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I noticed that unlike the single phase ac power sources, the power in three phase is constant which means the instantaneous power is the same as the real power which is $$3V_{rms}I_{rms}\cos{\theta}$$

But there is also a reactive power present.

$$3V_{rms}I_{rms}\sin{\theta}$$

Clearly, the complex power would just be the VI for each of the branches leading to the complex power 3VI but the reactive power is clearly missing in the instantaneous power which for single phase sources would have been $$s(t)=cos(θ)P+sin(θ)Q$$ (as shown in this link S = VI*/2 derivation)

But in this case only the real power is present in the instantaneous power. At first I thought I didn't understand something, but now I'm wondering if the reactive power is present but just flows between each load. Am I correct or is there something I don't understand?

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In a balanced three phase system, the power in each of the three phases behaves in the same way as it does in single-phase systems. When you add together the power in the three phases, the result is constant rather than pulsating. The reactive energy flows back and forth between storage elements in each of the three phases of the load and storage elements in the source or distribution system just as it does in a single phase system.

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  • \$\begingroup\$ I'm still confused about the reason for lack of mathematical presence for reactive power from the source. Is the reactive power supplied from source exactly equal the reactive power coming back from the load at any given time when considering all three branches together? \$\endgroup\$ Nov 1, 2018 at 2:12
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    \$\begingroup\$ Yes it is. The reactive VA behaves similarly to the real power with regard to adding together the three phases. \$\endgroup\$
    – user80875
    Nov 1, 2018 at 2:59

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