31 CHAPTER 3 CONVENTIONAL DESIGN SOLUTIONS 3.1 CONVENTIONAL DESIGN Conventional design is a trial and error method. It makes use of empirical relations, approximations and assumptions. (Say 1958) A method of construction is developed in America for small distribution transformers upto about 5 kva employing cores comprising long continuous strips of sheet steel, wound round the coils. (Sawhney 001) In power system network, the high voltage is decreased by the distribution substations to 3.3kV,.kV and 11kV in rural, urban and industrial areas. Ultimately, the voltage used in industrial and domestic premises has to be dropped to 433V or 30V with the help of 3 phase distribution transformers. The typical layout, values for the variables and constants are given in Appendix 4 and are used while solving the design problem. 3. SINGLE PHASE TRANSFORMER PROBLEM To design a 5 kva, 11000 / 400 V, 50 Hz, single phase, core type, natural air cooled distribution transformer with the following data. Transformer type = core Transformer constant, K = 0.5 Maximum flux density, B m = 1.1 Wb/m Current density, = 1.1 A/mm Window space factor, K w = 0. Ratio, H w / W w = Iron stacking factor, K i = 0.9
3 3..1 Solutions for Single Phase Transformer Problem (Sawhney 001) The design problem is solved by conventional / analytical method and the results obtained are given in Table 3.1, 3. and 3.3 below. Typical values for the variables and constants, if required are taken from Appendix 4 at the time of calculation. Table 3.1 Results of single phase transformer (Overall dimensions) kva : 5 Phase : 1 Frequency : 50Hz Voltage rating : 11000/400V Current rating : 0.4545/1.5 A Type : Core Type of cooling : AN S.No Particulars Symbol Value 1 3 4 5 8 9 10 11 1 13 14 15 1 1 18 19 0 1 3 4 Material Transformer constant Voltage per turn Circumscribing circle diameter Net iron area Flux density Main flux Weight of iron Specific iron loss Iron loss Width of core Depth of yoke Height of yoke Number of window Window space factor Height of window Width of window Window area Copper Area Distance between adjacent limbs Height of frame Width of frame Depth of frame Mean length of flux path K E t d A i B m m G i p i a H y K w H w W w A w A c D H W l i 0.35 mm thick HRS 0.5 (assumed) 1. 0.13 m 0.008m 1.1 Wb/ m (assumed) 0.00554 Wb 55.08 kg 1. W/kg 88.133 W 0.08 m 0.08 m 0.088 m 1 0. (assumed) 0.0 m 0.101 m 0.00 m 0.0041 m 0.4 m 0.38 m 0.311 m 0.08 m 1.08 m
33 Table 3. Results of single phase transformer (Winding) S.No. Particulars HV LV 1 3 4 5 Conductor area(bare) Current density Turns Length of mean turn Resistance Weight Total weight of copper G c =0. kg 0.413 mm 1.1 A/ mm 50 0.48 m 143 10.33 kg 11.33 mm 1.1 A/ mm (assumed) 38 0.48 m 0.1885 10.33 kg Table 3.3 Results of single phase transformer (Performance) 1 Total iron loss Total full load copper loss 3 Total full load loss 4 Efficiency at full load and at U.P.F 5 Cost of iron Cost of copper P c P T fl C i C c 88.133 W 59 W 14.133 W 9.14% Rs.058.80 Rs.198 3.3 THREE PHASE TRANSFORMER PROBLEM To design a 500 kva, 11000 / 433 V, delta/star, 50 Hz, three phase, core type, oil immersed natural cooled distribution transformer for the below mentioned data. The transformer is provided with tappings.5% and 5% on h.v. winding. Maximum temperature is not to exceed 45 o C with mean temperature rise of 35 o C of oil. Use cruciform core.
34 Transformer type = core Transformer constant, K = 0.45 Maximum flux density,b m = 1. Wb/m Current density, = 1.4 A/mm Window space factor, K w = 0.5 Ratio, H w / W w = 3 Iron stacking factor, K i = 0.9 3.3.1 Solutions for Three Phase Transformer Problem (Sawhney 001) The design problem is solved by conventional/analytical method and the results obtained are given in Table 3.4, 3.5 and 3. below. Typical values for the variables and constants are taken from Appendix 4 at the time of calculation. Table 3.4 Results of three phase transformer (overall dimensions) kva : 500 Phase : 3 Frequency : 50 Hz Delta/Star Line Voltage : HV : 11000V Phase Voltage : HV: 11000V LV : 433 V LV : 50V Line Current : HV :.43A Phase Current : HV : 15.15A LV :.8A LV :.8A Type : Core Type of cooling : ON 1. Material. Transformer constant 3. Voltage per turn 4. Diameter of circumscribing circle 5. Number of steps 0.35 mm thick HRS K 0.45 (assumed) E t d - 10.0 V 0 mm
35 Table 3.4 (Continued) Dimensions a 1 mm b 138 mm Net iron area A i 0.038 m 8 Flux density B m 1. Wb/ m (assumed) 9 Flux m 0.0453 Wb 10 Total Weight G i 140 kg 11 Specific iron loss p i 1.9 W/kg 1 Total iron loss 98 W 13 Depth of yoke 1 mm 14 Height of yoke H y 11 mm 15 Net yoke area A y 0.038 m 1 Number of window 1 Window space factor K w 0.5 (assumed) 18 Height of window H w 0.53 m 19 Width of window W w 0.51 m 0 Window area A w 189x 10 3 mm 1 Copper Area A c 0.045 m Volume of copper U c 0.035m 3 3 Distance between adjacent limbs D 0.511 m 4 Height of frame H 1.095 m 5 Width of frame W 1.43 m Depth of frame 0.1 m Mean length of flux path l i 4.81 m 8 Volume of iron U i 0.18 m 3
3 Table 3.5 Results of three phase transformer (winding) S.No. Winding HV LV 1. Connections Delta Star. Conductor area(bare) 10.8 mm 4.43 mm 3. Current density 1.4 A/ mm 1.4 A/ mm (assumed) 4. Turns per phase 1100(+0 for taps) 5 5. Coils 1 5. Depth of winding, b p, b s 5 mm 3 mm. Coil diameters Inside Outside 0.34 m 0.458 m 0.0 m 0.31 m 8. Length of mean turn 1.3 m 0.90 m 9. Length of mean turn of windings 1.0915 m 1.0915 m 10. Resistance/ phase.9 0.001 Table 3. Results of three phase transformer (Tank and performance) 1 Dimensions of tank Height H t 1.545 m Length L t 0.558 m Width W t 1.5 m 3 4 5 8 9 Cooling surface area Number of tubes Temperature rise of oil P. U. resistance P. U. reactance P. U. impedance Total core loss Total full load copper loss S t n t r x z P c.55 m 35 C 10 11 Total full load loss Efficiency at full load and U.P.F P T fl 0.0038 0.09 0.09 98 W 3190 W+(stray loss=319w) 0W 98.%