A34-Maximum Permissible Flux Density in Transformers at Rated Voltage and Frequency

As per the fundamental transformer formula, V (Applied or induced voltage in a winding in volts) =4.44x core flux (peak flux density in Tesla x net core area in square metres) x frequency (Hz) x number of turns

Flux Density B (T)= V (volts)/ 4.44x Frequency (f in Hz) x number of turns x net core area

From the above, it is clear that flux density in core varies as V/f as other parameters are constant for a transformer in service. Net core area is the gross area x stacking factor, the later depending on the thickness of lamination.

As per IEC 60076-1-2011, Power Transformers-General, (Clause5.4.3), power transformers shall be capable of continuous operation at no-load with a V/Hz of 110 % of the rated V/Hz. Combined voltage and frequency variations should not exceed the rated V/f ratio by 10%. But distribution transformers, up to 2500kVA 33 kV, shall be suitable for a continuous over fluxing of 12.5 % ?as per Clause 7.9.1 of IS 1180(Part 1) -2014.

As per above IEC, in addition to no-load over fluxing requirements, a power transformer shall be capable of continuous operation at rated power under an 'over fluxing' condition of 5 %, without damage.

To meet the above requirements, what shall be the maximum permissible flux density at rated voltage and frequency, for CRGO (cold rolled grain oriented) silicon steel laminations and rapidly solidified Fe-based amorphous strips – the usual core material used today for power transformers and distribution transformers?

In case of transformers, the maximum flux density in any part of the core and yokes, at normal voltage and frequency at all taps shall be such that the flux density under over-fluxing conditions as mentioned in standards, shall not exceed 1.9 Tesla for CRGO and 1.48T for conventional grade of Amorphous core and 1.56 T for high permeability Amorphous cores. These flux density values are with a 5 % margin to the saturation flux density of electrical steels being used today.

In case of transformers with VFVV (variable flux voltage variation i.e. taps on HV winding for LV terminal voltage variation or taps on the neutral end of auto-transformers) flux density will vary with tap changing and the over fluxing stipulation of flux density shall apply to highest value of working flux density at any tap.

?It is the operating experience that with the above maximum rated flux density, power transformers will be capable of withstanding over fluxing at no-load to the extent of 110 % continuous,125 % for one minute and 140 % for 5 second, a service condition during the load throw off in generator transformers, as specified in the Standard.

It may be noted that during the loading of the transformers, the over fluxing shall be reduced as mentioned in the relevant clauses in IEC/IS as below:

“At a current K times the transformer rated current (0 ≤ K ≤ 1), the over fluxing shall be limited in accordance with the following formula:

If the transformer is to be operated at V/Hz in excess of those stated above, this shall be identified by the purchaser in the enquiry.”

Even though for generator transformers 1.72 T maximum working flux density is normal, for other transformers maximum flux density of 1.65 T is preferred from noise considerations and from chances of over fluxing during tap changing to take care of voltage drop on secondary side. Let us consider a 132/11 kV transformer with OLTC on HV winding to get constant LV voltage during HV variation of +5% to -15 % (CFVV -Constant flux voltage variation). But in the field, even when grid voltage is constant, on-load tap-changer will be operated (to increase per turn voltage) to increase the transformer secondary voltage to compensate the voltage drop in secondary lines during loading. This results in over fluxing in the core. This is the reason utilities specify maximum flux density lower than the values shown in the above table. As example, maximum flux density of 1.7 T for Generator Transformers,1.60-1.65 T for interconnecting transformers and 1.55 T for step down transformers. Flux density lower than the limits as per above table (as low as 1.4 T) will also be used, when no load loss capitalisation rates are very high or the transformers are to be of extremely low noise, a requirement, for transformers to be installed in urban areas.

When transformer cores used to be made of 0.5 mm thick soft iron sheets during the first two decades of transformer engineering, maximum flux density was limited to 0.4-0.8 T. When silicon steel came in to picture during 1900’s, maximum flux density reached 1.3 T. With hot rolled steels, flux density reached to 1.5 T. During the second world war, in Germany transformers were made with flux density almost near to saturation levels to save scarce active materials. People living near to substation had to use ear buds to sleep. ?With the introduction of CRGO in 1950s, maximum flux density reached the levels of 1.7-1.8 T. Before the oil shock of 1970s, when energy costs were low, it was usual to adopt flux density of 1.8 T or higher for Generator Transformers. When the transformer over fluxing requirements were understood well, utilities started to fix 1.72 T as the maximum permissible rated flux density?in transformers with CRGO cores.?

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