109 APPENDIX 4 TYPICAL LAYOUT, VALUES AND CONSTANTS TYPICAL LAYOUT The purpose of a transformer is to transfer energy from the input to the output through the magnetic field. The layout of a partial typical core type transformer is shown in Figure A4.1. Figure A4.1 Typical layout of a transformer
110 OVERALL DIMENSIONS The overall dimension of a three phase core type transformer and a single phase shell type transformer is as shown in Figure A4.2(a) and A4.2(b) respectively. (a) Three phase core type transformer (b) single phase shell type transformer Figure A4.2 Overall dimensions of a transformer YOKE Area of yoke for hot rolled silicon steel is 15 to 25% greater than the core area. For cold rolled silicon steel, the area of yoke is equal to area of core. The section of yoke can either be taken as rectangular or it may be stepped. The yoke sections are shown in Figure A4.3.
111 Figure A4.3 Yoke cross sections FLUX DENSITY The usual values of maximum flux density B m for transformers using hot rolled silicon steel are: Distribution Transformers - 1.1 to 1.35 Wb/ Power Transformers - 1.25 to 1.45 Wb/ Lower values should be used for small rating transformers. For transformers using cold rolled grain oriented steel, the following values may be used: For transformers upto 132 kv - 1.55 Wb/ For 275 kv transformers - 1.6 Wb/ For 400 kv and generator transformers - 1.7 Wb/
112 CURRENT DENSITY The range of value of current density is as follows. For distribution and small power transformers - 1.1 to 2.3 A/ m self oil cooled type upto 50kVA Large power transformers, self oil cooled type - 2.2 to 3.2 A/ m or air blast Large power transformers with forced circulation - 5.4 to 6.2 A/ m of oil or with water cooling coils For minimum copper loss, the value of current density in each of the two windings should be equal. However, the current density in the relatively better cooled outer winding is made 5% greater than the inner winding. STACKING FACTOR The iron stacking factor, K i = 0.9 WINDOW SPACE FACTOR The following empirical formulae may be used for estimating the value of window space factor, K w Transformers of ratings Kw 10 (30 kv) between 50 to 200 kva
113 Space factor is large for large outputs and smaller for small outputs. For a transformer about 1000 kva, Kw 12 (30 kv) For a transformer about 20 kva, Kw 8 (30 kv) interpolated. The value of space factor for intermediate ratings can be LEAKAGE REACTANCE Long and thin coils give low value of leakage reactance and short and wide coils give large value of leakage reactance. WINDOW The ratio of height to width of window, Hw Ww is between 2 to 4. The width of window for maximum output is 0.7d. TRANSFORMER CONSTANT The value of transformer constant K for different types of transformers are given in Table A4.1. Table A4.1 Transformer constant, K Type Three phase core type (Distribution) Three phase core type (Power) Single phase core type Single phase shell type Three phase shell type K 0.45 0.6 to 0.7 0.75 to 0.85 1.0 to 1.2 1.3
114 RATIO OF WEIGHTS in Table A4.2. The general ratio of weight of iron to weight of copper is indicated Table A4.2 Ratio G i G c Distribution Transformers Type G G c i Single phase core type transformers (Small capacity) High voltage power transformers 1.5 to 3 < 1.5 2 times above value RATIO OF LENGTHS Typical values of ratio L mt / l i is given in Table A.4.3 Table A4.3 Ratio L /l mt i Three phase core type Single phase core type Single phase shell type Type L /l mt i 0.17 to 0.5 0.3 to 0.55 1.2 to 2.0 MULTI-STEPPED CORE The most economical dimensions of various steps for a multistepped core is given in Table A4.4.
115 Table A4.4 Dimensions of core steps Area percentage of circumscribing circle Gross Core Area, A gi Net core area, A i 64 58 Net core area, A i = K c d 2 Square Cruciform Three stepped 79 71 84 75 Four stepped K c 0.45 0.56 0.6 0.62 87 78 LOSS CURVE This curve is used to obtain specific iron loss and is shown in Figure A4.4 for different types of steel having 0.35 mm thick laminations. Figure A4.4 Loss curve The above are the typical values and constants used in the conventional design method of a transformer.
116 B at or B-H CURVE The B- at curves as supplied by sankey pressings Division of m/s Guest Keen Williams Ltd is shown in Fig. A4.5. The curve may be used to find the mmf required to establish the flux. Figure A4.5 B- at Curves