From 7f60ea012dd2524dae921a2a35adbf7ef21f2bb6 Mon Sep 17 00:00:00 2001 From: prashantsinalkar Date: Tue, 10 Oct 2017 12:27:19 +0530 Subject: initial commit / add all books --- 3760/CH1/EX1.1/Ex1_1.sce | 21 ++++++++++ 3760/CH1/EX1.10/Ex1_10.sce | 33 ++++++++++++++++ 3760/CH1/EX1.11/Ex1_11.sce | 31 +++++++++++++++ 3760/CH1/EX1.12/Ex1_12.sce | 28 +++++++++++++ 3760/CH1/EX1.14/Ex1_14.sce | 27 +++++++++++++ 3760/CH1/EX1.15/Ex1_15.sce | 27 +++++++++++++ 3760/CH1/EX1.16/Ex1_16.sce | 30 ++++++++++++++ 3760/CH1/EX1.18/Ex1_18.sce | 26 ++++++++++++ 3760/CH1/EX1.19/Ex1_19.sce | 10 +++++ 3760/CH1/EX1.2/Ex1_2.sce | 15 +++++++ 3760/CH1/EX1.20/Ex1_20.sce | 20 ++++++++++ 3760/CH1/EX1.21/Ex1_21.sce | 29 ++++++++++++++ 3760/CH1/EX1.22/Ex1_22.sce | 28 +++++++++++++ 3760/CH1/EX1.24/Ex1_24.sce | 18 +++++++++ 3760/CH1/EX1.25/Ex1_25.sce | 15 +++++++ 3760/CH1/EX1.26/Ex1_26.sce | 22 +++++++++++ 3760/CH1/EX1.27/Ex1_27.sce | 25 ++++++++++++ 3760/CH1/EX1.28/Ex1_28.sce | 51 ++++++++++++++++++++++++ 3760/CH1/EX1.29/Ex1_29.sce | 11 ++++++ 3760/CH1/EX1.3/Ex1_3.sce | 19 +++++++++ 3760/CH1/EX1.30/Ex1_30.sce | 15 +++++++ 3760/CH1/EX1.31/Ex1_31.sce | 11 ++++++ 3760/CH1/EX1.32/Ex1_32.sce | 28 +++++++++++++ 3760/CH1/EX1.33/Ex1_33.sce | 19 +++++++++ 3760/CH1/EX1.34/Ex1_34.sce | 26 ++++++++++++ 3760/CH1/EX1.35/Ex1_35.sce | 46 +++++++++++++++++++++ 3760/CH1/EX1.36/Ex1_36.sce | 23 +++++++++++ 3760/CH1/EX1.37/Ex1_37.sce | 12 ++++++ 3760/CH1/EX1.38/Ex1_38.sce | 40 +++++++++++++++++++ 3760/CH1/EX1.39/Ex1_39.sce | 14 +++++++ 3760/CH1/EX1.4/Ex1_4.sce | 13 ++++++ 3760/CH1/EX1.40/Ex1_40.sce | 17 ++++++++ 3760/CH1/EX1.41/Ex1_41.sce | 12 ++++++ 3760/CH1/EX1.42/Ex1_42.sce | 20 ++++++++++ 3760/CH1/EX1.43/Ex1_43.sce | 27 +++++++++++++ 3760/CH1/EX1.44/Ex1_44.sce | 31 +++++++++++++++ 3760/CH1/EX1.45/Ex1_45.sce | 22 +++++++++++ 3760/CH1/EX1.46/Ex1_46.sce | 8 ++++ 3760/CH1/EX1.48/Ex1_48.sce | 18 +++++++++ 3760/CH1/EX1.49/Ex1_49.sce | 32 +++++++++++++++ 3760/CH1/EX1.5/Ex1_5.sce | 40 +++++++++++++++++++ 3760/CH1/EX1.50/Ex1_50.sce | 38 ++++++++++++++++++ 3760/CH1/EX1.51/Ex1_51.sce | 17 ++++++++ 3760/CH1/EX1.52/Ex1_52.sce | 21 ++++++++++ 3760/CH1/EX1.53/Ex1_53.sce | 41 +++++++++++++++++++ 3760/CH1/EX1.54/Ex1_54.sce | 11 ++++++ 3760/CH1/EX1.55/Ex1_55.sce | 19 +++++++++ 3760/CH1/EX1.56/Ex1_56.sce | 20 ++++++++++ 3760/CH1/EX1.57/Ex1_57.sce | 11 ++++++ 3760/CH1/EX1.58/Ex1_58.sce | 8 ++++ 3760/CH1/EX1.59/Ex1_59.sce | 17 ++++++++ 3760/CH1/EX1.6/Ex1_6.sce | 15 +++++++ 3760/CH1/EX1.60/Ex1_60.sce | 18 +++++++++ 3760/CH1/EX1.61/Ex1_61.sce | 34 ++++++++++++++++ 3760/CH1/EX1.62/Ex1_62.sce | 24 +++++++++++ 3760/CH1/EX1.63/Ex1_63.sce | 17 ++++++++ 3760/CH1/EX1.64/Ex1_64.sce | 18 +++++++++ 3760/CH1/EX1.65/Ex1_65.sce | 26 ++++++++++++ 3760/CH1/EX1.66/Ex1_66.sce | 49 +++++++++++++++++++++++ 3760/CH1/EX1.67/Ex1_67.sce | 16 ++++++++ 3760/CH1/EX1.68/Ex1_68.sce | 16 ++++++++ 3760/CH1/EX1.69/Ex1_69.sce | 30 ++++++++++++++ 3760/CH1/EX1.70/Ex1_70.sce | 28 +++++++++++++ 3760/CH1/EX1.71/Ex1_71.sce | 26 ++++++++++++ 3760/CH1/EX1.72/Ex1_72.sce | 28 +++++++++++++ 3760/CH1/EX1.73/Ex1_73.sce | 18 +++++++++ 3760/CH1/EX1.74/Ex1_74.sce | 20 ++++++++++ 3760/CH1/EX1.75/Ex1_75.sce | 11 ++++++ 3760/CH1/EX1.76/Ex1_76.sce | 21 ++++++++++ 3760/CH1/EX1.77/Ex1_77.sce | 11 ++++++ 3760/CH1/EX1.78/Ex1_78.sce | 15 +++++++ 3760/CH1/EX1.79/Ex1_79.sce | 16 ++++++++ 3760/CH1/EX1.8/Ex1_8.sce | 34 ++++++++++++++++ 3760/CH1/EX1.9/Ex1_9.sce | 28 +++++++++++++ 3760/CH2/EX2.13/Ex2_13.sce | 42 ++++++++++++++++++++ 3760/CH2/EX2.15/Ex2_15.sce | 33 ++++++++++++++++ 3760/CH2/EX2.16/Ex2_16.sce | 9 +++++ 3760/CH2/EX2.17/Ex2_17.sce | 9 +++++ 3760/CH2/EX2.19/Ex2_19.sce | 27 +++++++++++++ 3760/CH2/EX2.21/Ex2_21.sce | 7 ++++ 3760/CH2/EX2.22/Ex2_22.sce | 8 ++++ 3760/CH2/EX2.23/Ex2_23.sce | 13 ++++++ 3760/CH2/EX2.25/Ex2_25.sce | 20 ++++++++++ 3760/CH2/EX2.26/Ex2_26.sce | 8 ++++ 3760/CH2/EX2.28/Ex2_28.sce | 15 +++++++ 3760/CH2/EX2.29/Ex2_29.sce | 22 +++++++++++ 3760/CH2/EX2.30/Ex2_30.sce | 32 +++++++++++++++ 3760/CH2/EX2.4/Ex2_4.sce | 13 ++++++ 3760/CH2/EX2.6/Ex2_6.sce | 8 ++++ 3760/CH2/EX2.7/Ex2_7.sce | 74 ++++++++++++++++++++++++++++++++++ 3760/CH2/EX2.8/Ex2_8.sce | 9 +++++ 3760/CH2/EX2.9/Ex2_9.sce | 10 +++++ 3760/CH3/EX3.10/Ex3_10.sce | 30 ++++++++++++++ 3760/CH3/EX3.11/Ex3_11.sce | 47 ++++++++++++++++++++++ 3760/CH3/EX3.12/Ex3_12.sce | 19 +++++++++ 3760/CH3/EX3.13/Ex3_13.sce | 29 ++++++++++++++ 3760/CH3/EX3.14/Ex3_14.sce | 30 ++++++++++++++ 3760/CH3/EX3.15/Ex3_15.sce | 11 ++++++ 3760/CH3/EX3.16/Ex3_16.sce | 15 +++++++ 3760/CH3/EX3.18/Ex3_18.sce | 22 +++++++++++ 3760/CH3/EX3.19/Ex3_19.sce | 14 +++++++ 3760/CH3/EX3.2/Ex3_2.sce | 25 ++++++++++++ 3760/CH3/EX3.20/Ex3_20.sce | 17 ++++++++ 3760/CH3/EX3.3/Ex3_3.sce | 22 +++++++++++ 3760/CH3/EX3.30/Ex3_30.sce | 7 ++++ 3760/CH3/EX3.32/Ex3_32.sce | 26 ++++++++++++ 3760/CH3/EX3.33/Ex3_33.sce | 21 ++++++++++ 3760/CH3/EX3.35/Ex3_35.sce | 34 ++++++++++++++++ 3760/CH3/EX3.36/Ex3_36.sce | 40 +++++++++++++++++++ 3760/CH3/EX3.37/Ex3_37.sce | 6 +++ 3760/CH3/EX3.39/Ex3_39.sce | 18 +++++++++ 3760/CH3/EX3.4/Ex3_4.sce | 25 ++++++++++++ 3760/CH3/EX3.40/Ex3_40.sce | 20 ++++++++++ 3760/CH3/EX3.41/Ex3_41.sce | 21 ++++++++++ 3760/CH3/EX3.42/Ex3_42.sce | 14 +++++++ 3760/CH3/EX3.43/Ex3_43.sce | 5 +++ 3760/CH3/EX3.5/Ex3_5.sce | 37 +++++++++++++++++ 3760/CH3/EX3.6/Ex3_6.sce | 25 ++++++++++++ 3760/CH3/EX3.8/Ex3_8.sce | 23 +++++++++++ 3760/CH4/EX4.11/Ex4_11.sce | 13 ++++++ 3760/CH4/EX4.12/Ex4_12.sce | 7 ++++ 3760/CH4/EX4.13/Ex4_13.sce | 16 ++++++++ 3760/CH4/EX4.14/Ex4_14.sce | 13 ++++++ 3760/CH4/EX4.15/Ex4_15.sce | 14 +++++++ 3760/CH4/EX4.16/Ex4_16.sce | 13 ++++++ 3760/CH4/EX4.17/Ex4_17.sce | 19 +++++++++ 3760/CH4/EX4.18/Ex4_18.sce | 25 ++++++++++++ 3760/CH4/EX4.19/Ex4_19.sce | 45 +++++++++++++++++++++ 3760/CH4/EX4.2/Ex4_2.sce | 17 ++++++++ 3760/CH4/EX4.20/Ex4_20.sce | 51 ++++++++++++++++++++++++ 3760/CH4/EX4.21/Ex4_21.sce | 46 +++++++++++++++++++++ 3760/CH4/EX4.22/Ex4_22.sce | 20 ++++++++++ 3760/CH4/EX4.23/Ex4_23.sce | 41 +++++++++++++++++++ 3760/CH4/EX4.24/Ex4_24.sce | 33 ++++++++++++++++ 3760/CH4/EX4.25/Ex4_25.sce | 18 +++++++++ 3760/CH4/EX4.26/Ex4_26.sce | 29 ++++++++++++++ 3760/CH4/EX4.27/Ex4_27.sce | 23 +++++++++++ 3760/CH4/EX4.28/Ex4_28.sce | 24 +++++++++++ 3760/CH4/EX4.29/Ex4_29.sce | 16 ++++++++ 3760/CH4/EX4.3/Ex4_3.sce | 28 +++++++++++++ 3760/CH4/EX4.30/Ex4_30.sce | 32 +++++++++++++++ 3760/CH4/EX4.31/Ex4_31.sce | 35 ++++++++++++++++ 3760/CH4/EX4.32/Ex4_32.sce | 21 ++++++++++ 3760/CH4/EX4.33/Ex4_33.sce | 35 ++++++++++++++++ 3760/CH4/EX4.34/Ex4_34.sce | 41 +++++++++++++++++++ 3760/CH4/EX4.35/Ex4_35.sce | 27 +++++++++++++ 3760/CH4/EX4.36/Ex4_36.sce | 55 ++++++++++++++++++++++++++ 3760/CH4/EX4.37/Ex4_37.sce | 22 +++++++++++ 3760/CH4/EX4.38/Ex4_38.sce | 28 +++++++++++++ 3760/CH4/EX4.39/Ex4_39.sce | 67 +++++++++++++++++++++++++++++++ 3760/CH4/EX4.4/Ex4_4.sce | 24 +++++++++++ 3760/CH4/EX4.40/Ex4_40.sce | 33 ++++++++++++++++ 3760/CH4/EX4.41/Ex4_41.sce | 16 ++++++++ 3760/CH4/EX4.42/Ex4_42.sce | 16 ++++++++ 3760/CH4/EX4.43/Ex4_43.sce | 22 +++++++++++ 3760/CH4/EX4.44/Ex4_44.sce | 19 +++++++++ 3760/CH4/EX4.45/Ex4_45.sce | 14 +++++++ 3760/CH4/EX4.46/Ex4_46.sce | 12 ++++++ 3760/CH4/EX4.48/Ex4_48.sce | 20 ++++++++++ 3760/CH4/EX4.49/Ex4_49.sce | 15 +++++++ 3760/CH4/EX4.5/Ex4_5.sce | 14 +++++++ 3760/CH4/EX4.50/Ex4_50.sce | 16 ++++++++ 3760/CH4/EX4.51/Ex4_51.sce | 27 +++++++++++++ 3760/CH4/EX4.52/Ex4_52.sce | 14 +++++++ 3760/CH4/EX4.53/Ex4_53.sce | 23 +++++++++++ 3760/CH4/EX4.54/Ex4_54.sce | 28 +++++++++++++ 3760/CH4/EX4.55/Ex4_55.sce | 22 +++++++++++ 3760/CH4/EX4.56/Ex4_56.sce | 15 +++++++ 3760/CH4/EX4.57/Ex4_57.sce | 22 +++++++++++ 3760/CH4/EX4.58/Ex4_58.sce | 14 +++++++ 3760/CH4/EX4.59/Ex4_59.sce | 47 ++++++++++++++++++++++ 3760/CH4/EX4.6/Ex4_6.sce | 17 ++++++++ 3760/CH4/EX4.60/Ex4_60.sce | 17 ++++++++ 3760/CH4/EX4.61/Ex4_61.sce | 52 ++++++++++++++++++++++++ 3760/CH4/EX4.62/Ex4_62.sce | 22 +++++++++++ 3760/CH4/EX4.63/Ex4_63.sce | 10 +++++ 3760/CH4/EX4.64/Ex4_64.sce | 16 ++++++++ 3760/CH4/EX4.66/Ex4_66.sce | 16 ++++++++ 3760/CH4/EX4.67/Ex4_67.sce | 23 +++++++++++ 3760/CH4/EX4.68/Ex4_68.sce | 25 ++++++++++++ 3760/CH4/EX4.69/Ex4_69.sce | 29 ++++++++++++++ 3760/CH4/EX4.70/Ex4_70.sce | 19 +++++++++ 3760/CH4/EX4.71/Ex4_71.sce | 10 +++++ 3760/CH4/EX4.72/Ex4_72.sce | 19 +++++++++ 3760/CH4/EX4.73/Ex4_73.sce | 17 ++++++++ 3760/CH4/EX4.74/Ex4_74.sce | 22 +++++++++++ 3760/CH4/EX4.75/Ex4_75.sce | 23 +++++++++++ 3760/CH4/EX4.77/Ex4_77.sce | 24 +++++++++++ 3760/CH4/EX4.78/Ex4_78.sce | 22 +++++++++++ 3760/CH4/EX4.81/Ex4_81.sce | 23 +++++++++++ 3760/CH4/EX4.82/Ex4_82.sce | 31 +++++++++++++++ 3760/CH4/EX4.83/Ex4_83.sce | 12 ++++++ 3760/CH4/EX4.84/Ex4_84.sce | 16 ++++++++ 3760/CH4/EX4.85/Ex4_85.sce | 12 ++++++ 3760/CH4/EX4.86/Ex4_86.sce | 20 ++++++++++ 3760/CH4/EX4.87/Ex4_87.sce | 24 +++++++++++ 3760/CH4/EX4.9/Ex4_9.sce | 22 +++++++++++ 3760/CH5/EX5.1/Ex5_1.sce | 99 ++++++++++++++++++++++++++++++++++++++++++++++ 3760/CH5/EX5.10/Ex5_10.sce | 36 +++++++++++++++++ 3760/CH5/EX5.11/Ex5_11.sce | 15 +++++++ 3760/CH5/EX5.12/Ex5_12.sce | 16 ++++++++ 3760/CH5/EX5.13/Ex5_13.sce | 14 +++++++ 3760/CH5/EX5.14/Ex5_14.sce | 18 +++++++++ 3760/CH5/EX5.15/Ex5_15.sce | 33 ++++++++++++++++ 3760/CH5/EX5.16/Ex5_16.sce | 18 +++++++++ 3760/CH5/EX5.17/Ex5_17.sce | 17 ++++++++ 3760/CH5/EX5.18/Ex5_18.sce | 15 +++++++ 3760/CH5/EX5.19/Ex5_19.sce | 40 +++++++++++++++++++ 3760/CH5/EX5.20/Ex5_20.sce | 18 +++++++++ 3760/CH5/EX5.21/Ex5_21.sce | 27 +++++++++++++ 3760/CH5/EX5.22/Ex5_22.sce | 21 ++++++++++ 3760/CH5/EX5.23/Ex5_23.sce | 21 ++++++++++ 3760/CH5/EX5.24/Ex5_24.sce | 26 ++++++++++++ 3760/CH5/EX5.27/Ex5_27.sce | 25 ++++++++++++ 3760/CH5/EX5.29/Ex5_29.sce | 12 ++++++ 3760/CH5/EX5.3/Ex5_3.sce | 26 ++++++++++++ 3760/CH5/EX5.31/Ex5_31.sce | 17 ++++++++ 3760/CH5/EX5.32/Ex5_32.sce | 15 +++++++ 3760/CH5/EX5.34/Ex5_34.sce | 16 ++++++++ 3760/CH5/EX5.35/Ex5_35.sce | 37 +++++++++++++++++ 3760/CH5/EX5.36/Ex5_36.sce | 27 +++++++++++++ 3760/CH5/EX5.37/Ex5_37.sce | 23 +++++++++++ 3760/CH5/EX5.38/Ex5_38.sce | 36 +++++++++++++++++ 3760/CH5/EX5.4/Ex5_4.sce | 17 ++++++++ 3760/CH5/EX5.41/Ex5_41.sce | 26 ++++++++++++ 3760/CH5/EX5.43/Ex5_43.sce | 22 +++++++++++ 3760/CH5/EX5.44/Ex5_44.sce | 16 ++++++++ 3760/CH5/EX5.45/Ex5_45.sce | 22 +++++++++++ 3760/CH5/EX5.46/Ex5_46.sce | 16 ++++++++ 3760/CH5/EX5.47/Ex5_47.sce | 24 +++++++++++ 3760/CH5/EX5.48/Ex5_48.sce | 15 +++++++ 3760/CH5/EX5.49/Ex5_49.sce | 16 ++++++++ 3760/CH5/EX5.5/Ex5_5.sce | 21 ++++++++++ 3760/CH5/EX5.53/Ex5_53.sce | 44 +++++++++++++++++++++ 3760/CH5/EX5.54/Ex5_54.sce | 15 +++++++ 3760/CH5/EX5.55/Ex5_55.sce | 14 +++++++ 3760/CH5/EX5.56/Ex5_56.sce | 26 ++++++++++++ 3760/CH5/EX5.57/Ex5_57.sce | 20 ++++++++++ 3760/CH5/EX5.58/Ex5_58.sce | 17 ++++++++ 3760/CH5/EX5.59/Ex5_59.sce | 17 ++++++++ 3760/CH5/EX5.6/Ex5_6.sce | 18 +++++++++ 3760/CH5/EX5.7/Ex5_7.sce | 16 ++++++++ 3760/CH5/EX5.8/Ex5_8.sce | 11 ++++++ 3760/CH5/EX5.9/Ex5_9.sce | 34 ++++++++++++++++ 3760/CH6/EX6.1/Ex6_1.sce | 14 +++++++ 3760/CH6/EX6.10/Ex6_10.sce | 78 ++++++++++++++++++++++++++++++++++++ 3760/CH6/EX6.11/Ex6_11.sce | 73 ++++++++++++++++++++++++++++++++++ 3760/CH6/EX6.13/Ex6_13.sce | 82 ++++++++++++++++++++++++++++++++++++++ 3760/CH6/EX6.14/Ex6_14.sce | 40 +++++++++++++++++++ 3760/CH6/EX6.15/Ex6_15.sce | 19 +++++++++ 3760/CH6/EX6.16/Ex6_16.sce | 32 +++++++++++++++ 3760/CH6/EX6.17/Ex6_17.sce | 20 ++++++++++ 3760/CH6/EX6.18/Ex6_18.sce | 27 +++++++++++++ 3760/CH6/EX6.19/Ex6_19.sce | 10 +++++ 3760/CH6/EX6.2/Ex6_2.sce | 40 +++++++++++++++++++ 3760/CH6/EX6.20/Ex6_20.sce | 36 +++++++++++++++++ 3760/CH6/EX6.21/Ex6_21.sce | 27 +++++++++++++ 3760/CH6/EX6.22/Ex6_22.sce | 21 ++++++++++ 3760/CH6/EX6.23/Ex6_23.sce | 56 ++++++++++++++++++++++++++ 3760/CH6/EX6.25/Ex6_25.sce | 46 +++++++++++++++++++++ 3760/CH6/EX6.26/Ex6_26.sce | 15 +++++++ 3760/CH6/EX6.27/Ex6_27.sce | 49 +++++++++++++++++++++++ 3760/CH6/EX6.28/Ex6_28.sce | 46 +++++++++++++++++++++ 3760/CH6/EX6.29/Ex6_29.sce | 60 ++++++++++++++++++++++++++++ 3760/CH6/EX6.3/Ex6_3.sce | 11 ++++++ 3760/CH6/EX6.30/Ex6_30.sce | 61 ++++++++++++++++++++++++++++ 3760/CH6/EX6.31/Ex6_31.sce | 23 +++++++++++ 3760/CH6/EX6.32/Ex6_32.sce | 14 +++++++ 3760/CH6/EX6.33/Ex6_33.sce | 20 ++++++++++ 3760/CH6/EX6.34/Ex6_34.sce | 17 ++++++++ 3760/CH6/EX6.35/Ex6_35.sce | 21 ++++++++++ 3760/CH6/EX6.36/Ex6_36.sce | 11 ++++++ 3760/CH6/EX6.37/Ex6_37.sce | 31 +++++++++++++++ 3760/CH6/EX6.4/Ex6_4.sce | 31 +++++++++++++++ 3760/CH6/EX6.41/Ex6_41.sce | 31 +++++++++++++++ 3760/CH6/EX6.43/Ex6_43.sce | 21 ++++++++++ 3760/CH6/EX6.44/Ex6_44.sce | 23 +++++++++++ 3760/CH6/EX6.45/Ex6_45.sce | 46 +++++++++++++++++++++ 3760/CH6/EX6.46/Ex6_46.sce | 11 ++++++ 3760/CH6/EX6.47/Ex6_47.sce | 60 ++++++++++++++++++++++++++++ 3760/CH6/EX6.48/Ex6_48.sce | 55 ++++++++++++++++++++++++++ 3760/CH6/EX6.49/Ex6_49.sce | 37 +++++++++++++++++ 3760/CH6/EX6.5/Ex6_5.sce | 35 ++++++++++++++++ 3760/CH6/EX6.50/Ex6_50.sce | 43 ++++++++++++++++++++ 3760/CH6/EX6.51/Ex6_51.sce | 28 +++++++++++++ 3760/CH6/EX6.53/Ex6_53.sce | 8 ++++ 3760/CH6/EX6.54/ex6_54.sce | 9 +++++ 3760/CH6/EX6.55/Ex6_55.sce | 20 ++++++++++ 3760/CH6/EX6.56/Ex6_56.sce | 17 ++++++++ 3760/CH6/EX6.57/Ex6_57.sce | 15 +++++++ 3760/CH6/EX6.58/Ex6_58.sce | 26 ++++++++++++ 3760/CH6/EX6.59/Ex6_59.sce | 14 +++++++ 3760/CH6/EX6.6/Ex6_6.sce | 15 +++++++ 3760/CH6/EX6.60/Ex6_60.sce | 14 +++++++ 3760/CH6/EX6.62/Ex6_62.sce | 18 +++++++++ 3760/CH6/EX6.63/Ex6_63.sce | 19 +++++++++ 3760/CH6/EX6.64/Ex6_64.sce | 28 +++++++++++++ 3760/CH6/EX6.65/Ex6_65.sce | 32 +++++++++++++++ 3760/CH6/EX6.7/Ex6_7.sce | 47 ++++++++++++++++++++++ 3760/CH6/EX6.8/Ex6_8.sce | 11 ++++++ 3760/CH6/EX6.9/Ex6_9.sce | 39 ++++++++++++++++++ 3760/CH7/EX7.1/Ex7_1.sce | 14 +++++++ 3760/CH7/EX7.10/Ex7_10.sce | 8 ++++ 3760/CH7/EX7.11/Ex7_11.sce | 18 +++++++++ 3760/CH7/EX7.12/Ex7_12.sce | 19 +++++++++ 3760/CH7/EX7.13/Ex7_13.sce | 22 +++++++++++ 3760/CH7/EX7.15/Ex7_15.sce | 9 +++++ 3760/CH7/EX7.2/Ex7_2.sce | 20 ++++++++++ 3760/CH7/EX7.3/Ex7_3.sce | 19 +++++++++ 3760/CH7/EX7.5/Ex7_5.sce | 30 ++++++++++++++ 3760/CH7/EX7.6/Ex7_6.sce | 19 +++++++++ 3760/CH7/EX7.7/Ex7_7.sce | 20 ++++++++++ 3760/CH7/EX7.8/Ex7_8.sce | 28 +++++++++++++ 3760/CH7/EX7.9/Ex7_9.sce | 9 +++++ 3760/CH8/EX8.1/ExA_1.sce | 14 +++++++ 3760/CH8/EX8.10/ExA_10.sce | 7 ++++ 3760/CH8/EX8.12/ExA_12.sce | 22 +++++++++++ 3760/CH8/EX8.13/ExA_13.sce | 14 +++++++ 3760/CH8/EX8.2/ExA_2.sce | 13 ++++++ 3760/CH8/EX8.3/ExA_3.sce | 35 ++++++++++++++++ 3760/CH8/EX8.4/ExA_4.sce | 24 +++++++++++ 3760/CH8/EX8.5/ExA_5.sce | 22 +++++++++++ 3760/CH8/EX8.6/ExA_6.sce | 28 +++++++++++++ 3760/CH8/EX8.7/ExA_7.sce | 24 +++++++++++ 3760/CH8/EX8.8/ExA_8.sce | 19 +++++++++ 3760/CH8/EX8.9/ExA_9.sce | 21 ++++++++++ 3760/CH9/EX9.3/ExB_3.sce | 31 +++++++++++++++ 3760/CH9/EX9.4/ExB_4.sce | 15 +++++++ 3760/CH9/EX9.5/ExB_5.sce | 21 ++++++++++ 3760/CH9/EX9.6/ExB_6.sce | 13 ++++++ 3760/CH9/EX9.7/ExB_7.sce | 8 ++++ 3760/CH9/EX9.8/ExB_8.sce | 14 +++++++ 332 files changed, 7922 insertions(+) create mode 100644 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3760/CH9/EX9.4/ExB_4.sce create mode 100644 3760/CH9/EX9.5/ExB_5.sce create mode 100644 3760/CH9/EX9.6/ExB_6.sce create mode 100644 3760/CH9/EX9.7/ExB_7.sce create mode 100644 3760/CH9/EX9.8/ExB_8.sce (limited to '3760') diff --git a/3760/CH1/EX1.1/Ex1_1.sce b/3760/CH1/EX1.1/Ex1_1.sce new file mode 100644 index 000000000..e48d24398 --- /dev/null +++ b/3760/CH1/EX1.1/Ex1_1.sce @@ -0,0 +1,21 @@ + +clc; +f=50; // frequency in Hz +Et=13; // emf per turn in volts +E1=2310; // primary voltage in volts +E2= 220; // secondary voltage in volts +B=1.4; // maximum flux density in Tesla +// calculating the number of turns in primary and secondary side +N2= round(E2/Et); //secondary side turns +printf('Number of secondary turns is %f\n',N2); +N1=round(N2*(E1/E2));// primary side turns +printf('Number of primary turns is %f\n',N1); +disp('The value of primary turns does not satisfy with the'); +disp('value of secondary turns so taking value of N2=18(next nearest integer)'); +N2=18; // new value of secondary turns +N1=18*(E1/E2); +printf('Number of primary turns is %f\n',N1); +printf('Number of secondary turns is %f\n',N2); +// calculating net core area +A=(220/(18*sqrt(2)*%pi*B*50))*10^4; // where N2=18 +printf('Net area of core is %f cm^2',A); diff --git a/3760/CH1/EX1.10/Ex1_10.sce b/3760/CH1/EX1.10/Ex1_10.sce new file mode 100644 index 000000000..2ab041e7c --- /dev/null +++ b/3760/CH1/EX1.10/Ex1_10.sce @@ -0,0 +1,33 @@ + +clc; +E1=250;// voltage on low tension side +E2=2500; // voltage on high tension side +k=E2/E1; //turns ratio +Z=380+230*%i; // given load connected to high tension side +Zl=Z/k^2; // load referred to low tension side +zl=0.2+0.7*%i; // leakage impedance of transformer +zt=Zl+zl; // total series impedance +ztm=abs(zt); // magnitude of total series impedance +I1=E1/zt; +I1m=abs(I1); // magnitude of primary load current +I2=I1m/k; // secondary load current +vt=5*abs(Z); +printf('secondary terminal voltage is %f V\n',vt); +R=500; // shunt branch resistance +X=250; // shunt branch leakage reactance +Ic=E1/R; // core less component of current +Im=E1/(%i*X); // magnetizing component of current +Ie=Ic+Im;// total exciting current +It=I1+Ie;// total current on low tension side +Itm=abs(It); +printf('primary current is %f A\n',Itm); +pf=cos(atan(imag(It),real(It))); +printf('power factor is %f lagging\n',pf), +lpf=real(Z)/abs(Z); +op=vt*I2*lpf; +printf('output power is %f W\n',op); +pc=Ic^2*R; // core less power +poh=I1m^2*real(zl); // ohmic losses +pin=E1*Itm*pf; // input power +n=(op/pin)*100; // efficiency +printf('efficiency of transformer is %f percent',n); diff --git a/3760/CH1/EX1.11/Ex1_11.sce b/3760/CH1/EX1.11/Ex1_11.sce new file mode 100644 index 000000000..7f7c5a7b9 --- /dev/null +++ b/3760/CH1/EX1.11/Ex1_11.sce @@ -0,0 +1,31 @@ +clc; +p=10000; // rated output of transformer +E1=2500; // primary side rated voltage +E2=250; // secondary side rated voltage +k=E2/E1; // turn's ratio +// initialising results of open circuit results on l.v side +Vo=250; //open circuit voltage +Io=1.4; // no load current +Po=105; // open circuit voltage +// initialising the results of short circuit results on h.v side +Vsc=104; // short circuit voltage +Isc=8; // short circuit current +Psc=320; // power dissipated +theta=Po/(Vo*Io); // no load power factor +Ic=Io*theta; // core less component of current +Im=Io*sqrt(1-theta^2); // magnetising component of current +Ro=round(Vo/Ic); // shunt branch resistance +Xo=round(Vo/Im); // shunt branch impedance +Zsc=Vsc/Isc; // short circuit impedance +reh=Psc/Isc^2; // total transformer resistance +xeh=sqrt(Zsc^2-reh^2); // total transformer leakage impedance +// equivalent circuit referred to l.v side +rel=reh*k^2; +xml=xeh*k^2; +printf('shunt branch resistance and reactance is %f ohm and %f ohm\n',Ro,Xo); +printf('value of transformer resistance and leakage reactance referred to l.v side is %f ohm and %f ohm\n',rel,xml); +// equivalent circuit referred to h.v side +Rch=Ro/k^2; +Xmh=Xo/k^2; +printf('shunt branch resistance and reactance referred to h.v side is %f ohm and %f ohm\n',Rch,Xmh); +printf('value of transformer resistance and leakage reactance referred to h.v side is %f ohm and %f ohm\n',reh,xeh); diff --git a/3760/CH1/EX1.12/Ex1_12.sce b/3760/CH1/EX1.12/Ex1_12.sce new file mode 100644 index 000000000..fdfb35e51 --- /dev/null +++ b/3760/CH1/EX1.12/Ex1_12.sce @@ -0,0 +1,28 @@ +clc; +P=200000; // rated power output of transformer +E1=11000; // primary side voltage +E2=400; // secondary side voltage +// initialising the results of the open circuit test performed on l v side +Vo=400; // open circuit voltage in V +Io=9; // no load current in A +Po=1500; // core loss in W +// initialising the results of short circuit test performed on h v side +Vsc=350; // voltage applied in short circuit test +Isc=P/(3*E1); // short circuit current +Psc=2100; // power dissipated in short circuit test +E2p=E2/sqrt(3); // per phase voltage +pop=Po/3; // per phase core loss +Ic=pop/E2p; // core loss current +Im=sqrt(Io^2-Ic^2); // magnetising component of current +R=E2p/Ic; // core loss resistance in ohm +X=E2p/Im; // magnetizing reactance +Rh=R*(E1/E2p)^2; // core loss resistance referred to h v side +Xh=floor(X*(E1/E2p)^2); // magnetizing component referred to h v side +printf('coreloss resistance and magnetizing reactance referred to h v side is %f ohm and %f ohm\n ',Rh,Xh); +Pscp=Psc/3; // ohmic loss per phase +Z=Vsc/Isc; // total impedance of transformer +Re=Pscp/Isc^2; // Total resistance of transformer refrred to high voltage side +Xe=sqrt(Z^2-Re^2); // total leakage impedance of transformer referred to h v side +printf('transformer resistance and leakage impedance referred to h v side are %f ohm and %f ohm\n',Re,Xe); +n=(1-(pop+Pscp/2^2)/(P/6+pop+Pscp/2^2))*100; // efficiency at half load +printf('efficiency at half load is %f percent',n); diff --git a/3760/CH1/EX1.14/Ex1_14.sce b/3760/CH1/EX1.14/Ex1_14.sce new file mode 100644 index 000000000..29d40e4b3 --- /dev/null +++ b/3760/CH1/EX1.14/Ex1_14.sce @@ -0,0 +1,27 @@ +clc; +p=20000; // rated power of transformer +vbh=2500; // base voltage in volts for h. v. side +vbl=250; // base voltage in volts for l. v. side +ibh=p/vbh; // base current in Ampere for h. v. side +zbh=vbh/ibh; // base impedance in ohm +ze=2.6+4.3*%i; // equivalent leakage impedance referred to h. v. side in ohm +zepu=ze/zbh; // per unit value in ohm +disp('Per unit value of equivalent leakage impedance referred to h. v. side is'); +disp(zepu); +k=vbl/vbh; // turn's ratio +zel=ze*k^2; // equivalent leakage impedance referred to l. v. side in ohm +ibl=p/vbl; // base current in Ampere for l. v. side +zbl=vbl/ibl; // base impedance for l. v. side +zelpu=zel/zbl; // per unit value in ohm +disp('Per unit value of equivalent leakage impedance referred to l. v. side is'); +disp(zelpu); +zepum=abs(zepu); // magnitude of per unit impedance +vhl=zepum*vbh; // total leakage impedace drop on h. v. side +vbl=zepum*vbl; // total leakage impedace drop on l. v. side +printf('Total leakage impedance drop on h. v. side and l. v. side are %f V and %f V respectively\n',vhl,vbl); +Ieh=4.8; // exciting current in Ampere +Iepu=Ieh/ibh; // p u value of exciting current referred to h. v. side +printf('Per unit value of exciting current referred to h. v. side is %f p.u. \n',Iepu); +Iel=Ieh/k; // exciting current referred to l. v. side +Ielpu=Iel/ibl; // p u value of exciting current referred to l. v. side +printf('Per unit value of exciting current referred to l. v. side is %f p.u. \n',Ielpu); diff --git a/3760/CH1/EX1.15/Ex1_15.sce b/3760/CH1/EX1.15/Ex1_15.sce new file mode 100644 index 000000000..c524c7a30 --- /dev/null +++ b/3760/CH1/EX1.15/Ex1_15.sce @@ -0,0 +1,27 @@ +clc; +P=10000; // rated power of transformer +vbh=2000; // base voltage for h v side in volts +ibh=P/vbh; // base current for h v side in Ampere +vbl=200; // base voltage for l v side in volts +ibl=P/vbl; // base current for l v side in Ampere +k=vbl/vbh; // turns ratio +r1=3.6; // resistance of h v side of transformer in ohm +x1=5.2; //leakage reactace h v side of transformer in ohm +z=vbh/ibh; // base impedance for h v side' +r1pu=r1/z; // p u value for resistance of h v side of transformer in ohm +x1pu=x1/z; // p u value for leakage reactance of h v side of transformer in ohm +r2=0.04; //resistance of l v side of transformer in ohm +x2=0.056; //leakage reactace l v side of transformer in ohm +// total resistance referred to h v side +re=r1+r2/k^2; +repu=re/z; +// total leakage impedance referred to h v side +xe=x1+x2/k^2; +xepu=xe/z; +printf('total per unit resistance and per unit leakage impedance referred to h v side are %f and %f\n',repu,xepu); +Z=vbl/ibl; // base impedance for l v side +Re=r2+r1*k^2; // total resistance referred to l v side +Repu=Re/Z; +Xe=x2+x1*k^2; //total leakage impedance referred to l v side +Xepu=Xe/Z; +printf('total per unit resistance and per unit leakage impedance referred to l v side are %f and %f ',Repu,Xepu); diff --git a/3760/CH1/EX1.16/Ex1_16.sce b/3760/CH1/EX1.16/Ex1_16.sce new file mode 100644 index 000000000..f7e463735 --- /dev/null +++ b/3760/CH1/EX1.16/Ex1_16.sce @@ -0,0 +1,30 @@ +clc; +P=200000; //rated power of transformer +E1=4000; // primary side rated voltage +E2=1000; // secondary side rated voltage +n=0.97; // efficiency +pfn=0.25; // power factor at no load +pff=0.8; // power factor at full load +vr=5; // percentage voltage regulation +Pl=((1/n)-1)*200000; // total losses at full load +Pf=Pl*0.6; // total losses at 60% of full load +Po=(Pl-Pf)/(1-0.36); // ohmic losses +Pc=Pl-Po; // core losses +re2=(Po/P)*100; // P U total resistance referred to l. v. side +xe2=(vr-re2*pff)/sqrt(1-pff^2); // P U total leakage reactance referred to l. v. side +re2=(re2*E2^2)/(100*P); // total resistance in ohms +disp('Total resistance referred to l. v. side is '); +printf('%f ohm',re2); +xe2=(xe2*E2^2)/(100*P); // total leakage reactance in ohms +disp('Total leakage reactance referred to l. v. side is '); +printf('%f ohm',xe2); +Rc=E2^2/Pc; +disp('Coreloss resistance is'); +printf('%f ohm',Rc); +Ie2=Pc/(E2*pfn); // exciting current in Ampere +Ic=Pc/E2; // core loss current +Im=sqrt(Ie2^2-Ic^2); // magnetizing component of exciting current +Xm=E2/Im; // magnetizing reactance +disp('Magnetizing reactance is '); +printf('%f ohm',Xm); +disp('All parameters are known. So, equivalent circuit diagram referred to l. v. side can be drawn.'); diff --git a/3760/CH1/EX1.18/Ex1_18.sce b/3760/CH1/EX1.18/Ex1_18.sce new file mode 100644 index 000000000..4dcbbda5d --- /dev/null +++ b/3760/CH1/EX1.18/Ex1_18.sce @@ -0,0 +1,26 @@ +clc; +P=20000; // rated power of transformer +E1=2500; // primary side voltage +E2=500; // secondary side voltage +r1=8; // primary resistance in ohm +x1=17; // primary leakage reactance in ohm +r2=0.3; // secondary resistance in ohm +x2=0.7; // secondary leakage reactane in ohm +k=E2/E1; // turns ratio +re2=r2+r1*k^2; // equivalent resistance referred to secondary winding +xe2=x2+x1*k^2; // equivalent leakage reactance referred to secondary winding +Il=P/E2; // full load secondary current +disp('case a'); +pf=0.8; // lagging power factor +vd=Il*(re2*pf+xe2*sqrt(1-pf^2)); // Voltage drop in impedance in volts +vt=E2-vd; // secondary terminal voltage +printf('secondary terminal voltage for a lagging power factor is %f v\n',vt); +vr=((E2-vt)/E2)*100; // voltage regulation +printf('voltage regulation for a lagging power factor is %f percent\n',vr); +disp('case b'); +pf=0.8; // leading power factor +vd=Il*(re2*pf-xe2*sqrt(1-pf^2)); // Voltage drop in impedance in volts +vt=E2-vd; // secondary terminal voltage +printf('secondary terminal voltage for a leading power factor is %f v\n',vt); +vr=((E2-vt)/E2)*100; // voltage regulation +printf('voltage regulation for a leading power factor is %f percent\n',vr); diff --git a/3760/CH1/EX1.19/Ex1_19.sce b/3760/CH1/EX1.19/Ex1_19.sce new file mode 100644 index 000000000..596f00942 --- /dev/null +++ b/3760/CH1/EX1.19/Ex1_19.sce @@ -0,0 +1,10 @@ +clc; +rpu=0.02; // P U equivalent resistance +xpu=0.05; // P U equivalent leakage reactance +E2=440; // Secondary full load voltage +pf=0.8; // lagging power factor +vr=rpu*pf+xpu*sqrt(1-pf^2); // P U voltage regulation +printf('Full load p.u. voltage regulation is %f or %f percent\n',vr,vr*100); +dv=E2*vr; // change in terminal voltage +V2=E2-dv; // secondary terminal voltage +printf('Secondary terminal voltage is %f V',V2); diff --git a/3760/CH1/EX1.2/Ex1_2.sce b/3760/CH1/EX1.2/Ex1_2.sce new file mode 100644 index 000000000..dce16da4e --- /dev/null +++ b/3760/CH1/EX1.2/Ex1_2.sce @@ -0,0 +1,15 @@ +clc; +f=50; // frequency in hertz +B=1.2; // maximum flux density in Tesla +A=75*10^-4; // net core area in m^2 +E1=220; // primary side voltage in volts +E2=600; // secondary side voltage in volts +E3=11; // tertiary side voltage in volts +n3=round(E3/2); // number of turns in half of the tertiary winding +Et=round(sqrt(2)*%pi*50*B*A); // calculating emf per turn +N3=Et*n3; // total number of turns in tertiary winding +printf('total number of turns in tertiary winding is %f\n',N3); +N2=round(E2*(n3/E3)); // total number of turns in secondary winding +printf('total number of turns in secondary winding is %f\n',N2); +N1=round(E1*(n3/E3)); // total number of turns in secondary winding +printf('total number of turns in primary winding is %f',N1); diff --git a/3760/CH1/EX1.20/Ex1_20.sce b/3760/CH1/EX1.20/Ex1_20.sce new file mode 100644 index 000000000..cb94ee7f0 --- /dev/null +++ b/3760/CH1/EX1.20/Ex1_20.sce @@ -0,0 +1,20 @@ +clc; +P=10000; // rated power of transformer in VA +E1=2000; // full load primary voltage +E2=400; // full load secondary voltage +k=E2/E1; // turns ratio +pf=0.8; // lagging power factor +// initialising results of short circuit test +v=60; // voltage applied for short circuit test +i=4; // short circuit current +p=100; // power dissipated in short circuit; +reh=p/i^2; // total resistance referred to h v side +zeh=v/i; // total impedance referred to h v side +xeh=sqrt(zeh^2-reh^2); // total leakage reactance referred to h v side +rel=reh*k^2; // resistance referred to l v side +xel=xeh*k^2; // reactance referred to l v side +i2l=P/E2; // full load secondary current +vr=i2l*(rel*pf+xel*sqrt(1-pf^2)); // voltage regulation +v2=E2+vr; // total voltage of secondary when transformer is operating on full load +v1=v2/k; // voltage applied to primary to deliver full load +printf('voltage applied to primary to deliver full load is %f v',v1); diff --git a/3760/CH1/EX1.21/Ex1_21.sce b/3760/CH1/EX1.21/Ex1_21.sce new file mode 100644 index 000000000..5f5ceb225 --- /dev/null +++ b/3760/CH1/EX1.21/Ex1_21.sce @@ -0,0 +1,29 @@ +clc; +zf=30+120*%i; // feeder impedance +E1=33000; // primary side voltage +E2=3300; // secondary side voltage +k=E2/E1; // turns ratio +P=100000; // load power +pf=0.8;// leading power factor of load +zl=0.3+1.4*%i; // leakage impedance referred to l v side +zfl=zf*k^2; // feeder impedance referred to l v side +vt=3300; // terminal voltage +il=P/(vt*pf); // load current +R=real(zfl)+real(zl); // total resistance referred to l v side +X=imag(zfl)+imag(zl); // total impedance referred to l v side +vfl=vt+il*(R*pf-X*sqrt(1-pf^2)); // voltage at the sending end of feeder referred to l v side +vf=vfl/k; // voltage at the sending end of feeder +printf('Voltage at the sending end of feeder is %f v\n',vf); +v2=vt+il*(real(zl)*pf-imag(zl)*sqrt(1-pf^2)); //voltage induced in secondary windings +v1=round(v2/k); +printf('voltage at the primary terminals of transformer is %f v\n',v1); +ap=il^2*R; +printf('active power loss is %f W\n',ap); +ar=il^2*X; +printf('reactive power loss is %f W\n',ar); +cp=P-P*%i*tan(acosd(pf)*(%pi/180)); // complex power at load end in VA +cps=cp+((ap+ar*%i) ); // complex power at feeder end in VA +pfs=cos(atan(imag(cps),real(cps))); +printf('power factor at the sending end is %f leading',pfs); + + diff --git a/3760/CH1/EX1.22/Ex1_22.sce b/3760/CH1/EX1.22/Ex1_22.sce new file mode 100644 index 000000000..58977276d --- /dev/null +++ b/3760/CH1/EX1.22/Ex1_22.sce @@ -0,0 +1,28 @@ +clc; +P=10000; // rated power of transformer +E1=2000; // primary side voltage +E2=200; // secondary side voltage +f=50; // frequency in hertz +po=125; // no load power +pfo=0.15; // no load power factor +zbh=E1^2/P; // base impedance on h v side +k=E2/E1; // turns ratio +zl=0.5+1*%i; // percent leakage impedance +zlh=zl*(zbh*k^2); // percent leakage impedance referred to h v side +Rc=E1^2/po; // coreloss resistance +Io=po/(E1*pfo); // No load current +Xm=E1/(Io*sqrt(1-pfo^2)); // magnetizing reactance +p=10000; // load power +pf=0.8; // power factor of load +il=p/(E2*pf); // secondary load current +ilp=il*k; // primary load current +vp=E1+ilp*(real(zlh)*pf+imag(zlh)*sqrt(1-pf^2)); +ap=ilp^2*real(zlh); // active power loss in series resistance +ar=ilp^2*imag(zlh); // reactive power loss in series reactance +Ap=vp^2/Rc; // active power loss in coreloss resistance +Ar=vp^2/Xm; // reactive power loss in magnetizing reactance +cpl=p*(1+%i*tan(acos(0.8))); // complex power at load end in VA +cpi=(real(cpl)+ap+Ap)+%i*(imag(cpl)+ar+Ar); // complex power input to transformer VA +printf('real power input to transformer is %f W\n',real(cpi)); +ipf=cos(atan(imag(cpi),real(cpi))); +printf('input power factor is %f lagging',ipf); diff --git a/3760/CH1/EX1.24/Ex1_24.sce b/3760/CH1/EX1.24/Ex1_24.sce new file mode 100644 index 000000000..9ada287e8 --- /dev/null +++ b/3760/CH1/EX1.24/Ex1_24.sce @@ -0,0 +1,18 @@ +clc; +pc1=52; // core loss at f=40 +f1=40; // frequency in hertz +pc2=90; // core loss at f=60 +f2=60; // frequency in hertz +f=[f1 f1^2;f2 f2^2]; +pc=[pc1;pc2]; +k=inv(f)*pc; +// proportionality constants for hysteresis and eddy current losses are +kh=k(1);disp(kh) // proportionality constants for hysteresis losses +ke=k(2);disp(ke) // proportionality constants for eddy current losses +// determining both losses at 50 hertz +f=50; +ph=kh*f; +printf('hysteresis losses at 50 hertz is %f W\n',ph); +pe=ke*f^2; +printf('eddy current losses at 50 hertz is %f W',pe); +// answer for eddy current losses is misprinted in book diff --git a/3760/CH1/EX1.25/Ex1_25.sce b/3760/CH1/EX1.25/Ex1_25.sce new file mode 100644 index 000000000..3db00e075 --- /dev/null +++ b/3760/CH1/EX1.25/Ex1_25.sce @@ -0,0 +1,15 @@ + +clc; +// subscripts 1 and 2 are used the quantities referred to 60 hz and 50 hz frequency respectively +v1=220; // rated voltage at 60 hz +f1=60; // operating frequency +ph1=340; // hysteresis loss at 60 hz +pe1=120; // eddy current loss at 60 hz +v2=230; // rated voltage at 50 hz +f2=50; // operating frequency +s=1.6; // Steinmetz's constant +B=(f1/f2)*(v2/v1); // ratio of flux densities Bm2/Bm1 +ph2=ceil(ph1*(50/60)*B^s); // hysteresis loss at 50 hz +pe2=pe1*(f2/f1)^2*(B)^2;// eddy current loss at 50 hz +pc=ph2+pe2; +printf('Total core loss at 50 hz is %f W',pc); diff --git a/3760/CH1/EX1.26/Ex1_26.sce b/3760/CH1/EX1.26/Ex1_26.sce new file mode 100644 index 000000000..957f6cb13 --- /dev/null +++ b/3760/CH1/EX1.26/Ex1_26.sce @@ -0,0 +1,22 @@ +clc; +// subscripts 1 and 2 are used to refer 50 hz and 60 hz quantity respectively +// voltage and current is same for both the cases +s=1.6; // Steinmetz's coefficient +poh1=1.6; // percentage ohmic losses +ph1=0.9; // percentage hysteresis losses +pe1=0.6; // percentage eddy current losses +f1=50; // frequency in hertz +f2=60; // frequency in hertz +B=f1/f2 // since voltage level are same for both cases ratio of flux densities i.e Bm2/Bm1=f1/f2 +ph2=ph1*(f2/f1)*B^s; // percentage hysteresis losses +pe2=pe1*(f2/f1)^2*B^2; // percentage eddy current losses +poh2=poh1; // since the voltage and current levels are same therefore ohmic losses are same +// for the total losses to be remain same at both the frequencies only ohmic losses can be varied +p=poh1+ph1+pe1; // total losses at 50 hz +pc=ph2+pe2; // total core losses at 60 hz +pnoh=p-pc; // permissible value for new ohmic losses +x=sqrt(pnoh/poh1); // factor by which output at 50 hz should be multiplied to get the same output at 60 hz +printf('ohmic losses at 60 hz is %f percent\n',poh2); +printf('hysteresis losses at 60 hz is %f percent\n',ph2); +printf('eddy current losses at 60 hz is %f percent\n',pe2); +printf('factor by which output at 50 hz should be multiplied to get the same output at 60 hz is %f ',x); diff --git a/3760/CH1/EX1.27/Ex1_27.sce b/3760/CH1/EX1.27/Ex1_27.sce new file mode 100644 index 000000000..c9332db01 --- /dev/null +++ b/3760/CH1/EX1.27/Ex1_27.sce @@ -0,0 +1,25 @@ +clc; +// subscripts 1 and 2 are used to indicate transformer of 11kv at 25hz and 22kv at 50 hz respectively +// for same current power is doubled therefore P2=2P1 +poh1=1.8; // ohmic losses as a percentage of total power P1 +ph1=0.8; // hysteresis losses as a percentage of total power P1 +pe1=0.3; // eddy current losses as a percentage of total power P1 +poh2=poh1/2; // ohmic losses do not change with frequency but changes with voltage since p1=2p1 we get the result shown +// since frequency also gets doubled whwn voltage levels double therefore there is no change in flux density i.e is Bm1=Bm2 +f1=25; // frequency in hertz +f2=50; // frequency in hertz +ph2=(f2/f1)*ph1; // hysteresis losses are directly proportional to frequency +pe2=(f2/f1)^2*pe1; // eddy current losses are directly proportional to frequency +// we know p2=2p1 +ph2p=ph2/2; // hysteresis losses as a percentage of total power P2 +pe2p=pe2/2; // eddy current losses as a percentage of total power P2 +printf('ohmic losses as a percentage of total power at 50 hz is %f percent\n',poh2); +printf('hysteresis losses as a percentage of total power at 50 hz is %f percent\n',ph2p); +printf('eddy current losses as a percentage of total power at 50 hz is %f percent\n',pe2p); +// efficiency at f1,v1 +n1=(1-((poh1+ph1+pe1)/100)/(1+((poh1+ph1+pe1)/100)))*100; +printf('efficiency at 25 hz is %f percent\n',n1); +// efficiency at f2,v2 +n2=(1-((poh2+ph2p+pe2p)/100)/(1+((poh2+ph2p+pe2p)/100)))*100; +printf('efficiency at 50 hz is %f percent',n2); + diff --git a/3760/CH1/EX1.28/Ex1_28.sce b/3760/CH1/EX1.28/Ex1_28.sce new file mode 100644 index 000000000..8202e42a4 --- /dev/null +++ b/3760/CH1/EX1.28/Ex1_28.sce @@ -0,0 +1,51 @@ +clc; +P=10000; // rated power of transformer in VA +E1=2500; // primary side voltage +E2=250; // secondary side voltage +pf=0.8; // power factor +//initialising the results of open circuit test +vo=250; // open circuit voltage +io=0.8; //no load current +po=50; // open circuit voltage +// initialising the results of open circuit test +vsc=60; // short circuit voltage +isc=3; // short circuit current +psc=45; // power dissipated in test +ifl=P/E1; // full load current on primary side +poh=psc*(ifl/isc)^2; // ohmic losses at full load current +disp('case a(1)'); +n=(1-(po+(poh/4^2))/(po+(poh/4^2)+(P*pf)/4))*100; // efficiency at 1/4 load +printf('efficiency at 1/4 load is %f percent\n',n); +disp('case a(2)'); +n=(1-(po+(poh/2^2))/(po+(poh/2^2)+(P*pf)/2))*100; // efficiency at 1/2 load +printf('efficiency at 1/2 load is %f percent\n',n); +disp('case a(3)'); +n=(1-(po+(poh/1^2))/(po+(poh/1^2)+(P*pf)/1))*100; // efficiency at full load +printf('efficiency at full load is %f percent\n',n); +disp('case a(4)'); +n=(1-(po+((poh*5^2)/4^2))/(po+((poh*5^2)/4^2)+(P*pf*5)/4))*100; // efficiency at 1*1/4 load +printf('efficiency at 5/4 load is %f percent\n',n); +// let maximum efficiency occurs at x times the rated KVA +// maximum efficiency occurs when core loss becomes equal to ohmic losses +x=sqrt(po/poh); +nm=(x*P)/1000; // VA output at maximum +nmax=(1-(2*po)/(nm*1000*pf+2*po))*100; +printf('KVA load at which maximum efficiency occurs is %f KVA\n',nm); +printf('Maximum efficiency is %f percent\n',nmax); +// from short circuit test +reh=psc/isc^2; // total resistance referred to h v side +zeh=vsc/isc; // total impedance referred to h v side +xeh=sqrt(zeh^2-reh^2); // total leakage reactance referred to h v side +er=(ifl*reh)/E1; //p u resistance +ex=(ifl*xeh)/E1; // p u reactance +vr=(er*pf+ex*sqrt(1-pf^2))*100; // p u voltage regulation +printf(' p u voltage regulation for lagging power factor is %f percent\n',vr); +dv=E2*(vr/100); // voltage drop in series impedance +v2=E2-dv; +printf('secondary terminal voltage for lagging power factor of 0.8 is %f v\n',v2); +// voltaage regulation for leading power factor +vr=(er*pf-ex*sqrt(1-pf^2))*100; // p u voltage regulation +printf(' p u voltage regulation for leading power factor is %f percent\n',vr); +dv=E2*(vr/100); // voltage drop in series impedance +v2=E2-dv; +printf('secondary terminal voltage for leading power factor of 0.8 is %f v\n',v2); diff --git a/3760/CH1/EX1.29/Ex1_29.sce b/3760/CH1/EX1.29/Ex1_29.sce new file mode 100644 index 000000000..44da56614 --- /dev/null +++ b/3760/CH1/EX1.29/Ex1_29.sce @@ -0,0 +1,11 @@ +clc; +p=20000; // rated capacity of transformer +n=0.98; // efficiency of transformer at full load and half load +c=[ 1 1; 1 1/4]; +o=[ ((1/n)-1)*p; ((1/n)-1)*(p/2)]; +l=inv(c)*o; +printf('Core losses are %f W\n',l(1)); +printf('Ohmic losses are %f W\n',l(2)); +re=l(2)/p; +printf('p.u. value of equivalent resistance is %f ',re); + diff --git a/3760/CH1/EX1.3/Ex1_3.sce b/3760/CH1/EX1.3/Ex1_3.sce new file mode 100644 index 000000000..f3d33b98e --- /dev/null +++ b/3760/CH1/EX1.3/Ex1_3.sce @@ -0,0 +1,19 @@ +clc; +f=50; // frequency in hertz +E1=2200; // supply voltage in volts +E2=220; // secondary side voltage in volts +P=361; // core loss in watts +Io=0.6; // exciting current in Ampere +Is=60; // secondary load current in Ampere +pf=0.8; // power factor +Ic=P/E1; // core loss component of current +printf('core loss component of exciting current is %f A\n',Ic); +Im=sqrt(Io^2-Ic^2); // magnetising component of current +printf('magnetising component of exciting current is %f A\n',Im); +ip=Is*(E2/E1); // primary current required to neutralise the secondary current +Iv=ip*pf+Ic; // total vertical compartment of primary current +Ih=ip*0.6+Im; // total horizontal compartment of primary current,pf cos(theta)=0.8 so sin(theta)=0.6 +Ip=sqrt(Iv^2+Ih^2); // toatl primary current +printf('Total primary current is %f A\n',Ip); +ppf=Iv/Ip; // primary power factor +printf('primary power factor is %f (lagging)',ppf); diff --git a/3760/CH1/EX1.30/Ex1_30.sce b/3760/CH1/EX1.30/Ex1_30.sce new file mode 100644 index 000000000..4dccd83b3 --- /dev/null +++ b/3760/CH1/EX1.30/Ex1_30.sce @@ -0,0 +1,15 @@ +clc; +P=100000; // VA of transformer +nmax=0.98; // maximum efficiency of transformer +pf=0.8; // power factor at which maximum efficiency occurs +l=80; // percentage of full load at which maximum efficiency occurs +po=P*pf*(l/100); // output at maximum efficiency +pl=((1/nmax)-1)*po; // total losses +pc=pl/2; // core loss +poh=pc; // at maximum efficiency variable losses are equal to constant losses +pohl=poh*(100/l)^2; // ohmic losses at full load +z=0.05; // p u leakage impedance +r=pohl/P; // p u resistance +x=sqrt(z^2-r^2); // p u leakage reactance +vr=(r*pf+x*sqrt(1-pf^2))*100; // voltage regulation +printf('Voltage regulation at 0.8 p.f. lagging is %f percent ',vr); diff --git a/3760/CH1/EX1.31/Ex1_31.sce b/3760/CH1/EX1.31/Ex1_31.sce new file mode 100644 index 000000000..b62b64521 --- /dev/null +++ b/3760/CH1/EX1.31/Ex1_31.sce @@ -0,0 +1,11 @@ +clc; +vdr=2; // percentage full load voltage drop in resistance +vdx=4; // percentage full load voltage drop in leakage reactance +// full load ohmic losses are equal to 0.02*VA rating of transformer which is equal to iron losses +n=100/(1+(vdr/100)+(vdr/100)); +printf('Efficiency on full load at unity p.f is %f percent\n',n); +// maximum voltage drop means voltage regulation is also maximum +pf=vdr/sqrt(vdr^2+vdx^2); +printf('Full load power factor at which voltage regulation is maximum is %f lagging\n',pf); +pf=vdx/sqrt(vdr^2+vdx^2); +printf(' load power factor at which voltage regulation is zero is %f leading',pf); diff --git a/3760/CH1/EX1.32/Ex1_32.sce b/3760/CH1/EX1.32/Ex1_32.sce new file mode 100644 index 000000000..4d63fa1b6 --- /dev/null +++ b/3760/CH1/EX1.32/Ex1_32.sce @@ -0,0 +1,28 @@ +clc; +P=20000; // rated VA of transformer +E1=3300; // rated voltage of primary +E2=220; // rated voltage of secondary +v2=220; // voltage at which load is getting delivered +p=14960; // load power in Watts +pf=0.8; // power factor at on load +pc=160; // core loss +pfo=0.15; // power factor at no load +il=p/(v2*pf); // load current +is=P/E2; // rated current of secondary +vr=1 ; // percentage voltage drop of rated voltage in total resistance +vx=3 ; // percentage voltage drop of rated voltage in total leakage reactance +re2=(E2*vr)/(is*100); // total resistance referred to secondary +xe2=(E2*vx)/(is*100); // total leakage reactance referred to secondary +poh=il^2*re2; // ohmic losses +pi=poh+pc+p; // total input power +// E2 as a reference +i2=il*(pf-%i*sqrt(1-pf^2)); +E2n=v2+i2*(re2+%i*xe2); // secondary winding voltage +io=pc/(pfo*E2); // no load current +ic=pc/E2; // core loss current +im=sqrt(io^2-ic^2); // magnetizing current +I=i2+(ic-im*%i); // total input current, negative sign before im indicates that it lags behind E2 by 90 degree +pfi=cos(atan(imag(I),real(I))); // input power factor +printf('Total input power is %f W \n',pi); +printf('Input power factor is %f lagging',pfi); + diff --git a/3760/CH1/EX1.33/Ex1_33.sce b/3760/CH1/EX1.33/Ex1_33.sce new file mode 100644 index 000000000..4be6cb6f6 --- /dev/null +++ b/3760/CH1/EX1.33/Ex1_33.sce @@ -0,0 +1,19 @@ +clc; +P=500000; // VA rating of transformer +E2=400; // rated secondary voltage +nmax=0.98; // maximum efficiency of transformer +l=80; // percentage of full load at which maximum efficiency occurs +ze2=4.5; // percentage impedance +pt=((1/nmax)-1)*P*(l/100); // total losses +pc=pt/2; // core loss = ohmic loss at maximum efficiency +poh=pc; // ohmic loss +pohl=poh*(100/l)^2; // full load ohmic losses +re2=(pohl/P)*100; // percentage resistance +xe2=sqrt(ze2^2-re2^2); // percentage leakage reactance +pfl=re2/ze2; // load power factor +vr=re2*pfl+xe2*sqrt(1-pfl^2); // voltage regulation +dv=(E2*vr)/100; // change in terminal voltage +V2=E2-dv; // Secondary terminal voltage +printf('Load power factor at which secondary terminal voltage is minimum is %f\n',pfl); +printf('Secondary terminal voltage is %f v',V2); +// answer for total losses is given wrong in the book diff --git a/3760/CH1/EX1.34/Ex1_34.sce b/3760/CH1/EX1.34/Ex1_34.sce new file mode 100644 index 000000000..0961f106a --- /dev/null +++ b/3760/CH1/EX1.34/Ex1_34.sce @@ -0,0 +1,26 @@ +clc; +P=5000; // rated VA of transformer +pc=40; // core loss , it remains fixed for whole day +poh=100; // ohmic losses +// data for duration 7 A.M to 1 P.M +p1=3000; // power consumed +pf1=0.6 // power factor of load +pk1=p1/pf1; // VA load +poh1=poh*(pk1/P)^2; // ohmic losses for given duration +// data for duration 1 P.M to 6 P.M +p2=2000; // power consumed +pf2=0.8 // power factor of load +pk2=p2/pf2; // VA load +poh2=poh*(pk2/P)^2; // ohmic losses for given duration +// data for duration 6 P.M to 1 A.M +p3=6000; // power consumed +pf3=0.9 // power factor of load +pk3=p3/pf3; // VA load +poh3=poh*(pk3/P)^2; // ohmic losses for given duration +// data for duration 1 A.M to 7 A.m =no load +poht=poh1*6+poh2*5+poh3*7; // energy lost in ohmic losses +pct=(pc*24); // daily energy lost as core loss +ptl=poht+pct; // total energy lost +po=p1*6+p2*5+p3*7; // output +n=(1-(ptl/(ptl+po)))*100; +printf('All day efficiency is %f percent',n); diff --git a/3760/CH1/EX1.35/Ex1_35.sce b/3760/CH1/EX1.35/Ex1_35.sce new file mode 100644 index 000000000..c2f4cf451 --- /dev/null +++ b/3760/CH1/EX1.35/Ex1_35.sce @@ -0,0 +1,46 @@ +clc; + +//V/f ratio is same for every case hence hysteresis losses and eddy current losses can be calculated separately +// data for column 1 +vt1=214; // terminal voltage +f1=50; // frequency in hz +p1=100; // power input in Watts +vp1=vt1; // per phase voltage +pv1=p1/3; // per phase power +pc1=pv1/f1; // core loss per cycle +// data for column 2 +vt2=171; // terminal voltage +f2=40; // frequency in hz +p2=72.5; // power input in Watts +vp2=vt2; // per phase voltage +pv2=p2/3; // per phase power +pc2=pv2/f2; // core loss per cycle +// data for column 3 +vt3=128; // terminal voltage +f3=30; // frequency in hz +p3=50; // power input in Watts +vp3=vt3; // per phase voltage +pv3=p3/3; // per phase power +pc3=pv3/f3; // core loss per cycle +// data for column 4 +vt4=85.6; // terminal voltage +f4=20; // frequency in hz +p4=30; // power input in Watts +vp4=vt4; // per phase voltage +pv4=p4/3; // per phase power +pc4=pv4/f4; // core loss per cycle +// Values of k1 and k2 have been obtained from graph +k1=0.39; +k2=(pc1-k1)/50; +F1=60; //frequency at which losses has to be calculated +ph1=k1*F1; //per phase hysteresis loss at 60 hz +pe1=k2*F1^2; // per phase eddy curent loss at 60 hz +pht=3*ph1; // total hysteresis loss +pet=3*pe1; // total eddy current loss +printf('Total hysteresis and eddy current losses at 60 hz are %f W and %f W respectively\n',pht,pet); +F2=40; //frequency at which losses has to be calculated +ph2=k1*F2; //per phase hysteresis loss at 40 hz +pe2=k2*F2^2; // per phase eddy curent loss at 40 hz +pht=3*ph2; // total hysteresis loss +pet=3*pe2; // total eddy current loss +printf('Total hysteresis and eddy current losses at 40 hz are %f W and %f W respectively',pht,pet); diff --git a/3760/CH1/EX1.36/Ex1_36.sce b/3760/CH1/EX1.36/Ex1_36.sce new file mode 100644 index 000000000..ad13631ce --- /dev/null +++ b/3760/CH1/EX1.36/Ex1_36.sce @@ -0,0 +1,23 @@ +clc; +E1=230; // primary rating of transformer 1 and transformer 2 +E2=400; // secondary rating of transformer 1 +e2=410; // secondary rating of transformer 2 +iv=25; // current feeded by voltage regulator to h v series winding +pc=200; // core loss in each transformer +r=1 // assuming resistance of transformer to be 1 +x=3*r // as per question leakage reactance is thrice of resistance +il1=(iv*E2)/E1; // primary current of transformer 1 +il2=(iv*e2)/E1; // primary current of transformer 2 +pf=r/sqrt(r^2+x^2); // power factor during short circuit +// As per the circuit diagram given in question, by Kirchoffs current law current through current coil of wattmeter W1 is given by +I=il2-il1; +// 2*core loss is the reading of wattmeter 2 +W=E1*I*pf; // reading of wattmeter 1 connected on l v side +// in circuit diagram if terminal a is connected to c and terminal b is connected to d the current I and Io (no load current) flow in the same direction of current coil of Wattmeter.Hence its reading is increased to +Wt=2*pc+W; +printf('reading of wattmeter as per the connection described is %f W\n',Wt); +// in circuit diagram if terminal c is connected to b and terminal d is connected to a the current I and Io (no load current) flow in the opposite direction through current coil of Wattmeter.Hence its reading is decreased to +Wt=2*pc-W; +printf('reading of wattmeter as per the connection described is %f W',Wt); + + diff --git a/3760/CH1/EX1.37/Ex1_37.sce b/3760/CH1/EX1.37/Ex1_37.sce new file mode 100644 index 000000000..9ed4f1f8e --- /dev/null +++ b/3760/CH1/EX1.37/Ex1_37.sce @@ -0,0 +1,12 @@ +clc; +E1=3300; // rated phase voltage of primary of a three phase transformer +v=360; // voltage injected in open delta h v winding to circulate full load current +vph=v/3; // voltage across each phase +P=300; // rated KVA of transformer +Pph=P/3; // KVA per phase +Iph=(Pph*1000)/E1; // per phase current +z=vph/Iph; +printf('Per Phase leakage impedance is %f ohms\n',z); +zb=E1/Iph; // base impedance +zpu=z/zb; +printf('leakage impedance per phase in per unit system is %f p.u',zpu); diff --git a/3760/CH1/EX1.38/Ex1_38.sce b/3760/CH1/EX1.38/Ex1_38.sce new file mode 100644 index 000000000..5df7964e5 --- /dev/null +++ b/3760/CH1/EX1.38/Ex1_38.sce @@ -0,0 +1,40 @@ +clc; +P=20000; // rated VA of transformer +E1=2300; // rated voltage of primary +E2=230; // rated voltage of secondary +pf=0.6; // power factor +n=0.96; // efficiency +ih=P/E1; // rated current of h v winding +il=P/E2; // rated current of l v winding +// As per the connections given in fig 14.1(a), two voltages are in series aiding +Et=E1+E2; // output voltage of autotransformer +disp('case a'); +// By Kirchoffs law at point b , supply current is given by +I=il+ih; +Pa1=Et*il; // VA rating of autotransformer +Po1=(Pa1/1000); // power output at full load unity power factor +Pt1=(E2*il)/1000; // power transformed +Pc1=(Po1-Pt1); // power conducted +printf('For the given connection, output power is %f kW\n',Po1); +printf('For the given connection, transformed power is %f kW\n',Pt1); +printf('For the given connection, conducted power is %f kW\n',Pc1); +disp('case b'); +// As per the connections given in fig 14.1(b), two voltages are in series opposition +Et=E1-E2; // output voltage of autotransformer +// By Kirchoffs law at point b , supply current is given by +I=il-ih; +Pa2=E1*I; // VA rating of autotransformer +Po2=Pa2/1000; // power output at full load unity power factor +Pt2=(E2*il)/1000; // power transformed +Pc2=(Po2-Pt2); // power conducted +printf('For the given connection, output power is %f kW\n',Po2); +printf('For the given connection, transformed power is %f kW\n',Pt2); +printf('For the given connection, conducted power is %f kW\n',Pc2); +pl=((1/n)-1)*P*pf; // losses in 2-winding transformer +// autotransformer operates at rated current and rated voltage so efficiency and losses remain constant +disp('Efficiency for case a'); +n1=(1-(pl/(Po1*1000*pf+pl)))*100; +printf('Efficiency of autotransformer for %f VA is %f percent\n',Po1,n1); +disp('Efficiency for case b'); +n2=(1-(pl/(Po2*1000*pf+pl)))*100; +printf('Efficiency of autotransformer for %f VA is %f percent',Po2,n2); diff --git a/3760/CH1/EX1.39/Ex1_39.sce b/3760/CH1/EX1.39/Ex1_39.sce new file mode 100644 index 000000000..a1e4ee69e --- /dev/null +++ b/3760/CH1/EX1.39/Ex1_39.sce @@ -0,0 +1,14 @@ +clc; +// connections have been made in fig 1.42 in book to suit voltage requirement of 3000V, 3500V and 1000V. +E1=1000; // primary winding of transformer +E2=2000; // secondary winding of transformer +E3=500; // tertiary winding of transformer +l1=1050; // load in KVA across 3500 V +l2=180; // load in KVA across 1000 V +i1=(l1*1000)/(E1+E2+E3); // current through load of 1050 KVA +i2=(l2*1000)/(E1); // current through load of 180 KVA +kt=l1+l2; // Total KVA load supplied +I=(kt*1000)/(E1+E2); +printf('current through %f KVA load is %f A\n',l1,i1); +printf('current through %f KVA load is %f A\n',l2,i2); +printf('current drawn from supply is %f A',I); diff --git a/3760/CH1/EX1.4/Ex1_4.sce b/3760/CH1/EX1.4/Ex1_4.sce new file mode 100644 index 000000000..e4dfeb90b --- /dev/null +++ b/3760/CH1/EX1.4/Ex1_4.sce @@ -0,0 +1,13 @@ +clc; +disp('weight of laminations is directly proportion to core volume density, which is directly proportional to product of area and height of limbs and while taking the ratio of weight of CRGO laminations and hot rolled laminations, height of limbs gets cancelled out(height of limbs are assumed to be equal). So, in the end ratio of weights of laminations is equal to ratio of area of core.Now area of core is given by maximum flux/flux density.According to question maximum flux remain same so ,while taking ratio of areas the maximum flux gets cancelled') +B1=1.2; //flux density in hot rolled steel laminations +B2=1.6; //flux density in CRGO steel laminations +W1=100; // weight of H.R core in kg +W2=W1*(B1/B2); // calculating weight of CRGO laminations in kg +s=((W1-W2)/W1)*100; // calculating saving in core material +printf('percentage saving in core material is %f percent\n',s); +disp('weight of wire is directly proportional to product of length of turn around core and cross section of wire.(Wire cross section is assumed to be same in CRGO and HR laminations so gets cancelled out while taking ratio) also the length of turn is inversely proportional to square root of flux density ') +w1= 80 // weight of Hot rolled wire +w2=w1*(sqrt(1.2/1.6)); // weight of CRGO wire +s=((w1-w2)/w1)*100; //saving in weight of wire +printf('Percentage saving in weight of wire is %f percent',s); diff --git a/3760/CH1/EX1.40/Ex1_40.sce b/3760/CH1/EX1.40/Ex1_40.sce new file mode 100644 index 000000000..4a5976531 --- /dev/null +++ b/3760/CH1/EX1.40/Ex1_40.sce @@ -0,0 +1,17 @@ +clc; +E1=2500; // primary side voltage +E2=250; // secondary side voltage +P=10000; // rated VA of transformer +// to achieve a voltage level of 2625, two equal parts of 125 V each of secondary winding are connected in parallel with each other and in series with primary winding +Eo=E1+E2/2; // desired output of autotransformer +il=P/E2; // rated current of l v winding +i=2*il; // Total output current +K=(i*Eo)/1000; // Auto transsformer KVA rating +ip=P/E1; // rated current of h v winding +I=i+ip; // current drawn from supply +Pt=(i*(E2/2))/1000; // KVA transformed +Pc=K-Pt; // KVA conducted +printf('KVA output of autotransformer is %f KVA\n',K); +printf('KVA transformed is %f KVA\n',Pt); +printf('KVA conducted is %f KVA',Pc); + diff --git a/3760/CH1/EX1.41/Ex1_41.sce b/3760/CH1/EX1.41/Ex1_41.sce new file mode 100644 index 000000000..e9499c8cf --- /dev/null +++ b/3760/CH1/EX1.41/Ex1_41.sce @@ -0,0 +1,12 @@ +clc; +E1=440; // primary supply voltage +E2=380; // voltage at which load at secondary terminal is being supplied +l1=40000; // power rating of load in watts +pf=0.8; // lagging power factor +I2=l1/(sqrt(3)*E2*pf); +// per phase KVA input=per phase KVA output +I1=(E2/E1)*I2; +In=I2-I1; +printf('Current in primary branch is %f A\n',I1); +printf('current in secondary branch is %f A\n',I2); +printf('current between neutral and tapping points is %f A',In); diff --git a/3760/CH1/EX1.42/Ex1_42.sce b/3760/CH1/EX1.42/Ex1_42.sce new file mode 100644 index 000000000..726360d18 --- /dev/null +++ b/3760/CH1/EX1.42/Ex1_42.sce @@ -0,0 +1,20 @@ +clc; +// From fig 1.45 +N1=1000; // no of turns on primary +N2=400; // no. of turns on secondary +n2=300; // no. of turns across points A and B +l1=600; // a load of 600 KW connected between points A and C +l2=60+60*%i; // load connected between points A and B +E=30000; // primary supply voltage +vac=E*(N2/N1); // secondary side voltage +I1=(l1*1000)/vac; // current through load of 600 KW +vab=(vac/N2)*n2; // volatge across pints A and B +I2=vab/l2 ; // load current through load of 60+60i +iba=I1+I2; // current through section Ab of winding +mfs=iba*n2+I1*(N2-n2); // seconadry mmf +ip=mfs/N1; +printf('primary current is %f%fi A\n',real(ip),imag(ip)); +Pi=(E*abs(ip)*cos(atan(imag(ip),real(ip))))/1000; +printf('primary power input is %f KW\n',Pi); +pf=cos(atan(imag(ip),real(ip))) +printf('power factor at primary terminal is %f lagging',pf) diff --git a/3760/CH1/EX1.43/Ex1_43.sce b/3760/CH1/EX1.43/Ex1_43.sce new file mode 100644 index 000000000..7effd027a --- /dev/null +++ b/3760/CH1/EX1.43/Ex1_43.sce @@ -0,0 +1,27 @@ +clc; +E=400; // supply voltage +l1=200; // load connected across 75% tapping +l2=400; // load connected between 25% and 100% tapping +t1=25; // 25% tapping point +t2=50; // 50% tapping point +t3=75; // 75% tapping point +V2=(t3/100)*E; // voltage across 200 ohm load +I2=V2/l1; // current through 200 ohm load +I1=(V2*I2)/E; +// from fig.(1.46 b), KCL at point d gives +idb=I2-I1; +// same secondary voltage is applied against load of 400 ohm +I2=V2/l2; // current through 400 ohm load +I1=(V2*I2')/E; +// from fig (1.46 c), KCL at point c gives +ica=I2-I1; +// superimposing the currents of above results current in three portion of winding can be known +icd=ica; +disp('current in section cd of winding is') +printf('%f A\n',icd); +ibc=I1; +disp('current in section bc of winding is') +printf('%f A\n',ibc); +iab=idb+I1; +disp('current in section ab of winding is') +printf('%f A\n',iab); diff --git a/3760/CH1/EX1.44/Ex1_44.sce b/3760/CH1/EX1.44/Ex1_44.sce new file mode 100644 index 000000000..7d3c13848 --- /dev/null +++ b/3760/CH1/EX1.44/Ex1_44.sce @@ -0,0 +1,31 @@ +clc; +P=100000; // VA rating of two winding transformer +E1=2000; // rated voltage of h v side +E2=200; // rated voltage of l v side +l=2.5; // percentage of loss in two winding transformer +vr=3; // percentage of voltage regulation in two winding transformer +z=4; // percentage of leakage impedance in two winding transformer +ih=P/E1; // full load current of h v side +il=P/E2; // full load current of l v side +V1=E1; // rated voltage on l v side of autotransformer +V2=E1+E2; // rated voltage on h v side of autotransformer +Il=il+ih; // rated current on l v side of autotransformer +printf('Rated voltage on l v and h v side of autotransformer are %f v and %f v respectively\n,',V1,V2); +printf('Rated current on h v and l v side of autotransformer are %f A and %f A respectively\n,',il,Il); +k=E1/V2; // turns ratio for auto transformer +K=((1/(1-k))*P)/1000; +printf('Rated KVA of autotransformer is %f KVA\n',K); +pl=(1-k)*l; //percent full load losses in autotransformer +n=100-pl; +printf('Efficiency of auto transformer is %f percent\n',n); +Z=(1-k)*z; +printf('Percentage impedance as an auto transformer is %f \n',Z); +VR=(1-k)*vr; +printf('percentage voltage regulation as an auto transformer is %f \n',VR); +Is=(1/(1-k))*(100/z); // short circuit p u current +Ish=(Is*il)/1000; +printf('Short circuit of auto transformer on h v side is %f KA \n',Ish); +Isl=(Is*Il)/1000; +printf('Short circuit of auto transformer on l v side is %f KA \n',Isl); + + diff --git a/3760/CH1/EX1.45/Ex1_45.sce b/3760/CH1/EX1.45/Ex1_45.sce new file mode 100644 index 000000000..3b79bf8dc --- /dev/null +++ b/3760/CH1/EX1.45/Ex1_45.sce @@ -0,0 +1,22 @@ +clc; +v1=10; // voltage applied to primary when secondary is short circuited +ip=60; // primary current when secondary is short circuited +k=0.8; // turns ratio +E1=250; // input voltage for load voltage has to be calculated +E2=200; // rated voltage of secondary +il=100; // load current +pfo=0.24; // power factor during short circuit test +f=(1-k)^2/k^2; // factor by which secondary impedance has to be multiplied for referring it to primary +// ze1=z1+f*z2 therefore by ohm s law +ze1=v1/ip; // total impedance referred to primary +re1=ze1*pfo; // total resistance referred to primary +xe1=ze1*sqrt(1-pfo^2); // total leakage reactance referred to primary +disp('case a'); +pf=0.8; // lagging power factor of load +Ip=(E2*il)/E1; // current in primary due to load current +v2=(E1-Ip*(re1*pf+xe1*sqrt(1-pf^2)))*k; +printf('Secondary terminal voltage at %f lagging power factor is %f v\n',pf,v2); +disp('case b') +pf=1; // unity power factor +v2=(E1-Ip*(re1*pf+xe1*sqrt(1-pf^2)))*k; +printf('Secondary terminal voltage at unity power factor is %f v',v2); diff --git a/3760/CH1/EX1.46/Ex1_46.sce b/3760/CH1/EX1.46/Ex1_46.sce new file mode 100644 index 000000000..a68bd686a --- /dev/null +++ b/3760/CH1/EX1.46/Ex1_46.sce @@ -0,0 +1,8 @@ +clc; +r1=9 ; // ratio of reactance to resistance for transformer 1 +r2=3 ; // ratio of reactance to resistance for transformer 2 +d=atand(r1)-atand(r2); // differene between angles of transformer's leakage impedance +// leakage impedance of both transformers are equal z1=z2, threefore currents in both transformers are equal that is i1=i2; +I=1/cos((d/2)*(%pi/180)); // ratio of numerical sum of i1 and i2 to phasor sum of i1 and i2 +k=cos((d/2)*(%pi/180)); +printf('ratio of full load KVA delivered to sum of both transformers KVA ratings is %f',k); diff --git a/3760/CH1/EX1.48/Ex1_48.sce b/3760/CH1/EX1.48/Ex1_48.sce new file mode 100644 index 000000000..f0b27a94f --- /dev/null +++ b/3760/CH1/EX1.48/Ex1_48.sce @@ -0,0 +1,18 @@ +clc; +P=400000; // rated KVA of transformer +P1=11000; // rated primary voltage +S2=6600; // rated secondary voltage +v1=360; // voltage recorded during short circuit of l v winding for first transformer +p1=3025; // power dissipated during short circuit of l v winding for first transformer +v2=400; // voltage recorded during short circuit of l v winding for second transformer +p2=3200; // power dissipated during short circuit of l v winding for second transformer +v3=480; // voltage recorded during short circuit test of l v winding third transformer +p3=3250; // power dissipated during short circuit of l v winding for third transformer +l1=(P+(v1/v2)*P+(v1/v3)*P)/1000; +printf('The greatest load that can be put on the transformers is %f KVA\n',l1); +is=P/S2; // secondary rated current +// transformer 1 is fully loaded , its carries full load current +re2=p1/is^2; // total resistance referred to secondary side +vd=is*re2; // voltage drop for transformer 1 +E2=S2-vd; +printf('Secondary terminal voltage is %f v',E2); diff --git a/3760/CH1/EX1.49/Ex1_49.sce b/3760/CH1/EX1.49/Ex1_49.sce new file mode 100644 index 000000000..8cc6265de --- /dev/null +++ b/3760/CH1/EX1.49/Ex1_49.sce @@ -0,0 +1,32 @@ +clc; +disp('case b'); +// KVA ratings and leakage impedances for the transformers are +k1=100; // KVA rating for transformer 1; +z1=0.02; // p u impedance for transformer 1; +k2=75; // KVA rating for transformer 2; +z2=0.03; // p u impedance for transformer 2; +k3=50; // KVA rating for transformer 3; +z3=0.025; // p u impedance for transformer 3; +disp('case b(1)'); +// assumng k1 as a base KVA +S=225; // load which has to be shared by three transformers +ze1=z1*100; // percentage impedance for transformer 1 +ze2=(k1/k2)*z2*100; // percentage impedance for transformer 2 +ze3=(k1/k3)*z3*100; // percentage impedance for transformer 3 +zt=(1/ze1)+(1/ze2)+1/(ze3); // total percentage leakage impedance +s1=S/(ze1*zt); +s2=S/(ze2*zt); +s3=S/(ze3*zt); +printf('load shared by transformer 1,2 and 3 are %f KVA, %f KVA and %f KVA respectively\n',s1,s2,s3); +disp('case b(2)'); +// since transformer 1 has lowest leakage impedance among three, it will be loaded to its rated capacity +S=k1*ze1*zt ; // total KVA shared +printf('greatest load that can be shared by transformers is %f KVA\n',S); +disp('case b(3)'); +// for successful parallel operation of transformer all the three leakage impedances based on their KVA rating should be equal.Since magnitude of leakage impedance of transformer1 is fixed that is 2 percent z2=z3=2 percent +ze1=2; +ze2=ze1*(k1/k2); +ze3=ze1*(k1/k3); +zt=(1/ze1)+(1/ze2)+(1/ze3); // Total leakage impedance +printf('magnitude of equivalent leakage impedance is %f percent\n',zt); + diff --git a/3760/CH1/EX1.5/Ex1_5.sce b/3760/CH1/EX1.5/Ex1_5.sce new file mode 100644 index 000000000..919be6efe --- /dev/null +++ b/3760/CH1/EX1.5/Ex1_5.sce @@ -0,0 +1,40 @@ +clc; +v1=240; // high voltage side voltage +v2=120; // low voltage side voltage +f1=50; // frequency in Hz +disp('v1 is directly proportional to product of frequency and maximum flux. considering q1 be maximum flux for v1 and q2 be maximum flux for v11 then Q=q2/q1 can be calculated as follow ') +disp('case a') +v11=240; // new supply voltage +f2=40; // new supply frequency +Q=(v11*f1)/(v1*f2); +v22=(v2*f2*Q)/f1; +printf('secondary voltage for case a is %f v\n',v22); +disp('case b') +v11=120; // new supply voltage +f2=25; // new supply frequency +Q=(v11*f1)/(v1*f2); +v22=(v2*f2*Q)/f1; +printf('secondary voltage for case a is %f v\n',v22); +disp('case c') +v11=120; // new supply voltage +f2=50; // new supply frequency +Q=(v11*f1)/(v1*f2); +v22=(v2*f2*Q)/f1; +printf('secondary voltage for case a is %f v\n',v22); +disp('case d') +v11=480; // new supply voltage +f2=50; // new supply frequency +Q=(v11*f1)/(v1*f2); +v22=(v2*f2*Q)/f1; +printf('secondary voltage for case a is %f v\n',v22); +disp('case e') +v11=240; // new supply voltage +f2=0; // new supply frequency +disp('since frequency is zero. Source is a DC source so a very high current will flow in primary side which will damage the transformer and the secondary induced emf is zero ') + + + + + + + diff --git a/3760/CH1/EX1.50/Ex1_50.sce b/3760/CH1/EX1.50/Ex1_50.sce new file mode 100644 index 000000000..9420898b4 --- /dev/null +++ b/3760/CH1/EX1.50/Ex1_50.sce @@ -0,0 +1,38 @@ +clc; +// shorts circuits test on two transformers gave the following results +P1=200000; // KVA of transformer 1 +V1=3; // percentage rated voltage +pf1=0.25; // lagging power factor for Xmer1 +P2=500000; // KVA of transformer 2 +V2=4; // percentage rated voltage +pf2=0.3 // lagging power factor for Xmer2 +l=560000; // load connected across parallel combination of transformers in KW +pf=0.8; // power factor of load +E1=11000; // Rated primary voltage +E2=400; // Rated secondary voltage +ib=1; // base current +vb=1; // base voltage +z1=(V1/100)*1; // base impedance +Ze1=z1*(pf1+%i*sqrt(1-pf1^2)); // p u impedance +z2=(V2/100)*1; // base imedance +Ze2=z2*(pf2+%i*sqrt(1-pf2^2)); // p u impedance +pb=P2; // base for p u conversion +ze1=(pb/P1)*Ze1; +ze2=(pb/P2)*Ze2; +zt=ze1+ze2; // total impedance +s=l/pf; // KVA rating of transformer +S=s*(pf-%i*sqrt(1-pf^2)); // complex form of KVA rating +s1=(S*ze2)/(zt); // KVA shared by first transformer +PF1=cos(atand(imag(s1),real(s1))*(%pi/180)); +s1w=round((abs(s1)*PF1)/1000); +printf('KW load shared by transformer 1 is %f at %f power factor lagging\n',s1w,PF1); +s2=(S*ze1)/(zt); // KVA shared by first transformer +PF2=cos(atand(imag(s2),real(s2))*(%pi/180)); +s2w=ceil((abs(s2)*PF2)/1000); +printf('KW load shared by transformer 2 is %f at %f power factor lagging\n',s2w,PF2); +i1=abs(s1)/P1; // p u current shared by transformer 1 +i2=abs(s2)/P2; // p u current shared by transformer 2 +vr=i1*(real(Ze1)*PF1+imag(Ze1)*sqrt(1-PF1^2)); // voltag regulation +dv=E2*vr; // change in terminal voltage +Vt=E2-dv; // terminal voltage +printf('Secondary terminal voltage is %f v',Vt); diff --git a/3760/CH1/EX1.51/Ex1_51.sce b/3760/CH1/EX1.51/Ex1_51.sce new file mode 100644 index 000000000..5a68492b3 --- /dev/null +++ b/3760/CH1/EX1.51/Ex1_51.sce @@ -0,0 +1,17 @@ +clc; +k1=1000; // Rated KVA of transformer1 +k2=500; // Rated KVA of transformer2 +ze1=0.02+%i*0.06; // p u leakage impedance of transformer 1 +ze2=0.025+%i*0.08; // p u leakage impedance of transformer 2 +zb=1000; // base impedance +Z1=(zb/k1)*ze1; // impedance of transformer 1 +Z2=(zb/k2)*ze2; // impedance of transformer 2 +zt=Z1+Z2; // total impedance +S=k1*(abs(zt)/abs(Z2)); // since ze1 vp; hence leading power factor +printf('Line current is %f A\n',ia); +printf('Power factor is %f leading',pf); diff --git a/3760/CH5/EX5.41/Ex5_41.sce b/3760/CH5/EX5.41/Ex5_41.sce new file mode 100644 index 000000000..8c342dd70 --- /dev/null +++ b/3760/CH5/EX5.41/Ex5_41.sce @@ -0,0 +1,26 @@ +clc; +n=1490; // speed of machine in rpm +p=4; // number of poles +f=50; // frequency +v=11000; // rated voltage of machine +p=20*10^6; // rated power of machine +v1=30; +v2=25; // per phase voltage for phase A of machine +i1=10; +i2=6.5; // per phase current for phase A of machine +ns=(120*f)/p; // synchronous speed of machine +xd=v1/i2; // d-axis synchronous reactance +xq=v2/i1; // q-axis synchronous reactance +disp('case a'); +ia=p/(sqrt(3)*v); // armature current +vt=v/sqrt(3); // per phase armature voltage +Ef=vt+ia*xq*%i; +de=atand(imag(Ef),real(Ef)); // load angle +id=ia*sind(de); // d-axis current +Ef1=abs(Ef)+id*(xd-xq); +printf('Per phase excitation value is %f V\n',ceil(Ef1)); +printf('Line value of excitation EMf is %f V\n ',ceil(sqrt(3)*Ef1)); +disp('case 2'); +pr=(vt^2*(xd-xq)*sind(2*de))/(2*xd*xq); +printf('Reluctance power developed by machine is %f KW per phase\n',pr/1000); +printf('Total reluctance power developed by machine is %f KW',(3*pr)/1000); diff --git a/3760/CH5/EX5.43/Ex5_43.sce b/3760/CH5/EX5.43/Ex5_43.sce new file mode 100644 index 000000000..26382f727 --- /dev/null +++ b/3760/CH5/EX5.43/Ex5_43.sce @@ -0,0 +1,22 @@ +clc; +p=100*10^3; // rated power of alternator +v=440; // rated voltage of alternator +m=3; // number of phases +l1=340; // friction and windage losses +l2=480; // open circuit core losses +rf=180; // field winding resistance at 75 degree cel. +ra=0.02; // armature resistance per phase +vf=220; // voltage applied to field winding +pf=0.8; // power factor +disp('At half load'); +ia=p/(sqrt(3)*v); // full load armature current +l3=(m*ia^2*ra)/4; // short circuit load loss at half load +l4=vf^2/rf; // field circuit loss +lt=l1+l2+l3+l4; // net loss +n=(1-(lt/((p/2)*pf+lt)))*100; +printf('Efficiency is %f percent\n',n); +disp('At full load'); +l3=m*ia^2*ra; // short circuit load loss at full load +lt=l1+l2+l3+l4; // net loss +n=(1-(lt/(p*pf+lt)))*100; +printf('Efficiency is %f percent\n',n); diff --git a/3760/CH5/EX5.44/Ex5_44.sce b/3760/CH5/EX5.44/Ex5_44.sce new file mode 100644 index 000000000..ebb4f944b --- /dev/null +++ b/3760/CH5/EX5.44/Ex5_44.sce @@ -0,0 +1,16 @@ +clc; +p=40000; // rated power of machine +v=400; // rated voltage of machine +l=1500; // short circuit load loss +m=3; // number of phases +ia1=1; // armature current in p.u. +ra=0.118; // dc armature resistance at 30 degree cel. +ia2=p/(sqrt(3)*v); // rated armature current +l1=l/p; // short circuit loss in p.u. +ra1=l1/ia1^2; +printf('Effective armature resistance is %f p.u.\n',ra1); +l2=l/m; // short circuit load loss per phase +ra2=l2/ia2^2; +printf('Effective ac armature resistance is %f ohm per phase\n',ra2); +r=ra2/ra; +printf('Ratio of ac to dc armature resistance is given as %f ',r); diff --git a/3760/CH5/EX5.45/Ex5_45.sce b/3760/CH5/EX5.45/Ex5_45.sce new file mode 100644 index 000000000..d1e0cbb64 --- /dev/null +++ b/3760/CH5/EX5.45/Ex5_45.sce @@ -0,0 +1,22 @@ +clc; +p=500*10^3; // rated power of alternator +v=11000; // rated voltage of alternator +m=3; // number of phases +l1=1500; // friction and windage losses +l2=2500; // open circuit core losses +ra=4; // armature resistance per phase +l3=1000; // field copper loss +pf=0.8; // power factor +disp('case a: Half load'); +ia=p/(sqrt(3)*v); // armature current +l4=(m*ia^2*ra)/4; // short circuit load loss at half load +lt=l1+l2+l3+l4; // net loss +n=(1-(lt/((p/2)*pf+lt)))*100; +printf('Efficiency is %f percent\n',n); +disp('case b'); +// for maximum efficiency variable losses=constant losses +iam=sqrt((l1+l2+l3)/(m*ra)); // armature current at maximum efficiency +pout=m*(v/sqrt(3))*iam*pf; // output power ta maximum efficiency +lt=2*(l1+l2+l3); // net losses +nm=(1-(lt/(pout+lt)))*100; +printf('Maximum efficiency is %f percent\n',nm); diff --git a/3760/CH5/EX5.46/Ex5_46.sce b/3760/CH5/EX5.46/Ex5_46.sce new file mode 100644 index 000000000..20511a3a1 --- /dev/null +++ b/3760/CH5/EX5.46/Ex5_46.sce @@ -0,0 +1,16 @@ +clc; +l=1800; // total load on factory +pf=0.6; // power factor +pfn=0.95; // desired power factor +// from phasor diagram 5.107 +l1=l/pf; // load in VA +a1=acosd(pf); // phase angle between terminal voltage and armature current +a2=acosd(pfn); // phase angle corresponding to desired power factor +k1=l1*sind(a1); // KVAr of load +k2=l*tand(a2); // combined KVAr +disp('case a'); +s=k1-k2; +printf('Synchronous condenser rating is %f KVA\n',floor(s)); +disp('case b'); +r=sqrt(l^2+k2^2); +printf('Total KVA of factory is %f KVA',r); diff --git a/3760/CH5/EX5.47/Ex5_47.sce b/3760/CH5/EX5.47/Ex5_47.sce new file mode 100644 index 000000000..4665a68f7 --- /dev/null +++ b/3760/CH5/EX5.47/Ex5_47.sce @@ -0,0 +1,24 @@ +clc; +l0=300; // total load on factory +pf=0.6; // lagging power factor +n=88; // percentage efficiency of motor +pfn=0.9; // desired power factor +l1=60; // mechanical load to be supplied +// from phasor diagram 5.108 +pi=l1/(n/100); // synchronous motor input +lt=pi+l0; // combined load +disp('case a'); +k=lt/pfn; +printf('Total load is %f KVA\n',k); +disp('case b'); +a1=acosd(pf); // phase angle between terminal voltage and armature current +a2=acosd(pfn); // phase angle corresponding to desired power factor +k1=l0*tand(a1); // KVAr of load +k2=lt*tand(a2); // combined KVAr +s=k1-k2; // leading KVAr supplied by synchronous motor +r=sqrt(s^2+pi^2); +printf('Capacity of synchronous motor is %f KVA\n',r); +disp('case c'); +pfs=pi/r; +printf('Synchronous motor operating power factor is %f leading',pfs); + diff --git a/3760/CH5/EX5.48/Ex5_48.sce b/3760/CH5/EX5.48/Ex5_48.sce new file mode 100644 index 000000000..491c0f712 --- /dev/null +++ b/3760/CH5/EX5.48/Ex5_48.sce @@ -0,0 +1,15 @@ +clc; +p0=1000; // full load power rating of substation +pf=0.71; // lagging power factor +pfn=0.87; // desired power factor +// from phasor dagram 5.109 +p1=p0*pf; // load KW +p2=sqrt(p0^2-p1^2); // load KVAr +pn=p0*pfn; // new power delivered to load +p0n=pn/pf; // new load KVA +pl=p0n-p0; +printf('Permissible additional load at %f lagging power factor is %f KVA\n',pf,pl); +p2n=sqrt(p0n^2-pn^2); // new load KVAr +p2ns=sqrt(p0^2-pn^2); // new load KVAr with the use of synchronous condensor +R=p2n-p2ns; +printf('Rating of synchronous condensor is %f KVA',R); diff --git a/3760/CH5/EX5.49/Ex5_49.sce b/3760/CH5/EX5.49/Ex5_49.sce new file mode 100644 index 000000000..f17b1c6d4 --- /dev/null +++ b/3760/CH5/EX5.49/Ex5_49.sce @@ -0,0 +1,16 @@ +clc; +p=4000; // load taken by industrial plant in KW +pf=0.8; // lagging power factor +l=400; // rating of induction motor to be replaced by synchronous motor +n=0.9; // efficiency of induction motor and synchronous motor +pf1=0.9; // lagging power factor at which induction motor operates +pf2=0.8; // leading power factor at which synchronous motor operates +A=p-%i*p*tand(acosd(pf)); // complex power of plant +pi=l/pf1; // power input to induction motor +B=pi-%i*pi*tand(acosd(pf1)); // complex power requirement of induction motor +C=pi+%i*pi*tand(acosd(pf2)); // complex power requirement of synchronous motor +pfn=cosd(atand(imag(A-B+C),real(A-B+C))); +printf('New power factor of the plant is %f lagging\n',pfn); +r=(abs(A-B+C)/sqrt(3))/(p/(sqrt(3)*pf)); // ratio of new line current to original line current +pr=(1-r)*100; +printf('Percentage reduction in line current is %f percent',pr); diff --git a/3760/CH5/EX5.5/Ex5_5.sce b/3760/CH5/EX5.5/Ex5_5.sce new file mode 100644 index 000000000..4ea7fe6f3 --- /dev/null +++ b/3760/CH5/EX5.5/Ex5_5.sce @@ -0,0 +1,21 @@ +clc; +v=230; // rated voltage of motor +f=50; // frequency +p=4; // number of poles +zs=0.6+3*%i; // synchronous impedance +ia1=10; // current drawn by motor at upf +ia2=40; // final current after load is inceased to certain value +vt=v/sqrt(3); // per phase voltage +al=atand(real(zs),imag(zs)); +Ef=sqrt((vt-ia1*real(zs))^2+(ia1*imag(zs))^2); // excitation EMF +t1=(ia2*abs(zs))^2; +t2=Ef^2+vt^2; +t3=-2*Ef*vt; // terms needed to evaluate load angle +de=acosd((t1-t2)/t3); // load angle +pi=(Ef*vt*sind(de-al))/abs(zs)+(vt^2*real(zs))/abs(zs)^2; // input power +pf=pi/(vt*ia2); +printf('Power factor is %f lagging\n',pf); +pd=3*(pi-ia2^2*real(zs)); // developed power +ns=(120*f)/p; // synchronous speed +T=(pd*60)/(2*%pi*ns); +printf('Torque developed is %f N-m',T); diff --git a/3760/CH5/EX5.53/Ex5_53.sce b/3760/CH5/EX5.53/Ex5_53.sce new file mode 100644 index 000000000..a192ba3bd --- /dev/null +++ b/3760/CH5/EX5.53/Ex5_53.sce @@ -0,0 +1,44 @@ +clc; +m=3; // number of phases +p=2; // number of poles +P=4*10^6; // rated power of generator +v=11000; // rated voltage of generator +as=72; // armature slots +cs=4; // conductor per armature slot +rs=24; // rotor slots +rp=10; // rotor slot angular pitch +cr=20; // conductors per rotor slot +z=0.1+2*%i; // armature leakage impedance per phase +pf=0.8; // lagging power factor +vt=v/sqrt(3); // terminal voltage +ia=P/(sqrt(3)*v); // full load armature current +// Open circuit characteristics have been plotted using table given in question.Per phase value of excitation voltage is obtained fron table +IF=[ 40 80 120 160 200 240 280 320 360]; +EA=[ 2490 4980 7470 9390 10620 11460 12030 12450 12660 ]; +plot(IF,EA/sqrt(3)); +xlabel('Field current'); +ylabel('open circuit voltage'); +title('open circuit characteristics'); +Er=vt+ia*(pf-%i*sqrt(1-pf^2))*z; // air gap voltage +printf('Air gap voltage is %f V\n',abs(Er)); +disp('Corresponding to magnitude of air gap voltage value of field MMF in terms of field current is obtained from O.C.C (for textbook refer fig. 5.114)'); +Fr=242; // field MMF in terms of field current +q=rs/p; // rotor slots per pole +kd=sind(q*rp/2)/(q*sind(rp/2)); // distribution factor +kp=1 ; // coil span factor for full pitch field coil +kw=kd*kp; // winding factor +Nf=(rs*cr)/p; // total field turns +F1f=(4*kw*Nf)/(%pi*p); // ratio of fundamental field mmf per pole to field current +Nph=(as*cs)/(m*p); // series turn per phase +q1=as/(m*p); // armature slots per pole per phase +v1=(p*180)/as; // armature slot angular pitch +kd=(sind(q1*v1/2))/(q1*sind(v1/2)); // distribution factor +kw=kd*kp; // winding factor +Fa=(0.9*m*Nph*ia*kw)/(p*F1f); // armature mmf in terms of field current +B=acosd(pf)+atand(imag(Er),real(Er)); // power factor angle + angle by which air gap voltage leads terminal voltage +Ff=sqrt(Fr^2+Fa^2-2*Fr*Fa*cosd(90+B)); // equivalent field current +printf('Equivalent field current is %f A\n',Ff); +// corresponding to equivalent field current, excitation voltage is obtained from O.C.C +Ef=7168; // excitation EMF per phase +vr=((Ef-vt)/vt)*100; +printf('Voltage regulation at full load %f lagging power factor is %f percent',pf,vr); diff --git a/3760/CH5/EX5.54/Ex5_54.sce b/3760/CH5/EX5.54/Ex5_54.sce new file mode 100644 index 000000000..0959e9af5 --- /dev/null +++ b/3760/CH5/EX5.54/Ex5_54.sce @@ -0,0 +1,15 @@ +clc; +p=2*10^6; // rated power of alternator +v=11000; // rated voltage of alternator +zs=0.3+5*%i; // synchronous impedance per phase +pf=0.8; // lagging power factor +vt=v/sqrt(3); // terminal voltage +ia=p/(sqrt(3)*v); // full load armature current +// with vt as reference phasor +Ef=vt+ia*(pf-sqrt(1-pf^2)*%i)*zs; +// now excitation level is same but load power fcator is leading +printf('Load current is %f A\n',ia); +de=cosd(atand(imag(Ef),real(Ef))); // angle between excitation and terminal voltage +vt=abs(Ef)*(de+sqrt(1-de^2)*%i)-ia*(pf+sqrt(1-pf^2)*%i)*zs; +printf('Terminal voltage at %f leading power factor is %f V per phase\n',pf,abs(vt)); +printf('Line terminal voltage is %f KV',(sqrt(3)*abs(vt))/1000); diff --git a/3760/CH5/EX5.55/Ex5_55.sce b/3760/CH5/EX5.55/Ex5_55.sce new file mode 100644 index 000000000..2c0d0c89b --- /dev/null +++ b/3760/CH5/EX5.55/Ex5_55.sce @@ -0,0 +1,14 @@ +clc; +p=30*10^6; // rated power of alternator +v=11000; // rated voltage of alternator +zs=0.005+0.70*%i; // p.u synchronous reactance +Ef=1.5; // p.u. excitation EMF +ia=1; // p.u. armature current +vt=1; // p.u. terminal voltage +t1=Ef^2-(real(zs)*ia)^2-(imag(zs)*ia)^2-1; +t2=sqrt((2*ia*real(zs))^2+(2*ia*imag(zs))^2); +t3=atand((2*ia*real(zs))/(2*ia*imag(zs))); // terms needed to find out power factor +pf=cosd(asind(t1/t2)-t3); +printf('Power factor is %f lagging\n',pf); +de=acosd((ia*abs(zs)^2-Ef^2-vt^2)/(-2*Ef*vt)); +printf('Load angle is %f degrees',de); diff --git a/3760/CH5/EX5.56/Ex5_56.sce b/3760/CH5/EX5.56/Ex5_56.sce new file mode 100644 index 000000000..583f094a1 --- /dev/null +++ b/3760/CH5/EX5.56/Ex5_56.sce @@ -0,0 +1,26 @@ +clc; +xd=1.2; // pu d-axis synchronous reactance +xq=0.8; // pu q-axis synchronous reactance +xe=0.1; // pu external reactance +vb=1; // voltage of infinite bus +pf=0.9; // lagging power factor +disp('case a'); +// vb=vt-j*ia*xe -(1)where ia is armature current +// ia=ia*(pf-%i*sqrt(1-pf^2)); // complex form of armature current +// vt*ia=1 therefore ia=1/vt solving equation 1 we get a quadratic equation in vt whose terms are +t1=1; +t3=-2*xe*sqrt(1-pf^2)-vb; +t5=(xe*sqrt(1-pf^2))^2-(pf*xe)^2; // terms of quadratic equation in terminal voltage +p= [t1 0 t3 0 t5]; +vt=roots(p); +ia=1/vt(2); // pu armature current +printf('Generator terminal voltage is %f pu\n',vt(2)); +printf('Armature current is %f pu\n',ia); +disp('case b'); +Ef=vt(2)+ia*(pf-%i*sqrt(1-pf^2))*%i*xq; +de=atand(imag(Ef),real(Ef)); +pa=acosd(pf); // power factor angle +id=ia*sind(de+pa); // d-axis component of armature current +Ef=abs(Ef)+id*(xd-xq); +printf('Load angle is %f degrees\n',de); +printf('Excitation voltage is %f pu',Ef); diff --git a/3760/CH5/EX5.57/Ex5_57.sce b/3760/CH5/EX5.57/Ex5_57.sce new file mode 100644 index 000000000..ecc525058 --- /dev/null +++ b/3760/CH5/EX5.57/Ex5_57.sce @@ -0,0 +1,20 @@ +clc; +xd=0.85; // reactance along d-axis +xq=0.55; // reactance along q-axis +vt=1; // pu bus voltage +Ef=1.2; // pu excitation EMF +// P=(Ef*vt*sin(de))/xd + (vt^2/2)*((1/xq)-(1/xd))*sin(2*de) where p is power and de is load angle +// for maximum power dp/dde(derivative with respect to load angle) is zero. Solving we get a quadratic equation whose terms are +p=[ (vt^2/2)*((1/xq)-(1/xd))*4 (Ef*vt)/xd -(vt^2/2)*((1/xq)-(1/xd))*2 ]; +l=roots(p); +an=l(2); +de=acos(an)*(180/%pi); // load angle + +pmax=(Ef*vt*sin(de*(%pi/180)))/xd + (vt^2/2)*((1/xq)-(1/xd))*sin(2*de*(%pi/180)); +printf('Maximum power output that motor can supply without loss of synchronization is %f pu\n',pmax); +// cos(de)=(vt^2/p)*((xd-xq)/(xd+xq))*sin(de)^3 where de is load angle for minimum excitation EMF +// by trial and error value of de is +de=63; +P=1; // pu power +Ef=(P-((vt^2/2)*((xd-xq)/(xd*xq))*sind(2*de)))/((vt/xd)*sind(de)); +printf('Minimum excitation EMF for machine to stay in synchronism is %f pu\n',Ef); diff --git a/3760/CH5/EX5.58/Ex5_58.sce b/3760/CH5/EX5.58/Ex5_58.sce new file mode 100644 index 000000000..70efa2c40 --- /dev/null +++ b/3760/CH5/EX5.58/Ex5_58.sce @@ -0,0 +1,17 @@ +clc; +p=3*10^6; // rated power of alternator +v=11000; // rated voltage of alternator +r=0.4; // per phase effective resistance +vl=12370; // line to line voltage at zero leading power factor +i=100; // load current at zero power factor +pf=0.8; // lagging power factor at which voltage regulation has to be determined +vt=vl/sqrt(3); // per phase terminal voltage +Ef=v/sqrt(3); // per phase excitation EMF +ia=p/(sqrt(3)*v); // full load phase current +// for zero power factor load angle=0 +zs=(vt-Ef)/i; // synchronous impedance +xs=sqrt(zs^2-r^2); // synchronous reactance +// From phasor diagram +Ef1=sqrt((Ef*pf+ia*r)^2+(Ef*sqrt(1-pf^2)+ia*xs)^2); // excitation EMF at 0.8 power factor +vr=((Ef1-Ef)/Ef)*100; +printf('Voltage regulation at %f lagging power factor is %f percent',pf,vr); diff --git a/3760/CH5/EX5.59/Ex5_59.sce b/3760/CH5/EX5.59/Ex5_59.sce new file mode 100644 index 000000000..970281870 --- /dev/null +++ b/3760/CH5/EX5.59/Ex5_59.sce @@ -0,0 +1,17 @@ +clc; +v=11000; // voltage of infinite bus +po=15*10^6; // output power of alternator +pf=0.8; // operating power factor of synchronous machine +p=130; // percentage increase in excitation EMF +m=3; // number of phases +ia=po/(sqrt(3)*pf*v); // per phase armature current +vb=v/sqrt(3); // per phase bus voltage +//from phasor diagrams in fig 5.117(a) and 5.117(b) +xs=(sqrt(((p/100)*vb)^2-(vb*pf)^2)-(vb*sqrt(1-pf^2)))/ia; // synchronous reactance +printf('Synchronous reactance of machine is %f ohms\n',xs); +de=asind((po*xs)/(m*vb^2)); +printf('Load angle of machine before excitation EMF is increased is %f degrees\n',de); +pf=cosd(de/2); +printf('Power factor of the machine before excitation EMF is increased is %f leading\n',pf); +ia=(2*vb*sind(de/2))/xs; +printf('Armature current of the machine before excitation EMF is increased is %f A',ia); diff --git a/3760/CH5/EX5.6/Ex5_6.sce b/3760/CH5/EX5.6/Ex5_6.sce new file mode 100644 index 000000000..848eec94f --- /dev/null +++ b/3760/CH5/EX5.6/Ex5_6.sce @@ -0,0 +1,18 @@ +clc; +v=6600; // rated voltage of motor +zs=1.5+12*%i ; // per phase synchronous impedance +pi1=1000; // input power +pf=0.8; // power factor +pi2=1500; // power at which power factor is to be found out +vt=v/sqrt(3); // per phase voltage +al=atand(real(zs),imag(zs)); +ia=(pi1*1000)/(sqrt(3)*v*pf); +Ef=sqrt((vt*pf-ia*real(zs))^2+(vt*sqrt(1-pf^2)+ia*imag(zs))^2); // excitation EMF +t1=(pi2*1000)/3; +t2=(vt^2/abs(zs)^2)*real(zs); +t3=abs(zs)/(vt*Ef); // terms needed to evaluate load angle +di=asind((t1-t2)*t3)+al; // load angle +ia=(sqrt(vt^2+Ef^2-2*Ef*vt*cosd(di)))/abs(zs); // new armature current +pfn=((pi2-pi1)*1000)/(ia*vt); +// as Ef*cos(di)+ia*ra> vt hence leading power factor +printf('New power factor is %f leading',pfn); diff --git a/3760/CH5/EX5.7/Ex5_7.sce b/3760/CH5/EX5.7/Ex5_7.sce new file mode 100644 index 000000000..d74e6e665 --- /dev/null +++ b/3760/CH5/EX5.7/Ex5_7.sce @@ -0,0 +1,16 @@ +clc; +v=2300; // rated voltage of motor +xs=12 ; // per phase synchronous reactance +p=200000; // VA rating of motor +l1=120000; // initial load +l2=60000; // final load +vt=v/sqrt(3); // rated per phase voltage +ia=l1/(3*vt); // minimum armature current +ia1=1.5*ia; // armature current at reduced load (50% increment) +pf=1/1.5; // power factor +Ef=sqrt((vt*pf)^2+(vt*sqrt(1-pf^2)+ia1*xs)^2); // excitation EMF +de=asind((l2*xs)/(3*vt*Ef)); // new load angle +ia2=(sqrt(vt^2+Ef^2-2*Ef*vt*cosd(de)))/xs; // new armature current +printf('New value of armature current is %f A\n',ia2); +pfn=l2/(3*vt*ia2); +printf('Power factor at new armature current is %f leading',pfn); diff --git a/3760/CH5/EX5.8/Ex5_8.sce b/3760/CH5/EX5.8/Ex5_8.sce new file mode 100644 index 000000000..f9282a7a3 --- /dev/null +++ b/3760/CH5/EX5.8/Ex5_8.sce @@ -0,0 +1,11 @@ +clc; +ef=1.2; // ratio of excitation voltage to rated per phase voltage +i=0.7; // ratio of armature current to rated current +r=0.01; // percentage resistance of motor +x=0.5; // percentage reactance of motor +// as per the expression given in book +t1=ef^2-(r*i)^2-(x*i)^2-1; +t2=sqrt((2*i*r)^2+(2*i*x)^2); +t3=atand((2*i*r)/(2*i*x)); // terms needed to find out power factor +pf=cosd(asind(t1/t2)-t3); +printf('Power factor is %f lagging',pf); diff --git a/3760/CH5/EX5.9/Ex5_9.sce b/3760/CH5/EX5.9/Ex5_9.sce new file mode 100644 index 000000000..630bb9e06 --- /dev/null +++ b/3760/CH5/EX5.9/Ex5_9.sce @@ -0,0 +1,34 @@ +clc; +v=400; // rated voltage of motor +zs=0.13+%i*1.3 ; // per phase synchronous impedance +p=100000; // VA rating of motor +l=4000; // stray losses +pl=75000; // power delivered to load +disp('case a'); +il=p/(sqrt(3)*v); // line current +vt=v/sqrt(3); // per phase rated voltage +pd=pl+l ; // power developed +poh=3*il^2*real(zs); +lt=poh+l; // total losses +pi=pl+lt; // input power +pf=pi/p; // power factor +n=(1-(lt/pi))*100; // efficiency +printf('Power factor is %f\n',pf); +printf('Efficiency is %f percent\n',n); +Ef1=round(sqrt((vt*pf-il*real(zs))^2+(-vt*sqrt(1-pf^2)+il*imag(zs))^2)); // excitation EMF +de=atand((-vt*sqrt(1-pf^2)+il*imag(zs))/(vt*pf-il*real(zs)))+acosd(pf); // load angle +printf('Excitation EMf at under excitation is %f v\n',Ef1); +printf('Load angle at under excitation is %f degrees \n',de); +Ef2=round(sqrt((vt*pf-il*real(zs))^2+(vt*sqrt(1-pf^2)+il*imag(zs))^2)); // excitation EMF +de=atand((vt*sqrt(1-pf^2)+il*imag(zs))/(vt*pf-il*real(zs)))-acosd(pf); // load angle +printf('Excitation EMf at over excitation is %f v\n',Ef2); +printf('Load angle at over excitation is %f degrees\n',de); +i=pi/(sqrt(3)*v); +printf('Input current is %f A\n',i); +disp('caes b'); +de=acosd(real(zs)/abs(zs)); // load angle +pmax=((vt*Ef1)/abs(zs))-((Ef1^2*real(zs))/abs(zs)^2); +pt=pmax*3; +printf('Load angle for maximum power output is %f degrees\n',de); +printf('Maximum output per phase is %f W\n',pmax); +printf('Total maximum output is %f W\n',pt); diff --git a/3760/CH6/EX6.1/Ex6_1.sce b/3760/CH6/EX6.1/Ex6_1.sce new file mode 100644 index 000000000..d8590e025 --- /dev/null +++ b/3760/CH6/EX6.1/Ex6_1.sce @@ -0,0 +1,14 @@ +clc; +// after changing dc supply terminals from phase a to phase b +disp('case a'); +P=2; // number of poles +te=(2/P)*120; +printf('Number of mechanical degrees through which rotor moves is %d degrees\n',te); +disp('case b'); +P=4; // number of poles +te=(2/P)*120; +printf('Number of mechanical degrees through which rotor moves is %d degrees\n',te); +disp('case c'); +P=6; // number of poles +te=(2/P)*120; +printf('Number of mechanical degrees through which rotor moves is %d degrees\n',te); diff --git a/3760/CH6/EX6.10/Ex6_10.sce b/3760/CH6/EX6.10/Ex6_10.sce new file mode 100644 index 000000000..634d1fc96 --- /dev/null +++ b/3760/CH6/EX6.10/Ex6_10.sce @@ -0,0 +1,78 @@ + + +clc; + +//from 6.9 problem +P=4; +r1=0.15; +x1=0.45; +r2=0.12; +x2=0.45; +Xm=28.5; +s=0.04; +V=400; +f=50; +Pfixed=400; +t=1.2; // rotor effective turns ratio + +//for part a +//According to the conditions and diagram +t1=complex(r1,x1); +t2=complex(0,Xm); +t3=complex(r1,x2+Xm); +Ze=(t1*t2)/(t3); +Re=real(Ze); +Xe=imag(Ze); +t4=complex(Re,(x2+Xe)); +SmT=(r2)/(sqrt((Re*Re)+((x2+Xe)*(x2+Xe)))); +Ve=(V/sqrt(3))*(Xm/(x2+Xm)); +Ws=(4*%pi*f)/P; +Tem=(3/Ws)*Ve^2*(1/2)*(1/(Re+sqrt(Re^2+(x2+Xe)^2))); +Pm=Tem*(1-SmT)*Ws; +Psh=Pm-Pfixed; +Tsh=Psh/(Ws*(1-SmT)); +mprintf('for part a \n slip = %f \n maximun torque = %f Nm \n power output = %f KW \n',SmT,Tem, Psh/1000); + + +//for part b +s=1; +I2st=(Ve)/(sqrt((r2+Re)*(r2+Re)+(x2+Xe)*(x2+Xe))); +Test=(3/Ws)*I2st*I2st*(r2); +mprintf(' for part b rotor current = %f A \n torque = %f Nm \n',I2st,Test); + + +//for part c +R=sqrt(Re^2+(x2+Xe)^2)-r2; +Ra=R/(t^2); +mprintf('for part c \n external resisitance value is = %f Ohm \n',Ra); + +//for part d +s1=0.04; +Pm=((3*(Ve)*(Ve))*r2*((1-s1)/s1))/(((Re+r2+((r2*(1-s1)/s1))))*((Re+r2+((r2*(1-s1)/s1))))+((x2+Xe)*(x2+Xe))); +mprintf('for part d \n power developed is %f KW \n',Pm/1000); + +//for part e +SmP=(r2)/(sqrt(((Re+r2)*(Re+r2))+((x2+Xe)*(x2+Xe)))+r2); +Pmn=((3/2)*Ve*Ve)/(Re+r2+sqrt((r2+Re)*(r2+Re)+(x2+Xe)*(x2+Xe))); +mprintf('for part e \n slip = %f \n power developed = %f KW',SmP,Pmn/1000); + + + + + + + + + + + + + + + + + + + + + diff --git a/3760/CH6/EX6.11/Ex6_11.sce b/3760/CH6/EX6.11/Ex6_11.sce new file mode 100644 index 000000000..2e9a99d24 --- /dev/null +++ b/3760/CH6/EX6.11/Ex6_11.sce @@ -0,0 +1,73 @@ +clc; +P=4; +r1=0.15; +x1=0.45; +r2=0.12; +x2=0.45; +Xm=28.5; +s=0.04; +V=400; +f=50; +Pfixed=400; + +//from problem 6.10 +Re=0.1476; +Xe=0.443; +r2=0.12; +x2=0.45; + +a=Xm/(x2+Xm); +//Ve=a*V1; +Wr=(4*%pi*f)/P; +b=(3/Wr)*(1/2)*(1/((Re)+(sqrt((Re*Re)+((x2+Xe)*(x2+Xe)))))); +//Tem=b*Ve*Ve + +//for part a +V1=230; +Ve1=a*V1; +Tem1=b*Ve1*Ve1; +mprintf('for part a \n maximum internal torque developed is %f Nm \n',Tem1); + +//for part b +V2=115; +Ve2=a*V2; +Tem2=b*Ve2*Ve2; +mprintf('for part b \n maximum internal torque developed is %f Nm \n',Tem2); + +//for f=25 Hz +Xe1=(1/2)*Xe; +x21=(1/2)*x2; +Ws1=(1/2)*Wr; + + +//for part c +V3=115; +Ve3=a*V3; +Tem3=(3/Ws1)*Ve3*Ve3*(1/2)*(1/((Re)+(sqrt((Re*Re)+((x21+Xe1)*(x21+Xe1)))))) +mprintf('for part c \n maximum internal torque developed is %f Nm \n',Tem3); + +//for f=5 Hz +Xe2=(1/10)*Xe; +x22=(1/10)*x2; +Ws2=(1/10)*Wr; + + +//for part d +f3=5; //f3=(1/10)*f +V4=23; +Ve4=a*V4; +Tem4=(3/Ws2)*Ve4*Ve4*(1/2)*(1/((Re)+(sqrt((Re*Re)+(((x22+Xe2)*(x22+Xe2))))))) +mprintf('for part d \n maximum internal torque developed is %f Nm \n',Tem4); + + + + + + + + + + + + + diff --git a/3760/CH6/EX6.13/Ex6_13.sce b/3760/CH6/EX6.13/Ex6_13.sce new file mode 100644 index 000000000..724c4c804 --- /dev/null +++ b/3760/CH6/EX6.13/Ex6_13.sce @@ -0,0 +1,82 @@ +//answer match + roots + +clc; +Pm=10000; +V=400; +f=50; +smT=0.1; +P=4; +Ns=(120*f)/P; + +//for (i) +disp('(i)'); +//As per given conditions the slip is given by equation Sfl2-0.4Sfl+0.01=0 +V=[1 -0.4 0.01]; +R=roots(V); +Sfl=R(2); +Nr=Ns*(1-Sfl); +mprintf('The slip is %f \n The rotor speed is %f r.p.m',Sfl,ceil(Nr)); + +//for (ii) +disp('(ii)'); +Pg=Pm/(1-Sfl); +Prot=Sfl*Pg; +mprintf('The rotor ohmic loss is %f W \n',Prot); + +//for (iii) +disp('(iii)'); +Tefl=Pg/(2*3.14*(Ns/60)); +Test=(4*Tefl)/((smT)+(1/smT)); +mprintf('starting torque is %f Nm \n',Test); + +//for (iv) +disp('(iv)'); +a=sqrt(((Sfl*Sfl)+(smT*smT))/((Sfl)*(Sfl)*(1+(smT)*(smT)))); +mprintf('starting current = %f full load current\n',a); + +//for (v) +disp('(v)'); +// answer is slightly different in book +b=sqrt((1/2)*(1+(smT/Sfl)^2)); +mprintf('stator current at maximun torque = %f full load current \n',b); + +//for (vi) +disp('(vi)'); +E=(Pm/Pg)*100; +mprintf('full load efficiency is = %f percent\n',E); + +//for (vii) +disp('(vii)'); +//As per given conditions +smT1=3*smT; +mprintf('New slip value is %f \n',smT1); + +//for (viii) +disp('(viii)'); +//According to the given conditions s1(2)-1.2s+0.09 +VV=[1 -1.2 0.09]; +RR=roots(VV); +s1=RR(2); +Nr1=Ns*(1-s1); +mprintf('full load slip is %f rotor speed is %f r.p.m',s1,Nr1); + +//for (ix) +disp('(ix)'); +Test1=((2)/((1/0.3)+(0.3)))*(2*Tefl); +mprintf('starting torque is %f Nm \n',Test1); + +//for (x) +disp('(x)'); +c=sqrt((s1^2+smT1^2)/(s1^2*(1+smT1^2))); +mprintf('starting current = %f full load current \n',c); + +//for (xi) +disp('(xi)'); +Protfl=s1*Pg; +mprintf('Rotor ohmic loss at full load torque is %f W \n',Protfl); + +//for (xii) +disp('(xii)'); +Pm1=(1-s1)*Pg; +E=Pm1/Pg; +mprintf('Efficiency is %f percent',E*100); diff --git a/3760/CH6/EX6.14/Ex6_14.sce b/3760/CH6/EX6.14/Ex6_14.sce new file mode 100644 index 000000000..e72918dfc --- /dev/null +++ b/3760/CH6/EX6.14/Ex6_14.sce @@ -0,0 +1,40 @@ + +clc; +Pm=60000; +P=6; +s=0.04; +V=400; +smT=0.2; +f=50; +Ns=(120*f)/P; + +Ws=(2*%pi*Ns)/60; +Wr=Ws*(1-s); +Tefl=Pm/Wr; + +//for part a +Tem=(((smT/s)+(s/smT))/2)*Tefl; +mprintf('for part a \n the maximun torque is %f Nm\n',Tem); + +//for part b +Prot=(s/(1-s))*(Pm); +mprintf('for part b \n the rotor ohmic loss is %f W\n',Prot); + +//for part c +smT1=2*smT; +mprintf('for part c \n THe new slip is %f \n',smT1); + +//for part d +//On analysis the slip is given by +s2=0.084; +mprintf('for part d \n full load slip is %f \n',s2); + +//for part e +T2=Pm/((Ws)*(1-s2)); +mprintf('for part e \n the full load torque is %f Nm\n',T2); + + + + + + diff --git a/3760/CH6/EX6.15/Ex6_15.sce b/3760/CH6/EX6.15/Ex6_15.sce new file mode 100644 index 000000000..e3e1159cc --- /dev/null +++ b/3760/CH6/EX6.15/Ex6_15.sce @@ -0,0 +1,19 @@ + +clc; +sfl=0.05; //Full load slip +//Test/Tem=a +//Tfl/Tem=b +a=1/2; +b=1/1.6; +//As per the given equation we get smT1^2-2.5smT1+1=0 +Q=[1 -2.5 1]; +R=roots(Q); +smT1=R(2); + +//For full load slip of 0.05 we get the equation smT2^2-0.20smT2+0.0025 +Q1=[1 -0.20 0.0025]; +R1=roots(Q1); +smT2=R1(1); + +P=((smT1-smT2)/smT1)*100; +mprintf('Percentage reduction in rotor circuit resistance is %f percent',P); diff --git a/3760/CH6/EX6.16/Ex6_16.sce b/3760/CH6/EX6.16/Ex6_16.sce new file mode 100644 index 000000000..9ddb18a45 --- /dev/null +++ b/3760/CH6/EX6.16/Ex6_16.sce @@ -0,0 +1,32 @@ + +clc; +r2=0.04; +x2=0.2; + +//As per given conditions we get a quadratic equation in smT which is smT^2-4*smT+1 +t1=1; t2=-4; t3=1; +p=[ t1 t2 t3]; +smT=roots(p); + +r22=x2*smT(2); +R=r22-r2; +mprintf('The external resistane needed to be inserted is %f Ohm \n',R); + + +//say V=400(Input voltage) +V=400; +//without external resistance +Ist=V/(sqrt((r2)*(r2)+(x2)*(x2))); +pf=r2/(sqrt((r2)*(r2)+(x2)*(x2))); + +//with external resistance +Ist1=V/(sqrt((r22)*(r22)+(x2)*(x2))); +pf1=r22/(sqrt((r22)*(r22)+(x2)*(x2))); + +a=((Ist-Ist1)/Ist)*100; +b=((pf1-pf)/pf)*100; +mprintf('Percentage in starting current is %f \n',a); +mprintf('Percentage in power factor is %f \n',b); + + + diff --git a/3760/CH6/EX6.17/Ex6_17.sce b/3760/CH6/EX6.17/Ex6_17.sce new file mode 100644 index 000000000..51e26e646 --- /dev/null +++ b/3760/CH6/EX6.17/Ex6_17.sce @@ -0,0 +1,20 @@ +clc; +//r2/x2=a +a=.5; +Test=25; + +//for part a +disp('For part a '); +//b=3(V1)2/r2Ws +//As per given conditions +b=Test*5; +//When rotor resistace is doubled +Test1=b*(1/4); +mprintf('The starting torque is %f Nm\n',Test1); +//for part b +disp('For part b'); +//resisance is half +Test2=b*(2/17); + + +mprintf('The starting torque is %f Nm',Test2); diff --git a/3760/CH6/EX6.18/Ex6_18.sce b/3760/CH6/EX6.18/Ex6_18.sce new file mode 100644 index 000000000..a869e26dd --- /dev/null +++ b/3760/CH6/EX6.18/Ex6_18.sce @@ -0,0 +1,27 @@ +//equation +clc; +//Test/Tefl=1.5; +d=1.5; +//Tem/Tefl=2.5; +e=2.5; + +//for part a + +//d=Test/Tefl; +//equation of torque gives following equation +Q=[1 -3.33 1]; +R=roots(Q); +smT=R(2); +mprintf('The slip at maximun torque is %f \n',smT) + +//for part b +//equation of torque gives +Q=[1 -1.665 0.111]; +R=roots(Q); +sfl=R(2); +mprintf('The slip at full load is %f \n',sfl) + +//for part c +//I2st=c*Isfl As per torque equation +c=sqrt((d)*(1/sfl)); +mprintf('The rotor current = %f times full load current \n',c) diff --git a/3760/CH6/EX6.19/Ex6_19.sce b/3760/CH6/EX6.19/Ex6_19.sce new file mode 100644 index 000000000..676c0b650 --- /dev/null +++ b/3760/CH6/EX6.19/Ex6_19.sce @@ -0,0 +1,10 @@ +clc; +Te=200; +s=0.04; +c=4; //given multiplying factor of leakage reactance + +//3V*V=a*WS +a=Te*s*(((1+(1/s))*(1+(1/s)))+((c+c)*(c+c))); +Test=a*(1/((1+1)*(1+1)+(c+c)*(c+c))); +Tem=a*(1/2)*(1/(1+sqrt((1)*(1)+(c+c)*(c+c)))); +mprintf('The starting torque is %f Nm \n The maximun Torque is %f Nm',Test,Tem); diff --git a/3760/CH6/EX6.2/Ex6_2.sce b/3760/CH6/EX6.2/Ex6_2.sce new file mode 100644 index 000000000..d9d044910 --- /dev/null +++ b/3760/CH6/EX6.2/Ex6_2.sce @@ -0,0 +1,40 @@ +clc; +Nf=1440; //full load speed +f=50; //frequency + +disp('case a'); + +P=fix((120*f)/Nf); //formula for finding poles +mprintf('The number of Poles is %d\n',P); + +disp('case b'); + + +Ns=(120*f)/P; //finding synchronous speed +s=(Ns-Nf)/Ns; //finding slip at full load +f2=s*f; //rotor frequency +mprintf('The full load slip is %f and the rotor frequency is %f Hz\n',s,f2); + +disp('case c'); + + +//speed of stator field w.r.t stator structure is Ns +Nss=Ns; +// answer for speed of stator field with respect to stator structure is given wrong in book +Wss=(2*%pi*Ns)/60; +Nsr=Ns-Nf; //speed of stator field w.r.t rotor structure +Wsr=(2*%pi*Nsr)/60; +printf('The speed of stator field w.r.t stator is %f rad/sec ,%f rpm\n and w.r.t rotor is %f rad/sec ,%f rpm\n',Wss,Nss,Wsr,Nsr); + +disp('case d'); + + +//speed of rotor field w.r.t stator structure is Nf+Ns +Nrr=(120*f2)/P; //speed of rotor field w.r.t rotor structure +Nrs=Nf+Nrr; +// answer for speed of rotor field with respect to rotor structure is given wrong in book +Wrs=(2*%pi*Nrs)/60; + +Wrr=(2*%pi*Nrr)/60; +//The stator and rotor fields are stationary w.r.t to each other +printf('The speed of rotor field w.r.t stator structure is %f rad/sec, %f rpm\n and w.r.t rotor structure is %f rad/sec, %f rpm and speed of rotor field w.r.t stator field is 0',Wrs,Nrs,Wrr,Nrr); diff --git a/3760/CH6/EX6.20/Ex6_20.sce b/3760/CH6/EX6.20/Ex6_20.sce new file mode 100644 index 000000000..8c7d78bca --- /dev/null +++ b/3760/CH6/EX6.20/Ex6_20.sce @@ -0,0 +1,36 @@ +clc; +sA=0.05; //slip + +//for part a +disp('for part a '); +//Torque is proportional to s/r2 +//As per given conditions sB=a*sA +a=4; +sB=a*sA; +mprintf('The slip is %d times previous slip and \n',a); + +//for part b +disp('for part b '); +//I2 is directly proportional to s/r2 +//As per given conditions I2B=b*I2A +b=sB/(a*sA); +//Rotor ohmic losses is directly proportional to I*I*r2 +//As per given conditions P2=c*P1 +c=a*b; +//As per given conditions Pf2=d*Pf1 +d=b; +mprintf('rotor current for new rotor resistance is equal to initial rotor current \n Rotor ohmic losses for new rotor resistance=%f times initial ohmic losses \n power factor for new rotor resistance is equal to initial power factor',c); + +//for part c +disp('for part c '); +//As per given conditions Wa=e*Ws +e=1-sA; +//Wb=f*Ws +b=1-sB; +//PB=g*PA +g=b/e; +mprintf('The power output is reduced to %f times previous value',g); + + + + diff --git a/3760/CH6/EX6.21/Ex6_21.sce b/3760/CH6/EX6.21/Ex6_21.sce new file mode 100644 index 000000000..b48ac82d9 --- /dev/null +++ b/3760/CH6/EX6.21/Ex6_21.sce @@ -0,0 +1,27 @@ +clc; +f=50; +P=6; +Pmsh=10000; //Shaft Output +N=930; +Pw=600; +Pf=0.01*Pmsh; //Friction and Windage losses +Ns=(120*f)/P; +NmT=800; //Speed at maximum torque + + +//for part a +disp('for part a'); +sfl=(Ns-N)/Ns; +Pm=Pmsh+Pf; +Pg=Pm/(1-sfl); +Pst=Pg+Pw; +mprintf('Total Rotor input is %f W \n Total Stator input is %f W \n',Pg,Pst); + +//for part b +disp('for part b'); +smT=(Ns-NmT)/Ns; +Ws=(2*%pi*Ns)/60; +Tefl=Pg/Ws; +Test=(((smT/sfl)+(sfl/smT))/2)*(2/((smT)+(1/smT)))*Tefl; +mprintf('Maximun Torque is %f Nm',Test); + diff --git a/3760/CH6/EX6.22/Ex6_22.sce b/3760/CH6/EX6.22/Ex6_22.sce new file mode 100644 index 000000000..c44f42765 --- /dev/null +++ b/3760/CH6/EX6.22/Ex6_22.sce @@ -0,0 +1,21 @@ +clc; +Pm=7500; +V=420; +f=50; +P=4; +s=0.04; +r1=1.2; +x1=1.4; +x2=1.4; +Xm=38.6; + +//As per Thevenin's Equivalent circuit +Re=(r1*Xm)/(Xm+x2); +Xe=(x1*Xm)/(x2+Xm); +Ve=(V/sqrt(3))*(Xm/(x2+Xm)); +r2=(3)*(1-s)*s*Ve*Ve*(1/Pm); +smT=r2/(sqrt((Re*Re)+((Xe+x2)*(Xe+x2)))); +Tem=((3*Ve*Ve)/((((120*f)/P)/60)*2*%pi))*(1/2)*(1/(Re+(sqrt((Re*Re)+((Xe+x2)*(Xe+x2)))))); +Test=((3*Ve*Ve)/((((120*f)/P)/60)*2*%pi))*(r2/(((Re+r2)*(Re+r2))+((Xe+x2)*(Xe+x2)))); +mprintf('maximum torque is %f Nm \n slip is %f \n starting torque is %f Nm',Tem,smT,Test); + diff --git a/3760/CH6/EX6.23/Ex6_23.sce b/3760/CH6/EX6.23/Ex6_23.sce new file mode 100644 index 000000000..177f13087 --- /dev/null +++ b/3760/CH6/EX6.23/Ex6_23.sce @@ -0,0 +1,56 @@ +clc; +Pm=100000; +V=420; +P=6; +f=50; +sfl=0.04; +smT=0.2; + +//for part a +disp('for part a'); +Pg=Pm/(1-sfl); +Ws=(4*%pi*f)/P; +Tefl=Pg/Ws; +//a=Tefl/Tem +a=(1/(2/((sfl/smT)+(smT/sfl)))); +Tem=a*Tefl; +mprintf('Maximum Torque is %f Nm \n',Tem); + +//for part b +disp('for part b'); +//b=Test/Tem +b=2/((1/smT)+(smT)); +Test=b*Tem; +mprintf('The starting Torque is %f Nm \n',Test) + +//for part c +disp('for part c'); +Prot=sfl*Pg; +mprintf('Rotor Ohmic losses are %f W \n',Prot) + +//for part d +disp('for part d'); +//Output is proportional to (s(1-s))/r2 +//Given conditions gives the equation as s1*s1-s1+0.0768 +Q=[1 -1 0.0768]; +R=roots(Q); +s1=R(2); +mprintf('Slip is %f \n',s1) + +//for part e +disp('for part e'); +Tefl=(Pm/(1-s1))/Ws; +mprintf('full-load torque is %f Nm \n',Tefl) + +//for part f +disp('for part f'); +smT1=2*smT; +mprintf('slip at maximum torque is %f',smT1); + + + + + + + + diff --git a/3760/CH6/EX6.25/Ex6_25.sce b/3760/CH6/EX6.25/Ex6_25.sce new file mode 100644 index 000000000..d24e286fa --- /dev/null +++ b/3760/CH6/EX6.25/Ex6_25.sce @@ -0,0 +1,46 @@ +clc; +P=10; +f=50; +Pm=48000; +pf=0.8; +f21=120; //min frequency range +f22=300; //max frequency range +Ns=(120*f)/P; + +//for f2=300 +Nr1=((120*f21)/P)-Ns; +//for f2=600 +Nr2=((120*f22)/P)-Ns; +mprintf('Thus the dc motor changes speed from %f to %f rpm \n',Nr1,Nr2) + +//for part b and c +s1=(Nr1+Ns)/Ns; +s2=(Nr2+Ns)/Ns; +Pr=Pm/pf; +Pr1=Pr/s1; +Pr2=Pr/s2; +R1=(s1-1)*Pr1*pf; +R2=(s2-1)*Pr2*pf; +T1=(R1*60)/(2*%pi*Nr1); +T2=(R2*60)/(2*%pi*Nr2); +// stator should be able to handle higher KVA +mprintf('KVA rating of induction motor stator is %f KVA\n',Pr1/1000) +mprintf('DC motor rating is %f KW \n Maximum torque output from DC motor is %f Nm \n',R2/1000,T1); + +//for part d +//When speed is limited to 2700 rpm +P1=((120*f22)-(120*f))/2700; +P1=ceil(P1); +mprintf('Number of Poles is %d \n',P1); + +//for part e +Nr11=((f22*120)/P1)-((120*f)/P1); +Nr22=((f21*120)/P1)-((120*f)/P1); +mprintf('Thus the new speed range of dc motor is from %f to %f rpm \n',Nr22,Nr11); + + + + + + + diff --git a/3760/CH6/EX6.26/Ex6_26.sce b/3760/CH6/EX6.26/Ex6_26.sce new file mode 100644 index 000000000..479c80f24 --- /dev/null +++ b/3760/CH6/EX6.26/Ex6_26.sce @@ -0,0 +1,15 @@ +clc; +f=50; +P=4; +Pm=10000; //Rated output +N=1425; +Nm=1200; //Speed at which maximun torque is developed + +Ns=(120*f)/P; +s=(Ns-N)/Ns; +Ws=(2*%pi*Ns)/60; +Tefl=(Pm/Ws)*(1/(1-s)); +smT=(Ns-Nm)/Ns; +Tem=Tefl*((s/smT)+(smT/s))*(1/2); +Test=Tem*(2)*(1/((1/smT)+(smT/1))); +mprintf('The starting torque is %f Nm',Test); diff --git a/3760/CH6/EX6.27/Ex6_27.sce b/3760/CH6/EX6.27/Ex6_27.sce new file mode 100644 index 000000000..d8556fde4 --- /dev/null +++ b/3760/CH6/EX6.27/Ex6_27.sce @@ -0,0 +1,49 @@ +clc; +fs=2; //slip frequency +V=400; +f=50; +V2=340; //New voltage +f2=40; //New frequency +smT=0.1; //slip at which it develops maximum torque + +//maximun torque's slip is directly proportional to (1/f) +smT1=(f/f2)*smT; + +//Maximun Torque is directly proportional to ((V*V)/(f*f)) +s=fs/f; +//Ted(Developed Torque) is proportional to (Tem/smT)*(s/smT) +//Ted1(400V,50Hz)proportional a +a=((V*V)/(f*f))*(s/smT); +//equating the developed torque equation +s1=a*(((f2)*(f2))/((V2)*(V2)))*(smT1); +fs1=s1*f2; +mprintf('The new slip frequency is %f Hz',fs1); + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/3760/CH6/EX6.28/Ex6_28.sce b/3760/CH6/EX6.28/Ex6_28.sce new file mode 100644 index 000000000..3132bc636 --- /dev/null +++ b/3760/CH6/EX6.28/Ex6_28.sce @@ -0,0 +1,46 @@ +clc; +f=50; +V=440; +P=4; +N=1490; //Rated speed +N1=1600; //New Speed + +Ns=(120*f)/P; +s=(Ns-N)/Ns; +//With neglecting resistances and leakage reactances +//Torque is directly proportional to s/(fr2) +//Appllying the condition for same torque we get +//a=s/f +a=(s/f); +//Ns/s=b +b=120/P; +//s=(Ns-N1)/Ns +//Using above equation we get equation (f*f)-7500f-400000 +Q=[1 -7500 400000] +R=roots(Q); +f1=R(2); +mprintf('Value of new Frequency is %f Hz',f1); + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/3760/CH6/EX6.29/Ex6_29.sce b/3760/CH6/EX6.29/Ex6_29.sce new file mode 100644 index 000000000..48d84d2cf --- /dev/null +++ b/3760/CH6/EX6.29/Ex6_29.sce @@ -0,0 +1,60 @@ +//debug +clc; +V1=420; //supply voltage +r1=2.95; +x1=6.82; +r2=2.08; +x2=4.11; +Iml=6.7; //magnetizing line current +Pw=269; //core loss +s=0.03; //slip +P=12; +f=50; +N=(120*f)/P; +Ns=(120*f)/P; + +Im=Iml/sqrt(3); +//V1=E1+Im(r1+jx1) +//Above equation on solving gives the solution as E1*E1+52.8E1-175572.65 +Q=[1 52.8 -175572.62]; +R=roots(Q); +E1=R(2); +Xm=E1/Im; +//As per the circuit diagram +a=r2/s; +Zf=(((r2/s)+x2*%i)*Xm*%i)/((r2/s)+((x2+Xm)*%i)); +Rf=real(Zf); +Zab=complex((real(Zf)+r1),(imag(Zf)+x1)); +I1=420/Zab; +I1M=sqrt((real(I1)*real(I1))+(imag(I1)*imag(I1))); +an1=atand(imag(I1),real(I1)); +pf=cosd(atand(imag(I1)/real(I1))); +I2=I1*(Xm*%i)*(1/((r2/s)+((x2+Xm)*%i))); +an2=atand(imag(I2),real(I2)); +I2M=sqrt((real(I2)*real(I2))+(imag(I2)*imag(I2))); +T=3*(60/(2*%pi*N))*I1M*I1M*Rf; + +mprintf('The power factor is %f Lag\n The input current is %f A lagging by an angle of %f degrees \n The output rotor current is %f A lagging by an angle of %f degrees \n The Torque developed is %f Nm \n',pf,I1M,-an1,I2M,-an2,T); + + +//For maximun Torque +X1=x1+Xm; +Re=(r1*Xm)/X1; +Xe=(x1*Xm)/X1; +smT=r2/(sqrt((Re)*(Re)+(x2+Xe)*(x2+Xe))); +Nm=Ns*(1-smT); +Tem=3*(E1)*(E1)*(1/(Re+(sqrt((Re)*(Re)+(x2+Xe)*(x2+Xe)))))*(1/2)*(1/(2*%pi*(N/60))); +mprintf('maximum torque developed is %f Nm \n corresponding speed is %f rpm',Tem,Nm); + + + + + + + + + + + + + diff --git a/3760/CH6/EX6.3/Ex6_3.sce b/3760/CH6/EX6.3/Ex6_3.sce new file mode 100644 index 000000000..0861c8ed8 --- /dev/null +++ b/3760/CH6/EX6.3/Ex6_3.sce @@ -0,0 +1,11 @@ + +clc; +f=50; //frequency of stator +P=6; +NofO=90; //number of oscillation +f2=NofO/60; //rotor frequency +s=f2/f; //slip +Ns=(120*f)/P; //synchronous speed +Nr=Ns*(1-s); //rotor speed + +mprintf('The rotor speed is %f rpm',Nr); diff --git a/3760/CH6/EX6.30/Ex6_30.sce b/3760/CH6/EX6.30/Ex6_30.sce new file mode 100644 index 000000000..7db1313f8 --- /dev/null +++ b/3760/CH6/EX6.30/Ex6_30.sce @@ -0,0 +1,61 @@ + +//In solution they have taken different value of speed at rated torque from what is given in question that is why answer is varying +clc; +P=4; +Pm=10000; //OUTPUT POWER +f=50; //FREQUENCY +N=1440; //SPEED AT WHICH RATED TORQUE IS OBTAINED +Ns=(120*f)/P; //SYNCHRONOUS SPEED + +s=(Ns-N)/Ns; +//Torque is directly proportional to the slip +//As per given conditions +s1=(1/2)*s; +Nr=Ns*(1-s1); +Pm1=(1/2)*(((Pm*60)/(2*%pi*N)))*((2*%pi*Nr)/(60)); +mprintf('The motor speed is %f rpm \n The power output is %f W',Nr,Pm1); + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/3760/CH6/EX6.31/Ex6_31.sce b/3760/CH6/EX6.31/Ex6_31.sce new file mode 100644 index 000000000..3dba3c754 --- /dev/null +++ b/3760/CH6/EX6.31/Ex6_31.sce @@ -0,0 +1,23 @@ + +clc; +N=1455; +Ns=1500; //General case considered in the problem +s1=(Ns-N)/Ns; + +//for V1=0.9V +//V1/V=a +a=0.9; +//T=(3VVs)/(Wsr2) +//As torque is constant +s2=(s1)/(a*a); +Nr=Ns*(1-s2); +//I=s1V/r2 +//I22/I21=b +b=(s2*a)/s1; +//Losses Ratio=c +R=b*b; + +d=((N-Nr)/N)*100; +e=((R-1)/1)*100; +mprintf('Percentage reduction in speed is %f percent\n',d); +mprintf('Percentage reduction in ohmic losses is %f percent\n',e); diff --git a/3760/CH6/EX6.32/Ex6_32.sce b/3760/CH6/EX6.32/Ex6_32.sce new file mode 100644 index 000000000..f4fa3c183 --- /dev/null +++ b/3760/CH6/EX6.32/Ex6_32.sce @@ -0,0 +1,14 @@ +clc; +P=7500; // rated power of induction motor +v=400; // rated voltage of motor +To=6; // no load torque +fs=0.04; // full load slip +p=6; // number of poles +f=50; // frequency +ns=(120*f)/p; // synchronous speed +Tl=(P*60)/(2*%pi*ns*(1-fs)); // full load torque +s=(To*fs*v^2)/(Tl*(v/2)^2); // slip at no load +no=ns*(1-s); +printf('No load speed of motor is %f rpm\n',no); + + diff --git a/3760/CH6/EX6.33/Ex6_33.sce b/3760/CH6/EX6.33/Ex6_33.sce new file mode 100644 index 000000000..56142dbbd --- /dev/null +++ b/3760/CH6/EX6.33/Ex6_33.sce @@ -0,0 +1,20 @@ +clc; +tr=2.5; // ratio of maximum torque to full load torque +sm=0.18; // maximum slip +r=1; // per phase rotor resistance +x2=r/sm; // rotor reactance +// using expression for tr we obtain a quadratic equation is s(full load slip) whose terms are +t1=1; +t2=-tr*2*sm; +t3=sm^2; +t=[ t1 t2 t3 ]; +s=roots(t); +x=sqrt((2*x2)/(((r/s(2))^2+x2^2)*s(2))); +printf('Minimum voltage that could be impressed so that motor can supply rated torque is %f times rated voltage or %f percent of rated voltage\n',x,x*100); +// from expression for maximum torque and full load torque we get a quadratic equation in R(externall resistance) whose terms are +t1=1; +t2=2-2*x2; +t3=1+x2^2-2*x2; +t=[ t1 t2 t3 ]; +R=roots(t); +printf('External resistance inserted in rotor circuit is %f ohms\n',R(2)); diff --git a/3760/CH6/EX6.34/Ex6_34.sce b/3760/CH6/EX6.34/Ex6_34.sce new file mode 100644 index 000000000..69f94a821 --- /dev/null +++ b/3760/CH6/EX6.34/Ex6_34.sce @@ -0,0 +1,17 @@ +clc; +f1=50; // rated frequency of 3- phase induction motor +f2=40; // applied frequency +vr=0.9; // ratio of applied voltage to rated voltage +m=3; // number o phases +fr=f2/f1; // ratio of frequencies +ir=fr/vr; +printf('Ratio of starting current at %d Hz to starting current at %d Hz is %f \n',f1,f2,ir); +tr=(m/f1)*(f2/m)*(fr/vr)^2; +printf('Ratio of starting torque at %d Hz to starting torque at %d Hz is %f \n',f1,f2,tr); +tmr=(m/f1)*(f2/m)*(fr/(vr)^2); +printf('Ratio of maximum torque at %d Hz to maximum torque at %d Hz is %f \n',f1,f2,tmr); +vr1=sqrt((m/f1)*(f2/m)*fr^2); +printf('For the same starting torque ratio of voltage at %d Hz to ratio of voltage at %d Hz is %f\n',f2,f1,vr1); +vr2=sqrt((m/f1)*(f2/m)*fr); +printf('For the same maximum torque ratio of voltage at %d Hz to ratio of voltage at %d Hz is %f\n',f2,f1,vr2); +// answer for ratio of v2/v1 for same starting torque is slightly different from what is given in book diff --git a/3760/CH6/EX6.35/Ex6_35.sce b/3760/CH6/EX6.35/Ex6_35.sce new file mode 100644 index 000000000..eecf2f645 --- /dev/null +++ b/3760/CH6/EX6.35/Ex6_35.sce @@ -0,0 +1,21 @@ +clc; +P=60000; // rated power of 3-phase induction motor +p=4; // number of poles +f=50; // frequency +po=3000; // no load losses +i=0.3; // ratio of rated current to rated voltage when motor is prevented from rotating +pi=4000; // power input when motor is prevented from rotating +pr=0.3; //ratio of mechanical losses to no load losses +pm=pr*po; // mechanical losses +lsc1=po-pm; // stator core loss +lsc2=pi/2; // stator copper loss=rotor copper loss +disp('case a'); +pg=P+pm+lsc2; // air gap power +s=lsc2/pg; +printf('Slip at rated load is %f\n',s); +disp('case b'); +pim=pi/i^2; // power input to motor during blocked rotor test +pg=pim-lsc1-lsc2; // air gap power +ws=(4*%pi*f)/p; // synchronous speed +T=pg/ws; +printf('Starting torque at rated applied voltage is %f Nm\n',T); diff --git a/3760/CH6/EX6.36/Ex6_36.sce b/3760/CH6/EX6.36/Ex6_36.sce new file mode 100644 index 000000000..e6d377fe2 --- /dev/null +++ b/3760/CH6/EX6.36/Ex6_36.sce @@ -0,0 +1,11 @@ +clc; +sm=0.2; // slip +f1=50; // rated frequency of 3- phase induction motor +f2=45; // applied frequency +fr=f2/f1; // ratio of frequenciesir=fr/vr; +ir=sqrt((sm^2+1)/(sm^2+fr^2)); +printf('Ratio of starting current at %d Hz to starting current at %d Hz is %f \n',f2,f1,ir); +tr=(sm^2+1)/(sm^2+fr^2); +printf('Ratio of starting torque at %d Hz to starting torque at %d Hz is %f \n',f2,f1,tr); +tmr=1/fr; +printf('Ratio of maximum torque at %d Hz to maximum torque at %d Hz is %f \n',f2,f1,tmr); diff --git a/3760/CH6/EX6.37/Ex6_37.sce b/3760/CH6/EX6.37/Ex6_37.sce new file mode 100644 index 000000000..a921d307f --- /dev/null +++ b/3760/CH6/EX6.37/Ex6_37.sce @@ -0,0 +1,31 @@ +clc; +P=20000; // rated power of induction motor +v=400; // rated voltage of motor +f=50; // frequency +m=3; // number of phases +p=4; // number of poles +r1=0.2; // stator resistance +x=0.45; // stator/rotor leakage reactance +xm=18; // magnetising reactance +s=0.04; // slip +pg=P/(1-s); // air gap power +pr=s*pg; // rotor copper loss +vp=v/sqrt(3); // per phase voltage +ve=(vp*xm)/(x+xm); // Thevenin voltage +re=(r1*xm)/(x+xm); // Thevenin resistance +xe=(x*xm)/(x+xm); // Thevenin reactance +// using Thevenin's theorrm and rotor copper loss expression we get a quadratic equation in r2 (rotor resistance) whose terms are +t1=pr/s^2; +t2=((2*pr*re)/s)-(m*ve^2); +t3=pr*((xe+x)^2+re^2); +t=[ t1 t2 t3]; +r2=roots(t); +disp('case a'); +ws=(4*%pi*f)/p; // synchronous speed +Tm=(m*ve^2)/(ws*2*(re+sqrt(re^2+(x+xe)^2))); +printf('Maximum internal torque is %f Nm\n',Tm); +Ti=(m*ve^2*r2(1))/(ws*((re+r2(1))^2+(x+xe)^2)); +printf('Initial starting torque is %f Nm\n',Ti); +disp('case b'); +sm=r2(1)/(sqrt(re^2+(xe+x)^2)); +printf('Slip at maximum torque is %f ',sm); diff --git a/3760/CH6/EX6.4/Ex6_4.sce b/3760/CH6/EX6.4/Ex6_4.sce new file mode 100644 index 000000000..cd614c991 --- /dev/null +++ b/3760/CH6/EX6.4/Ex6_4.sce @@ -0,0 +1,31 @@ +clc; +f1=50; //frequency of supply +f2=20; //frequency required by the load +P=4; +//for part a + +Nrf_ss=(120*f1)/P; //Speed of rotor field w.r.t stator structure +Nrf_rs=(120*f2)/P; //Speed of stator field w.r.t rotor structure +//Nr (+or-) speed of rotor field w.r.t rotor = speed of stator field w.r.t stator +//for +ve sign rotor must be driven in the direction of stator field at a speed +Nr1=Nrf_ss-Nrf_rs; +Nr2=Nrf_ss+Nrf_rs; +mprintf('The two speeds are %d and %d \n',Nr1,Nr2); + + +//for part b + +//for rotor speed Nr1 +s1=(Nrf_ss-Nr1)/Nrf_ss; +//for rotor speed Nr2 +s2=(Nrf_ss-Nr2)/Nrf_ss; +//On evaluation the ratio of voltages is found as + R=s1/s2; //R=E1/E2 +mprintf('The ratio of two voltages available at the slip rings at the two speeds is %d',R); + +//for part c + + + + + diff --git a/3760/CH6/EX6.41/Ex6_41.sce b/3760/CH6/EX6.41/Ex6_41.sce new file mode 100644 index 000000000..1dcdd6c94 --- /dev/null +++ b/3760/CH6/EX6.41/Ex6_41.sce @@ -0,0 +1,31 @@ +clc; +P=10000; // rated power of squirrel cage induction motor +V=400; // rated voltage of motor +m=3; // number of phases +// no load test results +Vo=400; // applied voltage +io=8; // no load current +Po=250; // no load power +// blocked rotor test +vb=90; // applied voltage +ib=35; // current +pb=1350; // input power +// ac resistance is 1.2 times dc resistance +rs=0.6; // per phase dc resistance of stator winding +pr=Po-m*(io/sqrt(3))^2*(1.2*rs); // no load rotational losses +znl=Vo/(io/sqrt(3)); // no load impedance +rnl=Po/(m*(io/sqrt(3))^2); // no load resistance +xnl=sqrt(znl^2-rnl^2); // no load reactance +zbr=vb/(ib/sqrt(3)); // block rotor test impedance +Rbr=pb/(m*(ib/sqrt(3))^2); // block rotor resistance +xbr=sqrt(zbr^2-Rbr^2); // block rotor reactance +x1=xbr/2; +xm=xnl-x1; +X2=xm+x1; +r2=(Rbr-1.2*rs)*(X2/xm)^2; +printf('Rotational losses are %f watts\n',pr); +printf('Stator resistance is %f ohms\n',1.2*rs); +printf('Rotor resistance is %f ohms\n',r2); +printf('Magnetising reactance is %f ohms\n',xm); +printf('Stator reactance is %f ohms\n',x1); +printf('Rotor reactance is %f ohms',x1); diff --git a/3760/CH6/EX6.43/Ex6_43.sce b/3760/CH6/EX6.43/Ex6_43.sce new file mode 100644 index 000000000..449e68d60 --- /dev/null +++ b/3760/CH6/EX6.43/Ex6_43.sce @@ -0,0 +1,21 @@ +clc; +p=10000; // rated power of SCIM +v=420; // rated voltage of SCIM +p=4; // number of poles +f=50; // frequency of SCIM +// results of blocked rotor test +vb=210; // applied voltage +ib=20; // applied current +pb=5000; // power dissipated +l=300; // stator core loss +rs=0.6; // dc stator resistance +m=3; // number of phases +R=(rs*3)/2; // per phase stator resistance +Rs=1.2*R; // Effective stator resistance per phase +pi=pb*(v/vb)^2; // power input at rated voltage during block rotor test +is=ib*(v/vb); // stator current at rated voltage during block rotor test +pg=pi-m*(is/sqrt(3))^2*Rs-l; // air gap power +ws=(4*%pi*f)/p; +printf('synchronous speed is %f rad/sec\n',ws); +T=pg/ws; +printf('Starting torque is %f Nm',T); diff --git a/3760/CH6/EX6.44/Ex6_44.sce b/3760/CH6/EX6.44/Ex6_44.sce new file mode 100644 index 000000000..a73fecad5 --- /dev/null +++ b/3760/CH6/EX6.44/Ex6_44.sce @@ -0,0 +1,23 @@ +clc; +p=6; // number of poles +m=3; // number of phases +f=50; // frequency of motor +P=40000; // rated power of induction motor +v=400; // rated voltage of induction motor +// results of blocked rotor test +vb=200; // applied voltage +ib=110; // applied current +pf=0.4; // power factor +f1=45; // frequency at starting torque is to be determined +e=380; // voltage at starting torque is to be determined +vbp=vb/sqrt(3); // per phase voltage during blocked rotor test +zb=vbp/ib; // total impedance referred to stator +R=zb*pf; // net resistance referred to stator +X=zb*(sqrt(1-pf^2)); // net reactance referred to stator +X=X*(f1/f); // net reactance at frequency=45 +Z=R+X*%i; // impedance at frequency=45 +v1=e/sqrt(3); // per phase stator +is=v1/(Z); // starting current +ws=(4*%pi*f)/p; // synchronous speed +T=(3/ws)*abs(is)^2*(R/2); +printf('Starting torque is %f Nm',T); diff --git a/3760/CH6/EX6.45/Ex6_45.sce b/3760/CH6/EX6.45/Ex6_45.sce new file mode 100644 index 000000000..168f5d7eb --- /dev/null +++ b/3760/CH6/EX6.45/Ex6_45.sce @@ -0,0 +1,46 @@ +clc; +v=400; // rated voltage of motor +m=3; // number of phases +r=2; // ratio of leakage reactance of stator to leakage reactance of rotor +ns=1000; // synchronous speed +n=960; // speed of motor +f=50; // frequency +// no load test results +Vo=400; // applied voltage +io=7.5; // no load current +pfo=0.135; // power factor +// blocked rotor test +vb=150; // applied voltage +ib=35; // current +pfb=0.44; // power factor +znl=Vo/(io*sqrt(3)); // no load impedance +rnl=znl*pfo; // no load resistance +xnl=sqrt(znl^2-rnl^2); // no load reactance +zbr=vb/(ib*sqrt(3)); // block rotor test impedance +Rbr=zbr*pfb; // block rotor resistance +xbr=sqrt(zbr^2-Rbr^2); // block rotor reactance +x2=xbr/3; // leakage reactance of rotor +x1=x2*2; // leakage reactance of stator +xm=xnl-x1; // magnetising reactance +r1=Rbr/2; // stator resistance/rotor resistance +V1=v/sqrt(3); // per phase stator voltage +Ve=(V1*xm)/(x1+xm); // thevenin voltage +Re=(r1*xm)/(x1+xm); // thevenin resistance +Xe=(x1*xm)/(x1+xm); // thevenin resistance +lr=sqrt(3)*v*io*pfo-m*io^2*r1; // rotational losses +s=(ns-n)/ns; // slip +ir=Ve/(Re+(r1/s)+%i*(Xe+x2)); // rotor current at slip +Pm=m*abs(ir)^2*r1*((1-s)/s); +disp('case a'); +Psh=Pm-lr; +printf('Mechanical power output is %f KW\n',Psh/1000); +disp('case b'); +wr=((2*%pi*f)*(1-s))/m; // speed at which motor is running +T=Psh/wr; +printf('Net torque is %f Nm\n',T); +disp('case c'); +lor=(Pm*s)/(1-s); // rotor/stator ohmic losses +Tl=lor*2+lr; // total losses +pi=Tl+Psh; // input power +ne=Psh/pi; +printf('Efficiency of motor is %f percent',ne*100); diff --git a/3760/CH6/EX6.46/Ex6_46.sce b/3760/CH6/EX6.46/Ex6_46.sce new file mode 100644 index 000000000..ca77363ab --- /dev/null +++ b/3760/CH6/EX6.46/Ex6_46.sce @@ -0,0 +1,11 @@ +clc; +f=60; // frequency +p=6; // number of poles +n=1175; // speed of induction motor +re=0.06; // reduction in frequency +dv=0.1; // reduction in voltage +ws1=(120*f)/p; // synchronous speed +s1=(ws1-n)/ws1; // slip +s2=((1-re)/((1-dv)^2))*s1; // new slip +ws2=ws1*(1-s2)*(1-re); +printf('New operating speed is %f rpm',ws2); diff --git a/3760/CH6/EX6.47/Ex6_47.sce b/3760/CH6/EX6.47/Ex6_47.sce new file mode 100644 index 000000000..4c12aa0ae --- /dev/null +++ b/3760/CH6/EX6.47/Ex6_47.sce @@ -0,0 +1,60 @@ +clc; +P=15000; // rated power of induction motor +V=400; // rated voltage of motor +f=50; // frequency +m=3; // number of phases +po=4; // number of poles +// no load test results +Vo=400; // applied line voltage +io=9; // no load line current +Po=1310; // power input +// blocked rotor test +vb=200; // line voltage +ib=50; // line current +pb=7100; // input power +pfo=po/(sqrt(3)*io*Vo); // no load power factor +pfb=pb/(sqrt(3)*ib*vb); // short circuit power factor +isc=(V/vb)*ib; // short circuit current +printf('Short circuit current is %d A\n',isc); +// circle diagram is drawn in fig 6.37 with scale 6 A= 1 cm +disp('case a'); +x=6; // scale +pps=(V/sqrt(3))*x; // per phase power scale +fp=P/3; // full load power per phase +// as per the construction we obtain OP=6.05 which corresponds to full load current +ifl=x*6.05; +printf('Full load line current is %f A\n',ifl); +// from fig angle POV1=29.5; +fpf=cosd(29.5); +printf('Full load power factor is %f lagging\n',fpf); +// full load slip is given by ratio ba/bP where ba=2.5, bP=38.5 +fs=2.5/38.5; +printf('Full load slip is %f \n',fs); +ws=(2*%pi*f*120)/(po*60); // synchronous speed +Ft=(3.85*pps*m)/ws; +printf('Full load torque is %f Nm\n',Ft); +// efficiency is given by ratio aP/dP where aP=3.6, dP=4.45 +ne=3.6/4.45; +printf('Full load efficiency is %f percent\n',ne*100); +disp('case b'); +// OP turns out to be tangent to circular locus, therefore +disp('Maximum power factor is 0.87 lagging'); +disp('Maximum line current is 36.3 A'); +disp('case c'); +// according to constructions given in solution we obtain AA'=5.3 from which maximum power output can be calculated +mpo=5.3*m*pps; +printf('Maximum output power is %f KW\n',mpo/1000); +// according to constructions given in solution we obtain CC'=8.45=radius of circle from which maximum power input can be calculated +mpi=8.45*m*pps+po; +printf('Maximum input power is %f KW\n',mpi/1000); +disp('case d'); +// according to constructions given in solution we obtain BB'=6.65 from which maximum torque can be calculated +Mt=(6.65*m*pps)/ws; +printf('Maximum torque is %f Nm\n',Mt); +// maximum slip is given by ratio fb'/BB' where fb'=1.58, BB'=6.65 +s=1.58/6.65; +printf('Maximum slip is %f \n',s); +disp('case e'); +// according to constructions given in solution we obtain DG=3.3 from which starting torque can be calculated +St=(3.3*m*pps)/ws; +printf('Starting torque is %f Nm\n',St); diff --git a/3760/CH6/EX6.48/Ex6_48.sce b/3760/CH6/EX6.48/Ex6_48.sce new file mode 100644 index 000000000..1c9688d8f --- /dev/null +++ b/3760/CH6/EX6.48/Ex6_48.sce @@ -0,0 +1,55 @@ +clc; +P=4500; // rated power of induction motor +V=400; // rated voltage of motor +f=50; // frequency +m=3; // number of phases +// no load test results +Vo=400; // applied line voltage +io=4.2; // no load line current +Po=480; // power input +// blocked rotor test +vb=215; // line voltage +ib=15; // line current +pb=1080; // input power +rs=1.2; // rotor resistance referred to stator per phase +nt=2; // stator to rotor turns ratio +pfo=Po/(sqrt(3)*io*Vo); // no load power factor +pfb=pb/(sqrt(3)*ib*vb); // short circuit power factor +isc=(V/vb)*(ib*sqrt(3)); // per phase short circuit current +iop=io/sqrt(3); // per phase no load current +x=1; // scale 1 A= 1 cm +// circle diagram is drawn in fig 6.38 +disp('case a'); +// value of maximum torque at starting is not given +// now we note Bf=4.6 and B'f=1.25 using these values external resistance to be inserted is calculated +re=(4.6/1.25)*1.2; // external resistance +printf('External resistance referred to rotor is %f ohms\n',re/nt^2); +// as per the construction we obtain OB=11.24 which is needed to calculate starting line current +is=11.24*sqrt(3); +printf('Starting current is %f A\n',is); +// angle OBB'=45.5 which is needed to calculate power factor +pf=cosd(45.5); +printf('power factor is %f lagging\n',pf); +pps=x*V; // per phase power scale +fp=P/m; // full load power per phase +disp('case b'); +// now torque is 1.25 times full load torque +// now we note NK=2.9 and N'K=2.1 using these values external resistance to be inserted is calculated +re=(2.9/2.1)*1.2; // external resistance +printf('External resistance referred to rotor is %f ohms\n',re/nt^2); +// as per the construction we obtain ON=14.35 which is needed to calculate starting line current +is=14.35*sqrt(3); +printf('Starting current is %f A\n',is); +// angle ONN'=58.3 which is needed to calculate power factor +pf=cosd(58.3); +printf('power factor is %f lagging\n',pf); +disp('case c'); +// we obtain OH=5.35 which is per phase output current +// thetag=41.3 +opf=cosd(41.3); +printf('Operating power factor is %f leading\n',opf); +po=m*5.35*V*opf; +printf('Output power is %f KW\n',po/1000); +// we note HL=3.95 and Ha=4.90 which is needed for efficiency +ne=3.95/4.9; +printf('Induction generator efficiency is %f percent',ne*100); diff --git a/3760/CH6/EX6.49/Ex6_49.sce b/3760/CH6/EX6.49/Ex6_49.sce new file mode 100644 index 000000000..9a4b8a793 --- /dev/null +++ b/3760/CH6/EX6.49/Ex6_49.sce @@ -0,0 +1,37 @@ +clc; +p=150000; // rated power of induction motor +v=400; // rated voltage of induction motor +m=3; // number of phases +r1=0.02; // stator resistance +r2=0.04; // rotor resistance +xm=9.8; // magnetising reactance +x1=0.2; // leakage reactance of stator or rotor +s=0.04; // slip +n=0.93; // efficiency +disp('case a'); +Zf=(((r2/s)+%i*x1)*%i*xm)/((r2/s)+%i*(xm+x1)); // per phase impedance offered to stator by rorating air gap field +z=r1+%i*x1; // impedance of stator +Z=Zf+z; // total impedance +is=v/(sqrt(3)*abs(Z)); // stator current +pg=m*is^2*real(Zf); // air gap power +l1=m*is^2*r1; // stator copper loss +l2=s*pg; // rotor copper loss +Tl=((1/n)-1)*p; // total losses +lr=Tl-(l1+l2); // rotational and core losses +printf('Rotational and core losses are %f W\n',lr); +disp('case b'); +s=-0.04; // slip +Zf=(((r2/s)+%i*x1)*%i*xm)/((r2/s)+%i*(xm+x1)); // per phase impedance offered to stator by rorating air gap field +Z=Zf+z; // total impedance +is=v/(sqrt(3)*abs(Z)); // stator current +pf=cosd(180-atand(imag(Z),real(Z))); // power factor +printf('Power factor at the generator terminal is %f leading\n',pf); +po=sqrt(3)*is*v*pf; // electrical output +printf('Electrical output is %f KW\n',po/1000); +pg=-m*is^2*real(Zf); // air gap power +l1=m*is^2*r1; // stator copper loss +l2=-s*pg; // rotor copper loss +Tl=l1+l2+lr; // total losses +pi=Tl+po; // mechanical power input +ne=po/pi; +printf('Efficiency is %f percent',ne*100); diff --git a/3760/CH6/EX6.5/Ex6_5.sce b/3760/CH6/EX6.5/Ex6_5.sce new file mode 100644 index 000000000..c00fb80ec --- /dev/null +++ b/3760/CH6/EX6.5/Ex6_5.sce @@ -0,0 +1,35 @@ +clc; +P=4; +N=1440; +f=50; +r2=0.2; +x2=1; +E2=120; + +//mistake in Te_fl + + +//for part a +disp('For part a'); +Ns=(120*f)/P; +I2_st=120/(sqrt((r2*r2)+(x2*x2))); +Rpf=(r2)/(sqrt((r2*r2)+(x2*x2))); +Ws=(2*3.14*Ns)/60; +Te_st=(3/Ws)*(I2_st)*(I2_st)*(r2/1); +s_fl=(Ns-N)/Ns; +I2_fl=(s_fl*E2)/(sqrt(r2*r2+(s_fl*x2*s_fl*x2))); +Rpf_fl=(r2)/(sqrt(r2*r2+(s_fl*x2*s_fl*x2))); +Te_fl=((3)*(I2_fl)*(I2_fl)*(r2))/(Ws*s_fl); +RATIOst_fl=I2_st/I2_fl; +RATIOtst_tfl=Te_st/Te_fl; +mprintf('At starting \n the rotor current is %f amp \n Rotor power factor is %f \n Torque is %f rad/sec\n',I2_st,Rpf,Te_st); +mprintf('At full load \n the rotor current is %f amp \n Rotor power factor is %f \n Torque is %f rad/sec\n',I2_fl,Rpf_fl,Te_fl); + + +//for part b +disp('For part b'); +r2_n=r2+1; +I2_stn=E2/(sqrt((r2_n*r2_n)+(x2*x2))); +Rpf_stn=(r2_n)/(sqrt(((r2_n)*(r2_n))+((x2)*(x2)))); +Te_stn=(3/Ws)*(I2_stn)*(I2_stn)*(r2_n/1); +mprintf('At starting \n the rotor current is %f amp \n Rotor power factor is %f \n Torque is %f rad/sec\n',I2_stn,Rpf_stn,Te_stn); diff --git a/3760/CH6/EX6.50/Ex6_50.sce b/3760/CH6/EX6.50/Ex6_50.sce new file mode 100644 index 000000000..fe99ba2f4 --- /dev/null +++ b/3760/CH6/EX6.50/Ex6_50.sce @@ -0,0 +1,43 @@ +clc; +v=400; // balanced supply voltage +i=10; // line current +f=50; // frequency of supply +m=3; // number of phases +pf=0.8; // lagging power factor +pfn=0.9; // improved power factor +disp('staor in star'); +i=i*(pf-%i*sqrt(1-pf^2)); // complex form of line current +il=real(i)/pfn; // line current at improved power factor +il=il*(pfn-%i*sqrt(1-pfn^2)); // complex form of new line current +//from fig. 6.39 +ic=-(imag(i)-imag(il)); // reactive component of current to be neutralised +// capacitor bank is star connected +xcs=v/(ic*sqrt(3)); // capacitance reactance +Cs=1/(2*%pi*f*xcs); // capacitance +K=m*ic*v/sqrt(3); +printf('Per phase value of capacitance for star connected capacitor bank is %f microfarad\n',Cs*10^6); +printf('Total KVA rating for star connected capacitor bank is %f KVA\n',K/1000); +// delta connected capacitor bank +// capacitor bank is delta connected, converting into equivalent star Xstar=Xdelta/3 +xcd=v/(ic*sqrt(3)); // capacitance reactance +Cd=1/(2*%pi*f*xcd*m); // capacitance +printf('Per phase value of capacitance for delta connected capacitor bank is %f microfarad\n',Cd*10^6); +printf('Total KVA rating for delta connected capacitor bank is %f KVA\n',K/1000); +disp('Stator in delta'); +i=(abs(i)/sqrt(3))*(pf-%i*sqrt(1-pf^2)); // complex form of line current +il=real(i)/pfn; // line current at improved power factor +il=il*(pfn-%i*sqrt(1-pfn^2)); // complex form of new line current +//from fig. 6.39 +ic=-(imag(i)-imag(il)); // reactive component of current to be neutralised +// capacitor bank is star connected +// capacitor bank is star connected, converting into equivalent delta Xdelta=3*Xstar +xcs=v/ic; // capacitance reactance +Cs=m/(2*%pi*f*xcs); // capacitance +K=m*ic*v; +printf('Per phase value of capacitance for star connected capacitor bank is %f microfarad\n',Cs*10^6); +printf('Total KVA rating for star connected capacitor bank is %f KVA\n',K/1000); +// delta connected capacitor bank +xcd=v/ic; // capacitance reactance +Cd=1/(2*%pi*f*xcd); // capacitance +printf('Per phase value of capacitance for delta connected capacitor bank is %f microfarad\n',Cd*10^6); +printf('Total KVA rating for delta connected capacitor bank is %f KVA\n',K/1000); diff --git a/3760/CH6/EX6.51/Ex6_51.sce b/3760/CH6/EX6.51/Ex6_51.sce new file mode 100644 index 000000000..f2edf37f2 --- /dev/null +++ b/3760/CH6/EX6.51/Ex6_51.sce @@ -0,0 +1,28 @@ +clc; +v=3300; // balanced supply voltage +p=500000; // rated power of induction motor +f=50; // frequency of supply +m=3; // number of phases +pf=0.7; // lagging power factor +pfn=0.9; // improved power factor +vc=420; // rated voltage of capacitor +n=0.86; // motor efficiency +i=p/(sqrt(3)*v*pf*n); // line current +i=i*(pf-%i*sqrt(1-pf^2)); // complex form of line current +il=real(i)/pfn; // line current at improved power factor +il=il*(pfn-%i*sqrt(1-pfn^2)); // complex form of new line current +//from fig. 6.39 +ic=-(imag(i)-imag(il)); // reactive component of current to be neutralised +// capacitor bank is delta connected +// capacitor bank is delta connected, converting into equivalent star Xstar=Xdelta/3 +xcd=v/(ic*sqrt(3)); // capacitance reactance +Cd=1/(2*%pi*f*xcd*m); // capacitance +// now each capacitor is rated at 420 V, number of capacitor connected in series is +n=ceil(v/vc); +C=Cd*n; +printf('Per phase value of each capacitance for delta connected capacitor bank is %f microfarad\n',C*10^6); +// let R be resistance of distribution circuit +// power lost without capacitor bank is m*abs(i)^2*R +// power lost with capacitor bank is m*abs(il)^2*R therefore +ps=(abs(i)^2-abs(il)^2)/abs(i)^2 +printf('Percentage saving in losses is %f percent',ps*100); diff --git a/3760/CH6/EX6.53/Ex6_53.sce b/3760/CH6/EX6.53/Ex6_53.sce new file mode 100644 index 000000000..0ad0b362a --- /dev/null +++ b/3760/CH6/EX6.53/Ex6_53.sce @@ -0,0 +1,8 @@ +clc; +fs=0.05; // full load slip +ir=6; // ratio of starting current and full load current +t=1; // ratio of starting torque to full load torque +x=sqrt(t/((ir^2)*fs)); +printf('Tapping point is at %f percent\n',x*100); +is=x^2*ir; +printf('Starting current is %f times full load current\n',is); diff --git a/3760/CH6/EX6.54/ex6_54.sce b/3760/CH6/EX6.54/ex6_54.sce new file mode 100644 index 000000000..c05ecbe28 --- /dev/null +++ b/3760/CH6/EX6.54/ex6_54.sce @@ -0,0 +1,9 @@ +clc; +vr=0.4; // voltage applied during blocked rotor test as a fraction of rated voltage +ir=2.5; // line current during blocked rotor test as a fraction of full load current +tr=0.3; // starting torque as a fraction of rated torque +is=1.5; // starting current as a fraction of full load current +isc=ir/vr; // short circuit current at rated load +x=sqrt(is/isc); // starting current as a fraction of short circuit current at rated load +T=(x/vr)^2*tr; +printf('Starting torque is %f percent of full load torque',T*100); diff --git a/3760/CH6/EX6.55/Ex6_55.sce b/3760/CH6/EX6.55/Ex6_55.sce new file mode 100644 index 000000000..07e3fee52 --- /dev/null +++ b/3760/CH6/EX6.55/Ex6_55.sce @@ -0,0 +1,20 @@ +clc; +v=440; // rated voltage of distribution circuit +im=1200; // maximum current that can be supplied +n=0.85; // efficiency of induction motor +pf=0.8; // power factor of motor +ir=5; // ratio of starting current to full load current +disp('case a'); +il=im/ir; //rated line current +p=sqrt(3)*v*il*n*pf; +printf('Maximum KW rating is %f KW\n',p/1000); +disp('case b'); +x=0.8; // rated of applied voltage and stepped down voltage +il=im/(x^2*ir); //rated line current +p=sqrt(3)*v*il*n*pf; +printf('Maximum KW rating is %f KW\n',p/1000); +disp('case c'); +// star-delta converter is same as autotransformer starter with 57.8 % tapping therefore +il=im/(0.578^2*ir); //rated line current +p=sqrt(3)*v*il*n*pf; +printf('Maximum KW rating is %f KW\n',p/1000); diff --git a/3760/CH6/EX6.56/Ex6_56.sce b/3760/CH6/EX6.56/Ex6_56.sce new file mode 100644 index 000000000..9a9bb42b3 --- /dev/null +++ b/3760/CH6/EX6.56/Ex6_56.sce @@ -0,0 +1,17 @@ +clc; +p=10000; // rated power of motor +v=400; // rated voltage of motor +n=0.87; // full load efficiency +pf=0.85; // power factor +ir=5; // ratio of starting current to full load current +tr=1.5; // ratio of starting torque to full load torque +disp('case a'); +vt=v/sqrt(tr); +printf('Voltage applied to motor terminal is %f V\n',vt); +disp('case b'); +ifl=p/(sqrt(3)*v*pf*n); // full load current +il=(ir*vt*ifl)/v; +printf('Current drawn by motor is %f A\n',il); +disp('case c'); +i=(vt/v)*il; +printf('Line current drawn from supply mains is %f A',i); diff --git a/3760/CH6/EX6.57/Ex6_57.sce b/3760/CH6/EX6.57/Ex6_57.sce new file mode 100644 index 000000000..af8f8eb2e --- /dev/null +++ b/3760/CH6/EX6.57/Ex6_57.sce @@ -0,0 +1,15 @@ +clc; +tm=2; // ratio of maximum torque to full load torque +r=0.2; // per phase rotor resistance referred to stator +x=2; // per phase reactance referred to stator +s=r/x; // slip at maximum torque +disp('case a'); +ts1=(2*s*tm)/(s^2+1); +printf('Ratio of starting torque to full load torque is %f\n',ts1); +disp('case b'); +ts2=ts1/3; +printf('Ratio of starting torque to full load torque with star-delta starter is %f\n',ts2); +disp('case c'); +t=0.7; // tapping point +ts3=ts1*t^2; +printf('Ratio of starting torque to full load torque with autotransformer starter is %f\n',ts3); diff --git a/3760/CH6/EX6.58/Ex6_58.sce b/3760/CH6/EX6.58/Ex6_58.sce new file mode 100644 index 000000000..3fb3a9549 --- /dev/null +++ b/3760/CH6/EX6.58/Ex6_58.sce @@ -0,0 +1,26 @@ +clc; +v=400; // supply voltage +f=50; // frequency of supply +// results of short circuit test +V=200; // applied voltage +i=100; // short circuit current +pf=0.4; // power factor +zsc=(V*sqrt(3))/i; // short circuit impedance +rsc=zsc*pf; // short circuit resistance +xsc=sqrt(zsc^2-rsc^2); // short circuit reactance +R=sqrt(((xsc^2+rsc^2)-3*((rsc/3)^2+(xsc/3)^2))/2); // resistance of feeder +disp('with star connection'); +ts1=(3*(v/sqrt(3))^2*rsc)/((R+rsc)^2+xsc^2); // product of starting torque and synchronous speed +// now two feeders are connected in parallel therefore net resistace of feeder is +rp=R^2/(R+R); +ts2=(3*(v/sqrt(3))^2*rsc)/((rp+rsc)^2+xsc^2); // product of new starting torque and synchronous speed +pr=(ts2-ts1)/ts1; +printf('Percentage increase in starting torque with star connection is %f percent\n',pr*100); +disp('With delta connection'); +ts1=(3*(v/sqrt(3))^2*(rsc/3))/((R+(rsc/3))^2+(xsc/3)^2); // product of starting torque and synchronous speed +// now two feeders are connected in parallel therefore net resistace of feeder is +rp=R^2/(R+R); +ts2=(3*(v/sqrt(3))^2*(rsc/3))/((rp+(rsc/3))^2+(xsc/3)^2); // product of new starting torque and synchronous speed +pr=(ts2-ts1)/ts1; +printf('Percentage increase in starting torque with delta connection is %f percent\n',pr*100); + diff --git a/3760/CH6/EX6.59/Ex6_59.sce b/3760/CH6/EX6.59/Ex6_59.sce new file mode 100644 index 000000000..7490c790b --- /dev/null +++ b/3760/CH6/EX6.59/Ex6_59.sce @@ -0,0 +1,14 @@ +clc; +z=1.2+3*%i; // per phase standstill impedance +v=400; // supply voltage +l=500; // length of feeder line +tr=30; // maximum percentage reduction possible in starting torque +ro=0.02; // resistivity of feeder material +// equating expression of starting torque with and without feeder we get a quadratic equation in R (feeder resistance) whose terms are +t1=(1-(tr/100)); +t2=2*real(z)*t1; +t3=t1*abs(z)^2-abs(z)^2; +p=[ t1 t2 t3 ]; +R=roots(p); +A=(ro*l)/R(2); +printf('Minimum allowable cross section is %f mm^2',A); diff --git a/3760/CH6/EX6.6/Ex6_6.sce b/3760/CH6/EX6.6/Ex6_6.sce new file mode 100644 index 000000000..f8f0eb3e4 --- /dev/null +++ b/3760/CH6/EX6.6/Ex6_6.sce @@ -0,0 +1,15 @@ +clc; +P=6; +f=50; +N_f=960; +Ns=(120*f)/P; +n1=800; +n2=400; + +s_fl=(Ns-N_f)/Ns; +s_1=(Ns-n1)/Ns; +s_2=(Ns-n2)/Ns; +Ratio_1=s_1/s_fl; +Ratio_2=s_2/s_fl; +mprintf('The Ratio at %d rpm is %f \n',n1,Ratio_1); +mprintf('The Ratio at %d rpm is %f \n',n2,Ratio_2); diff --git a/3760/CH6/EX6.60/Ex6_60.sce b/3760/CH6/EX6.60/Ex6_60.sce new file mode 100644 index 000000000..ca1da5f26 --- /dev/null +++ b/3760/CH6/EX6.60/Ex6_60.sce @@ -0,0 +1,14 @@ +clc; +f=50; // frequency +p=10; // number of poles +pb=120000; // power dissipated in block rotor test +// stator ohmic losses = rotor ohmic losses +pr=pb/2; // total rotor loss +disp('case a'); +ws=(4*%pi*f)/p; // synchronous speed +Ts=pr/ws; +printf('Starting torque is %f Nm\n',Ts); +disp('case b'); +pr=pr/3; // total rotor ohmic loss +Ts=pr/ws; +printf('Starting torque is %f Nm\n',Ts); diff --git a/3760/CH6/EX6.62/Ex6_62.sce b/3760/CH6/EX6.62/Ex6_62.sce new file mode 100644 index 000000000..d5a1a4b77 --- /dev/null +++ b/3760/CH6/EX6.62/Ex6_62.sce @@ -0,0 +1,18 @@ +clc; +s=0.03; // full load slip +R=0.015; // rotor resistance per phase +n=4; // number of step in starter +al=s^(1/n); +R1=R/s; // resistance of whole section +r1=R1*(1-al); +printf('Resistance of first element is %f ohms\n',r1); +r2=r1*al; +printf('Resistance of second element is %f ohms\n',r2); +r3=r1*al^2; +printf('Resistance of third element is %f ohms\n',r3); +r4=r1*al^3; +printf('Resistance of fourth element is %f ohms\n',r4); + + + + diff --git a/3760/CH6/EX6.63/Ex6_63.sce b/3760/CH6/EX6.63/Ex6_63.sce new file mode 100644 index 000000000..a3ae926c9 --- /dev/null +++ b/3760/CH6/EX6.63/Ex6_63.sce @@ -0,0 +1,19 @@ +clc; +fs=0.02; // full load slip +ir=2; // ratio of starting current to full load current +n=5; // number of section +R=0.03; // rotor resistance +//ir*ifl=(E2/R)*sm where ifl is full load current and E2 is induced voltage in rotor therefore +sm=fs*ir; // maximum slip +al=sm^(1/n); +R1=R/sm; // resistance of whole section +r1=R1*(1-al); +printf('Resistance of first element is %f ohms\n',r1); +r2=r1*al; +printf('Resistance of second element is %f ohms\n',r2); +r3=r1*al^2; +printf('Resistance of third element is %f ohms\n',r3); +r4=r1*al^3; +printf('Resistance of fourth element is %f ohms\n',r4); +r5=r1*al^4; +printf('Resistance of fifth element is %f ohms\n',r5); diff --git a/3760/CH6/EX6.64/Ex6_64.sce b/3760/CH6/EX6.64/Ex6_64.sce new file mode 100644 index 000000000..d3469b9a8 --- /dev/null +++ b/3760/CH6/EX6.64/Ex6_64.sce @@ -0,0 +1,28 @@ +clc; +v=3300; // rated voltage of induction motor +p=6; // number of poles +f=50; // frequency +t=3.2; // stator to rotor turns +r=0.1; // rotor resistance +x=1; // rotor leakage reactance +R=t^2*r; // rotor resistance referred to stator +X=t^2*x; // rotor reactance referred to stator +ws=(4*%pi*f)/p; // synchronous speed +disp('case a'); +is=(v/sqrt(3))/(sqrt(R^2+X^2)); +printf('Starting current at rated voltage is %f A\n',is); +Ts=(3*is^2*R)/ws; +printf('Starting torque at rated voltage is %f Nm\n',Ts); +disp('case b'); +is=50; // starting current +// is=Vp/(sqrt((R+rex)^2+X^2) where rex is external resistance and Vp is phase voltage +// solving above equation we get a quadratic equation in rex whose terms are +t1=1; +t2=2*R; +t3=(R^2+X^2)-((v/sqrt(3))/is)^2; +p=[ t1 t2 t3 ]; +rex=roots(p); +printf('External resistance referred to rotor is %f ohms\n',rex(2)/t^2); +Ts=(3*is^2*(R+rex(2)))/ws; +printf('Starting torque under new condition is %f Nm\n',Ts); + diff --git a/3760/CH6/EX6.65/Ex6_65.sce b/3760/CH6/EX6.65/Ex6_65.sce new file mode 100644 index 000000000..56458efde --- /dev/null +++ b/3760/CH6/EX6.65/Ex6_65.sce @@ -0,0 +1,32 @@ +clc; +p=6; // number of poles +v=400; // rated voltage of induction motor +m=3; // number of phases +f=50; // frequency +r1=0.2; // stator resistance +r2=0.5; // rotor resistance +xm=48; // magnetising reactance +x1=2; // leakage reactance of stator or rotor +n=1050; // speed of motor +ns=(120*f)/p; // synchronous speed +s=(ns-n)/ns; // operating slip +disp('case a'); +Zf=(((r2/s)+%i*x1)*%i*xm)/((r2/s)+%i*(xm+x1)); // per phase impedance offered to stator by rorating air gap field +z=r1+%i*x1; // impedance of stator +Z=Zf+z; // total impedance +is=v/(sqrt(3)*abs(Z)); // stator current +pf=cosd(atand(imag(Z),real(Z))); +printf('Stator line current is %f A\n',is); +disp('case b'); +Po=m*(v/sqrt(3))*is*pf; +// negative power indicates induction machine is acting as generator +printf('Power fed back to 3 phase supply system is %f W\n',-Po); +disp('case c'); +lr=600; // rotational and core losses +pg=m*is^2*real(Zf); // air gap power +l1=m*is^2*r1; // stator copper loss +l2=s*pg; // rotor copper loss +Tl=lr+l1+l2; // total losses +pi=-Po+Tl; // mechanical power input +ne=-Po/pi; +printf('Efficiency of induction motor is %f percent\n',ne*100); diff --git a/3760/CH6/EX6.7/Ex6_7.sce b/3760/CH6/EX6.7/Ex6_7.sce new file mode 100644 index 000000000..5a4acb72e --- /dev/null +++ b/3760/CH6/EX6.7/Ex6_7.sce @@ -0,0 +1,47 @@ +clc; +Psh=10000; +P=4; +f=50; +Pi=660; +Pw=420; +I_l=8; +rs=1.2; +Pi_fl=11200; +I_fl=18; +Ns=(120*f)/P; +Ws=(2*3.14*Ns)/60; + + +//for part a +disp('for part a '); + +Pstl=Pi-Pw-((3*I_l*I_l*rs)/(3)); +mprintf('The stator core loss is \n %f W \n',Pstl); + +//for part b +disp('for part b '); + +Pg=Pi_fl-Pstl-(3*(I_fl/sqrt(3))*(I_fl/sqrt(3))*rs); +Prl=Pg-Psh; +mprintf('The rotor loss is %f W \n',Prl); + +//for part c +disp('for part c '); + +Prol=Prl-Pw; +mprintf('The rotor ohmic loss is %f W \n',Prol); + +//for part d +disp('for part d '); + +s_fl=Prol/Pg; +Nr=Ns*(1-s_fl); +mprintf('Full Load speed of rotor is %f rpm \n',Nr); + +//for part e +disp('for part e '); + +Te=Pg/Ws; +Tsh=Psh/((Ws)*(1-s_fl)); +E=(Psh/Pi_fl)*100; +mprintf('The internal torque is %f Nm \n The shaft torque is %f Nm \n The motor Efficiency is %f percent',Te,Tsh,E); diff --git a/3760/CH6/EX6.8/Ex6_8.sce b/3760/CH6/EX6.8/Ex6_8.sce new file mode 100644 index 000000000..e725ae1cb --- /dev/null +++ b/3760/CH6/EX6.8/Ex6_8.sce @@ -0,0 +1,11 @@ +clc; +E=0.9; +L=45000; +Tl=((1/0.9)-1)*L; + +Rl=(Tl*2)/7; //According to the given conditoins +Pg=L+Rl+(Rl/2); + +s=Rl/Pg; + +mprintf('Slip is %f',s); diff --git a/3760/CH6/EX6.9/Ex6_9.sce b/3760/CH6/EX6.9/Ex6_9.sce new file mode 100644 index 000000000..a4c56a4ec --- /dev/null +++ b/3760/CH6/EX6.9/Ex6_9.sce @@ -0,0 +1,39 @@ + +clc; +P=4; +r1=0.15; +x1=0.45; +r2=0.12; +x2=0.45; +Xm=28.5; +s=0.04; +V=400; +f=50; +Pfixed=400; + +t1=complex((r2/s),x2); +t2=complex(0,Xm); +t3=complex((r2/s),(x2+Xm)); +T=(t1*t2)/t3; +Zab=complex(r1,x1)+T; +Rf=real(T); +I1=V/(sqrt(3)*abs(Zab)); +ian=atand(imag(Zab),real(Zab)); +Pf=cosd(ian); +I1_mag=sqrt(real(I1)*real(I1)+imag(I1)*imag(I1)); +Psti=sqrt(3)*I1_mag*V*Pf; +Pg=3*I1*I1*Rf; +ns=(2*f)/P; +nr=(1-s)*ns; +Ws=2*3.14*ns; +Pm=(1-s)*Pg; +Psh=Pm-Pfixed; +To=(Psh)/((1-s)*Ws); +Psto=3*I1_mag*I1_mag*r1; +Prto=s*Pg; +Tls=Psto+Prto+Pfixed; +Pi=Psh+Tls; +E=(1-(Tls/Pi))*100; + +mprintf('staror current = %f amp at lagging phase angle of %f w.r.t input voltage \n rotor speed = %f rps or %f rpm output torque = %f Nm \n Efficiency = %f percent',I1,ian,nr,nr*60,To,E); + diff --git a/3760/CH7/EX7.1/Ex7_1.sce b/3760/CH7/EX7.1/Ex7_1.sce new file mode 100644 index 000000000..c592868ab --- /dev/null +++ b/3760/CH7/EX7.1/Ex7_1.sce @@ -0,0 +1,14 @@ +clc; +p=6; // number of poles +c=40; // number of coils +w=2; // winding pitch for simplex lap winding +printf('Number of commutator segments is equal to number of coils=%f\n ',c); +k=1/3; // integer added(or subtracted) to calculate back pitch to make it an odd integer +yb=((2*c)/p)-k; +printf('Back pitch is %f \n',yb); +yf=yb-w; +printf('Front pitch for progressive winding is %f\n',yf); +yf=yb+w; +printf('Front pitch for retrogressive winding is %f\n',yf) +yc=1; +printf('For simplex lap winding, commutator pitch is equal to %f ',yc); diff --git a/3760/CH7/EX7.10/Ex7_10.sce b/3760/CH7/EX7.10/Ex7_10.sce new file mode 100644 index 000000000..4aca2e29d --- /dev/null +++ b/3760/CH7/EX7.10/Ex7_10.sce @@ -0,0 +1,8 @@ +clc; +disp('b(1)'); +c=12; // number of coils +r=0.1; // resistance of each coil +// any one coil connected to commutator segment is in parallel with other 11 series connected coils therefore +R=11*r; // resistance of 11 coil +req=(r*R)/(r+R); +printf('Resistance measured between two adjacent commutator segments is %f ohm\n',req); diff --git a/3760/CH7/EX7.11/Ex7_11.sce b/3760/CH7/EX7.11/Ex7_11.sce new file mode 100644 index 000000000..d36744414 --- /dev/null +++ b/3760/CH7/EX7.11/Ex7_11.sce @@ -0,0 +1,18 @@ +clc; +disp('a'); +s=24; // total number of slots +p=4; // number of poles +np=3; // number of phases +ph=60; // phase spread +// given armature has double layer winding and full pitch coil span +v=(p*180)/s; +printf('Slot angular pitch is %d degrees\n',v); +disp('Number of adjacent slots in one phase belt is'); +disp(ph/v); +cs=s/p; +printf('Coil span is %d slots\n',cs); +disp('Using this data winding table for the three phases is shown in Ex7.11') +disp('d'); +sp=s/(p*np); // slots per pole per phase +disp('Distribution factor is'); +disp(sind(ph/2)/(sp*sind(v/2))); diff --git a/3760/CH7/EX7.12/Ex7_12.sce b/3760/CH7/EX7.12/Ex7_12.sce new file mode 100644 index 000000000..952e75c57 --- /dev/null +++ b/3760/CH7/EX7.12/Ex7_12.sce @@ -0,0 +1,19 @@ +clc; +disp('a'); +s=24; // total number of slots +p=4; // number of poles +np=3; // number of phases +ph=120; // phase spread +// given armature has double layer winding and full pitch coil span +v=(p*180)/s; +printf('Slot angular pitch is %d degrees\n',v); +disp('Number of adjacent slots in one phase belt is'); +disp(ph/v); +cs=s/p; +printf('Coil span is %d slots\n',cs); +disp('Using this data winding table for the three phases is shown in Ex7.12') +disp('d'); +sp=s/(p*np); // slots per pole per phase +disp('Distribution factor is'); +disp(sind(ph/2)/(sp*sind(ph/(2*sp)))); + diff --git a/3760/CH7/EX7.13/Ex7_13.sce b/3760/CH7/EX7.13/Ex7_13.sce new file mode 100644 index 000000000..cf76204a3 --- /dev/null +++ b/3760/CH7/EX7.13/Ex7_13.sce @@ -0,0 +1,22 @@ +clc; +np=3; // number of phase +sp=9; // slots per pole +zs=4; // conductors per slot +f=0.8; // coil span as a fraction of pole pitch +ph=60; // phase spread +v=180/sp; // slot angular pitch +disp('Number of adjacent slots belonging to any phase is '); +disp(ph/v); +printf('Pole pitch is %f slots\n',sp); +c=floor(0.8*sp); +printf('Coil span is of %f slots\n',c); +disp('Using this data, winding table is shown in Ex7.13'); +t=(sp*zs*4)/2; // total turns in machine +spp=sp/np; // slots per pole per phase +kd=sind(ph/2)/(spp*sind(v/2)); // distribution factor +cp=c*v; // coil span in degrees +e=180-cp; // chording angle +kp=cosd(e/2); // coil span factor +kw=kd*kp; // winding factor +tp=(t*kw)/np; +printf('Number of effective turns per phase is %f',tp); diff --git a/3760/CH7/EX7.15/Ex7_15.sce b/3760/CH7/EX7.15/Ex7_15.sce new file mode 100644 index 000000000..ad69787dc --- /dev/null +++ b/3760/CH7/EX7.15/Ex7_15.sce @@ -0,0 +1,9 @@ +clc; +s=24; // number of slots +p=4; // number of poles +ph=60; // phase spread +ap=(p*180)/s; // slot angular pitch +pp=s/p; // pole pitch +printf('Pole pitch is %d slots\n',pp); +printf('slot angular pitch is %d degrees',ap); +disp('using these data, half coil and whole coil single layer concentric windings diagram are drawn'); diff --git a/3760/CH7/EX7.2/Ex7_2.sce b/3760/CH7/EX7.2/Ex7_2.sce new file mode 100644 index 000000000..a1458d2ca --- /dev/null +++ b/3760/CH7/EX7.2/Ex7_2.sce @@ -0,0 +1,20 @@ +clc; +p=4; // number of poles +c=12; // number of coils +// Number of commutator segments is equal to number of coils=12 +// Each coil has two coil side therefore total coil sides are 24 +s=(2*c)/2 ; // total number of slots required +k=1; // integer added(or subtracted) to calculate back pitch to make it an odd integer +w=2; // winding pitch +yb1=((2*c)/p)-k; // back pitch +// or +yb2=((2*c)/p)+k; // back pitch +disp('Back pitch is '); +disp(yb1,'or',yb2); +yf1=yb1-2; // front pitch for yb=5 +yf2=yb2-2; // front pitch for yb=7 +disp('front pitch for progressive winding is '); +disp(yf1,'or',yf2); +disp('It is desirable that (yb+yf)/2 should be equal to pole pitch that is 6(in terms of coil sides per pole). So choose yb=7 and yf=5'); +disp('Commutator pitch for progressive lap winding is'); +disp(1); diff --git a/3760/CH7/EX7.3/Ex7_3.sce b/3760/CH7/EX7.3/Ex7_3.sce new file mode 100644 index 000000000..36d579d0f --- /dev/null +++ b/3760/CH7/EX7.3/Ex7_3.sce @@ -0,0 +1,19 @@ +clc; +p=4; // number of poles +s=14; // number of slots +cp=2; // coil sides per slots +w=2; // winding pitch +C=(s*cp)/2; // number of coils +yb=(2*C)/p; +disp('Back pitch is'); +disp(yb); +yf=yb-w; +disp('Front pitch is'); +disp(yf); +disp('winding table for progressive lap winding is'); +disp('(1-8)-(3-10)-(5-12)-(7-14)-(9-16)-(11-18)-(13-20)-(15-22)-(17-24)-(19-26)'); +disp('-(21-28)-(23-2)-(25-4)-(27-6)'); +disp('from winding diagram') +disp('Brush A is touching segments 1 and 2 partly'); +disp('Brush B is at segment 5'); +disp('Brush C is at segment 8'); diff --git a/3760/CH7/EX7.5/Ex7_5.sce b/3760/CH7/EX7.5/Ex7_5.sce new file mode 100644 index 000000000..e8b631ff3 --- /dev/null +++ b/3760/CH7/EX7.5/Ex7_5.sce @@ -0,0 +1,30 @@ +clc; +disp('case a'); +s=30; // number of slots +c=60; // number of coils +p=4; // number of poles +k=1; // integer added(or subtracted) to calculate back pitch to make it an odd integer +tc=c*2; // total coil sides +u=tc/s; // coil sides per slots +yb1=(tc/p)+k; +yb2=(tc/p)-k; +disp('Back pitch is'); +disp(yb1); +disp('or'); +disp(yb2); +disp('for back pitch=29, top coil sides 1 and 3 in slot 1 are connected to bottom coil 30 and 32 in slot 8. Due to this arrangement split coils can be avoided. But for back pitch= 31, coil sides 34 which is in slot 9 has to be used, so split coils are needed ') +disp('case b'); +s=20; // number of slots +c=60; // number of coils +p=4; // number of poles +k=1; // integer added(or subtracted) to calculate back pitch to make it an odd integer +tc=c*2; // total coil sides +u=tc/s; // coil sides per slots +yb1=(tc/p)+k; +yb2=(tc/p)-k; +disp('Back pitch is'); +disp(yb1); +disp('or'); +disp(yb2); +disp('for back pitch=29, top coil sides 1,3 and 5 are connected to bottom coil 30, 32 and 34. Due to this arrangement split coils cannot be avoided. But for back pitch= 31, coil sides 1,3 and 5 are connected to bottom coil sides 32, 34 and 36 which are in slot 6,so split coils are not needed '); + diff --git a/3760/CH7/EX7.6/Ex7_6.sce b/3760/CH7/EX7.6/Ex7_6.sce new file mode 100644 index 000000000..ad8ff7729 --- /dev/null +++ b/3760/CH7/EX7.6/Ex7_6.sce @@ -0,0 +1,19 @@ +clc; +p=4; // number of poles +s=11; // number of slots +ts=2; // coil sides per slot +C=(s*ts)/2; // total coils +w=((2*C)+2)/(p/2); // winding pitch +// since both back and front pitch should be odd choose +Yb=7; +Yf=5; +disp('Back pitch is') +disp(Yb); +disp('Front pitch is') +disp(Yf); +yc=(C+1)/(p/2); +disp('commutator pitch'); +disp(yc); +disp('Using this data winding diagram can be drawn'); +disp('Winding table is'); +disp('(1-8)-(13-20)-(3-10)-(15-22)-(5-12)-(17-2)-(7-14)-(19-4)-(9-16)-(21-6)-(11-18)-1'); diff --git a/3760/CH7/EX7.7/Ex7_7.sce b/3760/CH7/EX7.7/Ex7_7.sce new file mode 100644 index 000000000..14c54e7fc --- /dev/null +++ b/3760/CH7/EX7.7/Ex7_7.sce @@ -0,0 +1,20 @@ +clc; +p=6; // number of poles +s=72; // number of slots +ts=4; // number of coil sides per slot +C=(s*ts)/2; // total number of coils +// To make commutator pitch an integer one coil is made dummy coil therefore +C=C-1; +yc=(C+1)/(p/2); +disp('commutator pitch'); +disp(yc); +yw=((2*C)+2)/(p/2); +disp('Winding pitch is'); +disp(yw); +// since back and front pitch should be odd choose +yb=49; +disp('Back pitch is'); +disp(yb); +yf=47; +disp('Front pitch is'); +disp(yf); diff --git a/3760/CH7/EX7.8/Ex7_8.sce b/3760/CH7/EX7.8/Ex7_8.sce new file mode 100644 index 000000000..744df0e7e --- /dev/null +++ b/3760/CH7/EX7.8/Ex7_8.sce @@ -0,0 +1,28 @@ +clc; +p=4; // number of poles +z=2540; // number of conductors +s=32; // number of slots +c=127; // number of commutator sectors=total number of coils +v=500; // induced voltage required +f=5*10^-3; // field flux per pole +a=2; // number of parallel paths +zs=ceil(z/s); // conductors per slot +// for zs=80 +Z=zs*s; // total conductors +t=floor(Z/(2*c)); // turn per coil +C=Z/(2*t); // actual number of coils +// It is necessary that actual coils should be same as commutator segments so one coil is made dummy +disp('commutor pitch is') +disp((c+1)/(p/2)); +disp('or'); +disp((c-1)/(p/2)); +disp('Winding pitch is') +disp(((2*c)+2)/(p/2)); +disp('or'); +disp(((2*c)-2)/(p/2)); +disp('For progressive winding, back pitch=65 and front pitch=63'); +disp('For retrogressive winding, back pitch=63 and front pitch=63'); +// since dumy coil is not in circuit, number of active conductor is +Z=c*t*2; +n=(v*a*60)/(f*Z*p); +printf('Speed for required induced voltage is %f rpm',n); diff --git a/3760/CH7/EX7.9/Ex7_9.sce b/3760/CH7/EX7.9/Ex7_9.sce new file mode 100644 index 000000000..e580e99b3 --- /dev/null +++ b/3760/CH7/EX7.9/Ex7_9.sce @@ -0,0 +1,9 @@ +clc; +p=8; // number of poles +c=240; // number of coils +r=10; // number of equilizer ring +Yeq=(2*c)/p; +printf('Equipotential pitch is %f coils\n',Yeq); +Ytp=(2*c)/(r*p); +printf('Tapping point pitch is %f coils',Ytp); +disp('Arrangement is shown in tabular form in example 7.9'); diff --git a/3760/CH8/EX8.1/ExA_1.sce b/3760/CH8/EX8.1/ExA_1.sce new file mode 100644 index 000000000..a478018e7 --- /dev/null +++ b/3760/CH8/EX8.1/ExA_1.sce @@ -0,0 +1,14 @@ +clc; +// answer is given wrong in the book +d=0.2; // mean diameter of mild steel ring +ac=50*10^-4; // cross sectional area of core +uo=4*%pi*10^-7; // free space permeability +ur=800; // relative permeability +f=1*10^-3; // required flux +N=200; // Number of turns +l=%pi*d // length of core +R=l/(uo*ur*ac); // reluctance of ring +printf('reluctance offered by ring is %f AT/Wb\n',R); +mmf=f*R; // mmf produced in ring +i=mmf/N; +printf('current required to produce the desired flux is %f A',i); diff --git a/3760/CH8/EX8.10/ExA_10.sce b/3760/CH8/EX8.10/ExA_10.sce new file mode 100644 index 000000000..6899006fd --- /dev/null +++ b/3760/CH8/EX8.10/ExA_10.sce @@ -0,0 +1,7 @@ +clc; +l=0.5; // length of conductor lying along Y-axis +B=1.2; // Flux density along the X-axis +v=2; // velocity of conductor +//e=Blv; for maximum induced emf all the three quantities should be perpendicular to each other +e=B*l*v; +printf('Maximum induced EMF in conductor is %f V',e); diff --git a/3760/CH8/EX8.12/ExA_12.sce b/3760/CH8/EX8.12/ExA_12.sce new file mode 100644 index 000000000..2c6304242 --- /dev/null +++ b/3760/CH8/EX8.12/ExA_12.sce @@ -0,0 +1,22 @@ +clc; +disp('case a'); +// as per the data taken from Ex 1_3 +rlg=24.948*10^5; // air gap reluctance for example 1_3(a) +rlc=12.474*10^5; // iron core reluctance for example 1_3(a) +rl=rlg+rlc; // net reluctance +N=500; // Number of turns +L=(N^2/rl)*1000; +printf('Inductance for case a is %f mH\n',L); +disp('case b'); +// as per the data taken from Ex 1_3 part(c) +B=1.254; // calculated flux density +H=3200; // magnetic field intensity obtained from magnetisation curve corresponding to the flux density calculated +uo=4*%pi*10^-7; // free space permeability +ur=B/(H*uo); // relative permeability of iron core +d=2.85*10^-2; // diameter of cross section +A=(%pi*d^2)/4; // area of core +l=0.5; // core length +rlc=l/(ur*uo*A); // reluctance of iron core for part C +rt=rlg+rlc; // net reluctance +L=(N^2/rt)*1000; +printf('Inductance for case b is %f mH\n',L); diff --git a/3760/CH8/EX8.13/ExA_13.sce b/3760/CH8/EX8.13/ExA_13.sce new file mode 100644 index 000000000..0c47fce1a --- /dev/null +++ b/3760/CH8/EX8.13/ExA_13.sce @@ -0,0 +1,14 @@ +clc; +// data taken from Ex A.7, fig A.16 +N1=200; // number of turns in coil 1 +f1=53.97*10^-3; // flux in outer limb containing coil 1 +m1=5000; // mmf for coil 1 +I1=m1/N1; // current in coil 1 +N2=100; // number of turns in coil 2 +f2=43.97*10^-3; // flux in outer limb containing coil 2 +m2=1102; // mmf for coil 2 +I2=m2/N2; // current in coil 2 +L1=(N1*f1)/I1; +printf('Inductance for coil 1 is %f H\n',L1); +L2=(N2*f2)/I2; +printf('Inductance for coil 2 is %f H\n',L2); diff --git a/3760/CH8/EX8.2/ExA_2.sce b/3760/CH8/EX8.2/ExA_2.sce new file mode 100644 index 000000000..7055ff815 --- /dev/null +++ b/3760/CH8/EX8.2/ExA_2.sce @@ -0,0 +1,13 @@ +clc; +ur=10000; // relative permeability of iron +lc=0.5; // core length +lg=4*10^-3; // air gap length +N=600; // number of turns +B=1.2; // desired flux density +uo=4*%pi*10^-7; // free space permeability +Ac=25*10^-4; // core area +mfc=(B*lc)/(uo*ur); // mmf for core +mfg=(B*lg)/uo; // mmf for air gap +mft=mfc+mfg; // net mmf +i=mft/N; +printf('exciting current required to establish the desired flux is %f A',i); diff --git a/3760/CH8/EX8.3/ExA_3.sce b/3760/CH8/EX8.3/ExA_3.sce new file mode 100644 index 000000000..7c06456b2 --- /dev/null +++ b/3760/CH8/EX8.3/ExA_3.sce @@ -0,0 +1,35 @@ +clc; +lc=0.5; // core length in metre +dc=2.85*10^-2; // diameter of cross section of core +lg=2*10^-3; // length of air gap +N=500; // Number oof turns of coil +f=0.8*10^-3; // air gap flux +uo=4*%pi*10^-7; // permeability of free space +HATM=[1500 2210 2720 3500 4100]; +BT=[0.9 1.1 1.2 1.275 1.3]; +plot(HATM,BT); +xlabel('magnetic field intensity'); +ylabel('flux density'); +disp('case a'); +ur=500; // relative permeability +Ac=(%pi/4)*dc^2; // Area of core +Rlg=lg/(uo*Ac); // reluctance of air gap +Rlc=lc/(uo*ur*Ac); // reluctance of iron core +Rt=Rlg+Rlc; // Total reluctance +I=(f*Rt)/N; // Exciting current +printf('Exciting current in coil is %f A\n',I); +disp('case b'); +Ag=(%pi/4)*(dc+2*lg)^2; // air gap area +Rlg=lg/(uo*Ag); // reluctance of air gap +I=(f*(Rlc+Rlg))/N; // Exciting current +printf('Exciting current after accounting for flux fringing is %f A\n',I); +disp('case c'); +Bg=f/Ac; // Air gap flux density +Atg=(Bg*lg)/uo; // air gap mmf +// from the plot we can get the values of core flux density and magnetic field intensity +Bc=1.245; // core flux density in Tesla +H=3200; // magnetic field intensity in Ats/m +Atc=H*lc; // core mmf +mt=Atg+Atc; // total mmf +I=mt/N; // Exciting current +printf('Exciting current for third case is %f A',I); diff --git a/3760/CH8/EX8.4/ExA_4.sce b/3760/CH8/EX8.4/ExA_4.sce new file mode 100644 index 000000000..3b10615de --- /dev/null +++ b/3760/CH8/EX8.4/ExA_4.sce @@ -0,0 +1,24 @@ +clc; +N=1000; // Number of turns +f=1*10^-3; // flux in central limb +Ac=8*10^-4; // Area of central limb +Ao=4*10^-4; // Area of outer limb +lg=2*10^-3; // length of air gap +lc=0.15; // length of central limb in metre +lo=0.25; // length of outer limb in metre +uo=4*%pi*10^-7; // permeability of free space +disp('case a'); +// for ur=infinity, reluctance offered by cast steel is zero +Rl1=lg/(uo*Ao); // reluctance offered by outer limb +Rl2=lg/(uo*Ac); // reluctance offered by central limb +// Assuming magnetic circuit as a close circuit, applying KVl in one of loop gives +I=(f*(Rl2+(Rl1/2)))/N; +printf('Coil current for first case is %f A\n',I); +disp('case b'); +ur=6000; // relative permability +Rlc1=(lc+lo)/(uo*ur*Ao); // reluctance of outer steel core (including the top) +Rlc2=(lc)/(uo*ur*Ac); // reluctance offered by central steel core +r=(Rlc1+Rl1)/2; // resultant of outer reluctance +// By kVL we get +I=(f*(Rlc2+Rl2+r))/N; +printf('Coil current for second case is %f A\n',I); diff --git a/3760/CH8/EX8.5/ExA_5.sce b/3760/CH8/EX8.5/ExA_5.sce new file mode 100644 index 000000000..4db15d1ed --- /dev/null +++ b/3760/CH8/EX8.5/ExA_5.sce @@ -0,0 +1,22 @@ +clc; +N=500; // number of turns in central limb +ac=600*10^-6; // cross sectional area of central limb +ao=375*10^-6; // cross sectional area of outer limb +f=0.9*10^-3; // required flux in Weber +lg=0.8*10^-3; // length of air gap +lc=180*10^-3; // length of central limb +lo=400*10^-3; // length of outer limb +uo=4*%pi*10^-7; // free space permeability +Bg=f/ac; // air gap flux density +Hg=Bg/uo; // magnetic field intensity in air gap +mg=Hg*lg; // mmf required for air gap +// from fig A.7,for B=1.5T, H for cast steel is 3000Ats/m +H=3000; // magnetic field intensity for cast steel +mc=H*lc; // mmf in central limb +Bo=f/(2*ao); // flux density in each outer limb +// for B=1.2, H=1400 +H=1400; // magnetic field intensity for cast steel for given flux density +mo=H*lo; // mmf for outer limb +// By KVL +I=(mg+mo+mc)/N; +printf('The exciting current required to establish the desired flux is %f A',I); diff --git a/3760/CH8/EX8.6/ExA_6.sce b/3760/CH8/EX8.6/ExA_6.sce new file mode 100644 index 000000000..14fb9ba3e --- /dev/null +++ b/3760/CH8/EX8.6/ExA_6.sce @@ -0,0 +1,28 @@ +clc; +N=400; // number of turns in coil +ac=20*10^-4; // area of cemntral limb +ao=15*10^-4; // area of outer iimb +lg=1*10^-3; // length of air gap +lc=40*10^-2; // length of central limb +lo=60*10^-2; // length of each outer limb +f=0.9*10^-3; // required flux +uo=4*%pi*10^-7; // free space permeability +Bg=f/ao; // air gap flux density +mg=(Bg*lg)/uo; // mmf or air gap +// for B=0.6,H=575 AT/m from fig A.7 +H=575; // magnetic flux intensity for given flux density +mo=H*lo; // mmf of outer limb which contain air gap +mt=mo+mg; // combined mmf of air gap and outer limb +// this mmf acts across the other outer limb +haeb=mt/lo; // magnetic field intensity in outer limb which does not contain air gap +// for H=1370.77, B=1.19 T from fig A.7 +Bo=1.19; // flux density for given magnetic field intensity +faeb=Bo*ao; // flux in outer limb +fnet=f+faeb; // net flux through central limb +Bc=fnet/ac; // flux density in central limb +// from fig A.7 +H=1900; // magnetic field intensity for given flux density +mc=H*lc; // mmf in central limb +// by KVL in one of the loop +I=(mc+mt)/N; +printf('Exciting current required to establish the given flux is %f A',I) diff --git a/3760/CH8/EX8.7/ExA_7.sce b/3760/CH8/EX8.7/ExA_7.sce new file mode 100644 index 000000000..78976b45f --- /dev/null +++ b/3760/CH8/EX8.7/ExA_7.sce @@ -0,0 +1,24 @@ +clc; +a=30*10^-4; // cross sectional area of ferromagnetic core +uo=4*%pi*10^-7; // free space permeability +ur=4000; // relative permeability for core +f=10*10^-3; // flux in central limb +n1=200; // number of turns in coil 1 +m1=5000; // mmf for coil 1 +n2=100; // number of turns in coil 2 +lc=0.3; // length of central limb +lo=0.6; // length of outer limb +lg=1*10^-3; // length of air gap +rc=lc/(uo*ur*a); // reluctance for central limb +ro=lo/(uo*ur*a); // reluctance for outer limb +rg=lg/(uo*a); // reluctance for air gap +mc=f*(rc+rg); // mmf in central limb +// by KML, flux in outer limb containing coil 1 is +f1=(m1-mc)/ro; +// By flux law at node a in fig A.17, flux in outer limb contaning coil 2 is +f2=f1-f; +// by mmf law , mmf in coil 2 is +m2=mc-f2*ro; +I2=m2/n2; // current in coil 2, upper polarity is assumed positive +printf('Current in coil 2 is %f A',I2); +disp('As the mmf of coil 2 is positive , assumed polarity is correct. Therefore terminal A is positive because current enters through it and terminal B is negative '); diff --git a/3760/CH8/EX8.8/ExA_8.sce b/3760/CH8/EX8.8/ExA_8.sce new file mode 100644 index 000000000..3820eeb03 --- /dev/null +++ b/3760/CH8/EX8.8/ExA_8.sce @@ -0,0 +1,19 @@ +clc; +l=0.8; // length of conductor +B=1.2; // flux density of uniform magnetic field +v=30; // speed of conductor +disp('case a'); +// conductor motion is normal to field flux +theta=90; // angle between direction of motion and field flux +e=B*l*v*sin(theta*(%pi/180)); +printf('EMF induced is %f V\n',e); +disp('case b'); +// conductor motion is at an angle of 30 degrees from direction of field +theta=30; // angle between direction of motion and field flux +e=B*l*v*sin(theta*(%pi/180)); +printf('EMF induced is %f V\n',e); +disp('case c'); +// conductor motion is parllel to field flux +theta=0; // angle between direction of motion and field flux +e=B*l*v*sin(theta*(%pi/180)); +printf('EMF induced is %f V\n',e); diff --git a/3760/CH8/EX8.9/ExA_9.sce b/3760/CH8/EX8.9/ExA_9.sce new file mode 100644 index 000000000..74e3923a3 --- /dev/null +++ b/3760/CH8/EX8.9/ExA_9.sce @@ -0,0 +1,21 @@ +clc; +// After deriving the expression +a=0.1; // side of square coil +N=100; // number of turns +n=1000; // speed of rotation on rpm +B=1; // flux density of a uniform magnetic field +disp('case a'); +theta=90; // angle of coil with the field +w=(2*%pi*n)/60; // angular speed of coil in rad/s +e=N*B*a^2*w*cos(theta*(%pi/180)); +printf('Emf induced in coil is %f V\n',e); +disp('case b'); +theta=30; // angle of coil with the field +w=(2*%pi*n)/60; // angular speed of coil in rad/s +e=N*B*a^2*w*cos(theta*(%pi/180)); +printf('Emf induced in coil is %f V\n',e); +disp('case c'); +theta=0; // angle of coil with the field +w=(2*%pi*n)/60; // angular speed of coil in rad/s +e=N*B*a^2*w*cos(theta*(%pi/180)); +printf('Emf induced in coil is %f V\n',e); diff --git a/3760/CH9/EX9.3/ExB_3.sce b/3760/CH9/EX9.3/ExB_3.sce new file mode 100644 index 000000000..32b11be6f --- /dev/null +++ b/3760/CH9/EX9.3/ExB_3.sce @@ -0,0 +1,31 @@ +clc; +vl=400; // line voltage +z=10+7.5*%i; // load impedance per phase +disp('For star connected load'); +vp=vl/sqrt(3); // phase voltage +ip=vp/abs(z);// phase and line current are same in the case of star connected load +an=atand(-imag(z),real(z)); +pf=cosd(an); +P=sqrt(3)*vl*ip; +pa=sqrt(3)*vl*ip*pf; +pr=-sqrt(3)*vl*ip*sind(an); +printf('Phase and line currents are %f A\n',ip); +printf('Power factor is %f lagging \n',pf); +printf('Total volt ampere is %f VA\n',P); +printf('Total active power is %f W\n',pa); +printf('Total reactive power is %f VAr\n',pr); +disp('For delta connected load'); +vp=vl // phase voltage and line voltage are same in the case of star connected load +ip=vp/abs(z); +il=ip*sqrt(3); +an=atand(-imag(z),real(z)); +pf=cosd(an); +P=sqrt(3)*vl*il; +pa=sqrt(3)*vl*il*pf; +pr=-sqrt(3)*vl*il*sind(an); +printf('Phase current is %f A\n',ip); +printf('Line current is %f A\n',il); +printf('Power factor is %f lagging\n',pf); +printf('Total volt ampere is %f VA\n',P); +printf('Total active power is %f W\n',pa); +printf('Total reactive power is %f VAr\n',pr); diff --git a/3760/CH9/EX9.4/ExB_4.sce b/3760/CH9/EX9.4/ExB_4.sce new file mode 100644 index 000000000..1f3ac3edd --- /dev/null +++ b/3760/CH9/EX9.4/ExB_4.sce @@ -0,0 +1,15 @@ +clc; +il=48; // load current(leading) +p=30; // load power in KW +vl=500; // line voltage +f=50; // supply frequency +pf=(p*1000)/(sqrt(3)*vl*il); +vp=vl/sqrt(3); // phase voltage +zp=vp/il; // magnitude of phase impedance +rp=zp*pf; +// since current is leading other parameter must be a capacitor +xc=zp*sqrt(1-pf^2); // reactance +c=(10^6)/(2*%pi*f*xc); +disp('circuit parameters are'); +printf('Load resistance is %f ohm\n',rp); +printf('Load capacitance is %f micro farad',c); diff --git a/3760/CH9/EX9.5/ExB_5.sce b/3760/CH9/EX9.5/ExB_5.sce new file mode 100644 index 000000000..0261d1582 --- /dev/null +++ b/3760/CH9/EX9.5/ExB_5.sce @@ -0,0 +1,21 @@ +clc; +zs=10+15*%i; // star connected load per phase +zd=12-15*%i; // delta connected load per phase +vl=400; // supply line voltage +disp('case a'); +// converting delta connected load to star connected load +zd=zd/3; +vp=vl/sqrt(3); +i1=vp/zs; // line current in star connected load +i2=vp/zd; // line current in delta connected load +i=abs(i1+i2); +printf('Total line current is %f A\n',i); +an=atand(imag(i1+i2),real(i1+i2)); +pf=cosd(an); +P=(sqrt(3)*vl*i*pf); +pr=sqrt(3)*vl*i*sqrt(1-pf^2); +printf('Power factor is %f leading\n',pf); +printf('Total power is %f W\n',P); +printf('Total reactve power is %f VAr',pr); + + diff --git a/3760/CH9/EX9.6/ExB_6.sce b/3760/CH9/EX9.6/ExB_6.sce new file mode 100644 index 000000000..0875e2030 --- /dev/null +++ b/3760/CH9/EX9.6/ExB_6.sce @@ -0,0 +1,13 @@ +clc; +w1=85; // reading of wattmeter 1; +w2=35; // reading of wattmeter 2; +P=w1+w2; // total input power +n=0.85; // efficiency of motor +vl=1100; // supply voltage +pf=cosd(atand((sqrt(3)*(w1-w2))/(w1+w2))); +il=(P*1000)/(sqrt(3)*vl*pf); // line current +ps=n*P; +printf('Input power is %f KW\n',P); +printf('Line current is %f A\n',il); +printf('power factor is %f lagging\n',pf); +printf('shaft power is %f KW',ps); diff --git a/3760/CH9/EX9.7/ExB_7.sce b/3760/CH9/EX9.7/ExB_7.sce new file mode 100644 index 000000000..be6d3d08d --- /dev/null +++ b/3760/CH9/EX9.7/ExB_7.sce @@ -0,0 +1,8 @@ +clc; +w1=2000; // reading of wattmeter 1 under no load +w2=-400; // reading of wattmeter 2 under no load, since the connections are reversed that is why negative sign +theta=atand((sqrt(3)*(w1-w2))/(w1+w2)); +pl=w1+w2; +pf=cosd(theta); +printf('No load losses are %f W\n',pl); +printf('No load power factor is %f lagging',pf); diff --git a/3760/CH9/EX9.8/ExB_8.sce b/3760/CH9/EX9.8/ExB_8.sce new file mode 100644 index 000000000..588b823f7 --- /dev/null +++ b/3760/CH9/EX9.8/ExB_8.sce @@ -0,0 +1,14 @@ +clc; +vl=230; // line voltage +f=50; // frequency of supply +c=100*10^-6; // value of capacitance in each phase +vp=230/sqrt(3); // phase voltage +zp=1/(2*%pi*f*c); // phase impedance +il=vp/zp; // line current +// value of cos(theta) is taken from figB.15 +w1=vl*il*cosd(120); +w2=vl*il*cosd(60); +printf('Reading of wattmeter 1 is %f W\n',w1); +printf('Reading of wattmeter 2 is %f W\n',w2); +p=w1+w2; +printf('Total input power is %f W',p); -- cgit