to evolve a means of applying a de-rating factor to standard transformer ratings to take account of the effects of harmonic distortion. Such transformers are sometimes referred to as "K-factor transformers"

The Problem

Non-Linear loads generate harmonic currents, which flow from the load back towards the power source, following the path of least impedance. Harmonic currents are currents having frequencies, which are whole number multiples of the fundamental supply frequencies. All odd harmonic currents adversely affect virtually every component in the power systems creating additional dielectric and thermal mechanical stresses, wiring (cables) experience heating beyond the normal 1²R, due to skin and proximity effects. This is particularly marked in the neutral conductor due to the additive nature of triplen harmonics i.e. 3rd, 9th, 15th, 21st, 27th, …ad infinitum, and more so in transformers as additional heating observed primarily in winding eddy current losses.

Incidentally it is interesting to note that harmonic distortion can have very significant effects on rotating machines, causing unusual speed differences and even contra-rotation.

In three phase transformers, the triplen harmonics are absorbed in the delta winding, creating extra heat, and do not therefore appear in the input current. However it must be remembered that any tapping cables also form part of the delta winding, and in addition to carrying the linear currents, also carry the triplen harmonic current.

In the search for protection, Primary over-current protection is ineffective, since the transformer loading will not be directly proportional to the RMS input current. Secondary protection is not fully effective either because it would not protect against the heating effects of the harmonic currents. Winding temperature sensors can be used, but again these would not sense overheating of the transformer ancillary equipment, i.e. terminals and winding tapping cables. It is of course preferable not to have tappings at all and if the power input to the transformer is from a stable supply, then they could well be dispensed with.

More Problems

It is apparent from the above that to simply derate a transformer to use in a harmonic situation, does not afford a suitable safety margin. First of all, its future loadings could well be increased to match the marked rating, but more importantly, the ancillary equipment may not be adequate even for the derated load. Thus it is crucial to design and rate a transformer to suit a given K-factor, but who is to decide the appropriate factor? In practice the extent of the THD can only be ascertained when the installation is up and running at full design load. Some empirical figures have been published, a graphical example of which is shown below.

APPROXIMATION OF K-FACTOR vs THD

There is no definitive relationship between K-Factor and THD.
Where possible use site data to calculate K-Factor.
K=1 - Purely linear no distortion
K=7 - 3 Phase, less than 50% non linear, 50%=linear
K=13 - 3 Phase non linear
K=20 - 1 Phase & 3Phase non linear
K=30 - 1 Phase non linear
The use of higher reactance transformers can cause increased voltage distortion since higher transformer impedance means higher source impedance, resulting in higher voltage distortion. Higher reactance transformers also give rise to increased harmonic effects, even the difference between 3% and 5% reactance is significant when multiplied by the harmonic order. So low reactance = lower impedance and less voltage distortion.

Terminal ratings quoted by the manufacturers will usually be with linear loads only. Where the effects of harmonic distortion are evident, the thermal/time constant of the terminal block compared with that of the transformer winding, will invariable mean that the terminal becomes the "First Fail" Point.
N.B. The harmonic heating effect is proportional to the square of the frequency and the cross sectional area of the conductor. Hence in order to predict the temperature rise it is essential to know the level of harmonic distortion at each frequency, this is one of the reasons why accurate predictions are virtually impossible at the design stage.

The Way Forward

U.L.1561 proposes a transformer "K-factor" figure based on the eddy current losses to be proportional to the square of both the harmonic current and the harmonic number! On this basis the higher the K-factor, the greater the heating effect of the harmonics on the transformer. However caution must be used in the application of any stated K-factor. Some are derived for ranges up to the 25th or even 50th harmonic, whilst others are limited to the 15th and even the small current levels associated with the higher harmonics, when multiplied by the square of the harmonic number can add significantly to the K-factor. Working details are best obtained by reference to the UL standards.

Which K-Factor is Right?

Accurate information about the load current makes K-factor selection easy. The chart below shows a K-13 wave shape and an alternative process for converting wave shape (from a harmonic analyser) to K-factor.
The first column shows the harmonic orders. The second column is the square of each harmonic order. The current wave shape is broken out in the third column and the fourth column is the square of each value. The last column is the product of columns two and four. Sums of the columns are at the bottom. Divide the sum of column five by the sum of column four and get K-factor.

H	H²	Wave	Wave²	H²*Wave²
1	1	100.00%	1.0000	1.0000
3	9	38.10%	0.1451	1.3058
5	25	22.9%	0.0522	1.3058
7	49	16.3%	0.0266	1.3058
9	81	12.7%	0.0161	1.3058
11	121	10.4%	0.0108	1.3058
13	169	8.8%	0.0077	1.3058
15	225	7.6%	0.0058	1.3058
17	289	6.7%	0.0045	1.3058
19	361	6.0%	0.0036	1.3058
21	441	5.4%	0.0030	1.3058
23	529	5.0%	0.0025	1.3058
25	625	4.6%	0.0021	1.3058
	SUM	52.9%	1.280	16.670
		16.67/1.28=K13

Determining the correct K-factor for the load is no easy task when you cannot measure the load characteristics. This is particularly true when specifying transformers for tenant space. It is virtually impossible to estimate the harmonic loads.

We suggest you access the web site of the copper development association: www.cda.org.uk and download CDA publication 144 and the software D12 that is under the heading "K-Factor calculation software D12". From which the K-Factor or Factor K (European) can be calculated from harmonic data. An approximation for derating can be obtained from the graph below, which is based on ANSI reference C57.110.

Typical Transformer Derating
(for nonlinear loads)

Preferred Solution For Triplen Harmonics

DELTA / INTERCONNECTED STAR (ZIG-ZAG) TRANSFORMER
This transformer connection cancels triplen harmonics in the Secondary windings hence only a minimal proportion of these harmonics appear in the delta Primary. The transformers should be low impedance for low distortion and be complete with Multi-Faraday screening for high common mode / transverse mode attenuation. The design of these transformers is a specialised area and it is important that the specifier appreciates the significance of the design criteria.

1. The connections above are shown with a double sized neutral, which is essential when supplying harmonic loads (see results below).
2. As the triplens are cancelled in the Secondary it is possible to protect the transformer Primary with fuses or MCB's etc.
3. A further advantage of this connection is that there is zero phase shift between input and output.
4. As in "2" if the Primary requires tappings there will be no additional, circulating, harmonic currents.
5. Our standard practice is to fit four Faraday screens on each transformer coil (12 screens in total).

Results From Practical Tests On A Typical Transformer

Example: 100KVA K20 P.D.U. Hi-Isolation Delta/Zig-Zag Transformer subjected to a Non-Linear load (K12)
Load Line Current 150Amps
Neutral Current 247Amps
Primary (Delta Current) 68.14Amps
THE TABULATED / GRAPHICAL RESULTS ON PAGES 7-9 SHOW:
A) The importance of double sized neutral (even with a Zig-Zag Secondary).
B) All the triplens flowing in the neutral into the Zig-Zag winding are shown to be insignificant when transferred to the Primary.
C) The inclusion of the Zig-Zag connection (with low reactance) has other advantages including
• Zero phase shift
• Static balancing characteristic
• Suitable for Primary protection with either or fuses / breakers
• Helps to maintain an acceptable fundamental voltage distortion

Test Results Cont. For The 100kva K20 Transformer (As on page 6)

100KVA K20 Transformer Results Cont.

TFS Connection

This is a method of connection designed to cancel harmonics on the Secondary of a PDU transformer. This connection operates on all the triplen harmonics together with the 5th,7th,17th and 19th but it has to have two outputs (Loads) connected to each transformer. In an ideal state these two loads should be balanced.

For the theory see "Positive and Negative Sequence Components" below and tabulated / graphical results on pages 11-13.

Positive And Negative Sequence Components

Understanding of positive and negative sequence currents is key to resolving the other harmonics we have identified as needed to be treated the 5th & 7th,5th is negative sequence and 7th is positive sequence in nature. The fact that they both flow through transformers and yet rotate in opposite direction allows us to use one phase-shift to remove pairs of positive and negative sequence harmonics from two separate sources. The case we are most interested in is the 30-degree phase-shift between two similar harmonic sources. As figure below illustrates, the phase sequence difference results in cancellation of both 5th & 7th harmonics (the result is the same for 17th & 19th etc. as well).

How a 30deg phase-shift between 2 sources result in cancellation of both 5th and 7th harmonic currents

Test Results Of A TFS Transformer

To continue reading on this subject or for a printed version download the file below:
PDU TRANSFORMERS IN COMPUTER SUPPLY APPLICATIONS by Alan Moorhouse Assoc.I.E.E., A.Inst.E., MBE