UNIVERSITY OF TORONTO FACULTY OF APPLIED SCIENCE AND ENGINEERING. MIDTERM EXAMINATION, February Forth Year Electrical and Computer Engineering

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1 NAME: LAST UNIVERSITY OF TORONTO FACULTY OF APPLIED SCIENCE AND ENINEERIN MIDTERM EXAMINATION, February 017 Forth Year Electrical and Computer Engineering ECE413 Energy Systems and Distribution eneration Examination Type A Examiner Reza Iravani Solutions FIRST STUDENT NO: Instructions: - Print down your name/student No on all pages (pages without name/student No will not be marked) - Answer all 3 questions - Non-programmable calculators are allowed - Use the back of the previous page for rough calculations (back pages will not be marked) - Do not unstaple this booklet Question Mark Total /5

2 Question 1: [8 points] The system shown in Figure 1 consists of a three-phase balanced, Y-configured source connected to two parallel loads through a line of impedance jω. The rms line to line voltage at loads terminal is V. The capacitive load reactive power is 15 kvar (three-phase) and the inductive load absorbs 48 kva (three-phase) at 0.8 power factor lagging. Load Terminal Isa Vsa a IΔ jxl RL -jxc -jxc Vsc Vsb Isb b -jxc c jxl RL jxl RL Isc Figure 1 a) Draw per-phase circuit diagram of the system of Figure 1 [1 point] and identify all impedance parameters (in physical units). [ points] Isa j 0.3 Ω 0.15 Ω Vsa Ω -jxc / 3 j 6 Ω j XL RL 4.5 Ω X c?, Q c 3 (v (L L)) X c, 5 kvar (415.6 V) X c, X c (415.6 V) 5000 VAR Ω R L?, P kw, P 3 (v (phase)), R L 38.4 kw V ( 3 ), R R L 4.5 Ω L X L?, Q L kvar, Q L 3 (v (phase)), X L 38.4 kw V ( 3 ) X L, X L 6 Ω Page of 7

3 b) Calculate current and voltage(phasors) of the source for phase (a). [ points] V sa?, I sa? Total Power at Load Terminal P 38.4 kw, Q 13.8 kvar I sa S L 3 V sa S L 38.4 kw + j 13.8 kvar (38.4 kw j 13.8 kvar) V ᵒ A Vsa will be considered as reference. (Students can consider line-line voltage as reference but they have to mention that.) V sa ( j) Ω ( A) + ( )V ᵒ c) Calculate active and reactive power of the source terminal. [ points] P 3 V sa I sa cos(φ) cos( ) kw Q 3 V sa I sa sin(φ) sin( ) kvar d) Calculate current I in delta-connected capacitive branch of Figure 1. [1 point] (phase sequence is abc) 0 degree I V ac j X c ᵒV j (34.54 Ω) ᵒ A a 30 n c b Page 3 of 7

4 Question : [7 points] The synchronous reactance of a 5 MVA, 13.8 kv, three-phase round-rotor generator is 18% and its resistance is negligible. a) The generator is delivering rated power at 0.8 power factor lagging at the rated terminal voltage to an infinit bus bar. Draw the equivalent per-phase circuit and phasor diagram of the system [ points] and determine the magnitude of the generated EMF (internal voltage) and the power angle (δ). [ points] Is EMF Xs Vt φ EMF δ Vt j XsIs Is Equivalent Per-Phase Diagram Phasor Diagram Is?, Is SL kv (4 kw j 3 kvar) kv ᵒ A 13.8 kv EMF j X s I s + ( 0ᵒ) 3 X s 18%, Z base V (line line) (13.8 kv) 5 MVA Ω, X s j Ω S base 13.8 kv EMF j Ω ( 0ᵒ) 8.9 kv 7.41ᵒ 3 EMF 8.9 kv and power angle 7.41ᵒ b) If the generator EMF (internal voltage) is 9 kv per phase, what are the maximum three-phase power that the generator can deliver to the infinite bus system and the corresponding power-angle (δ max). [3 points] E V 9 kv 7.97 kv P max sin(δ X max ) MVA s Ω δ max 90ᵒ Page 4 of 7

5 Question 3: [10 points] Based on open-circuit and short-circuit tests, parameters of a 50 kva, 400/100 V single-phase transformer are given in Figure. No-load loss of the transformer is 589 watts. jxl HV (1.5 Ω) RL HV (0.7 Ω) jxl LV (0.4 Ω) RL LV (0.175 Ω) jxm HV ( Ω) Rc HV ( Ω) : 1 Figure a) Determine voltage regulation and efficiency when the transformer delivers rated VA at 0.8 power factor leading and terminal voltage of 100 v. [ points] jxl HV (1.5 Ω) RL HV (0.7 Ω) jxl HV (1.6 Ω) RL HV (0.7 Ω) Is v 0 - LOAD Rated Load (Cos(φ) 0.8) leading Referred Diagram to HV side I s S V (40 + j 30 ) 103 VA ᵒ A 400 V V s (400 0ᵒ V) + (1.4 Ω + j 3.1 Ω) ( ᵒA) ᵒ V V. R. % % 400 Leakage loss 1.4 Ω (0.83 A) watts Ƞ watts watts watts watts 97.1 % Page 5 of 7

6 b) The transformer of Figure is connected to the system of Figure 3. Ratings of generator, line and load are given in Table 1. Draw an impedance diagram showing impedances in per-unit based on 5-kVA base and.4 kv at bus number 1. (neglect excitation branch!) [4 points] Vg 1 T1 400 v / 100 v VL 3 Load Figure 3 Z pu,new Z pu,old S b,new S b,old ( V b,old V b,new ) Table 1 Component Nominal Voltage Nominal power enerator 400 v.5 kva 100 v - Load 1600 v kva Impedance 10 % 1. + j Ω j 6.9 % X new (p. u. ) kva.5 kva 0. Z line (p. u. )?, Z base Ω, Z 1. + j Ω line(p. u. ) j p. u. 88 Z laod (p. u. ) new ( j0.069) 5 kva V (1600 kva 100 V ) j p. u. T 1 (1.4 + j 3.1)Ω j p. u. X XT1 RT1 Xline Rline 0. p.u p.u p.u p.u p.u p.u. Xload p.u. Rload Impedance Diagram Page 6 of 7

7 c) The single-phase generator, transformer, line and load of Figure 3 are used to construct the threephase balanced system of Figure 4. Draw per-phase diagram of the system of Figure 4 [ points] and specify all impedances based on V b V and power base of 15 kva at bus 3. [ points] (neglect excitation branch!) Vg 1 VL 3 Load Z-base on Delta Side : vb(line line) Figure 4 S b (Three Phase) (100 3 V) 15 kva 88 Ω Because Zbase is same on Delta side per-unit values will not change. However, Z-base on Y side: vb(line line) S b (Three Phase) (400 3 V) 15 kva 3456 Ω T 1 (1.4 + j 3.1)Ω 3456 Ω j p. u. X new (p. u. ) kva.5 kva ( ) p. u. Students should also notice the phase shift caused by Y-Delta connection and consider it in impedance diagram. X XT1 RT1 Xline Rline j p.u. J p.u p.u. J e -30j p.u p.u. J p.u. Xload p.u. Rload Page 7 of 7

R10. III B.Tech. II Semester Supplementary Examinations, January POWER SYSTEM ANALYSIS (Electrical and Electronics Engineering) Time: 3 Hours

R10. III B.Tech. II Semester Supplementary Examinations, January POWER SYSTEM ANALYSIS (Electrical and Electronics Engineering) Time: 3 Hours Code No: R3 R1 Set No: 1 III B.Tech. II Semester Supplementary Examinations, January -14 POWER SYSTEM ANALYSIS (Electrical and Electronics Engineering) Time: 3 Hours Max Marks: 75 Answer any FIVE Questions