64 Power Transformers 64.1 Transformer Construction The Transformer Core. Core and Shell Types. Transformer windings. Taps 64.2 Power Transformer Modeling The Three-Winding Ideal Transformer Equivalent Circuit. A Practical Three-Winding Transformer Equivalent Circuit. The Two-Winding Transformer 64.3 Transformer Performance 64.4 Transformers in Three-Pha Phase Shift in Y-A Connections Determining Per-Phase Equivalent Circuit Val Charles a. gross Transformers: An Example 64.5 Autotransformers 64.1 Transformer Construction The Transformer Core The core of the power TRANSFORMER is usually made of laminated cold-rolled magnetic steel that is grain oriented such that the rolling direction is the same as that of the flux lines. This type of core construction tends to reduce the eddy current and hysteresis losses. The eddy current loss P is proportional to the square of the product of the maximum flux density Bx(T), the frequency f(Hz), and thickness t(m)of the individual steel Pe=K,(Bmtf)2 (W) (64.1) K is dependent upon the core dimensions, the specific resistance of a lamination sheet, and the mass of the core. also Ph=Kh In Eq (64.2), P, is the hysteresis power loss, n is the Steinmetz constant(1.5< n<2.5)and kh is a constant dependent upon the nature of core material and varies from 3 X 10-m to 20X10-'m, where m= core mass in rams. The core loss therefore is P c 1999 by CRC Press LLC© 1999 by CRC Press LLC 64 Power Transformers 64.1 Transformer Construction The Transformer Core • Core and Shell Types • Transformer Windings • Taps 64.2 Power Transformer Modeling The Three-Winding Ideal Transformer Equivalent Circuit • A Practical Three-Winding Transformer Equivalent Circuit • The Two-Winding Transformer 64.3 Transformer Performance 64.4 Transformers in Three-Phase Connections Phase Shift in Y–D Connections • The Three-Phase Transformer • Determining Per-Phase Equivalent Circuit Values for Power Transformers: An Example 64.5 Autotransformers 64.1 Transformer Construction The Transformer Core The core of the power TRANSFORMER is usually made of laminated cold-rolled magnetic steel that is grain oriented such that the rolling direction is the same as that of the flux lines. This type of core construction tends to reduce the eddy current and hysteresis losses. The eddy current loss Pe is proportional to the square of the product of the maximum flux density BM (T), the frequency f (Hz), and thickness t (m) of the individual steel lamination. Pe = Ke(BMtf )2 (W) (64.1) Ke is dependent upon the core dimensions, the specific resistance of a lamination sheet, and the mass of the core. Also, Ph = Kh f BM n (W) (64.2) In Eq. (64.2), Ph is the hysteresis power loss, n is the Steinmetz constant (1.5 < n < 2.5) and Kh is a constant dependent upon the nature of core material and varies from 3210–3m to 20210–3m, where m = core mass in kilograms. The core loss therefore is Pe = Pe + Ph (64.3) Charles A. Gross Auburn University