Lecture03

Lecture03 - Notes on Phasor Notation and Diagrams...

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Page 1 Fundamentals of Power Systems Lecture 3 1 Notes on Phasor Notation and Diagrams ( ) ( ) ω == Re(V) cos m vt V t + cos( ) sin( ) jt mm m Ve V t jV t V Complex quantity (“underlined”) V m …Magnitude Practical notation and usage Mathematically correct I = 10 A 45 ° or Complex quantity, but underlining omitted ( ) () Im(V) sin m V t RMS value instead of magnitude For practical use phasor diagrams can are drawn with RMS values RMS values are given if not noted otherwise. If in doubt, ask! Fundamentals of Power Systems Lecture 3 2 Example: 3~ Balanced Circuit For the following circuit, find all the voltage and current values and phasors and use them to find the power flowing in each part of the circuit V bn V cn V an V ca V ab V bc I c I b I a I ca I bc I ab V an = 277.1 V 0 ° V bn = 277.1 V -120 ° V cn = 277.1 V +120 ° Z ab = 48.0 Ω ∠ 10 ° Z bc = 48.0 Ω ∠ 10 ° Z ca = 48.0 Ω ∠ 10 ° Z ca Z ab Z bc
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Page 2 Fundamentals of Power Systems Lecture 3 3 Example: 3~ Balanced Circuit V an V bn V cn V ca V ab V bc I ca Re Im I bc I ab V V V V V L L bn an ab 480 3 1 . 277 30 480 120 1 . 277 0 1 . 277 = = ° = ° ° = = ° = ° ° = = 20 10 10 48 30 480 A Z V I ab ab ab ° = ° = 100 10 120 1 A I I ab bc ° = ° = 140 10 120 1 A I I ab ca ° = ° + ° = = 10 3 . 17 20 30 3 10 A I I I ca ab a I a I c I b lag PF kVA A I V S p p , 985 . 0 ) cos( , 10 8 . 4 10 0 3 . 17 1 . 277 3 * = = ° = ° + = = φ kW PF S P 72 . 4 985 . 0 8 . 4 = = = kVAr S Q 83 . 0 ) sin( = = delivered from source to load
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Lecture03 - Notes on Phasor Notation and Diagrams...

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