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# 03 Phase Electrical Power is Constant !! Mathematical Proof ?

Published on 2020-12-16 15:08:33 Description :

Since the 3 phases ( both for voltage & current waveform ) are 120 degrees out of phase from each other, therefore 3 phase power is constant.

We can find it from mathematical proof that three-phase instantaneous power
P = 3* Vp*Ip* cos Ï†, constant all time
where Vp = phase voltage, Ip = phase current, Ï† =phase diff. between current & voltage

Lets instantaneous voltage , v1= Vpeak * sin Î¸ , v2= Vpeak *sin (Î¸-120) , V3= Vpeak *sin (Î¸-240)
AND instantaneous current, i1= Ipeak * sin (Î¸-Ï†) , i2= Ipeak * sin (Î¸-120-Ï†) ,i3= Ipeak * sin (Î¸-240-Ï†)
So, total instantaneous powers , P= v1 *i1 +v2 *i2+v3 *i3 =Vpeak * sinÎ¸ *Ipeak * sin (Î¸-Ï†) +Vpeak*sin (Î¸-120)*Ipeak * sin (Î¸-120-Ï†) +Vpeak*sin (Î¸-240)*Ipeak * sin (Î¸-240-Ï†)

Solving the equation, we get P = (3/2)*Vpeak*Ipeak*cos (Ï†).
But Vpeak = âˆš 2 Vp & Ipeak = âˆš 2 Ip

Therefore, Total Instantaneous Power, P = 3 *Vp*Ip*cos (Ï†)

#### Commment

IP OK

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