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Energy Systems I

by: Fredy Okuneva

Energy Systems I ECE 320

Fredy Okuneva
GPA 3.81


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Class Notes
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This 6 page Class Notes was uploaded by Fredy Okuneva on Thursday October 22, 2015. The Class Notes belongs to ECE 320 at University of Idaho taught by Staff in Fall. Since its upload, it has received 9 views. For similar materials see /class/227734/ece-320-university-of-idaho in ELECTRICAL AND COMPUTER ENGINEERING at University of Idaho.

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Date Created: 10/22/15
ECE 320 329 Transformers and Power Review Lesson 12 Consider a circuit as shown below two sources and an inductance between them Find an expression for the real power transferred from one source to the other in terms of the magnitude of the two voltages the reactance and the phase angle between them The easiest way to do this is to rst nd an expression for the current and then substitute that expression into the PReVI jX Define a current I from left to rightthrough X VI V2 1 JX Real powerto the source on the right as a load is P ReV2I Substituting V239V1 V239V2 P Re 7 JX JX We recall that v2v2 lv22 So the second term in the power expression is all imaginary v V Re JX Expand this by Euler39s identity Designatethe phase angles on each voltage as 61 and 62 V V P Rjcos62 7 91 j39sm62 7 61 Simplify P MRejcos62 91 t Siquot62 61 V2 39 V1 P LXll39sm62 7 61 This is what we are looking for Homeworkfor Lesson 12 Problem 2 Rp002 Vs100 V Rs002 15100 V Load power factor 090 lagging Xp008 Xs008 Units on the impedances are ohms Turns ratio 11 XM82 RC95 j F Restate the given Rp 002 RS 002 xp 008 XS 008 XM 82 BM BM 0122 RC 95 GC GC 0011 XM RC vS 100 15 100 pfload 090 Calculate the current and express as a complex quantity 6 acos090 6 25842 deg I I e 39 IS 09 7 0436i Calculate the center voltage of the transformer model B vS IsRS jXS E 1053 0063i Calculate the input current 1p IS EijBM EGC 1p 0919 7 0564i Calculate the input voltage VpEIpRpjXp Vp1116 0126i Calculate the voltage ratio and the energy efficiency IVsl IVpl VRO VRO 089 Vs 39 Is 39pfload I Rabpg Re peat the calculations 710 Rp and Rs only Rp 002 RS 002 V 100 S IS 100 CD acos090 9 6 J l t IS m vs ISRS jXS IS E7jBM EGC p E 1 Ip39Rp 1 j39Xp M 1 397 IVpl IVsl39IISI 39pfload Revp391p 6 lt VR 711 Repeat the calculations Xp and X8 only Rp 0 RS 0 vS 100 15 100 0 acos090 15 ISei is E vS 1512S jXS 1p 1S E7jBM EGC vp E IpRp jXp no 0942 XP 0 BM 0 GO 0 pfload 090 0 25842 deg IS 09 7 04361 E 1018 7 87181gtlt1073 l t 09 7 04361 Vp 1036 7 00171 VR1 0965 m 0957 XS 008 Xp 008 BM 0 GO 0 pfload 090 0 25842 deg S 09 7 04361 E 1035 00721 1p 09 7 04361 Vp 107 01441 VR2 0926 lvsl 39 llsl 39pfload 39 RelvpIE Repeat the calculations on 712 XM ly Rp 0 RS 0 XM 82 BM L XM VS 100 15 100 0 acos090 1399 IS 7 Ise E vS IsRS jXS 1 IS E7jBM EGC U VP E 1p39Rp 1 JI39Xp VR3 Ii IVpl IVsllIslPjoad RelvpIp Repeat the calculations Rp and XM only Rp 0 RS 0 X 39 82 B 1 M M XM VS 100 15 100 0 acos 090 15 ISeij39e E vS IsRS jXs 1p1S E7jBM EGC vp E IpRp iXp IVsl IVpl VR4 Xp0 XS0 BM 0122 GC 0 pfload 090 0 25842 deg IS 09 7 04361 E 1 1p 09 7 05581 v p 1 Xp0 XS0 1 BM 0122 RC 95 GO R GC 0011 pfload 090 0 25842 deg IS 09 7 04361 E 1 1p 0911 7 05581 V p1 VR41 lvsl39llsl39pfload Revp39lp n4 n4 0988 Summarizing the results 089 1 0942 0965 0957 0926 1 1 1 t 1 J low The series inductances alone give the best estimate of voltage ratio The series resistances give the best estimate of the energy ef ciency VR 7 The utilities are more interested in the voltage distribution on theirsystem than in the energy ef ciency when they use the series reactance only for their calculations


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