Practice Session 1

Practice Session 1 - ECSE 462 PRACTICE SESSION I (2009) The...

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ECSE 462 PRACTICE SESSION I (2009) The exercises are for practice only. Do NOT submit. Trigonometric Identities cos(A+B)=cosAcosB-sinAsinB cos(A-B)=cosAcosB+sinAsinB sin(A+B)=sinAcosB+cosAsinB sin(A-B)=sinAcosB-cosAsinB cos sin jx ex j x =+ 1. A voltage cos vV t ω ϕ can be expressed as Re jt e = . What is the phasor (or complexor) V ? Answer j VV e = . 2. A balanced 3 phase voltage vector in the a-b-c frame is: 0 0 cos cos 120 cos 240 a b c vt t ωϕ + ⎡⎤ ⎢⎥ +− ⎣⎦ The voltages can be written in the complexor form: Re a a bb c c V v e v V = . What is the phasor (complexor) vector a b c V V V ? 3. The voltages in Q.2 is transformed to the 0- α - β frame using the equations: 11 1 22 2 21 1 1 32 2 33 0 oa b c vv α β =−
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In the new frame, the voltages are expressed as: 0 0 Re jt V v vV e v V ω αα β ⎡⎤ ⎢⎥ = ⎣⎦ What is the phasor (complexor) vector 0 V V V α ? As the transformation from the 0- α - β frame to the 0-d-q frame is by the identity matrix, the stator quantities remain unchanged. The transformation from the 0-d-q
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Practice Session 1 - ECSE 462 PRACTICE SESSION I (2009) The...

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