7 Balanced 3-phase systems

# 7 Balanced 3-phase systems - Lecture 9 Balanced 3-phase(3...

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Lecture 9 Balanced 3-phase (3 φ ) systems Consider a 3-phase device as in Figure 1 in phasor domain, Figure 1 - Three phase system When there is a balanced system the angles of the voltages a, b, and c are shifted by 120º. 0 120 120 240 a b c VV V =∠ , , ,, That corresponds to the phasor diagram in Figure 2 Figure 2 - Phasor diagram of voltages In the time domain, the voltages would be

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() 2s i n 2 sin 120 2 sin 120 a b c Vt V t V t V t ω = =− =+ ± ± Similarly a balanced set of currents 120 120 240 a b c II I φ φφ =∠− =∠− − =∠− + , ,, Where abc VIVIVI =∠ −∠ . Figure 3 - Phase diagram with currents Some important properties are: 1. 0 III ++= or in time domain, () () () 0 it it it . Therefore the neutral or ground current is i g = i a + i b + i c = 0. Hence there is no need for returning wires. 2. The 3 φ instantaneous power is () () () () 3 P tP t =++ = constant. Where () () () ( ) 1c o s2 s i n2 aa a P tV t i t Q t ωω == −− , and cos , sin PV I QV I .
0 0.01 0.02 0.03 0.04 0.05 0.06 -2000 -1000 0 1000 2000 3000 4000 5000 6000 t Pa(t) Figure 4 - Instantaneous power of phase a Therefore individual phases deliver pulsating instantaneous power. P

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7 Balanced 3-phase systems - Lecture 9 Balanced 3-phase(3...

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