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If its comparing two voltages in a 3 phase system I think it would be:

(90 sin 120) - (70 sin 240) = 138.6 V.

Im sure someone will correct me if im wrong
 
In my question, suppose that 90v phase voltage(phase-N) and 70v phase voltage(phase-N) are from 2 different systems both having a phase angle of 120 degree, so when we measure the voltage across these 2 voltages using a voltmeter, the reading that it shows, how it can be calculated mathematically?
 
In my question, suppose that 90v phase voltage(phase-N) and 70v phase voltage(phase-N) are from 2 different systems both having a phase angle of 120 degree, so when we measure the voltage across these 2 voltages using a voltmeter, the reading that it shows, how it can be calculated mathematically?


I think it would depend on the earthing system and if there was any common points in the systems ie earth or neutral, if both are electrically separate from each other you may not measure any voltage at all. (not sure about the 120 degree phase angle as both systems are single phase?)
 
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In my question, suppose that 90v phase voltage(phase-N) and 70v phase voltage(phase-N) are from 2 different systems both having a phase angle of 120 degree, so when we measure the voltage across these 2 voltages using a voltmeter, the reading that it shows, how it can be calculated mathematically?


Well my take on your scenario there is it would be in essence a single phase 'split phase' system i.e two seperate phases but of the same origin so not 1 of brown, and 1 of black or grey but both of brown or black or grey.

The resultant voltage would then be 160V between the 'phases' but 90V and 70V between each phase and it's respective neutral.
 
I am still not getting my answer. In my case, both 90v & 70v are phase voltages of two different three phase systems & both are having an angle of 120 degree, what will be the phase to phase V between them?
OK consider another case, In a three phase system suppose one phase is having 70v & other is having 90v. what will be phase to phase voltage between these?
 
I am still not getting my answer. In my case, both 90v & 70v are phase voltages of two different three phase systems & both are having an angle of 120 degree, what will be the phase to phase V between them?
OK consider another case, In a three phase system suppose one phase is having 70v & other is having 90v. what will be phase to phase voltage between these?


you need to find the horizontal and vertical component of each voltage and solve as it is part of an unbalaced three phase system. too much to write on here but it is in all good electrical engineering books. Alternatively you could draw the phasor diagram to scale and measure. should be about 138.925V. This only works if it is one system see my earlier reply for different systems.
 
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For standard 120 degree between phases it is the L-N voltage multiply by the square root of 3.
Found this interesting breakdown of the calculation, whilst trawling the net.............

Reverting to basics, the instantaneous phase voltage of a single-phase system is expressed as V(t) = Vm x Sin(wt), where the wave's amplitude is Vm, and its frequency, in radians, is (wt)

Expressing the wave as a vector, having both magnitude and direction, the phase voltage in RMS, Vrms equals Vm/SQRT[2] at a reference angle, usually taken as zero.

The three-phase system has three phase voltages, Van, Vbn, and Vcn. Their corresponding vector notations are:

Van = Vrms at 0 deg (ref); Vbn = Vrms at -120 deg; Vcn = Vrms at +120 deg.

Because their magnitudes are equal, i.e., Van = Vbn = Vcn = Vrms, and given an A-B-C phase rotation, their corresponding complex phasor notations are:

Van = Vrms(1.0+j0.0) as reference.

Vbn = Vrms(-0.5-j0.866), lags Van by 120 deg

Vcn = Vrms(-0.5+j0.866), lags Van by 240 deg

The phase-phase voltages are related to the phase-neutral voltages as by vectoral addition:

Vab = Van-Vbn = Vrms [(1.0+j0.0)-(-0.5-j0.866)] = Vrms [1.5+j0.866)] = Vrms [1.5+j0.866] = SQRT(3)Vrms

Thus, the line voltage ( ph-to-ph)) is SQRT[3] times phase (ph-neutral) voltage. (QED)
 
As said earlier on the post, if both 3 phase systems are electically seperate then there will be no voltage between them.

You said both phases are at 120 deg, so are you saying both phases are in phase with each other? If you have two three phase installations (both having the same source) and measure between L1 of installation A and L1 of installation B you would also get 0 volts.
 

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