How to calculate transformer impedance?

There are three ways to explain Percentage Impedance:
1) It is the % voltage drop in secondary no load voltage when a rated full load zero power factor lagging current is taken from secondary. It is the price one has to pay for transferring the current from primary to secondary side. Higher the % impedance, higher the secondary voltage drop during loading. This drop (or rise with leading loads) depends on the X/R ratio of transformer and PF of the load. % voltage drop= %R cos phi +% X sin phi where cos phi is the PF of load.

2) It is the %voltage required on primary to circulate rated current on a shorted secondary. This is how it is measured at factory.

3) It is the (100/ %) times rated current that will flow in a shorted secondary, when rated voltage is maintained on primary terminals. This is what is happening, when a 3L fault occurs at transformer terminals during service. Transformer is to be designed to withstand these overcurrents till protection relay clears fault. This also decides the severity of arc flash on secondary circuit.. Higher the % impedance, less is the overcurrent and consequent destructive forces on windings and arc flash severity.

Till about the year 1900, engineers were trying to attain as low % impedance in transformer as possible, because of (1) above. Then when transformer ratings went up, engineers understood the beneficial effect of % impedance from (3) above and began to take a middle path, optimizing both aspects. In general, higher % impedance results in a copper machine- lean, tall, light unit ( more copper ,less core, higher copper loss /less iron loss) and less % impedance results in a core machine - bulky, short, heavy unit. For a particular kVA, there is a band of % impedance for economical designs, with minimum cost at one level. But one cannot go for optimum level as utilities would have standardized these % impedances for specific ratings in their grid from operational requirements.

How it is calculated:
Text books give the formulae for this. In IEC world, it is expressed on the base of max rating ( say in an ONAN/ONAF 16/20 MVA , on the base of 20 MVA) and IEEE world on the base of ONAN rating. There are two components to it % R ( load loss as a % of rating) plus % X. X is due to the flux generated in the radial gap between windings from winding currents and hence % impedance varies linearly with the load current, when expressed on the rated kVA. It is proportional to radial size of windings plus gap x square of number of turns and inversely proportional to height of windings.

In today's transformers % impedance varies 2-6 % for distribution units and 6-25 % for power transformers. %R varies from 1.5 % (100 kVA) to 0.10 % (500,000 kVA) .and %X 1.5- 25 % . X/R ratio varies from 10( DT) to 125 (Large Transformers) based on rating. Percentage impedance will be same on single phase basis or three phase basis as ohmic value remains the same.

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